Measurements of the Cosmological Parameters Omega and Lambda from the First 7 Supernovae at z >= 0.35

TL;DR

This study uses high-redshift Type Ia supernovae as standard candles to constrain the cosmological parameters $\Omega_M$ and $\Omega_\Lambda$ through the magnitude–redshift relation $m(z)$. A batch-discovery technique yields seven SNe with $z\ge0.35$, and their luminosities are calibrated against a low-redshift SN Ia sample, incorporating the width-luminosity (stretch) relation and cross-checks from color and spectral indicators. The analyses yield $\,\Omega_M=0.88^{+0.69}_{-0.60}$ for a $\Lambda=0$ cosmology and $\Omega_\Lambda=0.06^{+0.28}_{-0.34}$ for a flat universe (i.e., $\Omega_M=0.94^{+0.34}_{-0.28}$), with uncorrected results broadly consistent but less precise; the results disfavour Lambda-dominated flat cosmologies. Overall, the work demonstrates the viability of SN Ia distance measurements for cosmology and anticipates tighter constraints as more high-redshift SNe are obtained and analyzed.

Abstract

We have developed a technique to systematically discover and study high-redshift supernovae that can be used to measure the cosmological parameters. We report here results based on the initial seven of >28 supernovae discovered to date in the high-redshift supernova search of the Supernova Cosmology Project. We find a dispersion in peak magnitudes of sigma_{M_B} = 0.27 this dispersion narrows to sigma_{M_B,corr} = 0.19 after "correcting" the magnitudes using the light-curve "width-luminosity" relation found for nearby (z <= 0.1) type Ia supernovae from the Calan/Tololo survey (Hamuy et al. 1996). Comparing lightcurve-width-corrected magnitudes as a function of redshift of our distant (z = 0.35-0.46) supernovae to those of nearby type Ia supernovae yields a global measurement of the mass density, Omega_M = 0.88^{+0.69}_{-0.60} for a Lambda = 0 cosmology. For a spatially flat universe (i.e., Omega_M +Omega_Lambda = 1), we find Omega_M = 0.94 ^{+0.34}_{-0.28} or, equivalently, a measurement of the cosmological constant, Omega_Lambda = 0.06 ^{+0.28}_{-0.34} (<0.51 at the 95% confidence level). For the more general Friedmann-Lemaitre cosmologies with independent Omega_M and Omega_Lambda, the results are presented as a confidence region on the Omega_M-Omega_Lambda plane. This region does not correspond to a unique value of the deceleration parameter q_0. We present analyses and checks for statistical and systematic errors, and also show that our results do not depend on the specifics of the width-luminosity correction. The results for Omega_Lambda-versus-Omega_M are inconsistent with Lambda-dominated, low density, flat cosmologies that have been proposed to reconcile the ages of globular cluster stars with higher Hubble constant values.

Figures (7)

• Figure 1: Enlarged subimage showing the host galaxy of SN 1994am, and three neighboring galaxies before, during, and after the supernova explosion. (a) Isaac Newton 2.5-m Harris $R$-band observation on 19 December 1993, with 0.6 arcsec/pixel. (b) Kitt Peak 4-m Harris $R$-band observation on 4 February 1994, with 0.47 arcsec/pixel, near maximum light of the supernova (indicated by arrow). (c) Cerro Tololo 4-m Harris $R$-band observation on 15 October 1995, with 0.47 arcsec/pixel. (d) Hubble Space Telescope (WFPC2) F814W $I$-band observation on 13 January 1995, with 0.1 arcsec/pixel. At this resolution, the host galaxy of SN 1994am can be identified as an elliptical, providing strong evidence that SN 1994am is a type Ia supernova.
• Figure 2: (Continued on next page.)$R$-band light curve photometry points for the first seven high-redshift supernovae discovered by the Supernova Cosmology Project, and best-fit template SN Ia light curves. The left panels show the relative flux as function of observed time (not supernova-rest-frame time). The right panels show observed $R$-band magnitude versus observed time. Note that there is significant correlation between the error bars shown, particularly for observations with similar seeing, since the error bars depend on the uncertainty in the host-galaxy measurement that have been subtracted from these measurements (see text). An $I$-band light curve is also shown for SN 1994G; other photometry points in $I$ and $B$ for the seven supernovae are not shown on this plot. The rising slope (in mag/day) of the template light curve before rest-frame day $-$10 (indicated by the grey part of the curves) is not well-determined, since few low-redshift supernovae are discovered this soon before maximum light. A range of possible rise times was therefore explored (see text).
• Figure 2: continued.
• Figure 3: The difference between the measured and "theoretical" (Equation \ref{['simplemagz']} for $\Omega_{\rm M} = 1$, $\Omega_\Lambda=0$, and ${\cal M} = {\cal M}_{B,{\rm corr}}^{\{1.1\}}$) $B$ magnitudes (uncorrected for the width-luminosity relation) versus the best-fit stretch factor, $s$, for the high-redshift supernovae. The stretch factor is fit in the supernova rest frame, i.e., after correcting for the cosmological time dilation calculated from the host-galaxy redshift (see Equations \ref{['templates']} and \ref{['fitfunc']}). If different values of ($\Omega_{\rm M}$, $\Omega_\Lambda$) had been chosen the labels would change, but the data points would not vary significantly within their error bars, since the range of redshifts is not large for these supernovae. The upper axis gives the equivalent values of $\Delta m_{15} = 1.96(s^{-1}-1) + 1.07$ (Eq. \ref{['stodeltam15']}). The solid line shows the width-luminosity relation (Eq. \ref{['widthbrightrel']}) found by Hamuy et al. (1995, 1996) for an independent set of 18 nearby ($z \le 0.1$) SNe Ia, for which $0.8 \mathrel{\hbox{$<$} \hbox{$\sim$}} \Delta m_{15} \mathrel{\hbox{$<$} \hbox{$\sim$}} 1.75$ mag. This range of light-curve widths is indicated by the shaded region. The curve and data points outside of this range are plotted in a different shade to emphasize that the relation is only established within this range. A different choice of ($\Omega_{\rm M}$, $\Omega_\Lambda$) or of the magnitude zero-point ${\cal M}$ would move the line in the vertical direction relative to the points.
• Figure 4: Hubble diagrams for the first seven high-redshift supernovae, (a) uncorrected $m_B$, with low-redshift supernovae of Hamuy et al. (1995) for visual comparison; (b) $m_{B,{\rm corr}}$ after "correction" for width-luminosity relation. The square points are not used in the analysis, because they are corrected based on an extrapolation outside the range of light curve widths of low-redshift supernovae (see text and Table \ref{['tableone']}). Insets show the high-redshift supernovae on magnified scales. The solid curves in (a) and (b) are theoretical $m_B$ for ($\Omega_{\rm M}$, $\Omega_\Lambda$) = (0, 0) on top, (1, 0) in middle, and (2, 0) on bottom. The dotted curves, which are practically indistinguishable from the solid curves, are for the flat universe case, with ($\Omega_{\rm M}$, $\Omega_\Lambda$) = (0.5, 0.5) on top, (1, 0) in middle, and (1.5, $-$0.5) on bottom. The inner error bars on the data points show the photometry measurement uncertainty, while the outer error bars add the intrinsic dispersions found for low-redshift supernovae, $\sigma_{M_B}^{\rm Hamuy}$ for (a) and $\sigma_{M_B,{\rm corr}}^{\rm Hamuy}$ for (b), for comparison to the theoretical curves. Note that the zero-point magnitude used for (b), ${\cal M}_{B,{\rm corr}}^{\{1.1\}}$, and hence the effective $m_B$ scale, is shifted slightly from the uncorrected ${\cal M}_{B}$ used for the curves of (a).