The Quasar Proximity Effect as an Alternative Probe of Quasar Pair Distances

TL;DR

This work proposes using the quasar proximity effect as a flux-based proxy to constrain the line-of-sight separation between quasar pairs at high redshift, addressing large uncertainties in emission-line redshifts. By generating synthetic proximity-zone spectra from CROC simulations and applying Gaussian smoothing with a simple peak-finding algorithm, the authors demonstrate that the presence and location of a foreground-quasar–induced flux boost along the line of sight can constrain $d_{ m l.o.s.}$, especially for small sky-plane separations. The results indicate that for $d_{ m sky} ightarrow0.01$ pMpc, $d_{ m l.o.s.}$ can be estimated with $ abla d_{ m l.o.s.}\,rac{}{} ext{about }0.1-0.2$ pMpc for true $d_{ m l.o.s.} \gtrsim 2-3$ pMpc, and that even at $d_{ m sky}=1$ pMpc the method provides useful upper limits and ~1 pMpc-scale accuracy for $d_{ m l.o.s.} \gtrsim4$ pMpc. This approach offers a promising path to characterize the 3D configuration of quasar pairs and informs future work on more robust inference techniques and continuum-uncertainty handling.

Abstract

Recently discovered quasar pairs at high redshifts ($z\gtrsim$5) are likely precursors to supermassive black hole mergers, providing a promising window to high redshift quasar growth mechanisms. However, the large uncertainties on their relative distances along the line-of-sight ($d_{\rm l.o.s.}$) limits our ability to characterize quasar pairs. In this study, we explore synthetic quasar proximity zone spectra as an alternative method to constrain the line-of-sight distance of quasar pairs. We find that for small sky-plane separations ($d_{\rm sky}\approx 10-100$ pkpc), a simple peak finding algorithm can easily distinguish between scenarios of $d_{\rm l.o.s.} \lesssim1$ pMpc and $\gtrsim1$ pMpc. For cases where the true $d_{\rm l.o.s.} \geq 3$ pMpc, the accuracy of $d_{\rm l.o.s.}$ estimation is $\approx 0.2$ pMpc. Large sky-plane separations of $d_{\rm sky}=1$ pMpc have larger absolute uncertainties in $d_{\rm l.o.s.}$ estimates, but the method can still easily distinguish between scenarios where $d_{\rm l.o.s.}\lesssim4$ pMpc and $\gtrsim4$ pMpc. $d_{\rm l.o.s.}$ estimates have an uncertainty of $\approx$0.5 pMpc when true $d_{\rm l.o.s.} \gtrsim4$ pMpc. Our proof-of-concept study illustrates the potential use of quasar proximity zones to constrain the 3-dimensional quasar pair configuration, providing an avenue to characterize quasar pairs.

Figures (4)

• Figure 1: Top: Radiation profile in units of the ionization rate due to both quasars as a function of distance from the target quasar $Q_A$. Solid lines correspond to the scenario where $Q_A$ is the brighter one with $M_{1450}=-27$ and the foreground quasar $Q_B$ with $M_{1450}=-26$. Dash-dotted lines correspond to the inverted scenario where $Q_A$ is the dimmer one with $M_{1450}=-26$ and the foreground quasar $Q_B$ with $M_{1450}=-27$. We fix the sky-plane distance of the quasar pair at 10 pMpc. The three colored lines show the scenarios where the line of sight distance $d_{\rm l.o.s.}$ are 0 (blue), 2 pMpc (orange), and 6 pMpc (green), respectively. Black line corresponds to the contribution from all background galaxies, and the dashed black line the contribution from the target quasar. Middle: Light solid lines show the corresponding transmitted flux in the above three scenarios with the brighter target quasar, dashed lines trace the Gaussian smoothed spectra. Bottom: Light dash-dotted lines show the corresponding transmitted flux for the scenarios with a dimmer target quasar, dashed lines trace the Gaussian smoothed spectra. The smoothed spectra are very similar for the same $d_{\rm l.o.s.}$, regardless of whether or not the target quasar is the brighter one.
• Figure 2: Left: Dependence of predicted $d_{\rm l.o.s.}$ on the true relative distance in the quasar pair configuration case of $d_{\rm sky}=0.01$ pMpc and a brighter background target quasar. The boxes represent 50% of the $d_{\rm l.o.s.}$ predictions while the bars represent 90% of the predictions. Peak finding on spectra with a smoothing kernel of 250 km/s is sufficient to measure $d_{\rm l.o.s.} \geq 2~\rm~pMpc$ with consistently tight percentage accuracies. Peak finding can also robustly determine if the foreground quasar's $d_{\rm l.o.s.}$ is smaller than $2~\rm~pMpc$, given the non-overlapping errorbars of $d_{\rm l.o.s.}\geq2~\rm~pMpc$ and $d_{\rm l.o.s.}\leq 1~\rm~pMpc$ cases. Right: Same as left, except for brighter foreground quasar case.
• Figure 3: Same figure and quasar pair scenario as Fig. \ref{['fig:gammaflux_smalldsky']}, where $Q_A$ is the brighter one with $M_{1450}=-27$. We fix the line of sight distance to $d_\mathrm{l.o.s.}=6$ pMpc. The 3 colored lines show the scenarios where where the sky-plane distance $d_\mathrm{sky}$ are 0.01 pMpc (blue), 0.10 pMpc (orange), and 1.0 pMpc (green). The blue and orange lines completely overlaps due to the nearly identical transmitted flux. Grey line is a reference if the secondary quasar $Q_B$ does not exist.
• Figure 4: Same as the left panel of Fig.\ref{['fig:predict_dlos_boxplot1']}, but for the larger $d_{\rm sky}=1$ pMpc case.