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How neutral is the intergalactic medium surrounding the redshift z=7.085 quasar ULAS J1120+0641?

The quasar ULAS J1120+0641 at redshift z=7.085 has a highly ionised near zone which is smaller than those around quasars of similar luminosity at z~6. The spectrum also exhibits evidence for a damping wing extending redward of the systemic Lya redshift. We use radiative transfer simulations in a cosmological context to investigate the implications for the ionisation state of the inhomogeneous IGM surrounding this quasar. Our simulations show that the transmission profile is consistent with an IGM in the vicinity of the quasar with a volume averaged HI fraction of f_HI>0.1 and that ULAS J1120+0641 has been bright for 10^6--10^7 yr. The observed spectrum is also consistent with smaller IGM neutral fractions, f_HI ~ 10^-3--10-4, if a damped Lya system in an otherwise highly ionised IGM lies within 5 proper Mpc of the quasar. This is, however, predicted to occur in only ~5 per cent of our simulated sight-lines for a bright phase of 10^6--10^7 yr. Unless ULAS J1120+0641 grows during a previous optically obscured phase, the low age inferred for the quasar adds to the theoretical challenge of forming a 2x10^9 M_sol black hole at this high redshift.


INTRODUCTION
The spectra of quasars with redshifts z > ∼ 6 are an important probe of the ionisation state of the intergalactic medium (IGM) in the early Universe. The intergalactic Lyα opacity rapidly rises with increasing redshift, and consequently there has been much debate whether these quasars have been observed before the Universe was fully reionised (e.g. Becker et al. 2007;Lidz et al. 2007;Mesinger 2010). Studies of the small windows of Lyα transmission observed in close proximity to these objects provide important clues in this respect (Wyithe & Loeb 2004;Mesinger & Haiman 2004;Fan et al. 2006;Bolton & Haehnelt 2007a;Alvarez & Abel 2007;Maselli et al. 2009). These highly ionised "near zones" lie between the red edge of the Gunn & Peterson (1965) trough and the quasar Lyα emission line, and arise because the hydrogen close to these sources is highly ionised. Mortlock et al. (2011) (hereafter M11) have recently reported the highest redshift quasar found to date, ULAS J1120+0641 at z = 7.085, discovered using data from the UKIRT Infrared Deep Sky Survey (UKIDSS, Lawrence et al. 2007). In their analysis of the Lyα near zone observed in a low resolution (R ≃ 1400) VLT/FORS2 spectrum of moderate signal-to-noise, M11 find the extent and shape of the near zone is distinct from those around the much debated z ∼ 6 quasars. Assuming the quasar is embedded in a homogeneous IGM, M11 concluded the observed transmission profile of ULAS J1120+0641 is consistent with a surrounding IGM for which the volume averaged neutral fraction is fHI V > 0.1 at z ≃ 7.1.
In this Letter we examine the implications of the M11 observation in more detail using simulations of radiative transfer through an inhomogeneous IGM. These simulations have successfully explained the properties of Lyα near zones observed at z ≃ 6 in the context of a highly ionised IGM (Bolton et al. 2010). We begin in Section 2 by giving a brief overview of Lyα near zone sizes. In Section 3 we describe our numerical simulations before comparing them directly to the M11 measurement in Section 4. Finally in Section 5 we discuss the implications of our results and conclude. We assume the cosmological parameters Ωm = 0.26, ΩΛ = 0.74, Ω b h 2 = 0.023 and h = 0.72 throughout, and unless otherwise stated all distances are given in proper units.  (Fan et al. 2006) to correspond to a common absolute magnitude of M 1450 = −27. Note this scaling assumes R NZ ∝Ṅ 1/3 , whereṄ is the emission rate of ionising photons from the quasar, appropriate if the nearzone traces the boundary of the quasar H II region. If the nearzone extent is instead set by resonant absorption, R NZ ∝Ṅ 1/2 (Bolton & Haehnelt 2007a).

QUASAR NEAR ZONE SIZES
At the luminosities typical of observed z ≃ 6 quasars, and assuming an optically bright phase of tq ∼ 10 7 yr, the size of a quasar H II region expanding into a partially neutral IGM and that of a proximity zone embedded in an already highly ionised IGM are comparable (Bolton & Haehnelt 2007a). Further, if the surrounding IGM is significantly neutral, the red Gunn-Peterson (GP) damping wing will reduce the observed size of the near zone and Lyα absorption may extend redward of the quasar systemic redshift (Miralda-Escude & Rees 1998;Mesinger & Haiman 2004). Unfortunately, the possibility of confusing this damping wing with a collapsed region with a high H I column density in an otherwise highly ionised IGM complicates matters further. These issues make the interpretation of the Lyα near zones observed around these quasars with respect to the IGM ionisation state ambiguous (Bolton & Haehnelt 2007a;Maselli et al. 2007;Lidz et al. 2007).
A summary of the existing measurements of Lyα near zone sizes around high redshift quasars, compiled recently by Carilli et al. (2010), is displayed in Fig. 1. Interestingly, ULAS J1120+0641 has a small 1 near zone size given its bright absolute AB magnitude, M1450 = −26.6. This is demonstrated by the evolution of observed near zone sizes with redshift, rescaled to correspond to a common magnitude of M1450 = −27, in the right-hand panel of Fig. 1. M11 have noted that the small near zone size around ULAS J1120+0641, coupled with Lyα absorption redward of the systemic redshift from a putative red damping wing, may indicate the IGM surrounding ULAS J1120+0641 is significantly more neutral than around quasars at z ∼ 6. We now investigate this in more detail using realistic synthetic 1 The only quasar with a similarly small near zone is CFHQS J0210−0456 at z = 6.44 (Willott et al. 2010), but this object is considerably fainter and is consistent with the other z ≃ 6 quasars on accounting for its fainter luminosity. Note that for UVB4 we set Γ HI = 0 at z > 6.9. Bottom: The neutral hydrogen fraction averaged over 100 simulated sight-lines produced by the UVB models including (left) and excluding the quasar (right). The averaging is performed for display purposes only, and results in neutral regions being displayed as spikes with f HI ∼ 10 −2 . The crosses mark the position of all DLAs in the sight-lines constructed using UVB4, and the grey curve in the right panel shows the logarithm of f HI for UVB1 excluding the self-shielding approximation, multiplied by a factor of 0.01 for clarity.
absorption spectra which employ a variety of evolutionary histories for the IGM ionisation state.

NUMERICAL SIMULATIONS
We construct Lyα absorption spectra using a high resolution hydrodynamical simulation combined with a line-of-sight radiative transfer code (Bolton et al. 2010). The hydrodynamical simulation was performed using the GADGET-3 code (Springel 2005) and has a box size of 10h −1 comoving Mpc and a gas particle mass of 9.2 × 10 4 h −1 M⊙. A total of 100 sight-lines of length 96.6h −1 comoving Mpc were extracted around haloes identified in the simulation to construct skewers through the IGM density, temperature and peculiar velocity field. The largest halo mass in the simulation volume at z = 7.1 is 4.7 × 10 10 h −1 M⊙, which likely underestimates the ULAS J1120+0641 host halo mass. However, resolving the low density IGM is more important for modelling the Lyα absorption, and a small, high resolution simulation provides the best compromise (Bolton et al. 2010). Following M11 and Bolton et al. (2010), we assume the spectrum of the unobscured, radio quiet quasar ULAS J1120+0641 is a broken power law where fν ∝ ν −0.5 for 1050Å < λ < 1450Å and fν ∝ ν −1.5 for λ < 1050Å, yielding an ionising photon emission rate ofṄ = 1.3 × 10 57 s −1 . Table 1. Average H I fractions and the incidence of optically thick absorbers within 0.05 Mpc < R < 5 Mpc of the quasar host halo in all 100 simulated sight-lines including the self-shielding prescription. The absorber columns are estimated by integrating the H I densities over a scale of 20 kpc. From left to right, the columns list the volume and mass averaged H I fraction, the number of LLSs (10 17.2 cm −2 < N HI < 10 20.3 cm −2 ) and DLAs (N HI > 10 20.3 cm −2 ) per unit redshift and the fraction of sight-lines where there is at least one LLS or DLA, all prior to the quasar turning on. In the final four columns the latter are also given after a quasar with age 10 6 yr and 10 7 yr has ionised the surrounding IGM. Note that for models UVB3 and UVB4, where the IGM has a large neutral fraction, identifying LLSs becomes ambiguous. At z = 7.085, ∆z = 1 corresponds to ∼ 43.8 Mpc. Model The ionisation state of the IGM along the sight-lines prior to the quasar turning on was initialised using four different models for the background H I photo-ionisation rate, displayed in Fig. 2. However, it is important to note that reionisation is an inhomogeneous process, and as a result each model may be realised at the same time in different regions of the IGM (Mesinger & Furlanetto 2008). Furthermore, the ionisation state of the IGM in the vicinity of a massive host halo will be biased due the clustering of lower luminosity sources (Lidz et al. 2007;Wyithe et al. 2008). These models are thus designed to explore a range of different initial H I fractions in the IGM close to the quasar, but are not representative of global reionisation histories.
As we only compute the radiative transfer for the quasar ionising radiation, we also add a simple prescription for regions which are self-shielded from the ionising background. Assuming that the typical size of an H I absorber is the Jeans scale (Schaye 2001), the hydrogen number density where an H I absorber begins to self-shield can be approximated as nH ≃ 3.6 × 10 −3 cm −3 (ΓHI/10 −12 s −1 ) 2/3 (T/10 4 K) 2/15 . We use this expression to compute the density threshold at which hydrogen is self-shielded prior to being ionised by the quasar, and set the background photo-ionisation rate to zero in these regions. The weak temperature dependence is computed self-consistently using the gas temperature in our simulations. The lower panel of Fig. 2 displays the resulting neutral hydrogen fraction averaged over all 100 sightlines assuming tq = 10 7 yr and including (left panel) and excluding (right panel) ionising radiation from the quasar. The grey curve in the right panel also shows the H I fraction for UVB1 excluding the self-shielding model. Self-shielded regions become rapidly more common for ultra-violet background (UVB) models with decreasing H I photo-ionisation rates, increasing the volume averaged neutral fraction and producing a patchy ionisation structure along each sightline. A summary of the average H I fractions and incidence of optically thick absorbers in all models which include the self-shielding prescription is given in Table 1. Note that the quasar photo-ionises optically thick absorbers in its vicinity, significantly reducing the incidence of these systems. However, the impact of this process is reduced for shorter quasar ages or the smaller ionising photon mean free path associated with a larger IGM neutral fraction.

RESULTS
We compare the measured transmission profile around ULAS J1120+0641, described in detail by M11, to two of our simulated sight-lines in Fig. 3. For each sight-line we consider quasar ages of 10 6 yr and 10 7 yr, and for each quasar age the effect of optically thick absorbers is illustrated by models which include and exclude the self-shielding approximation. This qualitative comparison highlights an important point: for an initially neutral IGM (UVB4, orange curves) or a partially neutral IGM (UVB3, blue curves) and a short quasar bright phase (10 6 yr) a prominent damping wing with absorption extending redward of rest frame Lyα is present. However, optically thick absorbers will also have an impact on the near zone transmission profile redward of Lyα if a collapsed neutral region is close to the quasar; the presence of a damped Lyα absorber (DLA) with NHI ≃ 10 20.5 cm −2 at 3.1 Mpc, marked by the arrow in the right main panel, demonstrates this.
We may consider the relative likelihood of these possibilities by analysing the transmission profiles for all 100 of our simulated spectra. Considering the moderate signal-tonoise and low resolution of the observed spectrum of ULAS J1120+0641 and the difficulty of continuum fitting due to the complexity of the intrinsic Lyα and N V emission, we use two simple properties to characterise the transmission profile for a quantitative comparison. These are: the distance from the quasar where the transmitted fraction first falls below 10 per cent, RNZ (Fan et al. 2006), and the transmitted fraction at the rest frame Lyα wavelength, T1216. These are measured after smoothing the spectra with a box car window of width 2.4Å (rest frame) to remove fluctuations on smaller scales due to noise and absorption lines. The corresponding values 2 for ULAS J1120+0641 are RNZ = 1.9 ± 0.1 Mpc and T1216 = 0.80 ± 0.07 after removing the intrinsic absorption line at rest frame Lyα. Fig. 4 displays box-whisker and scatter plots of the distribution of these two quantities. Both quantities not only depend on the assumed UVB model but also on how long the quasar has been emitting ionising photons. For example, if self-shielding is included and the quasar has been bright for only 10 6 yr, both quantities for UVB3 are strongly affected by neutral gas in Lyman limit systems (LLSs). Note also the extended tail in the distribution of RNZ and T1216 when self-shielding is included for UVB1 and UVB2. This arises due to the stochastic occurrence of LLSs and DLAs close to the quasar, and is more prominent the shorter the time the   Figure 3. Simulated quasar spectra constructed using the four different UVB models displayed in Fig. 2. The spectra are processed to mimic the M11 spectrum by convolving with a Gaussian instrument profile with FWHM= 240 km s −1 , rebinning onto pixels of width 0.4Å (rest frame) and adding Gaussian distributed noise using the observed noise array. The observed transmission of ULAS J1120+0641 is shown by the light grey curve in each panel. Left: Sight-line 1. Note the impact of the red GP damping wing on the spectrum for models with a fully neutral IGM (orange curves). Right: Sight-line 2. In this sight-line a prominent red damping wing is seen for all UVB models when the self-shielding prescription is included. A DLA with N HI ≃ 10 20.5 cm −2 is present at the position marked by the arrow.
quasar has been bright and thus able to photo-ionise proximate optically thick absorbers. Fig. 4 suggests that the near zone around ULAS J1120+0641 is due to either (i) a partially (fully) neutral surrounding IGM with fHI V ∼ 0.1 (1.0) and a quasar bright phase of ∼ 10 6 yr (10 7 yr) or (ii) the presence of a high column density H I system in close proximity to the quasar. It is important to note, however, that (i) and (ii) are not mutually exclusive. In our modelling an abundance of optically thick absorbers close to a quasar is a generic prediction due to the shorter ionising photon mean free path expected when the IGM is only partially ionised. Our simulations confirm the suggestion of M11 that the spectrum of ULAS J1120+0641 is consistent with an already very highly ionised IGM ( fHI V ∼ 10 −3 -10 −4 ) if a DLA lies close to the quasar. However, this occurs in only ∼ 5 per cent of our sight-lines for tq = 10 6 -10 7 yr. A fully neutral IGM for tq = 10 6 yr is ruled out by the near zone size, but is consistent with the observed transmission for a bright phase duration of 10 7 yr. However, ionisation by lower luminosity sources expected to cluster around a massive quasar host halo (Lidz et al. 2007;Wyithe et al. 2008) may make this extreme possibility less likely in practice. We should caution, however, that if we have underestimated the number of proximate DLAs present at z ≃ 7, if the ionising spectrum of the quasar is much softer than assumed here, or if the environment of the quasar host halo is significantly overdense out to 2 Mpc from the quasar (but see Calverley et al. 2011), then we will overestimate the likelihood of a significantly neutral surrounding IGM and/or underestimate the age of the quasar.

DISCUSSION AND CONCLUSIONS
We have presented a large suite of realistic synthetic transmission spectra which model a variety of evolutionary his-tories for the ionisation state of the IGM surrounding the quasar ULAS J1120+0641. The transmission profiles depend on the age of the quasar, the photo-ionisation rate in the surrounding IGM and the presence of high column density absorbers arising from collapsed, high density regions. For the same initial conditions for the IGM ionisation state the Lyα transmission profile varies greatly due to the stochasticity of the optically thick absorbers and IGM density distribution along different sight-lines.
Inferences regarding the ionisation state of the surrounding IGM for Lyα transmission around ULAS J1120+0641 are correlated with the duration of the optically bright phase of the quasar. For a short bright phase duration of 10 6 yr, the data are consistent either with an IGM with a volume averaged neutral fraction fHI V ∼ 0.1 or a highly ionised IGM with fHI V ∼ 10 −3 -10 −4 and a proximate DLA. On the other hand, a bright phase of 10 7 yr is consistent with both a highly ionised IGM and proximate DLA or a fully neutral IGM. However, we find only ∼ 5 per cent of our simulated sight-lines exhibit a proximate DLA capable of producing a red damping wing, implying the former scenario is less likely (but see also the caveats in section 4). In either case, this suggests the quasar has not been bright for significantly more than ∼ 10 7 yr; a longer bright phase will produce a near-zone which is too large, either by enlarging the quasar H II region or photo-ionising progressively more proximate optically thick absorbers. A timescale of 10 7 yr is still a factor of five less than the e-folding time of a black hole growing at the Eddington rate and radiating with 10 per cent efficiency, as might be expected for a moderately spinning black hole. For a rapidly spinning black hole the discrepancy would be even larger (Sijacki et al. 2009  with an estimated mass of 2 × 10 9 M⊙ so early in the history of the Universe. A higher quality spectrum will hopefully exclude or confirm the possible presence of a proximate DLA by enabling the identification of associated metal lines and aid in narrowing constraints on the neutral fraction of the surrounding IGM. More general conclusions regarding the ionisation state of the IGM at z ∼ 7 are speculative due to the large fluctuations in the ionisation state expected on scales much larger than probed by the near zone of ULAS J1120+0641 (Mesinger & Furlanetto 2008). If the neutral fraction in the general IGM at z ∼ 7 is indeed fHI V ∼ 0.1 this is nevertheless consistent with a constant or weakly decreasing ionising emissivity between z ∼ 6−7. The rapid change in the photoionisation rate by two orders of magnitude or more in our models is balanced by a similar change in the number of LLSs and thus the mean free path of ionising photons (e.g. McQuinn et al. 2011). Since a constant or perhaps even rising emissivity is required for the completion of reionisation at z > ∼ 6 (Miralda-Escudé 2003; Bolton & Haehnelt 2007b), this may be compatible with the possibility that reionisation was yet to fully complete by z = 6 (Mesinger 2010). Lastly, the possibility of a significant neutral fraction in the IGM surrounding ULAS J1120+0641 make it an excellent target for searching for extended Lyα emission from the expanding ionisation front (Cantalupo et al. 2008) as well as studies of the IGM ionisation state using the redshifted 21 cm transition.