The posting continues Clem, Walt and Sergi's work on small sky patch analysis. Questions I want to answer here are, how strong is the dust foreground generated by PySM in the context of \(r\)? Does it match the reality? In order to get a clear conclusion, I made \(r\)-equivalent maps from PySM and Planck 353GHz full-sky maps, and put them together for a comparison.
PySM (arXiv:1608.02841) is a publicly available numerical code used for the simulation of Galactic emission in intensity and polarization at microwave frequencies - Clem has a CMB-S4 posting checking dust decorrelation in these models. In this analysis there are 3 PySM simulation maps involved.
On the data side there are 5 Planck maps available.
This analysis is computed by numpy, scipy and healpy - I made Python code on top of Walt's groundwork. Here is the recipe (same as in PIP XXX) of how I compute an \(r\)-equivalent map from a full-sky input map.
Figure 4.1 presents the smallfield \(|r|\)-equivalent maps in Galactic coordinates and the perspective of orthographic projection. I cut the highly saturated rim of each map to show \(|b| > 35^\circ\) only. The graticule used in these plots is defined by \((\Delta l, \Delta b) = (45^\circ, 20^\circ)\). Patches with negative \(r\) are marked by white crosses while the center of BICEP field (\(l=316.1^\circ,b=-58.3^\circ\)) is marked by a circular dot with color showing the magnitude coming from the measurement of BK14 - \(A_\text{dust@353GHz} = 4.300^{+1.200}_{-1.100} \mu\text{K}^2\) or \(r_d = 0.238^{+ 0.066}_{-0.061}\).
Note: The conversion is done by exploiting the modified blackbody law with \(\beta_d = 1.59\) and \(T_d = 19.6\text{K}\). We can scale \(A_\text{dust@353GHz}\) to \(A_\text{dust@150GHz}\) by multiplying the factor \(((150\text{GHz})^{\beta_d}B(\nu = 150\text{GHz}, T = T_d) \big/ (353\text{GHz})^{\beta_d}B(\nu = 353\text{GHz}, T = T_d))^2 = (0.0609)^2 \).
It is clear that d4_150 is an overestimate. d1_150 and d7_150 is closer to the reality but they still have higher \(r\). Moreover PySM models in general make the sky look more even - they cannot reproduce the spatial variation.
(Note: Pl353 Det Set Split is supposed to be the same as PIP XXX but they don't match. Walt has found this before and I again get the same conclusion.)
Updated on 20180503: I reran the analysis with the mask area increased to 1000 sq. deg. (~2.4% of sky). Now there is an extra option in all figures showing r/σ(r) from a larger area. Also the circular dot now has a color reflecting \(A_\text{dust}\) value from BK14.
In figure 4.2 I make histograms comparing Planck data vs. PySM d1/d4/d7 models. As before I drop all data in \(|b| \leq 35^\circ\), since the emission directly coming from Galactic plane is out of our intereset. One can see Planck data cluster around smaller \(r\).
I also make the following graphs in order to show how \(r_d\) varies over Galactic latitude \(b\). In figure 4.3, "r_d vs. b" presents every \(r_d\) value at a particular \(b\), while "median(r_d) vs. b" takes median over Galactic longitude \(l\). The vertical dashed black line indicates \(b\) of BICEP field center and the black dot stands for BK14 measurement.
Here are the nside = 8 HEALPix \(r\)-equivalent maps. In each FITS file it contains 4 columns: \(\big( r_d, \sigma(r_d), r_E, \sigma(r_E) \big)\). The latter two columns contain \(r\) and \(\sigma(r)\) derived from E-modes - under the assumption \(\alpha_{EE} = \alpha_{BB}\), I used \(C_l^{EE}\) in fitting to get amplitude \(A^{EE}_{\text{fit}}\), and calculated \(A^{BB}_{\text{fit}}\) by the relation \(A_{EE}/A_{BB} = 2\). They are relatively experimental so I did not show them in figure 4.1 .
And here are the nside = 8 HEALPix \(A^{BB}_\text{fit}\)-equivalent maps at 353GHz. They are in the unit of \( \mu\text{K}^{2}_{\text{CMB}} \).