The clustering of intermediate redshift quasars as measured by the Baryon Oscillation Spectroscopic Survey

TL;DR

This study measures the quasar two-point correlation function at intermediate redshift ($2.2<z<2.8$) using the large, uniform BOSS CORE quasar sample, deriving both redshift-space $\\xi(s)$ and projected $w_p(R)$ statistics to mitigate redshift errors. By fitting power-law forms and modeling redshift smearing, the authors infer a high bias ($b\sim3.5$–$3.9$) corresponding to host halos of order $M_h\sim2\times10^{12}\,h^{-1}\mathrm{M_\odot}$ and a quasar duty cycle near $1\%$. They test two halo-occupancy scenarios—lognormal halo-mass distributions and luminosity–halo scaling relations—and find both can reproduce the clustering, implying only a weak luminosity dependence within the sample’s dynamic range. The results support a picture in which luminous quasars at $z\sim2.4$ reside in rare, massive halos and will evolve into massive ellipticals, with implications for the evolving $M_{\rm BH}$–$M_{\rm gal}$ relation and black hole growth. Overall, the work provides tight constraints on quasar host halo masses, duty cycles, and occupancy, informing models of quasar triggering and galaxy–black hole co-evolution.

Abstract

We measure the quasar two-point correlation function over the redshift range 2.2<z<2.8 using data from the Baryon Oscillation Spectroscopic Survey. We use a homogeneous subset of the data consisting of 27,129 quasars with spectroscopic redshifts---by far the largest such sample used for clustering measurements at these redshifts to date. The sample covers 3,600 square degrees, corresponding to a comoving volume of 9.7(Gpc/h)^3 assuming a fiducial LambdaCDM cosmology, and it has a median absolute i-band magnitude of -26, k-corrected to z=2. After accounting for redshift errors we find that the redshift space correlation function is fit well by a power-law of slope -2 and amplitude s_0=(9.7\pm 0.5)Mpc/h over the range 3<s<25Mpc/h. The projected correlation function, which integrates out the effects of peculiar velocities and redshift errors, is fit well by a power-law of slope -1 and r_0=(8.4\pm 0.6)Mpc/h over the range 4<R<16Mpc/h. There is no evidence for strong luminosity or redshift dependence to the clustering amplitude, in part because of the limited dynamic range in our sample. Our results are consistent with, but more precise than, previous measurements at similar redshifts. Our measurement of the quasar clustering amplitude implies a bias factor of b~3.5 for our quasar sample. We compare the data to models to constrain the manner in which quasars occupy dark matter halos at z~2.4 and infer that such quasars inhabit halos with a characteristic mass of <M>~10^{12}Msun/h with a duty cycle for the quasar activity of 1 per cent.

Figures (18)

• Figure 1: The angular distribution of our quasar sample, in J2000 equatorial coordinates and Aitoff projection. We have rotated the reference line by $90^\circ$ so that the North and South Galactic survey regions appear contiguous in the left and right parts of the plot, respectively. Areas which we use in our analysis (light grey), have completeness to XDQSO targets of greater than 75 per cent. Other areas (dark grey) are mainly early survey regions where XDQSO was not used as the CORE targeting algorithm. The black areas depict imaging data in which the $u$-band chip was not operating, which are discarded from our analysis.
• Figure 2: The absolute magnitude distribution and number of quasars vs. redshift for our sample. (Upper) The $10^{\rm th}$, $25^{\rm th}$, $50^{\rm th}$, $75^{\rm th}$ and $90^{\rm th}$ percentiles of $M_i$ vs. redshift (see text). (Middle) The same percentiles now in $M_i-M_{\star,i}$ vs. redshift. (Lower) the (normalized) redshift distribution of quasars. The vertical dotted lines indicate the redshift ranges we consider in our study.
• Figure 3: The projected correlation function split by hemisphere (or Galactic latitude), compared to the fiducial sample. The dashed line corresponds to the projected correlation function for a real-space correlation function with $r_0=8\,h^{-1}$Mpc and a power-law slope of $-2$ to guide the eye. Note the weakly significant excess power at large scales for the south-only sample (see text).
• Figure 4: The projected correlation function split by whether the median seeing in $g$ band in a sector is better than $1.25"$ (SB125) or worse than $1.25"$ (SW125) compared to the fiducial sample. The dashed line corresponds to the projected correlation function for a real-space correlation function with $r_0=8\,h^{-1}$Mpc and a power-law slope of $-2$ to guide the eye. There is no statistically significant difference between the two halves of the data. This is typical of the other jackknife tests we have performed.
• Figure 5: The projected correlation functions, $w_p(R)$, for the six samples considered in this paper (Table \ref{['tab:samples']}). The error bars are the square roots of the diagonal elements of the covariance matrices, as determined by bootstrap resampling (see text). The dashed lines show the best fit power-laws with slope $-2$ (see Table \ref{['tab:results']}).