• Register
PhysicsOverflow is a next-generation academic platform for physicists and astronomers, including a community peer review system and a postgraduate-level discussion forum analogous to MathOverflow.

Welcome to PhysicsOverflow! PhysicsOverflow is an open platform for community peer review and graduate-level Physics discussion.

Please help promote PhysicsOverflow ads elsewhere if you like it.


New printer friendly PO pages!

Migration to Bielefeld University was successful!

Please vote for this year's PhysicsOverflow ads!

Please do help out in categorising submissions. Submit a paper to PhysicsOverflow!

... see more

Tools for paper authors

Submit paper
Claim Paper Authorship

Tools for SE users

Search User
Reclaim SE Account
Request Account Merger
Nativise imported posts
Claim post (deleted users)
Import SE post

Users whose questions have been imported from Physics Stack Exchange, Theoretical Physics Stack Exchange, or any other Stack Exchange site are kindly requested to reclaim their account and not to register as a new user.

Public \(\beta\) tools

Report a bug with a feature
Request a new functionality
404 page design
Send feedback


(propose a free ad)

Site Statistics

179 submissions , 139 unreviewed
4,419 questions , 1,731 unanswered
5,122 answers , 21,795 comments
1,470 users with positive rep
669 active unimported users
More ...

  What metric do you use to model a Galaxy

+ 4 like - 0 dislike

I'm not an expert in GR, I'd like to if there is a standard practice in using a particular metric to model an isolated rotating Galaxy. I thought about Kerr-Newmann metric but I guess is not the standard practice. I guess is common practice to use Newton + a correction term, but in that case I'd like to know what term is it and where is comes from. Can someone help me with some references?

Thank you  

asked Mar 16, 2019 in Astronomy by Dac0 (20 points) [ no revision ]

1 Answer

+ 3 like - 0 dislike

This depends on what do you need it for. You have to answer question such as

  1. Do you want to describe motion at non-relativistic velocities near the galaxy?
  2. Does the motion occur inside the galaxy or outside?
  3. What do you assume about the morphology of the galaxy? (What type of Galaxy is it?)

If the answer to 1. is yes, you can typically use the metric in the Newtonian limit, i.e.

$$ds^2 = -(1 + 2 \Phi) dt^2 + (1 - 2 \Phi)(dx^2 + dy^2 + dz^2)$$

where $\Phi$ is the Newtonian potential sourced by the galactic matter. Now you "just" need to find the right $\Phi$. The answer depends a lot on questions 2. and 3. For instance, an almost spherically symmetric galaxy can be modeled by a spherically symmetric potential that is given simply by $\Phi = -GM(r)/r$, where $M(r)$ is the mass enclosed in the radius $r$. On the other hand, the outside potential of a flattened, almost axially symmetric galaxy can be modeled by potentials such as the Vinti potential or generally a multipolar expansion.

answered Mar 17, 2019 by Void (1,635 points) [ revision history ]

Thank you Void. I think I got the idea and I would upvote your answer if I could... Unfortunately it seems I'm not yet able to vote :(

I don't know if any of the below URLs are useful?

1. The Cosmological Principle

2. Galaxy rotation curves with log-normal density distribution

3. Astronomy: a Rotating System of Satellite Galaxies Raises Questions

@JevanPipitone interesting links but not related to the question

I am trying to find relevant material however I am posting a comment not an answer so I am not claiming to be providing an answer. I found this:

under section "Halo density profiles"
"In order to accommodate a flat rotation curve, a density profile for a galaxy and its environs must be different than one that is centrally concentrated. Newton's version of Kepler's Third Law implies that the spherically symmetric, radial density profile $\rho(r)$ is:"

Rotation of Spiral Galaxies

Formula for Rotation curves of Galaxies

Rotation Curves

Example rotation curves for 1) a solid body, 2) the Solar System and 3) a spiral galaxy.

Void's post to the wikipedia article about Galaxy Types and morphology has some interesting and easy to understand information and I can see from the link there are types of galaxies such as Ellipticals, Shell, Spirals, Barred spiral, Super-luminous, Peculiar, Ring, Lenticular, Irregular, Ultra Diffuse, Dwarfs, Interacting, Starburst, Active, Blazars, Radio, Liners, Seyfert, Quasar, Luminous infrared. However it does not give a formula describing the characteristics of each of these galaxy types. For example this could be a formula for the visible shape such as a spiral, or it could be the distribution of ultraviolet and mid-infrared for a Super-luminous spiral, which would presumably require more than one formula.

I'm not an expert on this either like the original poster Dac0 wrote, I'm just interested in discussing physics, which is why I am writing comments rather than answers.

Your answer

Please use answers only to (at least partly) answer questions. To comment, discuss, or ask for clarification, leave a comment instead.
To mask links under text, please type your text, highlight it, and click the "link" button. You can then enter your link URL.
Please consult the FAQ for as to how to format your post.
This is the answer box; if you want to write a comment instead, please use the 'add comment' button.
Live preview (may slow down editor)   Preview
Your name to display (optional):
Privacy: Your email address will only be used for sending these notifications.
Anti-spam verification:
If you are a human please identify the position of the character covered by the symbol $\varnothing$ in the following word:
Then drag the red bullet below over the corresponding character of our banner. When you drop it there, the bullet changes to green (on slow internet connections after a few seconds).
To avoid this verification in future, please log in or register.

user contributions licensed under cc by-sa 3.0 with attribution required

Your rights