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Register a new userAn Empirical Fitting Method for Type Ia Supernova Light Curves. II. Estimating the First-Light Time and Rise Time
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WeiKang Zheng
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We investigate a new empirical fitting method for the optical light curves of Type Ia supernovae (SNe~Ia) that is able to estimate the first-light time of SNe~Ia, even when they are not discovered extremely early. With an improved ability to estimate the time of first light for SNe Ia, we compute the rise times for a sample of 56 well-observed SNe~Ia. We find rise times ranging from 10.5 to 20.5 days, with a mean of 16.0 days, and confirm that the rise time is generally correlated with the decline rate $Delta m_{15}(B)$, but with large scatter. The rise time could be an additional parameter to help classify SN~Ia subtypes.
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We examine the relationship between three parameters of Type Ia supernovae (SNe~Ia): peak magnitude, rise time, and photospheric velocity at the time of peak brightness. The peak magnitude is corrected for extinction using an estimate determined from MLCS2k2 fitting. The rise time is measured from the well-observed $B$-band light curve with the first detection at least 1~mag fainter than the peak magnitude, and the photospheric velocity is measured from the strong absorption feature of Si~II~$lambda$6355 at the time of peak brightness. We model the relationship among these three parameters using an expanding fireball with two assumptions: (a) the optical emission is approximately that of a blackbody, and (b) the photospheric temperatures of SNe~Ia are similar to each other at the time of peak brightness. We compare the precision of the distance residuals inferred using this physically motivated model against those from the empirical Phillips relation and the MLCS2k2 method for 47 low-redshift SNe~Ia ($0.005 < z< 0.04$) and find comparable scatter. However, SNe~Ia in our sample with higher velocities are inferred to be intrinsically fainter. Eliminating the high-velocity SNe and applying a more stringent extinction cut to obtain a low-v-golden sample of 22 SNe, we obtain significantly reduced scatter in the new relation, better than those of the Phillips relation and the MLCS2k2 method. After removing model peculiar velocities, our final scatter for the new relation is $0.108 pm 0.018$~mag.
We present a new empirical fitting method for the optical light curves of Type Ia supernovae (SNe~Ia). We find that a variant broken-power-law function provides a good fit, with the simple assumption that the optical emission is approximately the blackbody emission of the expanding fireball. This function is mathematically analytic and is derived directly from the photospheric velocity evolution. When deriving the function, we assume that both the blackbody temperature and photospheric velocity are constant, but the final function is able to accommodate these changes during the fitting procedure. Applying it to the case study of SN~2011fe gives a surprisingly good fit that can describe the light curves from the first-light time to a few weeks after peak brightness, as well as over a large range of fluxes ($sim 5$, mag, and even $sim 7$,mag in the $g$ band). Since SNe~Ia share similar light-curve shapes, this fitting method has the potential to fit most other SNe~Ia and characterize their properties in large statistical samples such as those already gathered and in the near future as new facilities become available.
We present SiFTO, a new empirical method for modeling type Ia supernovae (SNe Ia) light curves by manipulating a spectral template. We make use of high-redshift SN observations when training the model, allowing us to extend it bluer than rest frame U. This increases the utility of our high-redshift SN observations by allowing us to use more of the available data. We find that when the shape of the light curve is described using a stretch prescription, applying the same stretch at all wavelengths is not an adequate description. SiFTO therefore uses a generalization of stretch which applies different stretch factors as a function of both the wavelength of the observed filter and the stretch in the rest-frame B band. We compare SiFTO to other published light-curve models by applying them to the same set of SN photometry, and demonstrate that SiFTO and SALT2 perform better than the alternatives when judged by the scatter around the best fit luminosity distance relationship. We further demonstrate that when SiFTO and SALT2 are trained on the same data set the cosmological results agree.
We analyze the rise and fall times of type Ia supernova (SN Ia) light curves discovered by the SDSS-II Supernova Survey. From a set of 391 light curves k-corrected to the rest frame B and V bands, we find a smaller dispersion in the rising portion of the light curve compared to the decline. This is in qualitative agreement with computer models which predict that variations in radioactive nickel yield have less impact on the rise than on the spread of the decline rates. The differences we find in the rise and fall properties suggest that a single stretch correction to the light curve phase does not properly model the range of SN Ia light curve shapes. We select a subset of 105 light curves well-observed in both rise and fall portions of the light curves and develop a 2-stretch fit algorithm which estimates the rise and fall times independently. We find the average time from explosion to B-band peak brightness is 17.38 +/- 0.17 days. Our average rise time is shorter than the 19.5 days found in previous studies; this reflects both the different light curve template used and the application of the 2-stretch algorithm. We find that slow declining events tend to have fast rise times, but that the distribution of rise minus fall time is broad and single-peaked. This distribution is in contrast to the bimodality in this parameter that was first suggested by Strovink (2007) from an analysis of a small set of local SNe Ia. We divide the SDSS-II sample in half based on the rise minus fall value, tr-tf <= 2 days and tr-tf>2 days, to search for differences in their host galaxy properties and Hubble residuals; we find no difference in host galaxy properties or Hubble residuals in our sample.
While it is clear that Type Ia supernovae (SNe) are the result of thermonuclear explosions in C/O white dwarfs (WDs), a great deal remains uncertain about the binary companion that facilitates the explosive disruption of the WD. Here, we present a comprehensive analysis of a large, unique data set of 127 SNe$,$Ia with exquisite coverage by the Zwicky Transient Facility (ZTF). High-cadence (six observations per night) ZTF observations allow us to measure the SN rise time and examine its initial evolution. We develop a Bayesian framework to model the early rise as a power law in time, which enables the inclusion of priors in our model. For a volume-limited subset of normal SNe$,$Ia, we find that the mean power-law index is consistent with 2 in the $r_mathrm{ZTF}$-band ($alpha_r = 2.01pm0.02$), as expected in the expanding fireball model. There are, however, individual SNe that are clearly inconsistent with $alpha_r=2$. We estimate a mean rise time of 18.9$,$d (with a range extending from $sim$15 to 22$,$d), though this is subject to the adopted prior. We identify an important, previously unknown, bias whereby the rise times for higher-redshift SNe within a flux-limited survey are systematically underestimated. This effect can be partially alleviated if the power-law index is fixed to $alpha=2$, in which case we estimate a mean rise time of 21.7$,$d (with a range from $sim$18 to 23$,$d). The sample includes a handful of rare and peculiar SNe$,$Ia. Finally, we conclude with a discussion of lessons learned from the ZTF sample that can eventually be applied to observations from the Vera C. Rubin Observatory.
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