Fig.1  Z0 of the box300 simulation (z = 0) with predictions from the  halo model and Eulerian PT. Symbols are measurements of simulations in  real spacewith different πmax. The upper row of plots shows the effects  of adjusting the halo boundary radius in units of Rv but without a  cut-off to the halo mass function,while the bottom row demonstrates the  consequence of cutting the high-mass tails of the mass function with the  halo boundary fixed to Rv.

Dr. MENG Kelai  et al. ，Purple Mountain Observatory, Chinese Academy of Science, have  proposed a redshift-distortion-free correlation function at third order  in the non-linear regime for characterzing galaxy clustering  properties. 

The  zeroth-order component of the cosine expansion of the projected  three-point correlation function is proposed for the clustering analysis  of cosmic large-scale structure. These functions are third-order  statistics but can be measured similarly to the projected two-point  correlations. Numerical experiments with N-body simulations indicate  that the advocated statistics are redshift distortion free within 10 per  cent in the non-linear regime on scales of ∼0.2–10 h−1Mpc.In addition,  the maximal integration scale πmax parallel to the LOS during estimation  ought to be greater than ∼ 120 h−1Mpc. A serious concern is that shot  noise could ruin the estimation in the strongly non-linear regime if the  number density of points in a sample is too low. This requirement for a  robust Z0 measurement is tighter than that for the projected 2PCF, but  still weaker than the normal projected 3PCF, since Z0 is an integral of  the former.

As we expected,  the halo model provides satisfactory predictionto the dark matter Z0 of  simulations within ∼10 per cent, if theclassical Sheth–Tormen mass  functions are used. Our computationindicates that extending the halo  boundary is enough to yield a good fit to simulations, while a hard  cut-off to mass function is notas effective as previous works claimed.  Substituting new functionsof the halo mass distribution and halo biasing  in high precisiondoes not lead to significantly better agreement with  simulations.Since the angular dependence in the projected 3PCF and the  normal3PCF is smeared out in Z0, we conjecture that using an  anisotropichalo profile will probably not improve accuracy  significantly. Asignificant bias of the Z0 predicted by the halo model  comparedto simulations emerges in the weakly non-linear regime, where  thehalo models reduce to second-order PT; the latter is already knownto  be poor in predicting the dark matter 3PCF. A more precisebispectrum  from higher order perturbation theories may offer a wayto increase  precision (e.g. Valageas 2008; Sefusatti 2009; Bartoloet al. 2010).The  agreement between halo model and actual measurementlays the ground for  using these functions to perform joint analyses with the projected  two-point correlation functions, exploring galaxy clustering properties  in the framework of the halo model and relevant extensions.The work by  MENG Kelai (corresponding author),  PAN Jun,  István Szapudi, FENG  Longlong,  accepted by Monthly Notices of the Royal Astronomical  Society, has been published online (http://onlinelibrary.wiley.com/doi/10.1111/j.1365-2966.2011.18247.x/abstract;jsessionid=F29DA822621BA8ADCF8EDE0875496487.d02t01).