Issue 
A&A
Volume 568, August 2014



Article Number  A22  
Number of page(s)  32  
Section  Cosmology (including clusters of galaxies)  
DOI  https://doi.org/10.1051/00046361/201423413  
Published online  08 August 2014 
Online material
Appendix A: Visual inspection
In addition to the software cuts, we performed a visual inspection of the SN lightcurve fits. We discarded the following SNe Ia, for which the SALT2 fits were particularly poor^{20}:

1.
Fit probability <0.01 due to apparent problems in the photometry: SDSS739^{⋆}, SDSS1316^{⋆}, SDSS3256 (2005hn), SDSS6773 (2005iu), SDSS12780, SDSS12907, SDSS13327^{⋆}, SDSS16287, SDSS16578^{⋆}, SDSS16637^{⋆}, SDSS17176^{⋆}, SDSS18456, SDSS18643, SDSS19381 (2007nk), SDSS20376^{⋆}, SDSS20528 (2007qr), SDSS21810^{⋆}.

2.
Poor fit, probable 1986Glike: SDSS17886 (sn2007jh) (Stritzinger et al. 2011).

3.
Poor fit, 2002cxlike: SDSS20208 (sn2007qd) (McClelland et al. 2010; Foley et al. 2013).

4.
Pathological sampling leading to unstable fit results: SDSS17500^{⋆}, SDSS16692^{⋆}.
We also discarded the following four events that are >3σ outliers on the Hubble diagram:

1.
Overluminous: SDSS14782 (2006jp), SDSS15369 (2006ln).

2.
Subluminous: SDSS15459 (2006la), SDSS17568 (2007kb).
Last, a proper and stable determination of the date of maximum is necessary for SNe Ia entering in the training sample, because the date of maximum is held fixed in the training. We looked for remaining poorly sampled light curves in the training sample, and discarded the following nine SNe (only from the training sample):

1.
Too few observations after the epoch of peak brightness(despite a reported uncertainty on t_{0} passing the cuts): SDSS10434, SDSS19899, SDSS20470, SDSS21510.

2.
Too few observations before the epoch of peak brightness: SDSS6780, SDSS12781, SDSS12853 (2006ey), SDSS13072, SDSS18768.
Appendix B: Details on calibration systematics
Appendix B.1: Consistency of the CfAIII and CSP photometric calibration
A few lowz SNe Ia have been observed contemporaneously with several telescopes which provides a way to assess their relative calibration. Mosher et al. (2012) studied nine spectroscopically confirmed Type Ia supernova observed by both the CSP and the SDSSII surveys. The study provides us with stringent constraints on possible differences between the CSP calibration and the SDSS/SNLS calibration of B13. The Mosher et al. (2012) results are reproduced in Table B.1.
Calibration offsets.
Spectroscopically confirmed SNe Ia in common between CSP and CFA.
We performed a similar study on SNe Ia observed by both the CfAIII and CSP surveys. To increase the statistics available for this comparison, we consider SNe Ia from both the first (Contreras et al. 2010) and second (Stritzinger et al. 2011) CSP data release. The list of all SNe Ia in common is given in Table B.2.
We use SALT2 to interpolate between measurements (in phase and wavelength) as follows: for each SN Ia, we perform an initial fit using all available data to determine its shape, color, and date of maximum. Holding these parameters fixed, we redetermine the amplitude parameter x_{0} for each band independently. In a given band, comparing the values of obtained for two different instruments gives an estimate of the calibration difference between them. This method is similar to the Scorrection and spline interpolation applied in Mosher et al. (2012). However, instead of transforming the CfA data to bring them to the CSP native system, both sets data are transformed in the same manner. Applied to the same sample, the two methods deliver very similar results.
We exclude peculiar typeIa supernovae from the comparison. Light curves with aberrant photometric points were rejected: SN2005M U and r band light curves, SN2005ir, SN2006ev and SN2005mc r band. Finally, B, V and r′ band data for 2006hb are too long after maximum brightness to be reliably compared to CSP measurements. The results are given in the second part of Table B.1. Our analysis shows an excellent agreement in the B, V and i′ bands. The offset measured in r′ appears statistically significant, justifying the upward adjustment of the r′ calibration uncertainty quoted in C11. The U band also shows surprisingly good consistency considering the fact that CfAIII U band measurements are colorcorrected to the Landolt system using a color transformation determined using ordinary stars. However, given the small number of SNe Ia in the Uband comparison, we are concerned that the agreement may be fortuitous and do not revise the 0.07 mag uncertainty used by Hicken et al. (2009). This choice of a relatively large Uband uncertainty is justified in Sect. B.2 where a SN Uband colorcorrection error is evaluated.
Appendix B.2: Errors induced by the colortransformation of nearby supernova measurements
A substantial fraction of our lowz sample is composed of SNe Ia with photometry reported in the Landolt system, which means that flux measurements in the natural system have been transformed to the Landolt system using color transformations determined by ordinary stars. This procedure introduces errors because SNe Ia have spectral properties different from those of main sequence stars (see, e.g., the discussion in Jha et al. 2006, Sect. 2.4, hereafter J06). Here we seek quantitative estimates for these errors.
J06 provides effective filter transmissions for several combinations of UBVRI filter sets and CCD cameras used for the SN observations. Using these transmissions, along with an effective model of Landolt filters^{21}, we can compute synthetic magnitudes of stars in both the natural and the Landolt system. We use the stellar libraries of Gunn & Stryker (1983) and Pickles (1998), selecting stars in a range of U − B and B − V colors matching that of the SN calibration stars. For SNe, we use the SALT2 average spectral sequence ().
Using those synthetic magnitudes, we compare the “true” (synthetic) Landolt magnitude to the Landolt magnitude estimated with a color transformation of the (synthetic) natural magnitudes. For these color transformations, we use the color terms given in Table 3 of J06, and define to be the difference between those two values. The calibration bias for SNe is given by the difference of δm for SNe and main sequence stars. Indeed the latter value sets the normalization of SN magnitudes through the assignement of a zeropoint to the images. We label this difference Δm ≡ δm(SN) − δm(stars).
An uncertainty on the quantity Δm can be estimated by varying the SN model, the spectral library, or the filter transmissions. In practice, the uncertainty on the filter transmissions is dominant. Figure B.1 shows that δm is a function of the star color, which means that the filter model is inadequate. By construction, δm is colorindependent for real observations. One can adjust wavelength shifts of the filter transmissions in order to obtain a colorindependent value of δm for stars. This approach also results in a change of Δm that we can subsequently use as an estimate of the uncertainty due to approximate filter transmissions.
For the AndyCam CCD camera (CfA) with the Harris filter set (Harris et al. 1981), we have found ΔB = 0 ± 0.015 mag, ΔV = 0.03 ± 0.01 mag, and ΔR = 0.03 ± 0.03 mag. In other words, the colorcorrection does not significantly bias the measurements for the BVR bands. The situation for the Uband is, however, different. We have found a value as large as 0.1 for the 4Shooter camera (CfA), chip 1, with SAO filters. The values of δm for SNe and stars are represented in Fig. B.1 for this latter instrumental setup. One can also see on the figure that the residual color term is quite important. A Uband shift of ~3 nm is needed to obtain a flat distribution of δm, and in that case one finds an even larger value of ΔU = 0.15.
Fig. B.1
Synthetic values of as a function of B − V color for stars from Gunn & Stryker (1983, open circles) and Pickles (1998, filled squares), and for an average SN at various epochs, from −5 to + 30 days, based on the SALT2 spectral sequence. The natural effective filter set is that of the 4Shooter camera, chip 1, with SAO filters, given in Jha et al. (2006), Table 5. Only the difference between SN and stars are relevant here, not the absolute δU values. 

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A primary motivation for this study is the existence of significant calibration offsets between observerframe UV observations from different instruments (see, e.g., Krisciunas et al. 2013, for a longer discussion of this effect) and with restframe UV observations at higher redshift. Kessler et al. (2009a) found that this latter discrepancy was responsible for a large part of the difference between the SALT2 and MLCS2k2 (Jha et al. 2007) models, MLCS2k2 being trained solely on lowz SNe. This Uband offset introduced by the application of a colorcorrection to SNe data could explain some of the discrepancy. However, the Uband filter transmissions are too uncertain to secure a good interpretation of natural magnitudes. For this reason, we adopt the magnitudes that are colortransformed to the Landolt system for the lowz samples (except for the CSP data and the CfAIII BVri light curves where we use the natural magnitudes and measured filter response functions), but assign a coherent systematic uncertainty of 0.1 mag to the amplitude of Uband light curves.
In all bands, the (phase dependent) error introduced by color transformations is not included, so measurement errors are typically underestimated. As a consequence, the uncertainties in the fit lightcurve parameters are underestimated. The training of SALT2 is also affected by this problem. At present, we cannot afford discarding the colortransformed lowz and must deal with this issue. We estimate the measurement errors again for color transformed measurements in the lowz sample as follows. Since the SDSSII and SNLS measurement errors are reliable, we trained a version of SALT2 as described in Sect. 4, but considering only the SNLS and SDSSII measurements in the computation of the “errorsnake”. We then use this version with reliable modeling of the intrinsic dispersion to fit all the color transformed lowz light curves. For each lightcurve, we fit an adhoc two parameter (γ_{2} and γ_{3}) correction of the measurement errors σ_{i} affecting the measurement d_{i} by minimizing the following residual likelihood: (B.1)with , where m_{i} is the flux predicted by the best fit lightcurve model and the model value of the intrinsic dispersion. We simultaneously fit for γ_{1}, γ_{2} and γ_{3}. When the lightcurve contains less than five points, we fix the value of γ_{3} to zero. We then alter the errors in the lightcurve accordingly to the fit values of γ_{2} and γ_{3}. We found a mean value of 0.007 mag for γ_{2}.
Appendix C: Estimates of missing host stellar masses in the C11 sample
The C11 compilation is missing estimates of the galaxy host mass for 61 nearby SNe (mostly because of missing photometry for the host). We describe estimates obtained for 57 of the 61 missing galaxy mass values.
For 49 of the nearby SN host galaxies, we derived an estimate based on Ks photometry (Bell & de Jong 2001; Bell et al. 2003) from the 2003 2MASS AllSky Data Release of the Two Micron All Sky Survey (Skrutskie et al. 2006). The photometric data are extracted from the NASA/IPAC Extragalactic Database (NED) database. A linear model is fit between the mass and the Ks absolute magnitude on 51 objects with stellar mass estimates from C11. This linear model yields a residual of 0.15 dex and is used to provide galaxy mass estimates. For 8 galaxies without 2MASS Ks magnitudes, we rely on less precise models based on the total B band RC3 magnitude (de Vaucouleurs et al. 1991, three objects), the r CModel magnitude (1 object from the SDSS DR6, AdelmanMcCarthy et al. 2008), the B magnitude (three objects published in Hamuy et al. 2000), and the B magnitude in Strolger et al. (2002) for the lowluminosity host of SN 1999aw. The four remaining supernovae have no identified host and were assigned to the lowmass bin with an uncertainty on distance moduli of added in quadrature to the other sources of uncertainty.
Appendix D: Accuracy of the CMB distance prior
In Sect. 7, we summarized the dark energy constraints from the CMB in the form of a distance prior. A computationally intensive, but more general, approach is to directly compare the CMB data to theoretical predictions for the fluctuation power spectra computed from a Boltzmann code. In this appendix, we briefly compare the results from both approaches for a fit of the wCDM model to the combination of our SNe Ia JLA sample with CMB constraints.
The Planck collaboration (Planck collaboration XV 2014) has released code to compute the likelihood of theoretical models given Planck data^{22}. This enables the marginalization of several sources of systematic uncertainty in the CMB spectra, such as errors in the instrumental beams and contamination by astrophysical foregrounds. In our comparison we make use of the full Planck temperature likelihood complemented with the WMAP measurement of the large scale CMB polarization (Bennett et al. 2013). We use the CAMB Boltzmann code (Lewis et al. 2000, March 2013) for our computation of CMB spectra. We follow assumptions from Planck Collaboration XVI (2014), fitting for the baryon density today ω_{b} = Ω_{b}h^{2}, the cold dark matter density today ω_{c} = Ω_{c}h^{2}, θ_{MC}, the CosmoMC approximation of the sound horizon angular size computed from the Hu & Sugiyam (1996) fitting formulae, τ, the Thomson scattering optical depth due to reionization, ln(10^{10}A_{s}), the log power of the primordial curvature perturbations at the pivot scale k_{0} = 0.05 Mpc^{1}, n_{s}, the primordial spectrum index, and w, the dark energy equation of state parameter.
Fig. D.1
Comparison of two derivations of the 68 and 95% confidence contours in the Ω_{m} and w parameters for a flat wCDM cosmology. In one case, constraints are derived from the exploration of the full Planck+WP+JLA likelihood (blue). In the other case CMB constraints are summarized by the geometric distance prior described in Sect. 7.1 (dashed red). 

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Bestfit parameters of the wCDM fit for the full Planck+WP+JLA likelihood, and for the distance prior (DP+JLA).
We explored the Planck+WP+JLA likelihood with Markov chain Monte Carlo (MCMC) simulations of the posterior distribution assuming flat priors for parameters as given in Planck Collaboration XVI (2014, Table 1). Eight sample chains were drawn using CosmoMC (Lewis & Bridle 2002; Lewis 2013). Convergence of the simulation is monitored using the Gelman & Rubin (1992)R statistic^{23}.
The mean value of the posterior distribution and 68% limits for the fit parameters to the Planck+WP+JLA likelihood are given in Table D.1. Bestfit parameters obtained using the distance prior in Sect. 7.2 are shown for comparison. The 68% and 95% contours from these simulations are drawn in Fig. D.1. Overplotted is the Planck+WP+JLA contour from Fig. 16. The differences are small as expected from the fact that the supplementary constraints brought by the complete CMB power spectrum are weak compared to the supernova constraints.
Appendix E: Compressed form of the JLA likelihood
Figure 9 shows that the correlation between the nuisance parameters (α, β, Δ_{M}) and the cosmological parameter Ω_{m} is small as a result of the high density of SNe in this Hubble diagram (especially in the SDSS sample at intermediate redshifts). This suggests that, for a limited class of models (those predicting isotropic luminosity distances evolving smoothly with redshifts), the estimate of distances can be made reasonably independent of the estimate of cosmological parameters. In this appendix, we seek to provide the cosmological information of the JLA Hubble diagram in a compressed form that is faster and easier to evaluate and still remains accurate for the most common cases. Studies investigating alternate cosmology or alternate standardization hypotheses for SNeIa should continue to rely on the complete form.
Appendix E.1: Binned distance estimates
The distance modulus is typically well approximated by a piecewise linear function of log (z), defined on each segment z_{b} ≤ z<z_{b + 1} as: (E.1)with α = log (z/z_{b})/log (z_{b + 1}/z_{b}) and μ_{b} the distance modulus at z_{b}. As an example, for 31 logspaced control points z_{b} in the redshift range 0.01 <z< 1.3, the difference between the ΛCDM distance modulus and its linear interpolant is everywhere smaller than 1 mmag.
Such an interpolant can be fit to our measured Hubble diagram by minimizing a likelihood function similar to the one proposed in Eq. (15): (E.2)The free parameters of the fit are α, β, Δ_{M} and μ_{b} at the chosen control points. We use a fixed fiducial value of to provide uniquely determined μ_{b}. Results are compared to the best fit ΛCDM cosmology in Fig. E.1. The structure of the correlation matrix of the bestfit μ_{b} is shown in Fig. E.2. It displays significant large scale correlation mostly due to systematic uncertainties. The tridiagonal structure arises from the linear interpolation.
Fig. E.1
Binned version of the JLA Hubble diagram presented in Fig. 8. The binned points are solid circles. There are significant correlations between bins. The error bars are the square root of the diagonal of the covariance matrix given in Table F.2. 

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Fig. E.2
Correlation matrix of the binned distance modulus μ_{b}. 

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Fig. E.3
Comparison of the cosmological constraints obtained from the full JLA likelihood (filled contour) with approximate version derived by binning the JLA supernovae measurements in 20 bins (dashed blue contour) and 30 bins (continuous red contour). 

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Appendix E.2: Cosmology fit to the binned distances
Cosmological models predicting isotropic luminosity distances evolving smoothly with redshifts can be fitted directly to the binned distance estimates. We denote D_{L}(z;θ) the luminosity distance predicted by a model dependent of a set of cosmological parameters θ. A good approximation of the full JLA likelihood is generally given by the following likelihood function: (E.3)with: (E.4)M a free normalization parameter, and C_{b} the covariance matrix of μ_{b} (see Table F.2). As an illustration, a comparison of the cosmological constraints obtained from the approximate and full version of the JLA likelihood for the wCDM model is shown in Fig. E.3. For the models evaluated in Sect. 7 in combination with CMB and BAO constraints, the difference in bestfit estimates between the approximate and full version is at most 0.018σ and reported uncertainties differ by less than 0.3%.
We warn that the normalization parameter M must be left free in the fit and marginalized over when deriving uncertainties. Not doing so would be equivalent to introducing artificial constraints on the H_{0} parameter and would result in underestimated errors.
Appendix F: Data release
The lightcurve fit parameters for the JLA sample are given in Table F.3. We provide the covariance matrices, described in Sect. 5.5, of statistical and systematic uncertainties in lightcurve parameters. These two products contain all the information required to compute the likelihood function from Eq. (15) in a cosmological fit. We provide the necessary computer code in two forms: a CosmoMC plugin and an independent C++ code.
Alternatively, we deliver estimates of binned distance modulus μ_{b} obtained, as described in appendix E, for 31 control points
(30 bins) in Table F.1 and the associated covariance matrix in Table F.2. These values can be used to evaluate the approximate version of the JLA likelihood function proposed in Eq. (E.3).
In addition, we provide the retrained SALT2 model, the covariance matrix of calibration parameters, and the SNLS recalibrated light curves. The SDSSII light curves can be obtained from the SDSS SN data release (Sako et al. 2014)^{24}.
Binned distance modulus fitted to the JLA sample.
Covariance matrix of the binned distance modulus.
Parameters for the type Ia supernovae in the joint JLA cosmology sample.
© ESO, 2014
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