<p>In the solar neighborhood the stellar number density is about 0.14 stars per cubic parsec. This changes with a length scale of 220-450 pc as we move up or below the Milky Way disc, and 2.6 kpc radially. There are clearly local variations due to open and globular clusters, spiral arms etc. that happen over shorter length scales. But what is the sharpest stellar density gradient?</p>
<p>The question is somewhat ill-defined since density becomes ill-defined over distances short compared to stellar-distances (<span class="math-container">$\sim \rho(x)^{-1/3}$</span>). If one considers star locations as driven by a inhomogeneous Poisson process with local density <span class="math-container">$\rho(x)$</span>, we might want to find where <span class="math-container">$\rho'(x)/\rho(x)$</span> is highest.</p>

CC BY-SA 4.0
2022-06-11T07:26:13.030Z
You write yourself it might be ill-defined. It has to be highest on scales of stellar size as it, for instance, rises quickly from 0 to 1 at the edge of the Sun (or any other star). But that clearly is not what you look for. You might want to try a few "typical length scales", e.g. typical cloud diameter, star formation diameter, globular or open cluster sizes and check what gives you useful results.
planetmaker
CC BY-SA 4.0
2022-06-15T11:21:12.293Z
The answer is probably going to be a globular cluster or a nuclear star cluster, since those have very dense centers and very small scale lengths (on the order of a few parsecs).
Peter Erwin
CC BY-SA 4.0
2022-06-15T11:33:57.693Z
I'm not sure why you want "$\rho^{\prime}(x) / \rho(x)$", since that will be a maximum where $\rho(x)$ goes to zero. E.g., in the case of an exponential decay in density (as in the vertical and radial MW disk scale lengths you quote), that ratio evaluates to $h / x^{2}$ (where $h$ is the scale length), so the maximum is always at $x =$ infinity.
Peter Erwin
<galaxy><density>
What is the sharpest stellar number density variation known?
Anders Sandberg
# What is the sharpest stellar number density variation known?

(Asked by: username_0 on 2022-06-10)

In the solar neighborhood the stellar number density is about 0.14 stars per cubic parsec. This changes with a length scale of 220-450 pc as we move up or below the Milky Way disc, and 2.6 kpc radially. There are clearly local variations due to open and globular clusters, spiral arms etc. that happen over shorter length scales. But what is the sharpest stellar density gradient?

The question is somewhat ill-defined since density becomes ill-defined over distances short compared to stellar-distances ($\sim \rho(x)^{-1/3}$). If one considers star locations as driven by a inhomogeneous Poisson process with local density $\rho(x)$, we might want to find where $\rho'(x)/\rho(x)$ is highest.

**Tags:** galaxy, density
> **Comments:**
> **username_1**: You write yourself it might be ill-defined. It has to be highest on scales of stellar size as it, for instance, rises quickly from 0 to 1 at the edge of the Sun (or any other star). But that clearly is not what you look for. You might want to try a few "typical length scales", e.g. typical cloud diameter, star formation diameter, globular or open cluster sizes and check what gives you useful results.  
> **username_2**: The answer is probably going to be a globular cluster or a nuclear star cluster, since those have very dense centers and very small scale lengths (on the order of a few parsecs).  
> **username_2**: I'm not sure why you want "$\rho^{\prime}(x) / \rho(x)$", since that will be a maximum where $\rho(x)$ goes to zero. E.g., in the case of an exponential decay in density (as in the vertical and radial MW disk scale lengths you quote), that ratio evaluates to $h / x^{2}$ (where $h$ is the scale length), so the maximum is always at $x =$ infinity.  

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## 0 answers

