Smallfield \(r\)-equivalent Maps

— Kenny Lau


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 Simulation and Planck Data

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.

Maps pager
\(|r|\) and \(\sigma(r)\) maps from PySM simulations and Planck data. The northern (southern) Galactic hemishpere is shown on the left (right).

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 \(r\).

Histogram pager
Histogram of Planck data vs. PySM simulations. Only patches with \(|b| > 35^\circ\) are included in this statistics.

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.

Statistics pager
Statistics of Planck data vs. PySM simulations. Note that there are no PIP XXX data in the range \(|b| \leq 35^\circ\).


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 \( \mu\text{K}^{2}_{\text{CMB}} \).

Related postings and papers

  1. 2017 June 27: Checking dust decorrelation in models d1/d4/d7 and hipdt (Clem P.)
  2. The Python Sky Model: software for simulating the Galactic microwave sky (arXiv:1608.02841)
  3. Planck intermediate results. XXX. The angular power spectrum of polarized dust emission at intermediate and high Galactic latitudes (arXiv:1409.5738)
  4. Xspect, estimation of the angular power spectrum by computing cross-power spectra with analytical error bars (arXiv:1409.5738)