Preliminary Rejection of Global 21-cm Models with EDGES High-Band (ongoing work)

Transcription

1 Preliminary Rejection of Global 21-cm Models with EDGES High-Band (ongoing work) Raul Monsalve CASA, University of Colorado Boulder SESE, Arizona State University November 23, 216

2 2 Description Here I present a preliminary rejection of models, specifically some models introduced in Cohen et al. (216), Mirocha et al. (216), and others discussed in Mirocha et al. (213). The data used for this study correspond to an average spectrum from the EDGES High-Band system deployed in 215. This average spectrum is NOT the final EDGES spectrum. It is just a spectrum with an intermediate level of averaging and calibration. The capability for model probing/rejection of the definitive EDGES High-Band spectrum is higher. This report is a continuation to Report 77 on the ASU EDGES memo page. REFERENCES: 1. Cohen, A., Fialkov, A., Barkana, R., & Lotem, M. 216, 2. Mirocha, J., Furlanetto, S. R., & Sun, G. 216, 3. Mirocha, J., Harker, G., J. A., & Burns, J. O. 213, ApJ, 777, ASU EDGES Report 77,

3 3 Description The 21-cm model rejection is conducted using a p-value frequentist hypothesis testing approach. I consider two scenarios: 1. REFERENCE: m = fit(d) 2. NULL HYPOTHESIS: m = fit(d ) In both cases, I fit a foreground model to the data. This foreground model is the EDGES polynomial with five terms: model = 4 a i ν 2.5+i. (1) i= In the REFERENCE case, I fit the EDGES polynomial directly to the spectrum data, d. By doing this, I assume that the data do not contain a 21-cm signal. In the NULL HYPOTHESIS, I assume that the data do contain a 21-cm signal. Thus, I fit the EDGES polynomial to d = d d 21cm, where d 21cm represents the 21-cm model. The quality of the fits is quantified through the χ 2 statistics: REFERENCE: NULL HYPOTHESIS: χ 2 = i χ 2 = i [ ] d(νi ) m(ν i ) 2 σ(ν i ) [ d (ν i ) m ] (ν i ) 2. (2) σ(ν i )

4 4 Description The frequency-dependent spectral uncertainty, σ(ν), is obtained by modeling linearly the residuals of the REFERENCE case. This model for the uncertainty is shown in Figure 1. By construction, this uncertainty results in a Reduced Chi Square of one (χ 2 /df = 1) for the REFERENCE case. The degrees of freedom are computed as df = N ν N fg 1 = 24, where the number of spectral points is N ν = 246 at a resolution of 391 khz, and the number of foreground parameters is N fg = 5.

5 5 Description The rejection probability of a 21-cm model is given by: prob(χ 2 ; df) = 1 PDF(df) dχ 2, (3) χ 2 where PDF is the Probability Distribution Function for the χ 2 distribution. As the χ 2 statistics increases for a fixed df, the rejection probability increases. Here, we set a model rejection threshold of 95%. For 24 degrees of freedom, a probability of 95% corresponds to a Reduced Chi Square of Thus, I reject models with a Reduced Chi Square The results of this preliminary model rejection exercise are presented in Figures 2 through 7.

6 6 Preliminary Measured Sky Brightness Temperature and Residuals brightness temperature [K] residuals [mk] RMS = 2 mk frequency [MHz] Figure : (1): TOP: Measured sky brightness temperature. BOTTOM: In blue, residuals after fitting and removing a 5-term EDGES polynomial from data in top panel. These residuals have a weighted RMS of 2 mk. In red, the 1σ uncertainty model.

7 Preliminary Rejection of Models from Cohen et al. (216) The following two figures show results for models from Cohen et al. (216). The rejected models, as well as some of their key parameters, are: number f V c f X SED τ Soft Hard Soft Soft Soft MQ Soft MQ Soft Soft Hard & MQ Soft & MQ MQ NOTES: f : star formation efficiency V c : virial circular velocity f X : X-ray efficiency SED: Spectral energy distribution of X-ray sources (MQ: mini quasars) τ: CMB optical depth RESULT: Currently, 14 models are rejected.

8 8 Preliminary Rejection of Models from Cohen et al. (216) brightness temperature [mk] brightness temperature [mk] Currently Rejected at 95% Currently NOT Rejected frequency [MHz] Figure : (2): TOP: Models from Cohen et al. (216) preliminarily rejected. BOTTOM: Models preliminarily NOT rejected

9 Preliminary Residuals for Models from Cohen et al. (216) residuals [mk] residuals [mk] Currently Rejected at 95% Currently NOT Rejected frequency [MHz] 9 Figure : (3): In BLACK, nominal residuals without 21-cm model. In CYAN, residuals for models from Cohen et al. (216). TOP: cases preliminarily rejected. BOTTOM: cases preliminarily NOT rejected.

10 1 Preliminary Rejection of Models from Mirocha et al. (216) The following two figures show results for models from Mirocha et al. (216). These models are computed by: 1. projecting the measured (z 8) galaxy luminosity function to high redshifts, and by 2. accounting for recent values for the CMB optical depth. These aspects, in addition to inefficient heating by X-ray binaries (presumed sources of high-redshift X-rays), result in a signal with an absorption trough centered at 11 MHz. RESULT: Currently, 17 models are marginally rejected.

11 11 Preliminary Rejection of Models from Mirocha et al. (216) brightness temperature [mk] brightness temperature [mk] Currently Rejected at 95% Currently NOT Rejected frequency [MHz] Figure : (4): TOP: Models from Mirocha et al. (216) preliminarily rejected. BOTTOM: Models preliminarily NOT rejected

12 Preliminary Residuals for Models from Mirocha et al. (216) residuals [mk] residuals [mk] Currently Rejected at 95% Currently NOT Rejected frequency [MHz] 12 Figure : (5): In BLACK, nominal residuals without 21-cm model. In CYAN, residuals for models from Cohen et al. (216). TOP: cases preliminarily rejected. BOTTOM: cases preliminarily NOT rejected.

13 13 Preliminary Rejection of Models Discussed in Mirocha et al. (213) The following two figures show results for models initially discussed, but not shown, in Mirocha et al. (213). These models can be considered Cold EoR scenarios. Some of their characteristics are: 1. A strong Ly-α background at early times. 2. Negligible X-ray heating. 3. Reionization histories well-modeled by the common tanh form. Additionally, all these models satisfy two observational constraints: 1. They produce values of the Thomson scattering optical depth consistent (at the 2σ level) with the recent Planck results. 2. Reionization is complete (1 x HI >.99) at z = 6. RESULT: Currently, all the models provided (358) are rejected.

14 14 Preliminary Rejection of Models Discussed in Mirocha et al. (213) Currently Rejected at 95% brightness temperature [mk] frequency [MHz] Figure : (6): All (358) Cold EoR models provided, discussed initially in Mirocha et al. (213), are preliminarily rejected.

15 Preliminary Residuals for Models Discussed in Mirocha et al. (213) 16 Currently Rejected at 95% residuals [mk] frequency [MHz] 15 Figure : (7): In BLACK, nominal residuals without 21-cm model. In CYAN, residuals for Cold EoR models discussed in Mirocha et al. (213). All models provided (358) are rejected.

16 16 Comments 1. About 66% of the models probed, from Cohen et al. and Mirocha et al., can be preliminarily rejected (those with sharper and stronger features). 2. The spectrum used to probe these models is not the best EDGES spectrum. The best spectrum will produce stronger constraints. 3. The calibration uncertainty has not been considered in these rejections.