Ultraviolet background fluctuations with clustered sources

Abstract

We develop a count-in-cells approach to the distribution of ultraviolet background fluctuations that includes source clustering. We demonstrate that an exact expression can be obtained if the clustering of ionising sources follows the hierarchical ansatz. In this case, the intensity distribution depends solely on their 2-point correlation function. We show that the void scaling function of high redshift mock quasars is consistent with the Negative Binomial form, before applying our formalism to the description of HeII-ionising fluctuations at the end of helium reionization. The model inputs are the observed quasar luminosity function and 2-point correlation at z ∼ 3. We find that, for an (comoving) attenuation length 55 Mpc, quasar clustering contributes less than 30% of the variance of intensity fluctuations so long as the quasar correlation length does not exceed ∼ 15 Mpc. We investigate also the dependence of the intensity distribution on the large-scale environment. Differences in the mean HeII-ionising intensity between low-and high-density regions could be a factor of few if the sources are highly clustered. An accurate description of quasar demographics and their correlation with strong absorption systems is required to make more precise predictions. Recently, Dixon, Furlanetto & Mesinger (2014) have addressed the impact of quasar clustering using a seminumeric method, in which dark matter haloes are identified in realisations of the linear density field using the excursion set approach. They have found a relatively weak effect. However, given the current uncertainties on the demographics of high redshift quasars, it would be desirable to revisit this issue and explore a wider spectrum of quasar clustering amplitudes.In this paper, we will investigate this issue analytically c 0000 RAS

A self-consistent 3D model of fluctuations in the helium-ionizing background

“…As mentioned previously, Dixon et al (2014) showed that the impact of quasar clustering on ionizing background fluctuations was likely small. Recent work by Desjacques et al (2014) suggests that clustering could have a significant effect on background fluctuations at z ∼ 3 if the mean free path is comparable to the correlation length of quasars, r ξ ∼ 15 Mpc. The average mean free path in our simulations is substantially larger than this for the redshifts we are interested in (λ mfp > ∼ 25 Mpc), but it is reasonable to expect that the addition of mean free path fluctuations would enhance the effect of clustering to some degree.…”

“…Quasars are randomly placed in a cosmological volume 500 Mpc on a side from z = 4 to z = 2.5 following the Hopkins et al (2007) B-band quasar luminosity function (QLF). By placing quasars randomly we neglect their clustering; the effect of quasar clustering on fluctuations in the ionizing background is likely small (Dixon et al 2014) but could play a role when the mean free path is very short (Desjacques et al 2014; see Section 5.1). The ionizing spectrum of each quasar is determined by first converting the B-band luminosity to the luminosity at the H I ionizing edge with the constant conversion factor from Hopkins et al (2007) and assuming that the spectrum at ν > νH I is a power law Lν ∝ ν −α Q with αQ = 1.6 in agreement with Telfer et al (2002) and consistent with the recent estimate by Lusso et al (2015).…”

The Probability Distribution of Astrophysical Gravitational-Wave Background Fluctuations

“…This power-law behavior is known to arise from the nearest neighbor [40]. Similarly, bearing in mind that P (h 2 ) = P (h)/h, the large-h asymptotic scaling (21) implies…”

Multiple-scales approach to the averaging problem in cosmology

“…been considered in the past by refs. [41][42][43], and the upshot is that, if the number of sources is finite, then the probability of g 2 rel being higher than h is ∼ h −3 , for large h. Thus,…”