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Beyond Optical Depth: Future Determination of Ionization History from the CMB

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Beyond Optical Depth: Future Determination of Ionization History from the CMB Draft version January 31, 2020 Typeset using LATEX twocolumn style in AASTeX63 Beyond optical depth: Future determination of ionization history from the CMB D. J. Watts ,1 G. E. Addison ,1 C. L. Bennett ,1 and J. L. Weiland 1 1JHU Department of Physics and Astronomy, 3701 San Martin Drive, Baltimore MD, 21218, USA (Received October 1, 2019; Revised December 3, 2019; Accepted January 31, 2020) Submitted to ApJ ABSTRACT We explore the fundamental limits to which reionization histories can be constrained using only large-scale cosmic microwave background (CMB) anisotropy measurements. The redshift distribution of the fractional ionization x z affects the angular distribution of CMB polarization. We project e ¹ º constraints on the reionization history of the universe using low-noise full-sky temperature and E- ˆ TE mode measurements of the CMB. We show that the measured TE power spectrum, C` , has roughly ˆ EE one quarter of the constraining power of C` on the reionization optical depth τ, and its addition ˆ EE improves the precision on τ by 20% over using C` only. We also use a two-step reionization model min with an additional high-redshift step, parameterized by an early ionization fraction xe , and a late reionization step at zre. We find that future high signal-to-noise measurements of the multipoles min 10 6 ` < 20 are especially important for breaking the degeneracy between xe and zre. In addition, we show that the uncertainties on these parameters determined from a map with sensitivity 10 µK arcmin are less than 5% larger than the uncertainties in the noiseless case, making this noise level a natural target for future large sky area E-mode measurements. Keywords: Cosmic background radiation (317); Reionization (1383); Cosmological parameters (339); Cosmology (343) 1. INTRODUCTION zation at high signal-to-noise can be used to constrain Cosmic reionization is a poorly understood part of ionization histories. standard ΛCDM cosmology. Reionization, when neu- It is observationally known that after the universe be- tral hydrogen and helium in the intergalactic medium came neutral at the epoch of recombination, by z 6 (IGM) become ionized, creates a plasma that scatters it was ionized once again (e.g., Gunn & Peterson 1965; cosmic microwave background (CMB) photons (Rees Becker et al. 2001; Fan et al. 2006). Determinations of 1968; Basko & Polnarev 1980; Bond & Efstathiou 1984). the ionization fraction of the IGM have been made at This reduces the amplitude of the CMB anisotropy at redshifts 6 . z . 8 (Bouwens et al. 2015; McGreer et al. angular scales ` & 10 and creates additional polarized 2015; Greig et al. 2017; Bañados et al. 2018; Davies et al. power that dominates at scales ` . 10 (Zaldarriaga 2018; Mason et al. 2018; Greig et al. 2019; Mason et al. arXiv:1910.00590v2 [astro-ph.CO] 30 Jan 2020 1997). We illustrate the separate effects of reionization 2019) by probing the epoch of reionization via measure- and recombination on the E-mode power spectrum in ments of Lyman α emission, but these data are sparse, Figure 1. Because the temperature and E-mode po- and do not yet constrain the free electron fraction during TT TE EE the epoch of reionization (see, e.g., Planck Collaboration larization angular power spectra (C` , C` , and C` ) depend on the redshift of scattering, their characteri- I 2018, Figure 36). Commonly, CMB constraints on the reionization his- tory of the universe are derived assuming a sharp tran- Corresponding author: Duncan J. Watts sition from a neutral to fully ionized IGM. Measure- [email protected] ments of the large-scale CMB polarization constrain the ionization history by inferring the optical depth to the ¯ t0 last scattering surface of the CMB, τ cσTne t dt, ≡ tlss ¹ º 2 Watts et al. where c is the speed of light, σT is the Thomson scat- tering cross section, n t is the free electron number e ¹ º density, t0 is the current age of the universe, and tlss is the last time photons interacted with matter during the epoch of recombination. Determining the free elec- tron density n t is then an inverse problem that relies e ¹ º on assumptions and priors. For example, a tanh-like reionization history (e.g., Lewis 2008, Equation (B3)) with a transition from neutral to ionized at a single reionization redshift zre with width δzre 0:5 has been used (e.g., Hinshaw et al. 2013; Planck Collaboration VI 2018, Section 3.3). Observations from the Wilkinson Microwave Anisotropy Probe (WMAP) satellite were used to make a measurement of the optical depth from the surface of last scattering τ 0:089 0:014 (Hinshaw ± et al. 2013), although this decreases to τ 0:067 0:013 Figure 1. Effect of reionization on the CEE power spectrum. ± ` when using Planck 353 GHz data as a template to remove We take the difference between an E-mode signal with τ 0 2τ Galactic dust emission (Planck Collaboration XI 2016). and one with τ 0:06 with fixed As e− to demonstrate the EE Planck Collaboration I(2018) increased the precision of effects of tanh-like reionization on C` versus those from re- this measurement to τ 0:0544 0:0073. Pagano et al. combination. The black dashed line is the total CEE spectrum ± ` (2019) claim to have further reduced large-scale Planck when τ 0:06. The E-mode signal from recombination dom- systematics, reporting τ 0:059 0:006. inates above ` & 20, whereas the reionization signal emerges ± As a cross-check, it is possible to obtain competitive at multipoles ` . 20. constraints without using CMB polarization. Planck temperature measurements combined with Planck weak high-band experiment (Monsalve et al. 2017) measures lensing and baryon acoustic oscillation (BAO) data give the brightness temperature of the global 21 cm emission τ 0:067 0:016 (Planck Collaboration XIII 2016), con- from neutral hydrogen, T21, at frequencies 90–190 MHz ± sistent with results using WMAP temperature, Planck (redshifts 6.5–14.8). Monsalve et al.(2017) assume a hot weak lensing, and BAO data, τ 0:066 0:020 (Weiland IGM with spin temperature Ts 28 K TCMB and find ± et al. 2018). Weiland et al.(2018) include a compilation a lower limit of δzre & 0:5 with 95% confidence over the of τ measurements, and conclude that the measured redshift range 6:6 . z . 11. The brightness tempera- values are all consistent with τ 0:07 0:02. Unlike the ture has an rms scatter of 17 mK, which corresponds to ± Hubble constant H0, (e.g., Bernal et al. 2016, Freedman a xHi rms scatter of & 0:5, assuming a fixed spin temper- 2017, Addison et al. 2018, and Riess et al. 2019), the issue ature Ts 28 mK. With a future rms sensitivity 1 mK ∼ with reionization is not tension between measurements, measurement of T21, a percent-level determination of but a lack of desired precision. xHi z will be possible. ¹ º Using the one-to-one mapping of τ zre in tanh-like It is typically assumed that the universe was ionized $ reionization, Planck Collaboration I(2018) use the low- by ultraviolet photons from massive stars escaping from ` polarization power spectra to infer zre 7:67 0:73 galaxies. To confirm this, it is necessary to characterize ± (Planck likelihood Plik best fit), while measurements the emissivity of galaxies at the onset of star forma- of the kinetic Sunyaev–Zel’dovich effect at arcminute tion, to see whether enough ionizing photons are gen- scales by the South Pole Telescope (SPT) and the At- erated and can escape from galaxies on a short enough acama Cosmology Telescope (ACT) can be used to timescale (Madau & Dickinson 2014; McCandliss et al. limit the duration of inhomogeneous reionization to 2019). This requirement is fulfilled if there is a steep δzre < 2:8 at the 95% C.L. with the prior that reioniza- luminosity function with galaxies contributing down to tion ends by z 6 (Zahn et al. 2012; Sievers et al. 2013; an absolute magnitude MUV 13 (Bouwens et al. 2015; ∼ − Planck Collaboration Int. XLVII 2016). Finkelstein et al. 2019) and that a volume-averaged es- While the CMB probes the reionization process cape fraction of 5–20% is achieved (Madau & Dickinson through the scattering of photons by free electrons, 2014; Khaire et al. 2016; Finkelstein et al. 2019). Deter- direct observations of the neutral hydrogen fraction minations of the UV luminosity function through the would constrain the ionization state of the universe onset of reionization is limited by sensitivity to galaxies during the epoch of reionization directly. The EDGES up to redshift z . 10, and will be enabled by deep ob- Reionization Histories 3 servations by the James Webb Space Telescope (Robertson 2. MAXIMIZING INFORMATION USED et al. 2015). IN POWER SPECTRUM ANALYSIS Other potential mechanisms with different redshift In this section, we develop a formalism for extract- dependence have also been put forward. In particular, ing reionization information from a full-sky map of the binary black hole collisions can be a source of X-rays at intensity and linear polarization of the CMB. In Sec- z & 30, which can raise the ionizing fraction with less tion 2.1, we define the three likelihoods we use for dif- fractional contribution from star formation (Inayoshi ferent subsets of data; Wishart (for Cˆ TT + Cˆ TE + Cˆ EE), et al. 2016). Quasars and annihilating particles have ` ` ` χ2 (for Cˆ EE), and variance-gamma (for Cˆ TE). In Sec- also been proposed as ionizing mechanisms (Mapelli & ` ` tion 2.2, we characterize these likelihoods for the case Ripamonti 2008; Madau & Haardt 2015; Khaire et al.
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