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Estimating the effective lifetime of the $zsim6$ quasar population from the composite proximity zone profile

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 Added by Karna Morey
 Publication date 2021
  fields Physics
and research's language is English




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The lifetime of quasars can be estimated by means of their proximity zone sizes, which are regions of enhanced flux bluewards of the Lyman-$alpha$ emission line observed in the rest-frame UV spectra of high-redshift quasars, because the intergalactic gas has a finite response time to the quasars radiation. We estimate the effective lifetime of the high-redshift quasar population from the composite transmitted flux profile within the proximity zone region of a sample of $15$ quasars at $5.8leq zleq 6.6$ with precise systemic redshifts, and similar luminosities, i.e. $-27.6leq M_{1450}leq-26.4$, and thus a similar instantaneous ionizing power. We develop a Bayesian method to infer the effective lifetime from the composite spectrum, including robust estimates of various sources of uncertainty on the spectrum. We estimate an effective lifetime of the quasar population as a whole of $log_{10}(t_{Q}/{yr}) = 5.7^{+0.5 (+0.8)}_{-0.3 (-0.5)}$ given by the median and $68$th ($95$th) percentile of the posterior probability distribution. While our result is consistent with previous quasar lifetime studies, it poses significant challenges on the current model for the growth of supermassive black holes (SMBHs) located in the center of the quasars host galaxies, which requires that quasar lifetimes are more than an order of magnitude longer.



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In this paper, we study the sizes of quasar proximity zones with synthetic quasar absorption spectra obtained by post-processing a Cosmic Reionization On Computers (CROC) simulation. CROC simulations have both relatively large box sizes and high spacial resolution, allowing us to resolve Lyman limit systems, which are crucial for modeling the quasar absorption spectra. We find that before reionization most quasar proximity zone sizes grow steadily for $sim 10$ Myr, while after reionization they grow rapidly but only for $sim 0.1$ Myr. We also find a slow growth of $R_{rm obs}$ with decreasing turn-on redshift. In addition, we find that $sim 1-2%$ of old quasars ($30$ Myr old) display extremely small proximity zone sizes ($<1$ proper Mpc), of which the vast majority are due to the occurrence of a damped Ly$alpha$ absorber (DLA) or a Lyman limit system (LLS) along the line of sight. These DLAs and LLSs are contaminated with metal, which offers a way to distinguish them from the normal proximity zones of young quasars.
The lifetime of quasars is fundamental for understanding the growth of supermassive black holes, and is an important ingredient in models of the reionization of the intergalactic medium. However, despite various attempts to determine quasar lifetimes, current estimates from a variety of methods are uncertain by orders of magnitude. This work combines cosmological hydrodynamical simulations and 1D radiative transfer to investigate the structure and evolution of the He II Ly$alpha$ proximity zones around quasars at $z simeq 3-4$. We show that the time evolution in the proximity zone can be described by a simple analytical model for the approach of the He II fraction $x_{rm HeII}left( t right)$ to ionization equilibrium, and use this picture to illustrate how the transmission profile depends on the quasar lifetime, quasar UV luminosity, and the ionization state of helium in the ambient IGM (i.e. the average He II fraction, or equivalently the metagalactic He II ionizing background). A significant degeneracy exists between the lifetime and the average He II fraction, however the latter can be determined from measurements of the He II Ly$alpha$ optical depth far from quasars, allowing the lifetime to be measured. We advocate stacking existing He II quasar spectra at $zsim 3$, and show that the shape of this average proximity zone profile is sensitive to lifetimes as long as $sim 30$ Myr. At higher redshift $zsim 4$ where the He II fraction is poorly constrained, degeneracies will make it challenging to determine these parameters independently. Our analytical model for He II proximity zones should also provide a useful description of the properties of H I proximity zones around quasars at $z simeq 6-7$.
We calculate the distribution of HI within 750 proper kpc/h of a quasar, Lbol = 1.62e13 Lsun, powered by an SMBH, Mbh = 4.47e8 Msun, at z = 3. Our numerical model includes a cosmological hydrodynamic simulation that tracks the self consistent growth and thermal feedback of black holes calculated using GADGET-3 as well as a detailed post-processing ray tracing treatment of the non-uniform ionizing radiation field calculated using SPHRAY, which naturally accounts for the self shielding of optically thick systems. We show that the correct treatment of self shielding introduces a flattening feature into the neutral column density distribution around Log NHI = 20 and that regions with the lowest neutral fractions are not those with the highest density gas. For comparison, we solve a Ricatti equation which determines the equilibrium Hydrogen ionization fractions in the presence of a radiation field that falls off as 1/r^2 with regions above a given gas density threshold completely shielded from ionizing radiation. We demonstrate that these semi analytic models cannot reproduce the HI field calculated using SPHRAY. We conclude by comparing our models of this single proximity zone to observations by Hennawi and Prochaska of the absorption spectra of background quasars which are coincident on the sky with foreground quasars in their Quasars Probing Quasars (QPQ) series of papers. Compared to the QPQ sample, we find a factor of 3 fewer optically thick (Log NHI > 17.2) systems around our quasar, however the dark matter halo that hosts our simulated quasar, Mhalo = 5.25e12 Msun, is less massive than the typical QPQ host halo by a factor of four. Allowing for a linear scaling between halo mass, baryonic overdensity and number of absorbers, we estimate the typical host halo mass in the QPQ sample as 1.92e13 Msun.
We introduce a Bayesian approach coupled with a Markov Chain Monte Carlo (MCMC) method and the maximum likelihood statistic for fitting the profiles of narrow absorption lines (NALs) in quasar spectra. This method also incorporates overlap between different absorbers. We illustrate and test this method by fitting models to a mini-broad (mini-BAL) and six NAL profiles in four spectra of the quasar UM675 taken over a rest-frame interval of 4.24 years. Our fitting results are consistent with past results for the mini-BAL system in this quasar by Hamann et al. (1997b). We also measure covering factors ($C_{rm f}$) for two narrow components in the CIV and NV mini-BALs and their overlap covering factor with the broad component. We find that $C_{rm f}$(NV) is always larger than $C_{rm f}$(CIV) for the broad component, while the opposite is true for the narrow components in the mini-BAL system. This could be explained if the broad and narrow components originated in gas at different radial distances, but it seems more likely to be due to them produced by gas at the same distance but with different gas densities (i.e., ionization states). The variability detected only in the broad absorption component in the mini-BAL system is probably due to gas motion since both $C_{rm f}$(CIV) and $C_{rm f}$(NV) vary. We determine for the first time that multiple absorbing clouds (i.e., a broad and two narrow components) overlap along our line of sight. We conclude that the new method improves fitting results considerably compared to previous methods.
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