DETECTION OF HALO ASSEMBLY BIAS AND THE SPLASHBACK RADIUS

Transcription

1 DETECTION OF HALO ASSEMBLY BIAS AND THE SPLASHBACK RADIUS Surhud More (Kavli-IPMU) Collaborators: Hironao Miyatake (JPL), Masahiro Takada (Kavli IPMU), David Spergel (Princeton), Rachel Mandelbaum (CMU), Eduardo Rozo (Arizona), Eli Rykoff(Stanford), Benedikt Diemer, Neal Dalal, Anupreeta More, Masamune Oguri & Andrey Kravtsov (UChicago)

2 HALO ASSEMBLY BIAS Wechsler et al. 006 Dependence of the large scale clustering amplitude on secondary parameters other than the halo mass. See also: Lemson & Kaufmann 99, Gao et al. 005, 008 Observationally: Yang et al. 006, Weinmann et al. 006, Kauffmann et al. 03, Hearin et al. 04, but cf. Lin et al. 05

3 REDMAPPER CLUSTER SUBSAMPLES Less compact More compact 8648 redmapper clusters: z [0., 0.33] Subsamples based upon the average cluster-centric distance of member galaxies, <R mem > Control for halo mass using the weak gravitational lensing signal

4 REDMAPPER CLUSTER SUBSAMPLES Less compact Average separation (Mpc/h) Miyatake, SM, et al. 05 Number of cluster galaxies More compact 8648 redmapper clusters: z [0., 0.33] Subsamples based upon the average cluster-centric distance of member galaxies, <R mem > Control for halo mass using the weak gravitational lensing signal

5 WEAK GRAVITATIONAL LENSING 0 subsample large subsample small hr mem i hr mem i [h M /pc ] 0 c00m subsample large hr mem i subsample small hr mem i b R [h Mpc] M 00m [0 4 M /h] 4 6 c 00m b Same average halo mass, different large scale bias. b large hri /b small hri = , unity. For comparison, even if we Bias difference due to mass difference is. in the extreme case. Miyatake, SM, et al. 05

6 CLUSTERING OF GALAXY CLUSTERS Miyatake, SM, et al. 05 b large hri /b small hri =.40 ± 0.09 Shaded bands from weak lensing Projected clustering of galaxy clusters shows a significant and consistent difference as well SM, et al. 06

7 CLUSTERING OF GALAXY CLUSTERS Splashback radius and Halo Assembly bias < R/[h Mpc] 50, nals on larger scales, 0 ignificant di erence, a signature of assembly Miyatake, SM, et.48 al.±05 6 high cgal g.0 low cgal / g rm halo model fits to the measurements of the of each large clusterhri subsample. Following Ref. [8], small hri b /b =.40 ± a simple six parameter model fit to the WL.0 00m, c00m, qcen, o, M, b) NFW (R; M00m, c00m ) n +( qcen ) NFW,o (R; M00m, c00m0.5, o ) + (R; M ) + halo (R; b). () Shaded bands from weak lensing for 0 erm corresponds to the halo mass profile n qcen of clusters whose centers have been corblow cgal /bhigh cgal R [h Mpc] tified, while the second term corresponds to s with misidentified centers. We assume that FIG. 3. panel: HaloThe assembly bias fromnumber the projected clustering Figure 5. Detection of the halo assembly bias. Left ratio of the surface density profiles of our fiducial samples of photometric galaxies around ass profile is a smoothly truncated version of signal: The correspond projected to auto-correlation function of clusters fora single constant parameter fit to these data. Right the two galaxy cluster subsamples. The shaded regions the - and -sigma confidence regions for profile [9], proposed in Ref. [0], specified panel: The posterior distribution of the ratio the measurements shown inmem theileft panel. We detect the assembly bias di erence in the halo biases of the eachgiven of the large- and small-hr subsamples, relative to o mass and concentration Mis00m two samples parameter, at 6.6. There a significant covariance in the errors, hence the small point-to-point variation given the errors. The quoted significance accounts that of the full sample (i.e. all clusters). The clustering sig> Mpc/h, show a significant []. We adopt for vthe =covariance..6 for the smoothing nals at large separations, R ecommended in Ref. [0]. We simply condi erence, which is consistent with the WL measurements in 3.. Detection of Halo Assembly bias Fig. as shown by the shaded regions. gle mass bin for host halos. We assume that The mean number density profile of galaxies correlated lized profile of the positions of o -centered with clusters at large separations is proportional to the prodth respect to their true center is given by uct of the biases of clusters and galaxies in the photometric blarge hri /bsmall hri = , a.5 deviation from exp[ r /( o R00m )], where o describes SM, et al. 06 sample. We masses have shown unity. For comparison, even if we take the halo for above that these profiles are di erent f the o -centering radius to R. We also Projected clustering of galaxy clusters shows a significant and consistent difference as well

8 halo edges BOUNDARIES OF DARK MATTER HALOS sharp steepening of the density profile is present in the outskirts of the fast accreting halos Diemer & Kravtsov 04, ApJ 789, cf. also Adhikari et al. 04, PRD; More, Diemer & Kravtsov 05, in prep. dark matter density map in two different cluster-sized halos in a slice through the center of thickness =0.5 Rvir (density is reconstructed using phase-space sheet, cf. Hahn & Abel ) Where is the boundary of the halo? Diemer, Kravtsov, SM 03, Diemer & Kravtsov 04, SM et al. 05

9 halo edges BOUNDARIES OF DARK MATTER HALOS sharp steepening of the density profile is present in the outskirts of the fast accreting halos Diemer & Kravtsov 04, ApJ 789, cf. also Adhikari et al. 04, PRD; More, Diemer & Kravtsov 05, in prep. dark matter density map in two different cluster-sized halos in a slice through the center of thickness =0.5 Rvir (density is reconstructed using phase-space sheet, cf. Hahn & Abel ) Where is the boundary of the halo? Diemer, Kravtsov, SM 03, Diemer & Kravtsov 04, SM et al. 05

10 halo edges Figure. Projected density in a slice of thickness 0.5R00m through the center of two halos with low (left, = 0.8) and high (right, =.7) mass accretion rates. The halos have similar masses, Mvir =. 04 and.8 04 h M at z = 0. The white lines show Rvir (solid), R00m (dot-dashed), Rsp (dashed) sharp of the density profile present the outskirts of thepresented fast accreting and Rinfall (dotted;steepening see 3. for a detailed description of these radii). Ris Rinfall werein calculated using the calibrations in Section 3. halos rather than sp and the density profiles of the individual halos shown. Halos with a low mass accretion rate exhibit a caustic at a radius significantly larger than R00m, whereas < R00m (at z = 0). The visualizations were created using the algorithm of Kaehler et al. (0). fast-accreting halos have Rsp Diemer & Kravtsov 04, ApJ 789, BOUNDARIES OF DARK MATTER HALOS cf. 0 also Adhikari et al. 04, PRD; More, Diemer & Kravtsov 05, in prep. 4 = 0.8 =.7 0 / m d log /d log r 3 4 5dark matter density map in two different cluster-sized halos in a slice through the center of thickness =0.5 Rvir 6 (density is reconstructed using phase-space sheet, cf. Hahn & Abel ) halo?0.5 Where is the0. boundary of the r/r00m 5 r/r00m Figure. Spherically averaged density profiles (top panels) and their logarithmic slope (bottom panels) of the two halos shown in Figure. The slopes were Kravtsov, 03,bins.Diemer & Kravtsov 04, SM et computed using a profile smoothed with the fourth-order Savitzky &Diemer, Golay (964) filter over thesm 5 nearest The steepening around Rsp is very pronounced in both profiles, but the profile of the faster accreting halo reaches a steeper slope and at a smaller radius. The vertical lines in the bottom panels mark the same radii shown in Figure using the same line types, i.e. Rvir, Rsp, and Rinfall (defined as the radius where the mean radial velocity profile of v r reaches minimum) from left to right. For the slower accreting halo (left), the estimate of Equation 5 slightly underestimates the true Rsp. This disagreement is not surprising since the R of individual halos are expected to scatter around the median relation. al. 05

11 SPLASHBACK RADIUS: PHYSICAL ORIGIN Depends upon the mass accretion rate of halos Faster accreting halos have smaller splashback radii

12 SPLASHBACK RADIUS: PHYSICAL ORIGIN Depends upon the mass accretion rate of halos Faster accreting halos have smaller splashback radii

13 SPLASHBACK RADIUS: PHYSICAL ORIGIN.6.4 z =0.0 z =0.5 z =.0 z =.0 z =4.0 Rsp/R00m Redshift Mass accretion rate SM, DIEMER & KRAVTSOV 05 Depends upon the mass accretion rate of halos Faster accreting halos have smaller splashback radii

14 SPLASHBACK RADIUS 0 high c gal low c gal 0.5 g [h Mpc ] 0 highc =5.9 lowc =3. d log g/d log R Degrees of freedom = 8.0 R00m R [h Mpc] R [h Mpc] Use photometric galaxies with M i -5 log h <-.4 (assuming cluster redshift) Surface number density of such galaxies as a function of radius SM, et al. 06

15 SPLASHBACK RADIUS TOO SMALL? 3 4 More, S. et al... 3d Rsp /R00m 0 g (R) [h Mpc ] Mi -5 logh< Vpeak > 35kms Observed 0 00 Collisionless Expected d log g /d log R = d log M/d log a.0. R00m bserved surface.4 density of SDSS photometric galaxies around our subsample of redmapper clusters s with errorbars. The green shaded bands correspond to 68 and 95 percent confidence levels based.6 ta. Right panel:.8 The logarithmic derivative of the surface density profile as constrained by using the The vertical.0 shaded region corresponds to the 68 percent confidence level on the inferred splashback The vertical dashed line corresponds to the R00m of the cluster sample based on the weak lensing 3d [h Mpc] el: The comparison ofr the observed ratio of Rsp /R00m (shown as the green shaded band) as a ion ratefigureto that expected in standard collisionless dark matter model. The grey star corresponds. Top panels: The surface number density profiles, g (R), of SDSS photometric galaxies with di erent magnitude thresholds around the entire redmapper cluster sample with z [0., 0.33] and richness [0, 00], are shown using symbols with errorbars. The dashed lines correspond to (sub)-halo surface etion rate of our cluster halos in the standard cosmological model. The splashback radius is smaller than expected by about 0 percent.

16 THANK YOU!!! CONCLUSIONS First observational detection of halo assembly bias and the splashback radius on cluster scales!!! Assembly bias appears quite strong (realistic mocks required to check cluster finding systematics) The splashback radius is smaller than expected Could signal interesting new physics