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 geometric parallax 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.
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 apparent magnitude of 12 are not bright enough to determine the distance. The apparent magnitude depends on the intrinsic brightness of the star (the absolute magnitude) 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.
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 spectral type. 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.
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.
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.
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.
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 Gaia 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.
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.
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.
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.
