Open Astron. 2017; 26:111–119 Research Article David F. Crawford* A problem with the analysis of type Ia supernovae Abstract: Type Ia supernovae have light curves that The basis of the standard cosmological model is that have widths and magnitudes that can be used for test- the observed Hubble redshift of distant galaxies is a con- ing cosmologies and they provide one of the few direct sequence of an expanding universe. In this model red- measurements of time dilation. It is shown that the stan- shift is consequence of an expansion of the space be- dard analysis that calibrates the light curve against a tween galaxies and although it is mathematically the rest-frame average (such as SALT2) removes all the cos- same as if it was produced by a velocity it is not a mological information from the calibrated light curves. true velocity but a property of the distance between Consequently type Ia supernovae calibrated with these the galaxy and the observer. For example many differ- methods cannot be used to investigate cosmology. The ent observers scattered around the universe would ob- major evidence that supports the hypothesis of a static serve vastly different values of the redshift for the same universe is that the measurements of the widths of the observed galaxy. Then just like the Doppler effect any raw light curves of type Ia supernovae do not show time interval must be dilated as a direct function of the any time dilation. The intrinsic wavelength dependence pseudo velocity. Thus time dilation is an essential prop- shown by the SALT2 calibration templates is also con- erty of any expanding universe. sistent with no time dilation. Using a static cosmolog- The observed Hubble redshift, 푧, is defined as the ical model the peak absolute magnitudes of raw type ratio of the observed wavelength to the emitted wave- Ia supernovae observations are also independent of red- length, minus one. In an expansion model the ratio of shift. These results support the hypothesis of a static any observed time period to the emitted time period is universe. identical to the ratio of the wavelengths, namely (1+푧). This is true for any time interval and is the time dilation Keywords: cosmology:miscellaneous,supernovae:general that is applicable to the widths of the supernova light DOI https://doi.org/10.1515/astro-2017-0013 curves. Clearly the equivalent pseudo velocity is 푐푧. Received Aug 16, 2017; accepted Nov 16, 2017. Any challenge to the standard model must show that observations of SNe light-curve widths do not have time dilation even though the observed spectral lines show the Hubble redshift. An essential requirement of this analysis is that the wavelength of photons is in- 1 Introduction versely proportional to their energy. Thus a photon that has lost energy since its emission will be observed to Type Ia supernovae are transient phenomena that take have a lower energy and the observed Hubble redshift about twenty days to reach a peak brightness and then may be due to some "tired light" process like that de- the brightness decreases at a slower rate. Type Ia super- scribed in [7] which is a complete cosmology that shows novae (for brevity SNe) are also known for their remark- excellent agreement with all major cosmological obser- ably similar light curves and this property makes them vations. The first strong evidence for time dilation in type arXiv:1711.11237v3 [astro-ph.CO] 24 Jan 2018 excellent cosmological probes. For example the width of the light curves is one of the few cosmological observa- Ia supernovae was provided by Leibundgut et al. [18] tions that can directly measure time dilation at large with one supernova and Goldhaber et al. [9] with seven redshifts. SNe. This was quickly followed by multiple SNe results from Goldhaber [8], Goldhaber et al. [10], Perlmutter et al. [20]. These papers record developments in both SNe observations and analysis, the results of which are asserted to provide strong evidence for an expansion Corresponding Author: David F. Crawford: Astronom- model chiefly because they show that the width of type ical Society of Australia 44 Market St Naremburn 2065 NSW Ia supernova light curves appears to increase with red- Australia, shift in good agreement with an expanding model. E-mail: [email protected], Orcid: 0000-0003-0710-1683 Open Access. © 2017 D. F. Crawford et al., published by De Gruyter Open. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License Analysis of type Ia supernovae 112 The results of this paper are based on the extensive the supernova. The ability to determine the age from analysis of type Ia supernova observations provided subtle changes in the spectrum provides an indepen- by dent method of estimating the light-curve width of the [3] (hereafter B14). The raw observations are those used supernova. Provided it is not interpreted as a redshift by B14 but without SALT2 calibration. The results of dependence this light-curve width dependence is consis- this paper are based on the calibration templates for tent with a static cosmology. the SALT2 analysis and the raw type IA supernovae observations described in Section 2. There is an intrinsic variation of the shape of light 2 Methods curves of SNe with emitted wavelength, which con- founds any redshift variation and needs to be removed in order to measure the peak luminosity and width for 2.1 SALT2 templates each supernova. This removal is done by comparing the observations of each supernova to a reference light curve The B14 calibration method [12, 13] uses the SALT2 obtained from analyzing all the light curves in the rest- templates (Spectral Adaptive Light-curve Templates) frame (the emitted frame). The usual assumption is which provide the expected flux density of the supernova made that all the type Ia supernovae are identical irre- light curve as a function of the rest-frame wavelength spective of redshift. The great benefit of this approach and the difference between the observed epoch and the is that it provides an estimate of the intrinsic variations epoch of maximum response. The standard SALT2 tem- in the light curves that can be subtracted from any ob- plate file, 푆퐴퐿푇 2_푡푒푚푝푙푎푡푒_0.푑푎푡, provides the tem- served light curve. plate light curve for approximately 20 days prior to the However it is shown that in general this calibration maximum and 50 days after the maximum for rest-frame process removes all the effects of time dilation and other wavelengths from 200 nm to 920 nm in steps of 0.5 nm. systematic effects so that the calibrated light curves This template file for the JLA (Joint Light-curve Anal- cannot be used to test cosmologies. The standard set ysis) analysis was taken from the SNANA [17] website (SALT2) of templates that provide the reference light in the directory models/푆퐴퐿푇 2/푆퐴퐿푇 2.퐽퐿퐴 − 퐵14. curve as a function of rest-frame wave length show di- rect evidence of the variations of the original light curve widths with redshift. It shows that the standard deletion 2.2 Raw type Ia supernovae light curves of the expected time dilations is not needed and that the original observations are consistent with a static uni- Recently B14 have provided an update of the Conley verse. et al. [5] analysis with better optical calibrations and The major evidence that supports the hypothesis more SNe. This JLA (Joint Light-curve Analysis) list of a static universe is that a direct analysis of the raw sample has 720 SNe from the Supernova Legacy Survey SNe observations (i.e. without SALT2 calibrations) is (SNLS), nearby SNe (LowZ), the Sloan Digital Sky Sur- that the widths of the SNe light curves do not show vey (SDSS) [15, 17] and those revealed by the Hubble time dilation even though there are observed spectral Sky Telescope (HST) [22]. The B14 data file provided line redshifts. Furthermore using a static cosmology the the supernova name, the redshift, the apparent mag- absolute magnitudes are independent of redshift. The nitude and its uncertainty, the stretch parameter (푥1) implication is that the universe is static. and its uncertainty, the color parameter (C) and its un- There are two further findings from SNe observa- certainty, the host stellar mass and finally the survey tions that appear to support the expansion model. First number. The major use of the B14 data in this paper is is the apparent dependence of photometric-redshift ob- to identify an excellent set of type Ia SNe. servations on redshift. These are observations that pho- All of the original SNe observations were retrieved tometric properties of type Ia supernova spectra, as dis- from the SNANA [17] website using the index files tinct from spectral wavelength measurements used to shown in Table 1. The final column shows the number determine redshift, show a redshift dependence. How- of B14 SNe that were recovered from each set of files. ever what they show is a light-curve width dependence For each supernova the following data was ex- not a redshift dependence. Second the age of a spec- tracted: the supernova name and redshift and then for trum is the number of days between the observation of each epoch and for each filter the flux density and its the spectrum and the epoch of the peak magnitude of uncertainty. Most of the SNe were observed in four or Analysis of type Ia supernovae 113 Table 1. Index source files for B14 data rms of the other values was rejected. The values were re- jected in turn, starting with the largest discrepancy and file count finishing when the were no more rejections or there were lcmerge/LOWZ_JRK07 48 only four values left.