It is well known that a per cent level understanding of the anisotropy of the redshift-space galaxy clustering is needed to accurately recover cosmological information from the RSD signal in order to shed light on the issue of dark energy versus modified gravity. From a statistical point of view, the source of the anisotropy is the galaxy line-of-sight pairwise velocity distribution. It is therefore important to adopt a realistic functional form for this velocity PDF when fitting models to the data. To this purpose, in Paper I we introduced the GG prescription for the velocity PDF. In this work, we have continued the development of this model by making explicit the dependence of the GG distribution on quantities predictable by theory, namely its first three moments, and extending it to the more general concept of GQG. To keep the model as simple as possible, we have proposed an ansatz with two free dimensionless parameters that describe how infall velocity and velocity dispersion vary when moving from one place to another in our Universe. Since their interpretation is clear, these parameters can be theoretically predicted or, assuming a more pragmatic approach, tuned to simulations or used as nuisance parameters. State-of-the-art PT has proven successful in predicting the large-scale behaviour of the velocity PDF and the correspondent monopole and quadrupole of the redshift-space correlation function (e.g. Reid & White 2011; Wang, Reid & White 2014), at least for massive haloes, M ∼ 1013 M⊙. Unfortunately, by definition, any PT breaks down for small separations. Consequently, alternative approaches have been suggested in the literature, spanning from purely theoretical (e.g. Sheth 1996) to hybrid techniques in which N-body simulations plus an HOD are employed to deal with the issue of non-linearities (e.g. Tinker 2007; Reid et al. 2014). One of the main results from our work is to provide a framework in which perturbation and small-scale theories are smoothly joined, so that all available RSD information can be coherently extracted from redshift surveys. A fundamental requirement for a redshift-space model is that it must be precise on all scales interest, and it should inform the user of the scales on which the model can be trusted. We have compared to N-body simulations the well-known GSM (Reid & White 2011), the more recent ESM (Uhlemann et al. 2015) and the GQG prescription over a broad range of separations, from 0 to 80 h−1 Mpc. Different redshifts, from z = 0 to 1, and different tracers, namely DM particles and two mass-selected catalogues of DM haloes, have been considered. We have concluded that, among the three, QGQ is the only model capable of providing a precise redshift-space correlation function on scales down to ∼5 h−1 Mpc over the range of redshifts covered by future surveys. Keeping in mind that the range of validity of the models depends on tracer, redshift and order of the Legendre multipoles we are interested in, for finiteness, we can say that all the models converge to the expected amplitude on scales ≳30 h−1 Mpc, at least for multipole and quadrupole. Since these scales roughly coincide with the range of validity of state-of-the-art PTs, if we rely only on PT and if we are not interested in higher order multipoles, the most natural choice is the simplest model among the three, i.e. the GSM. As for the ESM, we have found it to be unbiased down to smaller scales and for higher order multipoles than the GSM, thus confirming the results by Uhlemann et al. (2015), but, on the other hand, it seems to behave even worse than the GSM on the smallest scales. We can therefore think of it as a natural extension of the GSM in the perspective of further PT developments. In particular, a better prediction of the third moment of the velocity PDF is required before the ESM can be applied to data on smaller scales. Formally, the same argument holds for the GQG model, none the less, since this latter is meant to include non-linear scales, it could be possible to obtain a prediction for the third moment by interpolating between (very) small and (very) large scales. More precisely, as shown in the lower-right panel of Fig. A1, the functions $c^{(3)}_t$ and $c^{(3)}_r$, which fully characterize the third moment, are peaked at r ≲ 10 h−1 Mpc. By adopting a model for the small-scale limit that includes those separation, most likely using simulations in a similar way to that proposed in Reid et al. (2014), we would then be able to interpolate between these peaks and their large-scale limit, which is trivially 0.
Citation: Reid & White 2011
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Citation: Reid & White 2011
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