N-body Simulations: Density vs Circular Profiles

In summary: A recent study has shown that the dynamics of the gravitational mass is not the only factor at play when it comes to the density profile of galaxies.
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N-body simulations of rotating galaxies involve density profile and circular profile. Would it be accurate to say that the essential difference between density profile and circular profile is that the former involves gravitational mass while the latter involves inertial mass?
 
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jedishrfu said:
I don’t think that’s the case since the equivalence principle holds that gravitational mass is equivalent to inertial mass.

https://en.m.wikipedia.org/wiki/Equivalence_principle

Do you have code examples that illustrate this? It could well be that different programmers used different names for the same thing.

My question was triggered by a paper by Navarro, Frenk, and White, where they do density profile and circular velocity profile of rotation curve in disk galaxies. It is seen that the density profile seems to adhere more closely than circular velocity profile to rotation curve.

It is true that the principle of equivalence makes no distinction between gravitational mass and inertial mass, in linear and rotational freefall of an object. Galaxies, however, involve a distribution of masses, which are themselves in graviational interaction, and therefore the situation is more complicated. How complicated is something to be be analyzed and debated. What I am trying to clarify, however, is can we make a distinction between density profile and circular velocity profile in terms of gravitational mass and inertial mass. Circular velocity profile involves the orbital velocity formula, which is derived by equating gravitational force and centrifugal force, and therefore involves inertial mass. Density profile, as the name indicates, deals with the density of matter. Now does that therefore imply that essentially only the dynamics of gravitational mass is being considered in density profile?
If you are technically familiar with N-body simulations, perhaps you could clarify this matter.
 
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Despite the broad profiles offered by distant galaxies, the precise nature of galactic evolution remains a hotly debated topic.
 
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1. What is an N-body simulation?

An N-body simulation is a computational method used in astrophysics to study the dynamics of a system of particles, such as stars or galaxies, interacting with each other through gravitational forces. In these simulations, each particle is represented by a point mass and their interactions are calculated using Newton's laws of motion and the law of universal gravitation.

2. How are density and circular profiles used in N-body simulations?

Density and circular profiles are two different ways of representing the distribution of particles in an N-body simulation. The density profile describes how the number of particles in a given volume changes with distance from the center of the system. The circular profile, on the other hand, describes how the average angular velocity of particles changes with distance from the center. These profiles are often used to analyze the structure and dynamics of galaxies and galaxy clusters.

3. What is the difference between a density profile and a circular profile?

While both density and circular profiles provide information about the distribution of particles in an N-body simulation, they describe different aspects of the system. The density profile gives information about the spatial distribution of particles, while the circular profile describes the rotational properties of the system. In other words, the density profile tells us where particles are located, while the circular profile tells us how they are moving.

4. How do density and circular profiles change over time in an N-body simulation?

The density and circular profiles can change over time in an N-body simulation due to the interactions between particles. As particles move and interact with each other, their distribution and velocities may change, leading to changes in the profiles. In addition, external factors such as tidal forces or mergers with other systems can also impact the profiles of an N-body simulation.

5. What can we learn from comparing density and circular profiles in N-body simulations?

By comparing density and circular profiles, we can gain insight into the structure and evolution of galaxies and galaxy clusters. For example, if the density profile is more concentrated towards the center, it may indicate the presence of a massive black hole. Similarly, comparing the circular profiles of different systems can reveal differences in their rotational properties, providing clues about their formation and evolution.

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