Modeling Quasar Proximity Zones in a Realistic Cosmological Environment with a Self-consistent Light Curve

We study quasar proximity zones in a simulation that includes a self-consistent quasar formation model and realistic IGM environments. The quasar host halo is $10^{13}\ M_{\mathrm{\odot}}$ at $z=6$, more massive than typical halos studied in previous work. Between $6<z<7.5$, the quasar luminosity varies rapidly, with a mean magnitude of $M_{UV,mean}=-24.8$ and the fluctuation reaching up to two orders of magnitude. Using this light curve to post-process the dense environment around the quasar, we find that the proximity zone size ($R_{p}$) ranges between $0.5-5$ pMpc. We show that the light curve variability causes a similar degree of scatter in $R_{p}$ as does the density fluctuation, both of which result in a standard deviation of $\sim 0.3$ pMpc). The $R_{p}$ traces the light curve fluctuations closely but with a time delay of $\sim 10^4\ \mathrm{yr}$, breaking the correspondence between the $R_{p}$ and the contemporaneous $M_{UV}$. This also indicates that we can only infer quasar activity within the past $\sim 10^4$ years instead of the integrated lifetime from $R_{p}$ in the later part of cosmic reionization. Compared with the variable light curve, a constant light curve underestimates the $R_{p}$ by 13% at the dim end ($M_{UV}\sim -23.5$), and overestimates the $R_{p}$ by 30% at the bright end ($M_{UV}\sim -26$). By calculating the $R_{p}$ generated by a number of quasars, we show that variable light curves predict a wider $R_{p}$ distribution than lightbulb models, and readily explain the extremely small $R_{p}$ values that have been observed.