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Stable dark matter halos

  1. Jun 26, 2009 #1
    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
     
  2. jcsd
  3. Jun 26, 2009 #2

    Wallace

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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 dependant 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 refering 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?
     
  4. Jun 27, 2009 #3

    Chronos

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    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.
     
  5. Jun 27, 2009 #4
    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 Gigayears (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
     

    Attached Files:

  6. Jun 27, 2009 #5

    Wallace

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    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.
     
    Last edited by a moderator: Apr 24, 2017
  7. Jun 27, 2009 #6

    Wallace

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    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.
     
  8. Jun 27, 2009 #7
    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
     
  9. Jun 30, 2009 #8

    Chronos

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    Agreed. The behavior of matter embedded in a DM halo is the devilish part. I had a dyslexic moment.
     
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