We present a new semi-analytical model of the population of satellite galaxies of the Milky Way, aimed at estimating the effect of the geometry of reionization at galaxy scale on the properties of the satellites. In this model reionization can be either: (A) externally-driven and uniform, or (B) internally-driven, by the most massive progenitor of the Milky Way. In the latter scenario the propagation of the ionisation front and photon dilution introduce a delay in the photo-evaporation of the outer satellites' gas with respect to the inner satellites. As a consequence, outer satellites experience a longer period of star formation than those in the inner halo. We use simple models to account for star formation, the propagation of the ionisation front, photo-evaporation and observational biases. Both scenarios yield a model satellite population that matches the observed luminosity function and mass-to-light ratios. However, the predicted population for scenario (B) is significantly more extended spatially than for scenario (A), by about 0.3 dex in distance, resulting in a much better match to the observations. The survival of the signature left by the local UV field during reionization on the radial distribution of satellites makes it a promising tool for studying the reionization epoch at galaxy scale in the Milky Way and nearby galaxies resolved in stars with forthcoming large surveys.
We use the publicly available subhalo catalogs from the Via Lactea simulation along with a Gpc-scale N-body simulation to understand the impact of inhomogeneous reionization on the satellite galaxy population of the Milky Way. The large-volume simulation is combined with a model for reionization that allows us to predict the distribution of reionization times for Milky Way mass halos. Motivated by this distribution, we identify candidate satellite galaxies in the simulation by requiring that any subhalo must grow above a specified mass threshold before it is reionized; after this time the phot…
We present the results of a set of numerical simulations aimed at studying reionization at galactic scale. We use a high resolution simulation of the formation of the Milky Way-M31 system to simulate the reionization of the local group. The reionization calculation was performed with the post-processing radiative transfer code ATON and the underlying cosmological simulation was performed as part of the CLUES project. We vary the source models to bracket the range of source properties used in the literature. We investigate the structure and propagation of the galatic ionization fronts by a visu…
We present an analysis of the evolution of the Lyman-series forest into the epoch of reionization using cosmological radiative transfer simulations in a scenario where reionization ends late. We explore models with different midpoints of reionization and gas temperatures. We find that once the simulations have been calibrated to match the mean flux of the observed Lyman-$α$ forest at $4 < z < 6$, they also naturally reproduce the distribution of effective optical depths of the Lyman-$β$ forest in this redshift range. We note that the tail of the largest optical depths that is most challenging …
Observations of the Milky Way (MW), M31, and their vicinity, known as the Local Group (LG), can provide clues about the sources of reionization. We present a suite of radiative transfer simulations based on initial conditions provided by the Constrained Local UniversE Simulations (CLUES) project that are designed to recreate the Local Universe, including a realistic MW-M31 pair and a nearby Virgo. Our box size (91 Mpc) is large enough to incorporate the relevant sources of ionizing photons for the LG. We employ a range of source models, mimicking the potential effects of radiative feedback for…
The period in which hydrogen in the intergalactic medium (IGM) is ionized, known as the Epoch of Reionization (EoR) is still poorly understood. The timing and duration of the EoR is expected to be governed by the underlying astrophysics. Furthermore, most models of reionization predict a correlation between the density and ionization field. Here we consider using the mean dispersion measure (DM) of high redshift Fast Radio Bursts (FRBs) as a probe of the underlying astrophysics and morphology of the EoR. To do this, we forecast observational scenarios by building mock data sets of non-repeatin…
A number of independent observations suggest that the intergalactic medium was significantly neutral at $z=7$ and that reionization was, perhaps, still in progress at $z=5.7$. The narrowband survey, SILVERRUSH, has mapped over $2,000$ Lyman-$α$ emitters (LAEs) at these redshifts. Previous analyses have assumed that reionization was over by $z=5.7$, but this data may actually sample the final stages of reionization when the last neutral islands were relegated to the cosmic voids. Motivated by these developments, we reexamine LAE void and peak statistics and their ability to constrain reionizati…
Neutral diffuse intergalactic gas that existed during the Epoch of Reionization (EoR) suppresses Lyman Alpha (Lya) flux emitted by background galaxies. In this chapter I summarise the increasing observational support for the claim that Lya photons emitted by galaxies at z>6 are suppressed by intervening HI gas. I describe key physical processes that affect Lya transfer during the EoR. I argue that in spite of the uncertainties associated with this complex multiscale problem, the data on Lya emitting galaxies at z=0-6 strongly suggests that the observed reduction in Lya flux from galaxies at z>…
Given that the reionization history of cosmic hydrogen is yet to be stringently constrained, it is worth checking the prospects of doing so using physically motivated models and available observational data. For this purpose, we use an extended version of the explicitly photon-conserving semi-numerical model of reionization, $\texttt{SCRIPT}$, which also includes thermal evolution of the intergalactic medium (IGM). The model incorporates the effects of inhomogeneous recombination and radiative feedback self-consistently and is characterized by five free parameters (two for the redshift-depende…
We combine available constraints on the local CII 158 $μ$m line luminosity function from galaxy observations (Hemmati et al. 2017), with the evolution of the star-formation rate density and the recent CII intensity mapping measurement in Pullen et al. (2018, assuming detection), to derive the evolution of the CII luminosity - halo mass relation over $z \sim 0-6$. We develop convenient fitting forms for the evolution of the CII luminosity - halo mass relation, and forecast constraints on the CII intensity mapping power spectrum and its associated uncertainty across redshifts. We predict the sen…
We combine observational data on a dozen independent cosmic properties at high-$z$ with the information on reionization drawn from the spectra of distant luminous sources and the cosmic microwave background (CMB) to constrain the interconnected evolution of galaxies and the intergalactic medium since the dark ages. The only acceptable solutions are concentrated in two narrow sets. In one of them reionization proceeds in two phases: a first one driven by Population III stars, completed at $z\sim 10$, and after a short recombination period a second one driven by normal galaxies, completed at $z\…
While the connection between high-redshift star formation and the local universe has recently been used to understand the observed population of faint dwarf galaxies in the Milky Way (MW) halo, we explore how well these nearby objects can probe the epoch of first light. We construct a detailed, physically motivated model for the MW satellites based on the state-of-the-art Via Lactea II dark-matter simulations. Our model incorporates molecular hydrogen (H_2) cooling in low-mass systems and inhomogeneous photo-heating feedback during the internal reionization of our own galaxy. We find that the …
The latest measurements of CMB electron scattering optical depth reported by Planck significantly reduces the allowed space of HI reionization models, pointing toward a later ending and/or less extended phase transition than previously believed. Reionization impulsively heats the intergalactic medium (IGM) to $\sim10^4$ K, and owing to long cooling and dynamical times in the diffuse gas, comparable to the Hubble time, memory of reionization heating is retained. Therefore, a late ending reionization has significant implications for the structure of the $z\sim5-6$ Lyman-$α$ (ly$α$) forest. Using…
A possible way to study the reionization of cosmic hydrogen is by observing the large ionized regions (bubbles) around bright individual sources, e.g., quasars, using the redshifted 21 cm signal. It has already been shown that matched filter-based methods are not only able to detect the weak 21 cm signal from these bubbles but also aid in constraining their properties. In this work, we extend the previous studies to develop a rigorous Bayesian framework to explore the possibility of constraining the parameters that characterize the bubbles. To check the accuracy with which we can recover the b…
We combine the high-resolution Aquarius simulations with three-dimensional models of reionization based on the initial density field of the Aquarius parent simulation, Millennium-II, to study the impact of patchy reionization on the faint satellite population of Milky Way halos. Because the Aquarius suite consists of zoom-in simulations of halos in the Millennium-II volume, we follow the formation of substructure and the growth of reionization bubbles due to the larger environment simultaneously, and thereby determine the reionization redshifts of satellite candidates. We do this for four diff…
Cosmological simulations of Population III star formation suggest an initial mass function (IMF) biased toward very massive stars (M>100Msun) formed in minihalos at redshift z>20, when the cooling is driven by molecular hydrogen. However, this result conflicts with observations of extremely-metal poor (EMP) stars in the Milky Way halo, whose r-process elemental abundances appear to be incompatible with those expected from very massive Population III progenitors. We propose a new solution to the problem in which the IMF of second-generation stars formed at z>10, before reionization, is deficien…
We investigate Lyman-$α$ transmission spikes at $z > 5$ in synthetic quasar spectra, and discuss their connection to the properties of the intergalactic medium and their ability to constrain reionization models. We use state-of-the-art radiation-hydrodynamic simulations from the Cosmic Reionization On Computers series to predict the number of transmission spikes as a function of redshift, both in the ideal case of infinite spectral resolution and in a realistic observational setting. Transmission spikes are produced in highly-ionized underdense regions located in the vicinity of UV sources. We…
The measurement of the optical depth to free electrons, tau_r, in the cosmic microwave background (CMB) provides an important constraint on reionization, but is degenerate to more complex reionization models. Small angular-scale CMB measurements of the kinetic Sunyaev-Zeldovich (kSZ) and Ostriker-Vishniac (OV) effects have the potential to break this degeneracy. We calculate the OV signal for various extended reionization histories described by a simple analytic form. These models are parametrized by dz, the duration of the reionization event. For reionization histories with identical values o…
Understanding the detailed process of cosmic reionization is one of the remaining problems in astrophysics and cosmology. Here we construct a model of cosmic reionization that includes contribution from high-$z$ galaxies and active galactic nuclei (AGNs), and calculate the reionization and thermal histories with the model. To keep the model to be general and realistic, we vary the escape fraction of ionizing photons, $f_{\rm esc}$, and the faint-end slope of the AGN luminosity function at high redshifts, $α_{\rm hz}$, within the constraints from the observed cosmic star formation history and t…
Globular clusters are unique tracers of ancient star formation. We determine the formation efficiencies of globular clusters across cosmic time by modeling the formation and dynamical evolution of the globular cluster population of a Milky Way type galaxy in hierarchical cosmology, using the merger tree from the Via Lactea II simulation. All of the models are constrained to reproduce the observed specific frequency and initial mass function of globular clusters in isolated dwarfs. Globular cluster orbits are then computed in a time varying gravitational potential after they are either accreted…
We investigate the connection between the epoch of reionization and the present day universe, by examining the extended mass reionization histories of dark matter halos identified at z=0. We combine an N-body dark matter simulation of a 600 Mpc volume with a three-dimensional, seminumerical reionization model. This provides reionization redshifts for each particle, which can then be connected with the properties of their halos at the present time. We find that the vast majority of present-day halos with masses larger than ~ few x 10^11 Msun reionize earlier than the rest of the universe. We al…
Upcoming 21cm surveys with the SKA1-LOW telescope will enable imaging of the neutral hydrogen distribution on cosmological scales in the early Universe. These surveys are expected to generate huge imaging datasets that will encode more information than the power spectrum. This provides an alternative unique way to constrain the reionization history, which might break the degeneracy in the power spectral analysis. Using Convolutional Neural Networks (CNN), we create a fast estimator of the neutral fraction from the 21cm maps that are produced by our large semi-numerical simulation. Our estimato…
We investigate the constraints on the reionization history of the Universe from a joint analysis of the cosmic microwave background and neutral hydrogen fraction data. The $\tanh$ parametrization and principal component analysis methods are applied to the reionization history respectively. The commonly used $\tanh$ parametrization is oversimplistic when the neutral hydrogen fraction data are taken into account. Using the principal component analysis method, the reconstructed reionization history is consistent with the neutral hydrogen fraction data. With the principal component analysis method…
We use the Fisher matrix formalism and semi-numerical simulations to derive quantitative predictions of the constraints that power spectrum measurements on next-generation interferometers, such as the Hydrogen Epoch of Reionization Array (HERA) and the Square Kilometre Array (SKA), will place on the characteristics of the X-ray sources that heated the high redshift intergalactic medium. Incorporating observations between $z=5$ and $z=25$, we find that the proposed 331 element HERA and SKA phase 1 will be capable of placing $\lesssim 10\%$ constraints on the spectral properties of these first X…
In this paper, we explore the constraints on the reionization history that are provided by current observations of the Lyman-alpha forest and the CMB. Rather than using a particular semi-analytic model, we take the novel approach of parametrizing the ionizing sources with arbitrary functions, and perform likelihood analyses to constrain possible reionization histories. We find model independent conclusions that reionization is likely to be mostly complete by z=8 and that the IGM was 50% ionized at z=9-10. Upcoming low-frequency observations of the redshifted 21 cm line of neutral hydrogen are …
Observations of the frequency dependence of the global brightness temperature of the redshifted 21 cm line of neutral hydrogen may be possible with single dipole experiments. In this paper, we develop a Fisher matrix formalism for calculating the sensitivity of such instruments to the 21 cm signal from reionization and the dark ages. We show that rapid reionization histories with duration delta z< 2 can be constrained, provided that local foregrounds can be well modelled by low order polynomials. It is then shown that observations in the range nu = 50 - 100 MHz can feasibly constrain the Lyman…
We propose a new reionization probe that uses cosmic microwave background (CMB) observations; the cross-correlation between fluctuations in the CMB optical depth which probes the integrated electron density, $δτ$, and the Compton $y$-map which probes the integrated electron pressure. This cross-correlation is much less contaminated than the $y$-map power spectrum by late-time cluster contributions. In addition, this cross-correlation can constrain the temperature of ionized bubbles while the optical-depth fluctuations and kinetic SZ effect can not. We measure this new observable using a Planck…
We explore the possibility of constraining model parameters of the Epoch of Reionization (EoR) from 21cm brightness temperature maps, using a combination of morphological descriptors constructed from the eigenvalues of the Contour Minkowski Tensor (CMT), Betti numbers (count of connected regions $n_{con}$ and holes $n_{hole}$) and the area of structures in the excursion set of the field. We use a three parameter model of EoR simulated using 21\textrm{cmFAST}, namely the ionizing efficiency of sources $ζ$, the minimum virial temperature $T_{vir}$ required for collapse into a halo and the maximu…
The Square Kilometre Array (SKA) will offer an unprecedented view onto the early Universe, using interferometric observations of the redshifted 21cm line. The 21cm line probes the thermal and ionization state of the cosmic gas, which is governed by the birth and evolution of the first structures in our Universe. Here we show how the evolution of the 21cm signal will allow us to study when the first generations of galaxies appeared, what were their properties, and what was the structure of the intergalactic medium. We highlight qualitative trends which will offer robust insights into the early …
We present proof of principle for a two way interplay between physics at very early Universe and late time observations. We find a relation between primordial mechanisms responsible for large scale power suppression in the primordial power spectrum and the value of reionization optical depth $τ$. Such mechanisms can affect the estimation of $τ$. We show that using future measurements of $τ$, one can obtain constraints on the pre-inflationary dynamics, providing a new window on the physics of the very early Universe. Furthermore, the new, re-estimated $τ$ can potentially resolve moderate discre…
The epoch of reionization (6 < z < 10) marks the period in our universe when the first large galaxies grew to fruition, and began to affect the universe around them. Massive stars, and potentially accreting supermassive black holes, filled the universe with ionizing radiation, burning off the haze of neutral gas that had filled the intergalactic medium (IGM) since recombination (z~1000). The evolution of this process constrains key properties of these earliest luminous sources, thus observationally constraining reionization is a key science goal for the next decade. The measurement of Lyman-al…
The discovery of fast radio bursts (FRBs) about a decade ago opened up new possibilities for probing the ionization history of the Intergalactic Medium (IGM). In this paper we study the use of FRBs for tracing the epoch of HeII reionization, using simulations of their dispersion measures. We model dispersion measure contributions from the Milky Way, the IGM (homogeneous and inhomogeneous) and a possible host galaxy as a function of redshift and star formation rate. We estimate the number of FRBs required to distinguish between a model of the Universe in which helium reionization occurred at z …
Reionizing the Universe with galaxies appears to require significant star formation in low-mass halos at early times, while local dwarf galaxy counts tell us that star formation has been minimal in small halos around us today. Using simple models and the ELVIS simulation suite, we show that reionization scenarios requiring appreciable star formation in halos with $M_{\rm vir} \approx 10^{8}\,M_{\odot}$ at $z=8$ are in serious tension with galaxy counts in the Local Group. This tension originates from the seemingly inescapable conclusion that 30 - 60 halos with $M_{\rm vir} > 10^{8}\,M_{\odot}$…
We investigate the cosmic reionization history by comparing semi-analytical models of the Lya forest with observations of high-z quasars and gamma ray bursts absorption spectra. In order to constrain the reionization epoch z_rei, we consider two physically motivated scenarios in which reionization ends either early (ERM, z_rei>= 7) or late (LRM, z_rei~6). We analyze the transmitted flux in a sample of 17 quasars spectra at 5.7<z<6.4 and in the spectrum of the gamma ray burst 050904 at z=6.3, studying the wide dark portions (gaps) in the observed absorption spectra. By comparing the statistics …
Constraining reionization with persistent homology: a novel summary statistic for wide-field Lyman-$α$ emitter observations
University of California, Los Angeles（加州大学洛杉矶分校）；Scuola Normale Superiore（比萨高等师范学院）；University of Tsukuba（筑波大学）；The University of Tokyo（东京大学）；Institute for Cosmic Ray Research, The University of Tokyo（东京大学宇宙射线研究所）；University of Catania（卡塔尼亚大学）；National Astronomical Observatory of Japan, National Institutes of Natural Sciences（日本国立天文台，国立自然科学研究院）；SOKENDAI (The Graduate University for Advanced Studies)（综合研究大学院大学）；Kavli Institute for the Physics and Mathematics of the Universe (WPI)（宇宙物质与物理学 Kavli 研究所）
The ages of globular clusters in our own Milky Way are known with precision of about \pm 1 Gyr, hence their formation at redshifts z>~3 and their role in hierarchical cosmology and the reionization of the intergalactic medium remain relatively undetermined. Here we analyze the effect of globular cluster formation on the observed rest-frame UV luminosity functions (LFs) and UV continuum slopes of high redshift galaxies in the Hubble Ultra Deep Fields. We find that the majority of present day globular clusters have formed during two distinct epochs: at redshifts z ~ 2-3 and at redshifts z>~6. Th…
We build a physical model for high-redshift Lyman Alpha emitters (LAEs) by coupling state of the art cosmological simulations (GADGET-2) with a dust model and a radiative transfer code (pCRASH). We post-process the cosmological simulation with pCRASH using five different values of the escape fraction of hydrogen ionizing photons (f_esc=0.05,0.25,0.5,0.75,0.95) until reionization is complete, i.e. the average neutral hydrogen fraction drops to <X_HI>~10^-4. Then, the only free-parameter left to match model results to the observed Lya and UV luminosity functions of LAEs at z~6.6 is the relative …
In this paper, we study the chemical properties of the stars in the dwarf satellites around the MW-like host galaxies, and explore the possible effects of several baryonic processes, including supernova (SN) feedback, the reionization of the universe and H$_2$ cooling, on them and how current and future observations may put some constraints on these processes. We use a semi-analytical model to generate MW-like galaxies, for which a fiducial model can reproduce the luminosity function and the stellar metallicity--stellar mass correlation of the MW dwarfs. Using the simulated MW-like galaxies, w…
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 $\gtrsim 0.…
High-signal to noise observations of the Ly$α$ forest transmissivity in the z = 7.085 QSO ULAS J1120+0641 show seven narrow transmission spikes followed by a long 240 cMpc/h trough. Here we use radiative transfer simulations of cosmic reionization previously calibrated to match a wider range of Ly$α$ forest data to show that the occurrence of seven transmission spikes in the narrow redshift range z = 5.85 - 6.1 is very sensitive to the exact timing of reionization. Occurrence of the spikes requires the most under dense regions of the IGM to be already fully ionised. The rapid onset of a long t…
Romanian Institute of Science and Technology（罗马尼亚科学技术研究院）
The next generation 21 cm surveys open a new window onto the early stages of cosmic structure formation and provide new insights about the Epoch of Reionization (EoR). However, the non-Gaussian nature of the 21 cm signal along with the huge amount of data generated from these surveys will require more advanced techniques capable to efficiently extract the necessary information to constrain the Reionization History of the Universe. In this paper we present the use of Bayesian Neural Networks (BNNs) to predict the posterior distribution for four astrophysical and cosmological parameters. Besides…
We combine a series of high-resolution simulations with semi-analytic galaxy formation models to follow the evolution of a system resembling the Milky Way and its satellites. The semi-analytic model is based on that developed for the Millennium Simulation, and successfully reproduces the properties of galaxies on large scales, as well as those of the Milky Way. In this model, we are able to reproduce the luminosity function of the satellites around the Milky Way by preventing cooling in haloes with Vvir < 16.7 km/s (i.e. the atomic hydrogen cooling limit) and including the impact of the reioni…
We present detailed radiative transfer simulations of the reionization history of the Milky Way by metal-poor globular clusters. We identify potential metal-poor globular cluster candidates within the Aquarius simulation using dark matter halo velocity dispersions. We calculate the local ionization fields via a photon-conserving, three dimensional non-equilibrium chemistry code and allow the model to propagate through to the present day. The key feature of the model is that globular cluster formation is suppressed if the local gas is ionized. We find that our spatial treatment of the ionizatio…
The cosmological process of hydrogen (HI) reionization in the intergalactic medium is thought to be driven by UV photons emitted by star-forming galaxies and ionizing active galactic nuclei (AGN). The contribution of QSOs to HI reionization at $z>4$ has been traditionally believed to be quite modest. However, this view has been recently challenged by new estimates of a higher faint-end UV luminosity function (LF). To set firmer constraints on the emissivity of AGN at $z<6$, we here make use of complete X-ray selected samples including deep Chandra and new COSMOS data, capable to efficiently me…
In the absence of complex astrophysical processes that characterize the reionization era, the 21-cm emission from neutral hydrogen (HI) in the post-reionization epoch is believed to be an excellent tracer of the underlying dark matter distribution. Assuming a background cosmology, it is modelled through (i) a bias function b(k,z), which relates HI to the dark matter distribution and (ii) a mean neutral fraction (x_{HI}) which sets its amplitude. In this paper, we investigate the nature of large scale HI bias. The post-reionization HI is modelled using gravity only N-Body simulations and a suit…
The neutral intergalactic medium in the post reionization epoch allows us to study cosmological structure formation through the observation of the redshifted 21 cm signal and the Lyman-alpha forest. We investigate the possibility of measuring the total neutrino mass through the suppression of power in the matter power spectrum. We investigate the possibility of measuring the neutrino mass through its imprint on the cross-correlation power spectrum of the 21-cm signal and the Lyman-alpha forest. We consider a radio-interferometric measurement of the 21 cm signal with a SKA1-mid like radio teles…
The Milky Way's (MW) satellite population is a powerful probe of warm dark matter (WDM) models as the abundance of small substructures is very sensitive to the properties of the WDM particle. However, only a partial census of the MW's complement of satellite galaxies exists because surveys of the MW's close environs are incomplete both in depth and in sky coverage. We present a new Bayesian analysis that combines the sample of satellites recently discovered by the Dark Energy Survey (DES) with those found in the Sloan Digital Sky Survey (SDSS) to estimate the total satellite galaxy luminosity …
Several experiments are underway to detect the cosmic redshifted 21-cm signal from neutral hydrogen from the Epoch of Reionization (EoR). Due to their very low signal-to-noise ratio, these observations aim for a statistical detection of the signal by measuring its power spectrum. We investigate the extraction of the variance of the signal as a first step towards detecting and constraining the global history of the EoR. Signal variance is the integral of the signal's power spectrum, and it is expected to be measured with a high significance. We demonstrate this through results from a simulation…
We study the impact of baryons on the distribution of dark matter in a Milky Way-size halo by comparing a high-resolution, moving-mesh cosmological simulation with its dark matter-only counterpart. We identify three main processes related to baryons -- adiabatic contraction, tidal disruption and reionization -- which jointly shape the dark matter distribution in both the main halo and its subhalos. The relative effect of each baryonic process depends strongly on the subhalo mass. For massive subhalos with maximum circular velocity $v_{\rm max} > 35 km/s$, adiabatic contraction increases the da…
The Murchison Widefield Array (MWA) team has derived new upper limits on the spherically averaged power spectrum of the 21-cm signal at six redshifts in the range $z \approx 6.5-8.7$. We use these upper limits and a Bayesian inference framework to derive constraints on the ionization and thermal state of the intergalactic medium (IGM) as well as on the strength of a possible additional radio background. We do not find any constraints on the state of the IGM for $z\gtrsim 7.8$ if no additional radio background is present. In the presence of such a radio background, the 95 per cent credible inte…
