Dating individual quasars with the HeII proximity effect
Gábor Worseck, Ilya S. Khrykin, Joseph F. Hennawi, J. Xavier Prochaska, Emanuele Paolo Farina
MMNRAS , 1–19 (2021) Preprint 6 January 2021 Compiled using MNRAS L A TEX style file v3.0
Dating individual quasars with the He II proximity effect Gábor Worseck, ★ Ilya S. Khrykin, , Joseph F. Hennawi, , J. Xavier Prochaska, , and Emanuele Paolo Farina Institut für Physik und Astronomie, Universität Potsdam, Karl-Liebknecht-Str. 24/25, D-14476 Potsdam, Germany Southern Federal University, Stachki Avenue 194, 344090, Rostov-on-Don, Russia Kavli Institute for the Physics and Mathematics of the Universe (WPI), UTIAS, The University of Tokyo, Kashiwa, Chiba 277-8583, Japan Department of Physics, University of California, Santa Barbara, CA 93106, USA Max-Planck-Institut für Astronomie, Königstuhl 17, D-69117 Heidelberg, Germany University of California - Santa Cruz, 1156 High St., Santa Cruz, CA, USA 95064 Max Planck Institut für Astrophysik, Karl–Schwarzschild–Straße 1, D-85748, Garching bei München, Germany
Accepted XXX. Received YYY; in original form ZZZ
ABSTRACT
Constraints on the time-scales of quasar activity are key to understanding the formation and growth of supermassive black holes(SMBHs), quasar triggering mechanisms, and possible feedback effects on their host galaxies. However, observational estimatesof this so-called quasar lifetime are highly uncertain ( 𝑡 Q ∼ –10 yr), because most methods are indirect and involve manymodel-dependent assumptions. Direct evidence of earlier activity is gained from the higher ionization state of the intergalacticmedium (IGM) in the quasar environs, observable as enhanced Ly 𝛼 transmission in the so-called proximity zone. Due to the ∼
30 Myr equilibration time-scale of He ii in the 𝑧 ∼ 𝑡 on ≤ 𝑡 Q , enabling up to ± . 𝑒 -folding time-scale 𝑡 S ∼
44 Myr of SMBH growth. Here we present the first statistical sample of 13accurate and precise measurements of He ii quasar proximity zone sizes from science-grade (signal-to-noise ratio (cid:38) HubbleSpace Telescope ( HST ) spectra, spanning (cid:39) (cid:39)
15 proper Mpc. Comparing these sizes to predictions from cosmologicalhydrodynamical simulations post-processed with one-dimensional radiative transfer, we infer a broad range of quasar on-timesfrom 𝑡 on (cid:46) 𝑡 on >
30 Myr that does not depend on quasar luminosity, black hole mass, or Eddington ratio. These resultspoint to episodic quasar activity over a long duty cycle, but do not rule out substantial SMBH growth during phases of radiativeinefficiency or obscuration.
Key words: intergalactic medium – quasars: absorption lines – quasars: general – quasars: supermassive black holes – darkages, reionization, first stars
Quasars are the most powerful sources of radiation that have emittedat an almost sustained high luminosity during the short (cid:46)
60 yrtime-frame accessible to modern astronomical observations (Schmidt1963). Most likely they are powered by accretion of baryons ontoSMBHs (e.g. Salpeter 1964; Lynden-Bell 1969; Rees 1984), and itis believed that past quasar phases are required to explain the 𝑀 BH = –10 𝑀 (cid:12) SMBHs found in the centres of nearby quiescent bulge-dominated galaxies (Soltan 1982; Kormendy & Richstone 1995; Yu& Tremaine 2002; Kormendy & Ho 2013). In numerical models ofgalaxy and black hole co-evolution, SMBH growth is triggered bygas inflow from major galaxy mergers (e.g. Di Matteo et al. 2005;Springel et al. 2005; Hopkins et al. 2005a,b, 2006, 2008; Capeloet al. 2015; Steinborn et al. 2018) and/or secular disc instabilities ★ E-mail: [email protected] Unless otherwise specified, we use the term “quasar” to refer to an unob-scured accreting supermassive black hole that radiates at a substantial fractionof its Eddington luminosity. (e.g. Hopkins & Quataert 2010; Novak et al. 2011; Bournaud et al.2011; Gabor & Bournaud 2013; Hopkins et al. 2016; Anglés-Alcázaret al. 2013, 2017, 2020), but the physical processes on the relevantscales (sub-pc to a few pc) are still not fully understood. In bothscenarios, kinetic and thermal feedback from stars and the SMBHself-regulate SMBH growth and obscuration. Once enough gas hasbeen expelled, the SMBH shines as a short-lived UV-bright quasaruntil feedback quenches SMBH growth, and potentially also the starformation in the host galaxy (e.g. Sanders et al. 1988; Di Matteo et al.2005; Springel et al. 2005; Hopkins et al. 2005b, 2006).Although these models successfully reproduce many observedproperties of galaxies and quasars, it remains challenging for them toexplain the prevalence of 𝑀 BH = –10 𝑀 (cid:12) SMBHs in 𝑧 em (cid:38) < yr after the Big Bang (Jiang et al. 2007; Kurket al. 2007; Mortlock et al. 2011; Venemans et al. 2013; De Rosa et al.2014; Wu et al. 2015; Mazzucchelli et al. 2017; Bañados et al. 2018;Shen et al. 2019; Wang et al. 2020; Yang et al. 2020). These earlySMBHs require either quasi-continuous Eddington-limited accretiononto massive black hole seeds (Sijacki et al. 2009; Di Matteo et al.2012; Johnson et al. 2013), super-Eddington accretion (Volonteri & © a r X i v : . [ a s t r o - ph . GA ] J a n G. Worseck et al.
Rees 2005; Pacucci et al. 2015; Inayoshi et al. 2016), or radiativelyinefficient accretion in possibly obscured phases (Madau et al. 2014;Volonteri et al. 2015; Pacucci et al. 2015; Davies et al. 2019).Constraining the characteristic time-scales governing quasar ac-tivity is key to understanding the existence of early SMBHs, quasartriggering mechanisms, and whether feedback from SMBH growthmight quench black hole fuelling and star formation. There is a grow-ing consensus from models of galaxy and black hole co-evolution thatfuelling, feedback, and quenching are intimately intertwined, whichconspire to produce episodic quasar activity on a wide range of time-scales (10 –10 yr, Ciotti & Ostriker 2001; Di Matteo et al. 2005;Hopkins et al. 2005b, 2006; Hopkins & Hernquist 2009; Hopkinset al. 2016; Novak et al. 2011; Gabor & Bournaud 2013; Steinbornet al. 2018; Anglés-Alcázar et al. 2017, 2020), often with significantvariability in the accretion rate down to the time resolution limit of thesimulation (10–100 yr, e.g. Novak et al. 2011; Anglés-Alcázar et al.2020). Such short-term changes in the accretion rate may explainwhy some quasars show strong variability in their luminosity and/ortheir emission lines on time-scales of days to decades (LaMassa et al.2015; Runnoe et al. 2016; MacLeod et al. 2016; McElroy et al. 2016;Yang et al. 2018). However, for longer time-scales the constraintsfrom observations are uncertain by several orders of magnitude (e.g.Martini 2004), because the methods (i) are necessarily more indirect,(ii) are sensitive to particular time-scales, (iii) often yield a popula-tion average, and (iv) involve many model-dependent assumptions.Comparisons of the quasar number density to their host dark matterhalo abundance inferred from quasar clustering studies constrainthe quasar duty cycle 𝑡 dc , i.e. the total time over the age of theUniverse that a galaxy hosts a quasar (Haiman & Hui 2001; Martini& Weinberg 2001). Due to varying assumptions on how quasarspopulate dark matter haloes applied to partially discrepant quasarclustering measurements at 𝑧 em ∼ yr (cid:46) 𝑡 dc (cid:46) yr, and may dependon redshift and/or luminosity (Porciani et al. 2004; Croom et al.2005; Adelberger & Steidel 2005; Shen et al. 2007; White et al.2008, 2012; Eftekharzadeh et al. 2015). Alternatively, the quasarduty cycle can be estimated by extending the Soltan (1982) argumentsuch that that the quasar luminosity function traces the gas accretionhistory onto SMBHs in present-day early-type galaxies. For present-day 𝑀 BH > 𝑀 (cid:12) SMBHs that shone as quasars at their Eddingtonlimit the inferred duty cycle is 𝑡 dc = (6–30) × yr (Yu & Tremaine2002; Marconi et al. 2004; Shankar et al. 2004). The quasar dutycycle is a population average that is insensitive to the duration ofindividual quasar episodes.The time distribution of high-accretion events, often called theepisodic quasar lifetime 𝑡 Q , can be predicted by current numericalmodels or observationally estimated based on light travel time argu-ments. It has been suggested that mismatches between the level ofnuclear activity and the ionization conditions of gas in and aroundthe host galaxies imply significant nuclear variability on time-scales 𝑡 Q ∼ . ∼
400 kpc) Ly 𝛼 nebulae around 𝑧 em ∼ 𝛼 emitters, enhanced byquasar-powered fluorescence, suggest quasar lifetimes of 1–40 Myrdepending on the emitter sample and the quasar opening angle (Adel-berger et al. 2006; Cantalupo et al. 2012; Trainor & Steidel 2013;Borisova et al. 2016; Marino et al. 2018). However, due to geometricdilution of the quasar flux, luminous Ly 𝛼 emitters at distances of several Mpc are more likely to be powered intrinsically (Khrykinet al. 2016).The quasar lifetime can also be constrained from the locally en-hanced UV radiation field in the quasar vicinity, the so-called prox-imity effect, which manifests itself as a region of enhanced IGM Ly 𝛼 transmission (e.g. Bajtlik et al. 1988; Scott et al. 2000; Dall’Aglioet al. 2008; Calverley et al. 2011). Because the IGM reacts to a changein the photoionization rate Γ within a finite equilibration time-scale 𝑡 eq ≈ Γ − , the existence of the proximity effect implies that quasarshad been emitting continuously for 𝑡 Q (cid:38) 𝑡 eq (e.g. Bajtlik et al. 1988).With an H i UV background photoionization rate Γ H i (cid:39) − s − measured in the 2 (cid:46) 𝑧 (cid:46) 𝛼 forest (Becker & Bolton 2013) oneobtains a weak lower limit 𝑡 Q (cid:38) .
03 Myr for the quasar population.During and shortly after H i reionization at 𝑧 (cid:38) .
7, the low IGMH i Ly 𝛼 transmission enables measurements of well-defined sizes ofH i proximity zones around individual quasars (Fan et al. 2006; Carilliet al. 2010; Eilers et al. 2017). The observation of any particularquasar is only sensitive to the time the quasar had been active priorto our observation at a random point during its current luminousepisode, henceforth called the on-time 𝑡 on ≤ 𝑡 Q . From their verysmall proximity zones given their luminosity, Eilers et al. (2020)concluded that 5–10 per cent of all 𝑧 em ∼ 𝑡 on (cid:46) . 𝛼 emission around them (Farina et al. 2019). However,because H i quickly equilibrates after quasar turn-on, 𝑧 em ∼ 𝑡 on > . 𝑧 ∼ 𝛼 forest dueto overdense environments around quasar hosts, quasar obscuration,and the small quasar boost to the overall H i photoionization rate (e.g.Liske & Williger 2001; Croft 2004; Hennawi & Prochaska 2007;Kirkman & Tytler 2008; Prochaska et al. 2013, but see Gonçalveset al. 2008). The low UV background in the post-reionization IGMincreases the chance to discover the transverse proximity effect inthe H i ( 𝑡 on >
11 Myr, Gallerani et al. 2008) and the He ii Ly 𝛼 forest ( 𝑡 on (cid:38) 𝑡 on <
10 Myr) orobscuration (Schmidt et al. 2018).Direct estimates of prolonged quasar activity can be inferred fromthe line-of-sight He ii proximity zones of 𝑧 em (cid:39) 𝑡 eq ≈ Γ − (cid:39)
30 Myr (Khrykin et al. 2016).This is comparable to the 𝑒 -folding time-scale of SMBH growth 𝑡 S ∼
44 Myr (Salpeter 1964), and may offer unique constraints onthe range of episodic quasar lifetimes in models of galaxy and blackhole co-evolution. In Khrykin et al. (2019, hereafter Paper I) weintroduced a new statistical Bayesian method to infer on-times ofindividual quasars from their He ii proximity zones, accounting forthe degeneracy between the initial ambient IGM He ii fraction andthe quasar on-time that had affected previous analyses (Syphers &Shull 2014; Zheng et al. 2015). Applying our method to six He ii-transparent quasars at 𝑧 em > . . 𝑡 on (cid:39) . . ∼ . < 𝑧 em < . MNRAS000
44 Myr (Salpeter 1964), and may offer unique constraints onthe range of episodic quasar lifetimes in models of galaxy and blackhole co-evolution. In Khrykin et al. (2019, hereafter Paper I) weintroduced a new statistical Bayesian method to infer on-times ofindividual quasars from their He ii proximity zones, accounting forthe degeneracy between the initial ambient IGM He ii fraction andthe quasar on-time that had affected previous analyses (Syphers &Shull 2014; Zheng et al. 2015). Applying our method to six He ii-transparent quasars at 𝑧 em > . . 𝑡 on (cid:39) . . ∼ . < 𝑧 em < . MNRAS000 , 1–19 (2021) ating individual quasars with the He II proximity effect He ii-transparent quasars, twelve of which have accurate and precisesystemic redshifts. In Section 2 we describe our observations andthe relevant parameters of our quasar sample. We present measure-ments of the He ii proximity zone sizes in Section 3. In Section 4we summarize our numerical model, before reporting on the inferredindividual quasar on-times and their relation to quasar propertiesin Section 5. We discuss our results and remaining uncertainties inSection 6, before concluding in Section 7.We assume a flat Λ CDM cosmology with dimensionless Hubbleconstant ℎ = . 𝐻 = ℎ km s − Mpc − ), density parameters ( Ω m , Ω b , Ω Λ ) = ( . , . , . ) for total matter, baryons, andcosmological constant, a linear dark matter power spectrum ampli-tude on a scale of 8 ℎ − comoving Mpc 𝜎 = .
8, a spectral indexof density perturbations 𝑛 𝑠 = .
96, and a helium mass fraction 𝑌 = .
24, consistent with Planck Collaboration et al. (2020). Properdistances are quoted explicitly in proper Mpc (pMpc). II PROXIMITY ZONES2.1
HST /COS spectra of He ii proximity zones
We use the
HST
UV spectra of seventeen out of twenty 𝑧 em < . 𝑧 em (cid:39) + + + 𝛼 contamination of the He ii quasar proximity zone. For two 𝑧 em (cid:39) .
94 quasars (SDSS J0818 + + HST ’s orbital shadow to exclude contamina-tion of their He ii proximity zones by geocoronal N i 𝜆 𝑧 em (cid:39) .
28 quasars (HE2QS J1706 + − − − + 𝑧 = . HST spectra were taken with the Cosmic Origins Spectro-graph (COS; Green et al. 2012), employing the G140L grating (12spectra) or the G130M grating (5 spectra). Their resolving power 𝑅 = 𝜆 / Δ 𝜆 varies with wavelength and with the spatial positionon the detector. Table 1 lists the appropriate values in the spectralrange of interest. The spectra were rebinned to 2–3 pixels per reso-lution element ( 𝑅 < (cid:39) .
24 Å pixel − , 10000 ≤ 𝑅 ≤ (cid:39) .
04 Å pixel − , 𝑅 > (cid:39) .
03 Å pixel − ), yielding a signal-to-noise ratio S/N = 𝑓 𝜆 ∝ 𝜆 𝛽 , fitted to spectral regions without strongemission and absorption features, but accounting for identified par-tial H i Lyman limit breaks (Worseck et al. 2019). Since our samplelacks contemporaneous and continuous spectral coverage from therest-frame extreme UV to the near UV, a detailed correction for cu-mulative H i Lyman continuum attenuation is not possible. As such,the fitted power laws do not represent the intrinsic quasar spectral en-ergy distributions (SEDs). The typical continuum error of a few percent does not affect our analysis. We do not account for quasar He iiLy 𝛼 and metal emission that is difficult to predict in detail in quasaraccretion disc models (e.g. Syphers et al. 2011a; Syphers & Shull2013). Only two quasars (SDSS J0936 + − 𝛼 absorption.Together with the seven 𝑧 em > . We obtained near-infrared spectra of 14 quasars (two from Paper I andtwelve from Table 1) to accurately measure their redshifts from theirnear-UV and optical emission lines. We successfully observed tenquasars with the Triple Spectrograph (TripleSpec, wavelength cover-age 1 . . 𝜇 m at 𝑅 ∼ + .
625 to2 . (Prochaska & Hennawi2009). Wavelength solutions were computed from OH sky emissionlines, and heliocentric corrections were applied. For all spectra, rel-ative fluxing was performed with a telluric standard star observedclose in time and in airmass to the science target. In the TripleSpecsample the S/N per 91 . − pixel ranges from 6 to 50 near thequasar emission lines of interest.Near-infrared spectra of two further quasars were successfully ob-tained with the Large Binocular Telescope Utility Cameras in theInfrared 1 and 2 (LUCI1/2; Seifert et al. 2003) in January 2014. Weused the N1 . + . . 𝜇 m and the 0 . (cid:48)(cid:48) slit ( 𝑅 ∼ + . . 𝜇 mand the 0 . (cid:48)(cid:48) slit ( 𝑅 ∼ routines. Each exposure was flat fielded andcleaned of cosmic ray hits using the procedure described in vanDokkum (2001). Wavelength calibration was achieved by matchingthe position of OH sky lines in the two-dimensional spectra, and skysubtraction was performed by subtracting subsequent pairs of framesthat had been taken in a standard ABBA dithering pattern. Relativeflux calibration and telluric correction of the extracted spectra wasperformed with A0V stars observed immediately after the sciencetargets. In the wavelength range of interest the LUCI1 (LUCI2) spec-trum of HS 1024 + + =
10 (S/N = .
13 Å (2 .
67 Å) pixel.HE2QS J1630 + . . 𝜇 m with the medium-resolution grating and the 0 . (cid:48)(cid:48) slit( 𝑅 ∼ . (cid:39)
15 per (cid:39) .
18 Å pixel. IRAF (Tody 1993) is distributed by the National Optical Astronomy Obser-vatory, which is operated by the Association of Universities for Research inAstronomy under a cooperative agreement with the National Science Foun-dation. MNRAS , 1–19 (2021)
G. Worseck et al.
Table 1.
Our sample of 17 quasars with He ii proximity zones, grouped by proximity zone size (Figs. 1 and 2). We list the name, position,
HST /COS resolvingpower and signal-to-noise ratio near He ii Ly 𝛼 in the quasar rest frame, quasar redshift, velocity (redshift) uncertainty, emission line and instrument for redshiftmeasurement, SDSS or Pan-STARRS1 𝑖 band magnitude corrected for Galactic extinction, absolute magnitude at 1450 Å rest frame, He ii-ionizing photonproduction rate 𝑄 , measured proximity zone size 𝑅 pz , and inferred quasar on-time 𝑡 on . Quasar R.A. Decl. 𝑅 S / N 𝑎 𝑧 em 𝜎 𝑣 Line Instrument 𝑚 𝑖 𝑀 log 𝑄𝑠 − 𝑅 pz 𝑡 on (J2000) (J2000) kms − mag mag pMpc MyrHE 2347 − h m . s − ◦ (cid:48) . (cid:48)(cid:48) . . [Oiii] FIRE – 𝑏 − . 𝑏 . − . ± . –SDSS J0818 + h m . s + ◦ (cid:48) . (cid:48)(cid:48) . Civ BOSS . − .
93 56 .
38 2 . ± . < . SDSS J1237 + h m . s + ◦ (cid:48) . (cid:48)(cid:48) . Mgii TripleSpec . − .
66 56 .
27 1 . ± . < . HE2QS J2149 − h m . s − ◦ (cid:48) . (cid:48)(cid:48) . Civ CAFOS . − .
83 56 . − . ± . < . HE2QS J1706 + h m . s + ◦ (cid:48) . (cid:48)(cid:48) . Civ CAFOS . − .
66 56 . − . ± . < . HE2QS J0233 − h m . s − ◦ (cid:48) . (cid:48)(cid:48) . Civ CAFOS . − .
17 56 .
47 4 . ± . < . HS 0911 + h m . s + ◦ (cid:48) . (cid:48)(cid:48) . H 𝛽 LUCI2 . − .
84 56 .
74 4 . ± .
19 1 . + . − . HE2QS J0916 + h m . s + ◦ (cid:48) . (cid:48)(cid:48) . Civ CAFOS . − .
12 56 .
45 3 . ± . < . SDSS J2346 − h m . s − ◦ (cid:48) . (cid:48)(cid:48) . Mgii TripleSpec . − .
97 56 .
79 2 . ± .
77 0 . + . − . HS 1700 + h m . s + ◦ (cid:48) . (cid:48)(cid:48) . Mgii TripleSpec . − .
33 57 .
34 7 . ± .
01 0 . + . − . HS 1024 + h m . s + ◦ (cid:48) . (cid:48)(cid:48) . Mgii LUCI1 . − .
54 56 .
62 9 . ± .
97 9 . + . − . Q 1602 + h m . s + ◦ (cid:48) . (cid:48)(cid:48) . Mgii TripleSpec . − .
99 56 .
80 6 . ± .
97 1 . + . − . PC 0058 + h m . s + ◦ (cid:48) . (cid:48)(cid:48) . Mgii TripleSpec . − .
46 56 .
19 7 . ± . > . SDSS J0936 + h m . s + ◦ (cid:48) . (cid:48)(cid:48) . . [Oiii] TripleSpec . − .
20 56 .
49 8 . ± .
15 11 . + . − . HE2QS J2157 + h m . s + ◦ (cid:48) . (cid:48)(cid:48) . . [Oiii] TripleSpec . − .
77 56 .
72 17 . ± . > . Q 0302 − h m . s − ◦ (cid:48) . (cid:48)(cid:48) . . [Oiii] TripleSpec . − .
21 56 .
89 13 . ± . > . SDSS J1253 + h m . s + ◦ (cid:48) . (cid:48)(cid:48) . . [Oiii] TripleSpec . − .
19 56 .
48 11 . ± . > . 𝑎 Signal-to-noise ratio per pixel near Heii Ly 𝛼 ( 𝑅 < : (cid:39) . Åpixel − , ≤ 𝑅 ≤ : (cid:39) . Åpixel − , 𝑅 > : (cid:39) . Åpixel − ). 𝑏 For HE 2347 − 𝑚 = . from its VLT/FORS2 spectrum calibrated to 𝐵 Vega = . (Worseck et al. 2008). For the quasar HE 2347 − 𝑅 ∼ . (cid:39)
40 per 12 . − pixel in the wavelength range of interest. The remaining quasars from our sample (5 from Paper I and 5 fromTable 1) have only optical spectra available, which cover their rest-frame far-UV emission lines. For four quasars from Table 1 we use 𝑅 ∼
200 discovery spectra taken with Calar Alto Faint Object Spec-trograph (CAFOS) at the Calar Alto 2 . − − + . (cid:48)(cid:48) slit, 𝑅 ∼ , ∼
60 per 2 . − pixelin the H i proximity region. SDSS J1319+5202 was observed with theKeck Echelette Spectrograph and Imager (ESI; Sheinis et al. 2002)using the 0 . (cid:48)(cid:48) slit ( 𝑅 ∼ ∼
60 per 10 km s − pixel. The H i proximity region of SDSS J1237 + ∼ . − pixel. The VLT and Keck spectra of HE 2347 − − Quasar redshifts were determined from UV-optical quasar emissionlines covered in the available optical and near-infrared spectra, ac-counting for their velocity shifts relative to systemic (traced by [O ii]emission or Ca ii absorption). The velocity shifts are due to bulkmotions in the quasar broad line region, with high-ionization linesshowing a strong dependence of the blueshift on the continuum lu-minosity (e.g. Gaskell 1982; Tytler & Fan 1992; Vanden Berk et al.2001; Richards et al. 2002, 2011; Hewett & Wild 2010; Shen et al.2016). We measured the mode of each emission line using the al-gorithm described in Hennawi et al. (2006), which accounts for lineblending (in particular C iv 𝜆 𝜆 𝛽 𝜆 𝜆𝜆 , > 𝜎 𝑣 of the velocity distributions in large quasarsamples (Richards et al. 2002; Boroson 2005; Richards et al. 2011;Shen et al. 2016). The redshift precision was our primary criterionfor the eventually adopted emission line and redshift in Table 1:(i) We preferred redshifts from detected narrow [O iii] 𝜆 >
10 across the line, peak to continuum ratio > .
3, 5quasars in Table 1). We assumed a luminosity-independent blueshiftof − . − w.r.t. the systemic frame, and assigned a velocityprecision 𝜎 𝑣 = . − based on the high-confidence sample inBoroson (2005), in good agreement with Hewett & Wild (2010) andShen et al. (2016).(ii) If [O iii] was not covered or not detected due to low S/N orthe Baldwin effect (e.g. Baldwin 1977; Stern & Laor 2012; Shen& Ho 2014; Shen 2016), we took broad Mg ii if the line was de-tected at S/N >
10 (6 quasars). We assumed a luminosity-independentblueshift of − . − , and a velocity precision 𝜎 𝑣 =
273 km s − propagated from the [O iii] velocity precision and the Mg ii velocitydistribution from Richards et al. (2002). These values are consistentwith more recent determinations (Hewett & Wild 2010; Shen 2016;Shen et al. 2016). MNRAS000
273 km s − propagated from the [O iii] velocity precision and the Mg ii velocitydistribution from Richards et al. (2002). These values are consistentwith more recent determinations (Hewett & Wild 2010; Shen 2016;Shen et al. 2016). MNRAS000 , 1–19 (2021) ating individual quasars with the He II proximity effect Table 2.
He ii-transparent quasars with measured systemic (Mg ii, H 𝛽 , H 𝛾 ,[O iii] or combinations thereof) redshifts 𝑧 lit from the literature. Quasar 𝑧 em 𝑧 lit ReferenceHS 1700 + . ± . . ± . Trainor & Steidel (2012)HE 2347 − . ± . . Syphers et al. (2011b) . ± . Shull & Danforth (2020)Q 0302 − . ± . . ± . Syphers & Shull (2014) . ± . Shen (2016) . Zuo et al. (2015) . Coatman et al. (2017)SDSS J1253 + . ± . . Coatman et al. (2017)SDSS J2346 − . ± . . ± . Zheng et al. (2015) . Zuo et al. (2015) (iii) If neither [O iii] nor Mg ii was usable, but broad H 𝛽 had beencovered in our 𝐾 band spectra, we took the H 𝛽 line, which reasonablytraces the systemic frame. We adopted a blueshift of −
109 km s − and a velocity precision 𝜎 𝑣 =
400 km s − (Shen et al. 2016). Onequasar from Table 1 and two quasars from Paper I have H 𝛽 redshifts.(iv) For the 10 quasars lacking near-infrared spectra of sufficientquality we measured the redshift from C iv covered in the opticalspectra. We corrected for the known correlation of the C iv blueshiftwith continuum luminosity (Hewett & Wild 2010; Richards et al.2011; Shen et al. 2016) using a sample of lower-redshift BOSSquasar spectra covering C iv and Mg ii (see Paper I for details). Ourdetermined blueshift w.r.t. Mg ii Δ 𝑣 = (cid:34) − . − . (cid:32) × 𝐿 𝜆, erg s − (cid:33)(cid:35) km s − (1)is in reasonable agreement with the independent determination byShen et al. (2016) for a distinct sample and line centring algorithm.Considering the large standard deviation 𝜎 𝑣 =
656 km s − of the cor-rected C iv redshifts w.r.t. the Mg ii redshifts, we ignored the smallerspread of the Mg ii redshifts about the systemic frame (Paper I).For all five He ii-transparent quasars with previous systemic red-shift determinations (Mg ii, H 𝛽 , H 𝛾 and/or [O iii]) from the literatureour results are broadly consistent, in spite of differences in the em-ployed methods (Table 2). The main sources of discrepancy are thetreatment of line asymmetries and the averaging of results for multi-ple emission lines. Optical photometry of the quasars was mainly obtained fromSDSS Data Release 12 (Alam et al. 2015), with the exception ofHE2QS J2311 − − − 𝑖 band point-spread-function AB magnitude 𝑚 𝑖 as 𝑀 ( 𝑧 em ) = 𝑚 𝑖 − (cid:18) 𝑑 𝐿 ( 𝑧 em ) Mpc (cid:19) − − 𝐾 ( 𝑧 em ) , (2)with the luminosity distance 𝑑 𝐿 in our adopted cosmology, and thebandpass correction 𝐾 that was obtained by scaling the Lusso et al.(2015) quasar UV SED to the 𝑖 band flux (Kulkarni et al. 2019). Thelatter assumption was necessary due to inaccurate relative fluxing ofmany of our HE2QS discovery spectra, and we estimate an error of0 . 𝑀 . We used the Lusso et al. (2015) SED to estimatethe quasar flux density at the H i Lyman limit 𝑓 𝜈, . Assuming a power-law SED 𝑓 𝜈 ∝ 𝜈 − 𝛼 𝜈 at frequencies 𝜈 > 𝜈 = . × Hz, the total He ii-ionizing photon production rate is 𝑄 = 𝜋𝑑 𝐿 ( + 𝑧 em ) ∫ ∞ 𝜈 𝑓 𝜈 ℎ P 𝜈 d 𝜈 = 𝜋𝑑 𝐿 ( + 𝑧 em ) − 𝛼 𝜈 𝑓 𝜈, ℎ P 𝛼 𝜈 , (3)with Planck’s constant ℎ P and the He ii Lyman limit frequency 𝜈 = 𝜈 .Due to cumulative IGM absorption by H i Lyman limit systems(e.g. Worseck & Prochaska 2011) and the He ii Lyman series, theHe ii-ionizing power has to be inferred by extrapolation of the SED.As in Paper I we assumed a power-law SED slope 𝛼 𝜈 = . 𝜈 > 𝜈 , consistent with recent measurements in stacked and com-posite quasar spectra (Shull et al. 2012; Stevans et al. 2014; Lussoet al. 2015). Since the actual value of 𝛼 𝜈 depends on the chosencontinuum windows, the total spectral coverage, and the exclusionof weak quasar emission lines (Stevans et al. 2014; Tilton et al.2016), the large range in 𝛼 𝜈 values from the literature is not sur-prising. SED reconstructions for two He ii-transmitting quasars withcomplete spectral coverage indicate quasar-to-quasar variations in 𝛼 𝜈 around our chosen value (Syphers & Shull 2013, 2014). A veryhard SED ( 𝛼 𝜈 = .
7; Tilton et al. 2016) increases 𝑄 by a factor 6 . 𝛼 𝜈 (cid:38)
2; Lusso et al.2018) are ruled out by the
HST /COS spectra, and would lead to amodest ∼ . 𝜈 > 𝜈 do not significantly change ourresults (Khrykin et al. 2016, 2019).Equation (3) assumes that the escape fraction of He ii-ionizingphotons is unity. Recently, Shull & Danforth (2020) have suggestedthat many quasars could have smaller escape fractions based on theobserved range in the IGM He ii/H i column density ratio. However,these observations are likely explained by radiative transfer in theIGM and the contribution of star-forming galaxies to the H i-ionizingbackground (e.g. Haardt & Madau 2012; Khaire & Srianand 2019;Puchwein et al. 2019; Faucher-Giguère 2020). Since the requiredsample-averaged H i Lyman continuum escape fraction of galaxies is ∼ 𝑧 ∼
3, which is within recent observational constraints(Grazian et al. 2017; Steidel et al. 2018; Fletcher et al. 2019), theHe ii/H i column density ratio does not uniquely constrain the He ii-ionizing escape fraction of unobscured quasars.
For the subset of 14 quasars with coverage of Mg ii or H 𝛽 emissionin their near-infrared spectra, single-epoch virial black hole masseswere estimated from scaling relationslog (cid:18) 𝑀 BH 𝑀 (cid:12) (cid:19) = 𝑎 + 𝑏 log (cid:18) 𝜆 c 𝐿 𝜆,𝜆 c erg s − (cid:19) + (cid:18) FWHMkm s − (cid:19) , (4)with ( 𝜆 c , 𝑎, 𝑏 ) = ( , . , . ) for Mg ii (Vestergaard & Osmer2009) and ( 𝜆 c , 𝑎, 𝑏 ) = ( , . , . ) for H 𝛽 (Vestergaard &Peterson 2006).Due to the varying spectral coverage and quality, measurements ofthe full width at half maximum (FWHM) of Mg (H 𝛽 ) were made for10 (6) quasars. We adopt the H 𝛽 measurements when available. Ta-ble 3 lists the measurements and the derived quantities. The spectrawere iteratively fit with a combination of a local power-law contin-uum, the Tsuzuki et al. (2006) Fe ii emission template, and Gaussianemission line profiles. Due to the modest S/N, a single Gaussianwas considered sufficient for most Mg ii lines. Each H 𝛽 emissionline was decomposed into one narrow and two broad Gaussians, MNRAS , 1–19 (2021)
G. Worseck et al.
Table 3.
Estimated black hole masses 𝑀 BH and Eddington ratios 𝐿 bol / 𝐿 Edd for the 14 quasars with measured FWHM of Mg ii or H 𝛽 decomposed into 𝑛 G Gaussian profiles. All quoted errors are 1 𝜎 statistical uncertainties. Quasar Line 𝑛 G FWHM log (cid:16) 𝑀 BH 𝑀 (cid:12) (cid:17) log (cid:16) 𝐿 bol 𝐿 Edd (cid:17) kms − HE 2347 − ±
19 9 . ± . − . ± . HS 1700 + ±
91 9 . ± .
10 0 . ± . HS 1024 + ±
415 9 . ± . − . ± . Q 1602 +
576 Mgii 1 ±
91 9 . ± .
11 0 . ± . PC 0058 + ±
320 9 . ± . − . ± . SDSS J0936 + ±
92 9 . ± .
10 0 . ± . SDSS J1237 + ±
274 8 . ± .
15 0 . ± . SDSS J2346 − ±
137 9 . ± . − . ± . Q 0302 −
003 H 𝛽 ±
320 9 . ± .
14 0 . ± . HE2QS J2157 + 𝛽 ±
324 9 . ± . − . ± . HS 0911 + 𝛽 ± . ± .
32 0 . ± . SDSS J1253 + 𝛽 ± . ± . − . ± . HE2QS J1630 + 𝛽 ±
230 9 . ± . − . ± . SDSS J1319 + 𝛽 ±
867 9 . ± . − . ± . and the nearby [O iii] doublet was considered simultaneously withtwo Gaussians for each line of the doublet. Bayesian joint posteriordistributions of the degenerate line parameters were estimated us-ing the Goodman & Weare (2010) affine-invariant ensemble samplerfor Markov Chain Monte Carlo (MCMC) as implemented in emcee (Foreman-Mackey et al. 2013). From the Mg ii and H 𝛽 broad lineparameter posterior distributions we computed the FWHM posteriorprobability density functions (PDFs), and adopt their median valuesand their equal-tailed 68 per cent credible intervals as our measure-ments and statistical uncertainties, respectively. Due to the inaccuratefluxing of the near-infrared spectra, the continuum luminosities at 𝜆 c were estimated from 𝑀 by extrapolating the Lusso et al. (2015)power-law continuum 𝑓 𝜈 ∝ 𝜈 − . , and assuming an uncertainty of0 . 𝑀 BH are much smallerthan the (cid:39) .
55 dex uncertainty in the scaling relations, as estimatedfrom the scatter of quasars with black hole masses from reverberationmapping (Vestergaard & Peterson 2006; Vestergaard & Osmer 2009;Shen 2013). Other scaling relations yield similar values to within 0 . . (cid:39) . 𝛽 FWHM measurements we obtained comparable virial blackhole masses.Bolometric luminosities were estimated with the bolometric cor-rection at 1450 Å from Runnoe et al. (2012)log (cid:18) 𝐿 bol erg s − (cid:19) = . + .
91 log (cid:32) × 𝐿 𝜆, erg s − (cid:33) − . , (5)where the last term is their advocated correction of the biased viewingangle onto the quasar accretion disc. In a fully ionized primordialhydrogen and helium plasma the Eddington luminosity of a quasaris (Shapiro 2005; Madau et al. 2014) 𝐿 Edd = 𝜋𝐺𝑐𝑚 p 𝜎 T ( − 𝑌 / ) 𝑀 BH = . × (cid:18) 𝑀 BH 𝑀 (cid:12) (cid:19) erg s − , (6)where 𝑚 p is the proton mass, 𝜎 T is the Thomson scattering crosssection, and natural constants are written in their usual symbols. We note that in the literature, most expressions for the quasar Eddingtonluminosity incorrectly assume a pure hydrogen plasma.
Expressing Equation (5) in magnitudes, the logarithmic Eddingtonratio islog (cid:18) 𝐿 bol 𝐿 Edd (cid:19) = − . 𝑀 − log (cid:18) 𝑀 BH 𝑀 (cid:12) (cid:19) − . . (7)Again, the statistical uncertainties in the Eddington ratios listed in Ta-ble 3 are smaller than the (cid:39) .
55 dex systematic uncertainty inducedby the virial black hole mass scaling relations. II PROXIMITY ZONE SIZES
In the quasar proximity zone the gas is more highly ionized, visiblein the spectrum as excess Ly 𝛼 transmission. One wishes to robustlyquantify its extent while limiting the impact of small-scale densityfluctuations and observational effects in heterogeneous samples, suchas differences in spectral resolution and S/N. To that aim, we adopteda procedure similar to work on H i quasar proximity zones at 𝑧 em ∼ HST /COS spectra with a Gaussian filterwith an FWHM of 1 pMpc at the respective quasar redshift. Thesmoothing FWHM corresponds to 4 . . .
24 Å pixel − . The proximity zone size 𝑅 pz is thendefined as the cosmological proper distance to the first pixel wherethe smoothed normalized flux drops below 0 .
1. At 𝑧 > 𝛼 transmission on similar scales rarely exceeds thisthreshold (Worseck et al. 2016, 2019), such that the He ii proximityzones are well defined. At lower redshifts the He ii proximity zonesizes become less distinct due to the emerging post-reionization He iiLy 𝛼 forest. However, our radiative transfer simulations (Section 4.1)account for density fluctuations in a predominantly ionized IGMwith an initial He ii fraction as low as 1 per cent, consistent withthe inferences from the He ii Ly 𝛼 forest (Worseck et al. 2019). Fur-thermore, we verified with realistic mock spectra that our HST /COSspectra are of sufficient quality to yield robust proximity zone sizes(Appendix A). Consequently, our quoted uncertainties 𝜎 𝑅 pz on theproximity zone sizes are based on the individual quasar redshift un-certainties, ranging from ∼ . (cid:39) 𝑅 pz . We also showthe spectral regions of the UV-optical emission lines used to deter-mine their systemic redshifts. The smoothed normalized flux dropssignificantly within several proper Mpc of each quasar, which a pos-teriori justifies our chosen smoothing scale. The flux shows somecontamination from unrelated low-redshift absorption (e.g. at nega-tive distances in Fig. 1 and 2), but this contamination is very unlikelyto affect the measurements of He ii proximity zone sizes. We seestrong diversity in the proximity zone sizes and flux profiles. MostHe ii proximity zones show structure due to IGM density fluctua-tions and radiative transfer effects, both of which have been probedwith high-resolution optical spectra of the coeval H i Ly 𝛼 absorption(Reimers et al. 1997; Hogan et al. 1997; Anderson et al. 1999; Heapet al. 2000; Smette et al. 2002; Fechner & Reimers 2007; Shull et al.2010; Syphers & Shull 2013, 2014; Zheng et al. 2019).The accurate and precise redshifts of all quasars plotted in Fig. 2suggest that large He ii proximity zone sizes 𝑅 pz > − + MNRAS , 1–19 (2021) ating individual quasars with the He II proximity effect R pz HE 2347 − z em = 2 . ± . M = − . R pz = ( − . ± .
15) pMpc z line = 2 . z em = 2 . R pz HE2QS J2149 − z em = 3 . ± . M = − . R pz = ( − . ± .
04) pMpc z line = 3 . z em = 3 . R pz HE2QS J1706+5904 z em = 3 . ± . M = − . R pz = ( − . ± .
03) pMpc z line = 3 . z em = 3 . R pz SDSS J1237+0126 z em = 3 . ± . M = − . R pz = (1 . ± .
87) pMpc z line = 3 . z em = 3 . R pz SDSS J2346 − z em = 3 . ± . M = − . R pz = (2 . ± .
77) pMpc z line = 3 . z em = 3 . R pz SDSS J0818+4908 z em = 2 . ± . M = − . R pz = (2 . ± .
25) pMpc z line = 2 . z em = 2 . R pz HE2QS J0916+2408 z em = 3 . ± . M = − . R pz = (3 . ± .
91) pMpc z line = 3 . z em = 3 . R pz HS 0911+4809 z em = 3 . ± . M = − . R pz = (4 . ± .
19) pMpc z line = 3 . z em =3.3500 H β − N o r m a li ze d Q u a s a r F l u x D e n s i t y R pz HE2QS J0233 − z em = 3 . ± . M = − . R pz = (4 . ± .
98) pMpc − − ] 010 F l u x D e n s i t y [ A r b i t r a r y U n i t s ] z line = 3 . z em = 3 . Figure 1.
Left:
Normalized
HST /COS spectra (grey; overplotted error bars are statistical 1 𝜎 Poisson errors) of nine quasars from Table 1 with measuredsmall He ii proximity zone sizes 𝑅 pz < 𝛼 transition relative to the quasar at the estimated systemic redshift 𝑧 em . Absorption at distances (cid:28) = 𝑅 pz , defined as the position where the smoothed flux falls below 0 . Right:
Spectral regions of the labelledquasar emission lines used to estimate the systemic redshifts. The flux density is shown in black, whereas the grey lines show the corresponding 1 𝜎 error array.Vertical dashed lines mark the measured mode of the emission lines, yielding the emission line redshifts 𝑧 line . The vertical solid lines mark the applied velocityoffsets to estimate the systemic redshifts 𝑧 em . MNRAS , 1–19 (2021) G. Worseck et al. R pz Q 1602+576 z em = 2 . ± . M = − . R pz = (6 . ± .
97) pMpc z line = 2 . z em = 2 . R pz PC 0058+0215 z em = 2 . ± . M = − . R pz = (7 . ± .
97) pMpc z line = 2 . z em = 2 . R pz HS 1700+6416 z em = 2 . ± . M = − . R pz = (7 . ± .
01) pMpc z line = 2 . z em = 2 . R pz SDSS J0936+2927 z em = 2 . ± . M = − . R pz = (8 . ± .
15) pMpc z line = 2 . z em = 2 . R pz HS 1024+1849 z em = 2 . ± . M = − . R pz = (9 . ± .
97) pMpc z line = 2 . z em =2.8521 Mg II R pz SDSS J1253+6817 z em = 3 . ± . M = − . R pz = (11 . ± .
12) pMpc z line = 3 . z em = 3 . R pz Q 0302 − z em = 3 . ± . M = − . R pz = (13 . ± .
13) pMpc z line = 3 . z em = 3 . − N o r m a li ze d Q u a s a r F l u x D e n s i t y R pz HE2QS J2157+2330 z em = 3 . ± . M = − . R pz = (17 . ± .
14) pMpc − − ] 0510 F l u x D e n s i t y [ A r b i t r a r y U n i t s ] z line = 3 . z em = 3 . Figure 2.
Similar to Fig. 1 for eight quasars with large He ii proximity zone sizes 𝑅 pz > and HE2QS J0916 + − 𝑅 pz < 𝜎 𝑣 ≤
400 km s − corresponding to 𝜎 𝑅 pz < . − − 𝑡 on < 𝑧 em = . ± . ∼ − onto the circumnuclearregion (Fig. 3), and even higher velocities if the gas resides in thecircumgalactic medium of the host galaxy. Redshift space distor-tions (Hui et al. 1997; Weinberg et al. 1997) significantly affect theHe ii transmission profile, possibly masking the He ii proximity ef-fect altogether. Conclusive evidence for or against HE 2347 − MNRAS000
400 km s − corresponding to 𝜎 𝑅 pz < . − − 𝑡 on < 𝑧 em = . ± . ∼ − onto the circumnuclearregion (Fig. 3), and even higher velocities if the gas resides in thecircumgalactic medium of the host galaxy. Redshift space distor-tions (Hui et al. 1997; Weinberg et al. 1997) significantly affect theHe ii transmission profile, possibly masking the He ii proximity ef-fect altogether. Conclusive evidence for or against HE 2347 − MNRAS000 , 1–19 (2021) ating individual quasars with the He II proximity effect v pz HE 2347 − v pz SDSS J1237+0126
N V at v = 5312 km/sN V at v = 5481 km/s v pz SDSS J2346 − v pz HS 0911+4809 − − − − ]01 T r a n s m i ss i o n v pz SDSS J1319+5202
Figure 3.
Normalized
HST /COS UV spectra (grey) and optical spectra (green) of the five quasars with sufficiently precise redshifts ( 𝜎 𝑣 ≤
400 km s − ; violetsquare with error bar) to measure small He ii proximity zones ( 𝑅 pz < 𝑣 < 𝑣 pz of the He ii proximity zone. Notethe different resolving powers for the H i spectra (SDSS J1319 + 𝑅 ∼ 𝑅 ∼ ,
000 otherwise) and the He ii spectra (HE 2347 − 𝑅 (cid:39) , + 𝑅 (cid:39) , 𝑅 (cid:39) associated with the quasar or its host galaxy, which is outside thescope of this work. Because of the extreme peculiar gas velocitiesthat are not represented in our simulations (Section 4.1), we excludeHE 2347 − + 𝑣 (cid:39)
500 km s − that is likely responsible for its small measured He iiproximity zone. No high-velocity infall is detected. The He ii trans-mission at 1500–2200 km s − may belong to the proximity zone.However, provided that our simulations approximately capture thedensity and velocity field around the quasar host halo, our strict andsimple definition of 𝑅 pz ensures a one-to-one comparison to ourmodels (Section 4.1) that include cases of misestimated proximityzone sizes due to the density field and peculiar velocities, similarto recent work on 𝑧 em ∼ − may eitherindicate a much larger proximity zone of SDSS J1237 + − + + 𝑣 (cid:39) −
900 km s − with strong asso-ciated C iv and N v in two components. The complex does not affectthe measurement of 𝑅 pz because the H i absorption in the rest of theproximity zone is much lower than expected for the 𝑧 (cid:39) . 𝛼 forest. In summary, except for the peculiar quasar HE 2347 − − − To explain the diversity in the measured proximity zone sizes and toinfer the on-times of the quasars, we used a combination of hydrody-namical simulations and one-dimensional radiative transfer simula-tions of He ii quasar proximity zones, described in detail in Khrykinet al. (2016, 2017). For their cosmological setting, we used the out-put of a Gadget-3 (Springel 2005) smooth particle hydrodynamicssimulation run in a cubic volume of ( ℎ − ) comoving Mpc con-taining 512 baryonic and dark matter particles, respectively. Us-ing periodic boundary conditions, we drew 1000 one-dimensionaldensity, velocity, and temperature distributions (skewers) in randomdirections around the most massive halo in the 𝑧 sim = . 𝑧 sim and the quasar redshifts (Table 1), we ac-counted for density evolution by rescaling the gas densities by a factor ( + 𝑧 em ) /( + 𝑧 sim ) . The resulting skewers have a length of 160 co- MNRAS , 1–19 (2021) G. Worseck et al. R sim t on = 1 Myr x HeII , = 0 . R sim = 10 .
45 pMpc R sim t on = 1 Myr x HeII , = 1 . R sim = 4 .
29 pMpc R sim t on = 10 Myr x HeII , = 0 . R sim = 21 .
44 pMpc R sim t on = 1 Myr x HeII , = 0 . R sim = 6 .
90 pMpc H e II T r a n s m i ss i o n R sim t on = 100 Myr x HeII , = 0 . R sim = 21 .
50 pMpc R sim t on = 1 Myr x HeII , = 0 . R sim = 10 .
45 pMpc
Figure 4.
Examples of He ii transmission spectra from our one-dimensional radiative transfer models of Q 1602 +
576 ( 𝑧 em = . 𝑀 = − . 𝑄 = . s − ). Resolved (smoothed) spectra are shown in grey (blue). The red dots mark the proximity zone sizes 𝑅 sim measured from the smoothed spectra.The left panels show the increase of 𝑅 sim with the quasar on-time 𝑡 on for a fixed initial He ii fraction 𝑥 He ii , = .
01, whereas the right panels show the dependenceof 𝑅 sim on 𝑥 He ii , for a fixed quasar on-time 𝑡 on = moving Mpc, sampled at d 𝑟 = . 𝑣 = . .
93 km s − at 𝑧 em = . . -Ray code (Mellema et al. 2006),which tracks the evolution of H i, He ii, 𝑒 − , and the gas tempera-ture to generate He ii Ly 𝛼 transmission spectra of quasar proxim-ity zones (Khrykin et al. 2016, 2017). Analogous to Paper I, wecreated a set of radiative transfer models for each quasar at itsrespective redshift 𝑧 em and photon production rate 𝑄 (Table 1),varying the quasar on-time 𝑡 on and the initial He ii fraction in theambient IGM at quasar turn-on 𝑥 He ii , (or equivalently the UVbackground photoionization rate Γ He ii ). We assumed for simplic-ity that the quasars emitted continuously at their inferred luminos-ity for a time 𝑡 on prior to our observation, i.e. as a “light bulb”.We considered a base-10 logarithmically spaced grid of on-timeslog ( 𝑡 on / Myr ) ∈ [− , ] with a step size Δ log ( 𝑡 on / Myr ) = . 𝑥 He ii , ∈ { . , . , . , . , . , . , . , . , . , . } . Be-cause the quasars are at lower redshifts than those from Paper I weincluded models with 𝑥 He ii , = .
01 representative of the IGM atthe end of He ii reionization (Khrykin et al. 2016; Worseck et al.2019). This resulted in a grid of 330 radiative transfer models perquasar, each with 1000 He ii Ly 𝛼 transmission spectra. Redshift erroris incorporated in our Bayesian inference (Section 4.2).Figure 4 shows an example of model He ii proximity zone spectravarying 𝑡 on (left) and 𝑥 He ii , (right) for the same density skewer.The model proximity zone size 𝑅 sim measured analogously to the HST /COS spectra (Section 3) depends on the quasar on-time, as theIGM responds to changes in the radiation field on the He ii equili-bration time-scale 𝑡 eq ≈ Γ − (cid:39)
30 Myr in the 𝑧 ∼ 𝑡 on (cid:46) 𝑡 eq the proximity zone size increases with 𝑡 on , but stalls for longer on-times (Paper I), as illustrated in the lowerleft panel of Fig. 4. The proximity zone size only weakly depends on the initial IGM He ii fraction due to its definition ( 𝑥 He ii < 𝑥
He ii , at 𝑅 sim , Khrykin et al. 2016) and the thermal proximity effect (Khrykinet al. 2017). This weak sensitivity combined with quasar redshiftuncertainties makes it challenging to infer 𝑥 He ii , (Paper I). Further-more, the joint distribution 𝑅 sim ( 𝑡 on , 𝑥 He ii , ) , estimated from the1000 spectra per model, is significantly blurred by density fluctua-tions at low initial He ii fractions. We did not account for the lowerresolving power of our HST /COS spectra or their data quality, be-cause they do not significantly affect our results (Appendix A).
To estimate the on-times of individual quasars in our sample, weperformed MCMC inference on their measured He ii proximity zones 𝑅 pz using the Bayesian statistical method introduced in Paper I.First, we incorporated the individual quasar redshift uncertaintiesinto the radiative transfer models by adding a Gaussian-distributedrandom deviate with a standard deviation 𝜎 𝑅 pz (Table 1) to each 𝑅 sim realization, similar to Paper I. For each resulting distribution 𝑅 (cid:48) sim wecan write a Bayesian likelihood L given the combination of modelparameters (cid:8) 𝑡 on , 𝑥 He ii , (cid:9) per quasar, L (cid:0) 𝑅 pz | 𝑡 on , 𝑥 He ii , (cid:1) = 𝑝 (cid:16) 𝑅 (cid:48) sim = 𝑅 pz | 𝑡 on , 𝑥 He ii , (cid:17) , (8)where 𝑝 ( 𝑅 (cid:48) sim = 𝑅 pz | 𝑡 on , 𝑥 He ii , ) is the PDF of the modelled He iiproximity zone sizes plus redshift error 𝑅 (cid:48) sim , evaluated at the value ofthe measured He ii proximity zone size 𝑅 pz . To construct this PDF weused kernel density estimation (KDE) on the respective set of 1000model spectra. An example KDE on the distribution of proximityzone sizes in one radiative transfer model is illustrated in the left panelof Fig. 5. We then computed the likelihood of each radiative transfermodel in our (cid:8) 𝑡 on , 𝑥 He ii , (cid:9) grid via Equation (8), and constructedeach quasar’s continuous two-dimensional likelihood by bivariatespline interpolation. MNRAS , 1–19 (2021) ating individual quasars with the He II proximity effect R sim [Mpc]0.00.20.40.6 p ( R s i m | t o n , x H e II , ) log ( t on / Myr) = 0.000 x HeII , = 0.05 R sim = R sim + σ R pz KDE R pz Q1602+576 z = 2.8608 ± R pz = 6.1 ± t on / Myr) = 0 . +0 . − . x HeII , = 0 . +0 . − . x HeII , -2.0-1.00.01.02.0 l og ( t o n / M y r) -2.0 -1.0 0.0 1.0 2.0log ( t on / Myr)
Figure 5.
Example of our Bayesian inference of the quasar on-time for Q 1602 + 𝑡 on = 𝑥 He ii , = .
05. The dashed linemarks the measured He ii proximity zone size. Right: Constraints on the quasar on-time and the initial He ii fraction from the Bayesian inference. The 95 per cent(dark blue) and 68 per cent per cent (light blue) credible regions from the MCMC calculations are shown. The histograms illustrate the corresponding estimatedmarginalized posterior PDFs.
To infer 𝑡 on for each individual quasar we sampled the respectivelikelihood with MCMC. Because the initial He ii fraction is quiteuncertain at the redshifts of interest due to large-scale UV backgroundfluctuations at the tail end of He ii reionization (Davies et al. 2017;Worseck et al. 2019), we chose to impose a uniform prior 0 . ≤ 𝑥 He ii , ≤
1. Similarly, we set a uniform prior on log ( 𝑡 on / Myr ) in therange 0 . 𝑡 on (cid:38) Γ −
1H i ≈ .
03 Myr at 𝑧 ∼ 𝑧 em (cid:38) 𝑡 dc = +
576 in the right panels of Fig. 5. Analogous to theresults in Paper I, the flat posterior PDF of 𝑥 He ii , signals the lack ofsensitivity of the He ii proximity zone size to the initial He ii fractionin the IGM. Yet, we are able to put tight constraints on the on-time ofQ 1602 +
576 due to the small uncertainty in its proximity zone sizefacilitated by its accurate and precise systemic redshift (Table 1).
Many studies on 𝑧 em ∼ 𝑧 em ∼ 𝑅 pz probes fully reionized gas in the quasar vicinity, and isalways smaller than the actual size of the ionized region. Moreover,simple scaling laws with luminosity 𝑅 ∝ − . 𝛾𝑀 with 𝛾 = / 𝛾 = /
2) for a neutral (ionized) IGM do not apply for smoothedspectra and a realistic IGM density field (Bolton & Haehnelt 2007;Davies et al. 2020). Although the H i proximity zone sizes of 𝑧 em ∼ 𝑡 on (cid:46) . . 𝑅 pz asa function of absolute magnitude 𝑀 for the combined sampleof 22 quasars. We see no clear relation between 𝑅 pz and 𝑀 .For the eight 𝑀 ∼ −
28 quasars with precise systemic redshiftsthere is a factor ∼ 𝑅 pz . We overplot predictions of theaverage 𝑅 pz ( 𝑀 ) from our radiative transfer simulations at themedian redshift 𝑧 em = .
29 of our combined sample . The modelpredictions for extreme values of the IGM He ii fraction before quasarturn-on 𝑥 He ii , ∈ { . , } and two representative on-times 𝑡 on ∈{ ,
10 Myr } cover a similar range of 𝑅 pz as the observations.IGM density fluctuations give rise to intrinsic scatter in the simulated 𝑅 pz that increases toward low He ii fractions, i.e. in the emerging He iiLy 𝛼 forest. The He ii fraction and the on-time are often degenerate(Khrykin et al. 2016, 2019), as illustrated by the overlapping curvesfor ( 𝑥 He ii , , 𝑡 on ) = ( . , ) and ( 𝑥 He ii , , 𝑡 on ) = ( ,
10 Myr ) .Never the less, the smallest precisely measured He ii proximity zonesizes require short on-times of (cid:46) (cid:38)
10 Myr. Therefore, our measurements aresensitive to 𝑡 on up to the He ii equilibration time-scale 𝑡 eq (cid:39)
30 Myrat 𝑧 ∼ 𝑧 em ∼ 𝑡 on (cid:38) . 𝑧 em ∼ . We verified that these relations do not change dramatically due to IGMdensity evolution in the redshift range of interest. MNRAS , 1–19 (2021) G. Worseck et al. − − − − − M − R p z [ p M p c ] Khrykin et al. (2019)Worseck et al. (2021) x HeII , = 0 . t on = 1 Myr x HeII , = 0 . t on = 10 Myr x HeII , = 1 . t on = 1 Myr x HeII , = 1 . t on = 10 Myr . . . . . . z e m Figure 6.
He ii proximity zone size 𝑅 pz as a function of quasar absolutemagnitude 𝑀 for the 22 quasars in our combined sample. Quasars fromTable 1 and Paper I are marked with circles and diamonds, respectively. Thecolour coding indicates the quasar redshift. 𝑅 pz errors have been calculatedfrom the individual redshift errors. The dotted line marks 𝑅 pz =
0. Overplot-ted is the average 𝑅 pz ( 𝑀 ) and its 16–84th percentile scatter from ourradiative transfer simulations at 𝑧 em = .
29 for different initial He ii fractions 𝑥 He ii , and quasar on-times 𝑡 on . (Davies et al. 2020), with shorter on-times being apparent as outliers(Eilers et al. 2017, 2018, 2020). In contrast, He ii proximity zonesizes probe 𝑡 on (cid:46)
30 Myr, so variations in the individual on-timescan effectively remove any correlation with luminosity.As shown in Fig. 7 the He ii proximity zone size does not dependon redshift. Some of the scatter in 𝑅 pz vs. redshift is due to the (cid:39) 𝑀 , but due to the lack of a clear correlationwith luminosity we do not take out this dependence. The large scatterin 𝑅 pz for the eight quasars at 𝑀 ∼ −
28 with precise systemicredshifts confirms that there is no evidence for a scaling with redshift.Our measurements do not support previous claims of a significantdecline of the luminosity-normalized 𝑅 pz at 𝑧 em > . 𝑅 pz with redshift for a large range of on-timesand IGM He ii fractions (Fig. 7). This is a direct consequence ofthe observational definition of 𝑅 pz and its insensitivity to the IGMHe ii fraction (Khrykin et al. 2016, 2019). Only for long on-timesand small He ii fractions is there a significant decrease with redshiftthat is driven by IGM density evolution. Similar shallow relationshave been obtained for H i proximity zones at 𝑧 em ∼ 𝑀 = −
27, somewhat fainter than the median 𝑀 of oursample, in order to facilitate comparison with Eilers et al. (2017).For the three 𝑀 ∼ −
27 quasars from Paper I small but uncertainproximity zone sizes indicate 𝑡 on (cid:28)
10 Myr irrespective of the initialIGM He ii fraction, consistent with our joint analysis in Paper I. Onthe other hand, the large He ii proximity zone of the 𝑀 ∼ − + 𝑧 em = . 𝑡 on > . . . z em − R p z [ p M p c ] Khrykin et al. (2019)Worseck et al. (2021) x HeII , = 0 . t on = 1 Myr x HeII , = 0 . t on = 10 Myr x HeII , = 1 . t on = 1 Myr x HeII , = 1 . t on = 10 Myr − − − M Figure 7.
Similar to Fig. 6 for the He ii proximity zone size 𝑅 pz as a func-tion of quasar redshift 𝑧 em The colour coding indicates the quasar absolutemagnitude. Overplotted is the average 𝑅 pz ( 𝑧 em ) and its 16–84th percentilescatter from our radiative transfer simulations at 𝑀 = −
27 for differentinitial He ii fractions 𝑥 He ii , and quasar on-times 𝑡 on . Figure 8 shows the MCMC estimates of the quasar on-time posteriorPDFs marginalized over the initial He ii fraction for the 16 quasarsincluded in our analysis (Table 1 excluding HE 2347 − ∼ ,
000 posterior samples depending on thewidth of the PDF. Many PDFs are (cid:29) .
01 Myr ≤ 𝑡 on ≤
100 Myr. Because the lower limit of our prior is physically motivatedby the H i proximity effect, while the flatness of the posterior at 𝑡 on (cid:38)
30 Myr is effectively determined by the equilibration time-scale, some of these posterior PDFs provide only limited constraintson 𝑡 on . Specifically, if the posterior at 𝑡 on = .
01 Myr is >
10 percent of its maximum, we quote a 1 𝜎 upper limit on 𝑡 on as the 84thpercentile of the posterior. Likewise, if the posterior at 𝑡 on =
100 Myris >
10 per cent of its maximum, we define a 1 𝜎 lower limit on 𝑡 on as the 16th percentile of the posterior. For the remaining quasars wequote the median of the posterior as a measurement of 𝑡 on with a 1 𝜎 equal-tailed credibility interval derived from the 16th and the 84thpercentile of the posterior, respectively.The upper panel of Fig. 8 shows the 𝑡 on posteriors of the fivequasars from Table 1 whose 𝑅 pz values are highly uncertain due toC iv redshift errors. Large redshift errors significantly broaden themodel 𝑅 sim distributions and result in weak constraints on 𝑡 on , sim-ilar to four quasars from Paper I. According to the above definition,we obtain 1 𝜎 upper limits on 𝑡 on . Quasars with more precise red-shifts ( 𝜎 𝑣 <
300 km s − ) have significantly narrower 𝑡 on posteriors,except SDSS J1237 + + 𝑡 on posteriors of the six quasars for which we obtain individual on-timemeasurements. Their posteriors span distinct ranges in 𝑡 on , indicating MNRAS000
300 km s − ) have significantly narrower 𝑡 on posteriors,except SDSS J1237 + + 𝑡 on posteriors of the six quasars for which we obtain individual on-timemeasurements. Their posteriors span distinct ranges in 𝑡 on , indicating MNRAS000 , 1–19 (2021) ating individual quasars with the He II proximity effect σ v >
600 km s − : 1 σ upper limits on t on SDSS J0818+4908HE2QS J2149 − − P o s t e r i o r P r o b a b ili t y D e n s i t y F un c t i o n σ v <
300 km s − : 1 σ upper/lower limits on t on SDSS J1237+0126PC 0058+0215HE2QS J2157+2330SDSS J1253+6817Q 0302 − t on [Myr]012 σ v <
300 km s − : t on measurementsHS 0911+4809SDSS J2346 − Figure 8.
MCMC estimates of the posterior PDFs of the quasar on-time 𝑡 on marginalized over the initial He ii fraction for the 16 quasars from Table 1included in our analysis. The posteriors are grouped by their shape and byquasar redshift error that determine the sensitivity of 𝑅 pz to 𝑡 on . The colourcoding distinguishes 𝑡 on posteriors for quasars with uncertain C iv redshifts(grey tones), and more precise redshifts yielding upper limits (blue), lowerlimits (red tones) and measurements (green tones) for 𝑡 on , respectively. an intrinsically broad distribution of quasar on-times from (cid:46) ∼
10 Myr.In Fig. 9 we plot the inferred quasar on-times or limits thereof asa function of quasar absolute magnitude. We also show the resultsfor the six 𝑧 em > . 𝑡 on . There is strong diversityin the quasar on-times with no obvious dependence on absolutemagnitude. This is similar to the lack of a trend in 𝑅 pz ( 𝑀 ) inFig. 6, but now we account for the redshift dependence and providequantitative constraints on 𝑡 on based on the observed scatter of He iiproximity zone sizes. Figure 10 shows the quasar on-time as a function of black hole massfor the 13 quasars for which both quantities are available (Table 3excluding HE 2347 − 𝑀 BH (cid:39) –10 𝑀 (cid:12) ) both quantities do not cor-relate, although the ± .
55 dex systematic uncertainty in the virial − − − − M t o n [ M y r ] ( σ v >
600 km s − )Measurement1 σ upper limit1 σ lower limitLarge redshift error Figure 9.
Inferred quasar on-time 𝑡 on as a function of absolute magnitude 𝑀 for the 22 quasars in our combined sample. Green symbols show 𝑡 on measurements (posterior median with 16–84th percentile range from Fig. 8),while blue and red symbols mark 1 𝜎 upper limits (84th percentile of the pos-terior) and 1 𝜎 lower limits (16th percentile of the posterior) for quasars withprecise systemic redshifts ( 𝜎 𝑣 <
300 km s − ), respectively. Limits derivedfor quasars with larger redshift errors are shown in grey. black hole masses significantly contributes to the observed scatter.Figure 11 shows the quasar on-time as function of the Eddington ra-tio 𝐿 bol / 𝐿 Edd . The 13 quasars roughly emit at their Eddington limitconsidering the systematic uncertainty induced by the virial blackhole mass measurements (Equation 7). The quasar on-time also doesnot correlate with the Eddington ratio. The dashed lines in Fig. 11indicate the 𝑒 -folding time-scale for SMBH growth 𝑡 S = 𝑐𝜎 T ( − 𝑌 / ) 𝜋𝐺𝑚 p 𝜖 ( − 𝜖 ) (cid:18) 𝐿 bol 𝐿 Edd (cid:19) − (9) (cid:39)
397 Myr 𝜖 ( − 𝜖 ) (cid:18) 𝐿 bol 𝐿 Edd (cid:19) − for different radiative efficiencies 𝜖 . For 𝜖 = . 𝐿 bol = 𝐿 Edd oneobtains 𝑡 S (cid:39)
44 Myr. This is significantly longer than the on-times 𝑡 on (cid:46) 𝑡 on valuesmay indicate episodic quasar lifetimes, i.e. that their SMBHs grewin short bursts with 𝑡 Q (cid:28) 𝑡 S . Unless most of our observed quasarsare radiatively inefficient ( 𝜖 (cid:28) .
1, e.g. Volonteri et al. 2015; Davieset al. 2019), their short on-times imply a small mass growth by (cid:46) 𝑡 on (cid:38)
10 Myr indicates that not all quasar episodes arethat short, so the He ii proximity zones may sample a possibly verybroad distribution of quasar lifetimes (Khrykin et al. in preparation).
The inferred quasar on-times depend on the assumed prior on theinitial He ii fraction in the surrounding IGM. Similar to Paper I,we adopted a uniform prior 0 . ≤ 𝑥 He ii , ≤ MNRAS , 1–19 (2021) G. Worseck et al. . . . . M BH /M (cid:12) )0.1110100 t o n [ M y r ] Measurement1 σ upper limit1 σ lower limit Figure 10.
Inferred quasar on-time 𝑡 on as a function of black hole mass 𝑀 BH for 13 He ii-transparent quasars (Table 3 excluding HE 2347 − 𝜎 statistical errors, while the bottom bar indicates the ± .
55 dexsystematic uncertainty in 𝑀 BH . (cid:15) = . (cid:15) = . (cid:15) = . L bol /L Edd t o n [ M y r ] Measurement1 σ upper limit1 σ lower limit Figure 11.
Inferred quasar on-time 𝑡 on as a function of Edding-ton ratio 𝐿 bol / 𝐿 Edd for 13 He ii-transparent quasars (Table 3 excludingHE 2347 − 𝜎 statistical errors, while the bottombar indicates the ± .
55 dex systematic uncertainty in 𝐿 bol / 𝐿 Edd . The dashedlines show the 𝑒 -folding time-scale of SMBH growth for different radiativeefficiencies 𝜖 . low median He ii fraction of 2–3 per cent at 𝑧 (cid:39) . 𝑥 He ii , prior,we repeated the analysis with a restricted uniform prior 0 . ≤ 𝑥 He ii , ≤ .
05 that is consistent with the inferences from the He ii
HS 1700+6416
HS 1024+1849 Q 1602+576 PC 0058+0215
SDSS J0936+2927
HE2QS J2157+2330 SDSS J1237+0126
Q 0302 − HS 0911+4809 P o s t e r i o r P r o b a b ili t y D e n s i t y F un c t i o n SDSS J1253+6817 t on [Myr] SDSS J2346 − Figure 12.
MCMC estimates of the posterior PDFs of the quasar on-time 𝑡 on for two uniform priors 0 . ≤ 𝑥 He ii , ≤ . ≤ 𝑥 He ii , ≤ .
05 (dashed) for 11 quasars with precise systemic redshifts. Thecolours indicate PDFs resulting in 𝑡 on measurements (green), 1 𝜎 upper limits(blue), and 1 𝜎 lower limits (red). Table 4.
On-times 𝑡 on for the 16 𝑧 em < . 𝑥 He ii , . Quasar . ≤ 𝑥 Heii , ≤ . ≤ 𝑥 Heii , ≤ . 𝑡 on [Myr] 𝑡 on [Myr]SDSS J0818 + < . < . SDSS J1237 + < . < . HE2QS J2149 − < . < . HE2QS J1706 + < . < . HE2QS J0233 − < . < . HS 0911 + . + . − . . + . − . HE2QS J0916 + < . < . SDSS J2346 − . + . − . < . HS 1700 + . + . − . . + . − . HS 1024 + . + . − . > . Q 1602 + . + . − . . + . − . PC 0058 + > . > . SDSS J0936 + . + . − . > . HE2QS J2157 + > . > . Q 0302 − > . > . SDSS J1253 + > . > . Ly 𝛼 absorption at 2 . < 𝑧 < . 𝑡 on to the ones fromSection 5.2 for the eleven 𝑧 em < . 𝑥 He ii , (Fig. 5). Upper and lower 1 𝜎 limitson 𝑡 on decrease by (cid:39) . (cid:39) . 𝑡 on measurements also shift to lower values by (cid:39) . 𝑡 on from (cid:46) . (cid:38)
10 Myr. Our constraints can be improved either by moreprecise systemic redshifts from CO or [C ii] 158 𝜇 m emission fromthe quasar host galaxies covered at mm to sub-mm wavelengths,or via better priors on 𝑥 He ii , from semi-numerical models of thefluctuating UV background at the end of He ii reionization (Davieset al. 2017) which is left to future work. MNRAS000
10 Myr. Our constraints can be improved either by moreprecise systemic redshifts from CO or [C ii] 158 𝜇 m emission fromthe quasar host galaxies covered at mm to sub-mm wavelengths,or via better priors on 𝑥 He ii , from semi-numerical models of thefluctuating UV background at the end of He ii reionization (Davieset al. 2017) which is left to future work. MNRAS000 , 1–19 (2021) ating individual quasars with the He II proximity effect B l a c k H o l e M a ss [ M (cid:12) ] Figure 13.
SMBH growth histories of the 13 He ii-transparent quasars withon-time constraints and measured black hole masses (circles). The lines showtheir exponential growth history assuming 𝜖 = . 𝐿 bol / 𝐿 Edd = Here we consider the implications of our inferred quasar on-timesfor the growth histories of their SMBHs to their measured masses.In our modelling we assumed that each quasar shone at a constant“light bulb” luminosity 𝐿 bol for the time 𝑡 on prior to our observation.Because the inferred on-times are generally much smaller than theSalpeter time, the light bulb model is still a good approximation tothe standard model of exponential mass growth 𝑀 BH ( 𝑡 ) = 𝑀 seed 𝑒 ( 𝑡 − 𝑡 seed )/ 𝑡 S (10)for a black hole with a constant radiative efficiency and Eddingtonratio that had a seed mass 𝑀 seed at some cosmic time 𝑡 seed . Figure 13illustrates the exponential growth scenario for the 13 He ii-transparentquasars with on-time constraints and estimated black hole masses.The growth times 𝑡 gr = 𝑡 − 𝑡 seed from a stellar remnant seed mass ∼ 𝑀 (cid:12) are 𝑡 gr ∼
700 Myr, and for continuous unobscured SMBHgrowth these would be equal to the on-times 𝑡 on . For about halfof our sample (7 out of 13) the on-times inferred from the He iiproximity zone sizes ( 𝑡 on (cid:46) 𝑡 S (cid:28) 𝑡 gr , implying SMBH growth during episodicquasar activity and/or in obscured phases.Episodic quasar activity on a wide range of time-scales has beenpredicted by many models of quasar and black hole co-evolution(e.g. Ciotti & Ostriker 2001; Hopkins et al. 2006; Novak et al. 2011;Anglés-Alcázar et al. 2017). Consider for simplicity a “blinking lightbulb” model in which every quasar episode of 𝑡 Q =
20 Myr is fol-lowed by a quiescent phase of 𝑡 off =
30 Myr. In this case, our obser-vations sample random times 𝑡 on ≤ 𝑡 Q , and after each quasar episodethe surrounding IGM will re-equilibrate to the He ii fraction impliedby the UV background ( 𝑡 eq ≈ Γ − (cid:39) 𝑡 blink = 𝑡 gr ( 𝑡 Q + 𝑡 off )/ 𝑡 Q ∼ For exponential growth at constant Eddington ratio, Equations (7) and (10)imply that during 𝑡 on the quasar absolute magnitude increases by Δ 𝑀 (cid:39) . 𝑡 on / 𝑡 S , which is small for most quasars in our sample. age of the Universe to acquire their black hole masses. The problem isexacerbated by shorter quasar lifetimes implied at lower initial He iifractions in the end stages of He ii reionization (Section 6.1). This in-dicates that either the off-times must be shorter than the equilibrationtime, such that the proximity zones do not disappear (see Davies et al.2020 for the similar case of 𝑧 ∼ 𝑡 off . X-ray-selected samples of Active Galactic Nuclei (AGN) revealed that thefraction of Compton-thin (equivalent line-of-sight hydrogen columndensity 𝑁 H = –10 cm − ) obscured AGN depends on X-rayluminosity and redshift (e.g. Merloni et al. 2014; Ueda et al. 2014;Buchner et al. 2015; Aird et al. 2015). While at 𝑧 ∼ ∼
70 per cent to ∼
30 percent (Ueda et al. 2014; Aird et al. 2015), at 𝑧 ∼ ∼
60 per cent independent of luminosity (Buchner et al. 2015;Aird et al. 2015), possibly increasing further toward higher redshifts(Vito et al. 2018). It is therefore plausible that much of the massgrowth occurred when the SMBH was obscured by gas and dust,such that SMBH mass and the duration of the UV-luminous quasarphase are uncorrelated. We will consider more complex lightcurvesthan the simple light bulb model in future work.
We have used a sample of 17 2 . < 𝑧 em < .
51 He ii-transparentquasars with science-grade (S/N (cid:38) HST /COS spectra (Worsecket al. 2019) to measure the sizes of their highly ionized He ii proximityzones. Given that these zones typically span only a few pMpc, precisemeasurements are often hampered by quasar redshift error. Therefore,we obtained ancillary near-infrared spectroscopy to measure accurateand precise systemic redshifts of 12 quasars from low-ionization UVand optical emission lines (Mg ii, H 𝛽 , [O iii]) that also allow forestimates of the quasar black hole masses and Eddington ratios.Together with two 𝑧 em > . − 𝜎 𝑅 pz (cid:46) (cid:46) 𝑅 pz (cid:46)
15 pMpc. Nine out of 13 quasars with accurate systemic redshiftshave 𝑅 pz > ∼ 𝑅 pz at similar luminosity is mainly due tovariations in the individual quasar on-time, but variations in the He iifraction due to patchy He ii reionization and IGM density fluctuationscontribute as well.(iii) Exploiting the sensitivity of 𝑅 pz to quasar on-times 𝑡 on shorterthan the equilibration time of He ii in the ambient IGM 𝑡 eq = 𝑡 on (cid:46) 𝑡 on >
30 Myr, larger than the typical ± . MNRAS , 1–19 (2021) G. Worseck et al. ity (Fig. 9), nor with black hole mass (Fig. 10) or Eddington ratio(Fig. 11).The predominantly short quasar on-times 𝑡 on <
10 Myr and thelack of correlation with the black hole properties suggest that our ob-servations sample the distribution of episodic quasar lifetimes. Unlessthese quasars are radiatively highly inefficient (Davies et al. 2019),their black holes must have grown in bursts significantly shorter thanthe 𝑒 -folding time-scale 𝑡 S ∼
44 Myr. Such short quasar lifetimessuggest a long quasar duty cycle that is, however, not well constrainedgiven the age of the Universe at 𝑧 < > . 𝑧 (cid:38) 𝑡 on (cid:38) . (cid:46) 𝑧 ∼ 𝑧 ∼
3, most of their mass must have been built up during phasesof obscuration or radiative inefficiency.The sensitivity of individual He ii proximity zones to the time-scaleof prior quasar activity of up to ∼
30 Myr offers a unique opportunityto constrain the underlying distribution of episodic quasar lifetimes(Khrykin et al. in preparation), which can be compared to predictionsfrom models of galaxy and black hole co-evolution. Moreover, weanticipate to more than double the sample of He ii-transparent quasarswith precise systemic redshifts in our ongoing joint program with
HST /COS and Gemini/GNIRS (PI Worseck) to further resolve quasaractivity on time-scales of several tens of Myr.
ACKNOWLEDGEMENTS
We would like to thank Robert Simcoe for sharing his reduced near-infrared spectrum of HE 2347 − . MNRAS , 1–19 (2021) ating individual quasars with the He II proximity effect This research made use of Astropy (Astropy Collaboration et al.2013, 2018), Numpy (van der Walt et al. 2011) and Matplotlib(Hunter 2007).
DATA AVAILABILITY
The data underlying this article will be shared on reasonable requestto the corresponding author.
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APPENDIX A: MOCK
HST /COS HE ii PROXIMITY ZONESPECTRA
In our radiative transfer models, the He ii proximity zone sizeswere determined from high-resolution (d 𝑟 = . 𝑣 = . .
93 km s − at 𝑧 em = . .
5) noise-free He ii prox-imity zone Ly 𝛼 transmission spectra that had not been degradedto the spectral resolution and quality of the actual HST /COS spec-tra. We explored the consequences of this simplification with fullyforward-modelled mock
HST /COS He ii proximity zone spectra oftwo quasars from our sample (Q 1602 +
576 taken with the G130Mgrating and SDSS J1253 + 𝑥 HeII , ∈ { . , . , . , . } andquasar on-time 𝑡 on ∈ { , , } Myr twenty model spectra wereconvolved with the respective
HST /COS line-spread functions. Giventhe actual quasar continuum flux, grating sensitivity, exposure time,background conditions and spectral binning, expected COS countsper pixel were computed from the convolved He ii transmission spec-tra. Realistic COS Poisson counts were simulated as Poisson deviatesof the expected counts, and then converted back to He ii transmis-sion. Finally, 𝑅 pz was determined in the same way as for the observedspectra. Redshift error was not included here.Figure A1 shows the observed HST /COS He ii proximity zonespectra and representative mock spectra of Q 1602 +
576 andSDSS J1253 + 𝑥 HeII , and 𝑡 on the 𝑅 pz distribution of which match best the measured values. Apartfrom the small-scale structure in the proximity zone sourced by thedensity field, the mock spectra resemble the observed spectra verywell. The bottom panels show the relative deviations of the proximityzone sizes determined in the mock spectra ( 𝑅 pz ) with respect to theones in the high-resolution noise-free model spectra ( 𝑅 sim ). For mostof the 240 mock spectra per quasar the values are very similar, inparticular for the range of quasar on-times our method is sensitiveto ( 𝑡 on <
30 Myr). For long quasar on-times 𝑡 on ∼
100 Myr, 𝑅 pz is sometimes significantly larger than 𝑅 sim due to subtle deviationsbetween the smoothed He ii transmission profiles when accountingfor the broad wings of the COS line-spread functions and the coarserbinning of the COS spectra. In G140L spectra, proximity zone sizes (cid:46) (cid:46) 𝑅 pz induced by quasar redshift error (Table 1). For larger 𝑅 sim the biasmonotonically decreases to (cid:46) 𝑅 sim , as expected. The intrinsic scatter of 𝑅 pz around 𝑅 sim is small, i.e. 𝑅 pz is robustly estimated in the COS spectra usedin our analysis (see the middle panels of Fig. A1). We verified therobustness of 𝑅 pz in the lowest-quality spectra (S/N ∼ This paper has been typeset from a TEX/L A TEX file prepared by the author.MNRAS , 1–19 (2021) G. Worseck et al. R pz Q 1602+576 z em = 2 . ± . M = − . R pz = (6 . ± .
97) pMpc R pz SDSS J1253+6817 z em = 3 . ± . M = − . R pz = (11 . ± .
12) pMpc N o r m a li ze d Q u a s a r F l u x D e n s i t y R pz Mock G130M spectrum t on = 1 Myr x HeII , = 0 . R pz = (7 . ± .
97) pMpc R sim = 7 .
88 pMpc R pz Mock G140L spectrum t on = 10 Myr x HeII , = 0 . R pz = (9 . ± .
12) pMpc R sim = 8 .
85 pMpc R sim [pMpc]01 R p z / R s i m − t on = 1 Myr t on = 10 Myr t on = 100 Myr R sim [pMpc] t on = 1 Myr t on = 10 Myr t on = 100 Myr Figure A1.
Comparison of observed
HST /COS He ii quasar proximity zone spectra (top panels, labelled) to representative realistic mock spectra (middlepanels). The left (right) panels show COS G130M (G140L) spectra, plotted in grey with statistical 1 𝜎 Poisson errors. Distances are for the He ii Ly 𝛼 transitionrelative to the quasar at redshift 𝑧 em , with negative distances indicating pixels in the quasar continuum. The violet squares with error bars mark the quasarredshift uncertainties. The blue lines show the flux smoothed with a Gaussian filter with FWHM 1 pMpc. The red dots mark the measured 𝑅 pz . The green solidlines in the middle panels show the smoothed high-resolution noise-free He ii transmission from our radiative transfer models employed in our MCMC analysis,yielding a different proximity zone size 𝑅 sim (green dashed). The bottom panels show the relative deviation of 𝑅 pz with respect to 𝑅 sim in the radiative transfermodels for three values of the quasar on-time 𝑡 on (labelled). The dashed lines mark zero deviation.MNRAS000