Strong Gravitational Lensing and Microlensing of Supernovae

Abstract

Strong gravitational lensing and microlensing of supernovae (SNe) are emerging as a new probe of cosmology and astrophysics in recent years. We provide an overview of this nascent research field, starting with a summary of the first discoveries of strongly lensed SNe. We describe the use of the time delays between multiple SN images as a way to measure cosmological distances and thus constrain cosmological parameters, particularly the Hubble constant, whose value is currently under heated debates. New methods for measuring the time delays in lensed SNe have been developed, and the sample of lensed SNe from the upcoming Rubin Observatory Legacy Survey of Space and Time (LSST) is expected to provide competitive cosmological constraints. Lensed SNe are also powerful astrophysical probes. We review the usage of lensed SNe to constrain SN progenitors, acquire high-z SN spectra through lensing magnifications, infer SN sizes via microlensing, and measure properties of dust in galaxies. The current challenge in the field is the rarity and difficulty in finding lensed SNe. We describe various methods and ongoing efforts to find these spectacular explosions, forecast the properties of the expected sample of lensed SNe from upcoming surveys particularly the LSST, and summarize the observational follow-up requirements to enable the various scientific studies. We anticipate the upcoming years to be exciting with a boom in lensed SN discoveries.

Keywords: (Cosmology:) cosmological parameters; (Cosmology:) distance scale; (ISM:) dust, extinction; Gravitational lensing: micro; Gravitational lensing: strong; Supernovae: general.

Fig. 1

Hubble Space Telescope image of SN Refsdal, the first strongly lensed SN system with spatially resolved images. Inset (a) shows the image SX that was detected in December 2015 (Kelly et al. 2016a), and inset (b) shows the multiple images S1, S2, S3 and S4 that were first discovered in November 2014 (Kelly et al. 2015). There is another image SY located in the northern most image of the spiral host galaxy, next to the top-right corner of the inset (a). Image taken from Grillo et al. (2018). Original image credit: NASA, ESA/Hubble

Fig. 2

Wide-field image from iPTF showing the portion of the CCD camera where iPTF16geu was found in modest seeing ($2^{″}$). The insets show how the strong lensing nature, a quadruple lens with an Einstein radius of only ${0.3}^{″}$, could be verified using HST imaging in the optical, and laser-guide-star adaptive-optics imaging from Keck in the Near-IR. Image credit: J. Johansson

Fig. 3

Panel a): Color image of SN Requiem showing arc-like images of the distant host galaxy (H1-H4), the three SN images (SN1-SN3) and an ellipse pointing out the expected location of SN4. Panels b-i): zoomed-in regions around the SN locations from the data taken in 2016 (b-e) and 2019 (f-i). Figure taken from Rodney et al. (2021)

Fig. 4

Examples of Type Ia SNe light curves with significant microlensing. Left panel: a map of microlensing magnifications ($\mu$, indicated by the color bar) on the source plane as a result from stars in the foreground lens galaxy. The map is for a lensed SN image with convergence $\kappa =0.6$, shear $\gamma =0.6$, and smooth dark matter fraction $s=0.6$. In this example, the Einstein radius for the mean microlens is $R_{\mathrm{Ein}}=7.2\times {10}^{-3}\mathrm{pc}$. The two circles in solid cyan and dashed magenta indicate the size of a SN Ia at 21 rest-frame days after explosion. Middle and right panels: microlensed light curves in the g-band (middle panel) and z-band (right panel) corresponding to the SN positions shown in the left panel (solid cyan and dashed magenta). The intrinsic light curve without microlensing is shown in dotted black. When the expanding photosphere of the SN crosses a microlensing caustic with high $\mu$, its light curve changes substantially relative to the no-microlensing case. Figure taken from Huber et al. (2019)

Fig. 5

Microlensing induced scatter (indicated by the color bar) for a point source lensed by a Singular Isothermal Sphere (SIS) macromodel as a function of stellar fraction and macro-magnification. For an SIS, the convergence and shear magnitude (shown in the $x$-axis) are the same at any given location on the lens plane. Scatter is lower for the lensed SN image that is far from the Einstein radius (with lower convergence/shear), but there is a limit since a convergence below 0.25 produces only single images (i.e., no strong lensing) and convergence below ∼0.35 produces a faint counterimage (close to lens center) that makes time-delay measurements more challenging. Image credit: Luke Weisenbach, modified based on Weisenbach et al. (2021)

Fig. 6

Light curves of SN Refsdal from Hubble Space Telescope imaging in multiple wavelength filters. Each row consists of the light curves obtained in the specific filter that is indicated in the leftmost panel. Each column shows one of the four SN images, S1-S4 (left to right), that are indicated on the top panels. Each panel shows the observed AB magnitude as a function of the observer-frame days. Figure taken from Rodney et al. (2016)

Fig. 7

Spectral evolution of core-collapse SN1999em based on the TARDIS simulation from Vogl et al. (2019, 2020). Three prominent spectral features, H$\beta$, FeII and H$\alpha$, are labelled. The SN phases are indicated by their rest-frame days after explosion. As the SN phase increases, the spectral features become stronger and the absorption wavelengths increase. Such a sequence of spectra of the first-appearing SN image provides the wavelength-phase relation, and a measurements of the absorption wavelength of a trailing SN image therefore provides information of its SN phase and thus its time delay relative to the first-appearing SN image. With each spectrum of signal-to-noise of 20, Bayer et al. (2021) showed that the time delays can be measured with uncertainties of $\sim 2$ days per spectral feature, even after accounting for the effects of microlensing. Figure taken from Bayer et al. (2021)

Fig. 8

Forecast of $H_0$ from SN Refsdal as a function of the time delay between SN images SX and S1, using the reference mass model of Grillo et al. (2020). The median values of $H_0$ (diamonds) with the 1$\sigma$ uncertainties in flat $\mathrm{\Lambda }$CDM are shown for 9 different hypothetical SX-S1 delays, each with an assumed uncertainty of 10 days. For comparison, the blue, magenta and red bands show, respectively, the 1$\sigma$ credible intervals from SH0ES (Riess et al. 2019), H0LiCOW (Wong et al. 2020) and Planck (Planck Collaboration et al. 2020). Figure taken from Grillo et al. (2020)

Fig. 9

Forecast of constraints on $H_0$ and ${\mathrm{\Omega }}_{\mathrm{m}}$ in flat $\mathrm{\Lambda }$CDM from a sample of 20 lensed SNe Ia from LSST with precise and accurate time-delay measurements. Assuming distance measurements of $D_{\mathrm{\Delta }t}$ and $D_{\mathrm{d}}$ with 6.6% and 5% uncertainties, respectively, for each lensed SN Ia, this modest sample is expected to yield $H_0$ and ${\mathrm{\Omega }}_{\mathrm{m}}$ with precisions of 1.3% and 19%, respectively. Figure taken from Suyu et al. (2020)

Fig. 10

Expected signal for HST observations through grisms G102 and G141 of a SN Ia at $z=1.5$ for different magnifications provided by lensing. The shaded regions in [orange, green, blue, red] indicate the 1$\sigma$ uncertainty per pixel in one-hour-long exposures for $\mathrm{\Delta }m=[1,1.5,2.0,2.5]$ mag of magnification, respectively. The observed spectrum of “SN Primo” (Rodney et al. , six hours exposure time) is also shown for comparison

Fig. 11

Specific intensity profile of the W7 explosion model of SNe Ia. Left: radial intensity profiles in different filters 14.9 rest-frame days after explosion, in units of the Einstein radius of the microlenses ($R_{\mathrm{Ein}}=2.2\times {10}^{16}\mathrm{cm}$ for this specific case). The vertical solid cyan lines indicate the radius that encloses 99.9% of the total projected specific intensity. The vertical black dashed lines are random locations of caustics – effects of microlensing are strong when the specific intensity of the SN crosses a caustic. Right panel: same as the left panel but for a SN Ia 39.8 rest-frame days after explosion. Figure extracted and modified from Huber et al. (2019)

Fig. 12

Specific intensity profiles from TARDIS (Kerzendorf and Sim ; Vogl et al. 2019) modelling of SN 1999em, a Type IIP SN (Vogl et al. 2020) projected on the plane of the sky (Bayer et al. 2021). Left: radial intensity profiles in different filters 11 rest-frame days after explosion, in units of the Einstein radius of the microlenses ($R_{\mathrm{Ein}}=2.9\times {10}^{16}\mathrm{cm}$ for this specific case). Right panel: same as the left panel but for 27 rest-frame days after explosion. Figure taken from Bayer et al. (2021)

Fig. 13

The observed color excess for the resolved images from HST of iPTF16geu as a function of wavelength. The absorption from the host galaxy dust grains is plotted in black. For Image 1 we can see that the host galaxy is the dominant source of extinction, and for images 2, 3, 4 there is a progressively larger contribution from the dust in the lens galaxy, with correspondingly higher values of the color excess. Figure taken from Dhawan et al. (2020)

Fig. 14

The expected distribution of unlensed SNe population (SNe Ia in blue shaded, and core-collapse SNe in red shaded) is enclosed by thick black line showing the red limit. The lensed population predicted by Monte Carlo simulations is shown for SNe Ia (blue circles) and core-collapse SNe (red triangles). Vertical line marks the single epoch limit for LSST. Figure taken from Quimby et al. (2014)

Fig. 15

Multicolor light curve of iPTF16geu showing that the unresolved supernova was 4.3 magnitudes (30 standard deviations) brighter than expected for its redshift. The magnitudes are measured with respect to time of maximum light in the R-band at P48 and in the g-, r-, and i-bands with the P60 telescope. The solid lines show the best-fitted SN Ia model to the data, while the dashed lines indicate the expected light curves at $z=0.409$ (without lensing). The bands represent the standard deviation of the brightness distribution for SNe Ia. To fit the observed light curves, a brightness boost from gravitational lensing of 4.3 magnitudes is required. Figure from Goobar et al. (2017)

Fig. 16

The number of lensed SNe Ia expected per year over the whole sky as a function of the imaging survey limiting magnitude depth. The different colors correspond to detection in different filters (g, r, i, z or y). The dotted (dashed) lines show the expected number of lensed SNe Ia detected through the magnification (image multiplicity) approach. The hybrid approach, a combination of magnification and image multiplicity, is indicated by the solid curve. For shallow image surveys with limiting depth brighter than ∼22 such as the ZTF survey, the magnification approach dominates in providing most of the expected lensed SNe. For deep image surveys with limiting depth fainter than ∼23 such as the LSST survey, the image multiplicity approach start to dominate. Figure taken from Wojtak et al. (2019)

Fig. 17

Cumulative number of lensed Type Ia and core-collapse supernovae detections by the LSST survey per year as a function of their peak $i$-band magnitude, as computed in Goldstein et al. (2019). Figure credit: Ana Sagués Carracedo

Fig. 18

Predicted system configurations for strongly lensed Type Ia supernovae in LSST as computed in Goldstein et al. (2019). Figure credit: Ana Sagués Carracedo