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  1.   1.  CMB
    1.   1.1  WMAP
    2.   1.2  Planck Legacy Archive
    3.   1.3  Planck Hillipop
    4.   1.4  High angular resolution CMB data sets
  2.   2.  BAO
    1.   2.1  1D measurements
    2.   2.2  BAO1D: Generic DV
    3.   2.3  2D measurements
    4.   2.4  BAO3D: constraints on DM, H(z) and f.σ8 as in DR12
  3.   3.  SNIa

1.  CMB

The determinations of the CMB temperature and polarization across the sky act as powerful constraints of the cosmological parameters. To achieve accurate cosmology measurements, a robust likelihood function must be developed that considers a variety of factors: the correlation of the temperature and polarization fields, the correlation of angular power spectrum estimators at different multipoles (ℓ) due to partial sky coverage, unresolved astrophysical foregrounds, and instrumental factors. The likelihood function is key as it can serve as the prime CMB analysis tool. CAMEL uses a variety of low-ℓ and high-ℓ likelihood functions. These functions are presented below.

1.1  WMAP

1.2  Planck Legacy Archive

The Planck Legacy Archive (PLA) gather all the information associated with the released Planck likelihood function. CAMEL is fully compatible with the Planck likelihood format (clik).
We recommend the user to read the Likelihood section of the Planck explanatory supplement for more details on the Planck likelihoods (see here)

1.3  Planck Hillipop

The Hillipop likelihood function is one of the three Planck high-ℓ (ℓ>50) likelihoods (see Planck 2015 results. XI.). It has been developed within the Planck collaboration at Laboratoire de l'Accélérateur Linéaire (LAL). It is based on a Gaussian approximation to compare the temperature and polarization cross-power spectra estimated ℓ-by-ℓ with models in the range ℓ = [50,2500].

The data consist of two sets of half-mission (I,Q,U Stokes parameters) maps at 100, 143 and 217 GHz. Frequency dependent apodized masks are applied to these maps in order to limit contamination from emission of diffuse Galactic dust, Galactic CO lines, nearby galaxies and extragalactic point sources. We ultimately retain 72, 62 and 48% of the sky at 100, 143 and 217 GHz, respectively. The same set of masks are used in temperature and polarization. Mask-deconvolved and beam-corrected cross-half-mission angular power spectra (first order aℓm correlation) are computed using Xpol (a polarized version of the Xspect code Tristram+ 2005, MNRAS 358 833). From the six above maps, three sets of six band-averaged angular cross-power spectra are derived for TT, EE and TE. We select the multipole ranges to limit contamination from diffuse Galactic dust emission at low-ℓ and noise at high-ℓ in each power spectrum. We derive a likelihood for each data information (hlpT, hlpE, and hlpX) and combining all (hlpTXE).
Note that we provide only hlpT and hlpTXE for now (the polarization data will be included in the near future).

As the angular power spectra are highly correlated, we developed a semi-analytical estimation of the covariance matrix, which encompassed the anticipated (ℓ-by-ℓ) correlations. The method employs data estimates only, with no reliance upon Monte-Carlo simulations. We worked intensively to achieve an accurate calculation of the 4-aℓm correlations. We tested the approximations used in the calculation with Monte-Carlo simulations and we found that a precision better than a few percents was achieved.

In addition to the CMB component, our model considers foreground residuals and calibration differences among maps. We use different models for the foreground’s angular power spectra in temperature and polarization. Our model includes contributions from CIB, Galactic dust, thermal and kinetic SZ effects, Poisson point sources, and cross-correlation between infrared galaxies and the temperature SZ effect. For model construction, we employed the Planck measurements of the millimeter sky (the 9 frequency band data from Planck permits a highly-accurate estimate of the angular power spectra and SED of the different astrophysical emission).

The Hillipop temperature likelihood function encloses 6+ cosmological parameters (6 from the base ΛCDM + eventual extensions), 6 parameters associated to calibration (1 absolute calibration and 5 calibrations at the map level relative to 143 GHz first half mission map) and 9 parameters corresponding to the amplitude of the angular power spectra of the astrophysical foregrounds considered in temperature (radio point-sources, IR point-sources, tSZ, kSZ, CIB, Galactic dust and CIBxtSZ). There is a maximum of 21+ free parameters in the Hillipop full likelihood function (19+ for hlpT).

par   A_planck     	  nui	  1		0.001	     0.9 	1.1
par   c0		  nui     0.		0.001     -0.05   0.05
par   c1		  nui     0.		0.001     -0.05   0.05
fix   c2		  nui     0.		0.001     -0.05   0.05
par   c3		  nui     0.		0.001     -0.05   0.05
par   c4		  nui     0.004		0.001     -0.05   0.05
par   c5		  nui     0.004		0.001     -0.05   0.05
par   Aradio              nui     1.		0.1       0.0     10
par   Adusty              nui     1.		0.1	  0.0     10
par   Asz                 nui     1		0.1       0.0     10
par   Acib                nui     1.		0.1       0.0     10
par   AdustTT		  nui	  1.	        0.1	  0.0     2
par   Aksz                nui     0.00        1.0	  0.0     10
par   Aszxcib             nui     0.00        1.0	  0.0     10

We recommend using the additional constraints as priors extracted from Planck data:

gauss1    AdustTT	1	0.2
gauss1    Acib		1	0.2
gauss1    Asz		1	0.2
gauss1    Aradio	1	0.2
gauss1    Adusty	1	0.2
gauss1    A_planck	1	0.0025
gauss1    c0		0	2e-3
gauss1	  c1		0	2e-3
gauss1	  c3		0	2e-3 
gauss1	  c4		0.0025	2e-3 
gauss1	  c5		0.0025	2e-3 

Note for polarisation, you should add two parameters for dust contamination and their associated prior:

par   AdustPP		  nui	  0.00        0.1	  0.0     2
par   AdustTP		  nui	  0.00        0.1	  0.0     2

gauss1    AdustPP	1	0.2
gauss1    AdustTP	1	0.2

1.4  High angular resolution CMB data sets

The high angular resolution CMB data sets (or VHL for very-high-ℓ likelihoods) include measurements from the ground-based Atacama Cosmology Telescope (ACT) and South Pole Telescope (SPT). As explained in Planck 2015 results. XI, the high-ℓ likelihoods includes ACT power spectra at 148 and 218GHz [ Das et al. 2014, JCAP 4 14 ], with a revised binning (described in Calabrese et al. 2013, PRD 87 103012) and final beam estimates [ Hasselfield et al. 2013, ApJS, 209, 17 ], together with SPT measurements in the range 2000<ℓ<13,000 from the 2540deg2 SPT-SZ survey at 95, 150, and 220 GHz [ George et al. 2015, ApJ 799 177 ]. ACT includes two different datasets from two different surveys: ACT_equat and ACT_south, corresponding to their two observed areas.

To assess the consistency between these data sets and Planck, we use the same templates for cosmic infrared background (CIB) fluctuations, the thermal SZ (tSZ) effect, kSZ effect, and CIBxtSZ components. As the choice for templates are different in Hillipop and plik (PLA likelihood), and as these templates have different formats in each case, we have two version of the parameter files ; those for plik are named '*_plik'.

Additional nuisance parameters for ACT and SPT are described below.


  • Calibrations: at each frequency and for each survey ACT_equat_148_cal, ACT_equat_220_cal and ACT_south_148_cal, ACT_south_220_cal
  • Dust amplitudes: one for each survey ACT_equat_ADust and ACT_south_ADust
  • Point sources amplitudes: for each cross-frequency and each survey ACT_equat_Aps_148x148, ACT_equat_Aps_148x220, ACT_equat_Aps_220x220 and ACT_south_Aps_148x148, ACT_south_Aps_148x220, ACT_south_Aps_220x220
par     ACT_equat_148_cal       nui     0.9991  0.002   0.9     1.1
par     ACT_equat_220_cal       nui     1.013   0.002   0.9     1.1
par     ACT_equat_ADust         nui     1.719   0.01    0.05    10
par     ACT_equat_Aps_148x148   nui     7.159   0.01    0.1     50
par     ACT_equat_Aps_148x220   nui     20      0.01    0.1     50
par     ACT_equat_Aps_220x220   nui     60      0.01    10      150
par     ACT_south_148_cal       nui     1.007   0.002   0.9     1.1
par     ACT_south_220_cal       nui     1.032   0.002   0.9     1.1
par     ACT_south_ADust         nui     1.3     0.01    0.05    10
par     ACT_south_Aps_148x148   nui     9       0.01    0.1     50
par     ACT_south_Aps_148x220   nui     16.29   0.01    0.1     50
par     ACT_south_Aps_220x220   nui     60      0.01    10      150


SPT likelihoods are coded for each survey corresponding to Story et al. 2012 (SPT_low), Reichard et al. 2012 (SPT_high) and George et al. 2014 (SPT_high_2014).
The additional nuisance parameters are:

  • For SPT_low: calibration (SPT_low_cal) and point source amplitude (SPT_low_Aps)
  • For SPT_high or SPT_high_2014
    • Calibrations: for each frequency SPT_high_95_cal, SPT_high_150_cal, SPT_high_220_cal
    • Dust amplitude: SPT_ADust. This is generally kept fixed, as in the SPT analyses.
    • Point sources amplitudes: one for each cross-frequency SPT_high_Aps_95x95, SPT_high_Aps_95x150, SPT_high_Aps_95x220, SPT_high_Aps_150x150, SPT_high_Aps_150x220, SPT_high_Aps_220x220
par     SPT_low_Aps             nui     20.32	0.01	1.	60
par     SPT_low_cal             nui     1.00	0.01	0	2            


par     SPT_high_95_cal         nui     0.9961  0.002   0.9     1.1
par     SPT_high_150_cal        nui     1.002   0.002   0.9     1.1
par     SPT_high_220_cal        nui     1.015   0.002   0.9     1.1
par     SPT_high_Aps_95x95      nui     7.425   0.01    0.1     50
par     SPT_high_Aps_95x150     nui     5.147   0.01    0.1     50
par     SPT_high_Aps_95x220     nui     8.8     0.01    0.1     50
par     SPT_high_Aps_150x150    nui     6.649   0.01    0.2     50
par     SPT_high_Aps_150x220    nui     14.15   0.01    1.5     50
par     SPT_high_Aps_220x220    nui     36.07   0.01    3       200
fix     SPT_ADust               nui     1

We recommend to use the following priors on calibration for SPT_high_2014:

gauss1 SPT_high_95_cal  1.01 .01
gauss1 SPT_high_150_cal 1.01 .01
gauss1 SPT_high_220_cal 1.01 .02

Data used for the two SPT likelihood are more or less the same (i.e. the 150 GHz channel). In order to combine these two likelihoods together one may want to avoid too much of double counting. Two things are possible :

  • removing from the SPT_low part the ell range in common with SPH_high. This can be done by adding to SPT_low.lik two parameters : first_bin=xx and last_bin=yy to select in the

SPT_low spectrum the wanted ell range (there are 47 bins from 650 to 3000).

  • removing the 150 GHz channel from the SPT_high likelihood. this can be done by adding to (e.g.) SPT_high.lik : remove_150 = 1 (other frequencies can also be removed).

In both cases, the required data are selected and its inverted covariance matrix is recomputed after eliminating the necessary rows and columns.

2.  BAO

BAO information is added using several C++ classes, implementing simple (1D) χ2 built from the Dv/rs measurements for the various projects (using a Gaussian constraint) or a bit more elaborate 2D constraint (also Gaussian) in the (H(z),DA(z)) plane. No additional nuisance parameters are needed to handle these.

2.1  1D measurements

Constraints on Dv/rs (at one or several redshifts) are managed by a single parameter file compiling all measurements.

# input data for BAO
# in/fix | name | num of data | z | value | error | out of diag| elements (eventually)
in 6dF 1 0.106 457 27
fix SDSS(R) 1  0.35 8.88 0.17
fix BOSS(DR9) 1 0.57 13.67 0.22
fix BOSS-CMASS(DR11) 1 0.57 2056 20 
fix BOSS-LOWZ(DR11) 1 0.32 1264 25 
fix WiggleZ 3 0.44 0.0916 0.0071 0.60 0.0726 0.0034 0.73 0.0592 0.0032 0.003068 0.0 0.00222005 
fix SDSS 2 0.20 0.1905 0.0061 0.35 0.1097 0.0036 0.002723

You can activate or remove data line-by-line or with in/fix parameter.

There is no free parameter associate to this likelihood, so you just need to add a line to your parameter file:


2.2  BAO1D: Generic DV

In order to help in studying forecasts, we introduced a very simple chi2 based on a list of Gaussian Dv measurements (at some zeff and r_drag(fid) values). You can add measurements as in the file Generic_example.lik :

#z_eff  rs(fid)   Dv_meas  error_DV
0.57    149.28    2056     20   

and add to your parameter file:


2.3  2D measurements

2D constraints in the (H(z),DA(z)) plane are implemented as correlated Gaussians. We use one file per dataset, in contrast with the 1D case above. We include 3 different 2D files:

  • Boss_anderson_dr11.lik : the BOSS results from Anderson et al 2011 (baseline)
  • BAO_LyaDR9_busca.lik : DR9 Lyα from Busca et al.
  • BossLya_DR9_Slosar2013.lik : DR9 Lyα from Slosar et al

Our baseline uses Anderson et al. 2011. The results from Lyα are a bit outdated (and not in perfect agreement with each other). Other similar measurements at other redshifts can be added in your par file.

There is no free parameter for this likelihood:


2.4  BAO3D: constraints on DM, H(z) and f.σ8 as in DR12

DR12 results from BOSS consist in simultaneous constraints on (DM(z), H(z), f.σ8(z)) for 3 redshift bins. This is implemented in the BAO3D class as correlated Gaussians, using the covariance matrix given in [Alam et al., 2016] (arXiv:1607.03155).

Add in you param file :

BAO_3DFile = BAO/boss_dr12.lik

do_mPk = true
class     z_max_pk 1.

Note the two mandatory class parameters, needed to compute 'sigma_8' (do_mPk to compute the matter P'_k's') at redshifts lower than z_max_pk.
WARNING: this dataset supersedes both the BOSS DR11 2D results and the BOSS DR11 LOWZ result (should be disabled "fix" in the BAO1D lik file) !

3.  SNIa

The SNIa part consists of the JLA data and likelihood made available by M. Betoule which are described here. More details are given in Betoule et al. 2014, A&A 568 A22. In addition to the usual cosmological parameters, this likelihood uses 4 nuisance parameters:

  • Mabs, the absolute SNIa max magnitude (in the photometric B band conventionally): SNIa data are only relative distance measurements
  • α, the light-curve stretch factor (brighter <-> slower evolution around max.)
  • β, the color factor (brighter <-> bluer at max)
  • ΔM, the SNIa max. magnitude, Mabs, is described as having 2 distinct values (differing by ΔM) in 2 host mass intervals (see fig 12 of the paper).

which have to be accounted for in the global likelihood parameters as follows:

par       Mabs          nui     -19.04          .03             -19.25          -18.85
par       alpha         nui     0.141           .01             0.10            .18
par       beta          nui     3.101           0.1             2.5             3.7
par       DeltaM	nui     -.076           0.03            -.13            -0.01