The ELM Survey. V. Merging Massive White Dwarf Binaries
Warren R. Brown, Mukremin Kilic, Carlos Allende Prieto, A. Gianninas, Scott J. Kenyon
aa r X i v : . [ a s t r o - ph . S R ] A p r Draft version July 28, 2018
Preprint typeset using L A TEX style emulateapj v. 5/2/11
THE ELM SURVEY. V. MERGING MASSIVE WHITE DWARF BINARIES * Warren R. Brown , Mukremin Kilic , Carlos Allende Prieto , , A. Gianninas and Scott J. Kenyon Smithsonian Astrophysical Observatory, 60 Garden St, Cambridge, MA 02138 USA Homer L. Dodge Department of Physics and Astronomy, University of Oklahoma, 440 W. Brooks St., Norman, OK, 73019 USA Instituto de Astrof´ısica de Canarias, E-38205, La Laguna, Tenerife, Spain Departamento de Astrof´ısica, Universidad de La Laguna, E-38206 La Laguna, Tenerife, Spain
Draft version July 28, 2018
ABSTRACTWe present the discovery of 17 low mass white dwarfs (WDs) in short-period P ≤ g ≃ <
10 Gyr. Four have & M ⊙ companions. Ifthe companions are massive WDs, these four binaries will evolve into stable mass transfer AM CVnsystems and possibly explode as underluminous supernovae. If the companions are neutron stars, thenthese may be milli-second pulsar binaries. These discoveries increase the number of detached, doubledegenerate binaries in the ELM Survey to 54; 31 of these binaries will merge within a Hubble time. Subject headings: binaries: close — Galaxy: stellar content — Stars: individual: SDSS J0751-0141,SDSS J0811+0225 — Stars: neutron — white dwarfs INTRODUCTION
Extremely low mass (ELM) WDs, degenerate objectswith log g < − ) surface gravity or . M ⊙ mass,are the product of common envelope binary evolution(e.g. Marsh et al. 1995). ELM WDs are thus the sign-posts of the type of binaries that are strong gravitationalwave sources and possible supernovae progenitors. Thegoal of the ELM Survey is to discover and characterizethe population of ELM WDs in the Milky Way.Previous ELM Survey papers have reported the dis-covery of 40 WDs spanning 0.16 M ⊙ to 0.49 M ⊙ foundin the Hypervelocity Star (HVS) Survey, the Sloan Dig-ital Sky Survey (SDSS), and in our own targeted sur-vey (Brown et al. 2010, 2011b, 2012b; Kilic et al. 2010b,2011a, 2012). We refer to this full sample of WDs asthe ELM Survey sample, but reserve the term “ELMWD” for those objects with log g <
7. All of ourWDs are found in short-period, detached binaries, 60%of which have merger times <
10 Gyr. Three notablesystems are detached binaries with <
40 min orbitalperiods (Kilic et al. 2011b,c). The eclipsing systemJ0651+2844 is the second-strongest gravitational wavesource in the mHz range (Brown et al. 2011c). We mea-sured its period change in one year with optical eclipsetiming (Hermes et al. 2012b). Other results from theELM Survey include the first tidally distorted WDs(Kilic et al. 2011c; Hermes et al. 2012a) and the first pul-sating helium-core WDs (Hermes et al. 2012c, 2013).Here we present the discovery of 17 new WD bina-ries identified from spectra previously obtained for theHVS Survey of Brown et al. (2005, 2006a,b, 2007a,b,2009, 2012a). Kilic et al. (2007a) analyzed the visually-identified WDs in the original dataset and discovered one [email protected], [email protected] * Based on observations obtained at the MMT Observatory, ajoint facility of the Smithsonian Institution and the Universityof Arizona.
ELM WD binary (Kilic et al. 2007b). This approachfailed to identify the lowest surface gravity WDs. Wenow fit stellar atmosphere models to the entire collectionof spectra not previously identified as WDs, and acquirefollow-up spectroscopy of new ELM WD candidates. Theresult of this effort is that we find low surface gravity ob-jects that might not be considered WDs if not for theirobserved orbital motion.We chose to call objects with 5 < log g < ∼ g = 6 . ± .
04 object inJ0651+2844, a 0 . ± . R ⊙ star, demonstrates itis a degenerate WD (Brown et al. 2011c; Hermes et al.2012b). Van Grootel et al. (2013) account for the un-usually long pulsation periods of the ELM WD pulsatorswith low mass WD models. Hence, calling our low sur-face gravity objects ELM WDs is appropriate.Interestingly, we find ELM WDs in binaries with > M ⊙ companions and rapid merger times. When these de-tached binaries begin mass transfer, Marsh et al. (2004)show that the extreme mass ratios will lead to sta- Brown et al.ble mass transfer. For the case of massive WD accre-tors, theorists predict large helium flashes that may ig-nite thermonuclear transients dubbed “.Ia” supernovae(Bildsten et al. 2007; Shen & Bildsten 2009) or may det-onate the surface helium-layer and the massive WD(Nomoto 1982; Woosley & Weaver 1994; Sim et al. 2012)and produce an underluminous supernova. However, thefinal outcome of such mergers is uncertain and they maynot trigger supernovae explosions (Dan et al. 2012). Ifthe companions are instead neutron stars, this would bethe first time a milli-second pulsar is identified throughits low-mass WD companion. Such systems allow mea-surement of the binary mass ratio and the neutron starmass through a combination of the pulsar orbit obtainedfrom radio timing and the WD orbit obtained from op-tical radial velocity observations.The importance of identifying the ELM WDs in theHVS Survey is that the HVS Survey is a well-definedand a nearly 100% complete spectroscopic survey. Witha complete sample of ELM WDs we can measure thespace density, period distribution, and merger rate ofELM WDs, and link ELM WD merger products to pop-ulations of AM CVn stars, R CrB stars, and possibly un-derluminous supernovae. In a stellar evolution context,our ELM WD survey complements studies of WD bina-ries with main sequence companions (e.g. Pyrzas et al.2012; Rebassa-Mansergas et al. 2012) and with sdB starcompanions (e.g. Geier et al. 2012; Silvotti et al. 2012).sdB stars are T eff > ,
000 K helium-burning precursorsto WDs (Heber 2009). Our ELM WDs, on the otherhand, have T eff < ,
000 K.We organize this paper as follows. In Section 2 wediscuss our observations and data analysis. In Section3 we present the orbital solutions for 17 new ELM WDbinaries. In Section 4 we discuss the properties of theELM WD sample. We conclude in Section 5. DATA AND ANALYSIS
Target Selection
The HVS Survey is a targeted spectroscopic survey of15 < g <
20 stars with the colors of ≃ M ⊙ main se-quence stars, stars which should not exist at faint magni-tudes in the halo unless they were ejected there. The tar-get selection is detailed in Brown et al. (2012a) and spans − . < ( g − r ) . − .
25, 0 . . ( u − g ) < .
07. Thiscolor selection fortuitously targets WDs in the approxi-mate range 10 , < T eff < ,
000 K and log g . . ferre code described byAllende Prieto et al. (2006) and synthetic DA WD purehydrogen spectra kindly provided by D. Koester. Thegrid of WD model atmospheres covers effective tempera-tures from 6000 K to 30,000 K in steps of 500 K to 2000K, and surface gravities from log g =5.0 to 9.0 in steps of0.25 dex. The model atmospheres are calculated assum-ing local thermodynamic equilibrium and include bothconvective and radiative transport (Koester 2008).We fit 2,000 spectra, mostly from the original HVS Sur-vey (Brown et al. 2005, 2006a,b, 2007a,b, 2009) but alsosome newly acquired data (Brown et al. 2012a). These2,000 spectra were not previously analyzed for the ELM Fig. 1.—
Surface gravity vs. effective temperature of the 57 WDcandidates (blue diamonds) and the previously published ELMSurvey WDs (red circles). The 17 newly discovered binaries areplotted with errorbars and parameters obtained from Gianninasstellar atmosphere models; the parameters of the other WDs wereobtained from Koester models. For reference, we plot theoreticaltracks for 0.16–0.45 M ⊙ hydrogen atmosphere WDs (green lines,Panei et al. 2007), main sequence tracks for 2, 3 and 6 M ⊙ stars(cyan lines, Girardi et al. 2004), and horizontal branch tracks for0.488, 0.495, and 0.500 M ⊙ stars (magenta lines, Dorman et al.1993). Zero-age main sequence (ZAMS) and zero-age horizontalbranch (ZAHB) isochrones are drawn with thick lines, as is the ho-mogenous helium-burning main sequence (He-MS) from Paczy´nski(1971). Survey because the spectra were not previously identi-fied as WDs. We fit both flux-calibrated spectra (for im-proved T eff constraints) as well as continuum-correctedBalmer line profiles (insensitive to reddening and fluxcalibration errors). For the continuum-corrected Balmerline profiles, we normalize the spectra by fitting a low-order polynomial to the regions between the Balmerlines. We adopt the parameters from the flux-calibratedspectra, except in cases where the spectra were obtainedin non-photometric conditions. The uncertainties in oursingle-epoch measurements are typically ±
500 K in T eff and ± . g . From these fits we identify 57 lowmass WD candidates. New Spectroscopic Observations
We obtain follow-up spectra for each of the candidatelow mass WDs to improve stellar atmosphere parametersand to search for velocity variability.Observations were obtained over the course of sevenobserving runs at the 6.5m MMT telescope betweenMarch 2011 and February 2013. We used the Blue Chan-nel spectrograph (Schmidt et al. 1989) with the 832 linemm − grating, which provides a wavelength coverage3650 ˚A to 4500 ˚A and a spectral resolution of 1.0 ˚A.All observations were paired with a comparison lamp ex-posure, and were flux-calibrated using blue spectropho-tometric standards (Massey et al. 1988). The extractedspectra typically have a signal-to-noise (S/N) of 7 perpixel in the continuum and a 14 km s − radial velocityerror.We obtained additional spectroscopy for g <
17 magELM WD candidates in queue scheduled time at thextremely Low Mass White Dwarf Survey. V. 3
Fig. 2.—
Gianninas model fits (smooth red lines) overplottedon the composite observed spectra (black lines) for the 17 WDbinaries. The Balmer lines are arranged from H12 (top) to H γ (bottom); left panel plots the K <
200 km s − binaries, rightpanel plots the K >
200 km s − binaries. − gratingand a 1.5 ′′ slit, providing wavelength coverage 3500 ˚Ato 5500 ˚A and a spectral resolution of 1.7 ˚A. All obser-vations were paired with a comparison lamp exposure,and were flux-calibrated using blue spectrophotometricstandards. The extracted spectra typically have a S/Nof 10 per pixel in the continuum and a 18 km s − radialvelocity error. ELM WD Identifications
Our follow-up observations provide improved stellar at-mosphere constraints, from which we determine that 24(42%) of the candidates are probable ELM WDs with5 < log g < g > g ≤ T eff vs. log g for allof the WDs with log g >
5. Previously published ELMSurvey stars are marked with red circles. The observedWDs overlap tracks based on Panei et al. (2007) mod-els for He-core WDs with hydrogen shell burning ((greenlines) Kilic et al. 2010b), but do not overlap main se-quence nor horizontal branch evolutionary tracks. Forreference, we also plot Girardi et al. (2002, 2004) solarmetallicity main sequence tracks for 2, 3, and 6 M ⊙ stars (cyan lines). A helium-burning horizontal branchstar can have a surface gravity similar to a degenerate HeWD (e.g., Heber et al. 2003), but only at a systematicallyhigher effective temperature than that targeted by theELM Survey. This is illustrated by Dorman et al. (1993)[Fe/H]=-1.48 horizontal branch tracks for 0.488, 0.495,and 0.500 M ⊙ stars (magenta lines), as well as the ho-mogenous helium-burning main sequence from Paczy´nski(1971). The zero-age main sequence and helium-burninghorizontal branch isochrones (thick lines) mark the lim-its.Seventeen of the WDs show significant velocity vari-ability, including twelve of the newly identified ELMWDs. The other ELM WDs have insufficient coverage fordetecting (or ruling out) velocity variability. We focusthe remainder of this paper on the 17 well-constrainedsystems. Improved Atmosphere Parameters
Our sample of 17 well-constrained systems containsfour log g ≃ − ≤ [Fe / H] ≤ .
5, 1 ≤ log g ≤ α = 0.8 prescription of the mixing-length theory for models where convective energy trans-port is important (Tremblay et al. 2010). We calculateatmosphere models for low surface gravities, and use agrid that covers T eff from 4000 K to 30,000 K in stepsranging from 250 to 5000 K and log g from 5.0 to 8.0 insteps of 0.25 dex.Our stellar atmosphere fits use the so-called spectro-scopic technique described in Gianninas et al. (2011).One difference between our work and Gianninas et al.(2011) is that we fit higher-order Balmer lines, up toand including H12, observed in the low surface gravityELM WDs. The higher-order Balmer lines are sensitiveto log g and improve our surface gravity measurement.For the handful of WDs in our sample with log g > T eff = 10,000 K, 0.2 M ⊙ H-richWD is ∼ yr (Paquette et al. 1986). Extreme horizon-tal branch stars, which can have surface gravities com-parable to the lowest gravity WDs, have longer ∼ yrdiffusion timescales (Michaud et al. 2008). These diffu-sion timescales are shorter than the WD evolutionarytimescale, suggesting there may be on-going accretionin these ultra-compact binary systems. Near- and mid-infrared observations are needed constrain the possibilityof accretion. We defer a detailed analysis of the metalabundances in ELM WDs to a future paper. For ourpresent analysis we exclude the wavelength ranges wherethe metal lines are present in our fits.Our error estimates combine the internal error of themodel fits, obtained from the covariance matrix of thefitting algorithm, and the external error, obtained frommultiple observations of the same object. Uncertaintiesare typically 1.2% in T eff and 0.038 dex in log g (seeLiebert et al. 2005, for details). A measure of the sys-tematic uncertainty inherent in the stellar atmospheremodels and fitting routines comes from Gianninas et al.(2011), who find a systematic uncertainty of ≈ . g . This is corroborated by the difference we ob-serve between the different fitting methods discussed inSection 2.1 and here: the mean difference and the dis-persion in T eff is 1 . ± .
3% and in log g is 0 . ± . g < M ⊙ Brown et al.
TABLE 1White Dwarf Physical Parameters
Object RA Dec T eff log g Mass g M g d helio (h:m:s) (d:m:s) (K) (cm s − ) ( M ⊙ ) (mag) (mag) (kpc)J0056 − ±
180 6 . ± .
044 0.17 17 . ± .
023 8.0 0.69J0751 − ±
240 5 . ± .
046 0.17 17 . ± .
015 8.0 0.75J0755+4800 7:55:19.483 48:00:34.07 19890 ±
350 7 . ± .
057 0.42 15 . ± .
019 9.7 0.18J0802 − ±
280 6 . ± .
048 0.20 18 . ± .
012 8.2 1.19J0811+0225 8:11:33.560 2:25:56.76 13990 ±
230 5 . ± .
054 0.17 18 . ± .
013 8.0 1.30J0815+2309 8:15:44.242 23:09:04.92 21470 ±
340 5 . ± .
046 0.17 17 . ± .
015 6.7 1.53J0840+1527 8:40:37.574 15:27:04.53 13810 ±
240 5 . ± .
053 0.17 19 . ± .
018 8.0 1.69J1046 − ±
230 7 . ± .
045 0.37 17 . ± .
020 10.2 0.36J1104+0918 11:04:36.739 9:18:22.74 16710 ±
250 7 . ± .
049 0.46 16 . ± .
016 10.3 0.18J1141+3850 11:41:55.560 38:50:03.02 11620 ±
200 5 . ± .
054 0.17 18 . ± .
018 8.0 1.56J1151+5858 11:51:38.381 58:58:53.22 15400 ±
300 6 . ± .
057 0.17 20 . ± .
033 8.0 2.57J1157+0546 11:57:34.455 5:46:45.58 12100 ±
250 5 . ± .
071 0.17 19 . ± .
021 8.0 2.29J1238+1946 12:38:00.096 19:46:31.45 16170 ±
260 5 . ± .
051 0.17 17 . ± .
019 8.0 0.68J1538+0252 15:38:44.220 2:52:09.49 11560 ±
220 5 . ± .
053 0.17 18 . ± .
015 8.0 1.28J1557+2823 15:57:08.483 28:23:36.02 12550 ±
200 7 . ± .
046 0.49 17 . ± .
029 11.2 0.18J2132+0754 21:32:28.360 7:54:28.24 13700 ±
210 5 . ± .
045 0.17 17 . ± .
019 8.0 0.96J2338 − ±
280 6 . ± .
050 0.27 19 . ± .
035 9.0 1.29
TABLE 2Binary Orbital Parameters
Object N obs P K γ
Spec. Conjunction M q τ merge (days) (km s − ) (km s − ) HJD-2450000 (days) ( M ⊙ ) (Gyr)J0056 − . ± . . ± . . ± . . ± . ≥ ≤ ≤ − . ± . . ± . . ± . . ± . ≥ ≤ ≤ . ± . . ± . . ± . . ± . ≥ ≤ ≤ − . ± . . ± . . ± . . ± . ≥ ≤ ≤ . ± . . ± . . ± . . ± . ≥ ≤ ≤ . ± . . ± . − . ± . . ± . ≥ ≤ ≤ . ± . . ± . . ± . . ± . ≥ ≤ ≤ − . ± . . ± . − . ± . . ± . ≥ ≤ ≤ . ± . . ± . . ± . . ± . ≥ ≤ ≤ . ± . . ± . − . ± . . ± . ≥ ≤ ≤ . ± . . ± . . ± . . ± . ≥ ≤ ≤ . ± . . ± . − . ± . . ± . ≥ ≤ ≤ . ± . . ± . − . ± . . ± . ≥ ≤ ≤ . ± . . ± . − . ± . . ± . ≥ ≤ ≤ . ± . . ± . . ± . . ± . ≥ ≤ ≤ . ± . . ± . − . ± . . ± . ≥ ≤ ≤ − . ± . . ± . . ± . . ± . ≥ ≤ ≤ Note . — Objects with significant period aliases: J0755+4800 (0.349 days), J0840+1527 (0.340 days), J1046 − and absolute magnitude M g = 8 . g -band magnitude come fromSDSS (Aihara et al. 2011) and d helio is our heliocentricdistance estimate. Orbital Elements
We calculate orbital elements and merger times in thesame way as previous ELM Survey papers, and so we re-fer the reader to those papers for the details of our anal-ysis. In brief, we measure absolute radial velocities us-ing the cross-correlation package RVSAO (Kurtz & Mink1998) and a high-S/N template. We use the entire spec-trum in the cross-correlation. We then use the summedspectra (Figure 2) as cross-correlation templates to maxi-mize our velocity precision for each individual object. Wecalculate orbital elements by minimizing χ for a circularorbit using the code of Kenyon & Garcia (1986). Figure 3 shows the periodograms for the 17 binaries, and Figure4 plots the radial velocities phased to the best-fit orbitalperiods. We use the binary mass function to estimatethe unseen companion mass; an edge-on orbit with incli-nation i = 90 ◦ yields the minimum companion mass M and the maximum gravitational wave merger time.Table 2 summarizes the binary orbital parameters.Columns include orbital period ( P ), radial velocity semi-amplitude ( K ), systemic velocity ( γ ), time of spectro-scopic conjunction (the time when the object is closestto us), minimum secondary mass ( M ) assuming i = 90 ◦ ,the maximum mass ratio ( q ), and the maximum gravita-tional wave merger time τ merge . The systemic velocitiesin Table 2 are not corrected for the WDs’ gravitationalredshifts, which should be subtracted from the observedvelocities to find the true systemic velocities. This cor-rection is a few km s − for a 0.17 M ⊙ helium WD, com-parable to the systemic velocity uncertainty.xtremely Low Mass White Dwarf Survey. V. 5 Fig. 3.—
Periodograms for the 17 WD binaries. The best orbital periods have the smallest χ values; some binaries are well constrainedand some have period aliases. Fig. 4.—
Observed velocities phased to best-fit orbits for the 17 WD binaries (Table 2). RESULTS
The orbital solutions constrain the nature of the ELMWD binaries. Here we discuss the systems with shortmerger times, massive companions, or that may be un-derluminous supernovae progenitors.
J0056 − The ELM WD J0056 − . ± . ± − . We can calculate its likely companionmass if we assume a distribution for the unknown or-bital inclination. Although radial velocity detections arebiased towards edge-on systems (see Section 4), we willassume that we are observing a random inclination forpurpose of discussion. The mean inclination angle for arandom sample, i = 60 ◦ , is then an estimate of the mostlikely companion mass. For J0056 − M ⊙ WD at an orbital separation of0.5 R ⊙ . This orbital separation rules out the possibilityof a main sequence companion.There is no evidence for a 0.61 M ⊙ WD in the spec-trum of J0056 − M ⊙ WD to be 15 - 100times less luminous than the 0.17 M ⊙ WD for coolingages of 100 Myr - 1 Gyr (Bergeron et al. 1995). A moreplausible evolutionary scenario for an ELM WD binarylike J0056 − M ⊙ ,J0056 − q ≤ − J0751 − The ELM WD J0751 − . ± .
067 hr or-bital period with aliases ranging between 1.85 and 2.05 hr(see Figure 3). The large 433 ± − semi-amplitudeindicates that the companion is massive, regardless ofthe exact period. The minimum companion mass is 0.94 M ⊙ . Assuming a random inclination distribution, thereis a 47% probability that the companion is > M ⊙ .Given that the ELM WD went through a com-mon envelope phase of evolution with its companion,J0751 − Chandra X-ray Observatory time to search for X-rayemission from a possible neutron star.For i = 60 ◦ , the companion is a 1.32 M ⊙ WD, andthe system will begin mass transfer in 290 Myr. The ex-treme mass ratio q ≤ − J0811+0225
The ELM WD J0811+0225 has an orbital period of19 . ± .
012 hr and a semi-amplitude of 221 km s − .These orbital parameters yield a minimum companionmass of 1.20 M ⊙ . That means the companion probablyexceeds a Chandrasekhar mass. For i = 60 ◦ , the mostlikely companion is a 1.70 M ⊙ neutron star at an orbitalseparation of 4.6 R ⊙ . There is no Fermi gamma-ray de-tection at this location, but additional observations areneeded to determine the nature of this system. J0840+1527
The ELM WD J0840+1527 has a best-fit log g =5 . ± .
053 near the limit of our model grid. Its best-fit orbital period is 12 . ± .
114 hr with a significantalias at 8.3 hr. Assuming this object is 0.17 M ⊙ , itsmost likely companion is a WD with a comparable mass,0.19 M ⊙ , at an orbital separation of 1.9 R ⊙ . If, on theother hand, J0840+1527 were a 3 M ⊙ main sequencestar, its companion would have an orbital separation of4.3 R ⊙ – a separation comparable to the radius of a 3 M ⊙ star, and thus physically implausible. There is noevidence for mass transfer in this system. We concludethat J0840+1527 is a pair of ELM WDs. J1141+3850, J1157+0546, and J1238+1946
J1141+3850, J1157+0546, and J1238+1946 are theother systems containing WDs near the low-gravity limitof our stellar atmosphere model grid, but their k = 158 -266 km s − semi-amplitudes are significantly larger thanthat of J0840+1527. If we assume that the objects are0.17 M ⊙ ELM WDs, then the binary companions haveminimum masses of 0.45 - 0.75 M ⊙ . If we instead as-sume that the objects are main sequence stars, then therequired orbital separations are comparable to the ra-dius of the main sequence star and physically impossible.There is no evidence for mass transfer in these systems.We conclude that J1141+3850, J1157+0546, andJ1238+1946 are ELM WDs with likely WD companions.For J1141+3850, there is a 36% probability that the com-panion is > M ⊙ , possibly a milli-second pulsar. ForJ1141+3850 and J1238+1946, mass transfer will begin in7-10 Gyr, making them AM CVn progenitors and possi-ble underluminous supernovae progenitors. J2132+0754
The ELM WD J2132+0754 has a well-constrained or-bital period of 6 . ± . ± − . The minimum companion mass is 0.95 M ⊙ , and there is a 48% probability that the companionis > M ⊙ , possibly a milli-second pulsar. For i = 60 ◦ ,the most likely companion is a 1.33 M ⊙ WD that willbegin mass transfer in 6 Gyr. That makes J2132+0754a likely AM CVn progenitor and another possible under-luminous supernovae progenitor.
J2338 − The ELM WD J2338 − . ± .
170 hr and a semi-amplitude of 133 ± − . In this case the companion is another ELM WD;for i = 60 ◦ , the most likely companion is a 0.17 M ⊙ WDat an orbital separation of 0.56 R ⊙ . Given the unitymass ratio, this system will undergo unstable mass trans-fer and will merge to form a single ∼ M ⊙ WD. Thissystem will merge in less than 1 Gyr. DISCUSSION
With these 17 new discoveries, plus the pulsating ELMWD discovery published by Hermes et al. (2013), theELM Survey has found 54 detached, double degeneratebinaries; 31 of the binaries will merge within a Hubbletime. Table 3 summarizes the properties of the systems.Eighty percent of the ELM Survey binaries are formallyELM WD systems.
Significance of Binary Detections
We find low mass WDs in compact binaries, binariesthat must have gone through common envelope evolu-tion. This makes sense because extremely low mass WDsrequire significant mass loss to form; the Universe isnot old enough to produce an extremely low mass WDthrough single star evolution. Yet four objects publishedin the ELM Survey have no significant velocity variabil-ity, two of which are ELM WDs (see Table 3). To under-stand whether or not these stars are single requires thatwe understand the significance of our binary detections.Each ELM Survey binary is typically constrained by10-30 irregularly spaced velocities with modest errors.Given that we determine orbital parameters by minimiz-ing χ , the F -test is a natural choice. We use the F -testxtremely Low Mass White Dwarf Survey. V. 7 Fig. 5.—
Orbital period vs. semi-amplitude for the ELM Surveybinaries. Previously published binaries are drawn with solid redcircles; the 17 binaries from this paper are drawn with solid bluediamonds. Dashed lines indicate approximate companion mass un-der the assumption that M = 0 . M ⊙ and i = 60 ◦ . to check whether the variance of the data around the or-bital fit is consistent with the variance of the data arounda constant velocity (we use the weighted mean of the ob-servations). F -test probabilities for the published ELMSurvey binaries are < .
01. In other words, our binarieshave significant velocity variability at the >
99% confi-dence level.In the null cases we need to calculate the likelihood ofnot detecting a binary. This is a trickier problem, andone that we approach with a Monte Carlo calculation.We start by selecting a set of observations (times, ve-locity errors) and an orbital period and semi-amplitude.We convert observation times to orbital phases using arandomly drawn zero time, and calculate velocities atthose phases summed with a randomly drawn velocityerror. We perform the F -test, using 0.01 as a detectionthreshold. We repeat this calculation 10,000 times for agiven orbital period and semi-amplitude, and then selecta new orbital period and semi-amplitude to iterate on.This analysis is done for each object.We find that the datasets for our 17 new binaries havea median 99.9% likelihood of detecting K = 200 km s − binaries, a 97% likelihood of detecting K = 100 km s − binaries, and a 44% likelihood of detecting K = 50 kms − binaries. It is no surprise that we are less likelyto detect a low semi-amplitude binary, but this analysissuggests that we can be quite confident of detecting K >
100 km s − systems. We find very similar likelihoods fordetecting binaries containing ELM WDs in the full ELMSurvey sample.The datasets for the null cases typically contain fewerobservations and so are not as well-constrained. ForJ0900+0234, a 0.16 M ⊙ ELM WD with no observed ve-locity variation (Brown et al. 2012b), the likelihoods ofdetecting a K = 200, 100, and 50 km s − binary are 87%,57%, and 10%, respectively. Additional observations arerequired to claim this ELM WD as non-variable.There is, of course, an orbital period dependence to thedetections, and periods near 24 hr are the most prob- Fig. 6.—
Gravitational wave merger time versus total systemmass for the ELM Survey. We calculate system mass assuming i = 60 ◦ when orbital inclination is unknown. Previously publishedELM Survey binaries are drawn with solid red circles, and the 17new binaries from this paper are drawn with solid blue diamonds.Six binaries have probable masses exceeding the Chandrasekharmass; three have merger times less than 10 Gyr, as indicated bythe dotted line. The minimum companion mass for J0811+0225 is1.2 M ⊙ . lematic. Taken together, our datasets have a median39% likelihood of detecting a K = 100 km s − binary at P = 24 hr. Yet we remain sensitive to longer periods:our datasets have median 99% and 98% likelihoods ofdetecting a K = 100 km s − binary at P = 18 hr and P = 36 hr, respectively.Figure 5 plots the observed distribution of P and K for the ELM Survey binaries. The dashed lines indicatethe approximate companion mass assuming M is 0.2 M ⊙ and i is 60 ◦ . At K = 100 km s − , we can detect compan-ion masses down to 0.1 M ⊙ at 2 hr orbital periods and0.55 M ⊙ companions at 2 day orbital periods. Systemswith K <
100 km s − are the realm of . M ⊙ com-panions, and we observe a half-dozen systems with theseparameters. Our incompleteness at K <
100 km s − im-plies there are quite likely more ELM WDs with ≃ M ⊙ companions; the remaining ELM WD candidates that donot show obvious velocity change in a couple observationsare possible examples of such low amplitude systems.Finally, orbital inclination acts to increase the diffi-culty of identifying lone ELM WDs. Consider the set of46 ELM WDs in Table 3 with log g <
7, two of whichare non-variable. Their median K is 240 km s − , a semi-amplitude that would appear <
50 km s − at i < ◦ .If the 46 objects have randomly distributed orbital in-clinations, one object should have i < ◦ and a second i < ◦ . We conclude there is no good evidence for alone ELM WD in our present sample. This is in starkcontrast to the population of 0.4 M ⊙ WDs in the solarneighborhood, of which 20%-30% are single (Brown et al.2011a).
The Future of ELM WDs
One of the most exciting aspects of our ELM WD bi-naries is that many have gravitational wave merger timesless than a Hubble time, and in one case as short as 1 Brown et al.
Fig. 7.—
Gravitational wave merger time versus mass ratio q for the ELM Survey. We calculate mass ratio assuming i =60 ◦ when orbital inclination is unknown. Previously publishedELM Survey binaries are drawn with solid red circles, and the 17new binaries from this paper are drawn with solid blue diamonds.Dotted lines mark the approximate thresholds for stability of masstransfer during the Roche lobe overflow phase (Marsh et al. 2004),drawn for systems that will merge in <
10 Gyr. Stable mass transfersystems will evolve into AM CVn systems; unstable mass transfersystems will possibly merge.
Myr (Brown et al. 2011c; Hermes et al. 2012b). A nat-ural question, then, is what will happen when the WDsmerge. Notably, 5 of our 17 new binaries have probablesystem masses (for i = 60 ◦ ) in excess of a Chandrasekharmass.Figure 6 plots the distribution of merger time and sys-tem mass for the ELM Survey binaries assuming i = 60 ◦ ,except when inclination is known. The majority of ourbinaries have probable masses below the Chandrasekharmass and are not potential supernova Type Ia progeni-tors, but six systems appear to have either neutron staror massive WD companions. The evolution of these sixsystems depends on the stability of mass transfer dur-ing the Roche lobe overflow phase, and thus on the massratio of the binary.Figure 7 plots the distribution of merger time and massratio q for the ELM Survey binaries, again assuming i = 60 ◦ except when inclination is known. The Chan-drasekhar mass systems generally have extreme q . . q ≥ /
3, such as J2338 − q ≃ /
2, such as J0651+2844, will experience either stable or unstable mass transfer depending on their spin-orbit coupling. After we constrain the remaining ELMWD candidates plotted in Fig. 1 we look forward to cal-culating their space density and merger rate. ELM WDsbinaries are clearly an important channel for AM CVnstar formation, and thus an important source of stronggravitational waves in the mHz regime. CONCLUSION
We perform stellar atmosphere fits to the entire col-lection of single-epoch spectra in the HVS Survey andidentify 57 new low mass WD candidates. Follow-upspectroscopy reveals 17 WDs with significant velocityvariability, 12 of which are ELM WDs. Presently, theELM Survey sample is consistent with all of the ELMWDs being part of close binaries. ELM WDs are thussignposts for binaries that are strong gravitational wavesources and possible supernovae progenitors.Four binaries in our sample contain log g ≃ g ≃ g <
6) WDs in our sample have metal lines in theirspectra. This issue will be studied in detail in a futurepaper; infrared observations are needed to constrain thepossibility of debris disks as the source of Ca and Mgaccretion in these compact binary systems.Recent discoveries of pulsations in several of our ELMWD targets (Hermes et al. 2012c, 2013) enable us toprobe the interiors of low-mass, presumably He-coreWDs using the tools of asteroseismology. Due to theHVS color selection, all of the newly identified systemsare hotter than 10,000 K and therefore too hot to showthe g-mode pulsations detected in cooler ELM WDs(C´orsico et al. 2012).Four binaries in our sample have massive & M ⊙ companions and <
10 Gyr merger times. If the unseencompanions are massive WDs, these extreme mass ratiobinaries will undergo stable mass transfer and will evolveinto AM CVn systems and potentially future .Ia or un-derluminous supernovae. Thus the systems J0751 − eLISA and other future gravita-tional wave detection experiments.We thank M. Alegria, P. Canton, S. Gotilla, J. McAfee,E. Martin, A. Milone, and R. Ortiz for their assistancewith observations obtained at the MMT Observatory,and P. Berlind and M. Calkins for their assistance withobservations obtained at the Fred Lawrence Whipple Ob-servatory. We also thank P. Bergeron and D. Koesterfor their invaluable assistance in the computation of ourstellar atmosphere model grids. This research makes useof the SAO/NASA Astrophysics Data System Biblio-graphic Service. This project makes use of data prod-ucts from the Sloan Digital Sky Survey, which has beenfunded by the Alfred P. Sloan Foundation, the Partic-ipating Institutions, the National Science Foundation,and the U.S. Department of Energy Office of Science.This work was supported in part by the Smithsonian In-stitution. Facilities:
MMT (Blue Channel Spectrograph),FLWO:1.5m (FAST)0 Brown et al.
TABLE 3Merger and Non-Merger Systems in the ELM Survey
Object T eff log g P K Mass M M (60 ◦ ) τ merge Ref(K) (cm s − ) (days) km s − M ⊙ M ⊙ M ⊙ GyrJ0022 − ≥ .
19 0.23 ≤ .
73 6J0056 − ≥ .
46 0.61 ≤ . − · · · ≥ .
62 0.85 ≤ . · · · − ≥ .
94 1.32 ≤ . ≥ .
81 1.12 ≤ .
22 2J0818+3536 10620 5.69 0.18315 170.0 0.17 ≥ .
26 0.33 ≤ . ≥ .
76 1.05 ≤ . ≥ .
47 0.61 ≤ .
18 0J0849+0445 10290 6.23 0.07870 366.9 0.17 ≥ .
64 0.88 ≤ .
47 4J0923+3028 18350 6.63 0.04495 296.0 0.23 ≥ .
34 0.44 ≤ .
13 2J1005+0542 15740 7.25 0.30560 208.9 0.34 ≥ .
66 0.86 ≤ . ≥ .
19 0.24 ≤ . ≥ .
26 0.33 ≤ .
16 4,9J1056+6536 20470 7.13 0.04351 267.5 0.34 ≥ .
34 0.43 ≤ .
085 0J1112+1117 9590 6.36 0.17248 116.2 0.17 ≥ .
14 0.17 ≤ . ≥ .
76 1.05 ≤ . ≥ .
86 1.20 ≤ . − ≥ .
09 0.11 ≤ . ≥ .
64 0.88 ≤ . ≥ .
46 0.60 ≤ .
10 4,9J1443+1509 8810 6.32 0.19053 306.7 0.17 ≥ .
83 1.15 ≤ . ≥ .
30 0.37 ≤ .
031 8J1741+6526 9790 5.19 0.06111 508.0 0.16 ≥ .
10 1.55 ≤ .
17 1J1840+6423 9140 6.16 0.19130 272.0 0.17 ≥ .
64 0.88 ≤ . − ≥ .
71 0.99 ≤ . − ≥ .
75 1.04 ≤ .
54 2J2132+0754 13700 6.00 0.25056 297.3 0.17 ≥ .
95 1.33 ≤ . − ≥ .
15 0.18 ≤ . · · · ≥ .
21 0.26 · · · ≥ .
57 0.78 · · · ≥ .
32 0.41 · · · ≥ .
90 1.18 · · ·
J0802 − ≥ .
57 0.76 · · ·
J0811+0225 13990 5.79 0.82194 220.7 0.17 ≥ .
20 1.71 · · ·
J0815+2309 21470 5.78 1.07357 131.7 0.17 ≥ .
47 0.63 · · ·
J0840+1527 13810 5.04 0.52155 84.8 0.17 ≥ .
15 0.19 · · ·
J0845+1624 17750 7.42 0.75599 62.2 0.40 ≥ .
19 0.22 · · · · · · ≤
24 0.16 · · · · · · · · · ≥ .
28 0.36 · · · − ≥ .
19 0.23 · · ·
J1104+0918 16710 7.61 0.55319 142.1 0.46 ≥ .
55 0.70 · · ·
J1151+5858 15400 6.09 0.66902 175.7 0.17 ≥ .
61 0.84 · · ·
J1157+0546 12100 5.05 0.56500 158.3 0.17 ≥ .
45 0.59 · · ·
J1422+4352 12690 5.91 0.37930 176.0 0.17 ≥ .
41 0.55 · · · ≥ .
46 0.62 · · · · · · ≤
35 0.25 · · · · · · · · · ≥ .
28 0.36 · · · ≥ .
58 0.78 · · · ≥ .
77 1.06 · · ·
J1557+2823 12550 7.76 0.40741 131.2 0.49 ≥ .
43 0.54 · · ·
J1625+3632 23570 6.12 0.23238 58.4 0.20 ≥ .
07 0.08 · · · ≥ .
52 0.70 · · · − · · · ≤
25 0.31 · · · · · · · · · − · · · ≤
43 0.42 · · · · · · · · · −
22 11170 6.35 1.01016 119.9 0.19 ≥ .
41 0.52 · · ·
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DATA TABLE
Table 4 presents our radial velocity measurements. The Table columns include object name, heliocentric Julian date(based on UTC), heliocentric radial velocity (uncorrected for the WD gravitational redshift), and velocity error.2 Brown et al.
TABLE 4Radial Velocity Measurements