A dense 01Mstar in a 51-minute orbital period eclipsing binary Kevin B. Burdge12 Kareem El-Badry345 Thomas R. Marsh6 Saul Rappaport12 Warren R.

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A dense 0.1Mstar in a 51-minute orbital period eclipsing

binary

Kevin B. Burdge1,2∗, Kareem El-Badry3,4,5, Thomas R. Marsh6, Saul Rappaport1,2, Warren R.

Brown3, Ilaria Caiazzo7, Deepto Chakrabarty1,2, V. S. Dhillon8,9, Jim Fuller7, Boris T. G¨

ansicke6,

Matthew J. Graham7, Erin Kara1,2, S. R. Kulkarni7, S. P. Littlefair8, Przemek Mr´

oz10, Pablo

Rodr´

ıguez-Gil9,11, Jan van Roestel7, Robert A. Simcoe1,2, Eric C. Bellm12, Andrew J. Drake7,

Richard G. Dekany13, Steven L. Groom14, Russ R. Laher14, Frank J. Masci14, Reed Riddle13,

Roger M. Smith13, & Thomas A. Prince7

1Department of Physics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA

2Kavli Institute for Astrophysics and Space Research, Massachusetts Institute of Technology,

Cambridge, MA 02139, USA

3Center for Astrophysics, Harvard & Smithsonian, 60 Garden Street, Cambridge, MA 02138

4Harvard Society of Fellows, 78 Mount Auburn Street, Cambridge, MA 02138

5Max-Planck Institute for Astronomy, K¨

onighstuhl 17, D-69117 Heidelberg, Germany

6Department of Physics, University of Warwick, Coventry CV4 7AL, UK

7Division of Physics, Mathematics and Astronomy, California Institute of Technology, Pasadena,

CA, USA

8Department of Physics & Astronomy, University of Shefﬁeld, Shefﬁeld S3 7RH, UK

9Instituto de Astrof´

ısica de Canarias, V´

ıa L´

actea s/n, La Laguna, E-38205 Tenerife, Spain

10Astronomical Observatory, University of Warsaw, Al. Ujazdowskie 4, 00-478 Warszawa, Poland

11Departamento de Astrof´

ısica, Universidad de La Laguna, E-38206 La Laguna, Tenerife, Spain

arXiv:2210.01809v1 [astro-ph.SR] 4 Oct 2022

12DIRAC Institute, Department of Astronomy, University of Washington, 3910 15th Avenue NE,

Seattle, WA 98195, USA

13Caltech Optical Observatories, California Institute of Technology, Pasadena, CA 91125, USA

14IPAC, California Institute of Technology, Pasadena, CA, USA

In over a thousand known cataclysmic variables (CVs), where a white dwarf is accreting

from a hydrogen-rich star, only a dozen have orbital periods below 75 minutes1–9. One

way to achieve these short periods requires the donor star to have undergone substantial

nuclear evolution prior to interacting with the white dwarf10–12, 14, 58, and it is expected that

these objects will transition to helium accretion. These transitional CVs have been proposed

as progenitors of helium CVs14–17, 57, 58. However, no known transitional CV is expected to

reach an orbital period short enough to account for most of the helium CV population,

leaving the role of this evolutionary pathway unclear. Here we report observations of ZTF

J1813+4251, a 51-minute orbital period, fully eclipsing binary system consisting of a star

with a temperature comparable to that of the Sun but a density 100 times greater due to its

helium-rich composition, accreting onto a white dwarf. Phase-resolved spectra, multi-band

light curves and the broadband spectral energy distribution allow us to obtain precise and

robust constraints on the masses, radii and temperatures of both components. Evolutionary

modeling shows that ZTF J1813+4251 is destined to become a helium CV binary, reaching

an orbital period under 20 minutes, rendering ZTF J1813+4251 a previously missing link

between helium CV binaries and hydrogen-rich CVs.

Using data from the Zwicky Transient Facility (ZTF)19, we recently conducted a systematic

period search of 1,220,038,476 unique sources using a graphics processing unit (GPU) based

implementation of the generalised Lomb-Scargle algorithm31, as part of an ongoing campaign

to identify and characterize short period astronomical variables33 (Methods). This effort led to the

identiﬁcation of ZTF J1813+4251, which exhibited strong ellipsoidal variations due to the tidal

deformation of a star22 and an eclipse, as seen in the lightcurves shown in Figure 1. The orbital

period of this source is just 51 minutes, despite a spectral energy distribution indicating that it hosts

a6000 K star of spectral type F. The Gaia eDR3 astrometric solution suggests that the source is

nearly a kiloparsec away, making it signiﬁcantly less luminous than an F type main-sequence star

given its apparent brightness. This ultracompact binary system had been excluded from previous

searches for ultracompact binaries33 because of its red color relative to other ultracompact systems.

On June 4 and July 5 2021, we obtained phase-resolved spectroscopic observations of ZTF

J1813+4251 using the Low Resolution Imaging Spectrometer (LRIS)23 on the 10-m W. M. Keck

I Telescope on Mauna Kea (Methods). Figure 2 illustrates these observations, revealing a late F

type stellar spectrum blanketed with metallic absorption lines characteristic of main sequence stars.

These absorption lines Doppler shift with a large velocity semi-amplitude of 461.3±3.4 km s−1due

to the short orbital period of the binary. Additionally, double-peaked emission lines of hydrogen,

helium, and calcium reveal an accretion disk, most prominently visible in the red half of the

spectrum, as seen in Figure 3.

On June 12, 2021, we obtained high speed images of ZTF J1813+4251 with the quintuple-beam

high speed photometer HiPERCAM35 on the 10.4-m Gran Telescopio Canarias (GTC) on La

Palma. This multi-color high signal-to-noise (SNR) light curve, illustrated in Figure 1, revealed

that the depth of the eclipse of the white dwarf varies as a function of wavelength, with a depth

of ∼50 percent in the HiPERCAM-usﬁlter centered at 3526 ˚

A, but only a ∼10 percent depth in

the HiPERCAM-zsﬁlter centered at 9156 ˚

A. This dependence of the eclipse depth on wavelength

indicates that the accreting white dwarf contributes a larger share of the luminosity at short wavelengths,

due to it having a substantially higher surface temperature (TWD = 12600 ±500 K) than the donor

star (TDonor = 6000 ±90 K). There are two photometric maxima per orbit due to ellipsoidal

variations, and the high signal-to-noise (SNR) HiPERCAM light curve also revealed a pronounced

“O’Connell” effect25, in which the peak ﬂux of these alternating maxima is substantially different

due to a modulation component at the orbital frequency. This effect may be due to a spot on the

donor star, which is tidally locked, and thus completes a rotation every orbital period.

The accretion disk seen in panels (d) and (e) of Figure 3 indicates that the donor star in

ZTF J1813+4251 is transferring matter to the white dwarf, and thus is ﬁlling its Roche-lobe. The

Roche-lobe has a scale-invariant geometry dependent only on the mass ratio of the system, and thus

the geometry of the donor depends only on this mass ratio51. In a binary system undergoing a total

eclipse, the time between mid-ingress and mid-egress depends only on the geometry of the donor

and the inclination of the system. This means that the eclipses in ZTF J1813+4251’s light curve

constrain the system to a unique mass ratio vs inclination relation45. Additionally, the depths of the

primary and secondary eclipse constrain a unique radius ratio between the white dwarf and that of

the donor, which, when combined with the overall geometry of the primary eclipse, yields a unique

solution for the radii divided by the semi-major axis (the scaled radii), orbital inclination, and thus

mass ratio, because the system is Roche lobe ﬁlling. These constraints, together with the precise

donor radial velocity semi-amplitude measured from the spectra (see the coadded spectrum in

Figure 2), allow for a robust determination of the system parameters on the basis of only Roche lobe

geometry and Kepler’s laws (Methods). We report these system parameters in Table 1. Because

the donors in transitional CVs are still transferring signiﬁcant hydrogen and have not switched to

primarily helium accretion yet, as seen in a helium CV (also known as AM CVns), these objects

often exhibit a mixture of hydrogen disk lines along with unusually strong helium lines in their

spectra as a result of their slowly transitioning to transferring mainly helium, and as result, we see

in panel (d) of Figure 3 that the disk also exhibits signiﬁcant helium emission.

A Niels Gehrels Swift observatory (Swift) X-ray telescope (XRT) observation of the system

revealed no detectable X-ray ﬂux, with the X-ray luminosity of the system, Lx, constrained to a 3σ

upper limit of Lx<1.22×1031 erg s−1given an assumed distance of 891+174

−135 pc inferred from Gaia

EDR328, an upper limit consistent with the typical x-ray luminosity of a non-magnetic cataclysmic

variable29 at these energies. The source was detected with the Swift Ultraviolet Optical Telescope

in the ultraviolet, constraining the temperature of the accreting white dwarf (Methods).

As seen in Figure 3, archival ZTF data captured an outburst of the object on September

21, 2019, brightening by over a factor of two relative to its quiescent brightness in the ZTF-g

and ZTF-rﬁlters. The ﬁnal observation of the night during which the outburst was detected

took place during the totality of the primary eclipse, and as a result the ﬂux was signiﬁcantly

attenuated, indicating that this brightening must have originated from the accretor. Because the

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Adense0:1Mstarina51-minuteorbitalperiodeclipsingbinaryKevinB.Burdge1;2,KareemEl-Badry3;4;5,ThomasR.Marsh6,SaulRappaport1;2,WarrenR.Brown3,IlariaCaiazzo7,DeeptoChakrabarty1;2,V.S.Dhillon8;9,JimFuller7,BorisT.G¨ansicke6,MatthewJ.Graham7,ErinKara1;2,S.R.Kulkarni7,S.P.Littlefair8,PrzemekMr´oz10,PabloR...

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A dense 01Mstar in a 51-minute orbital period eclipsing binary Kevin B. Burdge12 Kareem El-Badry345 Thomas R. Marsh6 Saul Rappaport12 Warren R.

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