ChandraObservations of Six QSOs atz≈ 3

We report the results of our Chandra observations of six QSOs at $z\sim 3$from the Palomer Transit Grism Survey. Our primary goal is to investigate thepossible systematic change of $\alpha_{ox}$ between $z>4$ and $z\sim 3$,between which a rapid rise of luminous QSO number density with cosmic time isobserved. The summed spectrum showed a power-law spectrum with photon index of$\Gamma \approx 1.9$, which is similar to other unabsorbed AGNs. Combining our$z\sim 3$ QSOs with X-ray observations of QSOs at $z>4$ from literaure/archive,we find a correlation of $\alpha_{\rm ox}$ with optical luminosity. This isconsistent with the fact that the luminosity function slope of the luminous endof the X-ray selected QSOs is steeper than that of optically-selected QSOs. Wediscuss an upper limit to the redshift dependence of $\alpha_{ox}$ using aMonte-Carlo simulation. Within the current statistical errors including thederived limits on the redshift dependence of $\alpha_{\rm ox}$, we found thatthe behaviors of the X-ray and optically-selected QSO number densities areconsistent with each other.Comment: 13 Pages, 3 Figures, Astronomical Journal in press, An entry in Table 2 corrected--Log Lx for PC 1000+4751 from 44.0 (incorrect) to 45.0 (correct). A few minor errors correcte