Source-linked AI summary
The Python Sky Model: software for simulating the Galactic microwave sky
Ben Thorne, Jo Dunkley, David Alonso, Sigurd Naess
TL;DR
The paper addresses the need for realistic Galactic-foreground simulations because polarized foregrounds are much stronger than the primordial CMB B-mode signal. It presents PySM, an accessible code using empirical models and public WMAP and Planck data to simulate full-sky microwave emission, including small-scale realizations. The authors conclude that the software is fast, portable, easy to use, and extensible, while its 2D parametric approach cannot capture the full frequency-dependent polarization complexity of Galactic foregrounds.
Problem
Primordial gravitational-wave B-mode polarization is at least several orders of magnitude weaker than polarized Galactic foregrounds, motivating realistic simulations for CMB polarization experiments.
Method
PySM combines public WMAP and Planck template maps with phenomenological frequency-scaling models, optional CMB and noise components, and Gaussian or lognormal small-scale realizations.
Results
PySM simulates full-sky intensity and polarization for four Galactic components, with alternative frequency prescriptions and support for experimental bandpasses and beams.
Takeaways & Limitations
The public code is fast, portable, easy to install, and designed to accommodate additional astrophysical complications and alternative models.
Takeaways & Limitations
Because PySM uses 2D sky maps and parametric extrapolations, it cannot fully reproduce the complex, frequency-dependent polarization of Galactic foregrounds.
Abstract
from arXiv · showhide
We present a numerical code to simulate maps of Galactic emission in intensity and polarization at microwave frequencies, aiding in the design of Cosmic Microwave Background experiments. This Python code builds on existing efforts to simulate the sky by providing an easy-to-use interface and is based on publicly available data from the WMAP and Planck satellite missions. We simulate synchrotron, thermal dust, free-free, and anomalous microwave emission over the whole sky, in addition to the Cosmic Microwave Background, and include a set of alternative prescriptions for the frequency dependence of each component that are consistent with current data. We also present a prescription for adding small-scale realizations of these components at resolutions greater than current all-sky measurements. The code is available at https://github.com/bthorne93/PySM_public.
1 INTRODUCTION
Precise CMB polarization measurements require realistic simulations of Galactic foregrounds because polarized foregrounds overwhelm the primordial B-mode signal. The paper presents a flexible, empirically based tool that uses public WMAP and Planck data to simulate these emissions.
- Primordial gravitational-wave B-mode polarization is predicted to be at least several orders of magnitude weaker than polarized Galactic foregrounds, even in clean sky regions.
- Realistic Galactic-emission simulations are needed to optimize extraction of the CMB polarization signal across multiple frequencies.
- The new Python code provides a flexible, easy-to-use simulator incorporating recent public Planck data and building on existing sky-modeling efforts.
2 LARGE-SCALE SIMULATIONS
PySM generates full-sky Galactic and CMB simulations by combining observational templates with phenomenological frequency-scaling models. Users can specify experimental characteristics and output choices, including bandpasses, beams, noise, components, and units.
- PySM simulates intensity and polarization for thermal dust, synchrotron, free-free, and anomalous microwave emission, with optional lensed CMB and white instrument noise.
- Users specify frequencies, beam widths, bandpass widths, noise, output components, and units for each simulation.
- Each component is extrapolated from pivot-frequency template maps using scaling laws and maps of spectral parameters, while alternative models remain extendable.
2.1 Synchrotron
The synchrotron models use template maps and spatially varying or curved spectral prescriptions to extrapolate emission across frequency. Alternative models represent latitude-dependent steepening and frequency curvature while retaining consistency with observational constraints.
- 2.1.1 Model 1: Nominal index: Synchrotron intensity uses a reprocessed, degree-scale-smoothed 408 MHz Haslam map, while polarization uses smoothed WMAP 23 GHz Q and U maps.
- 2.1.1 Model 1: Nominal index: The nominal model applies a direction-dependent power-law scaling using a spectral-index map derived from Haslam and WMAP polarization data.
- 2.1.2 Model 2: Spatially varying index: Model 2 sets δβ = −0.3, producing synchrotron indices from βs = −3.0 at the equator to βs = −3.3 at the poles.
- 2.1.3 Model 3: Curvature of index: Model 3 introduces curvature above a characteristic frequency, with positive C representing flattening and negative C representing steepening.
- 2.1.3 Model 3: Curvature of index: Figure 1 compares nominal and impactful alternative frequency-scaling spectra using RMS values from masked, beam-smoothed component maps.
2.2 Thermal dust emission
Thermal dust emission is modeled with modified-blackbody prescriptions anchored to Planck templates, while alternative models represent uncertain component structure and spatial variation. Tests indicate current Planck noise cannot distinguish substantial degree-scale variation in the dust spectral index.
- At frequencies above ≈70 GHz, polarized Galactic foregrounds are dominated by thermal dust, modeled as emission from interstellar grains heated by starlight.The spectrum in the CMB-experiment range is approximated by a modified blackbody with power-law emissivity.
- Model 1: Nominal index: A single 15.9 K dust component fits Planck data well, but intensity and polarization prefer spectral indices β = 1.51 ± 0.01 and β = 1.59 ± 0.02, respectively.The difference suggests multiple components with different polarization properties.
- The physical dust model remains uncertain in the number of components, spatial index variability, and spatial temperature variation.The nominal single-component model also omits potentially distinct emissivities and polarization efficiencies of silicate and carbonaceous grains.
- Model 1: Nominal index: The nominal PySM model uses Commander templates at 545 GHz for intensity and 353 GHz for polarization, with spatially varying βd and Td and a shared intensity-polarization index.The polarization template is smoothed to two degrees FWHM, with small-scale variations added separately.
- Models 2 and 3: Spatially variable index: ∼0.22 is the simulated noise dispersion of recovered βd, compared with 0.17 in the Planck analysis and 0.22 in a comparable calculation.Because the distributions are noise-dominated, models with significant degree-scale index variation remain consistent with the data.
- Model 4: Two dust temperatures: PySM includes multi-component alternatives, including a two-component model using Meisner–Finkbeiner templates and separate polarization construction from the 353 GHz Model 1 maps.The two-component prescription uses Nd = 2, while polarization angles and fractional polarization are inherited from the nominal dust templates.
2.3 Anomalous microwave emission
Anomalous microwave emission (AME) is a dust-correlated component important mainly from 20–40 GHz, with a variable peak frequency. PySM models it using Planck Commander templates and allows an adjustable polarization prescription.
- AME has a spectrum not well approximated by standard foreground models and is primarily important across 20–40 GHz with variable peak frequency.It has been detected in both compact objects and the diffuse sky and is spatially correlated with dust.
- PySM models AME with Planck Commander templates whose two emissivity components are calculated using SpDust2 for a cold neutral medium and shifted in log(ν)−log(I) space.The nominal AME model is unpolarized.
- Observations constrain AME polarization below 1–3% at 23–41 GHz, with a 0.22% upper limit from combined QUIJOTE and WMAP data for W43.PySM can instead assign a global polarization fraction of 2% by varying the fa parameter and uses dust polarization angles for the template.
2.4 Free-free
Free-free emission arises from electron–ion scattering and has a temperature- and emission-measure-dependent frequency scaling. PySM treats it as nominally unpolarized, despite small localized polarization effects.
- Free-free emission is caused by electrons scattering off ions, with frequency scaling determined by electron temperature and emission measure.Above 1 GHz, its spectrum is close to a power law of −2.14 and flattens abruptly at lower frequencies.
- The PySM nominal free-free model assumes the emission is unpolarized because the scattering is independent of direction.Small effects at dense-cloud edges can produce up to 10% polarization, but the estimated net sky polarization is below 1%.
2.5 CMB
PySM generates a lensed CMB realization from CAMB-derived angular power spectra using Taylens, while also supporting precomputed maps and artificial delensing.
- Taylens generates a lensed CMB realization from CAMB-derived spectra for temperature, polarization, lensing potential, and their cross-correlations.The nominal model uses ΛCDM parameters that best fit the Planck 2015 data.
- Users can run Taylens during simulation or supply a precomputed temperature and polarization map, with optional artificial delensing by a chosen suppression factor.This provides alternative workflows for including the CMB lensing signal.
2.6 Instrument
The instrument model represents the response with a top-hat bandpass, Gaussian white noise, and a Gaussian beam. Users specify channel frequencies and widths, while the simplified model omits realistic noise and bandpasses.
- The instrument response is modeled with a top-hat bandpass, Gaussian white noise, and a Gaussian beam profile.
- Users specify each channel’s central frequency and band width, with white-noise levels and beam FWHM set per band.
- The model does not capture realistic noise realizations or realistic bandpasses, but the code can be modified to incorporate them.
3 SMALL-SCALE SIMULATIONS
The method augments smoothed Galactic templates with modeled small-scale Gaussian or lognormal realizations, using extrapolated power spectra and spatial normalization. It produces continuous power-law behavior at the template-resolution transition, while imposing component-specific choices and limitations.
- Overview: The simulations combine original smoothed maps with added small-scale realizations, M = M0 + Mss, using Gaussian or lognormal fields.The authors restrict these realizations to Gaussian or lognormal forms despite expected non-Gaussianity of the real sky.
- 3.1 Polarization: Polarization small scales are generated by smoothing noise-dominated templates to ℓ∗ and adding Gaussian realizations drawn from fitted power-law spectra.Angular power spectra are computed on masked skies with PolSpice, and the WMAP or Planck Gal80 masks are used for synchrotron or dust.
- 3.1 Polarization: The synchrotron transition scale is ℓsynch∗ = 69, with fitted polarization slopes γsynch,EE = −0.66, γsynch,BB = −0.62, γdust,EE = −0.31, and γdust,BB = −0.15.The scale is estimated from the minimum of a fitted BB or EE signal-plus-noise model, then used to set the smoothing kernel.
- 3.1 Polarization: Spatially varying normalization modulates Gaussian polarization fields according to large-scale power measured in Healpix Nside = 2 patches and smoothed over 10°.This normalization is intended to reflect modulation of small-scale power by the large-scale emission.
- 3.1 Polarization: The resulting dust and synchrotron maps show power-law behavior continuous at ℓ = ℓ∗ in both analyzed regions.The figures compare original, smoothed, added-small-scale, and final spectra for selected patches and masked sky regions.
- Limitations: The normalization method cannot capture modulation variations below Nside 2 pixel scales, so normalization is inaccurate in sufficiently small regions.For intensity, the small-scale map is not correlated with polarization at small scales.
- 3.2–3.3 Intensity: For intensity, synchrotron uses a lognormal small-scale procedure with best-fit α = 0.6 over 200 < ℓ < 1000, while free-free fixes γ = −0.5 and uses α = 1.15.The free-free lognormal approach was rejected because its dynamic range produced unrealistically large small-scale variations; negative pixels required redrawing for less than 0.5% of pixels.
4 DISCUSSION
The paper presents accessible Galactic microwave-sky simulation software with alternative foreground models and small-scale realizations. It also identifies limitations from uncorrelated components, single-scale smoothing, non-Gaussian small scales, and the use of two-dimensional rather than three-dimensional foreground models.
- The software simulates Galactic microwave emission in polarization and intensity using nominal models plus alternatives consistent with current data.Its public, fast, portable implementation is designed to make further astrophysical extensions straightforward.
- Small-scale simulation methods recover power-law behavior for polarized components in both low- and high-signal sky patches with minimal noise bias.These simulations may aid forecasting for ground-based observations with partial sky coverage.
- The small-scale procedure does not correlate different simulated components and loses high-signal-to-noise information by smoothing at a single scale.Spatially varying signal-to-noise in the smoothing-scale definition could improve accuracy.
- The small-scale simulations omit the non-Gaussianity expected in practice.
- Using two-dimensional maps and parametric frequency extrapolations limits the ability to reproduce the frequency-dependent polarization of Galactic foregrounds.The paper points to three-dimensional realizations of the Galactic magnetic field and source distributions as a more realistic approach.