Is the dependence of spectral index on luminosity real in high-z QSO samples? Answer: No! Su-Min Tang, Shuang-Nan Zhang Tsinghua Center for Astrophysics 04/22/2006

Outline Introduction Determining factor for spurious correlations Data analysis of high-z QSO sample from Miyaji et al Implications from optical and X-ray luminosity functions Summary

Introduction If spectral index depends on optical luminosity, this is equivalent to a non-linear relationship between X-ray and optical luminosity: L_X ~ L_o^e, e \neq 1 An anti-correlation between alpha_ox and the optical luminosity (e<1) has been found for many years and has important implications in the theoretical studies of AGN evolution (e.g. Avni & Tananbaum 1982; Steffen et al. 2006): testing energy generation models; understanding discrepancies between X-ray and optical luminosity functions etc. An analysis of high-redshift quasars showed a anticorrelation of alpha_ox with optical luminosity (Miyaji et al. 2006). One of the problems with discovering such relationships is selection effects, as pointed out by Yuan et al

Why dispersions bring anticorrelation between aox and lo when e=1 Determining Factor of the spurious correlation: slope ～

Consequences of sigma_x 3 times

Spectral index-optical luminosity correlation Miyaji et al ： We find that alpha_ox is anti-correlated with optical luminosity. It might reflect the true behavior of the shift of alpha_ox with QSO power.

Dependences? lo=log10(L_2500), lx=log10(L_2 keV) ASURV

Simulations (e=1, sigma^2=0.4): spearman ’ s rho Unreal dependence comes from dispersion in luminosities sigma(lo)=sigma(lx)=0.28 Observation errors + light curve: sigma(lo)~0.17, simga(lx)~0..23 (sigma(lo^2+simga(lx)^2)^0.5 ~ (Strateva et al. 2006) lx lo R_sigma=sigma(lo)/sigma(lx)

Simulations (e=1, sigma^2=0.4): slope Unreal dependence comes from dispersion in luminosities sigma(lo)=sigma(lx)=0.28 lx lo

Conclusion for Miyaji ’ s sample Apparent dependences of spectral index on optical/X-ray luminosities can emerge even for a population with an intrinsically constant spectral index in the presence of dispersions in luminosities; The explanation of the observed spectral index – luminosity as a physical relation in QSOs in Miyaji et al. 2006, must be questioned.

Comparison of the X-ray and Optical luminosity functions (LFs) Assuming a complete broad line AGN sample including optical and X-ray observations (detections or upper limits), slopes in optical and X-ray LFs after correct transformation should be the same. Spectral index can be derived by comparing the two LFs. We use the optical LF given by Richards et al (2dF, SDSS & 2SLAQ) and the X-ray LF given by Barger et al (deep and wide-area Chandra surveys). Luminosity-independent spectral index is preferred

Richards et al If spectral index=const. X-ray; Broad line AGN Barger et al Optical A large part of X-ray bright broad line AGNs are missed in the luminous optical end? Optical absorption or False spectral index function?

Discussion: Optical absorption or False spectral index function? Barger et al. 2005: X-ray selected samples at the flux limit of the CDF-N/S essentially find all of the broad-line AGNs So We should be able to compare directly the broad-line AGN hard X-ray luminosity functions computed above with the optical QSO luminosity functions

X-ray; Broad line AGNs Optical; Croom et al A constant spectral index Barger et al Confirming: 1.The two methodologies are measuring the same sample; 2.The bolometric corrections used are appropriate

Dashed cyan lines are optical LF, solid lines in other colors are X-ray LF

Discussion: no spectral index dependence on luminosity in X-ray selected samples (Hasinger et al. 2004)

Summary A constant spectral index which does not depend on optical luminosity is entirely consistent with data in Miyaji’s high-z sample Large dispersions and narrow range of optical luminosity are most important for the apparent, yet fake, spectral index-optical luminosity correlation Luminosity-independent spectral index is preferred when compare the X-ray and optical luminosity functions. A luminosity-dependent spectral index as found by any authors (e.g. Vignali et al., Strateva et al. or Steffen et al.) is unacceptable if Barger et al.’s sample is as complete as they claim.