Forecasting the Observable Rates of Gravitationally Lensed Supernovae for the PASSAGES Dusty Starbursts

TL;DR

This study evaluates a targeted approach to discover gravitationally lensed supernovae in PASSAGES HyLIRGs to enable time-delay cosmography for measuring $H_0$ independently of the traditional distance ladder. By combining ALMA and VLA-based SFR maps with lens models, the authors estimate intrinsic SN rates and observer-frame rates, accounting for dust obscuration via $f_{ m unobsc}$ and a multiplicity factor $N_{ m eff}$. They demonstrate a strong link between Einstein radius and time delays, highlighting cluster lenses as favorable for long delays, and propose JWST monitoring to mitigate dust attenuation. The results indicate high SN yields in PASSAGES fields, suggesting that a concerted monitoring program, in concert with wide-area surveys, could yield enough lensed SNe to reach ~1% precision on $H_0$ in the coming decade.

Abstract

More than 60 years have passed since the first formal suggestion to use strongly-lensed supernovae to measure the expansion rate of the Universe through time-delay cosmography. Yet, fewer than 10 such objects have ever been discovered. We consider the merits of a targeted strategy focused on lensed hyperluminous infrared galaxies -- among the most rapidly star-forming galaxies known in the Universe. With star formation rates (SFRs) $\sim {200 - 6000}~\textrm{M}_\odot~\textrm{yr}^{-1}$, the $\sim 30$ objects in the Planck All-Sky Survey to Analyze Gravitationally-lensed Extreme Starbursts (PASSAGES) are excellent candidates for a case study, in particular, and have already led to the discovery of the multiply-imaged SN H0pe. Considering their lens model-corrected SFRs, we estimate their intrinsic supernova rates to be an extraordinary ${1.8 - 65}~\textrm{yr}^{-1}$ (core-collapse) and ${0.2 - 6.4}~\textrm{yr}^{-1}$ (Type Ia). Moreover, these massive starbursts typically have star-forming companions which are unaccounted for in this tally. We demonstrate a strong correlation between Einstein radius and typical time delays, with cluster lenses often exceeding several months (and therefore most favorable for high-precision $H_0$ inferences). A multi-visit monitoring campaign with a sensitive infrared telescope (namely, JWST) is necessary to mitigate dust attenuation. Still, a porous interstellar medium and clumpy star formation in these extreme galaxies might produce favorable conditions for detecting supernovae as transient point sources. Targeted campaigns of known lensed galaxies to discover new lensed supernovae can greatly complement wide-area cadenced surveys. Increasing the sample size helps to realize the potential of supernova time-delay cosmography to elucidate the Hubble tension through a single-step measurement, independent of other $H_0$ techniques.

Figures (8)

• Figure 1: Cartoon schematic demonstrating the calculation of effective multiplicity $\mathcal{N}_{\rm eff}$ per Equation \ref{['eqn:Neff']}, using an ALMA 870 $\mu$m image of the unlensed DSFG ALESS 112.1 as an example Hodge:2019aa. Mock caustic curves from an imaginary lensing galaxy are overlaid (radial=dashed, tangential=solid). Put simply, $\mathcal{N}_{\rm eff}$ is the weighted average of multiplicities ($n=1,2,3,...$), where the weights are the respective portions of the total SFR.
• Figure 2: Observable rate of core-collapse supernovae $\mathcal{R}_{\rm CC,obs}$ vs. redshift for the 21 PASSAGES galaxies considered, using $\mathcal{R}_{\rm CC,obs}$ as defined in Equation \ref{['eqn:RCC_obs']}. The unobscured fractions adopted are provided in Table \ref{['tab:computations']}. Colors show the effective multiplicity, $\mathcal{N}_{\rm eff}$, described in Equations \ref{['eqn:Neff']} and \ref{['eqn:Neff2']}. The increase with redshift is predominantly due to a general increase in SFR with $z$, which is also responsible for the trend observed in Fig. \ref{['fig:RIa_z']} (see § \ref{['sec:independent']}).
• Figure 3: For the same galaxies as in Fig. \ref{['fig:Rcc']}: predicted observer-frame rates $\mathcal{R}_{\rm Ia,obs}$ of Type Ia supernovae (the intrinsic rate $R_{\rm Ia}$ multiplied by the unobscured fraction $f_{\rm unobsc}$, the effective number of multiple images $\mathcal{N}_{\rm eff}$ and the time dilation factor, $(1+z)^{-1}$). In this regime of active star formation, $R_{\rm Ia}$ is primarily a function of SFR and weakly dependent on $M_\star$. Stellar masses are bounded by assuming that the sSFRs lie between 0.3 dex below and 0.9 dex above the star-forming main sequence. Colors of data points show this effective lower limit on $M_\star$ for 0.9 dex above the SFMS. A dashed gray line shows the expected rate for a galaxy exactly on the SFMS at $z=2$ according to the Speagle:2014aa treatment, and a second dashed line shows the observable rate for the same galaxy with an effective multiplicity of $\mathcal{N}_{\rm eff} = 4$.
• Figure 4: Redshift distribution of the observable rate of SNe Ia from PASSAGES estimated in Fig. \ref{['fig:RIa']}, $\mathcal{R}_{\rm Ia}$, but now removing the factor of $f_{\rm unobsc}$ (thus reducing uncertainties and improving legibility). Colors indicate the effective multiplicity $\mathcal{N}_{\rm eff}$. Transparent, smaller triangles indicate the intrinsic rates ($R_{\rm Ia}$) for each target (i.e., without factoring in the boost from multiple-imaging or the $1+z$ decrement from cosmological time dilation). The triangles for intrinsic rates are oriented to point towards their corresponding observable rates. This illustrates that since $\mathcal{N}_{\rm eff} \cdot (1+z)^{-1}$ is typically of order unity, these effects roughly cancel out.
• Figure 5: Intrinsic supernova rates (core-collapse on left, Type Ia on right), still rescaled by time dilation but excluding multiple imaging (and $f_{\rm unobsc.}$ correction), vs. redshift. Whereas $\mathcal{R}_{\rm CC,obs}$ and $\mathcal{R}_{\rm Ia,obs}$ represented the average rate at which supernova images appear, $R_{\rm CC}\cdot (1+z)^{-1}$ and $R_{\rm Ia}\cdot (1+z)^{-1}$ are the actual rate of individual supernova events, as if the galaxies were not lensed. We compare with the predictions made for a large sample of galaxy-galaxy lenses by Shu:2018ab, incorporating the corrections from Shu:2021ab, and the Frontier Fields considered by Petrushevska:2018abPetrushevska:2018aa. The sums of the Shu:2018ab and Petrushevska:2018ab samples are shown as large red circles and large black squares, respectively. Predicted rates for G165 Arc 2, the host galaxy of the Type Ia SN H0pe, are shown with open circles (based on SFR/$M_\star$ from Frye:2024aa). Similarly, the predicted rates for MRG-M0138 (based on Newman:2018aa) are indicated as black stars (with a dark red border on the right panel, highlighting SN Requiem/Encore). In the left panel, the MACS J1149 point with a dark red border is the host galaxy of the discovered core-collapse glSN Refsdal. The PASSAGES objects considered in this work have CCSN rates about 100 times greater than the Shu:2018ab sample (and similarly for SNe Ia). In the left panel, the gray curve shows the expectation of $R_{\rm CC}(z) \propto \psi(z)$ for the Madau:2014aa parameterization of the cosmic star formation rate density $\psi(z)$, which has units of $M_\odot~{\rm yr}^{-1}~{\rm Mpc}^{-3}$, rescaled arbitrarily to approximately match the Frontier Fields data points.