Synchrotron Curvature

[brandonshensley]

Opening a new issue to discuss the synchrotron curvature parameter, which may affect the design of the Simulation Suite (#103). We have gotten some feedback that synchrotron spectral complexity is a high priority concern.

The s3 model has curvature as a single global parameter. I propose considering a new synchrotron model that has the amplitude and beta improvements of s5 but that also includes curvature. This could be implemented as a global mean value in agreement with s3, but with fluctuations following the same power spectrum as synchrotron beta in s5. That leaves only the amplitude of fluctuations to be decided, and unfortunately current data are not informative here. We could iterate starting with something modest like a 10% standard deviation around the mean at ~1 degree scales and then refine if that produces something either too extreme or completely unnoticeable.

Thoughts very much welcome @NicolettaK, @seclark, @zonca, @giuspugl, @bthorne93, others.

[giuspugl]

Hi all, I started addressing this issue in order to have a data driven modelling of the synchrotron curvature.
Below the steps i followed :

• use the same template we adopted to modulate synchrotron small scales, i.e. HASLAM map rescaled it at 23 GHz, transformed in log pol tens i and smoothed at 5 deg (see https://github.com/galsci/pysm/pull/98)
• Normalize the template with MinMax rescaling so that we match the measurements of Kogut 2012 within the ARCADE observational footprint. Notice that these data are used also in PySM2 ( Thorne et al 2016 ), i.e. C = -0.052 \pm 0.005.

Which is a good approximation to the one shown in Kogut 2012 (fig. 4)

The full sky map of synchrotron curvature obtained with this approach is shown below :

Please let me know if this sounds a reasonable approach.

[NicolettaK]

This is great @giuspugl! Should we think about adding also Gaussian small scales with slope as the one we use for the beta_s?

[brandonshensley]

Agreed, really nice analysis @giuspugl! I agree with @NicolettaK that we should add in the small scales using the slope of the beta_s power spectrum.

[giuspugl]

Ok , i've included the small scales following the power law spectral index we fit for Bs with the SPASS data, i.e. gamma = -2.86 . I modulate small scales of curvature parameter Cs with exactly the same modulation map we adopted for Bs . Below you can find the power spectra

NB: The injection of small scales doesn't affect the global properties of the Cs mpa as expected, after that we are still consistent with the Kogut 2012 measurements.

[brandonshensley]

This looks great @giuspugl!

[zonca]

when you think this is complete, you can add a Jupyter Notebook with the final analysis in a gist and I can pick up from there

[giuspugl]

Here's a compiled notebook for the injection of synchro curvature
https://gist.github.com/giuspugl/4c632021f988dc63a70bb5198db6b819

[zonca]

Synchrotron curvature PySM 3

[zonca]

thanks @giuspugl, I can reproduce the notebook

Now, my plan would be:

• execute the notebook at 8192 and create the usual maps at 2048, 4096 and 8192 for C_s with small scales
• create the s7 model, similar to s3 (https://github.com/galsci/pysm/blob/main/pysm3/data/presets.cfg#L216-L228), but with the new IQU templates and beta_s from s5 and this C_s map.
• I would wait for someone to ask for it before creating a "small-scales-on-the-fly" model, I am worried otherwise we will have too many models.

@brandonshensley @NicolettaK @seclark ?