Transverse Proximity Effect Insights

• The transverse proximity effect is the off-axis impact of quasar ionizing radiation on intergalactic gas, reducing H I and HeII absorption when the radiation reaches the background sightline.
• Observations reveal that enhanced Lyα transmission along the line-of-sight contrasts with increased absorption transversely, indicating anisotropic quasar emission and environmental overdensities.
• Forward modeling that incorporates quasar age, obscuration, and IGM fluctuations disentangles ionization effects from geometrical light-travel delays, thus constraining quasar lifetimes.

The transverse proximity effect denotes the impact of a foreground quasar’s ionizing radiation on gas intersected not by the quasar’s own line of sight, but by a nearby background sightline. In the H I Ly$\alpha$ context, isotropic quasar emission should reduce the neutral hydrogen fraction near the foreground object and therefore produce less Ly$\alpha$ absorption in the background spectrum; in the HeII Ly$\alpha$ context, sufficiently strong foreground radiation should reduce HeII opacity and increase transmitted flux. Because the effect depends simultaneously on ionizing luminosity, the gas environment around quasars, finite light-travel-time geometry, and possible anisotropy or obscuration, it functions as a probe of quasar radiation fields, circumgalactic and intergalactic overdensity, and quasar lifetime (Jalan et al., 2018, Schmidt et al., 2017).

1. Conceptual relation to the line-of-sight proximity effect

The transverse proximity effect is the off-axis counterpart of the line-of-sight or longitudinal proximity effect. The line-of-sight effect is the observed deficit of H I absorbers close to a quasar along the direct sightline, caused by the quasar’s enhanced ionizing radiation. If quasar radiation were isotropic, one would expect an analogous deficit in the transverse direction as well. In practice, the observational situation is more complex: H I studies have found stronger absorption transverse to quasars than along the line of sight, whereas HeII studies have found statistical transmission enhancement in background sightlines near suitable foreground quasars (Jalan et al., 2018, Misawa et al., 2022, Schmidt et al., 2017).

In H I, the basic expectation is straightforward. Extra UV photons from a foreground quasar should lower the local neutral hydrogen fraction, so the transmitted Ly$\alpha$ flux in a nearby background spectrum should increase. In HeII, the same logic applies to harder photons above $4$ Ry: if the foreground quasar emits enough HeII-ionizing radiation, the nearby IGM should become more highly ionized, the HeII Ly$\alpha$ optical depth should decrease, and the transmitted flux should rise (Schmidt et al., 2017).

A common misconception is that the transverse proximity effect is simply a direct measure of quasar luminosity. The literature summarized here shows otherwise. The observed signal depends on whether quasar radiation actually reaches the transverse sightline, whether the gas lies in an overdense environment, whether the quasar has been active long enough for its photons to arrive, and whether obscuration or emission geometry suppresses illumination in the relevant direction (Jalan et al., 2018, Schmidt et al., 2017).

2. Geometry, observables, and ionization corrections

For projected quasar pairs, the proper three-dimensional distance from a foreground quasar to an absorber along a background sightline is written as

$r = \sqrt{r_\perp^2 + r_k^2},$

with

$r_k = \frac{c\,(z_f - z_a)}{(1+z_f)H(z_f)},$

and

$r_\perp = D_A(z_f)\,\theta.$

Here $z_f$ is the foreground quasar redshift, $\alpha$0 the absorber redshift, $\alpha$1 the angular diameter distance, and $\alpha$2 the angular separation. For the longitudinal effect, the relevant scale is simply the line-of-sight proper distance $\alpha$3 (Jalan et al., 2018).

The basic transmitted flux per pixel is defined by

$\alpha$4

where $\alpha$5 is the observed flux, $\alpha$6 the continuum, and $\alpha$7 the effective Ly$\alpha$8 optical depth. Analyses of the H I effect therefore use both the median transmitted flux $\alpha$9 and the pixel optical depth $\alpha$0 as functions of radial distance from the foreground quasar. Under photoionization equilibrium, the optical depth is modeled as depending on overdensity and photoionization rate, with

$\alpha$1

so the observed proximity-region optical depth reflects the combined effects of quasar photoionization, the metagalactic UV background, and overdensity around the quasar (Jalan et al., 2018).

The ionizing enhancement is encoded through

$\alpha$2

with

$\alpha$3

In an ideal high-resolution case one would correct the observed optical depth as

$\alpha$4

but for SDSS spectra with $\alpha$5 this scaling is not exact. A simulation-calibrated effective correction is therefore introduced:

$\alpha$6

The same general logic underlies HeII analyses, which estimate the foreground quasar photoionization rate at the background sightline and compare transmission near the foreground quasar redshift with control regions farther away along the same background spectrum (Jalan et al., 2018, Schmidt et al., 2017).

A further methodological point is that continuum placement and uncertainty propagation materially affect the inference. In the H I study of projected SDSS quasar pairs, the SDSS pipeline continuum is found to underestimate the true continuum in the Ly$\alpha$7 forest, so the spectra are refit with an iterative B-spline method and uncertainties from continuum placement, photon-counting noise, sightline-to-sightline scatter, emission-redshift error, and bootstrap variance are propagated explicitly (Jalan et al., 2018).

3. H I transverse proximity effect in projected quasar pairs

A large statistical H I analysis used spectra of 181 projected quasar pairs from SDSS DR12 in the redshift range $\alpha$8, with angular separations $\alpha$9 arcmin and proper transverse separations of $\alpha$0–$\alpha$1 kpc, median $\alpha$2 kpc. The sample excludes BAL quasars, DLAs, sub-DLAs, and LLSs in the proximity region, and requires a velocity separation $\alpha$3 to avoid physically associated pairs. The same foreground quasars are then used in two ways: their own sightlines probe the longitudinal proximity effect, while the background sightlines probe the transverse effect at the foreground quasar redshift (Jalan et al., 2018).

The principal observational result is an asymmetry between longitudinal and transverse directions. In the longitudinal direction, the transmitted flux increases as one approaches the quasar within about $\alpha$4 Mpc proper distance, which is the classic proximity-effect signature. In the transverse direction, the trend is reversed: there is more absorption near the foreground quasar, especially within about $\alpha$5 Mpc. The cumulative probability distributions of pixel optical depth also differ strongly, with lower optical depth than the control IGM sample in the longitudinal proximity region and higher optical depth than the control sample in the transverse region (Jalan et al., 2018).

After correcting the longitudinal data for quasar ionization using the low-resolution effective correction, an excess overdensity profile is inferred out to $\alpha$6 Mpc. A central result is that the ionization-corrected longitudinal overdensity profile matches the uncorrected transverse overdensity profile. This implies that the background sightline is sampling the same underlying overdense quasar environment, but with substantially weaker quasar ionization in the transverse direction. By matching the two profiles, the average transverse illumination is constrained to be $\alpha$7 of the longitudinal illumination at $\alpha$8 confidence (Jalan et al., 2018).

This combination of enhanced longitudinal transmission, enhanced transverse absorption, and matched overdensity profiles argues against a purely isotropic ionizing field. The result is frequently interpreted as evidence that quasars inhabit overdense environments while illuminating those environments anisotropically on Mpc scales (Jalan et al., 2018).

4. Anisotropy, obscuration, and BAL-quasar tests

Several physical explanations have been considered for the strong H I anisotropy. Overdensity around quasars is expected, but overdensity alone does not explain why the longitudinal direction shows lower absorption while the transverse direction shows higher absorption when the same general environment should be sampled statistically in both directions. Finite lifetime or episodic activity could suppress the transverse signal because the background sightline may not yet have been reached by the quasar’s photons; for the median transverse separation in the SDSS pair sample, the delay is about $\alpha$9 Myr. Gas inflow or outflow can also distort absorption positions, but is reported to be too small to explain the observed asymmetry. Among these interpretations, anisotropic obscuration is identified as the most probable explanation, and that interpretation is supported by the fact that all foreground quasars in the sample are Type-I AGNs, consistent with a dusty-torus picture in which ionizing radiation is blocked preferentially in equatorial or transverse directions (Jalan et al., 2018).

An exploratory BAL-quasar study was designed to probe this orientation hypothesis more directly. BAL troughs are widely believed to be observed if the central continuum is viewed from the side through powerful outflows near the dust torus, so BAL quasars may provide an orientation test of whether torus shielding drives the anisotropic H I absorption pattern. Using SDSS/BOSS DR16, the study assembled 12 projected quasar pairs with a BAL quasar in the foreground and a non-BAL quasar in the background, requiring $4$0, $4$1, $4$2, and no Ly$4$3 blending in the relevant Ly$4$4 region. The projected separations span roughly $4$5–$4$6 kpc (Misawa et al., 2022).

The BAL study finds optically thick gas around 2 of the 12 BAL quasars, with the strongest absorbers near PQ10 and PQ11 having $4$7 and $4$8, while the other 10 systems have much weaker absorbers, generally $4$9. The inferred covering fraction is

$\alpha$0

and the stacked background spectra yield a mean rest-frame equivalent width

$\alpha$1

The median stack gives only an upper limit,

$\alpha$2

because the mean stack is dominated by the two strong DLA-like systems (Misawa et al., 2022).

These results are broadly consistent with previous non-BAL quasar measurements in mean equivalent width and overall covering fraction, but they do not provide a statistically significant confirmation that BAL quasars alter the transverse signal in the way a simple torus-shielding model might predict. An important subtlety is that the strong BAL-quasar absorbers are DLA-like, with $\alpha$3, whereas optically thick systems in earlier non-BAL work are typically LLS-like, with $\alpha$4. The difference of about three orders of magnitude in column density suggests that the two samples may be tracing different physical populations. After removing the DLA-like systems, the BAL sample would have

$\alpha$5

which is more compatible with anisotropic obscuration, though still not statistically significant (Misawa et al., 2022).

The BAL result therefore constrains a second common misconception: BAL quasars do not yet provide a decisive falsification or confirmation of the dust-torus explanation. The current sample is too small, the Poisson uncertainties are large, and the detected optically thick absorbers may have a different physical origin from those around non-BAL quasars (Misawa et al., 2022).

5. HeII transverse proximity effect as a lifetime probe

The HeII transverse proximity effect is formulated analogously but operates in a regime where the background IGM is much more opaque and therefore potentially more sensitive to local ionizing sources. At $\alpha$6, the HeII IGM is described as highly opaque and close to the tail end of HeII reionization, with effective optical depths of order $\alpha$7 and a HeII fraction $\alpha$8. In this setting, even a modest local reduction in HeII abundance can produce a conspicuous transmission spike in a background HeII Ly$\alpha$9 spectrum (Schmidt et al., 2017).

A large HeII survey assembled 22 background quasars with HST/COS HeII Ly$r = \sqrt{r_\perp^2 + r_k^2},$0 transmission spectra and carried out a two-tiered foreground-quasar search around them. The program discovered 131 new quasars and, after combining them with known SDSS and BOSS objects and applying analysis cuts, produced a final usable sample of 66 foreground quasars with inferred HeII photoionization rates above the adopted threshold

$r = \sqrt{r_\perp^2 + r_k^2},$1

The flux dilution and ionization-rate estimator are written as

$r = \sqrt{r_\perp^2 + r_k^2},$2

and

$r = \sqrt{r_\perp^2 + r_k^2},$3

The transverse signal is measured statistically through a stacking analysis, using

$r = \sqrt{r_\perp^2 + r_k^2},$4

For the main stack with $r = \sqrt{r_\perp^2 + r_k^2},$5, the average HeII transmission rises from a background level of roughly $r = \sqrt{r_\perp^2 + r_k^2},$6 to about $r = \sqrt{r_\perp^2 + r_k^2},$7 near the quasar positions, corresponding to $r = \sqrt{r_\perp^2 + r_k^2},$8, and only about $r = \sqrt{r_\perp^2 + r_k^2},$9 of random stacks exceed the observed enhancement, giving a $r_k = \frac{c\,(z_f - z_a)}{(1+z_f)H(z_f)},$0 detection. A weaker threshold, $r_k = \frac{c\,(z_f - z_a)}{(1+z_f)H(z_f)},$1, yields $r_k = \frac{c\,(z_f - z_a)}{(1+z_f)H(z_f)},$2 with $r_k = \frac{c\,(z_f - z_a)}{(1+z_f)H(z_f)},$3 significance (Schmidt et al., 2017).

The HeII measurements show that the effect is statistical rather than deterministic. Among the four foreground quasars with the highest inferred $r_k = \frac{c\,(z_f - z_a)}{(1+z_f)H(z_f)},$4, only one is associated with a significant HeII transmission spike. This large object-to-object variance indicates that high inferred luminosity is necessary but not sufficient for an observable transverse signal. The variance is attributed to quasar age, anisotropic emission or obscuration, uncertainty in the EUV spectral slope, fluctuations in the HeII mean free path, and the stochastic density structure of the IGM (Schmidt et al., 2017).

Because the HeII signal depends on a finite transverse light-travel path, it provides a geometric constraint on quasar age. The stack remains significant at $r_k = \frac{c\,(z_f - z_a)}{(1+z_f)H(z_f)},$5 even when restricted to foreground quasars with

$r_k = \frac{c\,(z_f - z_a)}{(1+z_f)H(z_f)},$6

which is about $r_k = \frac{c\,(z_f - z_a)}{(1+z_f)H(z_f)},$7 proper Mpc. This implies a lower limit

$r_k = \frac{c\,(z_f - z_a)}{(1+z_f)H(z_f)},$8

interpreted as a lower bound on the episodic lifetime rather than the total duty-cycle lifetime (Schmidt et al., 2017).

6. Forward modeling, degeneracies, and current interpretation

Detailed HeII modeling extends the observational picture by incorporating finite age, obscuration, and stochastic IGM structure into a forward model. One such study post-processes a Nyx cosmological hydrodynamical simulation at $r_k = \frac{c\,(z_f - z_a)}{(1+z_f)H(z_f)},$9, using a $r_\perp = D_A(z_f)\,\theta.$0 Mpc box, synthetic skewers through density, temperature, and velocity fields, and a fluctuating HeII UV background model. The fluctuating UV background is described as necessary because homogeneous backgrounds fail to match the observed HeII transmission statistics; the adopted model is rescaled to $r_\perp = D_A(z_f)\,\theta.$1 amplitude. Quasar radiation is then added on top of the UV background, with the light-travel-time condition

$r_\perp = D_A(z_f)\,\theta.$2

and illumination occurring only where

$r_\perp = D_A(z_f)\,\theta.$3

Anisotropy is represented with a biconical geometry parameterized by an obscured sky fraction $r_\perp = D_A(z_f)\,\theta.$4 (Schmidt et al., 2017).

The statistical formalism is fully Bayesian. For each point on a grid in $r_\perp = D_A(z_f)\,\theta.$5, the model generates 5000 skewers with random IGM density realization, UV-background fluctuation, and quasar orientation, then uses a kernel density estimate to approximate the transmission distribution. Photon counts are treated with Poisson statistics, and flat priors are adopted over $r_\perp = D_A(z_f)\,\theta.$6 to $r_\perp = D_A(z_f)\,\theta.$7 and $r_\perp = D_A(z_f)\,\theta.$8 to $r_\perp = D_A(z_f)\,\theta.$9 Myr (Schmidt et al., 2017).

Applied to the six foreground quasars with the highest implied HeII photoionization rates, the inference suggests a heterogeneous, possibly bimodal distribution of quasar emission properties. The foreground quasar associated with the classic strong HeII transmission spike is inferred to be relatively old, around $z_f$0 Myr, and weakly obscured, with $z_f$1. By contrast, three other high-$z_f$2 quasars without strong HeII spikes are inferred to be either younger than $z_f$3 Myr or highly obscured, with $z_f$4. The remaining objects admit broader or bimodal posteriors. This suggests that a single universal quasar model does not describe all systems equally well (Schmidt et al., 2017).

The main unresolved issue is therefore not whether the transverse proximity effect exists, but how to disentangle its competing drivers. In H I, the effect is entangled with overdensity and anisotropic illumination; in HeII, it is also strongly modulated by patchy UV-background structure and non-Gaussian transmission statistics. A plausible implication is that the transverse proximity effect is best regarded not as a single observable with a single interpretation, but as a family of geometrically related phenomena whose diagnostic power depends on the ionization species, the spectral resolution, the foreground-quasar selection, and the statistical treatment of stochastic sightline variance (Jalan et al., 2018, Schmidt et al., 2017, Schmidt et al., 2017).