# Number density of stars on the Galactic plane

The number density of stars (e.g. the number of stars per cubic parsec) is given by $$N(z) = N(0) e^{-|z|/h}$$ where $z$ is the height above the Galactic plane, $h$ is the scale height for a specific component of the Galaxy, and $N(z)$ is the number density at different heights above the plane.

The scale heights for the thin disk and thick disks are:

• Halo stars: $h=3\textrm{kpc}$
• Thick disk: $h=1.5\textrm{kpc}$
• Thin disk stars: $h=300\textrm{pc}$
• Thin disk gas: $h=100\textrm{pc}$

Unfortunately I cannot find the values for the number density at the galactic plane: $N(0)$

Do you have any references in which I can find these numbers?

• Where did you get this formula, and didn't it provide a value for N(0)? Possibly helpful URLs: ned.ipac.caltech.edu/level5/Bothun2/Bothun4_2_2.html astro.virginia.edu/class/whittle/astr553/Topic05/Lecture_5.html
– user21
Nov 8, 2014 at 16:28
• @barrycarter I got it from a course on the Milky Way I did a few years back, it's not available online. Thanks for the link, I should have realised that the values for $N(z)$ depend on the radial distance from the Milky Way's core as your reference mentions. Nov 9, 2014 at 9:33
• I meant $N(0)$ of course. Nov 9, 2014 at 10:50
• The stellar halo is definitely not appropriately described by a vertically exponential, but by a (galactocentric) radial power-law. Also, for most disc populations, $\mathrm{sech}^2(z/h)$ gives a better description than the exponential, but these are details. Nov 9, 2014 at 16:09
• @barrycarter the UVA link is dead; try the Wayback Machine Jan 31, 2019 at 3:48

## 1 Answer

The number density of stars is not well constrained, because it hinges critically on the behaviour of the stellar mass function at low stellar masses. Low-mass stars tend to be dim and hard to detect. What is reasonably well constrained, instead is the mass density of stars, where low-mass objects contribute little, even if their number is large.

• I can't argue with the content of this, but it's not helpful for the question. The value of $N_0$ is of course defined for a particular mass range (as is the scale height). Dec 13, 2014 at 9:51