Underluminous 1991bg-like Type Ia supernovae are standardizable candles

It is widely accepted that the width-luminosity relation used to standardize normal Type Ia supernovae (SNe Ia) breaks down in underluminous, 1991bg-like SNe Ia. This breakdown may be due to the choice of parameter used as a stand-in for the width of the SN Ia light curve. Using the colour stretch parameter $s_\mathrm{BV}$ instead of older parameters resolves this issue. Here, I assemble a sample of 14 nearby 1991bg-like SNe Ia from the literature, all of which have independent host-galaxy distance moduli and little to no reddening. I use Gaussian process regression to fit the light curves of these SNe in $U/u$, $B$, $V$, $g$, $R/r$, $I/i$, and $H$, and measure their peak absolute magnitudes. I find statistically significant ($>5σ$ confidence level in the optical and $>4σ$ in the near-infrared) correlations between the peak absolute magnitudes of the 1991bg-like SNe Ia and their $s_\mathrm{BV}$ values in the range $0.2<s_\mathrm{BV}<0.6$. These correlations are broadly consistent with fits to $s_\mathrm{BV}<0.7$ SNe Ia with preliminary $B$- and $V$-band peak absolute magnitudes from the Carnegie Supernova Project and significantly inconsistent with similar fits to normal and transitional SNe Ia (with $0.7<s_\mathrm{BV}<1.1$). The underluminous width-luminosity relation shown here needs to be properly calibrated with a homogeneous sample of 1991bg-like SNe Ia, after which it could be used as a rung on a new cosmological distance ladder. With surface-brightness fluctuations (or another non-Cepheid method) used to calibrate distances to nearby 1991bg-like SNe Ia, such a ladder could produce an independent measurement of the Hubble-Lemaître Constant, $H_\mathrm{0}$.