<p>Discussions under <a href="https://astronomy.stackexchange.com/q/43786/7982">Mass of the stellar cluster (not the whole galaxy)</a> lead me to mention that when an <em>actual temperature</em> is inferred from a Doppler-broadened line profile (rather than just a linewidth expressed as an effective temperature), we assume that the <a href="https://en.wikipedia.org/wiki/Maxwell%E2%80%93Boltzmann_distribution" rel="nofollow noreferrer">Maxwell-Boltzoman velocity distribution</a> in the directions perpendicular to the line of sight is the same as that the one measured along the line of sight.</p>
<p>Have there been any examples of this kind of assumption turning out to be invalid later? Some situation where the distribution of velocities turned out to be substantially anisotropic?</p>
<p>I'm not asking for examples of anisotropic velocity distributions, I'm asking for a case where it seemed like a good assumption at the time, but later it turned out something more interesting was going on and the line-of-sight Doppler width <em>did not</em> represent the spread in perpendicular velocities.</p>

CC BY-SA 4.0
2021-05-14T12:50:33.093Z
Something like this, but for star clusters instead of galaxies? https://academic.oup.com/mnrasl/article/413/1/L81/1747626
Daddy Kropotkin
CC BY-SA 4.0
2021-05-14T12:52:57.847Z
This group found non-Gaussianity from the spectra of this system, but I think they say it's rather dubious https://iopscience.iop.org/article/10.1086/382721/fulltext/
Daddy Kropotkin
CC BY-SA 4.0
2021-05-14T13:02:33.213Z
@DaddyKropotkin thanks for your comments! My question is explicitly about anisotropy (mentioned twice) rather than departure from a Gaussian shape, but of course both can happen at the same time. Also "I'm asking for a case where (anisotropy) seemed like a good assumption at the time, but..."
uhoh
CC BY-SA 4.0
2021-05-14T13:34:33.713Z
Is "gaussian" in this context not the same as "isotropic"? I'm not sure I see the difference here
Daddy Kropotkin
CC BY-SA 4.0
2021-05-14T15:35:10.660Z
@DaddyKropotkin 20 minutes and I'll be at a real keyboard...
uhoh
CC BY-SA 4.0
2021-05-14T21:50:04.390Z
@DaddyKropotkin "isotropic" means "the same in all directions". A 3D Gaussian with different dispersion values in different directions is not isotropic. And an ideal gas will have a Maxwellian (not Gaussian) distribution that is isotropic.
Peter Erwin
CC BY-SA 4.0
2021-05-14T21:54:51.900Z
Are you asking specifically about astronomical observations of gas? Because I'm not sure how you would ever tell what the distribution of atomic or ionic (or electron or molecular) velocities perpendicular to the line of sight really was.
Peter Erwin
CC BY-SA 4.0
2021-05-15T12:39:10.777Z
Gotcha! Thanks!
Daddy Kropotkin
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2021-05-15T20:46:51.770Z
@DaddyKropotkin Sorry I'm late. An isotropic Gaussian distribution of velocities would be something like $$\exp\left(-\frac{v_r^2}{2\sigma}\right) = \exp\left(-\frac{v_x^2+v_y^2+v_z^2}{2\sigma}\right)$$ one $\sigma$ one temperature in any direction.  An *anisotropic* Gaussian distribution of velocities would be something like $$\exp\left(-\frac{v_x^2}{2\sigma_x}-\frac{v_y^2}{2\sigma_y}-\frac{v_z^2}{2\sigma_z} \right)$$ for example, where $\sigma_x, \sigma_y, \sigma_z$ are not all equal. When viewed along each of the three axes, the projected distributions would infer different temperatures.
uhoh
CC BY-SA 4.0
2021-05-15T20:55:28.277Z
@DaddyKropotkin now your question about measuring the distribution of gas velocities perpendicular to the line of sight is an important one. We might assume its the same as in the line of sight precisely because it's so hard to measure independently, but many astronomical objects are interpreted through modeling as well as observation. The way the question is written, perpendicular velocity distribution would not have to be observed directly, so let's see how things go.
uhoh
<observational-astronomy><astrophysics><spectroscopy><doppler-effect>
Any examples of a gas object temperature from Doppler broadening along one axis turning out to be wrong because velocity spread was not isotropic?
uhoh
# Any examples of a gas object temperature from Doppler broadening along one axis turning out to be wrong because velocity spread was not isotropic?

(Asked by: username_0 on 2021-05-14)

Discussions under [Mass of the stellar cluster (not the whole galaxy)](https://astronomy.stackexchange.com/q/43786/7982) lead me to mention that when an *actual temperature* is inferred from a Doppler-broadened line profile (rather than just a linewidth expressed as an effective temperature), we assume that the [Maxwell-Boltzoman velocity distribution](https://en.wikipedia.org/wiki/Maxwell%E2%80%93Boltzmann_distribution) in the directions perpendicular to the line of sight is the same as that the one measured along the line of sight.

Have there been any examples of this kind of assumption turning out to be invalid later? Some situation where the distribution of velocities turned out to be substantially anisotropic?

I'm not asking for examples of anisotropic velocity distributions, I'm asking for a case where it seemed like a good assumption at the time, but later it turned out something more interesting was going on and the line-of-sight Doppler width *did not* represent the spread in perpendicular velocities.

**Tags:** observational-astronomy, astrophysics, spectroscopy, doppler-effect

> **Comments:**
> **username_1**: Something like this, but for star clusters instead of galaxies? https://academic.oup.com/mnrasl/article/413/1/L81/1747626  
> **username_1**: This group found non-Gaussianity from the spectra of this system, but I think they say it's rather dubious https://iopscience.iop.org/article/10.1086/382721/fulltext/  
> **username_0**: @username_1 thanks for your comments! My question is explicitly about anisotropy (mentioned twice) rather than departure from a Gaussian shape, but of course both can happen at the same time. Also "I'm asking for a case where (anisotropy) seemed like a good assumption at the time, but..."  
> **username_1**: Is "gaussian" in this context not the same as "isotropic"? I'm not sure I see the difference here  
> **username_0**: @username_1 20 minutes and I'll be at a real keyboard...  
> **username_2**: @username_1 "isotropic" means "the same in all directions". A 3D Gaussian with different dispersion values in different directions is not isotropic. And an ideal gas will have a Maxwellian (not Gaussian) distribution that is isotropic.  
> **username_2**: Are you asking specifically about astronomical observations of gas? Because I'm not sure how you would ever tell what the distribution of atomic or ionic (or electron or molecular) velocities perpendicular to the line of sight really was.  
> **username_1**: Gotcha! Thanks!  
> **username_0**: @username_1 Sorry I'm late. An isotropic Gaussian distribution of velocities would be something like $$\exp\left(-\frac{v_r^2}{2\sigma}\right) = \exp\left(-\frac{v_x^2+v_y^2+v_z^2}{2\sigma}\right)$$ one $\sigma$ one temperature in any direction.  An *anisotropic* Gaussian distribution of velocities would be something like $$\exp\left(-\frac{v_x^2}{2\sigma_x}-\frac{v_y^2}{2\sigma_y}-\frac{v_z^2}{2\sigma_z} \right)$$ for example, where $\sigma_x, \sigma_y, \sigma_z$ are not all equal. When viewed along each of the three axes, the projected distributions would infer different temperatures.  
> **username_0**: @username_1 now your question about measuring the distribution of gas velocities perpendicular to the line of sight is an important one. We might assume its the same as in the line of sight precisely because it's so hard to measure independently, but many astronomical objects are interpreted through modeling as well as observation. The way the question is written, perpendicular velocity distribution would not have to be observed directly, so let's see how things go.  

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## 0 answers

