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Discovery of a double detonation thermonuclear supernova progenitor
Thomas Kupfer ,1Evan B. Bauer ,2Jan van Roestel ,3Eric C. Bellm ,4Lars Bildsten,5, 6 Jim Fuller,3
Thomas A. Prince,3Ulrich Heber ,7Stephan Geier,8Matthew J. Green,9Shrinivas R. Kulkarni ,3
Steven Bloemen,10 Russ R. Laher ,11 Ben Rusholme ,11 and David Schneider7
1Department of Physics and Astronomy, Texas Tech University, PO Box 41051, Lubbock, TX 79409, USA
2Center for Astrophysics |Harvard & Smithsonian, 60 Garden St, Cambridge, MA 02138, USA
3Division of Physics, Mathematics and Astronomy, California Institute of Technology, Pasadena, CA 91125, USA
4DIRAC Institute, Department of Astronomy, University of Washington, 3910 15th Avenue NE, Seattle, WA 98195, USA
5Kavli Institute for Theoretical Physics, University of California, Santa Barbara, CA 93106, USA
6Department of Physics, University of California, Santa Barbara, CA 93106, USA
7Dr. Karl Remeis-Observatory & ECAP, Astronomical Institute, Friedrich-Alexander University Erlangen-Nuremberg (FAU),
Sternwartstr. 7, 96049 Bamberg, Germany
8Institut f¨ur Physik und Astronomie, Universit¨at Potsdam, Haus 28, Karl-Liebknecht-Str. 24/25, D-14476 Potsdam-Golm, Germany
9Department of Astrophysics, School of Physics and Astronomy, Tel Aviv University, Tel Aviv 6997801, Israel
10Department of Astrophysics/IMAPP, Radboud University Nijmegen, P.O. Box 9010, 6500 GL Nijmegen, The Netherlands
11IPAC, California Institute of Technology, 1200 E. California Blvd, Pasadena, CA 91125, USA
(Received June 1, 2019; Revised January 10, 2019; Accepted October 26, 2021)
Submitted to ApJL
ABSTRACT
We present the discovery of a new double detonation progenitor system consisting of a hot sub-
dwarf B (sdB) binary with a white dwarf companion with an Porb=76.34179(2) min orbital period.
Spectroscopic observations are consistent with an sdB star during helium core burning residing on
the extreme horizontal branch. Chimera light curves are dominated by ellipsoidal deformation of the
sdB star and a weak eclipse of the companion white dwarf. Combining spectroscopic and light curve
fits we find a low mass sdB star, MsdB = 0.383 ±0.028 Mwith a massive white dwarf companion,
MWD = 0.725 ±0.026 M. From the eclipses we find a blackbody temperature for the white dwarf
of 26,800 K resulting in a cooling age of ≈25 Myrs whereas our MESA model predicts an sdB age of
≈170 Myrs. We conclude that the sdB formed first through stable mass transfer followed by a common
envelope which led to the formation of the white dwarf companion ≈25 Myrs ago.
Using the MESA stellar evolutionary code we find that the sdB star will start mass transfer in ≈6 Myrs
and in ≈60 Myrs the white dwarf will reach a total mass of 0.92 Mwith a thick helium layer of 0.17 M.
This will lead to a detonation that will likely destroy the white dwarf in a peculiar thermonuclear super-
nova. PTF1 J2238+7430 is only the second confirmed candidate for a double detonation thermonuclear
supernova. Using both systems we estimate that at least ≈1 % of white dwarf thermonuclear super-
novae originate from sdB+WD binaries with thick helium layers, consistent with the small number of
observed peculiar thermonuclear explosions.
Keywords: editorials, notices — miscellaneous — catalogs — surveys
1. INTRODUCTION
Most hot subdwarf B stars (sdBs) are core helium burning stars with masses around 0.5 Mand thin hydrogen
envelopes (Heber 1986,2009,2016). A large number of sdB stars are in close orbits with orbital periods of Porb <10 days
Corresponding author: Thomas Kupfer
tkupfer@ttu.edu
arXiv:2110.11974v1 [astro-ph.SR] 22 Oct 2021
2Kupfer et al.
(Napiwotzki et al. 2004;Maxted et al. 2001), with the most compact systems reaching orbital periods of .1 hour (e.g.
Vennes et al. 2012;Geier et al. 2013;Kupfer et al. 2017a,b,2020a,b). The only way to form such tight binaries is
orbital shrinkage through a common envelope phase followed by the loss of angular momentum due to the radiation
of gravitational waves (Han et al. 2002,2003;Nelemans 2010).
SdB binaries with white dwarf (WD) companions which exit the common envelope phase at Porb.2 hours will reach
contact while the sdB is still burning helium (Bauer & Kupfer 2021). Due to the emission of gravitational waves the
orbit of the binary will shrink until the sdB fills its Roche Lobe at a period of ≈30 −100 min, depending on the
evolutionary stage and envelope thickness of the hot subwarf (e.g. Savonije et al. 1986;Tutukov & Fedorova 1989;
Tutukov & Yungelson 1990;Iben & Tutukov 1991;Yungelson 2008;Piersanti et al. 2014;Brooks et al. 2015;Neunteufel
et al. 2019;Bauer & Kupfer 2021).
The known population of sdB + WD binaries consists mostly of systems with orbital periods too large to start
accretion before the sdB turns into a WD (Kupfer et al. 2015). Currently only four detached systems with a WD
companion are known to have Porb<2 hours (Vennes et al. 2012;Geier et al. 2013;Kupfer et al. 2017a,b;Pelisoli
et al. 2021). Just recently Kupfer et al. (2020a,b) discovered the first two Roche lobe filling hot subdwarfs as part
of a high-cadence Galactic Plane survey using the Zwicky Transient Facility (Kupfer et al. 2021). Both systems can
be best explained as Roche Lobe filling sdOB stars which have started mass transfer to a WD companion. The light
curves in both systems show deep eclipses from an accretion disc. Due to their high effective temperatures, both sdOB
stars are predicted to be in a short lived phase where the sdOB undergoes residual hydrogen shell burning.
The most compact known sdB binary where the sdB is still undergoing core-helium burning is CD–30◦11223. The
binary has an orbital period Porb =70.5 min and a high mass WD companion (MWD ≈0.75 M;Vennes et al. 2012;
Geier et al. 2013). The sdB in CD–30◦11223 will begin transferring helium to its WD companion in ≈40 Myr when
the system has shrunk to an orbital period Porb ≈40 min. After the WD accretes ≈0.1 M, helium burning is predicted
to be ignited unstably in the accreted helium layer on the WD surface (Brooks et al. 2015;Bauer et al. 2017). This
could either disrupt the WD even when the mass is significantly below the Chandrasekhar mass, a so-called double
detonation supernova (e.g. Livne 1990;Livne & Arnett 1995;Fink et al. 2010;Woosley & Kasen 2011;Wang & Han
2012;Shen & Bildsten 2014;Wang 2018) or just detonate the He-shell without disrupting the WD which results in a
faint and fast .Ia supernova with subsequent weaker He-flashes (Bildsten et al. 2007;Brooks et al. 2015). Therefore,
systems like CD–30◦11223 are predicted to be either the progenitors for double detonation thermonuclear supernovae
or perhaps faint and fast .Ia supernovae that do not disrupt the WD.
De et al. (2019,2020) presented the discovery of a sample of calcium-rich transients consistent with a thick helium
shell double detonation on a sub-Chandrasekhar-mass WD (Polin et al. 2019,2021). The majority of these transients
are located in old stellar populations with only a small sub-sample found in in star forming environments.
The question remains just how common systems like CD–30◦11223 are. To address this question we have conducted a
search for (ultra-)compact post-common envelope systems using the Palomar Transient Factory (PTF; Law et al. 2009;
Rau et al. 2009) and subsequently the Zwicky Transient Facility (ZTF; Graham et al. 2019;Masci et al. 2019) based
on a color selected sample from Pan-STARRS data release 1. The PTF used the Palomar 4800 Samuel Oschin Schmidt
telescope to image up to ≈2000 deg2of the sky per night to a depth of Rmould ≈20.6 mag or g0≈21.3 mag. PTF was
succeeded by the Zwicky Transient Facility which started science operation in March 2018 using the same telescope but
a new camera with a field-of-view of 47 deg2. Here we report the discovery of a new thermonuclear supernova double
detonation progenitor system consisting of an sdB with a WD companion: PTF1 J223857.11+743015.1 (hereafter
PTF1 J2238+7430) with orbital period of 76 min showing similar properties to CD–30◦11223.
2. OBSERVATIONS
2.1. Photometry
As part of the Palomar Transient Factory (PTF), the Palomar 48-inch (P48) telescope imaged the sky every night.
The reduction pipeline for PTF applies standard de-biasing, flat-fielding, and astrometric calibration to raw images
(Laher et al. 2014). Relative photometry correction is applied and absolute photometric calibration to the few per-
cent level is performed using a fit to SDSS fields observed in the same night (Ofek et al. 2012). The lightcurve of
PTF1 J2238+7430 has 144 epochs, with good photometry in the Rmould band with a typical uncertainty of 0.01-
0.02 mag. The majority of observations were conducted during the summer months June - August 2013 and 2014 and
the cadence is highly irregular, ranging from a few minutes to years. The object was also observed as part of the
Zwicky Transient Facility (ZTF) public survey (Graham et al. 2019;Bellm et al. 2019). Image processing of ZTF data
A new double detonation progenitor system 3
0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00
Phase
15.35
15.40
15.45
15.50
15.55
Magnitude [mag]
ZTF-
r
PTF-
R
0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00
400
300
200
100
0
100
200
300
400
RV (km\,s 1)
DBSP
ISIS
HIRES
ESI
0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00
Phase
25
0
25
RV (km\,s 1)
Figure 1. Left panel: Phase folded at Porb =76.341750 min ZTF and PTF light curve for PTF1 J2238+7430. Right panel:
Radial velocity plotted against orbital phase for PTF1 J2238+7430. The RV data were phase folded with the orbital period and
are plotted twice for better visualization. The residuals are plotted below.
is described in full detail in Masci et al. (2019). We extracted the light curve from ZTF data release 6 which consists
of 34 observations in ZTF-rtaken randomly over ≈1.5 years between August 2018 and November 2019.
High-cadence observations were conducted using the Palomar 200-inch telescope with the high-speed photometer
CHIMERA (Harding et al. 2016) which is a 2-band photometer which uses frame-transfer, electron-multiplying CCDs
to achieve 15 ms dead time covering a 5×5 arcmin field of view. Simultaneous optical imaging in two bands is enabled
by a dichroic beam splitter centered at 567nm. Data reduction was carried out with the ULTRACAM pipeline (Dhillon
et al. 2007) customized for CHIMERA. All frames were bias-subtracted and flat-fielded. 1300 observations in g0and
r0with a 5 sec exposure time were obtained on 2017-07-26 and 2700 observations in g0and i0with a 4sec exposure
time were obtained on 2017-12-14.
2.2. Spectroscopy
Optical spectra were obtained with the Palomar 200-inch telescope and the Double-Beam Spectrograph (DBSP; Oke
& Gunn 1982) using a low resolution mode (R∼1500). 31 consecutive exposures were obtained on 2017-05-25 and
2017-05-29 and 15 consecutive exposures were obtained on 2017-05-25 using a 180 sec exposure time. Each night an
average bias and normalized flat-field frame was made out of 10 individual bias and 10 individual lamp flat-fields. To
account for telescope flexure, an arc lamp was taken at the position of the target after each observing sequence. For the
blue arm, FeAr and for the red arm, HeNeAr arc exposures were taken. Both arms of the spectrograph were reduced
using a custom PyRAF-based pipeline 1(Bellm & Sesar 2016). The pipeline performs standard image processing and
spectral reduction procedures, including bias subtraction, flat-field correction, wavelength calibration, optimal spectral
extraction, and flux calibration.
Additionally PTF1 J2238+7430 was also observed with the William Herschel Telescope (WHT) and the ISIS spec-
trograph (Carter et al. 1993) using a medium resolution mode (R600B grating, R≈2500). 10 consecutive exposures
with an exposure time of 180 sec were obtained on 2017-07-26. 10 bias frames were obtained to construct an average
bias frame and 10 individual lamp flat-fields were obtained to construct a normalized flat-field. CuNeAr arc exposures
were taken before and after the observing sequence to correct for instrumental flexure. One dimensional spectra were
extracted using optimal extraction and were subsequently wavelength and flux calibrated.
To obtain high-resolution spectra, PTF1 J2238+7430 was observed with Keck/HIRES and Keck/ESI. We obtained
5 consecutive exposures with Keck/HIRES on 2017-08-14 and 2017-08-30 as well as 14 consecutive exposures with
Keck/ESI on 2018-07-20. ThAr arc exposures were taken at the beginning of the night. The spectra were reduced
1https://github.com/ebellm/pyraf-dbsp
4Kupfer et al.
3
2.8
2.6
2.4
2.2
2
1.8
1.6
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0.8
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normalized flux
H10
H9
H8
Hǫ
Hδ
Hγ
Hβ
60
40
20
0
-20
-40
-60
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A)
H12
H11
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ESI Hei4471
0.8
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ESI Hei4921
ESI Hei6678
HIRES Hei4026
HIRES Hei4471
HIRES Hei4921
10
5
0
-5
-10
-15
2.8
2.6
normalized flux
ESI Hei4026
∆λ(˚
A)
Figure 2. Left panel: Fit of synthetic LTE models to the hydrogen Balmer lines of a coadded DBSP spectrum. The normalized
fluxes of the single lines are shifted for better visualisation. Right panel: Fits of vrot sin ito the helium lines seen in the HIRES
and ESI spectra. The atmospheric parameters were fixed to the values derived from the WHT and DBSP spectra.
using the MAKEE2pipeline following the standard procedure: bias subtraction, flat fielding, sky subtraction, order
extraction, and wavelength calibration.
3. ORBITAL AND ATMOSPHERIC PARAMETERS AND LIGHT CURVE FITTING
As evident in Fig. 1PTF1 J2238+7430 shows strong periodic ellipsoidal variability in its light curve at Porb =
76.341750(1) min. This variability is caused by the tidal deformation of the sdB primary under the influence of the
gravitational force of the companion. We use the PTF and the ZTF lightcurve with its multi-year baseline and the
Chimera light curves to derive the orbital period of the systems. The analysis was done with the Gatspy module for
time series analysis which uses the Lomb-Scargle periodogram3(VanderPlas & Ivezi´c 2015). The error was derived
from bootstrapping.
Radial velocities were measured by fitting Gaussians, Lorentzians, and polynomials to the hydrogen and helium
lines to cover continuum, line, and line core of the individual lines using the FITSB2 routine (Napiwotzki et al. 2004).
The procedure is described in full detail in Geier et al. (2011). We fitted the wavelength shifts compared to the rest
wavelengths using a χ2-minimization. Assuming circular orbits, a sine curve was fitted to the folded radial velocity
(RV) data points (Fig. 1).
Atmospheric parameters such as effective temperature, Teff , surface gravity, log g, helium abundance, log y=
log n(He)
n(H), and projected rotational velocity, vrot sin i, were determined by fitting the rest-wavelength corrected av-
erage DBSP, ISIS and HIRES spectra with metal-line-blanketed LTE model spectra (Heber et al. 2000). Teff and
log gwere derived from the Balmer and helium lines from the ISIS and DBSP spectra whereas log yand vrot sin i
were measured with the HIRES spectra. High-resolution echelle spectra are not well suited to measure Teff and log g
because the broad hydrogen absorption lines span several orders and merging of the echelle spectra could introduce
2http://www.astro.caltech.edu/∼tb/ipac staff/tab/makee/
3http://dx.doi.org/10.5281/zenodo.14833
A new double detonation progenitor system 5
Table 1. Overview of the measured and derived parameters for PTF1 J2238+7430
Right ascension RA [hrs] 22:38:57.11
Declination Dec [◦] +74:30:15.1
Magnitudebg[mag] 15.244±0.023
Parallaxa$[mas] 1.0001 ±0.0225
Distance d[kpc] 1.00 ±0.03
Absolute Magnitude Mg[mag] 4.40 ±0.20
(reddening corrected)
Proper motiona(RA) µαcos(δ) [mas yr−1] 0.344 ±0.056
Proper motiona(Dec) µδ[mas yr−1]−1.833 ±0.051
Atmospheric parameters of the sdB
Effective temperaturecTeff [K] 23 600±400
Surface gravityclog g5.42±0.06
Helium abundancedlog y−2.11±0.03
Projected rotational velocitydvrot sin i[km s−1] 185±5
Orbital parameters
T0[BMJD UTC] 57960.47584170(3)
Orbital period Porb [min] 76.341750(1)
RV semi-amplitude K[km s−1] 378.0±3.7
System velocity γ[km s−1]−6.2±2.14
Binary mass function fm[M] 0.0597±0.0020
Derived parameters
Mass ratio q=MWD
MsdB 0.528 ±0.020
sdB mass MsdB [M] 0.383 ±0.028
sdB radius RsdB [R] 0.190 ±0.003
WD mass MWD [M] 0.725 ±0.026
WD radius RWD [M] 0.0109+0.0002
−0.0003
WD blackbody temperature Teff [K] 26,800 ±4600
Orbital inclination i[◦] 88.4+1.6
−3.3
Separation a[R] 0.615 ±0.010
Roche filling factor RsdB/RRochelobe 0.951 ±0.010
afrom Gaia eDR3 (Gaia Collaboration et al. 2016,2021)
bfrom PanSTARRS DR1 (Chambers et al. 2016)
cadopted from from DBSP and ISIS
dadopted from ESI and HIRES
systematic errors. The full procedure is described in detail in Kupfer et al. (2017a,b). PTF1 J2238+7430 shows typical
Teff , log g, and log yand vrot sin i=185±5 km s−1. The rotational velocity is consistent with a tidally locked sdOB star
(see Sec. 4.1). Table 1summarizes the atmospheric and orbital parameters.
To model the lightcurves obtained with CHIMERA we used the LCURVE code (Copperwheat et al. 2010). We use
a Roche geometry, and the free parameters in our fit are: the phase (t0), the scaled radii (r1,2), the mass ratio
q, the inclination i, secondary temperature TWD, and the velocity scale ([K+KWD ]/sin i). We use a passband-
dependent gravity-darkening law and use a gravity darkening value (yg,r) from Claret & Bloemen (2011) and find
β= 0.425 for g0,β= 0.395 for r0, and β= 0.37 for i0. We assume an uncertainty of 0.03 on the value and use a
Gaussian prior. We use fixed limb darkening coefficients (a1,a2,a3,a4) taken from Claret & Bloemen (2011). We
use a1= 0.82, a2=−0.65, a3= 0.55, and a4=−0.19 for g0,a1= 0.81, a2=−0.89, a3= 0.79, and a4=−0.27
for r0, and a1= 0.78, a2=−1.01, a3= 0.91, and a4=−0.31 for i0. We also model the relativistic beaming (F) as
in Bloemen et al. (2011). We calculate the beaming parameters by assuming a blackbody spectrum and using the
effective wavelength of the g0,r0, and i0filters. We find F= 1.80 for g0,F= 1.57 for r0, and F= 1.46 for i0. The full
6Kupfer et al.
0.47
3.6
3.4
3.2
3
0.46
0.45
0.44
0.43
0.42
0.1
0
-0.1
rel. Flux
∆Flux
g′, 2017-07-26
MJD - 57960 [days]
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0.08
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3
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0
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4
∆Flux
MJD - 58101 [days]
rel. Flux
1.6
1.5
1.4
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0.05
0
r′, 2017-07-26
-0.05
MJD - 57960 [days]
rel. Flux
∆Flux
0.49
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rel. Flux
i′, 2017-12-14
MJD - 58101 [days]
∆Flux
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3
2.95
0.472
MJD -57960 [days]
3.2
3.15
3.1
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rel. Flux
0.476
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rel. Flux
1.33
MJD -57960 [days]
0.48
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0.476
0.474
0.472
1.43
1.42
1.41
1.4
1.39
1.38
1.37
1.36
1.35
1.34
Figure 3. Chimera light curves un-binned (grey) and binned (black) shown together with the LCURVE fits (red) observed optical
SDSS bandpasses. The lower two panels show the region when the WD is being eclipsed by the sdB. The blue solid curve marks
the same model without eclipses of the WD. The lower panels show the region when the white dwarf is being eclipsed. Lower
left panel: g0light curve, Lower right panel: r0light curve
approach is also described in Kupfer et al. (2017a,b,2020a,b) and Ratzloff et al. (2019). In addition, we add a 2nd
order polynomial to correct for any long timescale trends which are the result of a changing airmass over the course of
the observations. The best value of χ2for this model was 1350 for 1300 data points for the g-band light curve which
includes also a weak eclipse of the hot WD. Although the eclipse is weak (≤1 %), the χ2for the non-eclipsing solution
is 1400 which is statistically significantly worse compared to the solution with the weak eclipse. We use the MCMC
sampler emcee (Foreman-Mackey et al. 2013) to determine the best-fit values and uncertainty on the parameters.
4. RESULTS
4.1. System parameters
Although, PTF1 J2238+7430 is a single-lined binary we can derive system parameters using the combined results
from the light curve analysis with results from the spectroscopic fitting. Parameters derived in this way by a si-
A new double detonation progenitor system 7
multaneous fit to the Chimera light curves are summarized in Table 1. The given errors are all 95 % confidence
limits.
We find that PTF1 J2238+7430 consists of a low mass sdB with a high-mass WD companion. We derive a mass
ratio q=MsdB/MWD = 0.528 ±0.020, a mass for the sdB MsdB = 0.383 ±0.028 M, and a WD companion mass
MWD = 0.725 ±0.026 M. PTF1 J2238+7430 is found to be eclipsing at an inclination angle of i= 88.4+1.6
−3.3
◦which
allows us to measure the radius and the black-body temperature of the WD companion. We determine a black-body
temperature of 26,800 ±4600 K for the WD and a radius of RWD = 0.0109+0.0002
−0.0003 R. The radius was found to be
<5% above the zero-temperature value and is fully consistent with predictions of at most a few percent above the
zero-temperature value for the radius.
We calculate the absolute magnitude (Mg) of PTF1 J2238+7430 using the visual PanSTARRS g-band magnitude
g=15.244±0.023 mag and the parallax from Gaia eDR3 (Gaia Collaboration et al. 2016,2021). Because the object is
located near the Galactic Plane, significant reddening can occur. Green et al. (2019) present updated 3D extinction
maps based on Gaia parallaxes and stellar photometry from Pan-STARRS 1 and 2MASS4and find towards the
direction of PTF1 J2238+7430 an extinction of E(g−r) = 0.24 ±0.03 at a distance of 1.00 kpc; this results in a total
extinction in the g-band of Ag= 0.84 ±0.11 mag, and with the corrected magnitude, we find an absolute magnitude
of Mg= 4.40 ±0.20 mag consistent with a hot subdwarf star (Geier et al. 2019).
4.2. Comparison with Gaia parallax
To test whether our derived system parameters are consistent with the parallax provided by Gaia eDR3, we compared
the measured parameters from the light curve fit to the predictions using the Gaia parallax. The approach follows
a similar strategy as described in Ratzloff et al. (2019) and Kupfer et al. (2020a). Using the absolute magnitude
Mg= 4.40 ±0.20 mag, we find a luminosity of L= 11.5±3.0 Lusing a bolometric correction BCg=−2.30 mag
derived for our stellar parameters from the MESA Isochrones & Stellar Tracks (MIST; Dotter 2016;Choi et al. 2016;
Paxton et al. 2011,2013,2015,2018). Using the Stefan-Boltzmann law applied to a black body (L= 4σπR2
sdBT4
eff ),
we can solve for the radius of the sdBs, and combined with R2
sdB =GMsdB/g, we can solve for mass of the sdBs:
MsdB =LsdB10log(g)
4πσGT 4
eff
(1)
Using these equations we find MsdB = 0.39 ±0.10 Mand RsdB = 0.17 ±0.03 R. Although the error bars are rather
large, this result is in agreement with the results from the light curve and spectroscopic fits.
4.3. Kinematics of the binary systems
We found that PTF1 J2238+7430 has evolved from a ≈2.1 Mstar and we expect the system is a member of a
young stellar population (see Sec. 5). Using the proper motion from Gaia eDR3 (Gaia Collaboration et al. 2016,2018,
2021), the distance and the systemic velocities (see Tab. 1) we calculate the Galactic motion for PTF1 J2238+7430.
We employed the approach described in Odenkirchen & Brosche (1992) and Pauli et al. (2006). As in Kupfer et al.
(2020a), we use the Galactic potential of Allen & Santillan (1991) as revised by Irrgang et al. (2013). The orbit was
integrated from the present to 3 Gyr into the past. We find that the binary moves within a height of 200 parsec of the
Galactic equator and with very little eccentricity between 9 and 10 kpc from the Galactic center. From the Galactic
orbit we conclude that PTF1 J2238+7430 is a member of the Galactic thin disk population consistent with being
member of a young stellar population.
5. PREDICTED EVOLUTION OF THE BINARY SYSTEM
5.1. Formation of the sdB + WD system
Ruiter et al. (2010) found that the dominant way to form compact double carbon-oxygen core WDs is through stable
mass transfer which forms the sdB followed by a phase of unstable mass transfer which forms the white dwarf com-
panion. They present a specific example which starts with a 2.88 Mand 2.45 Mbinary pair. In PTF1 J2238+7430
weak eclipses of the WD companion imply a blackbody temperature of 26 800 ±4600 K, implying a cooling time of
≈25 million years, significantly shorter than the predicted current age of the sdB of ≈170 million years (see Sec. 5.2).
4http://argonaut.skymaps.info/
8Kupfer et al.
1
2
3
5
MS MS
MS
post-MS
MS
sdB
RLOF
CEE
4
sdB WD
GWs
GWs
MS - main-sequence star RLOF - stable Roche-lobe overflow
CEE - common envelope evolution GW - gravitational waves
∙
∙
∙
Peculiar SN Ia
6
7
8
Runaway
sdB star
RLOF
Current phase
Figure 4. Visualization of the proposed evolutionary pathway for PTF1 J2238+7430. The red box marks the current evolu-
tionary phase. Each evolutionary phase is numbered according to their order in the evolution and the direction of the sequence
is marked with arrows.
Therefore, we predict that the sdB was formed first, and we propose the following evolutionary scenario (illustrated
in Fig. 4) for PTF1 J2238+7430 which explains all observational properties and is similar to the scenario discussed in
Ruiter et al. (2010).
The system started as a ≈2.14 Mmain sequence star (see Sect. 5.2) which will become the sdB, and a slightly
lower mass companion with an orbital period of a few weeks. The sdB progenitor evolves first and starts stable mass
transfer to the companion star. At the end of that phase the sdB has formed with the observed mass of ≈0.4 Mand
the orbital periods has substantially widened. The companion star has accreted ≈1.7 Mof material from the sdB
progenitor and turned into a ≈3.5–4 Mstar which will then evolve off the main sequence and overflow its Roche Lobe
while the sdB star is still burning helium. Due to the large mass ratio at this point, mass transfer will be unstable
and initiate a common envelope. The CE phase could happen either during the RGB or AGB phase of the secondary
depending on the binary separation at that point. In either case it would leave a compact binary with a massive WD
and an sdB at an orbital period of ≈86 minutes. The observed high WD mass of 0.725 ±0.026 Mis consistent with
the evolution from an intermediate mass main sequence star (Cummings et al. 2018). The final phase of unstable
mass transfer happened ≈25 million years ago, after which the WD cooled to its currently observed temperature
while gravitational wave radiation decreased the orbital period to the currently observed period of 76 minutes. As also
discussed in Ruiter et al. (2010), there could exist a substantial fraction of compact sdB+WD binaries where the sdB
was formed first through stable mass transfer.
5.2. Future evolution
To understand the future evolution of the system we employed MESA version 12115 (Paxton et al. 2011,2013,2015,
2018,2019). Bauer & Kupfer (2021) use MESA models to show that sdB stars with mass M.0.47 Mcan descend
A new double detonation progenitor system 9
220002400026000280003000032000 Teff [K]
5.2
5.4
5.6
5.8
log(g/cms−2)
Binary model
Single-star model
−10.0
−7.5
log(˙
M/Myr−1)
0.2
0.4
MsdB [M]
0.8
0.9
MWD [M]
He-shell detonation
0 20 40 60
Myr from now
25
50
75
Porb [min]
Figure 5. Left panel: Predicted evolution based on the MESA model for the PTF1 J2238+7430 system. The current observed
log gand Teff and error bars for the system are shown in red. The dashed curve shows the evolution the star would follow in
isolation, while the solid curve shows the trajectory it follows due to encountering the Roche limit, depicted by the gray shaded
region. Right panel: Future evolution of the system until the helium ignites.
from either lower-mass main sequence progenitors that ignite central He burning via an off-center degenerate He flash
(MZAMS .2.3 M), or they can descend from higher-mass main sequence progenitors that ignite He at the center under
non-degenerate conditions (MZAMS &2.3 M). They show that these scenarios lead to different H envelope structures
that influence the subsequent radius evolution of the sdB star, with stars descended from higher mass progenitors
having more compact envelopes and correspondingly higher log gvalues. The measured log gfor PTF1 J2238+7430
requires a relatively extended envelope with a radius that requires that sdB star descend from the lower-mass channel
with a progenitor mass around 2 M. We find that our best matching MESA model for the measured log gand Teff
of this system is a 0.41 MsdB model descended from a 2.14 Mmain sequence star that ignited the He core via a
degenerate He-core flash. This model has a sharp transition from the He core to an H envelope with solar composition.
When He ignites, we remove most of the envelope, leaving a thin H envelope layer of 10−3Mso that the subsequent
sdB evolution track matches the observed log gand Teff of PTF1 J2238+7430. Figure 5shows the log g–Teff evolution
of this MESA model, where it approaches the current observed state of PTF1J2238+7430 after ≈170 Myr of evolution,
and will encounter its Roche lobe and begin transferring mass soon after.
We model the future binary evolution of this system with a 0.75 MWD companion using the MESA binary capa-
bilities. The sdB is currently observed at 95% Roche Lobe filling and will continue to spiral in due to gravitational
wave radiation. In our model the sdB will soon fill its Roche lobe and start to donate its hydrogen rich envelope in
six million years at a low rate of .10−10 Myr−1(see Bauer & Kupfer 2021, for a detailed oberview). Because of the
large initial radius of the H envelope, mass transfer will proceed at this low rate for ≈50 Myr before the H envelope
is exhausted and the He core is finally exposed at a much more compact radius. While the sdB is still helium core
burning ≈60 Myr from today, the sdB will begin to donate helium rich material onto the WD at the expected rate of
≈10−8Myr−1, as shown in Figure 5. A helium rich layer will slowly build up for 10million years, reaching a critical
mass of 0.17 M. At this point the binary has an orbital period of ≈10 min. The sdB has been stripped down to a
mass of 0.25 M, and the WD has a total mass of 0.92 M.
10 Kupfer et al.
Our MESA model predicts that at this point the accreting WD will experience a thermonuclear instability that will
lead to a detonation that will likely destroy the WD in a thermonuclear supernova (Woosley & Kasen 2011;Bauer
et al. 2017). The structure of our MESA model at the point of detonation is very similar to the model for CD–30◦11223
in Bauer et al. (2017), and we have used similar modeling assumptions as those described in that work. At the time
of the thermonuclear supernova the sdB has an orbital velocity of 911 km s−1and will be released as a hyper-runaway
star exceeding the escape velocity of the Galaxy (Bauer et al. 2019;Neunteufel 2020;Neunteufel et al. 2021). Fig. 4
illustrates the evolutionary sequence proposed for PTF1 J2238+7430.
6. SUPERNOVA RATE ESTIMATE
Models of thermonuclear supernovae in WDs with thick (&0.1 M) helium shells indicate that they will yield
transients classified as peculiar Type I supernovae (Polin et al. 2019;De et al. 2019). PTF1 J2238+7430 together
with CD-30◦11223 therefore mark a small sample of double detonation peculiar thermonuclear supernova progenitors.
Using both systems we can estimate a lower limit of thermonuclear supernovae originating in compact hot subdwarf
+ WD binaries where the sdB donates helium rich material during helium core burning. Both systems will have an
age of ≈500 Myrs at the time of the helium shell detonation and are located within 1 kpc. Because of their young age,
we compare the rate of these double detonation progenitors to the supernova Ia rate as a function of star formation.
Under the assumption that these systems typically have an age of ≈500 Myrs at time of explosion we find a lower limit
of double detonation explosions of 2
500 kpc−2Myr−1from the two known systems. We can compare that to the local
star formation rate of 10−3Mkpc−2yr−1which leads to a double detonation rate of ≈4×10−6yr−1.Sullivan et al.
(2006) found a supernova Ia rate of 3.9±0.7×10−4SNe yr−1(Myr−1)−1of star formation. With a Galactic star
formation rate of ≈1Myr−1, we find that the rate at which peculiar thermonuclear supernovae with thick ≈0.15 M
helium shells occur in star forming galaxies could be at least 1 % of the type Ia supernova rate. This is in reasonable
agreement with the presently observed low rate of thick helium shell detonations.
De et al. (2019) presented the discovery of peculiar Type I supernova consistent with a thick helium shell double
detonation on a sub-Chandrasekhar-mass WD (Polin et al. 2019,2021). However, one of the distinct differences is
that the transient occurred in the outskirts of an elliptical galaxy which points to an old stellar population which
is in disagreement with our observed systems which represent a young population. More recently, De et al. (2020)
present a sample of calcium rich transients originating from double-detonations with helium shells. They find that the
majority of transients are located in old stellar populations. However, De et al. (2020) note that a small subsample
(iPTF16hgs, SN2016hnk and SN 2019ofm) were found in star forming environments, suggesting that there is a small
but likely non-zero contribution from young systems which could potentially be related to systems like CD-30◦11223
and PTF1 J2238+7430.
7. SUMMARY AND CONCLUSION
As part of our search for short period sdB binaries we discovered PTF1J2238+7430 using PTF and subsequently
ZTF light curves. We find a period of Porb=76.34179(2) min. Follow-up observations confirmed the system as an
sdB with MsdB = 0.383 ±0.028 Mand a WD companion with MWD = 0.725 ±0.026 M. High-speed photometry
observations with Chimera revealed a weak WD eclipse which allows us to measure the blackbody temperature and
radius of the WD. We find a temperature of 26,800 ±4600 K and a radius of RWD = 0.0109+0.0002
−0.0003 Rfully consistent
with cooling models for carbon-oxygen core WDs. We find a cooling age of ≈25 Myrs for the WD which is significantly
shorter than our age estimate for the sdB which is ≈170 Myrs. This can be explained by the sdB forming first through
stable mass transfer, followed by the WD forming ≈25 Myrs ago through a common envelope phase. This shows that
evolutionary scenarios where the sdB is formed first through stable mass transfer must be considered for compact sdB
binaries with WD companions.
We employed MESA to calculate the future evolution of the system and find that the sdB in PTF1J2238+7430 will
start mass transfer of the hydrogen rich envelope in ≈6 Myr. In ≈60 Myr, after a phase of hydrogen and helium
mass transfer, the WD will build up a helium layer of 0.17Mleading to a total WD mass of 0.92 M. Our models
predict that at this point the WD likely detonates in a peculiar thermonuclear supernova making PTF1 J2238+7430
the second known progenitor for a supernova with a thick helium layer. Using both systems we estimate that at least
1 % of type Ia supernova originate from compact sdB+WD binaries in young populations of galaxies with similar star
formation rates compared to the Milky Way. Although this is only a lower limit the estimate is broadly consistent
with the low number of observed peculiar thermonuclear supernovae.
A new double detonation progenitor system 11
ACKNOWLEDGMENTS
This research benefited from interactions that were funded by the Gordon and Betty Moore Foundation through
grant GBMF5076. This work was supported by the National Science Foundation through grants PHY-1748958 and
ACI- 1663688. TK would like to thank Ylva G¨otberg for providing the template for Fig. 4. TK acknowledge support
from the National Science Foundation through grant AST #2107982. DS was supported by the Deutsche Forschungs-
gemeinschaft (DFG) under grants HE 1356/70-1 and IR 190/1-1.
Observations were obtained with the Samuel Oschin Telescope at the Palomar Observatory as part of the PTF
project, a scientific collaboration between the California Institute of Technology, Columbia University, Las Cumbres
Observatory, the Lawrence Berkeley National Laboratory, the National Energy Research Scientific Computing Center,
the University of Oxford, and the Weizmann Institute of Science.
Based on observations obtained with the Samuel Oschin 48-inch Telescope at the Palomar Observatory as part of
the Zwicky Transient Facility project. ZTF is supported by the National Science Foundation under Grant No. AST-
1440341 and a collaboration including Caltech, IPAC, the Weizmann Institute for Science, the Oskar Klein Center at
Stockholm University, the University of Maryland, the University of Washington, Deutsches Elektronen-Synchrotron
and Humboldt University, Los Alamos National Laboratories, the TANGO Consortium of Taiwan, the University of
Wisconsin at Milwaukee, and Lawrence Berkeley National Laboratories. Operations are conducted by COO, IPAC,
and UW.
Some of the data presented herein were obtained at the W.M. Keck Observatory, which is operated as a scientific
partnership among the California Institute of Technology, the University of California and the National Aeronautics
and Space Administration. The Observatory was made possible by the generous financial support of the W.M. Keck
Foundation. The authors wish to recognize and acknowledge the very significant cultural role and reverence that the
summit of Mauna Kea has always had within the indigenous Hawaiian community. We are most fortunate to have the
opportunity to conduct observations from this mountain.
Some results presented in this paper are based on observations made with the WHT operated on the island of
La Palma by the Isaac Newton Group in the Spanish Observatorio del Roque de los Muchachos of the Institutio de
Astrofisica de Canarias.
This work has made use of data from the European Space Agency (ESA) mission Gaia (https://www.cosmos.esa.
int/gaia), processed by the Gaia Data Processing and Analysis Consortium (DPAC, https://www.cosmos.esa.int/
web/gaia/dpac/consortium). Funding for the DPAC has been provided by national institutions, in particular the
institutions participating in the Gaia Multilateral Agreement.
Facilities: PO:1.2m (PTF), PO:1.2m (ZTF), Hale (DBSP), ING:Herschel (ISIS), Keck:I (HIRES), Keck:II (ESI),
Hale (Chimera)
Software: Gatspy (VanderPlas & Ivezi´c 2015;Vanderplas 2015), FITSB2 (Napiwotzki et al. 2004), LCURVE (Copper-
wheat et al. 2010), emcee (Foreman-Mackey et al. 2013), MESA (Paxton et al. 2011,2013,2015,2018,2019), Matplotlib
(Hunter 2007), Astropy (Astropy Collaboration et al. 2013,2018), Numpy (Oliphant 2015), ISIS (Houck & Denicola
2000), MAKEE (http://www.astro.caltech.edu/∼tb/ipac staff/tab/makee/)
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