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Dipole of the Epoch of Reionization 21-Cm Signal BNL-114019-2017-JA Dipole of the Epoch of Reionization 21-cm Signal A. Slosar Submitted to Physical Review Letters June 2017 Physics Department Brookhaven National Laboratory U.S. Department of Energy USDOE Office of Science (SC), High Energy Physics (HEP) (SC-25) Notice: This manuscript has been authored by employees of Brookhaven Science Associates, LLC under Contract No. DE-SC0012704 with the U.S. Department of Energy. The publisher by accepting the manuscript for publication acknowledges that the United States Government retains a non-exclusive, paid-up, irrevocable, world-wide license to publish or reproduce the published form of this manuscript, or allow others to do so, for United States Government purposes. DISCLAIMER This report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor any agency thereof, nor any of their employees, nor any of their contractors, subcontractors, or their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or any third party’s use or the results of such use of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise, does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof or its contractors or subcontractors. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof. BNL-114019-2017-JA Dipole of the Epoch of Reionization 21-cm signal Anˇze Slosar1, ∗ 1Brookhaven National Laboratory, Upton, NY 11973, USA (Dated: March 28, 2017) The motion of the solar system with respect to the cosmic rest frame modulates the monopole of the Epoch of Reionization 21-cm signal into a dipole. This dipole has a characteristic frequency dependence that is dominated by the frequency derivative of the monopole signal. We argue that although the signal is weaker by a factor of ∼ 100, there are significant benefits in measuring the dipole. Most importantly, the direction of the cosmic velocity vector is known exquisitely well from the cosmic microwave background and is not aligned with the galaxy velocity vector that modulates the foreground monopole. Moreover, an experiment designed to measure a dipole can rely on differencing patches of the sky rather than making an absolute signal measurement, which helps with some systematic effects. I. INTRODUCTION However, the experimental challenges are daunting: the foregrounds are brighter than the signal by orders of mag- The earliest direct image of the universe comes from nitude and vary very strongly across the sky, which makes the observations of the Comic Microwave Background calibration of the instrument and beams to the required (CMB), which arises when photons and decouple from level of precision is very difficult. cosmic plasma a few hundred thousand years after the In this note we make a very simple point that one could big bang at a redshift of z ∼ 1100. The universe then attempt to measure the dipole of the signal rather than enters a period known as \dark ages", where neutral hy- the monopole. Although the signal is reduced by a fac- drogen slowly cools and collapses into halos, but the first tor of around 100, the systematic gains are very signif- stars have not yet ignited. The first luminous object icant. The problem is in many ways analogous to the form at redshifts of z ∼ 20 − 40, but very little is actu- Cosmic Microwave Background { measuring Cosmic Mi- ally known about this early period. With time, galaxies crowave Background (CMB) dipole is significantly easier form and start filling the universe with photo-ionizing ra- than measuring the CMB monopole or the CMB tem- diation which re-ionizes the hydrogen in the inter-galactic perature fluctuations. However, one should not take this medium in the process that is thought to have completed analogy too far for two reasons. First, while the sky by redshift of around z ∼ 6. This period in the evolu- signal on large scales is dominated by the CMB at fre- tion of the universe is known as the epoch of reionization quencies above ∼ 1GHz, this is not true for the 21-cm (EoR). It is thought that structure in the universe dur- EoR signal: a total dipole is going to be dominated by ing this period is characterized by growing bubbles of the foregrounds by order of magnitude at the relevant ionizied hydrogen surrounded by yet-to-be-ionized neu- frequencies. Second, while the dipole signal in the CMB tral hydrogen. The neutral hydrogen shines in radio in is two orders of magnitude larger than the higher order the 21-cm hydrogen line. Measurements of the redshifted mulitpoles, the same is not true for the the EoR signal, 21-cm line are thus thought to be the most promising way which has comparable or higher power at degree scales of constraining reionization (EoR) [1{3]. They will teach compared to dipole. Nevertheless, as we will discuss in us both about the astrophysics of this complex era in this paper, the dipole measurement still has several at- the evolution of the universe, as well as provide strong tractive features in regards of systematic effects. constraints on the value of the total optical depth to the surface of last-scattering, which will help with measure- ments of many cosmologically relevant parameters, most II. THE SIGNAL importantly the neutrino mass[4]. Up to now, most experiments in the field have focused on either measuring the fluctuations in the 21-cm line by While the details are poorly know, the general outline measuring the 21-cm brightness temperature and relying of the process of reionization and the general features of on the foreground smoothness to isolate it [5{8], or on at- the evolution of the 21-cm brightness temperature with tempting to measure the global signal, the monopole of cosmic time are understood. We will not go into detail, the 21-cm radiation from the EoR [9{11]. The latter mea- but refer reader to well know reviews [3]. surement is tempting, since the signal is relatively strong The upper plot of the Figure 1 shows the 21-cm global and simple back-of-the envelope calculations show that signal for a popular model. The monopole of the EoR it should be easily achiveable based on SNR calculations. signal is always observed relative to the CMB monopole and is sometimes seen in absorption and sometimes in emission. The magnitude of the observed signal is de- termined by the difference between the CMB and spin ∗ [email protected] temperatures at a given redshift, the latter being the ex- 2 citation temperature given by the relative occupancy of rest frame. The dipole signal is thus given by the two 21-cm states. Depending on the epoch, the gas d∆T vd is observed sometimes in absorption and sometimes in Tdip = T0 + ∆T (ν) − ν cos θ: (2) emission. The spin temperature is determined by ab- dν c sorption/emission of CMB photons, collisions with other We see that the dipole signal has three components species and resonant scattering of the Lyman-α photons. (corresponding to three terms in brackets above): the At very high redshifts z & 200, the spin temperature traditional frequency independent dipole, which would is still thermally coupled to CMB via residual Comp- match the CMB dipole in the absence of foregrounds, the ton scattering and therefore the expected signal is zero. traditional boosting of the frequency independent signal When this process becomes inefficient, the spin temper- due to Doppler shift and also a term that takes into ac- ature becomes collisionally coupled to gas, which cools count the frequency dependence of the EoR monopole −2 adiabatically as / (1 + z) and so is seen in absorp- signal. We plot both frequency dependent contributions −1 tion compared to CMB that cools / (1 + z) (the first in the Figure 1. We see that the derivative signal dom- through in the upper panel of Figure 1). At redshifts inates the signal. The total signal has the amplitude of z ∼ 40, gas becomes to rarefied for collisional coupling about 0:5mK. and radiative coupling brings spin temperature back to radiation temperature, erasing the signal. When first sources appear at z ∼ 20, they emit Lyman-α and X-ray III. THE FOREGROUND QUESTION photons, which re-couple spin temperature to gas tem- perature via WouthuysenField effect [12, 13]. However, The foregrounds, of course, are what is really difficult at that epoch, the gas is still colder than CMB result- about these measurements. To give an impression of how ing in a second bout of 21-cm being observed in absorp- difficult these can be, we plot a rough estimate of the fore- tion (the second through in the upper panel of Figure ground on Figure 2 at 60MHz. This figure is based on the 1). Later, Lyman-α coupling saturates and the gas tem- Global Sky Models (GSM) from [15]. We have masked perature rises above radiation temperature, giving rise pixels with temperature above 104K, since an experiment to overall signal in emission. At this complex period, with a finite angular resolution would be able to opti- there are large variations in the signal across space and mally downweight bright parts of the sky. The middle the total emission is driven by fluctuations in ionization, panel shows the dipole and quadrupole of the foreground density and gas temperature.
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