in the NIR spectrum relative to the observations
through optical filters. Thus, the fainter individual SN images are poorly resolved for the observations with the longest wavelengths in Fig. 4.
Furthermore, the SN Ia spectral energy distribution (redshifted to z = 0.4) peaks within the
F625W and F814W filters [see, e.g., (22)]. Dimming by interstellar dust in the line of sight is
roughly inversely proportional to wavelength
in the optical and NIR spectra (23). The biggest
impact from extinction by dust is therefore expected for the shortest wavelength, in F475W
filter observations, where the two faintest SN images cannot be detected above the background
light. The low-spatial-resolution light curves in
Fig. 2 are dominated by the two brightest SN
images, labeled 1 and 2 in Fig. 4D. The F625W-
F814W magnitude difference (color) of the
resolved images measured with HST indicates
small differences in relative extinction among
the SN images, except for image 4, which appears
to have about two magnitudes of additional
dimming in F814W.
Unaccounted dimming of light by scattering
on dust grains in the line of sight would lead to
an underestimation of the lensing amplification.
If corrections for differential extinction in the
intervening lensing galaxy among the SN images
are included, the result is a wider range for the
lensing magnification of iPTF16geu, between –4.1
and –4.8 mag (24).
The SN multiple-image positions in Fig. 3 were
used to construct a lensing model, with an isothermal ellipsoid galaxy lens (25, 26) with ellipticity ee = 0.15 ± 0.07 and mass M = 1.70 (±0.06) ×
1010 solar masses inside an ellipse with major
axis of 1.13 kpc and minor axis of 0.97 kpc. Details of the lensing model are presented in (24).
The lens model can be independently verified
through comparisons between the model-predicted
and observed velocity dispersion of the lensing
galaxy. From the model we derive an estimate,
However, the adopted smooth isothermal ellipsoid lens model predicts brightness differences
between the multiple SN images that are in disagreement with the observations. Including corrections for extinction in the resolved SN images
in the F814W filter, we find large discrepancies
between the model and measured magnitude differences for the multiple images of iPTF16geu:
Dmobs 1j −Dmmod 1j = (–0.3, –1.6, –1.5) mag for j = 2,
3, and 4, where the indices follow the numbering
scheme adopted in Fig. 4. The observed discrepancy between the smooth model predictions for
the SN images 1 and 2 compared to 3 and 4
(brighter by factors of 4 and 3, respectively)
cannot be accounted for by time delays between
the images, as they are predicted to be <35 hours
(24). Graininess of the stellar distribution and
dark matter sub-halos in the lens galaxy, in addition to the smooth mass profile, can cause variations to magnification without altering image
locations. These milli- and microlensing effects
(27, 28), small enough not to cause additional
resolved image separations, offer a plausible
explanation for the deviation from the smooth
Available forecasts for wide-field surveys (29)
suggest that about one strongly lensed SN Ia
could be expected in our survey, irrespective of
redshift and magnification, with approximately a
30% chance of being in a quad configuration. For
an average ellipticity of the lenses e = 0.3 (29), only
about 1% of the lensed SNe are expected to have
m > ~50 (30). We have performed an independent rate estimate, with a somewhat simplified
lensing simulation but including survey-specific
parameters, and confirmed that the probability
of detecting and classifying a highly magnified
SN Ia like iPTF16geu does not exceed the few-percent level (24).
iPTF16geu appears to be a rather unlikely event,
unless the actual rate of very magnified SNe is
higher than anticipated—for example, if the contribution from lensing by any kind of substructures
in galaxies is underestimated, or if we are otherwise lacking an adequate description of gravitational lensing at the ~1-kpc scale. The physical
scale probed by the resolved images of iPTF16geu
is comparable to the smallest of the 299 multiply imaged lensed systems in the Master Lens
Database, http://admin.masterlens.org (31). Using
the standard-candle nature of SNe Ia, we can
more easily detect strongly lensed systems with
sub–arc second angular separations, allowing exploration of the bending of light at scales less
than ~1 kpc—an otherwise challengingly small
distance in studies of gravitational lensing (32).
As demonstrated with iPTF16geu, discovered
while still brightening with a modest-sized telescope and suboptimal atmospheric conditions, the
locations of these rare systems can be identified in
advance of extensive follow-up imaging at high
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Fig. 4. High-spatial-resolution images from the
Hubble Space Telescope and the Keck Observatory
used to resolve the positions of the SN images,
the partial Einstein ring of the host galaxy, and
the intervening lensing galaxy. (A to C) HST/WFC3
observations of iPTF16geu obtained on 25 October
2016 in the F475W, F625W, and F814W bands, respectively. The images reveal four point sources, except for F475W where SN images 3 and 4 are too
faint. (D to F) NIR images obtained using adaptive
optics–aided Keck observations in the J-, H-, and
Ks-bands, respectively. All four SN images are clearly
seen in the J-band (D). For the H- and Ks-band
images, both the lensing galaxy at the center of the
system and the lensed partial Einstein ring of the
host galaxy are visible.