## Neutrino mass from galaxy surveys

Antony Lewis
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Joined: September 23 2004
Affiliation: University of Sussex
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### Neutrino mass from galaxy surveys

SDSS and 2df have been used to constrain the neutrino mass via the shape of the galaxy power spectrum by assuming the galaxy power spectrum is proportional to a linear 'matter' power spectrum on large scales. The question is, which matter spectrum should one use... do the galaxies trace the total matter (inc. neutrinos), just baryons + CDM, or just the baryons? And at what redshift should one evaluate the spectrum if the relevant one is not time independent?

Kevork Abazajian
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Joined: July 26 2005
Affiliation: Los Alamos National Laboratory
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### Neutrino mass from galaxy surveys

Since the CDM and neutrinos are effectively providing a gravitational potential in which galaxies form, it appears to me that the overall power due to CDM plus neutrinos plus baryons should be used.

Antony Lewis
Posts: 1353
Joined: September 23 2004
Affiliation: University of Sussex
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### Re: Neutrino mass from galaxy surveys

I can see the argument that galaxies might form in the peaks of potential wells, and hence be sensitive to the total power spectrum at formation. But this is different to the redshift of the survey, so at what redshift do you calculate the power spectrum?

If I plot the fractional difference in shape between the total power spectrum at z=0 and z=1 for mν = 0.15 I get something like

Pretty small.. but still, would be nice to be clear about what the right thing to do is. Probably the real answer is to run lots of simulations and see?

Anze Slosar
Posts: 183
Joined: September 24 2004
Affiliation: Brookhaven National Laboratory
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### Re: Neutrino mass from galaxy surveys

Antony Lewis wrote:I can see the argument that galaxies might form in the peaks of potential wells, and hence be sensitive to the total power spectrum at formation. But this is different to the redshift of the survey, so at what redshift do you calculate the power spectrum?
In principle you do it at around the effective redshift of your survey... But there are issues that are much more hassling (or so I think) than just the redshift of PS: for example for a finite survey width in redshift the transverse modes evolve differently to radial modes with redshift. Eisenstein et al, for example, quote constraint on Dv(z)=[Dm(z)2 cz/H(z)]1/3 in order to avoid this problem. Also, it is assumed that if you isotropise the power spectrum, you will get the shape of PS right, regardless of fingers of God: this is indeed the case for Kaiser model (for which then the ratio of true PS to isotropised PS can be expressed as a function of β~Ωm0.6/b), but Scoccimarro has criticised this recently ([astro-ph/0407214]), showing that you cannot ignore red-shift distortions "on large enough scales". Plus you have evolution of bias with redshift and other astro-physical effects. It can become fairly nasty...
Antony Lewis wrote: If I plot the fractional difference in shape between the total power spectrum at z=0 and z=1 for mν = 0.15 I get something like
Well, but the difference is very small at small k. In Eisenstein et all they claim NL effect are important already for k<0.1 Mpc/h...
Antony Lewis wrote: Probably the real answer is to run lots of simulations and see?
Now, this is something I don't quite grasp, either. Basically, hard-core gas dynamics simulations are too expensive to do the on large-enough scales... So in my rather limited understanding, there are basically two schools of doing simulations: a) Run very large DM simulations, find halos, populate halos with galaxies using some form of Halo Occupation Distribution model and do it so that you match say Luminosity distribution of SDSS. (see tinker et al. for example) b) Run somewhat smaller, but still large enough simulations, identify halos and sub-halos, use circular velocity as a proxy for mass and match cumulative mass distributions with measured cumulative luminosity distributions to get distribution of galaxies. (e.g. Tasitsiomi et al). Now, there is no baryons in either of them. I've talked to Simon White in Paris asking about baryon feedback and he tells me it shouldn't matter, baryon feedback could, in the worst case, change the luminosity of a galaxy in a given DM subhalo, but not its position, something like introducing a scatter between halo mass and galaxy luminosity (disclaimer: this is my understanding of what he told me). Now, what he is fairly strongly attacking, based on Millenium runs are HOD models saying that the basic mantra of HOD (i.e. what people use under a) above): "distribution of galaxies in a given halo depends on halo mass only" is wrong. They see a factor of 5 effect depending on halo formation redshift... So you could patch HOD by adding an extra parameter, but it would complicate it a bit. On the other hand, I've talked to Scoccimarro in Triest and he is somewhat sceptical over whether this is really that important and Seljak seems to be of a similar opinion...

In either case simulations are mostly DM only so the question of which PS to use is not that important because NL effects swallow you... So, the right thing to do would be to have simulations with DM, baryons and neutrinos, give each species the right PS early enough, taking care of correlations, run stuff forward with some sensible baryon physics, spit out data in very fine redshift slices, simulate the light-cone and compare the final output with what you see. And run huge MCMC varying all possible parameters and marginalise over all nuissance parameters in baryonic physics. This seems to be computationally somewhat too difficult to do right now.

Finally, millenium run seems to be doing some first order thing here... So they have this huge run with many redshift outputs and IDs on each DM particle... Then they sort of piggy-back baryon evolution on top of existing run. So DM doesn't see baryons, but baryons at redshift one know their history... This seems to be good enough to reproduce very many observables...