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We discuss the local X-ray volume emissivity at hard bands (2 - 10 keV) from the cross-correlation between surface brightness fluctuation of the cosmic X-ray background and nearby galaxies. We have found correlation signals between HEAO 1 A2 surface brightness $I$ and number counts $N$ of IRAS/ESO/UGC galaxies of $W_{xg} \equiv \frac{\langle \delta I \, \delta N \rangle} {\langle I \rangle \langle N \rangle} \sim (3-10) \times 10^{-3}$. We have constructed a detailed model explaining the correlation signal in terms of the local volume emissivity. The correlation is contributed by the Poisson noise process where the correlating sample galaxies themselves emit X-rays. In this case, the correlation between the X-ray luminosity of galaxies and the infrared luminosity (or optical diameter) should be taken into account to evaluate its contribution to $W_{xg}$. Also, for a low spatial resolution experiment such as the HEAO 1 A2, the clusterings of the X-ray sources with the sample galaxies contribute to $W_{xg}$. We present the formulation to take these effects into account for the analysis.
Monte-Carlo simulations have been made to simulate the correlation. These are useful in direct comparison with the observations and estimating the uncertainty due to the finite number of sources contributing to the correlation.
The results are consistent with the models where the 2 - 10 keV volume emissivity is ($\rho_x \sim 4 \times 10^{38} h_{50} erg\,s^{-1} \, Mpc^{-3}$), dominated by the AGN component (with $L_x > 10^{42} h_{50}^{-2} erg\,s^{-1}$ ). This provides a constraint at the present epoch to models of the cosmic X-ray background with evolving populations of sources.
This presentation represents a part of TM's dissertation toward the fulfillment of the PhD requirements of the University of Maryland.
