arXiv subjects

B. Ciardi

Publications and source records attributed to B. Ciardi.

At least 37 records · Page 2Linked to original sources

arXiv2020

Dispersion measure variability for 36 millisecond pulsars at 150MHz with LOFAR

Radio pulses from pulsars are affected by plasma dispersion, which results in a frequency-dependent propagation delay. Variations in the magnitude of this effect lead to an additional source of red noise in pulsar timing experiments, including pulsar timing arrays that aim to detect nanohertz gravitational waves. We aim to quantify the time-variable dispersion with much improved precision and characterise the spectrum of these variations. We use the pulsar timing technique to obtain highly precise dispersion measure (DM) time series. Our dataset consists of observations of 36 millisecond pulsars, which were observed for up to 7.1 years with the LOFAR telescope at a centre frequency of ~150 MHz. Seventeen of these sources were observed with a weekly cadence, while the rest were observed at monthly cadence. We achieve a median DM precision of the order of 10^-5 cm^-3 pc for a significant fraction of our sources. We detect significant variations of the DM in all pulsars with a median DM uncertainty of less than 2x10^-4 cm^-3 pc. The noise contribution to pulsar timing experiments at higher frequencies is calculated to be at a level of 0.1-10 us at 1.4 GHz over a timespan of a few years, which is in many cases larger than the typical timing precision of 1 us or better that PTAs aim for. We found no evidence for a dependence of DM on radio frequency for any of the sources in our sample. The DM time series we obtained using LOFAR could in principle be used to correct higher-frequency data for the variations of the dispersive delay. However, there is currently the practical restriction that pulsars tend to provide either highly precise times of arrival (ToAs) at 1.4 GHz or a high DM precision at low frequencies, but not both, due to spectral properties. Combining the higher-frequency ToAs with those from LOFAR to measure the infinite-frequency ToA and DM would improve the result.

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arXiv2020

The LOFAR Two Metre Sky Survey: Deep Fields. II. The ELAIS-N1 LOFAR deep field

The LOFAR Two-metre Sky Survey (LoTSS) will cover the full northern sky and, additionally, aims to observe the LoTSS deep fields to a noise level of ~10 microJy/bm over several tens of square degrees in areas that have the most extensive ancillary data. This paper presents the ELAIS-N1 deep field, the deepest of the LoTSS deep fields to date. With an effective observing time of 163.7 hours, it reaches a root mean square (RMS) noise level below 20 microJy/bm in the central region (and below 30 microJy/bm over 10 square degrees). The resolution is 6 arcsecs and 84862 radio sources were detected in the full area (68 sq. deg.) with 74127 sources in the highest quality area at less than 3 degrees from the pointing centre. The observation reaches a sky density of more than 5000 sources per sq. deg. in the central ~5 sq. deg. region. We present the calibration procedure, which addresses the special configuration of some observations and the extended bandwidth covered (115 to 177 MHz; central frequency 146.2 MHz) compared to standard LoTSS. We also describe the methods used to calibrate the flux density scale using cross-matching with sources detected by other radio surveys in the literature. We find the flux density uncertainty related to the flux density scale to be ~6.5%. By studying the variations of the flux density measurements between different epochs, we show that relative flux density calibration is reliable out to about a 3 degree radius, but that additional flux density uncertainty is present for all sources at about the 3 per cent level; this is likely to be associated with residual calibration errors, and is shown to be more significant in datasets with poorer ionosphere conditions. We also provide intra-band spectral indices, which can be useful to detect sources with unusual spectral properties. The final uncertainty in the flux densities is estimated to be ~10% for ELAIS-N1.

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arXiv2020

Comparing Foreground Removal Techniques for Recovery of the LOFAR-EoR 21cm Power Spectrum

We compare various foreground removal techniques that are being utilised to remove bright foregrounds in various experiments aiming to detect the redshifted 21cm signal of neutral hydrogen from the Epoch of Reionization. In this work, we test the performance of removal techniques (FastICA, GMCA, and GPR) on 10 nights of LOFAR data and investigate the possibility of recovering the latest upper limit on the 21cm signal. Interestingly, we find that GMCA and FastICA reproduce the most recent 2$σ$ upper limit of $Δ^2_{21} <$ (73)$^2$ mK$^2$ at $k=0.075~ h \mathrm{cMpc}^{-1}$, which resulted from the application of GPR. We also find that FastICA and GMCA begin to deviate from the noise-limit at \textit{k}-scales larger than $\sim 0.1 ~h \mathrm{cMpc}^{-1}$. We then replicate the data via simulations to see the source of FastICA and GMCA's limitations, by testing them against various instrumental effects. We find that no single instrumental effect, such as primary beam effects or mode-mixing, can explain the poorer recovery by FastICA and GMCA at larger \textit{k}-scales. We then test scale-independence of FastICA and GMCA, and find that lower \textit{k}-scales can be modelled by a smaller number of independent components. For larger scales ($k \gtrsim 0.1~h \mathrm{cMpc}^{-1}$), more independent components are needed to fit the foregrounds. We conclude that, the current usage of GPR by the LOFAR collaboration is the appropriate removal technique. It is both robust and less prone to overfitting, with future improvements to GPR's fitting optimisation to yield deeper limits.

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arXiv2020

Opening Reionization: Quantitative Morphology of the Epoch of Reionization and Its Connection to the Cosmic Density Field

We introduce a versatile and spatially resolved morphological characterisation of binary fields, rooted in the opening transform of mathematical morphology. We subsequently apply it to the thresholded ionization field in simulations of cosmic reionization and study the morphology of ionized regions. We find that an ionized volume element typically resides in an ionized region with radius $\sim8\,h^{-1}\mathrm{cMpc}$ at the midpoint of reionization ($z\approx7.5$) and follow the bubble size distribution even beyond the overlap phase. We find that percolation of the fully ionized component sets in when 25% of the universe is ionized and that the resulting infinite cluster incorporates all ionized regions above $\sim8\,h^{-1}\mathrm{cMpc}$. We also quantify the clustering of ionized regions of varying radius with respect to matter and on small scales detect the formation of superbubbles in the overlap phase. On large scales we quantify the bias values of the centres of ionized and neutral regions of different sizes and not only show that the largest ones at the high-point of reionization can reach $b\approx 30$, but also that early small ionized regions are positively correlated with matter and large neutral regions and late small ionized regions are heavily anti-biased with respect to matter, down to $b\lesssim-20$.

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arXiv2020

Tight Constraints on the Excess Radio Background at $z = 9.1$ from LOFAR

The ARCADE2 and LWA1 experiments have claimed an excess over the Cosmic Microwave Background (CMB) at low radio frequencies. If the cosmological high-redshift contribution to this radio background is between 0.1% and 22% of the CMB at 1.42 GHz, it could explain the tentative EDGES Low-Band detection of the anomalously deep absorption in the 21-cm signal of neutral hydrogen. We use the upper limit on the 21-cm signal from the Epoch of Reionization ($z=9.1$) based on 141 hours of observations with LOFAR to evaluate the contribution of the high redshift Universe to the detected radio background. Marginalizing over astrophysical properties of star-forming halos, we find (at 95% C.L.) that the cosmological radio background can be at most 9.6% of the CMB at 1.42 GHz. This limit rules out strong contribution of the high-redshift Universe to the ARCADE2 and LWA1 measurements. Even though LOFAR places limit on the extra radio background, excess of $0.1-9.6$% over the CMB (at 1.42 GHz) is still allowed and could explain the EDGES Low-Band detection. We also constrain the thermal and ionization state of the gas at $z = 9.1$ and put limits on the properties of the first star-forming objects. We find that, in agreement with the limits from EDGES High-Band data, LOFAR data constrain scenarios with inefficient X-ray sources and cases where the Universe was ionized by stars in massive halos only.

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arXiv2020

LOFAR 144-MHz follow-up observations of GW170817

We present low-radio-frequency follow-up observations of AT 2017gfo, the electromagnetic counterpart of GW170817, which was the first binary neutron star merger to be detected by Advanced LIGO-Virgo. These data, with a central frequency of 144 MHz, were obtained with LOFAR, the Low-Frequency Array. The maximum elevation of the target is just 13.7 degrees when observed with LOFAR, making our observations particularly challenging to calibrate and significantly limiting the achievable sensitivity. On time-scales of 130-138 and 371-374 days after the merger event, we obtain 3$σ$ upper limits for the afterglow component of 6.6 and 19.5 mJy beam$^{-1}$, respectively. Using our best upper limit and previously published, contemporaneous higher-frequency radio data, we place a limit on any potential steepening of the radio spectrum between 610 and 144 MHz: the two-point spectral index $α^{610}_{144} \gtrsim -2.5$. We also show that LOFAR can detect the afterglows of future binary neutron star merger events occurring at more favourable elevations.

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arXiv2020

The assembly of dusty galaxies at $z \geq 4$: statistical properties

The recent discovery of high redshift dusty galaxies implies a rapid dust enrichment of their interstellar medium (ISM). To interpret these observations, we run a cosmological simulation in a 30$h^{-1}$ cMpc/size volume down to $z \approx 4$. We use the hydrodynamical code dustyGadget, which accounts for the production of dust by stellar populations and its evolution in the ISM. We find that the cosmic dust density parameter ($Ω_{\rm d}$) is mainly driven by stellar dust at $z \gtrsim 10$, so that mass- and metallicity-dependent yields are required to assess the dust content in the first galaxies. At $z \lesssim 9$ the growth of grains in the ISM of evolved systems (Log$(M_{\star}/M_{\odot})>8.5$) significantly increases their dust mass, in agreement with observations in the redshift range $4 \lesssim z < 8$. Our simulation shows that the variety of high redshift galaxies observed with ALMA can naturally be accounted for by modeling the grain-growth timescale as a function of the physical conditions in the gas cold phase. In addition, the trends of dust-to-metal (DTM) and dust-to-gas (${\cal D}$) ratios are compatible with the available data. A qualitative investigation of the inhomogeneous dust distribution in a representative massive halo at $z \approx 4$ shows that dust is found from the central galaxy up to the closest satellites along polluted filaments with $\rm Log({\cal D}) \leq -2.4$, but sharply declines at distances $d \gtrsim 30$ kpc along many lines of sight, where $\rm Log({\cal D}) \lesssim -4.0$.

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arXiv2020

Cassiopeia A, Cygnus A, Taurus A, and Virgo A at ultra-low radio frequencies

The four persistent radio sources in the northern sky with the highest flux density at metre wavelengths are Cassiopeia A, Cygnus A, Taurus A, and Virgo A; collectively they are called the A-team. Their flux densities at ultra-low frequencies (<100 MHz) can reach several thousands of janskys, and they often contaminate observations of the low-frequency sky by interfering with image processing. Furthermore, these sources are foreground objects for all-sky observations hampering the study of faint signals, such as the cosmological 21 cm line from the epoch of reionisation. We aim to produce robust models for the surface brightness emission as a function of frequency for the A-team sources at ultra-low frequencies. These models are needed for the calibration and imaging of wide-area surveys of the sky with low-frequency interferometers. This requires obtaining images at an angular resolution better than 15 arcsec with a high dynamic range and good image fidelity. We observed the A-team with the Low Frequency Array (LOFAR) at frequencies between 30 MHz and 77 MHz using the Low Band Antenna (LBA) system. We reduced the datasets and obtained an image for each A-team source. The paper presents the best models to date for the sources Cassiopeia A, Cygnus A, Taurus A, and Virgo A between 30 MHz and 77 MHz. We were able to obtain the aimed resolution and dynamic range in all cases. Owing to its compactness and complexity, observations with the long baselines of the International LOFAR Telescope will be required to improve the source model for Cygnus A further.

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arXiv2020

Improved upper limits on the 21-cm signal power spectrum of neutral hydrogen at $\boldsymbol{z \approx 9.1}$ from LOFAR

A new upper limit on the 21-cm signal power spectrum at a redshift of $z \approx 9.1$ is presented, based on 141 hours of data obtained with the Low-Frequency Array (LOFAR). The analysis includes significant improvements in spectrally-smooth gain-calibration, Gaussian Process Regression (GPR) foreground mitigation and optimally-weighted power spectrum inference. Previously seen `excess power' due to spectral structure in the gain solutions has markedly reduced but some excess power still remains with a spectral correlation distinct from thermal noise. This excess has a spectral coherence scale of $0.25 - 0.45$\,MHz and is partially correlated between nights, especially in the foreground wedge region. The correlation is stronger between nights covering similar local sidereal times. A best 2-$σ$ upper limit of $Δ^2_{21} < (73)^2\,\mathrm{mK^2}$ at $k = 0.075\,\mathrm{h\,cMpc^{-1}}$ is found, an improvement by a factor $\approx 8$ in power compared to the previously reported upper limit. The remaining excess power could be due to residual foreground emission from sources or diffuse emission far away from the phase centre, polarization leakage, chromatic calibration errors, ionosphere, or low-level radio-frequency interference. We discuss future improvements to the signal processing chain that can further reduce or even eliminate these causes of excess power.

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arXiv2020

Constraining the intergalactic medium at $z\approx$ 9.1 using LOFAR Epoch of Reionization observations

We derive constraints on the thermal and ionization states of the intergalactic medium (IGM) at redshift $\approx$ 9.1 using new upper limits on the 21-cm power spectrum measured by the LOFAR radio-telescope and a prior on the ionized fraction at that redshift estimated from recent cosmic microwave background (CMB) observations. We have used results from the reionization simulation code GRIZZLY and a Bayesian inference framework to constrain the parameters which describe the physical state of the IGM. We find that, if the gas heating remains negligible, an IGM with ionized fraction $\gtrsim 0.13$ and a distribution of the ionized regions with a characteristic size $\gtrsim 8 ~h^{-1}$ comoving megaparsec (Mpc) and a full width at the half maximum (FWHM) $\gtrsim 16 ~h^{-1}$ Mpc is ruled out. For an IGM with a uniform spin temperature $T_{\rm S} \gtrsim 3$ K, no constraints on the ionized component can be computed. If the large-scale fluctuations of the signal are driven by spin temperature fluctuations, an IGM with a volume fraction $\lesssim 0.34$ of heated regions with a temperature larger than CMB, average gas temperature 7-160 K and a distribution of the heated regions with characteristic size 3.5-70 $h^{-1}$ Mpc and FWHM of $\lesssim 110$ $h^{-1}$ Mpc is ruled out. These constraints are within the 95 per cent credible intervals. With more stringent future upper limits from LOFAR at multiple redshifts, the constraints will become tighter and will exclude an increasingly large region of the parameter space.

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arXiv2020

The LOFAR Tied-Array All-Sky Survey: Timing of 21 pulsars including the first binary pulsar discovered with LOFAR

We report on the multi-frequency timing observations of 21 pulsars discovered in the LOFAR Tied-Array All-Sky Survey (LOTAAS). The timing data were taken at central frequencies of 149 MHz (LOFAR) as well as 334 and 1532 MHz (Lovell Telecope). The sample of pulsars includes 20 isolated pulsars and the first binary pulsar discovered by the survey, PSR J1658$+$3630. We modelled the timing properties of the pulsars, which showed that they have, on average, larger characteristic ages. We present the pulse profiles of the pulsars across the three observing bands, where PSR J1643$+$1338 showed profile evolution that appears not to be well-described by the radius-to-frequency-mapping model. Furthermore, we modelled the spectra of the pulsars across the same observing bands, using a simple power law, and found an average spectral index of $-1.9 \pm 0.5$. Amongst the pulsars studied here, PSR J1657$+$3304 showed large flux density variations of a factor of 10 over 300 days, as well as mode changing and nulling on timescales of a few minutes. We modelled the rotational and orbital properties of PSR J1658$+$3630, which has a spin period of 33 ms in a binary orbit of 3.0 days with a companion of minimum mass of 0.87$M_{\odot}$, likely a Carbon-Oxygen or Oxygen-Neon-Magnesium type white dwarf. PSR J1658$+$3630 has a dispersion measure of 3.0 pc cm$^{-3}$, making it possibly one of the closest binary pulsars known.

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arXiv2019

Cross-correlation between the 21-cm signal and [OIII] emitters during early cosmic reionization

We study statistics of the 21-cm signal from the epoch of reionization. We propose to use [OIII] line emitting galaxies to cross-correlate with the 21-cm signal from $z = 7 - 10$. To this aim, we employ simulations of reionization obtained post-processing the high-resolution cosmological hydrodynamic simulation Massive Black-II with the three-dimensional (3D) radiative transfer code CRASH to follow the propagation of ionizing photons from a variety of sources. We show that, during the early phases of reionization, the 21-cm signal is positively correlated with the spatial distribution of the [OIII] emitters on large scales $(k < 1h~\rm cMpc^{-1})$. This positive correlation is generated by the temperature-galaxy correlation and it is a few times larger than when we assume that the heating is saturated. As the reionized regions expand, the correlation changes its sign to negative from $z = 10$ to 8. The signals at this epoch can be detected by combining the Square Kilometre Array (SKA) and a wide-field [OIII] emitter survey. We also calculate the cross-power spectrum with a 3D [OIII] intensity field, aiming at exploiting future intensity mapping observations. We conclude that high-redshift [OIII] line emitters can be used to probe the reionization process when the intergalactic medium is largely neutral.

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arXiv2019

The first power spectrum limit on the 21-cm signal of neutral hydrogen during the Cosmic Dawn at z=20-25 from LOFAR

Observations of the redshifted 21-cm hyperfine line of neutral hydrogen from early phases of the Universe such as Cosmic Dawn and the Epoch of Reionization promise to open a new window onto the early formation of stars and galaxies. We present the first upper limits on the power spectrum of redshifted 21-cm brightness temperature fluctuations in the redshift range $z = 19.8 - 25.2$ ($54-68$ MHz frequency range) using 14 hours of data obtained with the LOFAR-Low Band Antenna (LBA) array. We also demonstrate the application of a multiple pointing calibration technique to calibrate the LOFAR-LBA dual-pointing observations centred on the North Celestial Pole and the radio galaxy 3C220.3. We observe an unexplained excess of $\sim 30-50\%$ in Stokes $I$ noise compared to Stokes $V$ for the two observed fields, which decorrelates on $\gtrsim 12$ seconds and might have a physical origin. We show that enforcing smoothness of gain errors along frequency direction during calibration reduces the additional variance in Stokes $I$ compared Stokes $V$ introduced by the calibration on sub-band level. After subtraction of smooth foregrounds, we achieve a $2σ$ upper limit on the 21-cm power spectrum of $Δ_{21}^2 < (14561\,\text{mK})^2$ at $k\sim 0.038\,h\,\text{cMpc}^{-1}$ and $Δ_{21}^2 < (14886\,\text{mK})^2$ at $k\sim 0.038 \,h\,\text{cMpc}^{-1}$ for the 3C220 and NCP fields respectively and both upper limits are consistent with each other. The upper limits for the two fields are still dominated by systematics on most $k$ modes.

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arXiv2019

On the usefulness of existing Solar-wind models for pulsar timing corrections

Dispersive delays due to the Solar wind introduce excess noise in high-precision pulsar timing experiments, and must be removed in order to achieve the accuracy needed to detect, e.g., low-frequency gravitational waves. In current pulsar timing experiments, this delay is usually removed by approximating the electron density distribution in the Solar wind either as spherically symmetric, or with a two-phase model that describes the contributions from both high- and low-speed phases of the Solar wind. However, no dataset has previously been available to test the performance and limitations of these models over extended timescales and with sufficient sensitivity. Here we present the results of such a test with an optimal dataset of observations of pulsar J0034-0534, taken with the German stations of LOFAR. We conclude that the spherical approximation performs systematically better than the two-phase model at almost all angular distances, with a residual root-mean-square (rms) given by the two-phase model being up to 28% larger than the result obtained with the spherical approximation. Nevertheless, the spherical approximation remains insufficiently accurate in modelling the Solar-wind delay (especially within 20 degrees of angular distance from the Sun), as it leaves timing residuals with rms values that reach the equivalent of 0.3 microseconds at 1400 MHz. This is because a spherical model ignores the large daily variations in electron density observed in the Solar wind. In the short term, broadband observations or simultaneous observations at low frequencies are the most promising way forward to correct for Solar-wind induced delay variations.

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arXiv2019

The seeds of supermassive black holes and the role of local radiation and metal spreading

We present cosmological hydrodynamical simulations including atomic and molecular non-equilibrium chemistry, multi-frequency radiative transfer (0.7-100 eV sampled over 150 frequency bins) and stellar population evolution to investigate the host candidates of the seeds of supermassive black holes coming from direct collapse of gas in primordial haloes (direct-collapse black holes, DCBHs). We consistently address the role played by atomic and molecular cooling, stellar radiation and metal spreading of C, N, O, Ne, Mg, Si, S, Ca, Fe, etc. from primordial sources, as well as their implications for nearby quiescent proto-galaxies under different assumptions for early source emissivity, initial mass function and metal yields. We find that putative DCBH host candidates need powerful primordial stellar generations, since common solar-like stars and hot OB-type stars are neither able to determine the conditions for direct collapse nor capable of building up a dissociating Lyman-Werner background radiation field. Thermal and molecular features of the identified DCBH host candidates in the scenario with very massive primordial stars seem favourable, with illuminating Lyman-Werner intensities featuring values of 1-50 J21. Nevertheless, additional non-linear processes, such as merger events, substructure formation, rotational motions and photo-evaporation, should inhibit pure DCBH formation in 2/3 of the cases. Local turbulence may delay gas direct collapse almost irrespectively from other environmental conditions. The impact of large Lyman-Werner fluxes at distances smaller than 5 kpc is severely limited by metal pollution.

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arXiv2019

A case study of hurdle and generalized additive models in astronomy: the escape of ionizing radiation

The dark ages of the Universe end with the formation of the first generation of stars residing in primeval galaxies. These objects were the first to produce ultraviolet ionizing photons in a period when the cosmic gas changed from a neutral state to an ionized one, known as Epoch of Reionization (EoR). A pivotal aspect to comprehend the EoR is to probe the intertwined relationship between the fraction of ionizing photons capable to escape dark haloes, also known as the escape fraction ($f_{esc}$), and the physical properties of the galaxy. This work develops a sound statistical model suitable to account for such non-linear relationships and the non-Gaussian nature of $f_{esc}$. This model simultaneously estimates the probability that a given primordial galaxy starts the ionizing photon production and estimates the mean level of the $f_{esc}$ once it is triggered. The model was employed in the First Billion Years simulation suite, from which we show that the baryonic fraction and the rate of ionizing photons appear to have a larger impact on $f_{esc}$ than previously thought. A naive univariate analysis of the same problem would suggest smaller effects for these properties and a much larger impact for the specific star formation rate, which is lessened after accounting for other galaxy properties and non-linearities in the statistical model.

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arXiv2018

X-ray background and its correlation with the 21 cm signal

We use high resolution hydrodynamical simulations to study the contribution to the X-ray background from high-$z$ energetic sources, such as X-ray binaries, accreting nuclear black holes and shock heated interstellar medium. Adopting the model discussed in Eide et al. (2018), we find that these X-ray sources during the Epoch of Reionization (EoR) contribute less than a few percent of the unresolved X-ray background. The same sources contribute to less than $\sim$2\% of the measured angular power spectrum of the fluctuations of the X-ray background. The outputs of radiative transfer simulations modeling the EoR are used to evaluate the cross-correlations of X-ray background with the 21~cm signal from neutral hydrogen. Such correlation could be used to confirm the origin of the 21 cm signal, as well as give information on the properties of the X-ray sources during the EoR. We find that the correlations are positive during the early stages of reionization when most of the hydrogen is neutral, while they become negative when the intergalactic medium gets highly ionized, with the transition from positive to negative depending on both the X-ray model and the scale under consideration. With {\tt SKA} as the reference instrument for the 21~cm experiment, the predicted S/N for such correlations is $<1$ if the corresponding X-ray survey is only able to resolve and remove X-ray sources with observed flux $>10^{-15}\,\rm erg\, cm^{-2} \, s^{-1}$, while the cumulative S/N from $l=1000$ to $10^{4}$ at $x_{\rm HI}=0.5$ is $\sim 5$ if sources with observed flux $>10^{-17}\,\rm erg\, cm^{-2} \, s^{-1}$ are detected.

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arXiv2018

X-ray ionization of the intergalactic medium by quasars

We investigate the impact of quasars on the ionization of the surrounding intergalactic medium (IGM) with the radiative transfer code \texttt{CRASH4}, now accounting for X-rays and secondary electrons. After comparing with analytic solutions, we post-process a cosmic volume ($ \approx 1.5\times 10^4$ Mpc$^3 h^{-3}$) containing a ULAS J1120+0641-like quasar (QSO) hosted by a $5 \times 10^{11} {\rm M}_\odot h^{-1}$ dark matter (DM) halo. We find that: (i) the average HII region ($R\sim3.2$~pMpc in a lifetime $t_f = 10^7$~yrs) is mainly set by UV flux, in agreement with semi-analytic scaling relations; (ii) a largely neutral ($x_{\textrm{HII}} < 0.001$), warm ($T\sim 10^3$~K) tail extends up to few Mpc beyond the ionization front, as a result of the X-ray flux; (iii) LyC-opaque inhomogeneities induce a line of sight (LOS) scatter in $R$ as high as few physical Mpc, consistent with the DLA scenario proposed to explain the anomalous size of the ULAS J1120+0641 ionized region. On the other hand, with an ionization rate $\dot{N}_{γ,0} \sim 10^{57}$~s$^{-1}$, the assumed DLA clustering and gas opacity, only one LOS shows an HII region compatible with the observed one. We deduce that either the ionization rate of the QSO is at least one order of magnitude lower or the ULAS J1120+0641 bright phase is shorter than $10^7$~yrs.

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