Original Research ARTICLE
Homogeneous vs Biased IGM: Impact on Reionization
- Independent Researcher, Pune, India
This paper considers the impact of large scale biasing of the IGM on reionization. The two simplest but extreme scenarios for IGM biasing are: an unbiased IGM which has a constant density and an IGM with density equal to the collapsed matter density. In this work, the relationship between the IGM density and the collapsed matter density is defined through an IGM bias parameter. The two extreme scenarios of homogeneous and perfectly biased IGM are produced for two extreme values of this bias parameter. It is found that, for the same level of reionization (i.e., for same global neutral hydrogen fraction). one could get very different 21 cm brightness temperature distributions for different values of this bias parameter. These distributions could give an order of magnitude more or less power as compared to the uniform case. It is also found that there exists a critical value for the IGM bias parameter for which there could be a near washout of the structure in the 21 cm brightness temperature distribution (i.e., zero power or a nearly uniform 21 cm brightness temperature distribution). To address the problem, a new method of generating 21 cm brightness temperature maps is used. The method uses the results of n-body simulations and then employs ray tracing to obtain the 21 cm brightness temperature maps. Towards the end, a prescription for the IGM bias parameter is given. This is derived within the framework of the Press-Schechter theory.
Epoch of Reionization (EoR) is considered as one of the most difficult challenges in modern cosmology (see e.g., Shapiro and Giroux, 1987; Gnedin and Ostriker, 1997; Barkana and Loeb, 2001, Barkana and Loeb, 2005; Furlanetto et al., 2009; Zaroubi, 2013; Cooray et al., 2019). Analysis of the EoR is demanding on observational (see e.g., Tozzi et al., 2000; Bernardi et al., 2009; Harker et al., 2010; Parsons et al., 2010; Hazelton et al., 2013; Thyagarajan et al., 2015; Dillon and Parsons, 2016; Thyagarajan et al., 2016; Mertens et al., 2018; Barry et al., 2019; Greig et al., 2020) as well as theoretical (see e.g., Madau et al., 1997; Ciardi et al., 2000; Benson et al., 2006; Furlanetto et al., 2006; Mesinger et al., 2011; Giri et al., 2018; Qin et al., 2018; La Plante and Ntampaka, 2019; Park et al., 2019; Liu and Shaw, 2020) fronts. The possibility of observing EoR in the radio window using the 21 cm radiation was suggested a long time ago (Wouthuysen, 1952; Field, 1959b; Sunyaev and Zeldovich, 1975). The 21 cm line emitted by the neutral hydrogen in the IGM gets redshifted to much larger wavelengths and a continuous distribution of neutral hydrogen gives rise to a continuum of emission in the radio window (for reviews, see Fan et al., 2006; Furlanetto et al., 2006; Choudhury, 2009; Pritchard and Loeb, 2012).
This paper explores the impact of large scale biasing of the IGM on the 21 cm power spectrum from EoR. Many earlier works have considered a clumpy IGM during the EoR (see e.g., Kohler et al., 2007; Pawlik et al., 2009; McQuinn et al., 2011; Raičević and Theuns, 2011; Finlator et al., 2012; Emberson et al., 2013; Jeeson-Daniel et al., 2014; So et al., 2014; Sobacchi and Mesinger, 2014; Trombetti and Burigana, 2014; Mao et al., 2020). Such an IGM is granular or clustered on small scales and is considered on subgrid level. Its eventual impact on the EoR power spectrum is considered by some authors (see e.g., Mao et al., 2020). This paper addresses large scale clumping or large scale biasing of the IGM. By large scale biasing one means how the distribution of the IGM is in the whole simulation box. Many numerical approaches of simulating EoR assume IGM to be having uniform density far from halo boundaries (see e.g., Mellema et al., 2006; Thomas and Zaroubi, 2008; Thomas et al., 2009; Ghara et al., 2015). While the early versions of semi-analytic methods determine the neutral hydrogen fraction,
In this work, α is termed as the IGM bias parameter and it notifies the biasing of the IGM with respect to the collapsed massive haloes1. For
The paper is organized as follows: The next section discusses the method of generating the 21 cm maps. The method is ideally suited to address the problem of impact of a biased IGM on EoR. The later section discusses the main results of the paper. A prescription for the IGM bias parameter within the Press-Schechter framework is then derived. This is followed by the conclusion of the work in the last section.
2 Method for Generating 21 cm Maps
The method used in this work (Raut, 2019) borrows ideas of semi-analytic methods (Furlanetto et al., 2004; Choudhury et al., 2009; Mesinger et al., 2011) and extensively numerical methods (Razoumov and Scott, 1999; Abel et al., 1999; Nakamoto et al., 2001). The parameters that are borrowed from semi-analytic approach are:
• The first step is to do N-body simulations and compute overdensity for each grid cell. I have used Illustris-1 simulations (Genel et al., 2014) for this step. The cosmological parameters used are wmap-9 (Hinshaw et al., 2013):
Second step assigns ionizing photons to each grid cell based on following prescription (Furlanetto et al., 2004).
• The next step is to split all the photons,
• The next step is to implement reionization. At each step of propagation of photon-rays, one computes the total weights of the photon-rays arriving in the grid cells. This total is compared with the amount of neutral hydrogen present in the grid cells. The photon-ray weights and neutral hydrogen counts are decremented at every step accounting for reionization. It is assumed at this step that each photon-ray can ionize amount of neutral hydrogen equal to the photon-ray weight (i.e., 100% ionization efficiency or a very large cross section for ionization reaction).
• The next step implements recombination. After the photon-ray weights and neutral hydrogen content of each grid cell is revised, the number of neutral hydrogen atoms that were ionized in that particular step,
• The final step is to terminate the photon-ray propagation and assign brightness temperature to each grid cell. The first part is implemented when the total of photon-ray weights falls below 0.1% of its initial value. For the second part, we use the well-known expression (Wouthuysen, 1952; Field, 1959a; Madau et al., 1997; Furlanetto et al., 2006),
3 The Biased IGM Analysis
This section discusses the effect of biased IGM on 21 cm brightness temperature distribution. The biasing of the IGM is modelled through Eq. 1 in the next two subsections.
3.1 Modification of the 21 cm Brightness Temperature Distribution With the IGM Bias Parameter
The 21 cm maps are generated for three values of α: 0, 0.5, and 1. As suggested earlier,
In this work, the global neutral hydrogen fraction, denoted by
The reionization data cubes are generated as discussed in the previous section. The 21 cm brightness temperature slices (midway through the simulation box) are shown in Figure 1. This is done for three values of the IGM bias parameter (
FIGURE 1. Brightness temperature slices midway through the simulation box. The slices are shown for three different values of α for three different redshifts. The values of redshift are indicated at the bottom-left side of each horizontal panel while the α values are shown at the top of each column.
As seen from Figure 1, the topology of the 21 cm brightness temperature distribution is changed as the IGM bias parameter is changed. For
These conclusions are fortified if one analyzes the 21 cm brightness temperature probability distributions. As seen from Figure 2, the probability distributions are opposite for
FIGURE 2. The 21 cm brightness temperature probability distribution (smoothed) for the whole simulation box for three values of redshifts and for three values of α The blue line is for the uniform (or for
One can also study the impact of the variation of the IGM bias parameter on the power spectrum. To obtain the power spectrum, the standard procedure is followed. First, the 21 cm brightness temperature distribution (
The spherically averaged dimensionless power spectrum is the obtained by averaging
As seen from Figure 3, for
FIGURE 3. The 21 cm brightness temperature distribution power spectrum for three different redshifts for three different values of the IGM bias parameter α. The value of redshift is mentioned at top of each plot while the value of α is mentioned at the bottom right corner of the third plot.
There is also a notable fall in the power spectrum for the
3.2 The Critical Value of the IGM Bias Parameter and the Uniform Distribution
The severe degradation of the 21 cm brightness temperature power spectrum is one of the main results of this paper and hence some further analysis is justified. Figure 4 shows the dependence of the power for three typical modes for three redshifts as a function of α. As mentioned before, these three modes are representative of the scales that would be measured by upcoming and future experiments. As seen from the figure, behavior of all the modes is similar: the plots are U-shaped. The power goes to almost zero for each mode for some value of α. Notably, this value of α seems to depend on the redshift alone and not on the scales. This means that all the scales hit minima at the same value of α. This observation indicates that there is indeed a near washout of
FIGURE 4. Dependence of power on the IGM bias parameter, α, for three typical modes for the three redshifts. The value of modes is indicated at the top left corner in the first plot. The value of redshift is indicated at the top of each box.
A critical value of the IGM bias parameter that causes a near uniform brightness temperature distribution is possibly a characteristic of the reionization process. To check this all three reionization parameters are varied from their fiducial values. This is done for the
FIGURE 5. Dependence of power on IGM bias parameter, α, for three typical modes for six different variations of reionization parameters. The value of modes is indicated at the top left corner in the first panel. The redshift is indicated at the bottom left. The parameter that is changed is indicated in the central portion of the plots. While one of the reionization parameter is changed, the other two are kept constant.
4 Prescription for IGM Distribution Based on Press-Schechter Theory
The IGM bias parameter being a constant throughout the box is ideally not possible but it is the next step to the other two extreme scenarios of it being equal to one or zero. These two extreme scenarios form basis of the EoR simulations done by many earlier works (see e.g., Mellema et al., 2006; Thomas and Zaroubi, 2008; Choudhury et al., 2009; Thomas et al., 2009; Mesinger et al., 2011; Ghara et al., 2015). A possible next step to a constant value for the IGM bias parameter is an IGM bias parameter that is a function of the overdensity parameter. This could be predicted within the framework of the Press-Schecheter theory. The following assumptions are employed to obtain the IGM distribution within this framework:
• The results of the Press-Schechter theory are exact,
• Baryons follow dark matter,
• All the baryons that are not part of galaxies (i.e., massive collapsed haloes) are considered as being part of the IGM.4
It is shown in the Supplementary Appendix that
FIGURE 6. Dependence of the IGM bias parameter on the overdensity parameter
This prescription should be able to give a good zeroth level baryon distribution. Environmental effects, baryonic physics and other astrophysical effects would give rise to modulations to this distribution. Using this prescription for the IGM density, one can now obtain the 21 cm brightness temperature distribution and it is shown in Figure 7.
FIGURE 7. Brightness temperature distribution, midway through the simulation box, for the three redshifts obtained using the Press-Schechter prescription.
The under dense grid cells are more in number than the over dense grid cells and they dominate the overall behaviour. For
FIGURE 8. Power spectrum of 21 cm brightness temperature distribution for the three redshifts obtained using the Press-Schechter prescription. For comparison, the power spectrum for a uniform IGM and for a perfectly biased IGM is also plotted.
5 Discussion and Conclusion
In this work we discussed how an IGM that is having varied bias with respect to the massive halo population could impact the 21 cm brightness temperature distribution. It is found that the distribution as well as the power spectrum are significantly affected with the difference in the IGM bias parameter α (Eq. 1), while, the global neutral hydrogen fraction remains constant. It is also found that for some critical value of the IGM bias parameter, the distribution becomes almost uniform causing a near washout of the 21 cm power spectrum. This critical value of the IGM bias parameter is different for different redshifts. Thus, it is essential to estimate the large scale distribution of the IGM. In this work, we also saw that this distribution could be estimated within the framework of the Press-Schechter theory. It was also observed that for
Many early large scale structure studies assume that the baryons follow dark matter or
There are possibly two future directions to the problem posed in this work: One could assume that the baryon fraction parameter,
The author would like to thank the Illustris collaboration for their N-body simulations. The author would also like to thank anonymous referees whose comments helped in improving the quality of the manuscript.
Data Availability Statement
The original contributions presented in the study are included in the article/Supplementary Material, further inquiries can be directed to the corresponding author.
The author confirms being the sole contributor of this work and has approved it for publication.
Conflict of Interest
The author declares that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.
The Supplementary Material for this article can be found online at: https://www.frontiersin.org/articles/10.3389/fspas.2021.633007/full#supplementary-material.
1Note that the bias parameter is defined with respect to collapsed matter density and not with respect to the underlying dark-matter density
4The baryons in uncollapsed haloes would give rise to a clumpy IGM. This will modify the recombination parameter and would make it position dependent. This complication is not considered in this work.
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Keywords: cosmology—theory, large scale structure, epoch of reionization, cosmology—galaxies, large scale structure formation
Citation: Raut D (2021) Homogeneous vs Biased IGM: Impact on Reionization. Front. Astron. Space Sci. 8:633007. doi: 10.3389/fspas.2021.633007
Received: 24 November 2020; Accepted: 20 January 2021;
Published: 29 March 2021.
Edited by:Carlo Burigana, Istituto di Radioastronomia di Bologna (INAF), Italy
Reviewed by:Emanuela Dimastrogiovanni, University of New South Wales, Australia
Kazuharu Bamba, Fukushima University, Japan
Copyright © 2021 Raut. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.
*Correspondence: Dinesh Raut, email@example.com