Abstract
Abstract Conventional Type Ia supernova (SN Ia) cosmology analyses currently use a simplistic linear regression of magnitude versus color and light curve shape, which does not model intrinsic SN Ia variations and host galaxy dust as physically distinct effects, resulting in low color–magnitude slopes. We construct a probabilistic generative model for the dusty distribution of extinguished absolute magnitudes and apparent colors as the convolution of an intrinsic SN Ia color–magnitude distribution and a host galaxy dust reddening–extinction distribution. If the intrinsic color–magnitude (M B versus B − V) slope differs from the host galaxy dust law R B , this convolution results in a specific curve of mean extinguished absolute magnitude versus apparent color. The derivative of this curve smoothly transitions from in the blue tail to R B in the red tail of the apparent color distribution. The conventional linear fit approximates this effective curve near the average apparent color, resulting in an apparent slope between and R B . We incorporate these effects into a hierarchical Bayesian statistical model for SN Ia light curve measurements, and analyze a data set of SALT2 optical light curve fits of 248 nearby SNe Ia at . The conventional linear fit gives . Our model finds and a distinct dust law of , consistent with the average for Milky Way dust, while correcting a systematic distance bias of ∼0.10 mag in the tails of the apparent color distribution. Finally, we extend our model to examine the SN Ia luminosity–host mass dependence in terms of intrinsic and dust components.
Highlights
Comparison to the Tripp Formula In the absence of measurement error, we can substitute Equations (5) and (4) into Equation (3) to obtain ms - ms = M0int + axs + bint csapp + (RB - bint)Es + sint. (7). By comparing this to Equation (6), we see that if the dust law RB is equal to the intrinsic color–magnitude slope bint, our model reduces to the Tripp formula, up to relabeling of the fit parameters, since (RB - bint)Es = 0 for every value of Es, regardless of the distribution of Es
The Tripp formula (Equation (1)) is widely used in conventional analyses of cosmological SN Ia light curve data. It is simplistic: by directly regressing extinguished absolute magnitudes against apparent color, it fails to take into account that both factors comprise the physically distinct effects of intrinsic SN Ia variation and extrinsic host galaxy dust
This shortcoming has led to estimates of the apparent color–magnitude slope bapp that are puzzlingly smaller than the normal Milky Way (MW) interstellar dust reddening– extinction law RB = 4.1
Summary
Type Ia supernova (SN Ia) rest-frame optical light curves have been used as cosmological distance indicators to trace the history of cosmic expansion, detect cosmic acceleration (Riess et al 1998; Perlmutter et al 1999), and to constrain the equation-of-state parameter w of dark energy (Garnavich et al 1998; Astier et al 2006; Wood-Vasey et al 2007; Kowalski et al 2008; Freedman et al 2009; Hicken et al 2009b; Kessler et al 2009a; Amanullah et al 2010; Conley et al 2011; Sullivan et al 2011; Betoule et al 2014; Rest et al 2014; Scolnic et al 2014a). Current approaches conceptually differ in how measured apparent colors are used to infer the SN Ia luminosities and estimate the photometric distance Methods such as MLCS, SNooPy, and BAYESN explicitly model the intrinsic SN Ia light curves and the effects of host galaxy dust extinction as separate. Simple-BayeSN analyzes the peak apparent magnitude, apparent color, and light curve shape obtained from light curve fits to the SN Ia photometric time series It models the SN Ia data as arising from a probabilistic generative process combining intrinsic SN Ia variations, host galaxy dust effects, and measurement error. Simple-BayeSN uses a hierarchical Bayesian framework to fit the SN Ia data on the Hubble Diagram, while coherently estimating the parameters driving the underlying effects
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