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Register a new userThe accuracy of semi-numerical reionization models in comparison with radiative transfer simulations
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Anne Hutter
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We have developed a modular semi-numerical code that computes the time and spatially dependent ionization of neutral hydrogen (HI), neutral (HeI) and singly ionized helium (HeII) in the intergalactic medium (IGM). The model accounts for recombinations and provides different descriptions for the photoionization rate that are used to calculate the residual HI fraction in ionized regions. We compare different semi-numerical reionization schemes to a radiative transfer (RT) simulation. We use the RT simulation as a benchmark, and find that the semi-numerical approaches produce similar HII and HeII morphologies and power spectra of the HI 21cm signal throughout reionization. As we do not track partial ionization of HeII, the extent of the double ionized helium (HeIII) regions is consistently smaller. In contrast to previous comparison projects, the ionizing emissivity in our semi-numerical scheme is not adjusted to reproduce the redshift evolution of the RT simulation, but directly derived from the RT simulation spectra. Among schemes that identify the ionized regions by the ratio of the number of ionization and absorption events on different spatial smoothing scales, we find those that mark the entire sphere as ionized when the ionization criterion is fulfilled to result in significantly accelerated reionization compared to the RT simulation. Conversely, those that flag only the central cell as ionized yield very similar but slightly delayed redshift evolution of reionization, with up to 20% ionizing photons lost. Despite the overall agreement with the RT simulation, our results suggests that constraining ionizing emissivity sensitive parameters from semi-numerical galaxy formation-reionization models are subject to photon nonconservation.
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A serious concern for semi-analytical galaxy formation models, aiming to simulate multi-wavelength surveys and to thoroughly explore the model parameter space, is the extremely time consuming numerical solution of the radiative transfer of stellar radiation through dusty media. To overcome this problem, we have implemented an artificial neural network algorithm in the radiative transfer code GRASIL, in order to significantly speed up the computation of the infrared SED. The ANN we have implemented is of general use, in that its input neurons are defined as those quantities effectively determining the shape of the IR SED. Therefore, the training of the ANN can be performed with any model and then applied to other models. We made a blind test to check the algorithm, by applying a net trained with a standard chemical evolution model (i.e. CHE_EVO) to a mock catalogue extracted from the SAM MORGANA, and compared galaxy counts and evolution of the luminosity functions in several near-IR to sub-mm bands, and also the spectral differences for a large subset of randomly extracted models. The ANN is able to excellently approximate the full computation, but with a gain in CPU time by $sim 2$ orders of magnitude. It is only advisable that the training covers reasonably well the range of values of the input neurons in the application. Indeed in the sub-mm at high redshift, a tiny fraction of models with some sensible input neurons out of the range of the trained net cause wrong answer by the ANN. These are extreme starbursting models with high optical depths, favorably selected by sub-mm observations, and difficult to predict a priori.
We present a detailed comparison of three different simulations of the epoch of reionization (EoR). The radiative transfer simulation (${rm C}^2$-RAY) among them is our benchmark. Radiative transfer codes can produce realistic results, but are computationally expensive. We compare it with two semi-numerical techniques: one using the same halos as ${rm C}^2$-RAY as its sources (Sem-Num), and one using a conditional Press-Schechter scheme (CPS+GS). These are vastly more computationally efficient than ${rm C}^2$-RAY, but use more simplistic physical assumptions. We evaluate these simulations in terms of their ability to reproduce the history and morphology of reionization. We find that both Sem-Num and CPS+GS can produce an ionization history and morphology that is very close to ${rm C}^2$-RAY, with Sem-Num performing slightly better compared to CPS+GS. We also study different redshift space observables of the 21-cm signal from EoR: the variance, power spectrum and its various angular multipole moments. We find that both semi-numerical models perform reasonably well in predicting these observables at length scales relevant for present and future experiments. However, Sem-Num performs slightly better than CPS+GS in producing the reionization history, which is necessary for interpreting the future observations.
Numerical simulations of 15 orbits of an equal-mass binary black hole system are presented. Gravitational waveforms from these simulations, covering more than 30 cycles and ending about 1.5 cycles before merger, are compared with those from quasi-circular zero-spin post-Newtonian (PN) formulae. The cumulative phase uncertainty of these comparisons is about 0.05 radians, dominated by effects arising from the small residual spins of the black holes and the small residual orbital eccentricity in the simulations. Matching numerical results to PN waveforms early in the run yields excellent agreement (within 0.05 radians) over the first $sim 15$ cycles, thus validating the numerical simulation and establishing a regime where PN theory is accurate. In the last 15 cycles to merger, however, {em generic} time-domain Taylor approximants build up phase differences of several radians. But, apparently by coincidence, one specific post-Newtonian approximant, TaylorT4 at 3.5PN order, agrees much better with the numerical simulations, with accumulated phase differences of less than 0.05 radians over the 30-cycle waveform. Gravitational-wave amplitude comparisons are also done between numerical simulations and post-Newtonian, and the agreement depends on the post-Newtonian order of the amplitude expansion: the amplitude difference is about 6--7% for zeroth order and becomes smaller for increasing order. A newly derived 3.0PN amplitude correction improves agreement significantly ($<1%$ amplitude difference throughout most of the run, increasing to 4% near merger) over the previously known 2.5PN amplitude terms.
Semi-numerical models of the reionization of neutral hydrogen (HI) based on the excursion set (ES) approach are known to violate photon number conservation at the few per cent level. In this work, we highlight a more severe, previously unrecognized shortcoming of ES models: the large-scale 21 cm power spectrum (equivalently, HI bias b_HI) is a relatively strong function of the spatial resolution used to generate ES ionization maps. We trace this problem to the fact that photon non-conservation in these models arises from a resolution-dependent mixture of spatially resolved, photon non-conserving bubbles, and partially ionized grid cells which are perfectly photon-conserving by construction. We argue that this inevitably leads to a resolution-dependence of b_HI, with the correct, converged value only emerging at very coarse resolution. Quantitatively, we find that b_HI can be non-converged by as much as ~20-25% in conservative ES implementations with grid sizes Delta x=5-10 cMpc/h, even when photon non-conservation is as small as ~3-4%. Thus, although numerically efficient, ES ionization maps coarse enough to produce a converged HI bias would wash out all topological features of the ionization field at scales k>~0.05 h/cMpc. We therefore present a new, explicitly photon conserving (PC) semi-numerical algorithm which distributes photons isotropically around sources while also accounting for anisotropic overlaps between nearby bubbles. Our PC algorithm predicts a resolution-independent value of b_HI consistent with the result of low-resolution ES maps, thus serving as a useful compromise between standard ES implementations and more expensive radiative transfer simulations.
In this work we present a new hybrid method to simulate the thermal effects of the reionization in cosmological hydrodynamical simulations. The method improves upon the standard approach used in simulations of the intergalactic medium (IGM) and galaxy formation without a significant increase of the computational cost allowing for efficient exploration of the parameter space. The method uses a small set of phenomenological input parameters and combines a semi-numerical reionization model to solve for the topology of reionization and an approximate model of how reionization heats the IGM, with the massively parallel texttt{Nyx} hydrodynamics code, specifically designed to solve for the structure of diffuse IGM gas. We have produced several large-scale high resolution cosmological hydrodynamical simulations ($2048^3$, $L_{rm box} = 40$ Mpc/h) with different instantaneous and inhomogeneous HI reionization models that use this new methodology. We study the IGM thermal properties of these models and find that large scale temperature fluctuations extend well beyond the end of reionization. Analyzing the 1D flux power spectrum of these models, we find up to $sim 50%$ differences in the large scale properties (low modes, $klesssim0.01$ s/km) of the post-reionization power spectrum due to the thermal fluctuations. We show that these differences could allow one to distinguish between different reionization scenarios already with existing Ly$alpha$ forest measurements. Finally, we explore the differences in the small-scale cutoff of the power spectrum and we find that, for the same heat input, models show very good agreement provided that the reionization redshift of the instantaneous reionization model happens at the midpoint of the inhomogeneous model.
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