Modeling the 3-point correlation function Felipe Marin Department of Astronomy & Astrophysics University of Chicago arXiv: Felipe Marin Department of Astronomy & Astrophysics University of Chicago arXiv:

06/01/2007Great Lakes Cosmology Workshop 8 Collaborators: Josh Frieman (KICP-Chicago & Fermilab) Josh Frieman (KICP-Chicago & Fermilab) Bob Nichol (ICG, Portsmouth) Bob Nichol (ICG, Portsmouth) Risa Wechsler (KICP-Chicago, now Stanford) Risa Wechsler (KICP-Chicago, now Stanford)

06/01/2007Great Lakes Cosmology Workshop 8 Correlation functions on LSS  Galaxy surveys show us that the (luminous) matter does not distribute very smoothly in the Universe  From cosmological N-body simulations, we can see that is also not the case for the dark matter  How do we get a more quantitative insight?  Can we infer DM clustering using galaxies?  Galaxy surveys show us that the (luminous) matter does not distribute very smoothly in the Universe  From cosmological N-body simulations, we can see that is also not the case for the dark matter  How do we get a more quantitative insight?  Can we infer DM clustering using galaxies? A. Kravtsov M. Tegmark

06/01/2007Great Lakes Cosmology Workshop 8 N-point statistics  One way to achieve this is using spatial N-point correlation functions: measure how more likely is to have certain configurations of N-points in a particular field than in a random distribution.  For instance, we can describe the probability that two objects (galaxies, dark matter particles, DM halos, etc.) are found at a distance r:  One way to achieve this is using spatial N-point correlation functions: measure how more likely is to have certain configurations of N-points in a particular field than in a random distribution.  For instance, we can describe the probability that two objects (galaxies, dark matter particles, DM halos, etc.) are found at a distance r:  This defines the two-point correlation function. Along with its Fourier counterpart, the Power Spectrum, have been measured in simulations and galaxy surveys, CMB,etc.

06/01/2007Great Lakes Cosmology Workshop 8 The need for a more complete description  It is possible that two distributions have the same 2-point statistics, but they look completely different!  2-point statistics just describe completely only Gaussian Fields.  They do not take into account non-spherical morphologies  It is possible that two distributions have the same 2-point statistics, but they look completely different!  2-point statistics just describe completely only Gaussian Fields.  They do not take into account non-spherical morphologies Sefusatti & Scoccimarro 2005

06/01/2007Great Lakes Cosmology Workshop 8 The three-point correlation function  The next order correlation is the three-point correlation function (3PCF): The probability to find 3 objects in a certain triangle configuration: 1 3  2  The value of the 3PCF depends on the overall scale of the triangle, as well as on its shape.  Useful to define the reduced 3PCF:  The value of the 3PCF depends on the overall scale of the triangle, as well as on its shape.  Useful to define the reduced 3PCF: u r r

06/01/2007Great Lakes Cosmology Workshop 8 N-body simulations & mock galaxy catalogs  We want to measure & compare the 3PCF of dark matter and galaxies in real & redshift space.  We use high-resolution N-body simulations run using ART code (Kravtsov et al. ’97,’04) with concordance LCDM parameters. Can detect dark matter halos of galactic size  Two boxes: L120 with 120 Mpc/h on the side & L200 with 200 Mpc/h on the side  Redshift space: long-distance observer approximation: peculiar velocities distortions  We want to measure & compare the 3PCF of dark matter and galaxies in real & redshift space.  We use high-resolution N-body simulations run using ART code (Kravtsov et al. ’97,’04) with concordance LCDM parameters. Can detect dark matter halos of galactic size  Two boxes: L120 with 120 Mpc/h on the side & L200 with 200 Mpc/h on the side  Redshift space: long-distance observer approximation: peculiar velocities distortions Kravtsov et al 04

06/01/2007Great Lakes Cosmology Workshop 8 From DM to galaxies  Kravtsov et al (2004), Conroy, Wechsler & Kravtsov (2006) : V max, of a DM halo is a good indicator of the stellar mass and henceforth, of the luminosity of a galaxy.  In order to get luminosities, for both L120 & L200 boxes, the r-band SDSS luminosity function is matched to the cumulative velocity function at the redshift of observation n(>V max,now )  Colors are assigned using the observed relation between local density and SDSS color (Wechsler et al. 2004, Tasitsiomi et al 2004).  Kravtsov et al (2004), Conroy, Wechsler & Kravtsov (2006) : V max, of a DM halo is a good indicator of the stellar mass and henceforth, of the luminosity of a galaxy.  In order to get luminosities, for both L120 & L200 boxes, the r-band SDSS luminosity function is matched to the cumulative velocity function at the redshift of observation n(>V max,now )  Colors are assigned using the observed relation between local density and SDSS color (Wechsler et al. 2004, Tasitsiomi et al 2004). Conroy,Wechsler & Kravtsov 06

06/01/2007Great Lakes Cosmology Workshop 8 Results: DM vs halos Equilateral triangles  Reduced 3PCF for DM particles & halos  Jack-knife error bars  Halos strongly biased w.r.t. DM particles  Strong scale dependence in real space, strong redshift evolution on small scales  Features of Q very washed out in redshift space  Reduced 3PCF for DM particles & halos  Jack-knife error bars  Halos strongly biased w.r.t. DM particles  Strong scale dependence in real space, strong redshift evolution on small scales  Features of Q very washed out in redshift space MWFN 2007

06/01/2007Great Lakes Cosmology Workshop 8 Why real-space Q so different from redshift-space Q?  Big effect in observation, in Galaxy biasing

06/01/2007Great Lakes Cosmology Workshop 8 Results: DM vs. halos Shape dependence  We measured Q(r,u=2,  ), for  = degrees  Blue line: Biased dark matter Q… see later…  The amplitude of Q(  ) is higher at elongated configurations: U-shape.  We measured Q(r,u=2,  ), for  = degrees  Blue line: Biased dark matter Q… see later…  The amplitude of Q(  ) is higher at elongated configurations: U-shape. MWFN 2007

06/01/2007Great Lakes Cosmology Workshop 8 Luminosities & Colors  Kayo et al. (2004): little or no dependence of Q for SDSS galaxies in color and luminosity, for equilateral triangles  Our results agree in general: need more volume?  Kayo et al. (2004): little or no dependence of Q for SDSS galaxies in color and luminosity, for equilateral triangles  Our results agree in general: need more volume? MWFN 2007

06/01/2007Great Lakes Cosmology Workshop 8 Comparison w/SDSS results.  We compare the 3PCF of our boxes to the recent measurements of the SDSS 3PCF by Nichol et al (2006)  There’s a good agreement within the errors in general with our L120 box results using V max,now  Here we use a much lower resolution than in our previous results: then features of Q(  ) are severely attenuated.  We compare results with bigger resolution: errors do not get much higher.  We compare the 3PCF of our boxes to the recent measurements of the SDSS 3PCF by Nichol et al (2006)  There’s a good agreement within the errors in general with our L120 box results using V max,now  Here we use a much lower resolution than in our previous results: then features of Q(  ) are severely attenuated.  We compare results with bigger resolution: errors do not get much higher.

06/01/2007Great Lakes Cosmology Workshop 8 Galaxy Biasing with 3PCF  The different 3PCF from Dark Matter and galaxies reflect differences in spatial distributions: galaxy bias  Higher-order statistics can provide constrains.  On large scales, where rms overdensities are small compared to unity, we can adopt a local bias model. This will affect the values of the correlation functions as well:  The different 3PCF from Dark Matter and galaxies reflect differences in spatial distributions: galaxy bias  Higher-order statistics can provide constrains.  On large scales, where rms overdensities are small compared to unity, we can adopt a local bias model. This will affect the values of the correlation functions as well:

06/01/2007Great Lakes Cosmology Workshop 8 Galaxy Biasing: results  Adopting c 1 =b 1 and c 2 =b 2 /b 1, using the JK error covariance matrix we get constrains in these parameters from the 3PCF, 2PCF & overdensities.  The three methods have a good agreement in real space, giving c 1 ~1.2 & c 2 ~ -0.2  In redshift space the agreement is not as good, but constrains from 3PCF are consistent with 2dF results: c 1 ~0.9& c 2 ~ -0.3  Adopting c 1 =b 1 and c 2 =b 2 /b 1, using the JK error covariance matrix we get constrains in these parameters from the 3PCF, 2PCF & overdensities.  The three methods have a good agreement in real space, giving c 1 ~1.2 & c 2 ~ -0.2  In redshift space the agreement is not as good, but constrains from 3PCF are consistent with 2dF results: c 1 ~0.9& c 2 ~ -0.3

06/01/2007Great Lakes Cosmology Workshop 8 Summary  The 3PCF for both galaxies and dark matter has a strong dependence on scale and shape.  The redshift space 3PCF is strongly attenuated w.r.t. the real space 3PCF.  The galaxy reduced 3PCF shows little dependence on luminosity & color.  Our model predictions are in good agreement with the last SDSS measurements  On scales of order 10 Mpc/h, a local bias scheme is in reasonable agreement with galaxy and DM distributions.  The 3PCF for both galaxies and dark matter has a strong dependence on scale and shape.  The redshift space 3PCF is strongly attenuated w.r.t. the real space 3PCF.  The galaxy reduced 3PCF shows little dependence on luminosity & color.  Our model predictions are in good agreement with the last SDSS measurements  On scales of order 10 Mpc/h, a local bias scheme is in reasonable agreement with galaxy and DM distributions.