tag:blogger.com,1999:blog-75275356680439261252024-03-19T01:06:26.968-07:00Exoplanet DiagramsThis blog is about extrasolar planets - planets around other stars. I will present high-quality plots on this topic and try to provide short explanations for a general non-scientific audience. It is supposed to give both basic and state-of-the-art information in concise but easily understandable figures. Feel free to use them for any non-profit purpose.nonnativenoobhttp://www.blogger.com/profile/09489612471884841558noreply@blogger.comBlogger20125tag:blogger.com,1999:blog-7527535668043926125.post-38520470830656044892016-03-04T07:38:00.001-08:002016-03-19T07:59:28.948-07:00Radial Velocity method: Moving around a common center of mass<div style="text-align: justify;">
<iframe align="left" height="240" mytubeid="mytube1" src="https://drive.google.com/file/d/0B3lNcd79K1I8dTgzczhnYzlUNXM/preview?autoplay=1" style="float: left; margin: 15px;" width="320"></iframe>The Radial Velocity (RV) method is the second-most successful technique to find exoplanets. In contrast to the more successful transit method it has an important advantage: it gives us the mass of the planet. However, it also has at least one major drawback: it is more complicated.<br />
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In this post I will try to explain how it works. There are two things you have to realize before you understand why and how the RV method can be used to detect planets.<br />
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(1) Although we usually say that a planet orbits a star, this is only half true. Actually, the planet and the star move around a common center of mass. So not only the planet is moving, but the star itself is moving too; however, it is of course not moving as much because it has much more mass.<br />
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(2) The light emitted by a moving object is shifted in wavelength/frequency. This is called the Doppler effect and works for all kinds of waves, e.g. sound waves and light. Because the star is moving, the light it emits is shifted to longer wavelengths when moving away from the observer and to shorter wavelengths when moving towards the observer. Light shifted to longer wavelengths is called <i>red-shifted,</i> for shorter wavelengths it is called <i>blue-shifted</i>.<br />
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Because the RV method really is about movement, I prepared a little video instead of a static diagram this time. It shows that planet and host star move around a common center of mass indicated by the black cross, and that the light coming towards the observer is shifted in color because of the movement of the star. Only the movement in the direction of the observer is important, which is called the radial movement. This is where the method gets its name from: we only measure the radial component of the velocity.<br />
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In the movie the stellar light is not shifted when the planet is exactly behind or in front of the star. In these positions the radial velocity of the star (and the planet too) is zero and no wavelength shift is caused. The higher the velocity of the star in the direction of the observer is, the higher is the wavelength shift.<br />
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<iframe align="left" height="240" mytubeid="mytube2" src="https://drive.google.com/file/d/0B3lNcd79K1I8cHpvaVMxM2YzRm8/preview" style="float: left; margin: 15px;" width="320"></iframe>
This also means the RV method works best if we look at a planetary system edge-on. The observer's viewing angle on the system is called inclination i. If i=90° we look at the system directly edge-on and the movement of the star is largest. If i=0° we look at the system from above and the star is not moving in our direction at all - and the RV method does not work anymore.<br />
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I tried to illustrate this in a second movie. Now the inclination of the system in respect to the observer has changed and our viewing angle is close to 0°. The radial movement of the star (in direction towards and away from the observer) is much smaller now and, thus, the wavelength shift is smaller too.<br />
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This inclination plays an important role, because observers usually do not know its exact value. However, the radial velocity of the star depends on it and, therefore, also the measured mass of the planet depends on the inclination. This is why planetary masses derived with the RV method are described as <i>m sin(i)</i>. <i>m</i> is the true mass of the planet and <i>sin(i)</i> is the sine of the inclination. Observers do not measure the true mass, but its "projection" on the angle i. So if we measure a low mass for a planet, this can mean two things: either we really have a low-mass planet with an angle i close to 90°, or we have a higher mass planet with an angle closer to 0° (or 180°). In the end we cannot be sure what kind of planet it is until we know what the inclination is.<br />
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The RV method only works as good as we can measure the radial velocity of the star, and this is where the really difficult part begins. If you want to measure the radial velocity of the Sun caused by the gravitational drag of the Earth, you have to have an instrument measuring velocities with a precision of about 10 cm/s. This is tiny. Just compare it to the <a href="https://en.wikipedia.org/wiki/Preferred_walking_speed">preferred walking speed of humans</a>, which is already more than a factor 10 higher. The rotation speed of the Sun is roughly 2 km/s. The radius of the Sun is 700000 km, which means you have to measure a change in distance of 10<sup>-10</sup> of the radius of the Sun <i>per second</i>. Or, finally, make yourself aware that Earth orbits the Sun with a speed of about 30 km/s.<br />
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Today the best instruments measure radial velocities down to below 1 m/s. Wavelength-stabilized spectrographs observe spectra of the stars and the spectral lines within these spectra can be used to determine their shift due to the Doppler effect. It might be hard to understand how difficult it is to get down to 1 m/s - or even 10 cm/s - if one has never tried to get velocities out of a spectrum. Maybe I can try to show this is one of my next posts in more detail, but think about it that way: the minimum width of a spectral line for the Sun with a rotation velocity of 2 km/s is at least a few km/s. This means you want to measure the position of the line more than a factor 1000 better than its width. The reason why this works at all is that the spectra have hundreds or even thousands of lines.<br />
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nonnativenoobhttp://www.blogger.com/profile/09489612471884841558noreply@blogger.comtag:blogger.com,1999:blog-7527535668043926125.post-75951513113520722792016-03-03T06:09:00.002-08:002016-03-03T06:09:28.200-08:00Exoplanets in the Milky Way: The view from above<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjd-YWqt54EMfEyHn6ZVIGGLNcUmtse6_bRsaOwTIdIt_8fk7a98V1Yh-xTHxQkK4IAL2_Vj_3hJ0zAmHkYVgkiGBJZffItWXHyukvMkK7dK4cJd7tR9arkjgpSxhvd0wxrGK_WKbA3Yh0/s1600/mw-exoplanets-dist.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="550" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjd-YWqt54EMfEyHn6ZVIGGLNcUmtse6_bRsaOwTIdIt_8fk7a98V1Yh-xTHxQkK4IAL2_Vj_3hJ0zAmHkYVgkiGBJZffItWXHyukvMkK7dK4cJd7tR9arkjgpSxhvd0wxrGK_WKbA3Yh0/s640/mw-exoplanets-dist.png" width="640" /></a></div>
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Finally my figure of the positions of exoplanets in the Milky Way is finished. Again you see my artist impression of a view from above on the Milky Way, but this time I added the positions of all the known exoplanets for which I could find a distance measurement. The exoplanet data are coming from <a href="http://exoplanet.eu/catalog/">exoplanet.eu</a>. There are a little bit more than 1000 exoplanets in this map, which means we only have distances for about half of all the exoplanets we know today.</div>
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The methods used to detect the planets are indicated by different colors and symbols. Most of the planets in this plot come from the RV method (618) and not from transits (313). At first this might be unexpected, but on average stars observed in RV campaigns are closer to the Sun than transit host-stars because a spectrum needs more light than a brightness measurement. For closer stars the distance is usually easier to determine than for stars far away, for example when using the parallax method.</div>
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A quite large number of planets detected by transits orbit stars further away than several thousand light years. This is especially true for those regions in the sky that were observed intensely by transit surveys as for example Kepler. I marked the Kepler field-of-view in the map where several distant planets were found.</div>
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The most distant exoplanets, however, were found by microlensing surveys - with the exception of the <a href="https://en.wikipedia.org/wiki/Sagittarius_Window_Eclipsing_Extrasolar_Planet_Search">SWEEPS transit survey</a>. These distant microlensing planets are all located on a line pointing to the center of the Milky Way. Why? This is due to the way the <a href="https://en.wikipedia.org/wiki/Methods_of_detecting_exoplanets#Gravitational_microlensing">microlensing method</a> works: to see an event we do not only need a planet around a star, we also need a background star which gets 'lensed'. Because the density of stars is highest in the galactic center, the probability to get a lensing event is largest there. Since it is a method which only requires photometric observations, you can see events caused by very distant planetary systems as long as the lensed source is bright enough - or the lensing effect strong enough - to be seen by your telescope.</div>
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In case you wonder how scientist get the distances to planetary systems that are so far away: This would lead too far in this post, but it is not by using the parallax. In these cases distances are usually estimated and, thus, the uncertainties are quite large. Because of the large uncertainty on the distance of the SWEEP exoplanets, one might argue that they possibly are not that far away.</div>
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I leave you with a list of names for the most distant planetary systems which are further away from the Sun than 20000 light years. The last two are transiting planets, the rest were all detected in microlensing events.</div>
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<span style="font-family: "Trebuchet MS",sans-serif;"><span style="font-size: small;">20961 ly - MOA-2010-BLG-353L b</span></span><br />
<span style="font-family: "Trebuchet MS",sans-serif;"><span style="font-size: small;">21190 ly - OGLE-2005-390L b</span></span><br />
<span style="font-family: "Trebuchet MS",sans-serif;"><span style="font-size: small;">22168 ly - OGLE-2008-BLG-355L b</span></span><br />
<span style="font-family: "Trebuchet MS",sans-serif;"><span style="font-size: small;">22820 ly - OGLE-2008-BLG-092L b</span></span><br />
<span style="font-family: "Trebuchet MS",sans-serif;"><span style="font-size: small;">23961 ly - MOA-2011-BLG-262L b</span></span><br />
<span style="font-family: "Trebuchet MS",sans-serif;"><span style="font-size: small;">24058 ly - MOA-2011-BLG-028L b</span></span><br />
<span style="font-family: "Trebuchet MS",sans-serif;"><span style="font-size: small;">25102 ly - MOA-2011-BLG-293L b</span></span><br />
<span style="font-family: "Trebuchet MS",sans-serif;"><span style="font-size: small;">25232 ly - MOA-2011-BLG-322L b</span></span><br />
<span style="font-family: "Trebuchet MS",sans-serif;"><span style="font-size: small;">26732 ly - KMT-2015-1 b</span></span><br />
<span style="font-family: "Trebuchet MS",sans-serif;"><span style="font-size: small;">27710 ly - SWEEPS-4 </span></span><br />
<span style="font-family: "Trebuchet MS",sans-serif;"><span style="font-size: small;">27710 ly - SWEEPS-11 </span></span>nonnativenoobhttp://www.blogger.com/profile/09489612471884841558noreply@blogger.comtag:blogger.com,1999:blog-7527535668043926125.post-21929213787895823002016-03-03T02:33:00.003-08:002016-03-03T02:33:48.426-08:00What Hipparcos saw and Gaia will see<div class="separator" style="clear: both; text-align: center;">
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjZ7kDli9_lR1KRv5MJU1u3ck7ppJqkAZRMm2_AQBni_g52FXP8l1fFRPhFYPsyEcM4zffwzC9GnSpUoacBKPqs9_nLSBFXMuu0TOw9MG6nPAYCPNblcmNBFEJ9ZG6SOqiCOwfDJ4YcbJA/s1600/mw-hipparcos-sptype.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="550" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjZ7kDli9_lR1KRv5MJU1u3ck7ppJqkAZRMm2_AQBni_g52FXP8l1fFRPhFYPsyEcM4zffwzC9GnSpUoacBKPqs9_nLSBFXMuu0TOw9MG6nPAYCPNblcmNBFEJ9ZG6SOqiCOwfDJ4YcbJA/s640/mw-hipparcos-sptype.png" width="640" /></a></div>
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In the last post I wrote about the Hipparcos mission and I would like to follow up with a few more nice plots. Hipparcos used the <a href="https://en.wikipedia.org/wiki/Parallax" target="_blank">geometric parallax</a> to measure the distances of stars in a rather limited volume around the Sun. Although it measured more than 100000 distances, this covers only a tiny fraction of stars in our Milky Way. Whether Hipparcos can measure the distance to a star depends mainly on two things: The star has to be bright enough to be seen and it has to be close enough to move in the sky by a parallax at least as large as the measurement precision of the instrument.</div>
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The latter is slightly better than one milli-arcsecond for Hipparcos and means that only stars that are not much further away than several thousand light years can be measured in distance. The first criterium is called the limiting magnitude, which is about 12 for Hipparcos. It means that stars fainter than an <a href="https://en.wikipedia.org/wiki/Apparent_magnitude" target="_blank">apparent magnitude</a> of 12 are not bright enough to determine the distance. The apparent magnitude depends on the intrinsic brightness of the star (the <a href="https://en.wikipedia.org/wiki/Absolute_magnitude" target="_blank">absolute magnitude</a>) and on the distance - if a star is further away it appears to be fainter. If a star is far away but very bright, it can still be seen by Hipparcos, although the distance cannot be measured if it is so far away that its parallax is smaller than the measurement precision of Hipparcos.</div>
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The picture on top shows you again my artist impression of the Milky Way in inverted colors. This time I try to show how far Hipparcos could see for a specific type of star which is called the <a href="https://en.wikipedia.org/wiki/Stellar_classification" target="_blank">spectral type</a>. A star with a spectral type M is cooler than the Sun and, therefore, its absolute brightness is lower. The hottest and most luminous stars are O stars. The Sun is a G2 star which has a (surface) temperature of slightly below 6000° Celsius. Unsurprisingly, more luminous stars like O stars can be seen in a much larger distance than cooler stars like F or even M stars. The distance to which a G2 star can be seen by Hipparcos is so small, its smaller than the size of the cross marking the position of the Sun in the picture. But O stars are so very bright, they can be seen throughout the entire galaxy.</div>
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In the upper left corner of the plot on top you find the color code for the type of the star and the distance to which this type of star can be seen by Hipparcos. Keep in mind that this does not necessary mean that the distance can be measured just because Hipparcos would be able to see the star.</div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg3cQmM-ZBogdvd6NwnqcpFgl_YbRMhcSTtIGIyFpu4uH8lnCxc1ZwOEWfQbh9b5JubccANFZ4bSz_9jL62sRbdG1ueeaXu9oj1s3a4SPcuj3GObHp2-a7Kg9Tp_yGN1u3GDDpRR19ABQ8/s1600/hipparcos-dist-hist-100.png" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="237" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg3cQmM-ZBogdvd6NwnqcpFgl_YbRMhcSTtIGIyFpu4uH8lnCxc1ZwOEWfQbh9b5JubccANFZ4bSz_9jL62sRbdG1ueeaXu9oj1s3a4SPcuj3GObHp2-a7Kg9Tp_yGN1u3GDDpRR19ABQ8/s320/hipparcos-dist-hist-100.png" width="320" /></a></div>
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The region close to the Sun is hard to see in the plot, so I prepared some more pictures to show what is going on there. On the left you see a histogram of the number of stars for a certain distance from the Sun. It shows that within a radius of 100 light years Hipparcos saw 2466 stars, in a radius of 20 light years 'only' 75 stars. The closest stars to the Sun are between 4 and 5 light years away in the Alpha Centauri system: Proxima Centauri, alpha Centauri A and alpha Centauri B.</div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg1SDmUO-ZubwLTel5jabEEQyZrfoQX9Y49NxRcztzjy5me6izj06gj-NnDqr7wSpIDq22slTT6eC-xAyH2zy8V0laCtezlpOWLGHrZqpCf3JhuXKkdKix66A9rP9cPjhq3Mxlxt2HLWx0/s1600/hipparcos-dist-hist-sptypes.png" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="232" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg1SDmUO-ZubwLTel5jabEEQyZrfoQX9Y49NxRcztzjy5me6izj06gj-NnDqr7wSpIDq22slTT6eC-xAyH2zy8V0laCtezlpOWLGHrZqpCf3JhuXKkdKix66A9rP9cPjhq3Mxlxt2HLWx0/s320/hipparcos-dist-hist-sptypes.png" width="320" /></a></div>
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For the first 400 to 500 light years the number of stars Hipparcos saw increases, then the numbers start to go down. The larger the distance gets, the larger the volume of the shell of the sphere gets in which we are looking for stars. And for the first few hundred light years this is close enough to see more and more stars. However, stars with a low absolute magnitude like M stars get 'invisible' for Hipparcos after a distance of about 120 light years. The further we go away, the more stars become undetectable by Hipparcos. At about 400 to 500 light years the increasing volume of the shell is counter-balanced by the quickly decreasing number of stars that still can be seen, and the absolute numbers start to go down. In a distance of about 4300 light years Hipparcos does not even see A stars anymore, which is where the mission provides virtually no distance measurements anymore. In the cumulative distribution you can see that in a distance of about 500 light years about 50 % of all the stars are located that Hipparcos could measure distances for.</div>
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So what ca we do to see more stars and measure their distances? To see more stars we need a better telescope, which practically means a larger telescope. To get larger distances we need a better measurement precision. This is what <a href="https://en.wikipedia.org/wiki/Gaia_%28spacecraft%29" target="_blank">Gaia</a> is supposed to do. Gaia will have a limiting magnitude of about 20 and will detect stars that are 1600 times fainter than what Hipparcos could see. The precision to measure the parallax will be better than 10 micro-arcseconds, which is more than a 100 times better than Hipparcos; distances of 300000 light years, which is three times the assumed diameter of the Milky Way, should be possible for very bright stars.</div>
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The plot at the bottom shows what Gaia will be able to see in terms of brightness. Hipparcos could see a G2 star only in the close neighborhood of the Sun, Gaia will see G stars in a radius of more than 40000 light years - larger than the distance from the Sun to the center of the Milky Way. And stars as luminous as F stars will be visible virtually all over our entire Galaxy.</div>
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This way it is assumed that Gaia will see about 1 % of all stars in the Milky Way. This is more than 1 billion stars! However, you still might think: Why 'only' one percent if it can look so 'far'? Well, this is because more than 70 % of the stars in our Milky Way are M stars - and M stars cannot be seen by Gaia in distances larger than about 5000 light years.</div>
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<i>Addendum: Writing about magnitudes is always a pain in the ***, which is because the definition is kind of backwards. The magnitude of a star stands for its brightness (either apparent or absolute). So we intuitively think that a high brightness (or luminosity) also means a high magnitude. However, the magnitude system is defined with a negative sign. A bright star has a smaller numerical value for its magnitude than a fainter star. This is confusing and sometimes leads to confusing (or even plain wrong) statements. I hope I manage to avoid this in my texts.</i></div>
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nonnativenoobhttp://www.blogger.com/profile/09489612471884841558noreply@blogger.comtag:blogger.com,1999:blog-7527535668043926125.post-2152490111291212402016-03-02T01:51:00.002-08:002016-03-02T02:05:04.777-08:00The Milky Way: A pre-Gaia map of our home galaxy<div class="separator" style="clear: both; text-align: center;">
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Today's post will be about the galaxy we live in: the Milky Way. It will not be about exoplanets. However, I will come back to this topic in one of my next blogs because I will try to show where the exoplanets we know are located in this 'map' of the Milky Way.</div>
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First of all: If somebody shows you a map of the Milky Way, you should immediately be aware of the fact that this cannot be a real map in the sense that everything that is shown represents a real object with a measured position. There is no real map of the galaxy we live in, simply because (a) we cannot travel out and make a picture from above or below, and (b) we can only see 'far' enough to observe a tiny fraction of the stars in the Milky Way. The latter will hopefully improve soon because <a href="http://sci.esa.int/gaia/" target="_blank">Gaia</a> is already operating and observes more stars of the Milky Way than was ever possible before. With a little bit of luck we will get a much better impression of how our galaxy looks like this year.</div>
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What you see in the picture is my own little <b>artist impression</b> of how the Milky Way might look like. Again I emphasize that this might be completely wrong. Every other picture, even the I guess most famous one by <a href="http://www.eso.org/public/images/eso1339e/" target="_blank">NASA (R. Hurt)</a>, probably is pretty much wrong too. This 'map' is just an illustration which is supposed to show four things we believe to know about our galaxy: (a) It is a (flat) spiral galaxy. (b) It has a bright center with a bar-like structure. (c) It has four spiral arms at roughly about these locations. (d) It has a diameter of roughly about 100000 light years (ly).</div>
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Additionally, I tried to incorporate some real astrophysical data into this map. The white circles are measurements of embedded clusters (by <a href="http://adsabs.harvard.edu/cgi-bin/nph-abs_connect?db_key=AST&db_key=PRE&qform=AST&arxiv_sel=astro-ph&arxiv_sel=cond-mat&arxiv_sel=cs&arxiv_sel=gr-qc&arxiv_sel=hep-ex&arxiv_sel=hep-lat&arxiv_sel=hep-ph&arxiv_sel=hep-th&arxiv_sel=math&arxiv_sel=math-ph&arxiv_sel=nlin&arxiv_sel=nucl-ex&arxiv_sel=nucl-th&arxiv_sel=physics&arxiv_sel=quant-ph&arxiv_sel=q-bio&sim_query=YES&ned_query=YES&adsobj_query=YES&aut_logic=OR&obj_logic=OR&author=^camargo%2C+d.&object=&start_mon=&start_year=&end_mon=&end_year=&ttl_logic=OR&title=&txt_logic=OR&text=&nr_to_return=200&start_nr=1&jou_pick=ALL&ref_stems=&data_and=ALL&group_and=ALL&start_entry_day=&start_entry_mon=&start_entry_year=&end_entry_day=&end_entry_mon=&end_entry_year=&min_score=&sort=SCORE&data_type=SHORT&aut_syn=YES&ttl_syn=YES&txt_syn=YES&aut_wt=1.0&obj_wt=1.0&ttl_wt=0.3&txt_wt=3.0&aut_wgt=YES&obj_wgt=YES&ttl_wgt=YES&txt_wgt=YES&ttl_sco=YES&txt_sco=YES&version=1" target="_blank">Camargo</a>) using the WISE telescope. The circles in cyan present the positions of molecular clouds coming from a catalogue by <a href="http://adsabs.harvard.edu/abs/2015ApJ...799...29E" target="_blank">Ellsworth-Bowers</a>. The only stellar data in the map are galactic cepheids (by <a href="http://adsabs.harvard.edu/abs/2000yCat..41430211B" target="_blank">Berdnikov</a>, shown in magenta), which are variable stars used for distance measurements. There certainly are other dataset that should be in there to have a more complete picture, but I think these three are good enough to get the general picture. These data points give you an idea of what is actually measured and used to conclude that the Milky Way looks like what I drew.<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhTlAKiwYieLVr80zj2Qw1abiAmsXuBX3zvhBC5vLmeKulHw4vEoQ-Yj_zz8cjiJdp2VxczNPzPH8jQCKrHXg4dgnyXg-ZLvl8vQYynCE_JTl-dxqzOnyx61qhxKBnmVbbhR04FGyWLgIw/s1600/mw-hipparcos-cut.png" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhTlAKiwYieLVr80zj2Qw1abiAmsXuBX3zvhBC5vLmeKulHw4vEoQ-Yj_zz8cjiJdp2VxczNPzPH8jQCKrHXg4dgnyXg-ZLvl8vQYynCE_JTl-dxqzOnyx61qhxKBnmVbbhR04FGyWLgIw/s320/mw-hipparcos-cut.png" width="310" /></a></div>
There is a fourth dataset in the picture which cannot be seen. This dataset is the one with the best distance
measurements for stars we have, at least until the first Gaia results
get published. It is the <a href="https://en.wikipedia.org/wiki/Hipparcos" target="_blank">Hipparcos</a>
data. However, all the data is located close to the black cross which marks the
position of our Sun in the Milky Way. Our position in the Milky Way is about 8200 parsec or roughly 27000 ly away from the galactic center.<br />
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On the left side you see a blowup of the region of the Sun, where I used the new Hipparcos catalogue (<a href="http://cdsarc.u-strasbg.fr/viz-bin/Cat?I/311" target="_blank">van Leeuwen, 2007</a>) to draw the positions of more than 100000 stars (white dots). Hipparcos measured the positions
of stars better than one milli-arcsecond, which means the most distant stars
in this catalogue are more than 3000 ly away. Of course, most of the
observed stars are much closer to the Sun; 90 % of the stars with measure distances are within a radius of 1660 ly.</div>
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Although the Hipparcos map consists of a huge number of measurements, the distances from the Sun are not nearly far enough to tell us something about the large-scale structure of the Milky Way. Gaia will hopefully be about a factor 100 better than this, which will do the trick and give us a pretty good picture about a large part of the Milky Way covering maybe even 1 % of all the stars in our galaxy. Still, Gaia will not be able to see everything; some parts will be blocked from view, and some stars are just too faint or too far away to be seen.</div>
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nonnativenoobhttp://www.blogger.com/profile/09489612471884841558noreply@blogger.comtag:blogger.com,1999:blog-7527535668043926125.post-35613783620094049252016-02-17T06:35:00.002-08:002016-02-17T06:35:28.790-08:00Biggest sunspots since 1990: larger than a transiting Earth<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjPrhOQpGacLlOkfTlK-NHdvmUOeQDxWfcKjpxJQJKlcNjDSdJzPkmISk1jOZUJvppOWJrP8iXBZg2xbKzSTHqdUCSCPqwXWo90Lc-vvRyFMuOuPSqbXxTQdSP8y67zxcySaMVm5_952Bg/s1600/sunspot-area-biggest.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="381" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjPrhOQpGacLlOkfTlK-NHdvmUOeQDxWfcKjpxJQJKlcNjDSdJzPkmISk1jOZUJvppOWJrP8iXBZg2xbKzSTHqdUCSCPqwXWo90Lc-vvRyFMuOuPSqbXxTQdSP8y67zxcySaMVm5_952Bg/s640/sunspot-area-biggest.png" width="640" /></a></div>
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This plot was inspired by this web page (<a href="http://spaceweather.com/sunspots/history.html" target="_blank">History's Biggest Sunspots</a>) and uses data from this database (<a href="http://fenyi.solarobs.unideb.hu/DPD/index.html" target="_blank">DPD</a>). It presents the area of the biggest sunspot of each month since January 1990. The sunspot area is given in millionth of the solar hemisphere, so 1000 means that 0.1 % of half of the Sun's surface is covered by the spot.</div>
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So why is this interesting for my exopanet blog? If we take a look at the radius ratio between Sun and Earth, which is about 110, we see that a transiting Earth will reduce the solar brightness by about 1/(110)² = 1/12100, which is approximately 100 millionth.</div>
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A comparison with the plot shows that there was almost no month in the last 25 years where the Sun did not have at least one spot with an area larger than 100 millionth of the solar hemisphere. So almost all of these spots cause brightness reductions larger than the transiting Earth. The Sun is not even a very active star, so chances are that many other stars have even more and larger spots. This might give you an impression why it is pretty hard to find small transiting planets around active stars.</div>
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However, the good thing is that spots change. The brightness variations they imprint on lightcurves are quite different from exoplanetary transits and they always change with time - although sometimes they change very slowly. A transiting planet usually does not change its transit (although there seem to be exceptions), so the same signal is coming again and again at a predictable time. If the transit is changing, either its shape or its transit time, you always have to be extra cautious because this takes you very close to what spots do.</div>
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By the way, this plot also shows the 11 year activity cycle of the Sun. Around 1997 and 2009 you can see periods with only very few and comparatively small spots. In between the biggest spots are much larger. The magnetic activity of the Sun changes: when it is high, it has a lot of spots and also many large spots; when it is low, you sometimes even have periods of days where not a single spot is seen. These magnetic cycle are also an issue when searching for exoplanets, although not so much for transit surveys. You can see the different levels of activity of a star in the radial velocity measurements, which might mimic the signal of a far-out planet with a long period. Again, stellar activity can mess up things quite a bit.</div>
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<br />nonnativenoobhttp://www.blogger.com/profile/09489612471884841558noreply@blogger.comtag:blogger.com,1999:blog-7527535668043926125.post-92129043836440546902016-02-14T13:14:00.001-08:002016-02-14T13:14:41.447-08:00Exoplanet discoveries: The growing number of planets<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjtLzefLHG_B11kc7kFxZRH-AFKiQwIv_k9uxshSbAA9A7NBGuBH89RAjprZ3c3njVY7lJDhzmwHXKy70CC53CnywB_QC7wc3QRm0CnsQ4IL0VXv6w3Q36grZ54Xu_f7S6rmFzgaiJHKgo/s1600/exoplanets-discovery-histogram.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="499" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjtLzefLHG_B11kc7kFxZRH-AFKiQwIv_k9uxshSbAA9A7NBGuBH89RAjprZ3c3njVY7lJDhzmwHXKy70CC53CnywB_QC7wc3QRm0CnsQ4IL0VXv6w3Q36grZ54Xu_f7S6rmFzgaiJHKgo/s640/exoplanets-discovery-histogram.png" width="640" /></a></div>
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People have been searching for planets ('wandering stars') for thousands of years, but the first detection of a planet around another star - not the Sun - was not that long ago. It has been suspected for a long time, but we only know since about 25 years that there actually are other planets orbiting around other stars.</div>
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If you take a look at the chart on top, you can see the number of known exoplanets over their discovery date. Usually, 51 Peg b is referred to as the first detected extrasolar planet - that is why I marked it with bold letters. However, it is easy to see that this is not the entire story of the detection of the first exoplanets. Clearly, there were five planets discovered before 51 Peg b - so what's the problem with them?</div>
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I guess the problem with these planets was three-fold. First, some people had a hard time believing the data. Especially the early detections by the radial velocity technique were not absolutely convincing because researchers were at the very limits of what their instruments could do. Second, the PSR planets are bodies with low masses around pulsars. Pulsars are neutron stars, stars at the end of their life cycle. This was not expected and many people were wondering whether this could really be a planet. Third, the first two exoplanets detected were huge with masses higher than 10 Jupiter-masses. Again, people were not sure whether this is a planet or not rather something like a 'small star'. In 1995 Mayor and Queloz presented a very clear signal of a planet with half the mass of Jupiter orbiting the solar-like star 51 Peg. This was so convincing that most scientist soon accepted it as the first definitive detection of an exoplanet.</div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi84-XZO5UbI6FBwOYoQqogIb8zBM584pWaTclY0Zd1ltU8AVHacJOnyDWjZ_bCqM2KBkmj7cBVmUNQJCLl5pa6Lkw4I9zsyPlyz__CIwnGCZ8z0o5KUf8py4399YxuVjbZAK_NbbyHnJY/s1600/exoplanets-discovery-histogram-dettype.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="498" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi84-XZO5UbI6FBwOYoQqogIb8zBM584pWaTclY0Zd1ltU8AVHacJOnyDWjZ_bCqM2KBkmj7cBVmUNQJCLl5pa6Lkw4I9zsyPlyz__CIwnGCZ8z0o5KUf8py4399YxuVjbZAK_NbbyHnJY/s640/exoplanets-discovery-histogram-dettype.png" width="640" /></a></div>
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This plot shows you the number of exoplanets per detection technique. The first thing that hits the eye is the huge number of detections by 'primary transit', which is the transit method. Half of the currently known planets were found using this technique. The second-most successful method is the radial velocity method.</div>
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In 2014 the number of detections peaks with almost 900 exoplanets found in this year. This is a little bit misleading because most of these planets were already known as Kepler planetary candidates - unconfirmed planets found by the Kepler mission. In 2014 many of these unconfirmed planets were suddenly counted as real planets, not because they actually were confirmed by e.g. detection with some other method (preferably RV), but based on a statistical argument. The short version of this argument is: Kepler planetary candidates with some specific properties (e.g. being part of a multi-planet system) are virtually always real planets.</div>
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It is interesting to see that the number of exoplanet detections seems to go down. The number in 2015 was lower than 2011, 2012, and 2013. This is certainly no real effect in the sense that there are no more new planets to be found out there. It rather reflects the fact that large, successful missions to find transiting planets, like CoRoT and Kepler, have ended and less data is obtained. Although there certainly will be new instruments dedicated to detect new exoplanets, with a number of more than 2000 known exoplanets the focus will probably shift to missions characterizing a selection of particularly interesting exoplanets in detail.</div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgA2nk36f9k5wOPaMAEFz_PaFSxPNnOLI3aCQCoRkxVRAVprmGALX8NInVMFt__kdQ30iPoi_u6jsHHVkNNtckpPmJEwjgrhK1xBA29EGdyF6NIIa35sFes2T7mTo8qds8QgnRGfoilZ2s/s1600/exoplanets-discovery-histogram-dettype-6plots.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="530" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgA2nk36f9k5wOPaMAEFz_PaFSxPNnOLI3aCQCoRkxVRAVprmGALX8NInVMFt__kdQ30iPoi_u6jsHHVkNNtckpPmJEwjgrhK1xBA29EGdyF6NIIa35sFes2T7mTo8qds8QgnRGfoilZ2s/s640/exoplanets-discovery-histogram-dettype-6plots.png" width="640" /></a></div>
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When presenting each detection method separately, we can see better how the number of detections is developing for each technique. The only method I do not show here is the astrometry technique which - according to exoplanet.eu - only has one detection.</div>
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The numbers coming from the RV method are more or less constantly rising since the 90s. Although it is resource intensive because one needs large telescopes and highly RV-stabilized spectrographs, this is our most important technique to detect the mass of exoplanets. Getting high-resolution spectra of the exoplanet system also helps analyzing other properties of the star and the planets.</div>
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After the detection of the first extrasolar planetary transit in 1999, most of the transiting planets came from Kepler from about 2010 on. Although the transit method is comparatively simple, the numbers go back since the Kepler main mission is over (and K2 is not obtaining as much and as good data). Data from ground is just not as fruitful, although it is producing a lot of results.</div>
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The numbers for microlensing and imaging are rising since about 2005. I hope this will continue because it is very good for our statistical understanding of exopanets; these methods probe different properties than RVs and transits, e.g. planets far away from their host stars, which will help to understand better how many planets there are, where they are, and what characteristics they have.</div>
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<br />nonnativenoobhttp://www.blogger.com/profile/09489612471884841558noreply@blogger.comtag:blogger.com,1999:blog-7527535668043926125.post-40987514509563617322015-08-05T13:09:00.003-07:002015-08-05T13:09:37.795-07:00All sky map of exoplanet host stars: Surveys (exoplanet.eu)<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgN455z6jvsC55O40xbaHNwOfQnfmxURNYWS7xfEuwxR7WnygO3XCfIIoUcLTyya2dMk3EAibFHTLsXMt5r6HrD4GtR1uJpRUBK2fXiorEfUYbuopa0pPMtFwxhHhVd31MZch8-C1NtHy4/s1600/exoplanet-map-survey.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="280" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgN455z6jvsC55O40xbaHNwOfQnfmxURNYWS7xfEuwxR7WnygO3XCfIIoUcLTyya2dMk3EAibFHTLsXMt5r6HrD4GtR1uJpRUBK2fXiorEfUYbuopa0pPMtFwxhHhVd31MZch8-C1NtHy4/s640/exoplanet-map-survey.png" width="640" /></a></div>
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There are many different surveys looking for new extra-solar planets. Right now the most successful technique is the transit method and there are many programs using this method. In this all sky map I was trying to show a few of these surveys which look at many stars, monitor their brightness, and try to find exoplanets in the stars' light curves.</div>
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Probably the most well-know survey is <a href="http://kepler.nasa.gov/" target="_blank">Kepler</a>; it's the instrument that found the most planets until now. However, it looked at a very limited area of the sky. You can see it on the left side of the map where the large number of black dots are.</div>
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<a href="http://sci.esa.int/corot/" target="_blank">CoRoT</a> was another space-based mission which was very successful; however, it did not nearly find as many exoplanets as Kepler. Its observing strategy was a bit different. CoRoT did not stare at one area in the sky all the time but switched its field of view every half year. One time it looked in the direction of the center of the Milky Way, which are the purple squares on the left side, and the next time it looked at an area in the opposite direction. These so-called 'anti-center' runs can be seen in the center of the map.</div>
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Also very successful is <a href="http://www.superwasp.org/" target="_blank">WASP</a>. The nice thing about this survey is that (1) it observes from the ground and (2) it looks (almost) everywhere in the sky. The 104 planets I got from exoplanet.eu (including SuperWASP) are really quite a number.</div>
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There are lots of different missions listed in the legend of the map and I do not want to go into detail on everyone of them. It is not a complete list of programs but rather what I could made out of the information provided by <a href="http://exoplanet.eu/">exoplanet.eu</a>. Unfortunately, it is kinda hard to find which planet was detected by which survey because this is not listed there. So the host stars (and planets) I plot here are named after the program they were found with - and this way I could plot them. However, this is not true for every planet found and also not true for every survey.</div>
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This is especially disappointing for the planets found with the RV method. I would have liked to plot all the RV planets coming from, e.g., <a href="http://exoplanets.ch/projects/harps/" target="_blank">HARPS</a>, which is an amazingly successful instrument, but I could not easily collect the necessary information. The host stars usually keep their name because they are bright, well-known objects (with HD or HR numbers). So it's not possible for me to get the survey from the name alone.</div>
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After all, this map is supposed to give an impression of which transit surveys there are and how they observe. It's not meant to be complete. Furthermore, the detection method listed in the database is not always 'transit'. This is because some systems are re-observed in RV to get the mass of the planet. Others, e.g., OGLE are no transit survey, although they do observe light curves. It can by chance also find transits but OGLE is actually looking for the signatures of microlensing events.</div>
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nonnativenoobhttp://www.blogger.com/profile/09489612471884841558noreply@blogger.comtag:blogger.com,1999:blog-7527535668043926125.post-85425300104114152292015-08-04T07:41:00.000-07:002015-08-04T07:41:17.215-07:00All sky map of exoplanet host stars: Multi-planet systems (exoplanet.eu)<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj62_Ey9EyG3xufvVHdS3SymwNrWszdyXVAbVDR5EjwifFc8ICTT5cox9FyYB9iAcMpbpuwt49Xz2imbdLIhe-cU1ZDhfY_9gZ9uqFeAlcjrQ7DYiWmzqWN9Fpln58BP9h0MoyUiNjfhvk/s1600/exoplanet-map-multis.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="282" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj62_Ey9EyG3xufvVHdS3SymwNrWszdyXVAbVDR5EjwifFc8ICTT5cox9FyYB9iAcMpbpuwt49Xz2imbdLIhe-cU1ZDhfY_9gZ9uqFeAlcjrQ7DYiWmzqWN9Fpln58BP9h0MoyUiNjfhvk/s640/exoplanet-map-multis.png" width="640" /></a></div>
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With this post I continue my series on exoplanet host star all sky maps. What you see is basically the same thing I showed <a href="http://exoplanet-diagrams.blogspot.de/2015/08/all-sky-map-of-exoplanet-host-stars.html" target="_blank">two posts ago</a>. This time, however, I choose the color to represent the number of exoplanets in the system. So the symbol tells you which method was used to detect the system and the color tells you how many planets are know right now in this system (August 3, 2015, <a href="http://exoplanet.eu/">exoplanet.eu</a>). The 740 lightyellow-colored host stars have only one planet, the one black circle in the Kepler field of view (Kepler-90 alias KOI-351) is the only exoplanet system with seven planets - all transiting the host star.</div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgwv9nYlwyMpvh16OV5RA2h0ldSbYVlsJ7AAUqoEoKnmMKGX-LcvSvZCVgYyWkE-wcIubGlWbhY5Gkin9-bo4lDcQEbKegI6u9-bXjrieQSI5pZuE2GxK1DVPLDbWe_cOslBTWDcDG5ISE/s1600/exoplanet-map-multis-zoom.png" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="378" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgwv9nYlwyMpvh16OV5RA2h0ldSbYVlsJ7AAUqoEoKnmMKGX-LcvSvZCVgYyWkE-wcIubGlWbhY5Gkin9-bo4lDcQEbKegI6u9-bXjrieQSI5pZuE2GxK1DVPLDbWe_cOslBTWDcDG5ISE/s400/exoplanet-map-multis-zoom.png" width="400" /></a></div>
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The Kepler field of view is so crowded that I include a zoom in on this region; it's the figure on the left side. The only seven planet system is on the top right of the Kepler FOV whereas the only transiting six planet system (Kepler-11) is pretty much at the bottom. In the all sky map you can see three other six planet systems, however, these where detected with the RV method.</div>
nonnativenoobhttp://www.blogger.com/profile/09489612471884841558noreply@blogger.comtag:blogger.com,1999:blog-7527535668043926125.post-56254633370852750912015-08-03T10:14:00.003-07:002015-08-03T10:14:59.467-07:00Exoplanet host stars: The Kepler field of view (exoplanet.eu)<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjIJN751Aytxm0kn5yHFk08mvQfVvzJRj0yUyWKhc1Db8xd4qmaTPvnIgpUHAYlsYQDC0RRHJvdpBDeUCXeaGWrYDj6Wb8FjYeJWTNvoCuvw8_QHZ22TdZrQO3mgmaf4dENK6q9Z2DAPbM/s1600/exoplanet-map-zoom.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="456" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjIJN751Aytxm0kn5yHFk08mvQfVvzJRj0yUyWKhc1Db8xd4qmaTPvnIgpUHAYlsYQDC0RRHJvdpBDeUCXeaGWrYDj6Wb8FjYeJWTNvoCuvw8_QHZ22TdZrQO3mgmaf4dENK6q9Z2DAPbM/s640/exoplanet-map-zoom.png" width="640" /></a></div>
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This is an addition to the post before. The plot shows the <i>Kepler field of view</i> in detail, all symbols and colors stay the same. This is the region in the sky from which we - by far - know the most planets around stars. Until July 23, 2015, Kepler has discovered 1879 confirmed exoplanets around 471 stars (according to <a href="http://exoplanetarchive.ipac.caltech.edu/">exoplanetarchive.ipac.caltech.edu</a>).</div>
nonnativenoobhttp://www.blogger.com/profile/09489612471884841558noreply@blogger.comtag:blogger.com,1999:blog-7527535668043926125.post-23930350389774050702015-08-02T10:02:00.000-07:002015-08-02T10:02:07.909-07:00All sky map of exoplanet host stars (exoplanet.eu)<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgmKKj2qIbKOixt2oLCTEd9oSRVEGE7dUY_qFNFpu8EicqcXiL31sS3BOnJ58Nez5niNxfVroewBnWo_-Yzd44SwkaJRMQa1rJx192fC4-7TMkzeUZ_GZaxbuSJzL0VjuTtk0SYhk21iiI/s1600/exoplanet-map.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="282" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgmKKj2qIbKOixt2oLCTEd9oSRVEGE7dUY_qFNFpu8EicqcXiL31sS3BOnJ58Nez5niNxfVroewBnWo_-Yzd44SwkaJRMQa1rJx192fC4-7TMkzeUZ_GZaxbuSJzL0VjuTtk0SYhk21iiI/s640/exoplanet-map.png" width="640" /></a></div>
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Today I'd like to show something not directly connected to the last couple of posts. This is an all sky map of exoplanet host stars. Different colors/symbols indicate the method used to detect the planet. The data was taken from <a href="http://exoplanet.eu/">exoplanet.eu</a>. Actually, I tried to plot all planetary systems know today, which according to exoplanet.eu should be 1228, but for some reason I am missing three in the transit method.</div>
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The underlying magenta colored points are about one million stars from the Tycho catalog (ESA Hipparcos satellite). The map is an aitoff projection of the sky in galactic coordinates and the Milky Way lies at the equator; this is why most of the stars are located there.</div>
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Most of the planets are detected with the transit method. However, the majority is located in the small area crowded with black dots - the <i>Kepler field of view</i>. When we talk about statistics of transiting exoplanets we are actually talking about a small part in the sky and not the entire sky. Astrophysicists just assume that it should be the same everywhere. The other black dots come from different surveys, e.g., <i>CoRoT</i> or <i>WASP</i>.</div>
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The picture is different when looking at planets detected with the radial velocity (RV) method. They seem to be more uniformly distributed. It's the second most successful technique with 454 stars having planets around them.</div>
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At least according to exoplanet.eu, so far there is only one astrometry planet and it is very close to the Kepler FOV - although it's not in it. The star is <a href="http://exoplanet.eu/catalog/hd_176051_b/">HD 176051 b</a>. So far it seems to be too difficult to detect planets with this method, but it is expected that with <a href="http://sci.esa.int/gaia/" target="_blank">GAIA</a> there will be many planets coming from this technique.</div>
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Imaging seems pretty much located to certain areas, avoiding the plane of the Milky Way as much as possible. This is probably a good idea since background stars that coincidentally stand close to the potential host stars make it more difficult to find planets - or might even be misinterpreted as bodies belonging to the system. </div>
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All microlensing planets come from a limited area in the direction of the center of the Milky Way, which in this map is at the edge. This illustrates nicely that microlensing really samples a quite different population of stars. All other techniques try to go away from the galactic center (and even the galactic plane) and only find exoplanets rather close to the Sun. The most distant microlensing planet, however, is about 25000 light years away - virtually in the center of the Milky Way.</div>
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The transit timing variation (TTV) planets are all in the Kepler FOV. For this method one needs good light curves and a long cadence to cover many transits, and this is what Kepler does best. According to exoplanet.eu there are only four TTV planets - which I do not think is true; there have to be much more. <a href="http://exoplanets.org/">exoplanets.org</a> says it's more like 60 (including some pulsar planets), which I believe is closer to the real number.</div>
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Finally, we have the planets around pulsars. There are a few in the Kepler FOV, but otherwise I do not really see a system there. I think it is nice to notice that <a href="http://exoplanet.eu/catalog/psr_1257_12_b/">PSR 1257 12 b</a> is the star with the first exoplanet detection in the year 1992 - and it actually is a three-planet system! I think is has to be one of the two triangles in the upper right. Usually, people cite 51 Peg b as the first exoplanet - it was the first around a solar-type star. I guess pulsars are just too different ...<a href="http://exoplanet.eu/catalog/psr_1257_12_b/"><br /></a></div>
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<br />nonnativenoobhttp://www.blogger.com/profile/09489612471884841558noreply@blogger.comtag:blogger.com,1999:blog-7527535668043926125.post-70716920072062215562015-07-30T10:55:00.000-07:002015-07-30T10:55:18.222-07:00Transits: Limb darkening - HD 209458 b in different colors (HST)<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiwEoWHpjuuyDQMCBFEZ4uPdNbWs_qlLc4HqB86MJtfh7HuM-YDpck9AHtjP3oA-2jKTEltapqXQcvcnqWUlawNTtfpj_GxYWGedchfPO1VvWjOcJeJ6OgsewaMdUAUHS6DuUyVEMYc5lI/s1600/hd209458-plot.png" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="640" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiwEoWHpjuuyDQMCBFEZ4uPdNbWs_qlLc4HqB86MJtfh7HuM-YDpck9AHtjP3oA-2jKTEltapqXQcvcnqWUlawNTtfpj_GxYWGedchfPO1VvWjOcJeJ6OgsewaMdUAUHS6DuUyVEMYc5lI/s640/hd209458-plot.png" width="264" /></a></div>
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In the previous post I presented theoretical transits of how the exoplanet HD 209458 b should look like in different colors. Now I will show how its transits really look like.</div>
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On the left you see observations of the <i>Hubble Space Teleskope</i> (HST) from 320 to 970 nm. The last transit, which is much nosier, is not from HST but <i>Spitzer</i> - a NASA space misson for infrared observations.</div>
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Actually, HST observed many spectra of the star covering a full transit. By averaging over different parts of the spectrum you get the transit in a certain color. The central wavelength of the interval over which was averaged is given on the right side of each transit. The colors range from the ultraviolet to the near-infrared.</div>
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The Spitzer data is special because it lies at a much higher wavelength in the far-infrared. There the star should have virtually no limb darkening anymore and the transit has a box shape. However, you cannot see that very well because it is much more difficult to get precise brightness measurements for these wavelengths. The star is much fainter there and, thus, the noise is much higher. Also the two instruments are pretty different which leads to non-equal measurement errors.</div>
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In the last post I showed what we should expect from theory - and the observations agree nicely with it. In UV and blue the shape of the transit is much rounder than for longer wavelength. Indeed, limb darkening is stronger for shorter wavelengths.<br />
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It is actually pretty hard to measure the limb darkening of stars; they are just too far away to spatially resolve them. Analyzing exoplanetary transits is one of the best methods to verify whether the theoretical predictions are really correct. And so far the models seem to work pretty well - although in detail observations and theory are not so easy to compare. After all, the exact shape of the transit depends on a lot of different things.<br />
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nonnativenoobhttp://www.blogger.com/profile/09489612471884841558noreply@blogger.comtag:blogger.com,1999:blog-7527535668043926125.post-36807965866507305522015-07-29T01:00:00.000-07:002015-07-29T01:00:08.321-07:00Transits: Limb darkening in theory<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjA834b8NA_FpKJ2jpG3nmvqWV90YRoSqlKg37eFD_suFajtoJkF1ozS-0hv58T213rnbAud3ykL4XN7JjuGcwzyu3k_XjVHDbFer05hm1IHbQyMGkPIdVlvZSlUBMBP13ZBoiv0Emhpr0/s1600/hd209458-plot-theory.png" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="640" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjA834b8NA_FpKJ2jpG3nmvqWV90YRoSqlKg37eFD_suFajtoJkF1ozS-0hv58T213rnbAud3ykL4XN7JjuGcwzyu3k_XjVHDbFer05hm1IHbQyMGkPIdVlvZSlUBMBP13ZBoiv0Emhpr0/s640/hd209458-plot-theory.png" width="264" /></a></div>
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Now let us take a look at limb darkening in transits. In the beginning I will start with <i>theoretical transits</i> - transit lightcurves generated on the computer. This makes explanations a bit easier, we will come to real data soon enough.</div>
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For demonstration purposes I chose one of the best known exoplanets today: <b>HD 209458 b</b>. In 1999 this was the first transiting planet ever observed (<a href="http://arxiv.org/pdf/astro-ph/9911436v1.pdf" target="_blank">Charbonneau 2000</a>), a true milestone in the history of astrophysics. It is a huge planet, about 1.3 times the radius of Jupiter but only 70 % of its mass. It is a good planet to start with because its large size results in a deep transit.</div>
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The figure on the left side shows simulated transits of HD 209458 b for different wavelengths. This is interesting because the limb darkening of the star depends on the color you are looking at. So in different colors the transit shape will be different. I added a bit of noise to the lightcurve to make it look more like a real observation. The noise is roughly consistent with the uncertainty of the Hubble Space Telescope data of this planet I will show in the next post.</div>
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All transits are normalized meaning that the (average) brightness outside of the transit is one. However, if I plot them all over each other we would not see them very well anymore; so transits observed at longer wavelengths are shifted downwards. The corresponding wavelength (in nm) is given on the right side of each transit lightcurve. On the very right it is indicated to which wavelength regime (UV, visible, IR) this wavelength belongs. Keep in mind that visible light goes from 380 to 750 nm.</div>
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The x-axis shows you the time of the observation of each data point in hours from transit center; the transit duration of HD 209458 b is about three hours.<br />
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What can we learn from this figure? Due to the limb darkening the transit shape is round for blue colors (shorter wavelengths) and gets more box-shaped for red colors (longer wavelengths). When going further into the infrared, the transit looses its round shape completely because there is (almost) no limb darkening of the stellar disk anymore. In real data this would be nice because dealing with limb darkening can be a nuisance; you just have to deal with a few parameters less you do not really know for sure. However, it is not that easy to obtain high-quality transit lightcurves in the infrared - even for the best instruments scientist have right now. This is what I will show you in the next post.<br />
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<span style="font-size: small;"><i>Addendum: A more technical note at the end. On the left side of the transits in the figure letters are written: U, B, V, R, I (and FIR). These letters indicate the photometric bands (Johnson filters) used to simulate the transit lightcurves which are important to know the theoretically expected </i><i><i>limb darkening</i>. If you know your star and the photometric filter, you can calculate how the limb darkening should be. Here I use the non-parametric limb darkening coefficients for the Johnson filters for a Sun-like star <a href="http://adsabs.harvard.edu/abs/2013A%26A...552A..16C" target="_blank">published in this paper</a>.</i></span><br />
<span style="font-size: small;"><i>FIR is not a real filter; it stands for far-infrared. I just assumed at this long wavelength the limb darkening is zero. This way we have a comparison how the transit would look like if there is no limb darkening at all.</i></span></div>
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nonnativenoobhttp://www.blogger.com/profile/09489612471884841558noreply@blogger.comtag:blogger.com,1999:blog-7527535668043926125.post-7362329856915923232015-07-29T00:45:00.000-07:002015-07-29T00:45:01.398-07:00Limb darkening: SDO 17.1 nm<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEihCEhk2PgSNZTAj6JJNzHIqwEv2_uYFKRXZrpDvyj68P4zZD_chcsKDEPayYST4z8wc5n-olWi_pvUBiLxUUVU-5rxka2T_iv0fBdo5RX6LmqGZHfnDaCnkX4lTGD2qu3vOh2rc7YSyzM/s1600/limb-darkening-sdo-UV-17.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="410" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEihCEhk2PgSNZTAj6JJNzHIqwEv2_uYFKRXZrpDvyj68P4zZD_chcsKDEPayYST4z8wc5n-olWi_pvUBiLxUUVU-5rxka2T_iv0fBdo5RX6LmqGZHfnDaCnkX4lTGD2qu3vOh2rc7YSyzM/s640/limb-darkening-sdo-UV-17.png" width="640" /></a></div>
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Finally, I come to the point where limb darkening actually is not 'darkening' anymore. I should rather say <i>limb brightening</i> here. In the figure you can see the brightness across the solar disk again normalized to the value at disk center. However, this time you see that the Sun is brighter on the edges than it is in the center.</div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhcCghhKNQQicks3J4YP6IN0ekjZ2nh3qSSfgxje-Uhyphenhyphen_UZglYOk1WC9MZKoLkzo6vDOCrRRpkQdgu8nWmawENoIyoeXSyCf4VQi41E9sRTcP3Aa2kerRY6vgt0R5tKGgtxyC7pDvXLaU8/s1600/20150701_122723_2048_0171.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhcCghhKNQQicks3J4YP6IN0ekjZ2nh3qSSfgxje-Uhyphenhyphen_UZglYOk1WC9MZKoLkzo6vDOCrRRpkQdgu8nWmawENoIyoeXSyCf4VQi41E9sRTcP3Aa2kerRY6vgt0R5tKGgtxyC7pDvXLaU8/s320/20150701_122723_2048_0171.jpg" width="320" /></a></div>
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I generated this plot from SDO images like the one on the left. They show the Sun in the extreme ultraviolet at a wavelength of 17.1 nm. At these short wavelengths the disk is very inhomogeneous and you see a lot of loop structures which show the magnetic field of the Sun. Like in the last blog on SDO 1600, this is not the photosphere we are seeing; it's not even really the chromosphere anymore, but more like layers above that. Here we start to see the <i>corona</i> of the Sun.</div>
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In this high-energetic wavelength regime the Sun has no sharp edge. The top panel shows how the brightness goes down after the peak at the edge, but it does not drop down to zero like in the other images I showed in previous posts. The bright loops extend far into outer layers of the Sun and you still get a significant amount of light from there.</div>
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Magnetic lines are connected to the activity of a star. The more active a star is, the more of these bright inhomogeneous structures it should have in its outer atmospheric layers. Like spots these structures rotate with the star and change all the time.</div>
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For wavelengths showing limb brightening, exoplanet transits would look very different for what we see in the visual or infrared. Transits can change significantly from one to the other because the magnetic structures change. Also, contrary to the visual wavelengths, the transits are deeper at the edges than in the center. However, transits at these short wavelengths (far-UV, EUV, or even X-rays) are very hard to detect.</div>
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nonnativenoobhttp://www.blogger.com/profile/09489612471884841558noreply@blogger.comtag:blogger.com,1999:blog-7527535668043926125.post-30797820438796575242015-07-25T05:35:00.001-07:002015-07-25T05:35:19.787-07:00Limb darkening: SDO 160 nm<div class="separator" style="clear: both; text-align: center;">
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg7KO7V-p7GDcUMNM0R21ek-EklZ1JOv5juF38syyB_LDodQzmt5OBiWhoVnI_kmm2wXGZb9LXpr9iUIXCc8s743s2LwF9VV1QdDoubzGdl8ZHdKA_oJxmPCFAKp-a4N8382UcEsn3mSRg/s1600/limb-darkening-sdo-UV-160.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="410" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg7KO7V-p7GDcUMNM0R21ek-EklZ1JOv5juF38syyB_LDodQzmt5OBiWhoVnI_kmm2wXGZb9LXpr9iUIXCc8s743s2LwF9VV1QdDoubzGdl8ZHdKA_oJxmPCFAKp-a4N8382UcEsn3mSRg/s640/limb-darkening-sdo-UV-160.png" width="640" /></a></div>
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I wrote a lot about limb darkening in the previous posts and tried to carefully explain that the Sun gets darker when you go from the center of the disk to the limb. This effect is stronger for shorter wavelengths (ultraviolet) than for longer wavelengths (infrared). Guess what: Today I show you that this is not true.</div>
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Well, to understand that I have to explain that what I wrote about previously is correct for the <i>photosphere</i> of the star. I mentioned this in <a href="http://exoplanet-diagrams.blogspot.de/2015/07/limb-darkening-with-color.html" target="_blank">another blog</a> already. If we talk about the photosphere, everything I wrote and showed before is correct. However, if I show you how the limb darkening of the Sun really looks like in an image, you will probably notice that the solar disk is brighter in the UV than in visual light.</div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh5anvGp7XQDubwFtvwRoqABJBBfPNspe2Cu_xHpH9OeSeN8gUwm4jZ4atm_yQFjnmE3EIEgddcbdh5t16yatN6obnTThBX-Y-M4-Poqra5iFexCeTaO3HMrH7Kii51Nay7JFF_reu-Yqg/s1600/20150701_121728_2048_1600.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh5anvGp7XQDubwFtvwRoqABJBBfPNspe2Cu_xHpH9OeSeN8gUwm4jZ4atm_yQFjnmE3EIEgddcbdh5t16yatN6obnTThBX-Y-M4-Poqra5iFexCeTaO3HMrH7Kii51Nay7JFF_reu-Yqg/s320/20150701_121728_2048_1600.jpg" width="320" /></a></div>
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Again I show a picture of the Solar Dynamics Observatory (SDO), however, this time <a href="http://exoplanet-diagrams.blogspot.de/2015/07/solar-limb-darkening.html" target="_blank">not in the visual</a> but in the ultraviolet (160 nm, see left image). Compared to the optical, the Sun has much more structure in this image.</div>
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In the top figure I present the brightness of the Sun in this wavelength from one edge to the other. To create this diagram, I used several dozen SDO images taken over a month, and averaged their brightnesses. Shown is the mean brightness and the error bars indicate how variable this brightness was in the course of one month. If you compare this graph to <a href="http://exoplanet-diagrams.blogspot.de/2015/07/solar-limb-darkening.html" target="_blank">the one for the visual</a>, you will notice that the limb darkening of the Sun is actually weaker in the UV. So comparing these two images you see the opposite of what I told you in the beginning and all the previous post on limb darkening.</div>
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The solution to this problem is: What you seen in this UV image of the Sun is not really the photosphere. You see a different part of the solar atmosphere which is slightly above the layer you see in <a href="http://exoplanet-diagrams.blogspot.de/2015/07/solar-limb-darkening.html" target="_blank">the visual image of a previous post</a>. You start seeing the <i>chromosphere</i>. And the chromosphere is different. There the Sun is hotter and a lot of light is emitted in shorter wavelengths. Because you see the emitting regions of the chromosphere better at the limb than in the center, you get more light from the limb. And the combination of all the light coming from different layers in the Sun in this UV wavelength interval makes up the figure I show in the top.</div>
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In this wavelength the brightness is still not higher in the limb than in the center, but in the next post I will show you a wavelength regime where we do not have limb darkening anymore - but <i>limb brightening</i>. With your naked eyes you will never see that because this is light you cannot receive with the human eye. So for us, the Sun has limb darkening.<br />
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I maybe should mention in the end, that the absolute brightness of the light coming from the chromosphere is much less than what you get from the photosphere. I always show normalized brightnesses, so this is something you cannot see in the figures. However, in absolute numbers there is much more light coming from the photosphere - which is basically the reason why we see it with the eye. But the relative contribution in the UV grows, which is the reason why we start detecting limb brightening for smaller wavelengths.</div>
<br />nonnativenoobhttp://www.blogger.com/profile/09489612471884841558noreply@blogger.comtag:blogger.com,1999:blog-7527535668043926125.post-7740132010936284142015-07-24T13:19:00.000-07:002015-07-24T13:19:05.863-07:00Limb darkening in a single spectral line<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgElvs7CLvbJl9EiUs-xf1KiYGxWZKszTkiODNf1QQUZGPgxSmNL4QcaomcgWPWAJIt9Y6Ej7afaJM1RlUxNq28utMB77-VvjPthqQVwocUAHqAQp20NHw7aB5epCwUiGwkcI-8gFaTZBw/s1600/solar-ld-models-Halpha.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="640" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgElvs7CLvbJl9EiUs-xf1KiYGxWZKszTkiODNf1QQUZGPgxSmNL4QcaomcgWPWAJIt9Y6Ej7afaJM1RlUxNq28utMB77-VvjPthqQVwocUAHqAQp20NHw7aB5epCwUiGwkcI-8gFaTZBw/s640/solar-ld-models-Halpha.png" width="622" /></a></div>
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If we take a look at a very small wavelength interval of the spectrum of a star - a single spectral line - limb darkening is quite different again. For this example I chose the Hα line, a spectral line of the hydrogen atom and a prominent line in many stellar spectra. In the lower panel of the figure you can see how the line, which is in absorption here, looks like. Its rest wavelength (in vacuum) is at 656.46 nm, which corresponds to a red color in the visible wavelength range. This is why, if we look at the Sun through a telescope with an Hα filter, the solar disk is red.</div>
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The continuum left and right to the line is normalized to one. This way it is easy to see that the center of the line is more than 40 % less bright than the continuum. What I show here are not observations but I use theoretical models of spectra - a computational calculation of how the spectrum of a certain star should look like. I used <a href="http://www.hs.uni-hamburg.de/index.php?option=com_content&view=article&id=32&Itemid=277&lang=de" target="_blank">PHOENIX spectra</a> of a Sun-like star, which are pretty close to what we observe in nature. Actually, I think it is really amazing that people can calculate a star in a computer.</div>
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What I'd like to show in this diagram is that if you go in small wavelengths steps from one side of the line to the other, the limb darkening changes<i> a lot</i>. The color code now is from the left side of the line (blue) to the right side of the line (red); each point of the line corresponds to the line with the same color in the upper panel. You can see that the violet/blue and the red lines, which are coming from outside the spectral line, show the limb darkening we saw in previous posts for the visual wavelength regime (large interval). Now if you go inside the line you see that the limb darkening dramatically decreases, meaning that the brightness on the limb goes up. It goes even further up then in the case of infra-red wavelengths. At the bottom of the Hα line the limb darkening is very weak; in the Hα core the solar disk looks much more uniformly bright than we see it with the eye.</div>
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This behavior is true for many spectral lines but not for all. Depending on where the spectral line is created in the atmosphere of the star, the spectral line might even get darker to the limb. The point is: <b>Different parts of a spectral line can have very different limb 'darkening'</b>. And what we usually see as limb darkening is the <i>continuum case</i>, which is the average over a large interval of the spectrum (and over many spectral lines).</div>
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<br />nonnativenoobhttp://www.blogger.com/profile/09489612471884841558noreply@blogger.comtag:blogger.com,1999:blog-7527535668043926125.post-17439495936402314212015-07-23T09:56:00.003-07:002015-07-23T09:56:48.938-07:00Limb darkening with color<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi8vNAy0RM7RafqQkQQvqRUsyD5FNz-KuLvvzLq7rDR8odEAnnNfT34BcPRFq92XLw2ReIWyQLljB8KGlGNaCOtgoZ3S-8JjYazcyuMhcTr3Se94R2TrNhjULMpH-EKvSDU0gR1jWJauQo/s1600/solar-ld-models-color.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="452" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi8vNAy0RM7RafqQkQQvqRUsyD5FNz-KuLvvzLq7rDR8odEAnnNfT34BcPRFq92XLw2ReIWyQLljB8KGlGNaCOtgoZ3S-8JjYazcyuMhcTr3Se94R2TrNhjULMpH-EKvSDU0gR1jWJauQo/s640/solar-ld-models-color.png" width="640" /></a></div>
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It is important to understand that limb darkening depends on
the color - the wavelength - you are looking at. So if you look at the Sun in the blue or in the red color, the limb darkening is different. This is what I would like to illustrate here. The x-axis shows the position on the disk, with zero being in the center and one being at the edge. The y-axis shows the brightness of the star divided by the value in the center.</div>
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The diagram visualizes how
limb darkening looks like for the <i>continuum</i>, which basically
means averaged over a large wavelength interval which in this case is in the
visual wavelength regime. The colors indicate the central wavelength of the used interval, each interval is 10 nm wide. So the 380 nm line (blue) shows how limb darkening looks like <i>on average</i> over the wavelengths from 375 to 385 nm.<br />
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The bottom line is: For all colors a star is brighter at the center than at the edge. But for longer wavelengths (red colors) the limb darkening is weaker than for short wavelengths (blue); the difference in brightness between center and limb is smaller for longer than for shorter wavelengths.</div>
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For comparison I also draw one line in the ultraviolet (100 nm) and one in the infrared (2500 nm). In these cases, which are imperceptible by the eye, limb darkening really looks very different. In the IR the disk is only 20 % darker at the edges than in the center, whereas for UV the limb of the star is virtually dark.</div>
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Especially interesting is the fact that the radius of the star is not equal for all colors. Where the distance from the disk center equals one the stellar disk is supposed to end and the brightness should be zero. However, this is not true. In the UV the brightness is still non-zero well beyond the 'defined' edge of the star. Zooming into that region we would see that this is true for all colors - in each color the star has a slightly different 'size'. Although this might seem to be weird when thinking about it the first time, it actually is not very surprising. What we call the edge or surface of the Sun is not a real boundary, the Sun does not suddenly stop within a meter or even a kilometer. What we see as surface of the Sun is the region in the atmosphere where the visible light is coming from - the <i>photosphere</i> - which is several hundreds of kilometer thick. Above that layer comes the chromosphere, and above that the corona. So the Sun, and other stars too, does not have a sharp edge. This, maybe, makes it easier to understand why in the diagram the Sun does not have the same radius for all colors.<br />
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<br />nonnativenoobhttp://www.blogger.com/profile/09489612471884841558noreply@blogger.comtag:blogger.com,1999:blog-7527535668043926125.post-19173337174320193162015-07-21T11:38:00.001-07:002015-07-21T11:38:52.685-07:00Solar limb darkening<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh46kINfgtNaHlubD3B1P6zdtrJHNWNmIjyX5zWn-rJyq2DJwOIDfp1XTpnxyPNnXUgsPD3Ppe8Lqwia8__-KefOhgKR6YgKPoq4ReDO8Yzq1PwUSXQJ5fx7DPkVFUuzLWQ31V5QTLNAVU/s1600/limb-darkening-sdo.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="418" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh46kINfgtNaHlubD3B1P6zdtrJHNWNmIjyX5zWn-rJyq2DJwOIDfp1XTpnxyPNnXUgsPD3Ppe8Lqwia8__-KefOhgKR6YgKPoq4ReDO8Yzq1PwUSXQJ5fx7DPkVFUuzLWQ31V5QTLNAVU/s640/limb-darkening-sdo.png" width="640" /></a></div>
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In my previous post on the <a href="http://exoplanet-diagrams.blogspot.de/2015/07/the-transit-method.html" target="_blank">transit method</a> I briefly mentioned limb darkening. I did not want to discuss it there and just ignored it, but I would like to come back to it now because it is an important effect - especially for transits. In this post I will talk about what limb darkening is, its relevance for transits I will discuss in another post.</div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiB4mnPH24bill3hYS3Sw5pPBGeg0U2kGKx2Py35ZlXYLoECBEs9ZoK8oZEhRf4qtLaO6IF-8WDV3lfC72EbFnsGZXU3qIac1YD-wqqLZuMdY9FW13engk_ea1z4sE7u8fLx_z7oyTJ-X4/s1600/20150720_121254_2048_HMII.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="200" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiB4mnPH24bill3hYS3Sw5pPBGeg0U2kGKx2Py35ZlXYLoECBEs9ZoK8oZEhRf4qtLaO6IF-8WDV3lfC72EbFnsGZXU3qIac1YD-wqqLZuMdY9FW13engk_ea1z4sE7u8fLx_z7oyTJ-X4/s200/20150720_121254_2048_HMII.jpg" width="200" /></a></div>
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To the left you see an image of the Sun (July 20, 2015) taken by the <a href="http://sdo.gsfc.nasa.gov/" target="_blank"><i>Solar Dynamics Observatory</i></a> (SDO), a NASA mission constantly observing the Sun. As you might notice the disk of the sun is <b>not</b> uniformly bright. The Sun is brighter in the center than it is on the edges. This is commonly referred to as limb darkening. The physical reason for this is that the Sun gets hotter the further you go down to the core. So if you look at material at the surface it is colder than material deeper in the Sun. In the center of the disk you see down to hotter material than at the edges, and hotter material emits more light.<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEirZWsjirFxNe8v4T_M1d13MDWufjaqVu934bpdUC3FyCs6gMFBvduXVETjtMbeBx9949-tmia8TzlncPTFsXNMv5CUEPzKJM5g7mpbW7bVTq_3uPTSa_VsIJuZwIhA3q_CSCahg8kUfl0/s1600/454px-Limb_darkening_layers.png" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="200" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEirZWsjirFxNe8v4T_M1d13MDWufjaqVu934bpdUC3FyCs6gMFBvduXVETjtMbeBx9949-tmia8TzlncPTFsXNMv5CUEPzKJM5g7mpbW7bVTq_3uPTSa_VsIJuZwIhA3q_CSCahg8kUfl0/s200/454px-Limb_darkening_layers.png" width="200" /></a></div>
I think the sketch on the <a href="https://en.wikipedia.org/wiki/Limb_darkening" target="_blank">wikipedia page</a> is pretty informative, so I do not bother to create a new one. It illustrates nicely that the length L you look through the stellar atmosphere is equal in the center and the limb of the star; however, you do not look down to material of the same temperature. And because in the disk center the material you see is hotter, this part of the Sun is brighter, too.<br />
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Now I finally come to my diagram in the beginning of this blog. It shows the brightness of the solar disk from one limb to the other. I determined this from SDO images (July 20, 2015) averaging several pictures stretching over almost five hours. The brightness is normalized to one, meaning that I just divided it by the brightness in the center of the disk. You can see the steep rise in brightness on the left limb of the disk, the maximum in the center, and the decline to the right edge. I averaged over about dozen images and the one-sigma error bars indicate how much the solar surface brightness has varied in these roughly five hours. For most points this is a change of at least several percent, so the solar surface brightness is varying all the time on a small scale.<br />
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That the disk is not really uniformly bright can be seen especially well in starspots. You can see a few in the SDO image. However, you can also see brighter regions, e.g., on the right side of the top diagram. I zoomed in to the region where a bump is visible. Here a small part of the disk is brighter than the surrounding area, and it is also quite variable because the error bars are large. We also should not forget that the Sun is rotating and features on its surface are slowly moving to the right; although this effect is very small during a couple of hours, it might contribute to the variability.<br />
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There is much more to talk about concerning this topic, but I will close for now with this: If the Sun would not have limb darkening, its brightness distribution from one limb to the other would look like the dashed magenta line in the diagram: full brightness everywhere. Not having a uniformly bright disk has severe effects on exoplanetary transits because the shape of the transit depends on how exactly the distribution looks like. I will talk about that in one of the upcoming post.<br />
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nonnativenoobhttp://www.blogger.com/profile/09489612471884841558noreply@blogger.comtag:blogger.com,1999:blog-7527535668043926125.post-58457884139367577692015-07-19T09:50:00.001-07:002015-07-19T09:54:10.223-07:00The transit method<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhOoY_UWTQ9qDfKijiLJ4b19_Q7N8qRPtgsamyqEY5lo6kgsq32o9AhUOEoCfS9QWdNVZXqegr-jkvu7yRfmoSDHR5Jxk5RNLrgRW-QEZLFL9ztIgrwilIjPL7daxdzb556jBOsC5zWl_w/s1600/explain-transit-method.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="424" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhOoY_UWTQ9qDfKijiLJ4b19_Q7N8qRPtgsamyqEY5lo6kgsq32o9AhUOEoCfS9QWdNVZXqegr-jkvu7yRfmoSDHR5Jxk5RNLrgRW-QEZLFL9ztIgrwilIjPL7daxdzb556jBOsC5zWl_w/s640/explain-transit-method.png" width="640" /></a></div>
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The transit method is one of the most important techniques to detect and to study extrasolar planets. Using this method, up to date 1210 exoplanets have been found (<a href="http://exoplanet.eu/" target="_blank">exoplanet.eu</a>), the majority by the unbelievably successful <a href="http://www.nasa.gov/mission_pages/kepler/main/index.html" target="_blank">NASA <i>Kepler</i> mission</a>, but also by the European mission <a href="http://sci.esa.int/corot/" target="_blank">CoRoT</a> and many ground-based programs.</div>
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Planets orbiting their host star can, if we look at the system from a favorable viewing angle, pass in front of the stellar disk. For most systems we will never see planetary transits because the orbits do not have the right inclination. But if we look at thousands of stars we will have - by chance - some planets moving between their host stars and us. When this happens, part of the star's light is blocked by the exoplanet and does not reach the Earth anymore.</div>
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The upper part of the diagram explains this in detail. The large yellow circle is the disk of the star and the small blue circle is the planet orbiting around it. From our point of view the orbit is only tilted a little bit, so when the planet orbits around its host star it will cross the stellar disk (although not directly in the center). If the plane of the orbit was tilted a little bit more, the planet would transit the star closer to the edge; if the tilt is large enough, it would not transit at all.</div>
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The lower part of the diagram shows the lightcurve, which is the measured brightness with time, of the system as it would be observed from our point of view. It is important to understand that for most systems we cannot resolve the star and the planet, which means we measure the brightness of both - star and planet. We cannot take a picture of the system as I plotted it; even in an image of the best telescopes we have, the system would always look like a point. Most systems are so far away that we have not yet the technology to separate planet and star.</div>
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For simplicity I assume here that the planet itself emits no light at all. In reality, this is not true, but for many systems the contribution of the planet is so small that you cannot see it.</div>
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In the diagram the same planet is plotted four times at different positions of its way around the star. In the lightcurve these four positions are indicated on the time axis. I will explain these four situations in detail:<br />
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<ol>
<li>The planet is not yet on the stellar disk. In the lightcurve the brightness of the system is at 100 % because all of the light coming from the star can be see.</li>
<li>The planet just moved onto the stellar disk. During the time period when the planetary disk moves on the stellar disk, but is not yet complete on it, the brightness goes down steeply. This is the beginning of the transit, which is also called <i>ingress</i>.</li>
<li>Now the planet is completely on the stellar disk and the brightness dropped down to a lower level. As long as the entire disk of the planet is on the star, the brightness stays down there. This flat bottom is again a simplification; in reality, the brightness will change, even during the transit, because the stellar disk is not equally bright in all parts. In particular, it is darker at the edges than in the center, which is referred to as <i>limb-darkening</i>. However, I will ignore this effect here. Important is that the brightness goes down to a constant value of 0.99, so the light we receive from the system is 1 % less than when there is no transit. It is easy to understand where this comes from: The planetary disk blocks 1 % of the stellar disk, so 1 % of the light cannot reach us anymore. You now know <i>the size of the planet relative to the star</i>. The relative disk size is 1 %, the relative radius is the square-root of it<sup>a</sup>: 10 %. In our example the radius of the planet is 10 % the radius of the star. This is the beauty of the transit method: Just by measuring the depth of the transit, which can be easily done by anybody, we know the radius of the planet.</li>
<li>The planet moved on its orbit to the other side of the star. When it moved off the disk, which is called <i>egress</i>, the lightcurve went up steeply back to the 100 % brightness it had before the transit. Now the planet moves around the star and will in a certain period of time, depending on its orbital period, come back for another transit.</li>
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Like every other technique the transit method has strong and weak points. On the plus side: It is a conceptually easy method and requires only to measure brightnesses of many stars. From the lightcurve you easily get two important, fundamental properties of the planet: its<b> radius relative to the star</b> and its <b>orbital period</b>, which is how long the planet takes to move once entirely around the star. From this you can already learn quite a lot about the planet. However, on the down side: The probability to see a transit is low; even worse, it depends on the planet's distance from its host star. I will certainly talk about this in a separate post, but it means that far out planets are very hard to detect. One might also considered it as a weak point that it is not possible to measure a planet's mass from its transit - at least not in every case and in a simple manner. Since the mass is a very fundamental property, one has to get the mass somehow, which usually is by using the radial velocity (RV) technique.<br />
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In the end I would like to mention that until about a year ago it was not considered to be good practice to announce a new planet just because transits in a lightcurve were found. There are some other problems I did not mention here, which make it possible that the "transits" you observe do not really come from a planet. So one always had to check the system with the RV technique; only if the planet was found there, too, it was accepted as a real exoplanet. However, this has changed lately and you do not always have to backup a transit detection anymore. Although this might be based on good reasons, some astrophysicists are not very happy with it - maybe I will talk about this controversy in some other post.<br />
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<sup id="fn1">a. Simple geometry: The area A of a circular disk is πR<sup>2</sup>. If you have the area ratio and want the radius ratio you have to square-root the first to get the latter.</sup>
nonnativenoobhttp://www.blogger.com/profile/09489612471884841558noreply@blogger.comtag:blogger.com,1999:blog-7527535668043926125.post-54784882727994905922015-07-18T12:29:00.000-07:002015-07-24T12:45:36.242-07:00Multi-planet systems with at least 3 (exoplanet.eu)<div style="text-align: left;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj_1CkFPVtd2VwOtd2WBTgEBs2GnGVjpKrLPnrGKKOIPQbgiiWWrfYkYdqbjwrc7YKHilWYdOjgTsjZNEIuYmXqlOQ9dE1gSPXa2KgYEopCFETB-ZTAW9YYcUUEhYfqe7D0PRhyLIDM5vA/s1600/multis-EU.png" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj_1CkFPVtd2VwOtd2WBTgEBs2GnGVjpKrLPnrGKKOIPQbgiiWWrfYkYdqbjwrc7YKHilWYdOjgTsjZNEIuYmXqlOQ9dE1gSPXa2KgYEopCFETB-ZTAW9YYcUUEhYfqe7D0PRhyLIDM5vA/s1600/multis-EU.png" /></a></div>
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This plot shows the 156 exoplanet systems with at least three planets known to date according to <a href="http://exoplanet.eu/" target="_blank">exoplanet.eu</a>. Additionally, the solar system is drawn at the very beginning. The x-axis gives the distance of the planet to its host star (in Astronomical Units); note that it is a logarithmic scale, so planets a little bit further to the right are actually much further away from the star. The thick green line illustrates the distance of the Earth from the Sun. To the left of each system its name is given.</div>
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The orange circles at a distance of (almost) zero illustrate the size of the star <i>relative to the Sun</i>, so it's the star's radius compared to the Sun's radius, which is shown at the upper left. All the other circles (green, yellow, pink) to the right of the orange stars indicate the planets, and their sizes <i>are not in proportion to the stellar sizes</i>. The relative planet sizes are only correct when comparing planets but not in relation to the stars. The scale of the planets was arbitrarily chosen so that the large planets are not too big and the small planets are still visible.</div>
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Now we have again the complication that planets are detected using different methods. Some of these systems were found with the transit method, others were detected with the RV technique. For the latter we usually only have the masses but not the radii; these systems are colored pink and the circle sizes correspond to the masses. The other systems have known radii derived from transits and they have yellow colors. To be able to roughly compare masses and radii with each other, I again <b>assume a density</b>: I define that all planets with one Jupiter radius must have the mass of Jupiter. Although this probably makes good sense for large planets, it most likely is pretty wrong in the case of small (rocky) planets. One should keep this is mind when comparing pink and yellow circles.</div>
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On the right side of the panel the number of planets in the system is given. The solar system is still the one with the most planets known but this will certainly change in the near future. Right below it you can already see one system with seven and four systems with six planets.<br />
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I do not want to go into detail on individual systems here, but rather give some general remarks:<br />
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The fact that most RV systems have huge planets compared to the transiting ones is not rooted in the way I present it; the RV technique is not yet capable of measuring the masses of the smaller planets detected with transits. You can also see that in my post on <a href="http://exoplanet-diagrams.blogspot.de/2015/07/exoplanets-by-detection-method.html" target="_blank">detection methods</a>.<br />
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Most exoplanets are closer to the star than the solar planets; exoplanets with orbital periods of years and decades, which would be far out in a system, are very tough to detect.<br />
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Finally, the smallest planets usually orbit stars smaller than the sun. This again is caused by the transit and RV method, which depend of the relative sizes or masses of host star and planet. Thus, the conclusion that less massive stars have less massive planets is tricky because for the more massive stars they are much harder to find.<br />
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In upcoming posts I will present diagrams of - and talk in detail about - several systems shown here individually. As you might already suspect, all of these systems are highly interesting.<br />
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<a href="https://drive.google.com/open?id=0B3lNcd79K1I8MEpBUHhkcTYzOTg" target="_blank">(Link to a hi-res pdf version of this diagram.)</a><br />
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<span style="font-size: small;"><i>Addendum: In this diagram I only considered planets from transits or RVs. This is why HR 8799 (direct imaging) and PSR 1257 12 (timing) are not included. Unfortunately, for quite a number of shown systems planets are missing; this is due to the exoplanet.eu database not providing the semi-major axis (distance) of these planets.</i></span></div>
nonnativenoobhttp://www.blogger.com/profile/09489612471884841558noreply@blogger.comtag:blogger.com,1999:blog-7527535668043926125.post-30677971458860277602015-07-17T13:01:00.002-07:002015-07-18T07:27:16.071-07:00Exoplanets by detection method (exoplanet.eu)<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg1DNrBbbxP7uGZ-cc8QednjycAjBXoTuyRZqE1JNlxeMJ6qEx3aantf76XxGqYczKQwdDs8Rkbr3WCpRgw4Q_OM5wzf6VXQ3ukNiZszy3pvww-Q6M5_LTHnqmlyTI0XY2AtUKWi2eO8Y0/s1600/exoplanets-det-meth-EU.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="558" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg1DNrBbbxP7uGZ-cc8QednjycAjBXoTuyRZqE1JNlxeMJ6qEx3aantf76XxGqYczKQwdDs8Rkbr3WCpRgw4Q_OM5wzf6VXQ3ukNiZszy3pvww-Q6M5_LTHnqmlyTI0XY2AtUKWi2eO8Y0/s640/exoplanets-det-meth-EU.png" width="640" /></a></div>
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This figure shows a total of 1932 planets with masses (in Jupiter mass) over distance of the planet to its host star (semi-major axis in Astronomical Units). Different marker symbols (with different colors) stand for the method used to detect the planet. The data is taken from <a href="http://exoplanet.eu/" target="_blank">exoplanet.eu</a>.</div>
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The transit method cannot derive the planetary mass. This is why I have two different categories for transits: a regular one (black circles) and 'Transit R' (yellow circles). The first category has masses measured with a different technique, usually the radial velocity method. The 'R' category, which are virtually all the small transiting planets, do not have their masses measured yet. So how do I know it then? I know the radius from the transit method and <b>assume a density</b>. So the masses of the yellow circles are probably incorrect to some degree; however, it gives me a rough estimate where they might lie and I can plot all planets in this graph.</div>
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One could probably give an entire lecture just on this one picture. I will only give some brief notes.</div>
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<li style="text-align: justify;">Using different symbols illustrates nicely which types of planets are discovered by which method. E.g., the transit method is good in finding planets close to the star down to very small sizes. However, it works bad for long period planets.</li>
<li style="text-align: justify;">The very far out planets are all detected by direct imaging. However, they are also huge which might in many cases not really qualify them as something we would call a planet - they are just too massive and more like a thing between a planet and a star. Strangely, two close-in planets are marked as directly imaged, too. This is incorrect and caused by an error in the database. These points indicate Kepler-70 b and c which are not imaged planets. Actually, they were not even seen in transits and are, in my opinion, highly disputable.</li>
<li style="text-align: justify;">The smallest planet is Kepler-37 b which only is about 30 % the radius of the Earth. This means it is smaller than Mercury.</li>
<li style="text-align: justify;">The solar system planets do not really look like they are a part of the distribution but are located to the lower edge of the exoplanet distribution. However, it is exciting that we slowly start to see exoplanets with roughly the same size and distance than Earth. I think it cannot be emphasized enough that this information alone does not tell us much about whether the conditions on these planets are comparable to Earth at all.</li>
<li style="text-align: justify;">In the end I should probably point out that the most important method to determine the masses of exoplanets is the radial velocity technique (RV). You can see that it covers a large range of masses and distances. Although its results are extremely important, we should not forget that it does not give us the exact mass of the planet. The result still depends on how well we can determine the mass of the star and, which is the bigger challenge, what the inclination of the planet's orbit around the star is. The latter is in most of the cases completely unknown.</li>
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<br />nonnativenoobhttp://www.blogger.com/profile/09489612471884841558noreply@blogger.com