PTF1 J082340.04+081936.5: A hot subdwarf B star with a low mass white dwarf companion in an 87 minute orbit
Thomas Kupfer, Jan van Roestel, Jared Brooks, Stephan Geier, Tom R. Marsh, Paul J. Groot, Steven Bloemen, Thomas A. Prince, Eric Bellm, Ulrich Heber, Lars Bildsten, Adam A. Miller, Martin J. Dyer, Vik S. Dhillon, Matthew Green, Puji Irawati, Russ Laher, Stuart P. Littlefair, David L. Shupe, Charles C. Steidel, Somsawat Rattansoon, Max Pettini
aa r X i v : . [ a s t r o - ph . S R ] D ec Draft version December 8, 2016
Preprint typeset using L A TEX style emulateapj v. 01/23/15
PTF1 J082340.04+081936.5: A HOT SUBDWARF B STAR WITH A LOW MASS WHITE DWARF COMPANIONIN AN 87 MINUTE ORBIT
Thomas Kupfer , Jan van Roestel , Jared Brooks , Stephan Geier , Tom R. Marsh , Paul J. Groot , StevenBloemen , Thomas A. Prince , Eric Bellm , Ulrich Heber , Lars Bildsten , Adam A. Miller , Martin J.Dyer , Vik S. Dhillon , Matthew Green , Puji Irawati , Russ Laher , Stuart P. Littlefair , David L.Shupe , Charles C. Steidel , Somsawat Rattansoon and Max Pettini Draft version December 8, 2016
ABSTRACTWe present the discovery of the hot subdwarf B star (sdB) binary PTF1 J082340.04+081936.5. Thesystem has an orbital period P orb =87.49668(1) min (0.060761584(10) days), making it the second-mostcompact sdB binary known. The lightcurve shows ellipsoidal variations. Under the assumption thatthe sdB primary is synchronized with the orbit, we find a mass M sdB = 0 . +0 . − . M ⊙ , a companionwhite dwarf mass M WD = 0 . +0 . − . M ⊙ and a mass ratio q = M WD M sdB = 1 . +0 . − . .The future evolution was calculated using the MESA stellar evolution code. Adopting a canonicalsdB mass of M sdB = 0 .
47 M ⊙ we find that the sdB still burns helium at the time it will fill its Rochelobe if the orbital period was less than 106 min at the exit from the last common envelope phase. Forlonger common envelope exit periods the sdB will have stopped burning helium and turned into a C/Owhite dwarf at the time of contact. Comparing the spectroscopically derived log g and T eff with our MESA models, we find that an sdB model with a hydrogen envelope mass of 5 × − M ⊙ matches themeasurements at a post-common envelope age of 94 Myr, corresponding to a post-common envelopeorbital period of 109 min which is close to the limit to start accretion while the sdB is still burninghelium. Subject headings: (stars:) binaries (including multiple): close – stars: individual(PTF1 J082340.04+081936.5) – (stars:) subdwarfs – (stars:) white dwarfs INTRODUCTION [email protected] Division of Physics, Mathematics and Astronomy, CaliforniaInstitute of Technology, Pasadena, CA 91125, USA Department of Astrophysics/IMAPP, Radboud UniversityNijmegen, PO Box 9010, NL-6500 GL Nijmegen, The Nether-lands Department of Physics, University of California, Santa Bar-bara, CA 93106, USA Institute for Astronomy and Astrophysics, Kepler Center forAstro and Particle Physics, Eberhard Karls University, Sand 1,72076 T¨ubingen, Germany Department of Physics, University of Warwick, CoventryCV4 7AL, UK Dr. Remeis-Sternwarte & ECAP, Astronomical Institute,University of Erlangen-Nuremberg, Germany Kavli Institute for Theoretical Physics, Santa Barbara, CA93106, USA Center for Interdisciplinary Exploration and Research in As-trophysics (CIERA) and Department of Physics and Astron-omy, Northwestern University, 2145 Sheridan Road, Evanston,IL 60208, USA The Adler Planetarium, 1300 S. Lakeshore Drive, Chicago,IL 60605, USA Department of Physics & Astronomy, University ofSheffield, Sheffield, S3 7RH, UK Instituto de Astrofsica de Canarias (IAC), E-38200 La La-guna, Tenerife, Spain National Astronomical Research Institute of Thailand, 191Siriphanich Building, Huay Kaew Road, Chiang Mai 50200,Thailand Spitzer Science Center, California Institute of Technology,Pasadena, CA 91125, USA Infrared Processing and Analysis Center, California Insti-tute of Technology, Pasadena, CA 91125, USA Institute of Astronomy, Madingley Road, Cambridge CB30HA, UK
Hot subdwarf B stars (sdBs) are core helium burningstars with masses around 0.5 M ⊙ and thin hydrogen en-velopes (Heber 1986, 2009, 2016). A large fraction ofsdBs are members of short-period binaries with periodsbelow ≈
10 days (Maxted et al. 2001; Napiwotzki et al.2004). Orbital shrinkage through a common envelope(CE) phase is the only likely formation channel for suchshort period sdB binaries (Han et al. 2002, 2003).Evolutionary studies have shown that the orbital pe-riod of a hot subdwarf with a white dwarf companion hasto be P orb .
120 min on exit from the last CE to still havean sdB that is core or shell helium burning when it fillsits Roche lobe assuming that the further orbital periodevolution is set by the emission of gravitational wavesonly. In the subsequent evolution, if helium burning isstill ongoing, the sdB fills its Roche lobe first and startsto transfer He-rich material onto the white dwarf (e.g.Tutukov & Fedorova 1989; Tutukov & Yungelson 1990;Iben & Tutukov 1991; Yungelson 2008). If the systemhas a mass ratio q = M sdB /M WD .
2, stable mass-transfer is possible (Savonije et al. 1986; Wang et al.2009). Mass transfer starts at orbital periods rangingfrom 16 to 50 min. Subsequently the semi-detached sys-tem evolves to shorter periods with typical mass trans-fer rates of ˙ M ≈ − M ⊙ yr − (e.g. Savonije et al.1986; Yungelson 2008; Piersanti et al. 2014; Brooks et al.2015).CD − ◦ orb = 70.52986 min) and is the onlyknown system where the sdB is still expected to be burn-ing helium when it will fill its Roche lobe (Vennes et al.2012; Geier et al. 2013). After accreting 0.1 M ⊙ , He- TABLE 1Summary of the observations of PTF1 J0823
Date UT Tele./Inst. N exp
Exp. time (s) Coverage (˚A)/Filter
Photometry mould g ′ Spectroscopy burning is predicted to be ignited unstably in the ac-creted helium layer. This in turn triggers the igni-tion of carbon in the core which might disrupt the WDeven when the mass is significantly below the Chan-drasekhar mass (e.g. Livne 1990; Livne & Arnett 1995;Fink et al. 2010; Woosley & Kasen 2011; Geier et al.2013; Shen & Bildsten 2014). If the WD is not disrupted,the unstable burning of the He-shell will detonate theshell and may be observed as a faint and fast .Ia super-nova (Bildsten et al. 2007). This increases the orbitalseparation, but gravitational wave radiation drives thedonor back into contact, resuming mass transfer and trig-gering several subsequent weaker flashes (Brooks et al.2015).Inspired by the discovery of CD − ◦ ′′ Samuel Oschin Schmidt telescope toimage up to ≈ of the sky per night toa depth of R mould ≈ . g ′ ≈ . OBSERVATIONS AND DATA REDUCTION
Photometry
As part of the Palomar Transient Factory, the Palo-mar 48-inch (P48) telescope images the sky every night.The reduction pipeline for PTF applies standard de-biasing, flat-fielding, and astrometric calibration to rawimages (Laher et al. 2014). Relative photometry correc-tion is applied and absolute photometric calibration tothe few percent level is performed using a fit to SDSSfields observed in the same night (Ofek et al. 2012). Thelightcurve of PTF1 J0823 has 144 epochs with good pho-tometry in the R mould band with a typical uncertainty of0.01 mag. The cadence is highly irregular, ranging from10 minutes to years with an average separation of about10 days.High cadence observations were conducted using the2.4-m Thai National Telescope (TNT) with the high-speed photometer ULTRASPEC (Dhillon et al. 2014).ULTRASPEC employs a 1024x1024 pixel frame-transfer,electron-multiplying CCD (EMCCD) in conjunctionwith re-imaging optics to image a field of 7.7 ′ x7.7 ′ at (windowed) frame rates of up to ∼
200 Hz. Observationswere obtained with the g ′ filter on January 31 2016 over1h50min with an exposure time of 3.9 sec and a deadtime of 15 ms leading to a total of 2404 epochs. Data re-duction was carried out with the ULTRACAM pipeline(Dhillon et al. 2007). All frames were bias-subtractedand flat-fielded. Spectroscopy
Optical spectra of PTF1 J0823 were obtained with thePalomar 200-inch telescope and the Double-Beam Spec-trograph (DBSP; Oke & Gunn 1982) over 3 nights usinga low resolution mode ( R ∼ PyRAF -based pipeline (Bellm & Sesar 2016). The pipeline per-forms standard image processing and spectral reductionprocedures, including bias subtraction, flat-field correc-tion, wavelength calibration, optimal spectral extraction,and flux calibration.On April 13 2016, we obtained 12 consecutive spectrausing the William Herschel Telescope (WHT) and theISIS spectrograph (Carter et al. 1993) using a mediumresolution mode (R600B grating, R ≈ IRAF routines. One dimensional spectrawere extracted using optimal extraction and were subse-quently wavelength and flux calibrated.Additionally, PTF1 J0823 was also observed on March1 2016 using Keck with the HIRES spectrograph ( R ≈
36 000). The full data set consists of 6 spectra which weretaken consecutively. ThAr arc exposures were taken at https://github.com/ebellm/pyraf-dbsp ∆ R V ( k m s − ) Phase -50 R V ( k m s − ) -200-100 Fig. 1.—
Radial velocity plotted against orbital phase. The RVdata were phase folded with the orbital period and are plotted twicefor better visualization. The residuals are plotted below. The RVswere measured from spectra obtained with P200/DBSP (black di-amonds), WHT/ISIS (blue squares) and Keck/HIRES (red trian-gles). the beginning of the night. The spectra were reducedusing the
MAKEE pipeline following the standard pro-cedure: bias subtraction, flat fielding, sky subtraction,order extraction, and wavelength calibration.Table 1 gives an overview of all observations and theinstrumental set-ups. ORBITAL AND ATMOSPHERIC PARAMETERS
The dominant variation in lightcurve is due to theellipsoidal deformation of the sdB primary. This iscaused by the tidal influence of the compact compan-ion. The lightcurve also shows Doppler boosting, causedby the orbital motion of the sdB (Shakura & Postnov1987; Bloemen et al. 2011; Geier et al. 2013). Theephemeris has been derived from the PTF lightucrve us-ing the
Gatspy module for time series analysis which usesthe Lomb-Scargle periodogram (VanderPlas & Ivezi´c2015). Because of the timebase of more than fiveyears, the derived orbital period of P orb =87.49668(1) min(0.060761584(10) days) is accurate to 1 ms. The errorwas estimated by bootstrapping the data.To obtain radial velocities, we followed the procedureas described in detail in Geier et al. (2011). To fit thecontinuum, line and line core of the individual lines wefitted Gaussians, Lorentzians and polynomials to thehydrogen and helium lines using the FITSB2 routine(Napiwotzki et al. 2004). The wavelength shifts com-pared to the rest wavelengths of all suitable spectral lineswere fitted simultaneously using a χ -minimization. Wefound consistent velocities between the 6 HIRES spectraand the ISIS spectra taken at the same orbital phase, aswell as consistent velocity amplitudes between the ISISand DBSP spectra. However, we found a significant off-set of the systematic velocities between the DBSP andthe ISIS spectra. In the night of January 30 2016 thesystemic velocity of the DBSP spectra was shifted by50 km s − . The DBSP calibration spectra were taken atthe beginning and end of the night. For ISIS the cal-ibration lamps where taken at the position of the tar- ∼ tb/ipac staff/tab/makee/ http://dx.doi.org/10.5281/zenodo.14833 get before, after and during the sequence and the ve-locities from the HIRES spectra are consistent with theISIS spectra. Therefore, we conclude that the offset inthe DBSP spectra is due to instrumental flexure becausethe calibration lamps were not taken at the positionof the object. We corrected the velocities measured inthe DBSP spectra to fit the systemic velocity obtainedby the ISIS spectra. All velocities were folded on theephemeris which was derived from the photometric data.Assuming circular orbits, a sine curve was fitted to thefolded radial velocity (RV) data points. We find a semi-amplitude K= 211 . ± . − and a systemic velocityof γ = 33 . ± . − (Fig. 1).The atmospheric parameters of effective temperature,T eff , surface gravity, log g , helium abundance, log y , andprojected rotational velocity, v rot sin i , were determinedby fitting the rest-wavelength corrected average DBSP,ISIS and HIRES spectra with metal-line-blanketed LTEmodel spectra (Heber et al. 2000). The most sensitivelines for log g and T eff are the Balmer lines close tothe Balmer jump. We used the hydrogen lines H12(3750˚A) up to H β in the WHT/ISIS spectrum to mea-sure T eff and log g with v rot sin i as a free parame-ter and found T eff =27 100 ±
500 K, log g =5.50 ± v rot sin i =122 ±
21 km s − (Fig. 2). The HIRES spectraare not well suited to measure T eff and log g becausethe broad hydrogen absorption lines span several or-ders and merging of the echelle spectra could introducesystematic errors. However, the high-resolution HIRESspectra are well suited to measure the projected rota-tional velocity v rot sin i of the sdB in lines which arenot affected by order merging. The three helium lines(4026 , , eff and log g , and most sensitive to rotationalbroadening v rot sin i and the helium abundance log y .Therefore, they were used to measure log y and v rot sin i ,keeping T eff and log g fixed to the values measured fromthe ISIS spectra. We found v rot sin i =132 ± − andlog y = − ± eff and log g were derived from the DBSP spectrumkeeping log y and v rot sin i fixed to the values measuredfrom HIRES. Although, the DBSP spectrum only covershydrogen lines down to H9 (3835 ˚A) we find good agree-ment within the errors with the parameters derived fromthe ISIS spectra. However, because of the larger coverageof Balmer lines, the further analysis will be done usingT eff and log g from the ISIS spectra.Table 2 shows the atmospheric parameters and Table 3summarizes the orbital parameters. LIGHTCURVE ANALYSIS
To model the lightcurve, we used the
LCURVE code(Copperwheat et al. 2010).
LCURVE uses many points ina grid to model the surfaces of the stars with a shape ac-cording to the Roche geometry. We assume co-rotationand an eccentricity of zero. The flux that each pointon the grid emits is calculated by assuming a blackbodyof a certain temperature at the bandpass wavelength,corrected for limb darkening, gravity darkening, Dopplerbeaming and the reflection effect.We use information from spectroscopy and the P48lightcurve to fix or constrain some of the model param- -0.01 H11 -5-10 -0.01 H10 -5-10-15 -0.02 -5-10 n o r m a li z e dflu x r e s i du a l s λ (˚A) λ (˚A) r e s i du a l s H12 λ (˚A) r e s i du a l s n o r m a li z e dflu x n o r m a li z e dflu x H8 -10-20-30 -0.02 H ǫ -10-30-40 -0.02 -20 -5-10-15-20 -0.02-0.04 λ (˚A) r e s i du a l s n o r m a li z e dflu x λ (˚A) λ (˚A) r e s i du a l s n o r m a li z e dflu x r e s i du a l s H9 n o r m a li z e dflu x -0.02-0.04 H γ -10-20-30-40 -0.02 H β -10-20-30-40 -0.02 -10-20-30-40 n o r m a li z e dflu x r e s i du a l s n o r m a li z e dflu x n o r m a li z e dflu x r e s i du a l s λ (˚A) λ (˚A) H δ r e s i du a l s λ (˚A) Fig. 2.—
Fit of synthetic LTE models to the hydrogen Balmer lines of a coadded ISIS spectrum. The normalized fluxes of the single linesare shifted for better visualisation.
TABLE 2Summary of atmospheric parameter PTF1 J0823
Telescope T eff (K) log g log y v rot sin i (K) (km s − )DBSP 26 700 ±
600 5.49 ± − a a ISIS 27 100 ±
500 5.50 ± − a ± b b − ± ± ±
500 5.50 ± − ± ± a fixed to the values derived from HIRES b fixed to the values derived from ISIS eters. First, we fix the orbital period to the value asdetermined in section 3. Second, we fix the primary tem-perature (T eff ), primary radial velocity amplitude ( K ),the surface gravity of the primary ( g ) and the rotationalvelocity ( v rot sin i , see section 3). As an additional con-straint we use as a lower limit for the white dwarf radiusthe zero-temperature mass radius relation by Eggleton(quoted from Verbunt & Rappaport 1988). We use thesame method to account for limb darkening and grav-ity darkening as described in Bloemen et al. (2011): theClaret limb darkening prescription Claret (2004) and thegravity darkening prescription from von Zeipel (1924)with a passband specific gravity darkening coefficient.We investigated how the limb darkening coefficient af-fects the results by adding it as free parameter with β = 0 . − .
0. The co-variance between the limb darken-ing parameter and system parameters is negligible com-pared to the uncertainty on the parameters. Therefore,we kept the limb darkening coefficients fixed for the anal- ysis. The limb darkening coefficients are a = 0 . = − . = 0 . = − .
079 for the limbdarkening coefficient β = 0 . eff =27 100 K andlog g =5.50 using the models from Bloemen et al. (2011).We did not use any limb darkening or gravity darkeningin the white dwarf model, since these do not affect thelight curve. This leaves as free parameters in the modelthe mass ratio q , the inclination i , secondary tempera-ture T WD , the scaled radii of both components r sdB , WD ,the velocity scale ([ K + K WD ] / sin i ) and the beamingparameter B ( F λ = F ,λ [1 − B v r c ], see Bloemen et al.2011). Besides these system parameters we add a thirdorder polynomial to correct for any residual airmass ef-fects.To determine the uncertainties on the parameterswe combine LCURVE with emcee (Foreman-Mackey et al.2013). emcee is an implementation of an MCMC samplerand uses a number of parallel chains to explore the solu-tion space. We use 2048 chains and let them run until thechains stabilized to a solution, which took approximately6000 generations.With the surface gravity ( g ) and projected rotationalvelocity ( v rot sin i ), we have three equations at hand thatconstrain the system, with the sdB mass M sdB the onlyfree parameter. The binary mass function f m = M sin ( i )( M WD + M sdB ) = P orb K πG (1) TABLE 3Overview of the derived parameter for PTF1 J0823
Right ascension RA [hrs] 08:23:40.04Declination Dec [ ◦ ] +08:19:36.5Visual magnitude a m V ± Atmospheric parameter of the sdB
Effective temperature T eff [K] 27100 ± g ± y –1.47 ± v rot sin i [km s − ] 132 ± Orbital parameter T [BJD UTC] 57418.6202(2)Orbital period P orb [d] 87.49668(1)RV semi-amplitude K [km s − ] 211.7 ± γ [km s − ] 33.3 ± f m [M ⊙ ] 0.0597 ± Derived parameter
Mass ratio q = M WD M sdB . +0 . − . sdB mass M sdB [M ⊙ ] 0 . +0 . − . sdB radius R sdB [R ⊙ ] 0 . +0 . − . WD mass M WD [M ⊙ ] 0 . +0 . − . Orbital inclination i [ ◦ ] 52 +8 − Separation a [R ⊙ ] 0 . +0 . − . Distance d [kpc] 1 . +0 . − . Derived parameter assuming the canonical sdB mass
Mass ratio q = M WD M sdB . +0 . − . sdB mass M sdB [M ⊙ ] 0.47 (fixed)sdB radius R sdB [R ⊙ ] 0 . +0 . − . WD mass M WD [M ⊙ ] 0 . +0 . − . Orbital inclination i [ ◦ ] 51 +4 − Separation a [R ⊙ ] 0 . +0 . − . Distance d [kpc] 1 . +0 . − . a taken from the APASS catalog (Henden et al. 2016) He i i i -2-4-6 λ (˚A) n o r m a li z e dflu x + c Fig. 3.—
Best fits of v rot sin i to the helium lines seen in theHIRES spectra. The atmospheric parameters were fixed to thevalues derived from the WHT spectra. can be combined withsin i = ( v rot sin i ) P orb πR sdB (2)and R sdB = s M sdB Gg (3) R e s i du a l s BJD-245718 r e l a t i v e flu x -0.002 Fig. 4.— lightcurve obtained with ULTRASPEC shown togetherwith the
Lcurve fit. The residuals are plotted below. with P orb being the orbital period, K the velocity semi-amplitude, M WD the mass of the companion and R sdB the radius of the sdB. The approach is described in fulldetail in Geier et al. (2007). A strict lower mass limit forthe sdB can be derived, because the inclination cannotexceed 90 ◦ . We found a lower limit for the sdB massM sdB > .
25 M ⊙ . The error is dominated by the sur-face gravity, which has to be estimated from the modelatmosphere fit. SYSTEM PARAMETERS M W D ( M ⊙ ) M sdB (M ⊙ ) Fig. 5.—
White dwarf mass versus sdB mass. The curved linescorrespond to synchronization with the corresponding error. Thedashed vertical line marks the canonical sdB mass of 0 .
47 M ⊙ . Thecontours show the results from the lightcurve fit with 1 σ (red), 2 σ (blue), 3 σ (black) confidence. Because the system is not eclipsing we cannot obtaina unique solution for the component masses from thelightcurve analysis. In order to determine masses andradii of both the sdB and the WD companion, we com-bined the results from the lightcurve analysis with theassumption of tidal synchronization of the sdB primaryto the orbit. The given errors are all 95 % confidencelimits.We find that both components have nearly the samemass. A mass ratio q = M WD /M sdB = 1 . +0 . − . , a massfor the sdB M sdB = 0 . +0 . − . M ⊙ and a WD compan-ion mass M WD = 0 . +0 . − . M ⊙ were derived (Fig. 5).The inclination is found to be i = 52 +8 − ◦ (Fig. 6). Thebeaming factor is B = 1 . +0 . − . , which is consistent withthe theoretical value 1.74 (for an sdB with T eff = 27 100,log g = 5 . m V ), the sdB mass, T eff and log g as described in Ramspeck et al. (2001). We find a dis-tance to PTF1 J0823 of d = 1 . +0 . − . kpc.An overview of the derived system parameter is givenin Table 3. DISCUSSION
Evolutionary history
In the standard scenario, the so-called 2nd commonenvelope channel, the system starts as a low mass binarywith ≈ ⊙ components. The initially more massive starfirst evolves to become a WD. Subsequently, the sdBprogenitor fills its Roche lobe at the tip of the red-giantbranch (RGB), forming an sdB with a canonical massof M WD = 0 .
47 M ⊙ , set by the helium core flash, witha WD companion (Han et al. 2002, 2003). Han et al.(2002) showed that the binding energy of the envelopeis very small at the tip of the RGB for a 1 M ⊙ star andtherefore the orbital shrinkage in the CE phase is not sig-nificant. They predict that sdB+WD binaries are formed M sdB (M ⊙ ) I n c li n a t i o n ( ◦ ) Fig. 6.—
Inclination versus sdB mass. The curved lines corre-spond to synchronization with the corresponding error. The dashedvertical line marks the canonical sdB mass of 0 .
47 M ⊙ . The con-tours show the results from the lightcurve fit with 1 σ (red), 2 σ (blue), 3 σ (black) confidence. with orbital periods longer than found in PTF1 J0823.In a different picture an ultracompact sdB+WD binarycan also be formed from a more massive main-sequencebinary where the sdB progenitor is > ⊙ . This sdBprogenitor ignites helium non-degenerately in the coreand fills its Roche lobe during the Hertzsprung gap orat the base of the RGB, resulting in an sdB with ei-ther a lower or higher mass compared to the tip of theRGB (Nelemans 2010; Geier et al. 2013). In such sys-tems, the envelope is more tightly bound and the or-bital shrinkage required to eject the CE becomes higher(Nelemans 2010; Geier et al. 2013). Geier et al. (2013)showed that CD − ◦ ⊙ progenitor for the sdB with a 3 - 4 M ⊙ companionfor the WD progenitor. The WD companion inPTF1 J0823 is, with an upper mass limit of M WD =0 .
58 M ⊙ , less massive than in CD − ◦ orb =129 . Future evolution
To understand the future evolution of the system, weused the code
MESA (Paxton et al. 2011, 2013, 2015).For the model we assumed an sdB with a canonicalmass M sdB = 0 .
47 M ⊙ with a white dwarf companionof M WD = 0 .
49 M ⊙ . Using release version 8118, weconstruct binary simulations that model the full stellarstructure equations for the sdB and treat the WD as apoint mass. We ran a set of simulations with periods,when the system exits the CE (post-CE orbital period),ranging from 87 to 120 minutes. The evolution of thesystem is governed by the loss of angular momentumdue to radiation of gravitational waves. We record thepost-CE age at which the orbital periods match the ob-served period of 87 minutes, shown by the dotted bluecurve in Fig. 7, and the age at which the stars makecontact, shown by the dashed-dotted red curve. Re-
90 95 100 105 110 115 120Post-CE Orbital Period (minutes)10 P o s t - C E A g e ( y r s ) He core burning lifetimeHe shell burning lifetimeAge at observationAge at contact
Fig. 7.—
The model post-CE orbital period is shown on the x-axis, with the post-CE age on the y-axis. The dashed grey anddashed-dotted black lines show the core and shell He burning life-times of the sdB, respectively. The dotted blue curve shows theages of the models when the orbital period matches the periodthat we observed for this system. The red curve shows the ages atwhich the stars make contact. Systems with initial orbital periodslonger than 106 minutes will make contact after the sdB finishesHe burning. cent modeling of asteroseismic observations of sdB stars(Constantino et al. 2015) points to convective cores muchlarger than found with the Schwarzschild condition. Atpresent, there is no clear consensus on the physics neededto achieve these larger cores, which prolongs the lifetimeof the He burning phase. To accommodate such an out-come, we performed runs with element diffusion active(Michaud et al. 2007; Schindler et al. 2015), doublingthe convective core mass (from 0 . M ⊙ to 0 . M ⊙ )and the core-burning lifetime (from 80 Myr to 152 Myr).The data from these runs are shown in Figures 7 and 8.If contact is made after core and shell He burning havefinished (dashed grey and dashed-dotted black curves inFig. 7) and the sdB has become a C/O WD with a0 . M ⊙ core and 0 . M ⊙ He envelope, the componentthat used to be the sdB will overflow its Roche lobe atan orbital period of less than 2 minutes, leading to aprompt merger and formation of an R CrB type star andsubsequent evolution into a massive single WD. Figure7 shows that the post-CE orbital period lower limit forthis outcome is 106 min.On the other hand, if the post-CE orbital period isless than 106 minutes, contact is made during the Heburning phase, a merger may be avoided and the sdB willdonate its remaining helium in an AM CVn type system(Brooks et al. 2015).
Current age
Figure 8 shows the position of PTF1 J0823 in the T eff –log g diagram overplotted with the confirmed sdB+whitedwarf systems in compact orbits as well as theoreti- T e(cid:11) [1000 K] l og ( g [ c m s − ] ) HeMS ZAEHB
Fig. 8.— T eff – log g diagram of the compact binary sdBstars with confirmed white dwarf companions (Kupfer et al. 2015).The red triangle marks PTF1 J0823. The helium main sequence(HeMS), the zero-age EHB (ZAEHB) and the terminal-age EHB(TAEHB) are superimposed with EHB evolutionary tracks byHan et al. (2002) (dashed lines: m env = 0 .
000 M ⊙ , dotted lines: m env = 0 .
001 M ⊙ , dashed-dotted lines: m env = 0 .
005 M ⊙ us-ing 0 .
45 M ⊙ models). The red solid line shows the EHB evolu-tionary track calculated with MESA using a 0 .
47 M ⊙ model with m env = 5 × − M ⊙ . cal evolutionary tracks. The sdBs with WD compan-ions populate the full extreme horizontal branch (EHB)band homogeneously with a small fraction of sdBs hav-ing evolved off the EHB. The values of T eff and log g forPTF1 J0823 are consistent with an sdB on the EHB inthe core helium burning stage.In a comparison of the spectroscopically derived T eff and log g with our MESA models, we find that an sdBmodel with a 5 × − M ⊙ hydrogen envelope matchesthe atmospheric parameter at a post-CE age of 94 Myr(Fig. 8), corresponding to a post-CE orbital period of109 min which is close to the limit where the sdB stillburns helium when filling its Roche lobe. CONCLUSION AND SUMMARY
Motivated by the possible existence of detachedhot (ultra-)compact binaries such as CD − ◦ orb =87.49668(1) min wasfound which makes PTF1 J0823 the second-most com-pact sdB system known so far. Although the system isnot eclipsing we have been able to derive a mass for thesdB of M sdB = 0 . +0 . − . M ⊙ and WD companion mass of M WD = 0 . +0 . − . M ⊙ by assuming a tidally locked sdB.The distance was found to be d = 1 . +0 . − . kpc.Although the solution allows for a wide range of com-panion masses we can exclude a massive white dwarf inPTF1 J0823: M WD < .
58 M ⊙ . The upper limit on theWD mass is only possible if the sdB is also on the upperlimit of its mass range with M sdB ≈ .
54 M ⊙ which isnot excluded, though only possible if the system evolvedfrom a more massive binary system with main sequencecomponents > ⊙ . If the sdB has a canonical mass of0 .
47 M ⊙ the companion is a low-mass white dwarf witha mass of 0 . < M WD < .
54 M ⊙ .Kupfer et al. (2015) found that a significant fraction ofthe sdB binaries host WDs of masses below 0.6 M ⊙ butall have longer periods of at least a few hours. Therefore,PTF1 J0823 is the first sdB with a confirmed low masswhite dwarf companion in a tight orbit.We calculated the evolutionary history of PTF1 J0823using MESA , assuming a canonical sdB mass ( M sdB =0 .
47 M ⊙ ), and a companion mass of M WD = 0 .
49 M ⊙ .We found that the sdB will burn helium for 152 Myr andsuch a system will start accretion while the sdB is stillburning helium if the orbital period after the system leftthe common envelope was smaller than 106 min.If the system reaches contact after the helium burn-ing has finished, the most likely outcome is a doublewhite dwarf merger and subsequent evolution into anR CrB star with a mass of 0 . . M ⊙ , which is themost common mass range for R CrB stars (Saio 2008;Clayton 2012). The final evolutionary stage will be asingle massive WD.However, if the sdB still burns helium when the sys-tem reaches contact the sdB starts to accrete helium-richmaterial onto the WD companion and the most likelyoutcome is a helium accreting AM CVn type system.Therefore, compact sdB binaries with WD companionsand post-CE orbital periods .
100 min might contributeto the population of AM CVn binaries with helium stardonors.Whether PTF1 J0823 is an R CrB progenitor orwhether a merger is prevented and the system forms anAM CVn type system remains elusive and requires moredetailed evolutionary calculations as well as more accu-rate mass measurements which will be available through
Gaia photometry and parallaxes.
ACKNOWLEDGMENTS
This work was supported by the GROWTH projectfunded by the National Science Foundation under GrantNo 1545949. JvR acknowledges support by the Nether-lands Research School of Astronomy (NOVA) and the foundation for Fundamental Research on Matter (FOM).TRM acknowledge the support from the Science andTechnology Facilities Council (STFC), ST/L00733. Thisresearch was partially funded by the Gordon and BettyMoore Foundation through Grant GBMF5076 to LarsBildsten. This work was supported by the National Sci-ence Foundation under grants PHY 11-25915, AST 11-09174, and AST 12-05574. This work was supported inpart by the National Science Foundation under GrantNo. PHYS-1066293 and the hospitality of the AspenCenter for Physics where parts of this paper was written.We thank the referee for helpful and timely comments.Observations were obtained with the Samuel OschinTelescope at the Palomar Observatory as part of the PTFproject, a scientific collaboration between the CaliforniaInstitute of Technology, Columbia University, Las Cum-bres Observatory, the Lawrence Berkeley National Labo-ratory, the National Energy Research Scientific Comput-ing Center, the University of Oxford, and the WeizmannInstitute of Science. Some of the data presented hereinwere obtained at the W.M. Keck Observatory, which isoperated as a scientific partnership among the Califor-nia Institute of Technology, the University of Californiaand the National Aeronautics and Space Administration.The Observatory was made possible by the generous fi-nancial support of the W.M. Keck Foundation. The au-thors wish to recognize and acknowledge the very sig-nificant cultural role and reverence that the summit ofMauna Kea has always had within the indigenous Hawai-ian community. We are most fortunate to have the op-portunity to conduct observations from this mountain.Some results presented in this paper are based on obser-vations made with the WHT operated on the island ofLa Palma by the Isaac Newton Group in the Spanish Ob-servatorio del Roque de los Muchachos of the Institutiode Astrofisica de Canarias.
Software:
PyRAF (Bellm & Sesar 2016),
MAKEE
Gatspy (VanderPlas & Ivezi´c2015),
LCURVE (Copperwheat et al. 2010), emcee (Foreman-Mackey et al. 2013),
MESA (Paxton et al.2011, 2013, 2015),
FITSB2 (Napiwotzki et al. 2004)