Can Softening Length Affect Dark Matter Halo Stability in N-Body Simulations?

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Discussion Overview

The discussion revolves around the stability of dark matter halos in N-body simulations, particularly focusing on the effects of softening length on halo structure over time. Participants explore the setup of halos, the choice of softening lengths, and the implications of these choices on simulation outcomes, with a specific interest in the transition from cusp to core profiles in dark matter distributions.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant describes their setup of a dark matter halo using an NFW profile and questions why the cusp transitions to a core after approximately 2 Gyr, despite using a well-established simulation code (Gadget2).
  • Another participant suggests that the issue may relate to the choice of co-moving versus proper coordinates and mentions the MAX_PHYS parameter, which could affect softening length over time.
  • Concerns are raised regarding the limitations of modeling dark matter due to its non-interactive nature, with references to the Bullet Cluster as a significant case study.
  • A participant clarifies their research focus on the motion of galaxies within a pre-formed halo rather than the evolution of dark matter, emphasizing the need for high resolution in their simulations.
  • Discussion includes the idea that the softening length, set as the third root of particle mass, may be too large, leading to insufficient force resolution in the central regions of the halo.
  • Another participant notes that the core formation appears to coincide with the radius equal to the softening length, suggesting that the simulation may not accurately resolve dynamics below this scale.
  • Participants discuss the implications of using different particle masses and softening lengths, with one expressing confusion about discrepancies observed at larger radii compared to analytic predictions.

Areas of Agreement / Disagreement

Participants express varying opinions on the implications of softening length and the appropriate parameters for simulations. There is no consensus on the best approach to resolve the issues raised, and multiple competing views on the modeling of dark matter halos remain evident.

Contextual Notes

Participants highlight the limitations of simulations, including the inability to resolve certain scales due to softening lengths and the complexities of modeling gravitational interactions in dark matter scenarios.

Who May Find This Useful

This discussion may be of interest to researchers and students involved in astrophysics, particularly those focused on dark matter simulations, N-body methods, and gravitational dynamics.

florian101
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Hello
I try to get stable dark matter halos with n-body simulations. I set up the halo following a NFW-profile and I define the velocity distribution with a Gauss distribution or Edington inversion (the result is the same).
After approximately 2Gyr my cusp turns into a core...??
I use about 1 mil particles but the problem does not depend on the particles mass at all.
Obviously my particles in the center get a bit hot but I don't know what I am doing wrong... I am using a program to set up the halo which is well proofed and should give correct results.
All my simulations are done using Gadget2 which is also a well proofed n-body code...
The only possibility I could imagine is the softening length... I am using the third root of the mass as softening length for the particles and that is what is advised in the literature...?
Sometimes I use a higher values to absolutely avoid hard collisions...
I would be very thankful for any ideas what I could make wrong...
thank you very much
and best regards
florian
 
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Hmm, I suspect the answer to your question probably can't be given from the information that you've supplied, but the answer may well be sufficiently subtle that it would be hard for you to give enough information, e.g. all the nitty gritty details of how you set up your halo.

I can give you some general things to look at/think about though. Are you using co-moving or proper co-ordinates? Since there is a time dependence to the effect (e.g. something happens after 2Gyrs) check the MAX_PHYS parameter in your parameter file (this is described in the Gadget2 User Guide). I can't remember the details but this in combination with other parameters can give you a time dependent softening, at least in terms of co-moving co-ordinates, or something, I can't remember the details. Maybe your softening length is okay initially, but then shifts to an unsuitable value?

What literature are you referring to for the softening length? From memory, softening length requirements for cosmo sims are normally given in terms of the original grid spacing, assuming you are starting at high redshift from a uniform grid. This will relate to particle mass but exactly how depends on the co-ordinate system you are using.

I'm somewhat confused about what you are trying to do, normally an NFW profile is observed to occur after the fact, e.g. you let your simulation run from a near homogenous set of initial conditions and then find that the halos that have formed have NFW mass profiles. I'm not sure what you gain by starting from an already formed halo, but then again I don't know what you are researching?
 
The trouble with dark matter is it does not interact with anything else save by gravitational effects. This is difficult to model. The Bullet Cluster paper is probably the best attempt to date.
 
thanks for the answers... I will try to provide some more details of what I am trying to do...

First of all it is true that if you start with a distribution of matter and let gravity work you will end up with a universe full of DM halos. I am not interested in DM evolution... I just assume I have a DM halo and I try to investigate the motion of galaxies within the halo. Therefore I start with a halo not with matter distribution... the advantage is that my resolution is much better...

The softening length is recommended as the third root of the mass of the particles by several authors (e.g. have a look to this paper http://arxiv.org/abs/astro-ph/0504573).

I use proper coordinate since the Gadget2 parameter

ComovingIntegrationOn

is set to zero. I don't know any MAX_PHYS parameter... I attached the Gadget2 parameterfile I am using but in principle it is the standard file (I had to convert it to a txt file otherwise it was not possible to upload it to this forum)...

Furthermore I attached two plots which show the DM profile in the initial conditions (after0_0.pdf) and after 0.9 Giga years (after0.9.pdf)... In general I noticed a slowly destruction of the cusp... (I run the simulation at the moment and will provide more plots as soon as possible)... The solid line close to the measured points represents the analytic profile used to set up the halo... the lower lines are a core profile with the same parameters as the cusp profile and a exponential disc profile but they are not important for this problem so just ignore them...
thank you very much for help
and best regards
florian
 

Attachments

Looks like you maxphys parameters (I couldn't recall the exact name, I was referring to SofteningHaloMaxPhys etc that you have in your parameter file) are okay, since they are the same as the initial softenings. That being said I don't normally work in proper co-ordiantes with Gadget, you should check the users guide for details.

In any case, it looks as though your core kicks in at the radius roughly equal to the DM softening length of 0.125 Kpc, which to me makes sense, you don't have force resolution below this scale, so the forces between the particles at the very centre of the halo wash out, flattening the profile. It's not clear from you post whether you have only DM particles in the sim or some of the others that have softening lengths in your parameter file (disk, bulge, star...) but all of those have longer softening lengths, which will make the problem worse.

Simulations will always have a limited range of applicability, since you never have infinite resolution (be it resolution in mass, distance, time...). At some point you will not be able to 'believe' your results in a certain regime, in this case there will be a radius below which you can't resolve the halo properly given your simulation. Remember that 0.125 Kpc is a very short scale, corresponding to the very inner region of the Halo. Plotting in Log-Log space (which is the correct thing to do) may make this region look bigger to you than it really it. It may well be that you are doing everything correctly, you just need to ignore the very central part in your analysis?

A shorter softening length may help get closer, but you would probably need more particles. Have a look at http://adsabs.harvard.edu/abs/2003MNRAS.338...14P" paper on the numerical convergence of DM halo sims. It may help guide you as to what regions of your simulation you can expect to accurately model, and hence what regions you need to worry about the results in.

Hope that helps, if you are doing this as a research project with a supervisor it would be worth talking to them, as they should know what it going on. I hope my comments can offer some assistance in the meantime.
 
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Chronos said:
The trouble with dark matter is it does not interact with anything else save by gravitational effects. This is difficult to model. The Bullet Cluster paper is probably the best attempt to date.

On the contrary, the fact that DM is collisionless makes it very simple to model, you simply need to worry about gravity. On the other hand 'gas physics' (everything else in astro, like the formation of stars, AGN, Supernovae etc etc) are much harder to implement in cosmo simulations. Many many advances have been made by using DM only simulations (which are done routinely) due to their relative simplicity. You can make quite accurate statements about, for instance, the abundance of galaxy clusters, using these simulations. These DM N-body simulation results form a key part of the current evidence for the LCDM model.
 
Thanks Wallace... Yes it makes sense that I should not trust the simulation for smaller scales then the softening length... Just for completeness I use dark matter particles with different mass and therefore different softening length... The name Star, Bulge, disk... what you find in the parameterfile are just Gadget names I use all types as DM particles... (type 1 is the lightest DM particle type 2 the second...)
I am just a bit confused why I see the difference to the analytic function already at 800pc... Because the softening length of the very heavy particles should not effect the light particles in the center (heavy particles will never come into the inner region of the halo...
anyway thanks for helping
and best regards
florian
 
Wallace said:
On the contrary, the fact that DM is collisionless makes it very simple to model...
Agreed. The behavior of matter embedded in a DM halo is the devilish part. I had a dyslexic moment.
 

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