# The Candidate Progenitor Companion Star of the Type Ib/c SN 2013ge

Ori D. Fox Space Telescope Science Institute, 3700 San Martin Drive,
Baltimore, MD 21218, USA  Schuyler D. Van Dyk Caltech/IPAC, Mailcode 100-22,
Pasadena, CA 91125, USA  Benjamin F. Williams University of Washington,
Seattle, WA 98195, USA  Maria Drout David A. Dunlap Department of Astronomy
and Astrophysics, University of Toronto
50 St. George Street, Toronto, Ontario, M5S 3H4 Canada  Observatories of the
Carnegie Institution for Science, 813 Santa Barbara St., Pasadena, CA 91101,
USA  Emmanouil Zapartas Département d’Astronomie, Université de Genève, Chemin
Pegasi 51, CH-1290 Versoix, Switzerland  Nathan Smith Steward Observatory,
University of Arizona 933 N. Cherry Ave., Tucson, AZ 85721, USA  Dan
Milisavljevic Department of Physics and Astronomy, Purdue University, 525
Northwestern Avenue, West Lafayette, IN 47907-2036, USA  Integrative Data
Science Initiative, Purdue University, West Lafayette, IN 47907, USA  Jennifer
E. Andrews Gemini Observatory/NSF’s NOIRLab, 670 N. A’ohoku Place, Hilo, HI
96720, USA  K. Azalee Bostroem DIRAC Institute, Department of Astronomy,
University of Washington, 3910 15th Avenue NE, Seattle, WA 98195, USA)  Alexei
V. Filippenko Department of Astronomy, University of California, Berkeley, CA
94720-3411, USA  Sebastian Gomez Space Telescope Science Institute, 3700 San
Martin Drive, Baltimore, MD 21218, USA  Patrick L. Kelly Minnesota Institute
for Astrophysics, 116 Church St. SE, Minneapolis, MN 55455, USA  S. E. de Mink
Max Planck Institute for Astrophysics, Karl-Schwarzschild-Str. 1, 85748
Garching, Germany  Anton Pannekoek Institute for Astronomy, University of
Amsterdam, Science Park 904, 1098XH Amsterdam, The Netherlands  Justin Pierel
Space Telescope Science Institute, 3700 San Martin Drive, Baltimore, MD 21218,
USA.  Armin Rest Space Telescope Science Institute, 3700 San Martin Drive,
Baltimore, MD 21218, USA.  Department of Physics and Astronomy, The Johns
Hopkins University, Baltimore, MD 21218, USA  Stuart Ryder School of
Mathematical and Physical Sciences, Macquarie University, NSW 2109, Australia
Astronomy, Astrophysics and Astrophotonics Research Centre, Macquarie
University, Sydney, NSW 2109, Australia  Niharika Sravan  Division of Physics,
Mathematics, and Astronomy, California Institute of Technology, Pasadena, CA
91125, USA  Lou Strolger  Space Telescope Science Institute, 3700 San Martin
Drive, Baltimore, MD 21218, USA.  Qinan Wang Department of Physics and
Astronomy, The Johns Hopkins University, Baltimore, MD 21218, USA  Kathryn E.
Weil Department of Physics and Astronomy, Purdue University, 525 Northwestern
Avenue, West Lafayette, IN 47907, USA

###### Abstract

This Letter presents the detection of a source at the position of the Type
Ib/c supernova (SN) 2013ge more than four years after the radioactive
component is expected to have faded. This source could mark the first post-SN
direct detection of a surviving companion to a stripped-envelope Type Ib/c
explosion. We test this hypothesis and find the shape of the source’s spectral
energy distribution is most consistent with that of a B5 I supergiant. While
binary models tend to predict OB-type stars for stripped-envelope companions,
the location of the source on a color-magnitude diagram (CMD) places it
redward of its more likely position on the main sequence (MS). The source may
be temporarily out of thermal equilibrium, or a cool and inflated non-MS
companion, which is similar to the suggested companion of Type Ib SN 2019yvr
that was constrained from pre-SN imaging. We also consider other possible
physical scenarios for the source, including a fading SN, circumstellar shock
interaction, line of site coincidence, and an unresolved host star cluster,
all of which will require future observations to more definitively rule out.
Ultimately, the fraction of surviving companions (“binary fraction”) will
provide necessary constraints on binary evolution models and the underlying
physics.

supernovae: general — supernovae: individual (SN 2013ge) — binaries: close —
stars: massive

<EMAIL_ADDRESS>

##  1 Introduction

Core-collapse supernovae (CCSNe) arise from the deaths of massive stars
($M_{\rm ZAMS}\gtrsim 8$ M⊙). Stripped-envelope explosions — SNe IIb, Ib, and
Ic — refer to the subset of CCSNe with progenitors that have lost all, or
almost all, of their outer hydrogen and helium envelopes in pre-SN mass loss.
Traditional single-star evolution models explain this mass loss with line-
driven winds (e.g., Heger et al., 2003), where progenitor mass and metallicity
correlate with the degree of mass lost.

New evidence over the past 15 years has begun to shift this paradigm. For
example, Smartt (2009) highlights a lack of massive, single-star progenitors
to SNe Ib/c detected in pre-explosion imaging. Smith et al. (2011) find that
an initial mass function (IMF) of solely single stars cannot adequately
reproduce the observed fractions of stripped-envelope SNe. Drout et al. (2011)
show that SNe Ib/c have relatively low ejecta masses; stellar winds are
generally too weak to remove the entire outer envelope on their own (Smith,
2014), except perhaps in the most massive (and rare) stars. Sana et al. (2012)
report that $>30$% of massive stars form in some sort of interacting binary
system.

Binary-star physics is important for our understanding of massive-star
evolution and many areas of astrophysics, from galactic chemical evolution to
gravitational-wave detection (Belczynski et al., 2016). While massive binary
star models for SN progenitors have existed for decades (e.g., Podsiadlowski
et al., 1992), the detailed physics (e.g., winds, mass exchange, rotation)
remain unconstrained (e.g., Zapartas et al., 2017; Eldridge et al., 2017). A
comprehensive, statistically complete sample of direct companion observations
is necessary to measure the binary fraction, stellar type, and mass
distribution, but such observations remain sparse.

The search for a surviving binary companion star to a stripped-envelope SN is
demanding, requiring high-resolution and subpixel astrometric precision.
Furthermore, optical searches are likely insufficient, as potential surviving
companions may be hot, blue main-sequence (MS) stars with a mass distribution
peaking at $\sim 9$–10 M⊙, which typically correspond to O-type and B-type
stars peaking at ultraviolet (UV) wavelengths $<2000\,\AA$ (e.g., Zapartas et
al., 2017). To date, only a handful of candidate companion direct detections
exist: the Type IIb 1993J (Van Dyk et al., 2002; Maund et al., 2004; Fox et
al., 2014), the Type IIb 2001ig (Ryder et al., 2018), the Type IIb 2011dh
(Bersten et al., 2012; Benvenuto et al., 2013; Folatelli et al., 2014), and
the Type Ibn SN 2006jc (Maund et al., 2016; Sun et al., 2020). The nature of
some, if not all, of these sources is still ambiguous. In any case, no post-
explosion detections of a binary companion exist yet for fully stripped SNe
Ib/c, although pre-explosion spectral energy distributions (SEDs) suggest the
possible presence of a companion source in the case of SN Ib iPTF13bvn (Cao et
al., 2013; Eldridge & Maund, 2016; Folatelli et al., 2016) and SN Ib 2019yvr
(Kilpatrick et al., 2021; Sun et al., 2021).

SN 2013ge is a Type Ic (or possibly a Ib) SN discovered on 2013 Nov. 8.796
2013 (UT dates are used throughout this paper) in NGC 3287 (Nakano et al.,
2013). Multiwavelength (radio to X-ray) observations were obtained from $-13$
to +457 days relative to maximum light, including a series of optical spectra
and Swift UV–optical photometry beginning 2–-4 days post-detection. Drout et
al. (2016) presented a detailed analysis of these data. The properties of the
SN 2013ge light curves are within the distribution observed for SNe Ib/c, but
several unique features stand out. The spectrum is predominantly that of a
fully stripped SN Ic, but Drout et al. (2016) give it a Type Ib/c
classification owing to evidence for weak He features at early times. Drout et
al. (2016) derive a pseudobolometric light curve for SN 2013ge assuming
$E(B-V)_{\rm tot}=0.067$ mag. Although not the faintest stripped-envelope
explosion ever seen, the bolometric light curve of SN 2013ge is fainter by
nearly an order of magnitude compared to many other SNe Ib/c. It also evolves
more slowly and shows two distinct components in the $u$ and UV bands,
including a relatively long rise time ($\sim 4$–6 days) for the first
component. To describe these characteristics, Drout et al. (2016) proposed
different potential progenitor scenarios, including an extended envelope, a
small ejection $<1$ yr prior to explosion, or an asymmetric ejection of a
small amount of nickel-rich material at high velocities.

Here we present deep, late-time HST/WFC3 observations of the position of SN
2013ge more than 4 years after we expect the SN radioactive component to have
faded, with an intent to search for a surviving companion. Section 2 presents
our HST observations and detection of a point source at the position of SN
2013ge. We include estimates for reddening, distance, and metallicity. Our
analysis is given in Section 3, where we fit the detected point source with an
SED and consider various physical origins, including the progenitor star’s
surviving companion. Section 4 discusses our conclusions.

##  2 Observations

Table 1: HST/WFC3 Imaging  UT Date | MJD | Epoch | Filter | Exposure | SN Magnitude | Star B Magnitude
---|---|---|---|---|---|---
|  | (days) |  | (s) | Vega (err) | Vega (err)
20161031 | 57692 | 1088 | F814W | 780 | 23.84 (0.09) | 25.67 (0.25)
F555W | 710 | 24.41 (0.05) | 25.54 (0.08)
20170601 | 57905 | 1301 | F300X | 1200 | — | —
F475X | 350 | — | —
20190502 | 58605 | 2001 | F814W | 780 | 24.79 (0.14) | 25.77 (0.30)
F555W | 710 | 25.36 (0.11) | 25.44 (0.12)
20201026 | 59148 | 2544 | F275W | 13803 | 25.03 (0.13) | 25.04 (0.09)
F336W | 8090 | 24.96 (0.05) | 24.75 (0.05)
F438W | 1000 | 25.83 (0.15) | 25.87 (0.17)
F555W | 700 | 26.23 (0.17) | 25.57 (0.11)

Table 1 summarizes the observations obtained of SN 2013ge with the HST
WFC3/UVIS channel as part of program GO-16165 (PI O. Fox), as well as archival
data for GO-15166 (PI A. Filippenko), GO-14762 (PI J. Maund), and GO-14668 (PI
A. Filippenko). The individual UVIS flc frames in all bands are obtained from
the Barbara A. Mikulski Archive for Space Telescopes (MAST) at
http://dx.doi.org/10.17909/c55c-rc43. The data followed standard pipeline
processing. The frames in each band then have cosmic-ray hits masked and are
combined into mosaics by running them through AstroDrizzle in PyRAF.

We locate the position of the SN in the new image mosaics using the HST/WFC3
data from 2016 and 2019 to track the SN as it fades in the F555W filter.
Figure 1 identifies the fading source and a bright, neighboring source that
does not get fainter, which we call “Source B.” The nature of Source B is not
clear, but it is located 2.8 UVIS pixels from the fading source.

###  2.1 HST/WFC3 Photometery

We perform photometry by running DOLPHOT (Dolphin, 2000) on individual (flc)
images, which are calibrated and aligned to a reference drizzled frame. Source
detection is performed on a virtual stack, and photometry is obtained by
forced point-spread-function (PSF) fitting to each source on the individual
frames. The individual flc measurements are merged to provide single
measurements for each star in each observed bandpass. We make no charge-
transfer efficiency (CTE) corrections as images have already been corrected
for CTE prior to the photometry. We apply standard aperture corrections
measured from the isolated bright stars in each exposure to account for any
differences between the true PSF and the model. We did not measure photometry
on the 2017 F300X and F475X data (GO-14762) because the combination of the “X”
filters and subarray readout are not supported currently by DOLPHOT. The
photometry for these filters is beyond the scope of this paper, but we list
the data-set in Table 1 as a reference.

Table 1 lists the photometry for both the fading source and Source B. Given
that the F555W and F814W photometry of Source B is consistent with no change
of flux, combined with the fact that the location of Source B is separated
from the candidate companion by more than 2 pixels, we conclude that Source B
is not significantly contributing to the photometry of the fading source.
Figure 2 plots the F555W photometry of the fading source for future reference.

Figure 1: Late-time HST/WFC3 UVIS imaging of the position of SN 2013ge
spanning 2016 through 2020 as summarized in Table 1. The F555W images offers
the only constant filter throughout all three epochs and show the fading SN to
the southeast of a constant, brighter source (“Source B”). We use the centroid
of this fading source to obtain PSF photometry for the analysis in the paper,
as described in the text.

###  2.2 Distance and Reddening Estimates

Distance: Drout et al. (2016) adopted a distance of $23.7\pm 1.7$ Mpc,
corresponding to the NED distance after correcting for Virgo, Great Attractor,
and Shapley Supercluster infall, and H0 = 73 km s-1 Mpc-1. The distance,
however, is quite uncertain. Cosmicflows-3 (Tully et al., 2016) yields a much
smaller value of 14.6 Mpc, whereas the distance from the Numerical Action
Methods model (NAM; Kourkchi et al., 2020) is 21.8 Mpc. For lack of any more
precise estimator of the distance, and given that the NAM distance is
consistent (within the errors) with the value chosen by Drout et al. (2016),
we adopt that latter distance here as well. This distance serves as a
conservative estimate since a closer distance would only correspond to a less-
massive star.

Reddening: Drout et al. (2016) adopted a total reddening to SN 2013ge of
$E(B-V)_{\rm tot}=0.067$ mag and $R_{V}=3.1$. This consists of a Galactic
foreground of $E(B-V)_{\rm Gal}=0.02$ mag from Schlafly & Finkbeiner (2011),
and a host-galaxy contribution of $E(B-V)_{\rm host}=0.047$ mag based on the
empirical relationship between the equivalent width (EW) of Na i D and dust
(Poznanski et al., 2012). Given that quantitative relations between Na i D EW
and $E(B-V)$ may be highly uncertain (Phillips et al., 2013), we explored
other possible reddening and extinction laws, but found that different values
did not significantly change any of our conclusions. For the rest of this
paper, we therefore assume the same values used by Drout et al. (2016) listed
above.

Figure 2: $V$-band light-curve evolution of SN 2013ge. The early-time data are
from Drout et al. (2016), while the late-time photometry points were obtained
by HST and listed in Table 1. Overplotted is the typical slope from the
radioactive decay (Dessart et al., 2016), scaled to the observed light-curve
as a reference. The light curve shows signs of continued fading, which may
signify some component of CSM shock interaction at these wavelengths. However,
like for SN 1993J, the dominant blue component of the SED in Figure 3 is
evidence for the emerging component of a hot, blue source not associated with
CSM interaction that we consider to be the putative progenitor companion. This
scenario is discussed further in Section 3.2. Figure 3: Photometry of SN
2013ge obtained in 2020 (red circle; Table 1). For comparison, overplotted are
several different stellar models scaled to roughly the observed F275W value
with an applied extinction $E(B-V)=0.067$ mag and $R_{V}=3.1$. Also shown are
the synthetic photometry for the B5 I model (black circle). Specific stellar
model properties are as follows (temperature, log $Z$ metallicity, and log $g$
gravity): B5 I (14000, -0.3, 2.44), A0 I (9730, -0.3, 2.14), B0 I (19000,
-0.3, 3.0), B0 III (29000, -0.3, 3.5), B5 III (15000, -0.3, 3.5). The left and
right ordinate axes are not directly aligned owing to the fact that any flux
corresponds to a different Vega magnitude in each filter. The overplotted
models should only be used for qualitative comparisons. While no model from
the catalog matches perfectly to the observations, we find the SED is most
consistent with a B5 I (supergiant) or III (giant).

Figure 4: Single-star evolutionary tracks of 10 and 12 M⊙ stars in MIST for
different HST/WFC3 filters, plotted in both (left) temperature and (right)
color space. Overplotted are values for SN 2013ge (solid circles), in addition
to the calculated limiting magnitudes of our designed observations (dashed
horizontal lines). The source detected at the position of SN 2013ge is redward
of the MS and consistent with $\sim 12$ M⊙ B5 I star crossing the Hertzsprung
Gap (HG) toward becoming a giant, with an absolute magnitude F275W $=-6.5$
(Vega).

##  3 Analysis

Figure 3 plots the 2020 SED of the primary source in Figure 1. We first
consider the possibility that the source is the surviving companion to the
progenitor of SN 2013ge, which would mark the first post-explosion direct
detection of a surviving companion to a fully stripped-envelope SN Ib/c. We
also outline other possible scenarios, including a fading SN, CSM interaction,
a line-of-sight coincidence, and a star cluster to which the progenitor
belonged.

###  3.1 The Companion Scenario

We start with the initial assumption that the detected source is the surviving
companion star of the primary star that exploded. We fit the photometry with
spectra from Castelli and Kurucz Stellar Atmosphere Models (Castelli & Kurucz,
2004) using stsynphot111https://stsynphot.readthedocs.io/en/latest/index.html
and extinction222https://extinction.readthedocs.io/en/latest/. Figure 3 shows
comparisons of various stellar models. We find the best-fitting spectrum
(i.e., lowest $\chi^{2}$) is a B5 I model ($T_{\rm eff}=14,000$ K and log g =
2.44), assuming a reddening consistent with an extinction of $E(B-V)\sim
0.067$ mag and $R_{V}=3.1$. We note that the synthetic photometry results do
not perfectly align with the spectrum because a constant flux corresponds to a
different Vega magnitude in each filter, so that the two ordinate axes (left
and right) do not correspond one-to-one. The overplotted models should only be
used for qualitative comparisons.

Figure 4 goes on to plot the absolute magnitudes of the source in a color-
magnitude diagram (CMD). Overplotted as a reference are single-star
evolutionary models for a 10 and 12 M⊙ star from MIST (Choi et al., 2016).
Assuming that a single star currently dominates the light, the detected source
is consistent with a 12 M⊙ B5 I-type star crossing the Hertzsprung Gap (HG)
toward becoming a red supergiant, with an absolute magnitude F275W $=-6.5$
(Vega). We note that if the galaxy distance is indeed 14.6 Mpc (see Section
2.2), then the absolute magnitude would be dimmer by $\sim 0.7$ mag,
corresponding to a 10 M⊙ star.

The position on the CMD is redward of the MS. One possibility for this is that
it is a very luminous MS star that is reddened by pre-existing or newly formed
dust, although the optical spectra did not indicate significant reddening or
evidence for late-time dust formation (Drout et al., 2016). Furthermore, a
large mid-infrared sample of SNe indicates that dust formation is not common
in SNe Ib/c, most likely owing to the high velocities of these SE ejecta
(e.g., Szalai et al., 2019).

A cool and inflated non-MS companion is unusual in existing model predictions
because the companion would need to have a similar initial mass as the primary
Claeys et al. (2011). In this case, the companion may have also evolved past
its MS at the moment of the progenitor’s explosion. The star passes through
this position during the hydrogen-shell burning phase on a relatively short
thermal timescale, making the likelihood of it being at this evolutionary
state at the time of the primary explosion $\lesssim 1.0\%$ (Zapartas et al.,
2017). Alternatively, the companion might be a blue central helium burning
star. This is a slower evolutionary phase and hence more likely and has been
suggested for stars in binaries that have gained mass (e.g. Justham et al.,
2014). It is interesting to note that modeling of the pre-explosion photometry
of the Type Ib SN 2019yvr also suggests that the potential companion is not an
MS star (Sun et al., 2021).

Another possibility is that the companion was temporarily brought out of
thermal equilibrium by the primary star, either pre-SN or post-SN. The thermal
timescale is of the order of 10,000 years. In the pre-SN scenario, mass
transfer from the primary would cause the companion to grow in size and become
more luminous (e.g., Claeys et al., 2011). This scenario requires fine-tuning
as the SN needs to have happened within a thermal timescale of the the last
mass transfer event. In the post-SN scenario, interaction of the SN ejecta
with the companion would leave the companion’s envelope in an inflated state
that gives it a cool and inflated position on the CMD (e.g., Ogata et al.,
2021).

###  3.2 Fading Source and Shock Interaction

One common explanation for a late-time detection of a SN is that the source is
still fading or is driven by shock interaction with a dense CSM, but such
scenarios are typically associated with SNe with known shock interaction, such
as SNe IIn (e.g., Fox et al., 2020). The early spectra of SN 2013ge show no
signs of CSM interaction, although one explanation for the unusual double peak
may have been a small ejection $<1$ yr prior to the explosion (Drout et al.,
2016). While SNe Ib/c typically explode in a low-density environment formed by
years of progenitor winds, some SNe Ib/c are known to exhibit early-time CSM
interaction (e.g., Hosseinzadeh et al., 2017), and a growing number of late-
time observations have revealed that some SNe Ib/c may encounter a pre-
existing shell years after the initial explosion (e.g., Milisavljevic et al.,
2012), including SN 2019yvr discussed above (Sun et al., 2021).

While SN 2013ge is too faint for late-time spectra, Figure 2 shows the light
curve of SN 2013ge. The only consistent filter across all the late-time HST
photometry is F555W (Table 1). The fluxes are significantly above any fading
emission from the radioactive decay, but the F555W photometry alone cannot
rule out the possibility of declining shock interaction.

The UV photometry offers a powerful tool for disentangling this scenario and
is reminiscent of the Type IIb SN 1993J, which showed both a declining shock-
interaction component at optical wavelengths and an emerging UV component from
the surviving companion (Fox et al., 2014). The shape of the late-time SED for
SN 2013ge in Figure 3 is too blue to be explained by shock interaction alone,
which is a flatter spectrum across all bands (see Fig. 11 of Fox et al.
(2014)). While we cannot definitively rule out a shock-interaction component
in the optical bands, any such component is not strongly impacting our UV
analysis.

###  3.3 Line-of-Sight Coincidence or Stellar Cluster

The photometric SED of the putative stellar companion may not be easily
distinguishable from some clusters or even just a handful of stars within a
cluster. The WFC3 scale of 0″.0396 pixel-1 corresponds to $\sim 3.8$ pc
pixel-1 at 20 Mpc. We consider several examples. The association Ru 141 has a
physical radius of $\sim 7$ pc and a single dominant star (Camargo et al.,
2009). If SN 2013ge exploded in such an environment, we estimate a $\sim 30$%
chance of having the unassociated star land on the same pixel as SN 2013ge.
NGC 2004 (20 Myr and $R_{\rm eff}\approx 6$ pc) is one of the worst-case
scenarios with $\sim 10$ stars brighter than $M_{\rm F275W}>-5$ mag
(Niederhofer et al., 2015). At a distance of $\sim 20$ Mpc, such a cluster
would be spread over $\sim 4$ pixels, implying the potential for up to 3
bright stars per pixel. The radii of both of these clusters, however, are
quite a bit smaller than the size of a typical OB association, which is often
spread over $\sim 10$–20 pc (Smith et al., 2010). Accounting for a factor of
$\sim 3$–10 times larger in area, we therefore conclude that the likelihood of
a chance alignment with an unresolved cluster or a bright star in a host
cluster for our system is $<10\%$.

We can infer a minimum age of the progenitor system by assuming that all of
the observed light is attributable to the most massive star in the system or
the associated unresolved cluster. We assume our measured F438W luminosity of
$-5.5$ is the maximum luminosity of any surviving companion (i.e., higher-mass
stars would have yielded a larger luminosity). By comparing this luminosity to
the PARSEC models (Bressan et al., 2012), it corresponds to an evolved star of
12 M⊙ and a cluster age of $\sim 20$ Myr. This is consistent with our model
fitting in Figures 3 and 4. If the flux is contributed by several stars, the
cluster would be even older.

##  4 Conclusion and Future Work

This study reports the first potential post-explosion direct detection of a
surviving companion star to a stripped-envelope SN of Type Ic (or possibly
Ib). If the source is a single star, it is consistent with a $\sim 12$ M⊙ B5 I
star with an absolute magnitude of F275W $=-6.5$ (Vega). The case for the
surviving companion still requires additional observations and theoretical
advancements. Similar to the case of SN 1993J (Fox et al., 2014), ongoing deep
HST UV photometry will be able to rule out shock interaction by confirming
that, even if the source fades in the optical, it is not fading in the UV.
Similar to the analysis of SN 2017ein (Van Dyk et al., 2018), a complete SED
of SN 2013ge should be compared to existing photometry of star clusters to
rule out the possibility of any confusion from such a source. The prospect of
further constraining the distance or reddening is slim given that HST cannot
obtain observations of resolved stellar populations at this distance (e.g.,
the TRGB method), although such an experiment may be possible with JWST. From
the theoretical perspective, the possibility of a cool, inflated non-MS
companion must be better understood using existing binary evolution models,
including BPASS (Eldridge et al., 2017) and population synthesis (Zapartas et
al., 2017). These models, however, are limited by not accounting for accretion
and generally not predicting evolved companions. In this case, a more
empirical comparison to evolved stars with UV spectra is likely necessary.

Looking forward, the field would benefit from working on a larger sample. A
comprehensive, statistically complete sample of direct companion observations
is necessary to measure the fraction of surviving companions in binaries
(which we refer to as the “binary fraction”), the stellar types, and the mass
distribution. Deep upper limits also help in this respect. Many of the model
variants of Zapartas et al. (2017) predict a surviving companion in a majority
of cases, and the associated mass distributions tend to be quite broad,
peaking at $\sim 10$–12 M⊙. Deep upper limits down to the detection threshold
at this particular mass range present a testable hypothesis: observations of
historical stripped-envelope SNe should result in a nondetection roughly half
the time (assuming a roughly symmetric distribution). As the sample grows, the
binary fraction can more thoroughly constrain the various models, and
ultimately distinguish between stellar progenitor and binary evolution
scenarios.

## Acknowledgements

This research is based on observations made with the NASA/ESA Hubble Space
Telescope obtained from the Space Telescope Science Institute (STScI), which
is operated by the Association of Universities for Research in Astronomy,
Inc., under NASA contract NAS 5–26555. These observations are associated with
programs GO-16165 (PI O. Fox), GO-15166 (PI A. Filippenko), GO-14762 (PI J.
Maund), and GO-14668 (PI A. Filippenko); we are also grateful for the
associated funding from NASA/STScI. O.D.F. would like to thank Karl Gordon for
useful conversations on dust. E.Z. acknowledges support from the Swiss
National Science Foundation Professorship grant (project PP00P2 176868; PI
Tassos Fragos). M.R.D. acknowledges support from the NSERC through grant
RGPIN-2019-06186, the Canada Research Chairs Program, the Canadian Institute
for Advanced Research (CIFAR), and the Dunlap Institute at the University of
Toronto. In addition to the NASA/STScI funding, A.V.F. received support from
the Miller Institute for Basic Research in Science (where he was a Miller
Senior Fellow) and the Christopher R. Redlich Fund. D. M. acknowledges NSF
support from grants PHY-1914448 and AST-2037297.

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#  In situ control of integrated Kerr nonlinearity

Chaohan Cui  James C. Wyant College of Optical Sciences, The University of
Arizona, Tucson, Arizona 85721, USA  Liang Zhang  James C. Wyant College of
Optical Sciences, The University of Arizona, Tucson, Arizona 85721, USA
Linran Fan<EMAIL_ADDRESS>James C. Wyant College of Optical
Sciences, The University of Arizona, Tucson, Arizona 85721, USA

Kerr nonlinearity in nanophotonic cavities provides a versatile platform to
explore fundamental physical sciences and develop novel photonic technologies
[1, 2, 3]. This is driven by the precise dispersion control and significant
field enhancement with nanoscale structures. Beyond dispersion and pump
engineering, the direct control of Kerr nonlinearity can release the ultimate
performance and functionality of photonic systems. Here, we report the in situ
control of integrated Kerr nonlinearity through its interplay with the
cascaded Pockels nonlinear process [4, 5, 6]. Kerr nonlinearity is tuned over
10 dB dynamic range without modifying photonic structures. Fano resonance is
observed with nonlinear spectrum, in contrast to standard linear transmission.
This confirms the quantum interference between competing optical nonlinear
pathways. Besides nonlinearity enhancement, we also demonstrate the novel
capability to suppress the material intrinsic nonlinearity. Finally, we use
the tunable nonlinearity to control the spectral brightness and coincidence-
to-accidental ratio of single-photon generation. This work paves the way
towards the complete nanoscale control of optical nonlinear processes at
quantum level.

The dynamic control of optical properties plays an indispensable role in a
great number of fields. The linear optical properties such as refractive index
and absorption can be modified in nanophotonic circuits using a wide variety
of phenomena including thermal [7], electrical [8, 9], mechanical [10], and
free-carrier effects [11]. It allows the modulation of optical fields with
broad applications ranging from laser systems to optical communications.
Recently, such linear control has also been used to demonstrate novel
functions including the reconfigurable generation of topological photonic
states [12, 13], the photonic acceleration of machine learning algorithms [14,
15], and the realization of universal photonic quantum gates [16, 17].

Figure 1: Effective Kerr nonlinearity with cascaded Pockels process. a,
Intrinsic Kerr process. Two pump photons are annihilated to generation one
signal and one idler photon b, Cascaded Pockels process. Two pump photons are
annihilated to generation one second-harmonic photon, which drives the
parametric down-conversion to generate one signal and one idler photon. Figure
2:  Enhancement of Kerr nonlinearity. a, Scanning electron microscope image of
the fabricated aluminum nitride device with the ring cavity (blue), the bus
waveguide for second-harmonic field (purple), and the bus waveguide for pump,
idler, and signal fields (green). Scale bar 20 $\mu$m. b, Pump transmission
(green) and second-harmonic (purple) spectrum. Two sets of modes for FWM, with
(red) and without (gray) Pockels phase-matching, are labeled. c, The output
optical spectrum of the stimulated FWM. d, The output signal (red and gray)
and second-harmonic power (purple) with different pump power. e, The pump
efficiency (red and gray) and second-harmonic power (purple) with different
idler input power. Results in c, d, and e using the reference mode set and the
mode set with Pockels phase-matching are presented in red and gray
respectively. Experimental data (circles) are fitted with the theoretical
model (solid lines).

Similarly, the control of optical nonlinear properties will lead to
significant scientific and technological advances. The nonlinearity
enhancement into single-photon strong-coupling regime is essential to build
deterministic quantum gates [18, 19, 20]. The nonlinearity suppression is
critical to fundamentally improve the sensitivity of optical sensors [21, 22]
and the capacity of optical communications [23, 24]. The phase inversion of
the nonlinear interaction can enable the generation of novel soliton states
[25, 26]. Currently, optical nonlinear processes can only be controlled
indirectly using intra-cavity photon number and dispersion. Therefore, the
achievable nonlinearity and functionality are limited to the material’s
intrinsic property. In this Letter, we use a novel method to control Kerr
nonlinearity beyond the material limit. By designing its interference with
cascaded Pockels processes [4, 5, 6], the complete amplitude and phase control
of Kerr nonlinearity can be realized. Besides the enhancement of Kerr
nonlinearity [27], we also observe novel effects including the nonlinearity
suppression and Fano resonances in the nonlinear regime. The effective Kerr
nonlinearity is highly tunable over 10 dB dynamic range with fixed photonic
structures. We further validate the control of Kerr nonlinearity in both
classical and quantum regime through nonlinear frequency conversion and
single-photon generation.

In the degenerate configuration of Kerr nonlinear processes, two pump photons
are annihilated to generate one signal and one idler photon, or vice versa
(Fig. 1a). The nonlinearity is fixed by the material property and photonic
structure. To modify the Kerr nonlinearity, we design a cascaded Pockels
nonlinear process shown in Fig. 1b. In this process, two pump photons first
combine to generate one second-harmonic photon. Then the second-harmonic
photon drives the parametric down-conversion process in the same photonic
cavity to generate one signal and one idler photon. The effective interaction
Hamiltonian for the cascaded Pockels nonlinear process is

$H_{\mathrm{I}}=-\frac{1}{2}\hbar(g_{c}\hat{b}_{p}^{\dagger
2}\hat{b}_{s}\hat{b}_{i}+g_{c}^{*}\hat{b}_{p}^{2}\hat{b}_{s}^{\dagger}\hat{b}_{i}^{\dagger}),$
(1)

with $\hat{b}_{p}$, $\hat{b}_{s}$, and $\hat{b}_{i}$ the annihilation
operators of the pump, signal, and idler modes respectively (Supplementary
Information section I). The effective cascaded Pockels nonlinear strength
$g_{c}$ at single-photon level is defined as

$g_{c}=\frac{-i|g_{2}|^{2}}{i\Delta+\gamma/2},$ (2)

with $g_{2}$ the Pockels nonlinear strength, $\Delta$ the frequency detune
between the pump and second-harmonic modes, and $\gamma$ the decay rate of the
second-harmonic mode. This interaction Hamiltonian has the same form with
intrinsic Kerr nonlinear processes. With highly efficient Pockels nonlinear
processes, the effective Kerr nonlinearity can be significantly enhanced.

Figure 3: Quantum interference between nonlinear processes. a, Schematic for
the quantum interference between intrinsic Kerr and cascaded Pockels process.
b, Vector diagram showing the coherent interaction between the intrinsic Kerr
and cascaded Pockels process. Phase $\varphi$ can be controlled by the
frequency detune $\Delta$. Intrinsic Kerr nonlinearity is normalized to 1, and
the tuning range of the effective Kerr nonlinearity is bounded to the circle
with radius $\xi$. c, Calculated effective Kerr nonlinearity $|g_{\rm
eff}/g_{3}|$ in logarithm scale. d, Calculated maximum and minimum effective
Kerr nonlinearity. The shaded area indicates the accessible range of the
effective Kerr nonlinearity.

To implement the cascaded Pockels nonlinear process, we use a nanophotonic
ring cavity made of aluminum nitride (Fig. 2a). The phase-matching condition
for the Pockels nonlinear process is satisfied using a high-order transverse-
magnetic (TM) second-harmonic mode and a fundamental TM pump mode
(Supplementary Information section II). Strong second-harmonic generation is
observed with pump wavelength near 1518 nm (Fig. 2b). The second-harmonic
generation efficiency is measured as $\eta\approx 1800\%/$W, leading to the
estimated Pockels nonlinear strength $g_{2}\approx 2\pi\times 81$ kHz
(Supplementary Information section II). With the small decay rate of the
second-harmonic mode ($\gamma\approx 2\pi\times 4.5$ GHz), we can expect the
enhanced Kerr nonlinearity around $|g_{\rm c}|\approx 2\pi\times 3$ Hz at zero
frequency detune, which is six-fold higher than the intrinsic value
($g_{3}\approx 2\pi\times 0.5$ Hz).

The enhancement of the Kerr nonlinearity is first verified with stimulated
four-wave mixing (FWM) for frequency conversion in the classical domain. With
strong pump ($P_{p}$), we measure the conversion from the idler input
($P_{i}$) to the signal output ($P_{s}$). We use two sets of modes from the
same nanophotonic cavity to measure the intrinsic and enhanced Kerr single-
photon nonlinearity respectively. The pump mode of the reference set is not
phase-matched to the Pockels nonlinear process. Therefore, only the intrinsic
Kerr nonlinearity contributes to the nonlinear frequency conversion. The pump
mode of the other set is phase-matched to the Pockels nonlinear process. As a
result, the enhanced Kerr nonlinearity dominates the nonlinear frequency
conversion. The two sets of modes share similar quality factors and coupling
conditions. Consequently, the influence of different cavity-enhancement
factors and extraction efficiencies can be eliminated (Supplementary
Information section II). The generation of the signal field is observed from
the output optical spectrum with both mode sets (Fig. 2c). Comparing the two
mode sets, the signal output of the phase-matched set is significantly higher
than the reference set even though smaller pump and idler inputs are used. To
calibrate the enhancement factor, we fix the input idler power ($P_{i}$) and
vary the input pump power ($P_{p}$). To achieve the same signal output
($P_{s}$), the cascaded Pockels nonlinear process uses 7.5 dB less pump power
than the intrinsic Kerr nonlinearity (Fig. 2d). This agrees well with the
difference between the enhanced and intrinsic Kerr single-photon nonlinearity
($|g_{c}/g_{3}|\approx 6$).The critical role of the Pockels nonlinear process
is further confirmed by the increased second-harmonic generation with respect
to the pump power (Fig. 2d). The same conclusion is obtained from the
measurement with different input idler power ($P_{i}$). With the same pump
power, the cascaded Pockels process can generate approximately 15 dB stronger
signal output. The second-harmonic generation remains constant during the
process, which confirms that the second-harmonic field is generated from the
pump.

Figure 4: Continuous tuning of Kerr single-photon nonlinearity in quantum
regime. a, c, Single-photon generation rate from spontaneous FWM using
effective Kerr nonlinearity with $\xi=0.14$ and $\xi=0.92$ respectively. The
data is normalized to the count rate with the intrinsic Kerr nonlinearity
(gray dashed line). b, d, Single-photon generation rate from spontaneous
parametric down-conversion with $\xi=0.14$ and $\xi=0.92$ respectively. e,
Single-photon generation rate (red circle) with different pump power.
Calculated background dark count (black dashed), pump-induced noise (green
dashed), signal photon rate (red dashed), and total photon rate (red solid)
are plotted. All photon counting data are measured from signal resonances. f,
Signal-idler coincidence count with frequency detune $\Delta=-2\pi\times 0.7$
GHz (red point) and $\Delta=2\pi\times 1.5$ GHz (blue point). Pump power is 1
mW. The accidental coincidence outside the coherent window is normalized to 1.
g, CAR under different pump power with frequency detune $\Delta=-2\pi\times
0.7$ GHz (red) and $\Delta=2\pi\times 1.5$ GHz (blue). Circle, measured CAR
from signal-idler coincidence. Line, calculated CAR from calibrated signal and
noise photon rates.

The coherent interaction between multiple nonlinear processes can be used to
tune the overall nonlinear response. This enables the complete control over
the amplitude and phase of the Kerr single-photon nonlinearity. Taking both
the intrinsic Kerr and cascaded Pockels nonlinear processes into account (Fig.
3a), the effective Kerr nonlinearity can be written as

$\displaystyle g_{\rm
eff}=g_{3}+g_{c}=g_{3}-\frac{ig_{2}^{2}}{i\Delta+\gamma/2}$ (3)

The relative phase $\varphi$ between the two nonlinear processes can be
controlled by the frequency detune $\Delta$ (Fig. 3b). Both constructive and
destructive interference can be realized, leading to the enhancement and
suppression of the Kerr nonlinearity respectively (Fig. 3c). Here, we define
the relative strength between the two nonlinear processes as

$\displaystyle\xi=|g_{2}|^{2}/(g_{3}\gamma).$ (4)

The maximum and minimum effective single-photon nonlinearity $|g_{\rm
max/min}|=g_{3}\left(\frac{\sqrt{1+\xi^{2}}\pm\xi}{\sqrt{1+\xi^{2}}\mp\xi}\right)^{1/2}$
can be obtained at frequency detunes
$\Delta=\frac{\gamma}{2}(\xi\mp\sqrt{1+\xi^{2}})$. Therefore, larger tuning
dynamic range can be achieved with more efficient Pockels nonlinear processes
(Fig. 3d).

To verify the quantum interference between the cascaded Pockels and the
intrinsic Kerr nonlinear processes, we perform single-photon generation with
spontaneous FWM. The frequency detune $\Delta$ is precisely controlled through
the device temperature (Supplementary Information section II). The pump light
is tuned in resonance with the pump mode to ensure that the intra-cavity pump
photon number remains constant. The single-photon generation rate of the
signal channel (proportional to $|g_{\rm eff}|^{2}$) is recorded to infer the
effective Kerr single-photon nonlinearity. We use two different Pockels
nonlinear strengths corresponding to $\xi=0.14$ and $\xi=0.92$ respectively by
selecting two different phase-matching modes. The single-photon count rate
shows Fano lineshape in both cases (Fig. 4a and c), indicating the coherent
interaction between two competing optical nonlinear processes. Larger tuning
dynamic range of the Kerr nonlinearity is achieved with the stronger Pockels
nonlinear strength ($\pm 0.6$ dB with $\xi=0.14$ vs. $\pm 3.6$ dB with
$\xi=0.92$), which matches our theoretical model (Fig. 3c). As reference, we
also measure the single-photon generation rate with parametric down-conversion
by pumping a visible laser into the cavity under different frequency detune
(Fig. 4b and d), which shows Lorentzian lineshape. This confirms the quantum
interference between the broad-band intrinsic Kerr process and the narrow-band
cascaded Pockels nonlinear process. It is noteworthy that Fano resonances in
our experiment can only be observed with nonlinear spectrum, as the
interference happens between highly nonlinear processes. This is in contrast
to Fano resonances introduced by linear coupling between resonators, where
linear transmission is sufficient to observe the asymmetric lineshape [28].

Finally, we demonstrate the control of the coincidence-to-accidental ratio
(CAR) of the single-photon generation by changing the Kerr single-photon
nonlinearity. CAR is a critical parameter to characterize the quality of
single photon sources. In the low pump regime, background noise and leaking
pump dominate the total photon count. Therefore, CAR can be improved by
increasing the pump power. In the high pump regime, multi-photon generation
becomes the major noise source. As a result, CAR drops with increased pump
power. We first set the frequency detune $\Delta=2\pi\times 1.5$ GHz with
$\xi=0.92$ to achieve the maximum nonlinearity suppression (blue point in Fig.
4c). We measure the coincidence count between signal and idler photons to
extract the dependence of CAR on the pump power (Fig. 4f and g). The maximum
CAR of $9\pm 1$ is achieved using 3 dBm pump power. Next, we set the frequency
detune $\Delta=-2\pi\times 0.7$ GHz to realize the maximum nonlinearity
enhancement (red points in Fig. 4c). The maximum achievable CAR is $47\pm 2$
with -2 dBm pump power, corresponding to more than five-fold improvement. We
also calibrated photon rates of the background noise, pump-induced noise, and
parametric photon pairs (Fig. 4e) to directly calculate CAR, which agrees with
the result obtained from the coincidence measurement (Fig. 4f) (Supplementary
Information III).

We have demonstrated the in situ control of local Kerr nonlinearity by
designing the quantum interference between intrinsic Kerr and cascaded Pockels
processes. Nonlinear efficiency and novel functionalities beyond material
limits are realized. Further improvement can be readily achieved using
nanophotonic materials with larger Pockels nonlinearity [29, 30, 31] and low
loss design [32]. It can benefit a wide range of fields requiring strong Kerr
nonlinearity, including all-photonic signal processing [33], nonlinear
frequency conversion [34], and optical frequency comb [35, 36, 37, 38, 39].
More intriguingly, the demonstration of nonlinearity suppression and phase
control can open unique prospects for the study of nonlinear physics and
photonic technologies in both classical and quantum regime.

Methods

Device fabrication. Devices are fabricated from 1-$\mu$m AlN grown on sapphire
substrates by MOCVD. FOx-16 resist is used for patterning photonic circuits
with electron-beam lithography. After development with TMAH, plasma etching
with ${\rm Cl}_{2}$/${\rm BCl}_{3}$/Ar is used to transfer the pattern to the
AlN layer. Finally, ${\rm SiO}_{2}$ cladding is deposited by plasma-enhanced
chemical vapor deposition (PECVD).

CAR measurement. When calculating CAR, the coincidence count is averaged
within the coincidence peak ($\pm$ 1 ns) at zero delay. The accidental count
is estimated by averaging the coincidence count with large time delay outside
the peak.

Acknowledgments CC, LZ, and LF acknowledge the support from U.S. Department of
Energy, Office of Advanced Scientific Computing Research, (Field Work Proposal
ERKJ355); Office of Naval Research (N00014-19-1-2190); National Science
Foundation (ECCS-1842559). Device fabrication is performanced in the OSC
cleanrooms at the University of Arizona, and the cleanroom of Arizona State
University. Superconducting nanowire single-photon detectors are supported by
NSF MRI INQUIRE.

Data availability The data that support the findings of this study are
available from the corresponding author upon reasonable request

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