BeyondPLANCK

BeyondPlanck

Overview and background

As of 2020 and into the foreseeable future, ESA's Planck satellite measurements represent the state-of-art in terms of full-sky observations of the microwave sky between 30 and 857GHz, and the work by the Planck collaboration in terms of processing and interpreting these observations are summarized in a series of 150 papers. Despite these massive efforts, several known outstanding issues regarding the final Planck maps remained unresolved at the end of the funded analysis phase, and several external initiatives were started to address these. One of these was BeyondPlanck, which aimed to re-process the Planck LFI data within a self-consistent end-to-end Bayesian framework, in which both instrumental and astrophysical parameters are fitted jointly. This work started in 2018, and was successfully concluded in 2022. The final results from this project are described in a series of 17 papers, and the products made available through the Planck Legacy Archive. A long-term goal is to apply these techniques to a wide range of state-of-the-art experiments, and this work is organized within the Cosmoglobe project.

Data model

The main novel feature of the BeyondPlanck processing is a single joint parametric data model that accounts for both astrophysical and instrumental parameters on the form:

where

• t denotes time sample and j denotes LFI radiometer index
• g denotes the instrumental gain
• P is the pointing matrix
• M denotes the component-frequency mixing matrix, which depends on both astrophysical foreground spectral parameters, beta, and the instrument bandpass
• a^c denotes the spatial amplitude map of component c
• B denotes beam convolution (either with the symmetric main beam response, the asymmetric far-sidelobe beam response, or full 4pi response)
• s^orb denotes the orbital CMB dipole
• s^fsl denotes the sky signal observed through the far sidelobes
• s^1Hz denotes electronic 1Hz spike contamination
• n^corr denotes instrumental correlated noise
• n^w denotes instrumental white noise

Explicitly, the sum over components reads as follows (neglecting for notational simplicity bandpass integration; this is accounted for in the actual processing)

In addition to these explicit parameters, the model also includes hyper-parameters for some of the stochastic fields, perhaps most notably the CMB power spectrum, C_l, which describes the variance of the CMB field, and the correlated noise power spectral density, N_corr(f), as a function of temporal frequency.

For further information regarding this data model, see BeyondPlanck overview paper and references therein.

Data sets

The above data model is fitted using the following combination of datasets:

• Planck LFI time-ordered data for 30, 44 and 70 GHz
• 9-year WMAP frequency maps at Ka-band (33 GHz), Q-band (41 GHz), and V-band (61 GHz). The temperature component is sampled at full angular resolution with a white noise model, while polarization is sampled at low resolution with a dense covariance matrix
• Planck PR4 HFI 353 GHz in polarization
• Planck PR4 HFI 857 GHz in temperature
• Haslam 408 MHz, reprocessed by Remazeilles et al. (2014)

Posterior distribution and Gibbs sampling

Let omega be the set of all free parameters in the above data model. The BeyondPlanck data model is then fitted to the listed data sets by mapping out the full joint posterior distribution by Monte Carlo sampling,

where the likelihood is defined by the white noise distribution

The prior, P(omega), is summarized in the BeyondPlanck overview paper, and consists of a mixture of informative and algorithmic priors.

In practice, the posterior mapping is performed using Gibbs sampling with the following Gibbs chain,

Four independent chains are run for each 1000 iterations, and the first 200 samples are excluded as burn-in, leaving a total of 3200 samples for final analysis. All products listed below are derived from those post-burn-in 3200 samples.

Products

The BeyondPlanck products are available both through the Planck Legacy Archive and through the Cosmoglobe homepage.

Markov Chain files

The full Markov Chains are provided on an HDF5 format, which have convenient IO wrappers for most commonly used programming languages (Python, C/C++, Fortran etc.). Three types of chain files are provided, corresponding to 1) full chains; 2) resampled CMB temperature chains; and 3) resampled CMB polarization chains. Each chain file stores each complete sample in a separate HDF dataset ("folder") marked "NNNNNN" (e.g., "000010" for sample number 10). The internal structure of each sample folder is summarized below for each chain file type. (Only main variables are listed below.)

Example traceplots from the BeyondPlanck chain file. For discussion of this plot, see Basyrov et al. (2022).

Full chains

Description	Markov chains from main run that includes both astrophysical and instrumental parameters.
Filename	BP_c000{1,2,3,4}_v2.h5
Number of samples per chain	1000
Size per chain file	1.7 TB

HDF path	Description	Specification	Notes
ame/amp_alm	(Unconvolved) a_lm's of AME component map (T-only)	uK_RJ at 22 GHz	Ordered according to libsharp convention
ame/nu_p_map	AME nu_peak sky map	GHz in flux density units	See Andersen et al. (2022) for details
cmb/amp_alm	(Unconvolved) a_lm's of CMB component map (T,Q,U)	uK_cmb	Ordered according to libsharp convention
cmb/sigma_l	Angular power spectrum of CMB component map, sigma_l	uK_cmb^2	Ordered as {TT,TE,TB,EE,EB,BB}
dust/amp_alm	(Unconvolved) a_lm's of dust component map (T,Q,U)	uK_RJ at 857 GHz for T; at 353 GHz for Q,U	Ordered according to libsharp convention
dust/beta_map	Thermal dust spectral index, beta_d, map (T,Q,U)	Unitless	Spatially constant but variable
dust/T_map	Thermal dust temperature, T_d, map (T,Q,U)	Kelvin	Fixed to Planck PR4; does not vary with sample
ff/amp_alm	(Unconvolved) a_lm's of free-free component map (T-only)	uK_RJ at 40 GHz	Ordered according to libsharp convention
md/{channel label}	4-element array with {monopole, d_x, d_y, d_z} corrections	Same units as respective frequency channel	Only monopoles and Haslam dipoles are non-zero
radio/amp	Radio source amplitude per object (T-only)	mJy at 30 GHz	Ordered according to BP/Planck Commander point source catalog
radio/spec_ind	Radio source spectral index per object (T-only)	Unitless
synch/amp_alm	(Unconvolved) a_lm's of synchrotron component map (T,Q,U)	uK_RJ at 408 MHz in T; at 30 GHz in Q,U	Ordered according to libsharp convention
synch/beta_map	Synchrotron spectral index, beta_s, sky map	Unitless	See Svalheim et al. (2022) for details
tod/{channel label}/1Hz_ampl	1Hz amplitude per radiometer and PID	Volt
tod/{channel label}/1Hz_temp	Binned 1Hz template per radiometer	Unitless	Binned between 0 and 1 sec
tod/{channel label}/accept	Accept flag per radiometer and PID	Unitless	0 = rejected, 1 = accepted
tod/{channel label}/chisq	Reduced normalized chisq per radiometer and scan	sigma	See Ihle et al. (2022) for details
tod/{channel label}/gain	Total gain per radiometer and scan	V/K	See Gjerløw et al. (2022) for details
tod/{channel label}/map	Frequency map for given channel (T,Q,U)	uK_cmb	See Basyrov et al. (2022) for details
tod/{channel label}/rms	Frequency standard devivation map for given channel (T,Q,U)	uK_cmb	See Basyrov et al. (2022) for details
tod/{channel label}/xi_n	Noise power spectral density parameters for radiometer and PID	{sigma_0, alpha, fknee, A_s}	See Ihle et al. (2022) for details

Resampled CMB temperature chains

Description	Markov chains from CMB temperature analysis. These are produced by imposing a CMB confidence mask on the CMB component, while fixing instrumental and (most of the) astrophysical parameters at the values sampled in the main run. Each CMB temperature sample in these chain represents one in-painted Gaussian constrained realization with full-sky coverage. These samples are useful for CMB temperature analysis. See Colombo et al. (2022) and Paradiso et al. (2022) for details.
Filename	BP_c000{1,2,3,4}_Tresamp_v2.h5
Number of samples per chain	1000
Size per chain file	15 GB

HDF path	Description	Specification	Notes
cmb/amp_alm	(Unconvolved) a_lm's of CMB component map (T,Q,U)	uK_cmb	Ordered according to libsharp convention
cmb/sigma_l	Angular power spectrum of CMB component map, sigma_l	uK_cmb^2	Ordered as {TT,TE,TB,EE,EB,BB}
cmb/D_l	Ensemble averaged (theory) angular power spectrum of CMB component map, D_l	uK_cmb^2	Ordered as {TT,TE,TB,EE,EB,BB}

Resampled CMB polarization chains

Description	Markov chains from CMB polarization analysis. These are produced by resampling the CMB a_lms for l <= 64, while fixing instrumental and (most of the) astrophysical parameters at the values sampled in the main run. These samples are useful for low-resolution CMB polarization analysis. See Colombo et al. (2022) and Paradiso et al. (2022) for details.
Filename	BP_c000{1,2,3,4}_Presamp_v2.h5
Number of samples per chain	50.000
Size per chain file	2.3 GB

HDF path	Description	Specification	Notes
cmb_lowl/amp_alm	(Unconvolved) a_lm's of CMB component map (T,Q,U), lmax = 64	uK_cmb	Ordered according to libsharp convention

Frequency maps

BeyondPlanck frequency maps at 30, 44 and 70 GHz. For further discussion, see Basyrov et al. (2022).

The BeyondPlanck frequency FITS maps are produced by averaging individual frequency map samples over Gibbs iterations, and thus correspond to posterior mean maps. We note that error propagation with these maps is challenging, and these are primarily provided for visualization and comparison purposes. For precision scientific analysis, operating with the individual samples provided in the chain files is highly encouraged to propagate errors properly.

Note 1: Unlike Planck DR3, but similar to Planck PR4, the BeyondPlanck frequency maps retain the CMB Solar dipole. Note 2: Unlike Planck, but similar to WMAP, the BeyondPlanck frequency maps retain the relativistic kinematic quadrupole. Instead of subtracting this signal, it is included as an additional component in the signal model.

Sky map file data structure

Filename = BP_{FREQ}_IQU_n{NSIDE}_v2.fits
EXTNAME = 'FREQ-MAP' : Data columns
Column Name	Data Type	Units	Description
I_MEAN	Real*4	uK_cmb	The signal intensity map
Q_MEAN	Real*4	uK_cmb	The signal Stokes Q map
U_MEAN	Real*4	uK_cmb	The signal Stokes U map
I_RMS	Real*4	uK_cmb	The signal intensity white noise RMS
Q_RMS	Real*4	uK_cmb	The signal Stokes Q white noise RMS
U_RMS	Real*4	uK_cmb	The signal Stokes U white noise RMS
I_STDDEV	Real*4	uK_cmb	The signal intensity posterior std (~ systematic uncertainty)
Q_STDDEV	Real*4	uK_cmb	The signal Stokes Q posterior std (~ systematic uncertainty)
U_STDDEV	Real*4	uK_cmb	The signal Stokes U posterior std (~ systematic uncertainty)
Keyword	Data Type	Value	Description
PIXTYPE	string	HEALPIX
COORDSYS	string	GALACTIC	Coordinate system
ORDERING	string	RING	Healpix ordering
NSIDE	Int	512 or 1024	Healpix Nside
FIRSTPIX	Int*4	0	First pixel number
LASTPIX	Int*4	3145727 or 12582911	Last pixel number
FREQ	string	nnn	The frequency channel

Component maps

BeyondPlanck CMB map. Rows show Stokes T, Q, and U, while columns show posterior mean and standard deviation. For further discussion, see Colombo et al. (2022).

Full-resolution raw posterior mean CMB map

Filename = BP_cmb_IQU_n1024_v2.fits
EXTNAME = 'FREQ-MAP' : Data columns
Column Name	Data Type	Units	Description
I_MEAN	Real*4	uK_cmb	The CMB intensity map
Q_MEAN	Real*4	uK_cmb	The CMB Stokes Q map
U_MEAN	Real*4	uK_cmb	The CMB Stokes U map
I_STDDEV	Real*4	uK_cmb	The CMB intensity posterior std
Q_STDDEV	Real*4	uK_cmb	The CMB Stokes Q posterior std
U_STDDEV	Real*4	uK_cmb	The CMB Stokes U posterior std
Keyword	Data Type	Value	Description
COORDSYS	string	GALACTIC	Coordinate system
ORDERING	string	RING	Healpix ordering
NSIDE	Int	1024	Healpix Nside

Low-resolution raw posterior mean CMB map

Filename = BP_CMB_QU_map_n8_v2.fits
EXTNAME = 'FREQ-MAP' : Data columns
Column Name	Data Type	Units	Description
TEMPERATURE	Real*4	uK_cmb	Low-resolution CMB intensity map
Q-POLARIZATION	Real*4	uK_cmb	Low-resolution CMB Stokes Q map
U-POLARIATION	Real*4	uK_cmb	Low-resolution CMB Stokes U map
Keyword	Data Type	Value	Description
COORDSYS	string	GALACTIC	Coordinate system
ORDERING	string	RING	Healpix ordering
NSIDE	Int	8	Healpix Nside

Single in-painted high-resolution CMB temperature sample

Filename = BP_cmb_resamp_I_n1024_v2.fits
EXTNAME = 'FREQ-MAP' : Data columns
Column Name	Data Type	Units	Description
I_Stokes	Real*4	uK_cmb	The CMB intensity map
Keyword	Data Type	Value	Description
COORDSYS	string	GALACTIC	Coordinate system
ORDERING	string	RING	Healpix ordering
NSIDE	Int	1024	Healpix Nside

Posterior mean AME map

Filename = BP_ame_I_n1024_v2.fits
EXTNAME = 'FREQ-MAP' : Data columns
Column Name	Data Type	Units	Description
I_MEAN	Real*4	uK_RJ	The AME intensity map
I_NU_P_MEAN	Real*4	GHz	AME nu_peak frequency mean
I_STDDEV	Real*4	uK_RJ	AME intensity posterior std
I_NU_P_STDDEV	Real*4	GHz	AME nu_peak frequency rms
Keyword	Data Type	Value	Description
COORDSYS	string	GALACTIC	Coordinate system
ORDERING	string	RING	Healpix ordering
NSIDE	Int	1024	Healpix Nside
FWHM	Real*4	120	Smoothing FWHM in arcmin
NU_REF_T	Real*4	22.0	AME reference frequency in GHz

Full-resolution raw posterior mean thermal dust map

Filename = BP_dust_IQU_n1024_v2.fits
EXTNAME = 'FREQ-MAP' : Data columns
Column Name	Data Type	Units	Description
I_MEAN	Real*4	uK_RJ	Posterior mean intensity map
Q_MEAN	Real*4	uK_RJ	Posterior mean Stokes Q map
U_MEAN	Real*4	uK_RJ	Posterior mean Stokes U map
P_MEAN	Real*4	uK_RJ	Posterior mean polarization amplitude, P = sqrt(Q^2 + U^2)
I_BETA_MEAN	Real*4	Unitless	Posterior mean spectral index, beta_d, in intensity
QU_BETA_MEAN	Real*4	Unitless	Posterior mean spectral index, beta_d, in polarization
I_T_MEAN	Real*4	Kelvin	Posterior mean dust temperature, T_d, in intensity
QU_T_MEAN	Real*4	Kelvin	Posterior mean dust temperature, T_d, in polarization
I_STDDEV	Real*4	uK_RJ	Posterior rms intensity map
Q_STDDEV	Real*4	uK_RJ	Posterior rms Stokes Q map
U_STDDEV	Real*4	uK_RJ	Posterior rms Stokes U map
P_STDDEV	Real*4	uK_RJ	Posterior mean polarization amplitude, P = sqrt(Q^2 + U^2)
I_BETA_STDDEV	Real*4	Unitless	Posterior rms spectral index, beta_d, in intensity
QU_BETA_STDDEV	Real*4	Unitless	Posterior rms spectral index, beta_d, in polarization
I_T_STDDEV	Real*4	Kelvin	Posterior mean rms temperature, T_d, in intensity
QU_T_STDDEV	Real*4	Kelvin	Posterior mean rms temperature, T_d, in polarization
Keyword	Data Type	Value	Description
COORDSYS	string	GALACTIC	Coordinate system
ORDERING	string	RING	Healpix ordering
NSIDE	Int	1024	Healpix Nside
FWHM	Real*4	10	Smoothing FWHM in arcmin
NU_REF_T	Real*4	545	Reference frequency in temperature in GHz
NU_REF_P	Real*4	353	Reference frequency in polarization in GHz

Full-resolution raw posterior mean free-free map

Filename = BP_freefree_I_n1024_v2.fits
EXTNAME = 'FREQ-MAP' : Data columns
Column Name	Data Type	Units	Description
I_MEAN	Real*4	uK_RJ	Posterior mean intensity map
I_TE_MEAN	Real*4	Kelvin	Posterior mean electron temperature, T_e. (Fixed in current analysis)
I_STDDEV	Real*4	uK_RJ	Posterior rms intensity map
I_TE_STDDEV	Real*4	Kelvin	Posterior rms electron temperature, T_e. (Zero i in current analysis)
Keyword	Data Type	Value	Description
COORDSYS	string	GALACTIC	Coordinate system
ORDERING	string	RING	Healpix ordering
NSIDE	Int	1024	Healpix Nside
FWHM	Real*4	30	Smoothing FWHM in arcmin
NU_REF_T	Real*4	40.0	Reference frequency in temperature in GHz

Full-resolution raw posterior mean synchrotron map

Filename = BP_synch_IQU_n1024_v2.fits
EXTNAME = 'FREQ-MAP' : Data columns
Column Name	Data Type	Units	Description
I_MEAN	Real*4	uK_RJ	Posterior mean intensity map
Q_MEAN	Real*4	uK_RJ	Posterior mean Stokes Q map
U_MEAN	Real*4	uK_RJ	Posterior mean Stokes U map
P_MEAN	Real*4	uK_RJ	Posterior mean polarization amplitude, P = sqrt(Q^2 + U^2)
I_BETA_MEAN	Real*4	Unitless	Posterior mean spectral index, beta_d, in intensity
QU_BETA_MEAN	Real*4	Unitless	Posterior mean spectral index, beta_d, in polarization
I_STDDEV	Real*4	uK_RJ	Posterior rms intensity map
Q_STDDEV	Real*4	uK_RJ	Posterior rms Stokes Q map
U_STDDEV	Real*4	uK_RJ	Posterior rms Stokes U map
P_STDDEV	Real*4	uK_RJ	Posterior mean polarization amplitude, P = sqrt(Q^2 + U^2)
I_BETA_STDDEV	Real*4	Unitless	Posterior rms spectral index, beta_d, in intensity
QU_BETA_STDDEV	Real*4	Unitless	Posterior rms spectral index, beta_d, in polarization
Keyword	Data Type	Value	Description
COORDSYS	string	GALACTIC	Coordinate system
ORDERING	string	RING	Healpix ordering
NSIDE	Int	1024	Healpix Nside
FWHM	Real*4	60	Smoothing FWHM in arcmin
NU_REF_T	Real*4	0.408	Reference frequency in temperature in GHz
NU_REF_P	Real*4	30	Reference frequency in polarization in GHz

Ancillary data

CMB confidence masks

CMB confidence masks for temperature (top) and polarization (bottom). For further discussion, see Colombo et al. (2022).

The BeyondPlanck processing involves two different CMB confidence masks, with high and low resolution, respectively:

• BP_CMB_I_analysis_mask_n1024_v2.fits -- CMB T-only analysis mask at Nside=1024
• BP_CMB_QU_map_n8_v2.fits -- CMB T+P analysis mask at Nside=8

Both maps are defined in Galactic coordinates with HEALPix ring ordering.

Revised LFI bandpass profiles

Comparison of Planck (orange) and BeyondPlanck (blue) bandpasses for all 30, 44 and 70 GHz radiometers. For further discussion, see Svalheim et al. (2022).

As discussed by Zonca et al. (2010) and Svalheim et al. (2022), the official Planck LFI bandpasses measured from ground were affected by measurement errors. These have been partially mitigated in the updated BeyondPlanck processing, and the improved bandpass profiles are provided in the form of ASCII tables. Each file is called BP_bandpass_LFI_{radiometer}_v2.dat, and contains an array with {nu, tau} on each line. The symbol '#' indicates comments.

Additional information

• BeyondPlanck was an effort to generalize the Planck-developed component separation code called Commander to also support time-domain analysis. The BeyondPlanck software is thus an integral part of the latest Commander3 code, which is available from the Cosmoglobe GitHub repository
• The Commander documentation describes both the installation procedure and the Commander parameter file
• The BeyondPlanck papers are published in a Special Issue of Astronomy & Astrophysics called "BeyondPlanck: end-to-end Bayesian analysis of Planck LFI"