Recovering the H ii region size statistics from 21-cm tomography

Abstract

We introduce a novel technique, called "granulometry", to characterize and recover the mean size and the size distribution of H II regions from 21-cm tomography. The technique is easy to implement, but places the previously not very well defined concept of morphology on a firm mathematical foundation. The size distribution of the cold spots in 21-cm tomography can be used as a direct tracer of the underlying probability distribution of H II region sizes. We explore the capability of the method using large-scale reionization simulations and mock observational data cubes while considering capabilities of SKA1-low and a future extension to SKA2. We show that the technique allows the recovery of the H II region size distribution with a moderate signal-to-noise ratio from wide-field imaging (SNR 3), for which the statistical uncertainty is sample variance dominated. We address the observational requirements on the angular resolution, the field-of-view, and the thermal noise limit for a successful measurement. To achieve a full scientific return from 21-cm tomography and to exploit a synergy with 21cm power spectra, we suggest an observing strategy using wide-field imaging (several tens of square degrees) by an interferometric mosaicking/multi-beam observation with additional intermediate baselines (∼ 2 − 4 km) in a SKA phase 2.

Studying the morphology of reionization with the triangle correlation function of phases

“…Apart from noise and instrumental resolution, there will be some other important questions to solve before applying our method to true 21cm tomographic data. Kakiichi et al (2017) proved that the cold spots in 21cm tomographic images trace H ii regions more efficiently at low redshift (z ≤ 7) and high filling fraction (x H ii ≥ 0.4): earlier in the reionisation process, cold spots due to a local underdensity rather than ionisation are more frequent (see Sec. 2).…”

“…A thorough comparison of these methods is made in Lin et al (2016) for simulated clean 21cm maps and in Giri et al (2018a) for maps including observational effects. A new method, which the authors call granulometry, has been recently presented in Kakiichi et al (2017). The idea is to successively sieve a binary field with a spherical hole of increasing radius R. Depending on how many ionised pixels are sieved, one can build the probability distribution of H ii regions sizes.…”

“…This research made use of astropy, a communitydeveloped core Python package for astronomy (Astropy Collaboration et al 2013, 2018; matplotlib, a Python library for publication quality graphics (Hunter 2007); scipy, a Python-based ecosystem of open-source software for mathematics, science, and engineering (Jones et al 2001) -including numpy (Oliphant 2006), and emcee, an implementation of the affine invariant MCMC ensemble sampler (Foreman-Mackey et al 2013).…”

The variance of dispersion measure of high-redshift transient objects as a probe of ionized bubble size during reionization

“…Furlanetto et al (2004)) and numerically (e.g. Iliev et al (2006); Zahn et al (2007); Kakiichi et al (2017); Giri et al (2017)). These BSDs are approximately consistent with each other and can be expressed by a skewed lognormal distribution.…”

Optimal identification of H ii regions during reionization in 21-cm observations

“…In this study we show how the image segmentation method known as over-segmentation with superpixels can be used to identify ionized regions in tomographic 21-cm images. We describe it as well as the methods used in Kakiichi et al (2017) and Giri et al (2018) in terms of the theory of image segmentation and compare the new method to these previously proposed ones. As no real data is available we base our exploration, just as the previous studies mentioned above did, on mock observations constructed from reionization simulations and a telescope model.…”