Modifications to the cosmic 21-cm background frequency spectrum by scattering via electrons in galaxy clusters

The cosmic 21-cm background frequency spectrum related to the spin-flip transition of neutral hydrogen present during and before the era of reionization is rich in features associated with physical processes that govern transitions between the two spin states. The intervening electrons in foreground galaxy clusters inversely Compton scatter the 21-cm background spectrum and modify it just as the cosmic microwave background (CMB) spectrum is modified by inverse-Compton scattering. Towards typical galaxy clusters at low redshifts, the resulting modification is a few tenths milli-Kelvin correction to the few tens milli-Kelvin temperature of 21-cm signal relative to that of the cosmic microwave background blackbody spectrum. The modifications are mostly associated with sharp changes in the cosmic 21-cm background spectrum such as due to the onset of a Lyman-$\alpha$ radiation field or heating of neutral gas. Though low-frequency radio interferometers that are now planned for 21-cm anisotropy measurements are insensitive to the mean 21-cm spectrum, differential observations of galaxy clusters with these interferometers can be utilized to indirectly establish global features in the 21-cm frequency spectrum. We discuss the feasibility to detect the spectrum modified by clusters and find that, for upcoming interferometers, while a detection towards an individual cluster is challenging, one can average signals over a number of clusters, selected based on the strength of the Sunyave-Zel’dovich effect at high radio frequencies involving CMB scattering alone, to establish the mean 21-cm spectrum.

Figure 1

The scattering kernel $P_1(\nu ,{\nu }_0)$ with ${\nu }_0=100\mathrm{MH}z$ for a cluster with $k_B{T}_e=7\mathrm{KeV}$; for a different ${\nu }_0$, kernel can be shifted in $\log (\nu /{\nu }_0)$. Any sharp features in the prescattered spectrum with variations over a frequency range less than the typical width of the scattering kernel will be broadened after scattering. The difference leads to a decrement followed by an increment if the incoming radiation has a dip on the blackbody CMB spectrum, while the opposite happens if the prescattered spectrum has an increase on top of the CMB spectrum.

Figure 2

(a) The incoming radiation spectrum plotted in terms of the brightness temperature relative to CMB. Three features are shown: A broad absorption due to collisional coupling between spin and gas temperatures when $30<z<200$ [3], coupling induced by Ly-$\alpha$ radiation from first luminous sources when $20<z<30$ [5] (labeled Ly-$\alpha$), and an increase in the gas temperature when heated by soft x rays during reionization at a redshift below 20 [4] (labeled X-ray). (b) The difference spectrum after scattering through a galaxy cluster with an electron temperature of 7 keV and an optical depth of 0.005, consistent with known clusters at low redshifts [22] with the optical depth profile smeared over a beam of 5 arcminutes to be consistent with typical beam sizes expected for upcoming interferometers. The overall offset in the spectrum, at a brightness temperature $\sim -0.35\mathrm{mK}$ with no frequency dependence at the Rayleigh-Jeans tail, is due to scattering of the CMB blackbody with no 21-cm signatures. The 21-cm signatures lead to variations up to 0.2 mK, While the broad dip at very low frequencies leads to a decrement and an increment, Ly-$\alpha$ and x-ray features combine to given an overall increase towards clusters at a frequency around $\sim 75\mathrm{MH}z$; This is associated with the sharp dip related to the Lyman-$\alpha$ induced coupling of gas and spin temperatures at a redshift around 20. The dot-dashed line is the scattered spectrum only involving the broad dip and the x-ray heating increment; the latter leads to an increment followed by a decrement.

Figure 3

The brightness temperature difference spectrum towards and away from a cluster with a beam-smeared average optical depth of 0.005 and an electron temperature of 7 keV that can be targeted with upcoming low-frequency radio interferometers [same as Fig. 2b]; the optical depth and electron temperature values are typical of low-redshift clusters [22]. Since underlying 21-cm signatures are global, one can also stack spectra towards a large sample of clusters to improve the signal-to-noise ratio. The errors bars assume experimental parameters similar to SKA with a system noise temperature of 1000 K at 100 MHz, and a scaling of ${\nu }^{-2}$ to other frequencies, a 5 MHz bandwidth, synthesized beam of $5^{\prime }$, and a yearlong integration. The larger errors indicated by horizontal lines assume observations towards an individual cluster, while error bars show the improvement by averaging over observations of 10 clusters, though in planned observations $\sim \mathrm{\text{few}}$ hundred massive clusters will be imaged in a given field of view instantaneously. A large uncertainty in establishing the exact signal-to-noise for detection is the foreground distribution within clusters, such as point sources, and the extent to which such sources can be removed [21].