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The methodology involved in deriving the Hubble Constant via the calibration of the corrected peak luminosities of Type Ia supernovae (SNe) is reviewed. We first present a re-analysis of the Calan-Tololo (C-T) and Center for Astrophysics (CfA) Type Ia SN surveys. Bivariate linear least squares and quadratic boot-strapped fits in peak apparent magnitude and light curve shape are employed to correct this heterogeneous sample of peak apparent magnitudes, resulting in an homogeneous (and excellent) secondary distance indicator: the so-called corrected peak luminosity. We next provide an empirical calibration for this corrected luminosity, using Cepheid-based distances for seven nearby spiral galaxies host to Type Ia SNe. Included in this sample is the spectroscopically peculiar SN 1991T (in NGC 4527), whose corrected peak luminosity is shown to be indistinguishable from that of so-called ``normal SNe. A robust value of the Hubble Constant is derived and shown to be H0=73+/-2(r)+/-7(s) km/s/Mpc.
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Type Ia supernovae (SNe) are the best standard candles available today in spite of an appreciable intrinsic variation of their luminosities at maximum phase, and of probably non-uniform progenitors. For an unbiased use of type Ia SNe as distance indicators it is important to know accurately how the decline rate and colour at maximum phase correlate with the peak brightness. In order to calibrate the Hubble diagram of type Ia SNe, i.e. to derive the Hubble constant, one needs to determine the absolute brightness of nearby type Ia SNe. Globular cluster systems of early type Ia host galaxies provide suitable distance indicators. We discuss how Ia SNe can be calibrated and explain the method of Globular Cluster Luminosity Functions (GCLFs). At present, the distance to the Fornax galaxy cluster is most important for deriving the Hubble constant. Our present data indicate a Hubble constant of H_0=72+-4 km/s/Mpc. As an appendix, we summarise what is known about absolute magnitudes of Ias in late-type galaxies.
The Calan/Tololo supernova survey has discovered ~30 Type Ia supernovae out to z~0.1. Using BVI data for these objects and nearby SNe Ia, we have shown that there exists a significant dispersion in the intrinsic luminosities of these objects. We have devised a robust chisquare minimization technique simultaneously fitting the BVI light curves to parametrize the SN event as a function of (tb,m, m15(B)) where tb is the time of B maximum, m is the peak BVI magnitude corrected for luminosity variations, and m15(B) is a single parameter describing the whole light curve morphology. When properly corrected for m15(B), SNe Ia prove to be high precision distance indicators,yielding relative distances with errors 7-10%. The corrected peak magnitudes are used to construct BVI Hubble diagrams (HD), and with Cepheid distances recently measured with the HST to four nearby SNe Ia (37C, 72E, 81B, 90N) we derive a value of the Hubble constant of 63.1+/-3.4 (internal) km/s/Mpc. This value is ~10-15% larger than the value obtained by assuming that SNe Ia are perfect standard candles. As we have shown in Paper V, there is now strong evidence that galaxies with younger stellar population appear to host the slowest-declining, and therefore most luminous SNe Ia. Hence, the use of Pop I objects such as Cepheids to calibrate the zero point of the SNe Ia HD can easily bias the results toward luminous SNe Ia, unless the absolute magnitude-decline relation is taken into account.
In this work, we propose a cosmological model-independent and non-local method to constrain the Hubble Constant $H_0$. Inspired by the quasi cosmological model-independent and $H_0$-free properties of the `shifted Hubble diagram of HII galaxies (HIIGx) defined by Wei et al. (2016), we joint analyze it with the parametric type Ia supernova (SN Ia) Hubble diagram (e.g. the joint-lightcurves-analysis sample, JLA) and get a Bayesian Inference of Hubble constant, $H_0 = 71 pm 20 mathrm{km s^{-1} Mpc^{-1}}$. Although with large uncertainty, we find that $H_0$ is only strongly degenerate with the B-band absolute magnitude ($M_B$) of SN Ia but almost independent on other nuisance parameters. Therefore the accuracy can be simultaneously improved by a tight constraint of $M_B$ through a cosmological and $H_0$ independent way. This method can be extended further to get more-literally non-local results of $H_0$ by using other Hubble diagrams at higher redshifts.
The most precise local measurements of $H_0$ rely on observations of Type Ia supernovae (SNe Ia) coupled with Cepheid distances to SN Ia host galaxies. Recent results have shown tension comparing $H_0$ to the value inferred from CMB observations assuming $Lambda$CDM, making it important to check for potential systematic uncertainties in either approach. To date, precise local $H_0$ measurements have used SN Ia distances based on optical photometry, with corrections for light curve shape and colour. Here, we analyse SNe Ia as standard candles in the near-infrared (NIR), where intrinsic variations in the supernovae and extinction by dust are both reduced relative to the optical. From a combined fit to 9 nearby calibrator SNe with host Cepheid distances from Riess et al. (2016) and 27 SNe in the Hubble flow, we estimate the absolute peak $J$ magnitude $M_J = -18.524;pm;0.041$ mag and $H_0 = 72.8;pm;1.6$ (statistical) $pm$ 2.7 (systematic) km s$^{-1}$ Mpc$^{-1}$. The 2.2 $%$ statistical uncertainty demonstrates that the NIR provides a compelling avenue to measuring SN Ia distances, and for our sample the intrinsic (unmodeled) peak $J$ magnitude scatter is just $sim$0.10 mag, even without light curve shape or colour corrections. Our results do not vary significantly with different sample selection criteria, though photometric calibration in the NIR may be a dominant systematic uncertainty. Our findings suggest that tension in the competing $H_0$ distance ladders is likely not a result of supernova systematics that could be expected to vary between optical and NIR wavelengths, like dust extinction. We anticipate further improvements in $H_0$ with a larger calibrator sample of SNe Ia with Cepheid distances, more Hubble flow SNe Ia with NIR light curves, and better use of the full NIR photometric data set beyond simply the peak $J$-band magnitude.
Cross-filter K corrections for a sample of normal Type Ia supernovae (SNe) have been calculated for a range of epochs. With appropriate filter choices, the combined statistical and systematic K correction dispersion of the full sample lies within 0.05 mag for redshifts z<0.7. This narrow dispersion of the calculated K correction allows the Type Ia to be used as a cosmological probe. We use the K corrections with observations of seven SNe at redshifts 0.3 < z <0.5 to bound the possible difference between the locally measured Hubble constant (H_L) and the true cosmological Hubble constant (H_0).
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