Studying neutral hydrogen structures during the epoch of reionization using fractal dimensions

Bandyopadhyay, Bidisha; Choudhury, Tirthankar Roy; Seshadri, T. R.

doi:10.1093/mnras/stw3347

Cited by 9 publications

(5 citation statements)

References 72 publications

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“…Therefore we need to explore other summary statistics that are sensitive to the non-Gaussian information contained in the signal. Examples of such summary statistics that have been studied previously are the bispectrum (Majumdar et al 2018;Watkinson et al 2019), the position-dependent power spectrum (Giri et al 2019b), size distributions (Kakiichi et al 2017;Giri et al 2018aGiri et al , 2019a and fractal dimensions (Bandyopadhyay et al 2017).…”

Section: Introductionmentioning

confidence: 99%

Measuring the topology of reionization with Betti numbers

Giri,

Mellema

2020

Preprint

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The distribution of ionised hydrogen during the epoch of reionization (EoR) has a complex morphology. We propose to measure the three-dimensional topology of ionised regions using the Betti numbers. These quantify the topology using the number of components, tunnels and cavities in any given field. Based on the results for a set of reionization simulations we find that the Betti numbers of the ionisation field show a characteristic evolution during reionization, with peaks in the different Betti numbers characterising different stages of the process. The shapes of their evolutionary curves can be fitted with simple analytical functions. We also observe that the evolution of the Betti numbers shows a clear connection with the percolation of the ionized and neutral regions and differs between different reionization scenarios. Through these properties, the Betti numbers provide a more useful description of the topology than the widely studied Euler characteristic or genus. The morphology of the ionisation field will be imprinted on the redshifted 21-cm signal from the EoR. We construct mock image cubes using the properties of the low-frequency element of the future Square Kilometre Array and show that we can extract the Betti numbers from such datasets if an observation time of 1000 h is used. Even for a much shorter observation time of 100 h, some topological information can be extracted for the middle and later stages of reionization. We also find that the topological information extracted from the mock 21-cm observations can put constraints on reionization models.

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Section: Introductionmentioning

confidence: 99%

Measuring the topology of reionization with Betti numbers

Giri,

Mellema

2020

Preprint

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“…(Furlanetto et al 2006a). Topological features of the ionization field could also contain information regarding cosmological initial conditions (Bandyopadhyay et al 2017;Kapahtia et al 2017;Bag et al 2018). All these interesting connections would remain obscured in the low-resolution maps thus making them somewhat ineffective while interpreting the 21 cm data.…”

Section: Discussionmentioning

confidence: 99%

Photon number conservation and the large-scale 21 cm power spectrum in semi-numerical models of reionization

Choudhury

Paranjape

2019

2019 URSI Asia-Pacific Radio Science Conference (AP-RASC)

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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 resolutiondependence 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 ∆x = 5-10h −1 cMpc, 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 0.05h/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.

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“…A homogeneous distribution in three dimensions has a D q = 3. [7] show that the topology of reionisation exhibits a significant multi-fractal behaviour. These authors find that the fractal dimension is relatively insensitive to the minimum halo mass of the star-forming galaxies, however it was sensitive to the mass averaged ionisation fraction.…”

Section: Fractal Dimensionsmentioning

confidence: 93%

“…An alternative to classifying the ionised (neutral) regions embedded in the 21-cm signal is through a fractal dimensions analysis. Applied to reionisation ( [7]), this provides a direct means to quantify the deviation away from a homogenous distribution, as well as the degree of clustering and lacunarity (a measure of the size of the ionised regions). The fractal dimension, D q , also known as the Minkowski-Bouligand dimension, is a measure of how complicated the topology of the field in question is.…”

Section: Fractal Dimensionsmentioning

confidence: 99%

Inference from the 21cm signal

Greig

2019

Preprint

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In the previous chapters we have discussed in-depth the astrophysical and cosmological information that is encoded by the cosmic 21-cm signal. However, once we have a measurement, how do we extract this information from the signal? This chapter focusses on the inference of the interesting astrophysics and cosmology once we obtain a detection of the 21-cm signal.Essentially, inference of the astrophysics can be broken down into three parts:

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Studying neutral hydrogen structures during the epoch of reionization using fractal dimensions

Cited by 9 publications

References 72 publications

Measuring the topology of reionization with Betti numbers

Measuring the topology of reionization with Betti numbers

Photon number conservation and the large-scale 21 cm power spectrum in semi-numerical models of reionization

Inference from the 21cm signal

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