## [1101.1650] The cosmological bulk flow: consistency with $\Lambda$CDM and $z\approx 0$ constraints on $\sigma_8$ and $\gamma$

 Authors: Adi Nusser, Marc Davis Abstract: We derive estimates for the cosmological bulk flow from the SFI++ catalog of Tully-Fisher (TF) measurements of spiral galaxies. For a sphere of radius $40 \hmpc$ centered on the Milky Way (MW), we derive a bulk flow of $333 \pm 38\kms$ towards Galactic $(l,b)=(276^\circ,b=14^\circ)$ within a $3^\circ$ $1\sigma$ error. Within a $100\hmpc$ we get $257\pm 44\kms$ towards $(l,b)=(279^\circ, 10^\circ)$ within a $6^\circ$ error. These directions are at a $40^\circ$ angle with the Supergalactic plane, close to the apex of the motion of the Local Group (LG) of galaxies after correcting it for the Virgocentric infall \citep{st10}. Our findings are consistent with the $\Lambda$CDM model with the latest WMAP best fit cosmological parameters. But the bulk flow allows independent constraints. For WMAP inferred Hubble parameter $h=0.71$ and baryonic mean density parameter $\Omega_b=0.0449$, the constraint from the bulk flow on the matter mean density $\Omega_m$, the normalization of the density power spectrum, $\sigma_8$, and the growth index, $\gamma$, can be expressed as $\sigma_8\Omega_m^{\gamma-0.55}(\Omega_m/0.266)^{0.28}=0.86\pm 0.11$ (for $\Omega_m\approx 0.266$). Fixing $\sigma_8=0.8$ and $\Omega_m=0.266$ as favored by WMAP, we get $\gamma=0.495\pm 0.096$. These local constraints are independent of the biasing relation between mass and galaxies. Our results are based on a method termed \ace\ (All Space Constrained Estimate) which reconstructs the bulk flow from an all space three dimensional peculiar velocity field constrained to match the TF measurements. For comparison, a maximum likelihood estimate (MLE) is found to lead to similar bulk flows, but with larger errors. [PDF]  [PS]  [BibTex]  [Bookmark]

Discussion related to specific recent arXiv papers
Syksy Rasanen
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### [1101.1650] The cosmological bulk flow: consistency with $\ This paper studies the bulk flow of galaxies on scales up to 100$h^{-1}$ Mpc using a single survey of spiral galaxies, with distances determined from the Tully-Fisher relation; the sample has 2859 galaxies. (The authors say they use the inverse Tully-Fisher relation instead of the Tully-Fisher relation; I confess ignorance of the difference.) The velocities are reconstructed by generating a random basis of velocity fields from a $\Lambda$CDM power spectrum and fitting the coefficients, demanding that on very large scales, the result agrees with $\Lambda$CDM. The results are found to be consistent with $\Lambda$CDM. This might not be interesting, were it not for the contrary claim of 0911.5516, which argues that there are flows in significant excess of the $\Lambda$CDM expectation on 100$h^{-1}$ Mpc scales. (There are other papers claiming large bulk flows on even larger scales.) The present authors hint that miscalibration between different catalogues in the composite used in 0911.5516 could be the origin of the bulk flow found there. On the other hand, the assumption of a vanilla $\Lambda$CDM model seems to be heavily used in the present analysis, and it is not transparent how much this biases the results. Christopher Gordon Posts: 14 Joined: September 27 2004 Affiliation: University of Canterbury Contact: ### Re: [1101.1650] The cosmological bulk flow: consistency wit In our paper we used a different approach http://arxiv.org/pdf/1010.4276 and we also found that the SFI++ catalogue was consistent with $\Lambda$CDM, see table 1. But, we found that the SN peculiar velocity data where mildly inconsistent with $\Lambda$CDM at the two sigma level. Syksy Rasanen Posts: 119 Joined: March 02 2005 Affiliation: University of Helsinki ### [1101.1650] The cosmological bulk flow: consistency with$\

I had missed that paper, thanks.

Maciej Bilicki
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### [1101.1650] The cosmological bulk flow: consistency with $\ Just to shortly explain what the inverse T-F relation is: you fit the two parameters "s" and "eta_0" in the relation eta = s * M + eta_0, where eta = log("line_width") is a measure of the galaxy's circular velocity and M is the absolute magnitude. In the original T-F relation it was rather M = a * eta + b. Now for the results of the paper. The interesting thing is the discrepancy with the results of Watkins et al. 2009 and Feldman et al. 2010. They also use the SFI++ catalog and present results also for this catalog alone, together with other catalogs (including the "Composite"). Their bulk flow from SFI++ alone grows from ~20 Mpc/h, whereas it decreases for Nusser and Davis although they use the same data. So what is the reason? I can see at last two: different methods are used to estimate the bulk flow; the data are handled differently. For example, it is interesting that Watkins et al. present results up to ~60 Mpc/h. Nusser and Davis use the same data and claim to have measured the bulk flow up to ~100 Mpc/h, although their sample is smaller! The bulk flow issue seems to be far from settled IMO. Syksy Rasanen Posts: 119 Joined: March 02 2005 Affiliation: University of Helsinki ### [1101.1650] The cosmological bulk flow: consistency with$\

So in the inverse relation you determine the circular velocity from the magnitude, and not vice versa?

Maciej Bilicki
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### [1101.1650] The cosmological bulk flow: consistency with $\ Not exactly :) The circular velocity is your observable, as is the observed magnitude and redshift. What you want is a mean relation between a measure of the circular velocity and absolute magnitude. The latter is calculated from the observed m and redshift. The question is what is your "x" in the f(x)=a*x+b fit. In the ITF, the "x" is absolute magnitude M. For more details, take a look at the recent Davis et al. paper http://arxiv.org/abs/1011.3114 Syksy Rasanen Posts: 119 Joined: March 02 2005 Affiliation: University of Helsinki ### [1101.1650] The cosmological bulk flow: consistency with$\

I don't understand... To me the equations are the same, with some terms moved from one side to the other.

Maciej Bilicki
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### [1101.1650] The cosmological bulk flow: consistency with $\ They are in a sense... It's only the question of what you fit with your linear regression or whatever, i.e. what is your x and what is your y. But it's still the same Tully-Fisher relation that is dealt with :) Maybe someone else will make it clearer... Ben Weiner Posts: 3 Joined: September 01 2010 Affiliation: Steward ### [1101.1650] The cosmological bulk flow: consistency with$\

The reason to use the inverse TF relation is that there is intrinsic scatter in the relation and there is also an apparent magnitude limit. If you aren't careful with how you treat the scatter you can introduce a Malmquist-type bias. Malmquist biases are more severe with a larger dispersion in the population (brightness of a not-exactly-standard candle, or scatter about a relation).

Typical methods of fitting y on x effectively assign the scatter to y, the dependent variable. If you make magnitude the dependent variable then your fitted relation will be biased - it will have biases in zeropoint and slope - because you're missing some fraction of low luminosity galaxies and you're not missing an equal fraction at all velocities. If you make velocity the dependent variable, then the scatter is parallel to the selection limit, so to speak, and the fitted relation is less biased.

Discussions of fitting relations with both observational errors and scatter can be found in the appendix of Weiner et al 2006, http://adsabs.harvard.edu/abs/2006ApJ...653.1049W and B. Kelly 2007, http://adsabs.harvard.edu/abs/2007ApJ...665.1489K. My paper is Tully Fisher-oriented, although the fitting issues are general; Kelly's paper is more statistically sophisticated and correct.

Syksy Rasanen
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### [1101.1650] The cosmological bulk flow: consistency with \$\

That makes it a little clearer, thanks.