Models and simulations1,2,3,4 of the epoch of reionization predict that spectra of the 21-centimetre transition of atomic hydrogen will show a clear fluctuation peak, at a redshift and scale, respectively, that mark the central stage of reionization and the characteristic size of ionized bubbles. This is based on the assumption5,6,7 that the cosmic gas was heated by stellar remnants—particularly X-ray binaries—to temperatures well above the cosmic microwave background at that time (about 30 kelvin). Here we show instead that the hard spectra (that is, spectra with more high-energy photons than low-energy photons) of X-ray binaries8,9 make such heating ineffective, resulting in a delayed and spatially uniform heating that modifies the 21-centimetre signature of reionization. Rather than looking for a simple rise and fall of the large-scale fluctuations (peaking at several millikelvin), we must expect a more complex signal also featuring a distinct minimum (at less than a millikelvin) that marks the rise of the cosmic mean gas temperature above the microwave background. Observing this signal, possibly with radio telescopes in operation today, will demonstrate the presence of a cosmic background of hard X-rays at that early time.
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We are grateful to S. Naoz for drawing our attention to the work of T. Fragos, who provided us with detailed model spectra of X-ray binaries, which helped motivate this study. This work was supported by Israel Science Foundation grant number 823/09, and by the LabEx ENS-ICFP (grant numbers ANR-10-LABX-0010 and ANR-10-IDEX-0001-02 PSL*).
The authors declare no competing financial interests.
Extended data figures and tables
We show the same data as in Fig. 3 (with the same nomenclature), but as a function of 1 + z, where z is the redshift, a direct observable (given that the observed wavelength is 21(1 + z) cm). This presentation has the advantage of clearly separating out the early and late reionization cases, while showing that reionization does not affect the redshift of the new minimum (solid curves) at k = 0.5 Mpc−1. Indeed, this minimum marks the cosmic heating transition (to within 2% in redshift in all our model calculations), while the minimum at k = 0.1 Mpc−1 is typically delayed owing to the evolving power spectrum shape (see Extended Data Fig. 2). We consider wavenumbers k = 0.1 Mpc−1 (a and b) and k = 0.5 Mpc−1 (c and d), for each of our two cases for galactic halos, atomic cooling (a and c) or massive halos (b and d). The results shown (here and in Fig. 3) correspond to a total of four different reionization histories. Late reionization with atomic cooling reaches 1/4, 1/2, 3/4 and full reionization at z = 10.7, 8.7, 7.7 and 7.0; the corresponding redshifts for early reionization are 11.8, 10.0, 9.1 and 8.4. Massive halos give a sharper reionization transition, with late reionization advancing through z = 10.3, 8.9, 8.3 and 7.7, while early reionization corresponds to z = 11.4, 10.2, 9.7 and 9.0.
We show examples of full power spectra corresponding to the data shown in Fig. 3 and Extended Data Fig. 1, for the cases with fX = 1 and late reionization. We compare the new XRB spectrum9 (solid curves) to the previously adopted soft spectrum (dashed curves), and show the saturated heating case for reference (dotted curves). We consider atomic cooling (a) or massive halos (b). In order of increasing cosmic age, we consider three key moments (which fall at different redshifts for the various cases, based on Extended Data Fig. 1): the minimum fluctuation at k = 0.5 Mpc−1 (blue curves), the minimum at k = 0.1 Mpc−1 (green curves), and the midpoint of reionization (red curves). For the new spectrum, strong evolution is predicted in the power spectrum shape, because large-scale fluctuations from X-ray heating dominate (up to k ≈ 0.5 Mpc−1) at the heating transition (blue solid curves) but then rapidly decline so that density fluctuations come to dominate (at k > 0.1 Mpc−1 at the time shown in green solid curves), with an eventual large-scale boost by the ionized bubbles (red solid curves).
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Fialkov, A., Barkana, R. & Visbal, E. The observable signature of late heating of the Universe during cosmic reionization. Nature 506, 197–199 (2014). https://doi.org/10.1038/nature12999
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