<p>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.</p>

CC BY-SA 3.0
2014-12-13T09:51:56.203Z
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).
ProfRob
CC BY-SA 3.0
2014-11-10T08:45:42.563Z
2014-11-10T08:45:42.563Z
Walter
<p>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.</p>

<p>The scale heights for the thin disk and thick disks are:</p>

<ul>
<li>Halo stars: $h=3\textrm{kpc}$</li>
<li>Thick disk: $h=1.5\textrm{kpc}$</li>
<li>Thin disk stars: $h=300\textrm{pc}$</li>
<li>Thin disk gas: $h=100\textrm{pc}$</li>
</ul>

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

<p>Do you have any references in which I can find these numbers?</p>

CC BY-SA 3.0
2014-11-09T09:33:08.340Z
@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.
Dieudonné
CC BY-SA 3.0
2014-11-09T10:50:40.940Z
I meant $N(0)$ of course.
Dieudonné
CC BY-SA 3.0
2014-11-09T16:09:08.547Z
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.
Walter
CC BY-SA 4.0
2019-01-31T03:48:09.973Z
@barrycarter the UVA link is dead; try the [Wayback Machine](https://web.archive.org/web/20070322120107/http://www.astro.virginia.edu/class/whittle/astr553/Topic05/Lecture_5.html)
David Moles
<milky-way><disk>
Number density of stars on the Galactic plane
Dieudonné
# Number density of stars on the Galactic plane

(Asked by: username_0 on 2014-11-08)

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?

**Tags:** milky-way, disk
> **Comments:**
> **username_0**: @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.  
> **username_0**: I meant $N(0)$ of course.  
> **username_1**: 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.  
> **username_2**: @barrycarter the UVA link is dead; try the [Wayback Machine](https://web.archive.org/web/20070322120107/http://www.astro.virginia.edu/class/whittle/astr553/Topic05/Lecture_5.html)  

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## 1 answers

### Answer by username_1 on 2014-11-10. Score: 2

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.

> **Comments:**
> **username_3**: 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).  

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