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Register a new userThe Type Ia Supernova Color-Magnitude Relation and Host Galaxy Dust: A Simple Hierarchical Bayesian Model
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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 a intrinsic SN Ia color-magnitude distribution and a host galaxy dust reddening-extinction distribution. If the intrinsic color-magnitude ($M_B$ vs. $B-V$) slope $beta_{int}$ differs from the host galaxy dust law $R_B$, this convolution results in a specific curve of mean extinguished absolute magnitude vs. apparent color. The derivative of this curve smoothly transitions from $beta_{int}$ 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 $beta_{app}$ between $beta_{int}$ and $R_B$. We incorporate these effects into a hierarchical Bayesian statistical model for SN Ia light curve measurements, and analyze a dataset of SALT2 optical light curve fits of 248 nearby SN Ia at z < 0.10. The conventional linear fit obtains $beta_{app} approx 3$. Our model finds a $beta_{int} = 2.3 pm 0.3$ and a distinct dust law of $R_B = 3.8 pm 0.3$, consistent with the average for Milky Way dust, while correcting a systematic distance bias of $sim 0.10$ 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.
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Kim et al. (2013) [K13] introduced a new methodology for determining peak-brightness absolute magnitudes of type Ia supernovae from multi-band light curves. We examine the relation between their parameterization of light curves and Hubble residuals, based on photometry synthesized from the Nearby Supernova Factory spectrophotometric time series, with global host-galaxy properties. The K13 Hubble residual step with host mass is $0.013pm 0.031$ mag for a supernova subsample with data coverage corresponding to the K13 training; at $ll 1sigma$, the step is not significant and lower than previous measurements. Relaxing the data coverage requirement the Hubble residual step with host mass is $0.045pm 0.026$ mag for the larger sample; a calculation using the modes of the distributions, less sensitive to outliers, yields a step of 0.019 mag. The analysis of this article uses K13 inferred luminosities, as distinguished from previous works that use magnitude corrections as a function of SALT2 color and stretch parameters: Steps at $>2sigma $ significance are found in SALT2 Hubble residuals in samples split by the values of their K13 $x(1)$ and $x(2)$ light-curve parameters. $x(1)$ affects the light-curve width and color around peak (similar to the $Delta m_{15}$ and stretch parameters), and $x(2)$ affects colors, the near-UV light-curve width, and the light-curve decline 20 to 30 days after peak brightness. The novel light-curve analysis, increased parameter set, and magnitude corrections of K13 may be capturing features of SN~Ia diversity arising from progenitor stellar evolution.
We investigate the origin of the colour-magnitude relation (CMR) observed in cluster galaxies by using a combination of a cosmological N-body simulation of a cluster of galaxies and a semi-analytic model of galaxy formation. The departure of galaxies in the bright end of the CMR with respect to the trend denoted by less luminous galaxies could be explained by the influence of minor mergers
A string of recent studies has debated the exact form and physical origin of an evolutionary trend between the peak luminosity of Type Ia supernovae (SNe Ia) and the properties of the galaxies that host them. We shed new light on the discussion by presenting an analysis of ~200 low-redshift SNe Ia in which we measure the separation of Hubble residuals (HR; as probes of luminosity) between two host-galaxy morphological types. We show that this separation can test the predictions made by recently proposed models, using an independently and empirically determined distribution of each morphological type in host-property space. Our results are partially consistent with the new HR--age slope, but we find significant scatter in the predictions from different galaxy catalogues. The inconsistency in age illuminates an issue in the current debate that was not obvious in the long-discussed mass models: HR--host-property models are strongly dependent on the methods employed to determine galaxy properties. While our results demonstrate the difficulty in constructing a universal model for age as a proxy for host environment, our results indeed identify evolutionary trends between mass, age, morphology, and HR values, encouraging (or requiring, if such trends are to be accounted for in cosmological studies) further investigation.
In this letter we present a study of the color magnitude relation of 468 early-type galaxies in the Virgo Cluster with Sloan Digital Sky Survey imaging data. The analysis of our homogeneous, model-independent data set reveals that, in all colors (u-g, g-r, g-i, i-z) similarly, giant and dwarf early-type galaxies follow a continuous color magnitude relation (CMR) that is best described by an S-shape. The magnitude range and quality of our data allows us to clearly confirm that the CMR in Virgo is not linear. Additionally, we analyze the scatter about the CMR and find that it increases in the intermediate-luminosity regime. Nevertheless, despite this observational distinction, we conclude from the similarly shaped CMR of semi-analytic model predictions that dwarfs and giants could be of the same origin.
We present a comprehensive statistical analysis of the properties of Type Ia SN light curves in the near infrared using recent data from PAIRITEL and the literature. We construct a hierarchical Bayesian framework, incorporating several uncertainties including photometric error, peculiar velocities, dust extinction and intrinsic variations, for coherent statistical inference. SN Ia light curve inferences are drawn from the global posterior probability of parameters describing both individual supernovae and the population conditioned on the entire SN Ia NIR dataset. The logical structure of the hierarchical model is represented by a directed acyclic graph. Fully Bayesian analysis of the model and data is enabled by an efficient MCMC algorithm exploiting the conditional structure using Gibbs sampling. We apply this framework to the JHK_s SN Ia light curve data. A new light curve model captures the observed J-band light curve shape variations. The intrinsic variances in peak absolute magnitudes are: sigma(M_J) = 0.17 +/- 0.03, sigma(M_H) = 0.11 +/- 0.03, and sigma(M_Ks) = 0.19 +/- 0.04. We describe the first quantitative evidence for correlations between the NIR absolute magnitudes and J-band light curve shapes, and demonstrate their utility for distance estimation. The average residual in the Hubble diagram for the training set SN at cz > 2000 km/s is 0.10 mag. The new application of bootstrap cross-validation to SN Ia light curve inference tests the sensitivity of the model fit to the finite sample and estimates the prediction error at 0.15 mag. These results demonstrate that SN Ia NIR light curves are as effective as optical light curves, and, because they are less vulnerable to dust absorption, they have great potential as precise and accurate cosmological distance indicators.
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