No rungs attached: A distance-ladder free determination of the Hubble constant through type II supernova spectral modelling

TL;DR

This study introduces a distance-ladder-independent determination of the Hubble constant using Type II supernovae via a tailored expanding photosphere method (EPM) empowered by a spectral emulator that interpolates radiative-transfer models. Applying this to ten SNe II at $z\,\sim\,$0.01–0.04, the authors derive $H_0 = 74.9 \pm 1.9$ km s$^{-1}$ Mpc$^{-1}$ (stat) with a systematic uncertainty likely comparable to the statistical error, indicating a precision competitive with leading one-step methods. The approach leverages rigorous time-of-explosion constraints, GP-based light-curve interpolation, flux-calibrated spectra, and a Bayesian ensemble EPM that jointly fits all SNe to quantify intrinsic scatter via $\sigma_{int}$. The results support local $H_0$ values and provide an independent cross-check on the Hubble tension, while highlighting systematic avenues to improve in future dedicated SN II datasets (e.g., adH0cc and Nearby SN Factory) and via cross-validation with more sophisticated radiative-transfer models. Overall, this work demonstrates the viability of tailored EPM with spectral emulation as a robust, independent probe of cosmic expansion.

Abstract

The ongoing discrepancy in the Hubble constant ($H_0$) estimates obtained through local distance ladder methods and early universe observations poses a significant challenge to the $Λ$CDM model, suggesting potential new physics. Type II supernovae (SNe II) offer a promising technique for determining $H_0$ in the local universe independently of the traditional distance ladder approach, opening up a complimentary path for testing this discrepancy. We aim to provide the first $H_0$ estimate using the tailored expanding photosphere method (EPM) applied to SNe II, made possible by recent advancements in spectral modelling that enhance its precision and efficiency. Our tailored EPM measurement utilizes a spectral emulator to interpolate between radiative transfer models calculated with TARDIS, allowing us to fit supernova spectra efficiently and derive self-consistent values for luminosity-related parameters. We apply the method on public data for ten SNe II at redshifts between 0.01 and 0.04. Our analysis demonstrates that the tailored EPM allows for $H_0$ measurements with precision comparable to the most competitive established techniques, even when applied to literature data not designed for cosmological applications. We find an independent $H_0$ value of $74.9\pm1.9$ (stat) km/s/Mpc, which is consistent with most current local measurements. Considering dominant sources of systematic effects, we conclude that our systematic uncertainty is comparable to or less than the current statistical uncertainty. This proof-of-principle study highlights the potential of the tailored EPM as a robust and precise tool for investigating the Hubble tension independently of the local distance ladder. Observations of SNe II tailored to $H_0$ estimation can make this an even more powerful tool by improving the precision and by allowing us to better understand and control systematic uncertainties.

Figures (32)

• Figure 1: EPM regression principle. The EPM uses multiple spectroscopic observations to measure the ratio of the photospheric angular diameter $\theta$ (Eq. \ref{['eq:theta']}) and the photospheric velocity $v_\mathrm{ph}$ for different times. These measurements (shown in blue) fall on a straight line (red). We can determine the SN luminosity distance $D_\mathrm{L}$ from the inverse of the slope of this line and the time of explosion from the intercept (see Eq. \ref{['eq:theta/v']}).
• Figure 2: Example of the time-of-explosion determination. We fit an inverse exponential model (Eq. \ref{['eq:inv_exp_model']}) to the observed flux curves (black error bars), modelling the available bands (here $g$ and $r$) jointly with a shared explosion time $t_0$. The colored bands (cyan for $g$, red for $r$) show the 95% confidence regions of the fits. The bottom panel displays the $t_0$ posterior along with the inferred value relative to the first detection and its uncertainty. Finally, the inflated flux errors, including the additional fitted uncertainty $\sigma_\mathrm{add}$, are shown in grey. Here, the reported $g$-band uncertainties accurately capture the scatter around the model, resulting in minimal error inflation. In contrast, the $r$-band errors show noticeable inflation, with $\sigma_\mathrm{add}$ around 0.06mag.
• Figure 3: Example of the GP interpolation of the photometry. We plot the observed magnitudes and their uncertainties in black; the interpolated values at the spectral epochs are shown in red. The colored bands, finally, indicate the 68% confidence interval of the interpolated light curve and the dashed line the median.
• Figure 4: Example of the linear flux calibration procedure. The plot shows the measured ratios of the photometric and spectroscopic flux $F_\mathrm{phot} / F_\mathrm{spectrum}$ for the first epoch of SN 2006it as a function of wavelength in black. We perform a Bayesian fit of the ratios (see \ref{['sec:flux_calibration']}) to identify all possible linear flux calibration corrections. Of the possible curves 68% fall within the dark grey contour and 95% within the light grey contour. Although the underlying curves are straight, the contours naturally exhibit curvature. An important part of the fit is inflating the measured errors if necessary, accounting for additional unquantified uncertainties, such as the mixing of different photometric systems or underestimated uncertainties in the interpolated magnitudes. In the plot, the inflated errors are highlighted in red. In this specific example, the errors are substantially inflated because the data points deviate significantly from a linear trend within the measurement uncertainties.
• Figure 5: Procedure to determine $\theta/v_\mathrm{ph}$ and $E(B-V)$ as described in \ref{['sec:theta/v']}.