Modelling galaxy clustering: halo occupation distribution versus subhalo matching.

We model the luminosity-dependent projected and redshift-space two-point correlation functions (2PCFs) of the Sloan Digital Sky Survey (SDSS) Data Release 7 Main galaxy sample, using the halo occupation distribution (HOD) model and the subhalo abundance matching (SHAM) model and its extension. All the models are built on the same high-resolution N-body simulations. We find that the HOD model generally provides the best performance in reproducing the clustering measurements in both projected and redshift spaces. The SHAM model with the same halo-galaxy relation for central and satellite galaxies (or distinct haloes and subhaloes), when including scatters, has a best-fitting χ2/dof around 2-3. We therefore extend the SHAM model to the subhalo clustering and abundance matching (SCAM) by allowing the central and satellite galaxies to have different galaxy-halo relations. We infer the corresponding halo/subhalo parameters by jointly fitting the galaxy 2PCFs and abundances and consider subhaloes selected based on three properties, the mass Macc at the time of accretion, the maximum circular velocity Vacc at the time of accretion, and the peak maximum circular velocity Vpeak over the history of the subhaloes. The three subhalo models work well for luminous galaxy samples (with luminosity above L*). For low-luminosity samples, the Vacc model stands out in reproducing the data, with the Vpeak model slightly worse, while the Macc model fails to fit the data. We discuss the implications of the modelling results.

Efficient deconvolution of noisy periodic interference signals.

The interference signal formed by combining two coherent light beams carries information on the path difference between the beams. When the path difference is a periodic function of time, as, for example, when one beam is reflected from a vibrating surface and the other from a fixed surface, the interference signal is periodic with the same period as the vibrating surface. Bessel functions provide an elegant and efficient means for deconvoluting such periodic interference signals, thus making it possible to obtain the displacement of the moving surface with nanometer resolution. Here we describe the mathematical basis for the signal deconvolution and employ this technique to obtain the amplitude of miniature capillary waves on water as a test case.