J.Wagner:The cosmological Cheshire cat

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J.Wagner:The cosmological Cheshire cat

New postby Maxim Khlopov on Fri 19 Jun 2020 16:11

VIA lecture by Jenny Wagner "The cosmological Cheshire cat -- how to characterize dark matter halo shapes without seeing them" was given on 19.06.2020. Its presentation is attached and the record is in VIA library
The following questions were put in the course of the talk:
Shantanu: Please clarify: what is PIEMD?
Shantanu: Do you assume substructure in your halo model?
Shantanu: which of these cases corresponds to dwarf spheroidals?
Shantanu: 1. Within this formalism can you explain the empirical observation of constant surface density of dark matter haloes found by Donato et al (2009) or Kormendy & Freeman (2004)?
Shantanu: I presume you assumed Newtonian gravity? How easy it is to extend this formalism to non-Newtonian gravity theories
Sotiris Loucatos: On p 6 in the various profiles, what is the reason of strong fluctuations at large r?
Shantanu: Since Prof. Liliya Williams is also on the online, would you like to answer the first question? (either within this model or on basis of the model you mentioned in your VIA talk many years ago)
Shantanu: I will write the reference
Vlad: What if the structure is built by substructures as halo stars show?
Liliya Williams: Hi, what is the question? Modified gravity? In our formalism, gravity comes in in the equation that connects kinetic and potential energy and the total energy, so whichever way modified gravity will change that will affect our result for differential energy distribution.
Shantanu: No, my first question is whether this model can explain the constant surface density of dark matter haloes first found by Kormendy & Freeman (2004) and also by Donato et al (2009) (reference to MNRAS provided above)
Shantanu: what about self-interacting DM?
You are welcome to continue discussion of this topic in replies to this post
pdf of J.Wagner's presentation
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Re: J.Wagner:The cosmological Cheshire cat

New postby Jenny Wagner on Fri 19 Jun 2020 22:20

Dear Shantanu,

thanks a lot for your ensemble of questions!
Some of the answers would have taken too long in the talk, so let me get back to them here:
1) what is a PIEMD:
Take a look at Eq.(6) of this paper: https://ui.adsabs.harvard.edu/abs/2005M ... L/abstract

2) do you assume substructure in your halo model:
Yes and no, depends on the viewpoint, since we could consider the n_p particles that are interacting as "substructure" given that, in simulations, their mass is usually several thousand solar masses. On the other hand, when I want to describe the entire dark matter halo, I am (so far) only interested in the final state of the halo, which would correspond to a thermal equilibrium state if that existed.

3) which of these cases corresponds to dwarf spheroidals:
In principle, any case can be applied to them, it just depends on how you sort the dwarves into the hierarchy of masses you want to model. The most important lesson that I learnt from setting up a halo model is that halos are an emergent quantity and their behaviour decisively depends on how we define them (e.g. where we put r_max). If your dwarf spheroidals are some satellites of a galaxy in a large galaxy cluster and you are interested in the halo of the overall galaxy cluster, the dwarves would be microscopic particles and averaged over. If you are interested in the halo of such a dwarf spheroidal you can measure the half-light radius and define this as the outer boundary, then you arrive at case number 4.

4) can this model explain the observations made by Donato or Kormendy & Freeman:
This is a point that I didn't address in the talk: on the slides, I also had a minimum radius r_min, which, in the end, was defined to be the radial position of the innermost particle. This value has to be larger than zero in order to keep all quantities finite. Extrapolating to 0 means that the PDF becomes infinite, hence, the formalism breaks down. This is to be expected because, the simplified assumptions may not be valid on these scales anymore. At least, we do not know what happens below the scales we observe. So r_min makes sure that we are only using the model down to scales we can resolve/observe. The cusp-core debate is -- to some extend -- related to this issue: for simulations, we cannot know the behaviour of the mass density below the radius of convergence (=r_min for the simulations). For observations the same applies due to the finite resolution of the spectrograph (to determine the rotation curves). Anything else is an extrapolation into a regime that my model does not provide, on purpose.
The other point is that Donato et al include the luminous matter content to explain the cores, while my approach is currently only considering dark matter. However, I hope to reproduce the effect that luminous matter flattens the inner mass density profiles, as also found in simulations.

5) how easy it is to extend this formalism to non-Newtonian gravity theories:
So far, the model is based on a probability density function of a power-law that is motivated by a scale-free Newtonian gravity. If your modified gravity theory provides you with another PDF, then it is quite easy to transfer the formalism. Yet, so far, I am still working on a mathematically sound derivation from Newtonian gravity to the PDF that I showed, so it may be a bit more difficult than previously assumed.

6) what about self-interacting DM:
Self-interactions break the assumptions that the particles are collisionless (=independent). Hence, we cannot simply multiply the individual PDFs for all particles, but the joint p_E of the entire ensemble is more complicated since it has to account for correlations among the particles. Despite that, it is straightforward to include this feature into the formalism, given the collisional model.

I hope that these answers are helpful. If not, don't hesitate to ask further.

Best regards and thanks a lot for the great discussion!
Jenny Wagner
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Re: J.Wagner:The cosmological Cheshire cat

New postby Jenny Wagner on Fri 19 Jun 2020 22:26

Dear Sotiris Loucatos,

during the talk, you asked the question, on p 6 in the various profiles, what is the reason of strong fluctuations at large r?

Let me give you a more detailed answer after rereading the respective paper of the Aquarius simulation:
https://ui.adsabs.harvard.edu/abs/2010M ... N/abstract

There it reads that the bumps in the outer regions may be traced to the presence of substructure and unrelaxed tidal debris.

Hope this now answers the question to your full satisfaction.
With best regards,
Jenny Wagner
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