Simulation data

Introduction

---

The 2013 Planck data release is supported by a set of simulated maps of the model sky, by astrophysical component, and of that sky as seen by Planck. The simulation process consists of

1. modeling each astrophysical component of the sky emission for each Planck detector, using pre-Planck data and the relevant characteristics of the Planck instruments (namely the detector plus filter transmissions curves).
2. simulating each detector's observation of each sky component following the Planck scanning strategy and using the best estimates of the detector's beam and noise properties (now obtained in flight), then combining these timelines into a single one per detector, and projecting these simulated timelines onto observed maps (the fiducial sky), as is done with the on-orbit data;
3. generating Monte Carlo realizations of the CMB and of the noise, again following the Planck scanning strategy and using our best estimates of the detector beams and noise properties respectively.

The first step is performed by the Planck Sky Model (PSM), and the last two by the Planck Simulation Tools (PST), both of which are described in the sections below.

The production of a full focal plane (FFP) simulation, and including the many MC realizations of the CMB and the noise, requires both HFI and LFI data and includes large, computationally challenging, MC realizations. They are too large to be generated on either of the DPC's own cluster. Instead the PST consists of three distinct tools, each designed to run on the largest available supercomputers, that are used to generate the fiducial sky realization, the CMB MC, and the noise MC respectively. The simulations delivered here are part of the 6th generation FFP simulations, known as FFP6. They were primarily generated on the Hopper and Edison systems at NERSC, with some of the LFI noise MCs generated on the Louhi system at CSC.

While FFP6 includes our best measurements of the detector band-passes, main beams and noise power spectral densities, and is guaranteed to be internally self-consistent, there are a number of differences with the real data that should be borne in mind, although all tests performed to date indicate that these are statistically insignificant:

• the beams do not include far side-lobes;
• the detector noise characteristics are assumed stable: a single noise spectrum per detector is used for the entire mission;
• it assumes perfect calibration, transfer function deconvolution and deglitching;
• it uses the HFI pointing solution for the LFI frequencies, rather than the DPC's two focal plane model.
• it uses a different map-maker to HFI, and as a consequence implements very slightly different data cuts - primarily at ring boundaries - resulting in marginally different hit-maps.

The Planck Sky Model

---

Overall description

The Planck Sky Model, PSM, consists of a set of data and of code used to simulate sky emission at millimeter-wave frequencies; it is described in detail in Delabrouille et al., (2013) delabrouille2012, henceforth the PSM paper..

The main simulations used to test and validate the Planck data analysis pipelines (and, in particular, component separation) makes use of simulations generated with version 1.7.7 of the PSM software. The total sky emission is built from the CMB plus ten foreground components, namely thermal dust, spinning dust, synchrotron, CO lines, free-free, thermal Sunyaev-Zel'dovich (SZ) effect (with first order relativistic corrections), kinetic SZ effect, radio and infrared sources, Cosmic Infrared Background (CIB).

The CMB is modeled using CAMB. It is based on adiabatic initial perturbations, with the following cosmological parameters:

• T_CMB = 2.725
• H = 0.684
• OMEGA_M = 0.292
• OMEGA_B = 0.04724
• OMEGA_NU = 0
• OMEGA_K = 0
• SIGMA_8 = 0.789
• N_S = 0.9732
• N_S_RUNNING = 0
• N_T = 0
• R = 0.0844
• TAU_REION = 0.085
• HE_FRACTION = 0.245
• N_MASSLESS_NU = 3.04
• N_MASSIVE_NU = 0
• W_DARK_ENERGY = -1
• K_PIVOT = 0.002
• SCALAR_AMPLITUDE = 2.441e-9

and all other parameters are set to the default standard of the Jan 2012 version of CAMB. In addition, this simulated CMB contains non-Gaussian corrections of the local type, with an f_NL parameter of 20.4075.

The Galactic ISM emission comprises five components: thermal dust, spinning dust, synchrotron, CO lines, and free-free emission. We refer the reader to the PSM publication for details. For the simulations generated here, however, the thermal dust model has been modified in the following way: instead of being based on the 100 micron map of Schlegel, Finkbeiner and Davis (2008) schlegel1998, henceforth SFB, the dust template uses an internal release of the 857 GHz Planck observed map itself, in which point sources have been subtracted, and which has been locally filtered to remove CIB fluctuations in the regions of lowest column density. A caveat is that while this reduces the level of CIB fluctuations in the dust map in some of the regions, in regions of moderate dust column density the CIB contamination is actually somewhat larger than in the SFD map (by reason of different emission laws for dust and CIB, and of the higher resolution of the Planck map).

The other emissions of the galactic ISM are simulated using the prescription described in the PSM paper. Synchrotron, free-free and spinning dust emission are based on WMAP observations, as analyzed by Miville-Deschenes et al. (2008) Miville2008. Small scale fluctuations have been added to increase the variance on small scales and compensate the lower resolution of WMAP as compared to Planck (in particular for the HFI channels). The main limitation of these maps is the presence at high galactic latitude of fluctuations that may be attributed to WMAP noise. The presence of noise and of added Gaussian fluctuations on small scales may result in a few occasional pixels being negative (e.g. in the spinning dust maps). Low frequency foreground maps are also contaminated by some residuals of bright radio sources that have not been properly subtracted from the templates of diffuse emission.

The CO maps are simulated using the CO J=1-0 observations of Dame et al. (2001)dame2001. The main limitations are limited sky coverage, lower resolution than that of Planck high frequency channels, line ratios (J=2-1)/(J=1-0) and (J=3-2)/(J=2-1) constant over the sky. The CO in the simulation is limited to the three lowest ¹²CO lines.

Galaxy clusters are generated on the basis of cluster number counts, following the Tinker et al. (2008) (Tinker2008) mass function, for the cosmological parameters listed above. Clusters are assumed perfectly spherical, isothermal, and are modeled using the universal pressure profile of Arnaud et al. (2010) arnaud2010. Relativistic corrections following Itoh et al. (1998) Nozawa1998 are included to first order. The simulated kinetic SZ effect assumes no bulk flow, and a redshift-dependent average cluster velocity compatible with the linear growth of structures.

Point sources comprise radio sources (based on extrapolations across frequencies of radio observations between 800 MHz and 5 GHz) and infrared sources (based on extrapolations in frequencies of IRAS sources). One caveat is that due to the unevenness of the radio source surveys, the equatorial southern part of the sky has less faint radio sources than the northern part. Although all the missing sources are well below the Planck detection level, this induces a small variation of the total emission background over the sky. Check the individual faint point source emission maps if this is a potential problem for your applications. See also the PSM paper for details about the PSM point source simulations. The PSM separates bright and faint point source; the former are initially in a catalog, and the latter in a map, though a map of the former can also be produced. In the processing below, the bright sources are simulated via the catalog, but for convenience they are delivered as a map.

Finally, the far infrared background due to high redshift galaxies has been simulated using a procedure is based on the distribution of galaxies in shells of density contrast at various redshifts (Castex et al., PhD thesis; paper in preparation). This simulation has been modified by gradually substituting an uncorrelated extra term of CIB emission at low frequencies, artificially added in particular to decorrelate the CIB at frequencies below 217 GHz from the CIB above that frequency, to mimic the apparent decorrelation observed in the Planck Early Paper on CIB power spectrum (Planck early paper XVIII planck2011-6-6).

While the PSM simulations described here provide a reasonably representative multi-component model of sky emission, users are warned that it has been put together mostly on the basis of data sets and knowledge pre-existing the Planck observations themselves. While it is sophisticated enough to include variations of emission laws of major components of the ISM emission, different emission laws for most sources, and a reasonably coherent global picture, it is not (and is not supposed to be) identical to the real sky emission. The users are warned to use these simulations with caution.

PSM Products

PSM maps of the CMB and of the ten foregrounds are given in the following map products:

• HFI_SimMap_cmb_2048_R1.10.fits
• HFI_SimMap_co_2048_R1.10.fits
• HFI_SimMap_firb_2048_R1.10.fits
• HFI_SimMap_strongps_2048_R1.10.fits
• HFI_SimMap_faintps_2048_R1.10.fits
• HFI_SimMap_freefree_2048_R1.10.fits
• HFI_SimMap_synchrotron_2048_R1.10.fits
• HFI_SimMap_thermaldust_2048_R1.10.fits
• HFI_SimMap_spindust_2048_R1.10.fits
• HFI_SimMap_kineticsz_2048_R1.10.fits
• HFI_SimMap_thermalsz_2048_R1.10.fits

All files contains a single BINTABLE extension with either a single map (for the CMB file) or one map for each HFI frequency (for the foreground components). In the latter case the columns are named F100, F143, … , F857. Units are microK_CMB for the CMB, and MJy/sr for the others. The structure is given below for multi-column files.

FITS file structure

1. EXTNAME = 'SIM-MAP' : Data columns
Column Name	Data Type	Units	Description
F100	Real*4	MJy/sr	100GHz signal map
F143	Real*4	MJy/sr	143GHz signal map
F217	Real*4	MJy/sr	217GHz signal map
F353	Real*4	MJy/sr	353GHz signal map
F545	Real*4	MJy/sr	545GHz signal map
F857	Real*4	MJy/sr	857GHz signal map
Keyword	Data Type	Value	Description
PIXTYPE	string	HEALPIX
COMP	string	component	Astrophysical omponent
COORDSYS	string	GALACTIC	Coordinate system
ORDERING	string	NESTED	Healpix ordering
NSIDE	Int	2048	Healpix Nside for LFI and HFI, respectively
FIRSTPIX	Int*4	0	First pixel number
LASTPIX	Int*4	50331647	Last pixel number, for LFI and HFI, respectively
BAD_DATA	Real*4	-1.63750E+30	Healpix bad pixel value
BEAMTYPE	string	GAUSSIAN	Type of beam
BEAMSIZE	Real*4	size	Beam size in arcmin
PSM-VERS	string		PSM Versions used

The Fiducial Sky Simulations

---

For each detector, fiducial time-ordered data are generated separately for each of the ten PSM components using the LevelS software #reinecke2006 as follows:

• the detector's beam and PSM map are converted to spherical harmonics using beam2alm and anafast respectively;
• the beam-convolved map value is calculated over a 3-dimensional grid of sky locations and beam orientations using conviqt;
• the map-based timelines are calculated sample-by-sample by interpolating over this grid using multimod;
• the catalogue-based timelines are produced sample-by-sample by beam-convolving any point source laying within a given angular distance of the pointing at each sample time using multimod.

For each frequency, fiducial sky maps are generated for

• the total sky signal (including noise),
• the foreground sky alone (excluding CMB but including noise),
• the point source sky, and
• the noise alone

All maps are built using the MADAM destriping map-maker #[keihanen2010 interfaced with the TOAST data abstraction layer . In order to construct the total timelines required by each map, for each detector TOAST reads the various component timelines separately and sums then, and, where necessary, simulates and adds a noise realization time-stream on the fly. HFI frequencies are mapped at HEALPix resolution Nside=2048 using ring-length destriping baselines, while LFI frequencies are mapped at Nside=1024 using 1s baselines.

Products delivered

A single simulation is delivered, which is divided into two types of products: six files of the full sky signal at each HFI frequency: this is the basic simulation product.

• HFI_SimMap_100_2048_R1.10_nominal.fits
• HFI_SimMap_143_2048_R1.10_nominal.fits
• HFI_SimMap_217_2048_R1.10_nominal.fits
• HFI_SimMap_353_2048_R1.10_nominal.fits
• HFI_SimMap_545_2048_R1.10_nominal.fits
• HFI_SimMap_857_2048_R1.10_nominal.fits

These files have the same structure as the equivalent SkyMap products described in the Frequency Maps chapter, namely one BINTABLE extension with three columns containing 1) Signal, 2) hit-count, and 3) variance. Units are K_CMB for all channels.

Three files containing 1) the sum of all astrophysical foregrounds, 2) the point sources alone, and 3) the noise alone: which are subproducts of the above, and are in the form of the PSM maps described in the previous section.

• HFI_SimMap_foreground_2048_R1.10_nominal.fits
• HFI_SimMap_noise_2048_R1.10_nominal.fits
• HFI_SimMap_ps_2048_R1.10_nominal.fits

These files have the same structure as the PSM output maps described above, namely a single BINTABLE extension with 6 columns named F100 -- F857 each containing the given map for that HFI band. Units are alway K_CMB.

Note that the CMB alone is not delivered as a separate product, but it can be recovered by simple subtraction of the component maps for the total signal map.

Monte Carlo realizations of CMB and of noise

---

The CMB MC set is generated using FEBeCoP #mitra2010, which generates an effective beam for each pixel in a map at each frequency by accumulating the weights of all pixels within a fixed distance of that pixel, summed over all observations by all detectors at that frequency. It then applies this effective beam pixel-by-pixel to each of 1000 input CMB sky realizations.

The noise MC set is generated just as the fiducial noise maps, using MADAM/TOAST. In order to avoid spurious correlations within and between the 1000 realizations, each stationary interval for each detector for each realization is generated from a distinct sub-sequence of a single statistically robust, extremely long period, pseudo-random number sequence.

Products delivered

100 realizations of the CMB (lensed) and of the noise are made available. They are named

• HFI_SimMap_cmb-{nnnn}_2048_R1.10_nominal.fits
• HFI_SimMap_noise-{nnnn}_2048_RelNum_nominal.fits

where nnnn ranges from 0000 to 0099.

The FITS file structure is the same as for the other similar products above, with a single BINTABLE extension with six columns, one for each HFI frequency, named F100, F143, … , F857. Units are always microK_CMB.

References

---

<biblio force=false>

1. References

</biblio>