Wouthuysen-Field coupling strength and application to high-redshift 21-cm radiation

By C. Hirata. 2005

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The first ultraviolet sources in the universe are expected to have coupled the H I spin temperature to the gas kinetic temperature via scattering in the Lyα resonance (the 'Wouthuysen-Field effect'). By establishing an Hi spin temperature different from the temperature of the cosmic microwave background, the Wouthuysen-Field effect should allow observations of H I during the reionization epoch in the redshifted 21-cm hyperfine line. This paper investigates four mechanisms that can affect the strength of the Wouthuysen-Field effect that were not previously considered. (1) Photons redshifting into the Hi Lyman resonances may excite an H atom and result in a radiative cascade terminating in two-photon 2s 1/2 → 1s 1/2 emission, rather than always degrading to Lyα as usually assumed. (2) The fine structure of the Lyα resonance alters the photon frequency distribution and leads to a suppression of the scattering rate. (3) The spin-flip scatterings change the frequency of the photon and cause the photon spectrum to relax not to the kinetic temperature of the gas but to a temperature between the kinetic and spin temperatures, effectively reducing the strength of the Wouthuysen-Field coupling. (4) Near line centre, a photon can change its frequency by several times the line width in a single scattering event, thus potentially invalidating the usual calculation of the Lyα spectral distortion based on the diffusion approximation. It is shown that (1) suppresses the Wouthuysen-Field coupling strength by a factor of up to ∼2, while (2) and (3) are important only at low kinetic temperatures. Effect (4) has a ≤3 per cent effect for kinetic temperatures T k ≥ 2 K. In particular, if the pre-reionization intergalactic medium was efficiently heated by X-rays, only effect (1) is important. Fitting formulae for the Wouthuysen-Field coupling strength are provided for the range of T k ≥ 2 K and Gunn-Peterson optical depth 10 5 < TOP < 10 7 so that all of these effects can be easily incorporated into 21-cm codes.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/b55e4c74cd69066057af446e7aa143bc15c4c63e

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Citations in the corpus

New Limits on 21cm EoR From PAPER-32 Consistent with an X-Ray Heated IGM at z=7.7 (2013, background): “…contrast corresponds physically to a situation in which the spin temperature remains tightly coupled to the gas temperature via the Wouthuysen-Field effect21 (Wouthuysen 1952; Field 1958; Hirata 2006), but in which heating of the neutral gas by any mechanism (X-rays, Ly-α, or shocks) is negligible.”
The global 21-centimeter background from high redshifts (2006, methodology): “H collisions (Zygelman 2005), H–e− collisions (Smith 1966; Furlanetto & Furlanetto, in preparation) and the Wouthuysen–Field effect (Wouthuysen 1952; Field 1958; Hirata 2006) as described in Section 2.”
Reionization and the Cosmic Dawn with the Square Kilometre Array (2012, background): “(5) Here Tc is the color temperature of the Ly-α spectrum which is almost equal to TK in situations relevant for the EoR (see Hirata 2006, for details).”
Simulating cosmic reionization at large scales – II. The 21-cm emission features and statistical signals (2006, background): “This could occur either throughcollisions with other hydrogen atoms and free electrons (Purcell & Field 1956; Field 1959; Allison & Dalgarno 1969; Zygelman 2005) or through Ly-α photon pumping (Wouthuysen 1952; Field 1959; Hirata 2006; Chuzhoy & Shapiro 2005).”
Fundamental physics with the Square Kilometre Array (2018, background): “…the nature of the mean and fluctuating 21-cm signal due to two main reasons: optical pumping of the hyperfine levels due to Lyman-α photons (the so-called Wouthuysen-Field effect; Hirata, 2006), and heating of the gas by X-rays (Furlanetto, 2006; Pritchard & Furlanetto, 2007; Fialkov et al., 2014).”
What does the first highly redshifted 21-cm detection tell us about early galaxies? (2018, background): “…from https://academ ic.oup.com /m nras/article/483/2/1980/5222679 by guest on 24 O ctober 2021 Shapiro 2006; Furlanetto & Pritchard 2006; Hirata 2006), which results in an intergalactic medium (IGM) that remains cooler than the cosmic microwave background (CMB) prior to (and in some…”
21 cm cosmology in the 21st century (2011, background): “These atomic cascades are illustrated in figure 2, where the probability of converting a Lyn photon into a Lyα photon is set by the atomic rate coefficients and can be found in tabular form in [25, 30].”
21-cm fluctuations from inhomogeneous X-ray heating before reionization (2006, background): “Subsequently, they may generate Lyα photons, as discussed in Pritchard & Furlanetto (2006) and Hirata (2006).”
PAPER-64 CONSTRAINTS ON REIONIZATION: THE 21 cm POWER SPECTRUM AT z = 8.4 (2015, methodology): “As in P14, we consider a “weak heating” scenario in which Ts is coupled to the gas temperature via the Wouthuysen-Field effect (Wouthuysen 1952; Field 1958; Hirata 2006), but little heating has taken place prior to reionization, so that Ts < Tγ .”
Fast large volume simulations of the 21-cm signal from the reionization and pre-reionization epochs (2009, unknown): “The radiative coupling is given by xα = SαJα Jc , (9) with Jc ≈ 5.552 × 10−8(1 + z) m−2s−1Hz−1sr−1 and Sα is a correction factor of order unity (Chen & Miralda-Escudé 2004; Hirata 2006; Chuzhoy & Shapiro 2007; Furlanetto & Pritchard 2006; Furlanetto et al. 2006).”
21cmfast: a fast, seminumerical simulation of the high‐redshift 21‐cm signal (2010, methodology): “They then quickly and locally cascade with a fraction f recycle(n) passing through Lyα and inducing strong coupling (Hirata 2006; Pritchard & Furlanetto 2006).”