Subject: Re: LSST can measure the neutrino mass

From: Jon Thaler

Submitted: Mon, 07 Jul 2003 17:49:46 -0500

Message number: 136 (previous: 135, next: 137 up: Index)

On Thursday, July 3, 2003, at 07:54 AM, Michael Strauss wrote:

> John,
>   I believe you are assuming that we have redshifts for all the
> galaxies in the LSST sample.  We will definitely have photometric
> (but not spectroscopic) redshifts; it will be very interesting to ask
> what sort of precision is needed in the photo-z's to do this
> calculation.  A rather optimistic number is 3% accuracy in (1+z).  And
> you will need to worry about:
>   -Non-linearity in the redshift-distance relation;
>   -Non-linear clustering
>   -Evolution in the galaxy population, and in the bias relative to the 
> DM
>   -Evolution in the clustering of the dark matter
>   -Effects of peculiar velocities, both linear and non-linear, and
>      evolution thereof.
>   -The luminosity and type dependence of galaxy bias.
>
> 				      -Michael Strauss

I think 5% z resolution requirement is adequate, but 3% would be 
better.  I agree that systematic errors will be a big issue.

I assume standard parameters (Omega_m = 0.3, Omega_Lambda = 0.7, h = 
0.7).

The 2dFGRS radial velocity resolution is about 85 km/sec [1].  At small 
z (their <z> ~ 0.1) this corresponds to a radial distance resolution of 
about 0.85 h^(-1) Mpc.  That’s good enough to measure the cosmological 
mass density by looking at the difference between radial and angular 
2-point correlation functions [2].

If LSST achieves 5% z resolution, then (at z = 1) the radial distance 
resolution is about 120 Mpc.  That’s not good enough for the Omega_m 
measurement.  However, because the neutrino mass is so small, its 
measurement requires sensitivity to correlations on large distance 
scales.  Finite mass neutrinos suppress density fluctuations on scales 
smaller than the free streaming distance when the neutrinos become 
nonrelativistic.  The associated wavenumber is knr = 
0.026*(Mnu/1eV)^(0.5)*Omega_m^(0.5)*h Mpc^(-1) [3].  At the lower limit 
on the neutrino mass (Mnu ~ 0.04 eV), knr ~ 2*10^(-3) Mpc^(-1) (a 
distance scale of 310 Mpc).  For Mnu = 0.4 eV, the distance scale is 
100 Mpc.  So, the LSST ought see the suppression of radial correlations 
for most of the range of allowed neutrino masses.  Clearly 3% z 
resolution would help us here.

The transverse distance scale at z = 1 is 80 kpc per arcsec, so 
resolution is not the issue.  Rather, large sky coverage is important: 
310 Mpc is 1.1° on the sky.  We'll get to small enough k that we may 
not need CMB data to help us out.

We'll gain both from the large data set and from the reach to small k.  
I haven't thought enough about systematics to say anything useful.

1. Colless, et al., MNRAS 328,1039 (2001).
2. Peacock, et al., Nature 410, 169 (2001).
3. Elgarøy, et al,, Phys. Rev. Lett, 89, 061301(2002),
    Doroshkevich, et al., Sov. Astron. Lett. 6, 252 (1980).

Jon


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