THE ELM SURVEY. II. TWELVE BINARY WHITE DWARF MERGER SYSTEMS^*

To study the binary fraction of ELM WDs and to find future merger systems, we have undertaken an MMT survey of all previously identified ELM WDs from the SDSS DR4 area (Eisenstein et al. 2006; Liebert et al. 2004) and the Hypervelocity Star survey of Brown et al. (2006). The latter sample is described in a companion paper by Brown et al. (2010a). Part of the SDSS DR4 sample was discussed earlier in Kilic et al. (2010b). Here, we present radial velocity observations of seven more ELM WD candidates from the Sloan Digital Sky Survey (SDSS) sample. The combined sample contains 23 WDs. We also report on Chandra X-ray observations of three ELM WDs to search for X-ray evidence of milli-second pulsar (MSP) companions.

While almost all SDSS ELM WDs show radial velocity variations, none show evidence of main-sequence or neutron star companions in the optical, radio (Agüeros et al. 2009a), or X-ray (this paper and Agüeros et al. 2009b). Hence, they are almost certainly binary WD systems. Out of the 20 short period binary systems in our sample, 12 have merger times shorter than a Hubble time. Our ELM survey has now tripled the number of known merging WD systems. Based on our sample and previously known short period binary WD systems, we study the mass–period distribution and future evolutionary prospects, including the connections to unusual stellar populations and underluminous supernovae (SNe).

Our paper is organized as follows. In Section 2 we discuss our radial velocity and X-ray observations. In Section 3 we present an analysis of the optical spectroscopy and X-ray data and the nature of the companions. In Section 4 we discuss the sample characteristics of ELM WDs, including the binary fraction, mass–period distribution, merging systems, and the implications for underluminous SNe and other unusual merger products. We conclude in Section 5.

Eisenstein et al. (2006) identified 13 low-mass WD candidates with log g < 7. Kilic et al. (2010b) discuss follow-up observations of four of these targets. We selected 6 more targets for follow-up MMT spectroscopy. These targets are SDSS J002228.45+003115.5, J002207.65−101423.5, J123410.36−022802.8, J162542.10+363219.1, J204949.78+ 000547.3, and J225242.25−005626.6. We also observed SDSS J234536.48−010204.8, another ELM WD candidate identified by Liebert et al. (2004).

There are three more targets in the Eisenstein et al. (2006) ELM WD sample that lack follow-up spectroscopy. These targets (SDSS J1056+6536, J1426+0100, and J1630+4233) have log g > 6.9 based on the model fits by Eisenstein et al. (2006) and log g ≈ 7 based on the fits by Kilic et al. (2007a). Radial velocity observations of these objects will be useful for the identification of more short-period binary WD systems.

We used the 6.5 m MMT equipped with the Blue Channel Spectrograph to obtain moderate resolution spectroscopy of seven ELM WD candidates over 17 different nights between 2008 September and 2010 July. We operate the spectrograph with the 832 line mm⁻¹ grating in second order, providing wavelength coverage 3600 Å to 4500 Å and a spectral resolution of 1.0–1.2 Å, depending on the slit size used. We obtain all observations at the parallactic angle, with a comparison lamp exposure paired with every observation. We flux-calibrate using blue spectrophotometric standards (Massey et al. 1988), and we measure radial velocities using the cross-correlation package RVSAO (Kurtz & Mink 1998). Our radial velocity measurement procedures are described in Kilic et al. (2009, 2010b).

2.2.1. Motivation

2.2.2. Data Analysis

3.1.1. J0022+0031

3.1.2. J0022−1014

3.1.3. J1234−0228

3.1.4. J1625+3632

3.1.5. J2049+0005

Figure 9 shows the best-fit WD model to our MMT spectrum of J2049+0005. This star was identified as a T_eff = 8660 K and log g = 5.48 WD by Eisenstein et al. (2006). Further analysis of the same SDSS spectrum by Kilic et al. (2007a) suggested that J2049+0005 has log g < 5, and therefore is not a WD. Similarly, our model fits to the higher resolution and higher signal-to-noise ratio MMT spectrum find a best-fit solution that is exactly our lowest gravity model (log g = 5). This model poorly matches the high-order Balmer lines, indicating that the surface gravity is lower than log g = 5 and that J2049+0005 is most likely an A star.

Zoom In Zoom Out Reset image size

3.1.6. J2252−0056

3.1.7. J2345−0102

Kilic et al. (2007b, 2010b), Brown et al. (2010a), and this paper discuss radial velocity observations of 11 ELM WD candidates identified in the SDSS DR4 (Eisenstein et al. 2006) and 12 ELM WDs identified in the Hypervelocity Star Survey of Brown et al. (2006). One of the targets is common to both samples. In addition, one of the DR4 targets (J2049+0005) is most likely an A-star. Kilic et al. (2009, 2010c), Kawka et al. (2010), and Steinfadt et al. (2010) describe radial velocity observations of two more ELM WDs identified in the literature. Thus, there are 23 (candidate) ELM WD systems with comprehensive radial velocity measurements. All but three of these systems (J1448+1342, J2252−0056, and J2345−0102) are in binary systems.

Limiting this sample to 19 WDs with M ⩽ 0.25 M_☉, 18 are in short period binary systems. Thus, close binary evolution is required for the formation of ELM WDs. The only system that does not display significant radial velocity variations, J1448+1342, is at the upper mass limit of this selection; all 18 WDs with M < 0.25 M_☉ are indeed binaries. The average velocity semi-amplitude of these 18 binaries is 236 km s⁻¹, whereas the upper limit for the velocity semi-amplitude of J1448+1342 is 35 km s⁻¹. An average system viewed at i ⩽ 85 would be consistent with the observations of J1448+1342. For a randomly distributed sample of orbital inclinations, there is a 1.1% chance that i ⩽ 85. Thus, there is a 21% likelihood of finding one of the 19 systems with i ⩽ 85. It is possible that J1448+1342 is a pole-on binary system (see also Brown et al. 2010a). Hence, the binary fraction of M ⩽ 0.25 M_☉ WDs is at least 95% and it may be as high as 100%.

This result is in contrast to the binary fraction of slightly more massive WDs. Maxted et al. (2000), Napiwotzki et al. (2004), and Brown et al. (2010) demonstrate that about 30%–50% of M ≈ 0.4 M_☉ WDs are single (see also Kilic et al. 2010a). Single low-mass WDs may form through enhanced mass loss from a metal-rich progenitor star (Kilic et al. 2007c), but we do not expect even the most metal-rich stars to loose enough mass to create ∼0.2 M_☉ WDs. Here we confirm this expectation that the lowest mass WDs all form in close binary systems.

Double degenerate (DD) merger systems are one of the two main accepted formation channels for Type Ia supernovae (Iben & Tutukov 1984; Branch et al. 1995; Kotak 2008; Di Stefano 2010, and references therein). However, only a handful of DD systems are known to have combined mass above the Chandrasekhar limit and short enough orbital periods to merge through gravitational wave radiation within a Hubble time. Napiwotzki et al. (2001) started the heroic SPY survey for short period DD systems. They used the Very Large Telescope to observe 1014 stars brighter than 16.5 mag, including 75% of the known WDs accessible from the southern hemisphere. Napiwotzki et al. (2004) report that the SPY survey discovered about 100 new DD systems, one of which is a potential SNe Ia progenitor (WD 2020−425; Napiwotzki et al. 2007). Geier et al. (2010) describe the discovery of another massive DD merger system and also a summary of the current discoveries from the SPY survey (their Figure 4).

Figure 10 shows the total masses and periods for the short period DD systems (including sdB + WD) discovered by the SPY survey (kindly made available to us by S. Geier) and our ELM WD sample. To explain the observed SNe Ia rate, only one out of 1000 WDs is expected to be a SNe Ia progenitor (Nelemans et al. 2001). Hence, the relatively few number of potential SNe Ia progenitors in the SPY survey is not surprising. What is striking is that the number of merger systems found in the SPY survey is significantly smaller than our ELM WD survey. We discovered 12 binary WD merger systems (τ_merge < τ_hubble) in a sample of 23 stars, whereas the SPY survey discovered a handful of such systems in a sample of 1000 stars. The reason for this is the binary common envelope evolution required to form ELM WDs.

Zoom In Zoom Out Reset image size

Figure 11 shows the total masses and periods for previously identified WD + WD binary systems in the literature (Nelemans et al. 2005; Napiwotzki et al. 2007). There were only six double WD merger systems known prior to our work. With the additional 12 merger systems presented in Table 4, we now have tripled the number of WD merger systems known.

Zoom In Zoom Out Reset image size

Nelemans et al. (2001) studied the period and mass distribution of double WD systems using population synthesis models. The details of these models including selection effects due to orbital evolution of the systems (disappearance of the shortest period systems due to mergers), target selection biases in the current surveys, and different cooling models are discussed in their paper. Nelemans et al. (2001) find a correlation between the masses and periods; more massive WD primaries have longer periods. This is not surprising; shorter period systems would start interacting earlier in their evolution compared to longer period systems and experience enhanced mass loss during the red giant phase, hence end up as lower mass WDs. They also find that the mass ratio distribution peaks at q = 1, favoring equal mass binary components. This distribution is consistent with the observed mass ratio distribution of binary WDs known prior to our work.

Figure 12 shows the masses and orbital periods for our sample of ELM WDs and the previously known binary WD systems in the literature compared to the population synthesis models of Nelemans et al. (2001, 2004, kindly made available to us by G. Nelemans). Depending on which cooling model is used, the model predictions change somewhat (see Nelemans et al. 2004, for a discussion of the cooling models used here). However, the main trend in the mass versus period distribution is evident; lower mass primaries are in shorter period systems. This result is consistent with the observed distribution of masses and periods for previously known binary WD systems and the ELM WD systems. All but one of the M < 0.3 M_☉ systems have periods shorter than a day,¹⁰ whereas the majority of the more massive WDs have periods longer than a day.

Zoom In Zoom Out Reset image size

The overall number distribution of the population synthesis models and the observations cannot be directly compared without taking into account the obvious biases in the target selection. The sample of previously known binary WDs are selected from a magnitude limited sample down to 16–17 mag, whereas our sample mainly comes from fainter targets selected from the SDSS, which has its own spectroscopic target selection bias. Nevertheless, an overabundance of 0.17 M_☉ WDs is evident in Figure 12. A comparison between the population synthesis models using Hansen (1999, top panel) and the modified Driebe et al. (1998, bottom panel) cooling models shows that the expected number of the lowest mass WDs changes depending on the cooling model used. The latter models predict a significantly larger number of 0.17 M_☉ WDs. Based on the Panei et al. (2007) models, a 0.25 M_☉ WD cools 4× faster than a 0.17 M_☉ WD down to an absolute magnitude of M_g = 10 mag. Hence, the observed mass distribution of ELM WDs in a magnitude-limited survey is skewed toward lower mass objects (Brown et al. 2010b). Population synthesis models and a large, unbiased, magnitude-limited survey of low-mass and ELM WDs like that of Brown et al. (2010a) will be useful to constrain the ELM WD cooling models.

Another important prediction of the population synthesis models is that there should not be many systems with periods less than an hour.¹¹ We have three ELM WD systems with periods close to 1 hr. The shortest period system, J1053+5200 has a period of 61 min (Kilic et al. 2010b; Mullally et al. 2009). The shortest period hydrogen-rich cataclysmic variable (CV) V485 Cen has an orbital period of 59 minutes (Augusteijn et al. 1996). Both short period binary WDs and CVs are expected to contribute to the AM CVn population, which contains interacting WD binary systems with orbital periods ranging from a few minutes to about an hour. The two longest period AM CVn systems have periods of 56 min and 66 min, respectively (Roelofs et al. 2007). It seems that hydrogen-deficient AM CVn interacting binary systems have periods less than about an hour and the hydrogen-rich detached WD systems have orbital periods about an hour or longer.

Before the SDSS, ELM WDs were traditionally found as companions to MSPs. The masses for the MSP companions are usually measured from the pulsar timing measurements since the WDs are usually too faint for follow-up optical spectroscopy. van Kerkwijk et al. (1996) and Bassa et al. (2006) obtained Keck and VLT spectroscopy of companions to two MSP systems. van Kerkwijk et al. (1996) derive T_eff = 8550 ± 25 K and log  g = 6.75 ± 0.07 for the companion to PSR J1012+5307, whereas Bassa et al. (2006) obtain T_eff = 10,090 ± 150 K and log  g = 6.44 ± 0.20 for the companion to PSR J1911-5958A. These two WDs are included in Figure 8.

Kilic et al. (2007a, 2007b) discovered the lowest surface gravity WD known at the time, SDSS J0917+4638, with log g = 5.55. Brown et al. (2010a) discovered two WDs with even lower surface gravities, SDSS J1233+1602 and J2119−0018. These WDs are included in our ELM WD sample and in Figure 8. Based on the Serenelli et al. (2001, 2002) and Panei et al. (2007) models, all of these WDs, including the two MSP companions, have M ⩾ 0.17 M_☉. There are about a dozen WDs in Figure 8 with M ≈ 0.17 M_☉, but none below that mass limit. However, this result is most likely due to observational biases present in the SDSS and the Hypervelocity Star Survey. The former is, of course, an incomplete spectroscopic survey and the latter has a color selection that excludes T_eff⩽ 10,000 K objects with log g = 5–6 (see Figure 1 in Brown et al. 2010a). Based on the Panei et al. (2007) models, a 0.16 M_☉ WD takes 15 Gyr to cool down from 9200 K to about 7000 K with an increase in surface gravity from log g = 5.7 to 6.4 and a decrease in luminosity from M_g = 8.1 to 11.1 mag. Such WDs are not included in the Hypervelocity Star Survey color selection.

Based on radio timing measurements, 45 out of 99 MSPs with periods less than 20 ms have companions less massive than 0.17 M_☉ (B. Kızıltan 2010, private communication). The spectral types of the companions are unknown. However, a large fraction of these objects are expected to be low-mass WDs; nature produces M < 0.17 M_☉ WDs in MSP systems. Lower mass ELM WDs should be produced in binary WD systems as well. Population synthesis calculations for double WDs do not predict many WDs below 0.17 M_☉, but such WDs may eventually be found in double WD systems in the SDSS or other spectroscopic surveys.

The end result of the future evolution of the 12 ELM WD merger systems in our sample depends on the mass ratios of the two components. The systems with extreme mass ratios (q ⩽ 0.2) should have stable mass transfer at initial Roche lobe filling. Stable mass transfer leads to the formation of AM CVn systems that transfer angular momentum back to the orbit, which increases the orbital period. If the higher mass WDs in such systems have masses close to the Chandrasekhar limit, accretion may result in a Type Ia SNe explosion. However, the probability of such an event is small (⩽7%) for our systems. This probability would be higher if sub-Chandrasekhar mass WD explosions also contribute to the observed Type Ia SNe population (Sim et al. 2010; Kromer et al. 2010, and references therein). However, our ELM survey is biased against SNe Ia progenitors due to the selection of very low-mass primaries.

Figure 13 shows the mass ratios and periods for our ELM WD sample plus the previously known binary WD systems. Single-lined systems are shown as filled triangles, whereas the double-lined systems and the eclipsing WD system NLTT 11748 are shown as filled circles. Open circles mark the objects with merger times shorter than a Hubble time. Out of the 18 merger systems, six have mass ratios smaller than 0.25 (assuming an average inclination of 60°), and are likely to form AM CVn systems. These six systems also have the highest total mass (M₁ + M₂) in our sample. J1233+1602 is the most extreme case with M₁ + M₂ = 1.37 M_☉ for i = 60°. It is striking that the number of extreme mass ratio systems in our sample (six) is the same as the number of AM CVn systems found in the SDSS Data Relase 5 area (Roelofs et al. 2007). These systems are potential SNe.Ia progenitors (Bildsten et al. 2007).

Zoom In Zoom Out Reset image size

Based on a magnitude-limited sample of six ELM WD mergers, Brown et al. (2010b) find that half of their sample has mass ratios of ≈0.15 and they estimate a contribution factor of ≳3% to the AM CVn formation rate from the observed population of ELM WDs. The fraction of extreme mass ratio systems in our survey is also 50% (six out of 12 ELM WDs), supporting the conclusions reached by Brown et al. (2010b).

The other six ELM WD systems in our sample have mass ratios larger than 0.4. Kilic et al. (2010a) discuss various evolutionary scenarios for these objects. These systems will merge within a Hubble time and form a variety of exotic objects including underluminous SNe, extreme helium stars (RCrB), or single helium-enriched subdwarf O stars. The merger rate of ELM WDs is roughly the same as the observed rate of underluminous SNe (Brown et al. 2010b).

SDSS J1234−0228 is a unique ELM WD merger system. There is a 85% chance that the combined mass of the two stars in this system is lower than 0.45 M_☉. Therefore, within the next few billion years, this system will merge and likely form a a single low-mass WD. There are several scenarios to explain the presence of single low-mass (∼0.4 M_☉) WDs, including enhanced mass loss from metal-rich progenitors (Kilic et al. 2007c) and mass loss through common envelope evolution with a low-mass brown dwarf or planetary mass companion (Nelemans & Tauris 1998). Single low-mass WDs can also form through mergers of two lower-mass WDs (Iben et al. 1997; Saio & Jeffery 2000), though no such progenitors have been found until now. Here we have uncovered a potential progenitor system for a future single low-mass WD, J1234−0228.

About 10% of DA WDs are low mass (Liebert et al. 2005) and half of these low-mass WDs are single (Napiwotzki et al. 2004), corresponding to a space density of 2.5 × 10⁵ kpc⁻³ (Sion et al. 2009). The SDSS DR4 WD catalog covers 4783 square degrees with g = 15–20 mag (Eisenstein et al. 2006). We estimate the local space density using the modified 1/V_max method and the disk model of Roelofs et al. (2007). Based on one system, J1234−0228, the space density of merging WD systems that can form single low-mass WDs is 1.1 kpc⁻³. This number is likely uncertain by a factor of 10 due to incompleteness of the SDSS spectroscopic target selection. Nevertheless, it is several orders of magnitude smaller than the estimated space density of single low-mass WDs. Hence, this formation channel does not significantly contribute to the single low-mass WD population in the solar neighborhood.