THE OCCURRENCE OF WIDE-ORBIT PLANETS IN BINARY STAR SYSTEMS

Because binary stars are so common in the Milky Way, a matter of interest in astronomy is the prevalence of planets in such systems. Observational and theoretical studies of star formation, protoplanetary disks, and long-term dynamical stability of planets in three-body systems have occupied the attention of many astronomers (see, e.g., the Introduction in Haghighipour 2006).

Searches for evidence of planetary systems in orbit around stars in binary systems have involved various techniques. For planets with orbital semi-major axes up to about 10 AU, but typically substantially less than this, precision radial velocities (PRVs), transits and microlensing have been most useful (e.g., Roell et al. 2012). Techniques relevant for planets with semi-major axes of tens to hundreds of astronomical units include direct imaging of warm planets (e.g., Vigan et al. 2012; Brandt et al. 2014) and of dusty debris disks (Rodriguez & Zuckerman 2012). However, typical direct imaging campaigns have, so far, only been sensitive to planets with masses of a few Jupiters or greater and with detections too few to make any meaningful statistical comparisons between planetary systems around single stars and those in binary star systems. Also, the existence of a dusty debris belt alone does not necessarily imply the existence of a planet. Thus, the unearthing of any additional techniques sensitive to wide-orbit planetary systems in binary star systems would be of value.

In the present Letter, we consider a new method for the investigation of planets in binary star systems—the presence or absence of heavy elements in the atmospheres of white dwarf (WD) stars. The photospheres of at least 25% of field WDs are externally polluted with detectable quantities of elements heavier than helium (Zuckerman et al. 2003, 2010; Koester et al. 2014). A wide range of evidence indicates that this pollution is from the accretion of extrasolar asteroids and, occasionally, perhaps even a rocky planet (e.g., Jura 2003; Jura et al. 2009; Gaensicke et al. 2012; Jura & Young 2014; Barstow et al. 2014) or a portion thereof (e.g., Zuckerman et al. 2011). The implied mass of these extrasolar asteroid belts is often comparable to or greater than that of the Sun's belt, while the presence of multiple major planets that gravitationally perturb the orbits of the smaller objects is likely (e.g., Zuckerman et al. 2010; Debes et al. 2012; Veras et al. 2013; Mustill et al. 2014 and references therein). A variety of extensive theoretical calculations demonstrate that this interpretation of the observational data is sound (e.g., Rafikov 2011; Metzger et al. 2012; Veras et al. 2013; Mustill et al. 2014; Wyatt et al. 2014; Frewen & Hansen 2014). To the best of our knowledge, no other model for the heavy element pollution of WD atmospheres is now seriously considered.

One result from the Kepler satellite—at relatively small semi-major axes, many planetary systems are densely packed—suggests the plausibility of similarly complex systems of gravitationally interacting major planets and rocky debris at larger semi-major axes such as those sampled with WD studies. The existing data on externally polluted WDs has motivated detailed models for the evolution of extended two- and three-planet systems from the main sequence through the giant branches and well into the WD phase (Veras et al. 2013; Mustill et al. 2014).

Our primary goal is a comparison between binary stars and single stars of the frequency of planetary systems that, on the main sequence, had semi-major axes greater than a few astronomical units. That is, because WD progenitors are A- and F-type main sequence stars, when they were red giants (on the asymptotic giant branch), all orbiting objects of planet mass or less with semi-major axes out to a few astronomical units would have been destroyed (e.g., Jura 2008). We consider only the situation where a planetary system orbits one member of a binary (no circumbinary planets). Although we focus on binary star systems that contain a WD and a main sequence companion, the conclusions are applicable to earlier stages of stellar evolution, specifically when the WD was a main sequence star; thus, our results can be compared to studies of planets in main sequence binary star systems (see Section 4). Note that when the progenitor of the WD was on the main sequence it was the primary and the current main sequence star was the secondary.

We want to compare the frequency of planetary systems around the WD in a binary star system with their frequency around single WDs. Planetary system occurrence frequency around single WDs has been measured in the optical with spectrometers on the Very Large Telescope (VLT) and Keck telescopes (Zuckerman et al. 2003, 2010) and in the ultraviolet with the Cosmic Origins Spectrograph (COS) on the Hubble Space Telescope (HST; Koester et al. 2014). For a wide range of WD effective temperature, calcium is the element most easily detected optically, while for hot WDs, silicon is the element most easily detected (in the UV).

Based on results from papers cited in the third paragraph in Section 1, with a few caveats, the existence of a planetary system is considered established when either calcium or silicon is detected in the photosphere of a WD. One caveat is the possibility of radiative levitation of silicon in the atmosphere of an appropriately hot WD (Chayer 2014; Koester et al. 2014; Barstow et al. 2014 and references therein). Another caveat would be the possibility of accretion by a WD of interstellar rather than planetary system matter. While on occasion such a possibility cannot be conclusively ruled out, the suite of papers cited in Section 1 establishes beyond any reasonable doubt that such an occurrence would represent the exception rather than the rule.

For a sample of single DA (hydrogen atmosphere) WDs with temperatures <10,000 K, Zuckerman et al. (2003) found Ca in the photospheres of ∼25%. For a sample of single DB (helium atmosphere) WDs with temperatures between 13,500 and 19,500 K, Zuckerman et al. (2010) deduced that about one-third have Ca in their photospheres. For a sample of DA WDs with temperatures between 17,000 and 27,000 K, Koester et al. (2014) found Si in the photospheres of ∼50%. Because of the possibility of radiative levitation of silicon, interpretation of this fraction is somewhat complex and we refer the reader to Koester et al. (2014) and Barstow et al. (2014) for details. However, in any event, Koester et al. conclude that the fraction of the COS sample with surrounding planetary systems is certainly not smaller than the fraction deduced optically in the two Zuckerman et al. studies.

WDs in binary systems appear in a variety of classes: well separated common proper motion (cpm) pairs, double degenerates, Sirius-like, and moderately close or very close red dwarf/white dwarf (RD/WD) pairs. The very close RD/WD pairs and many known double degenerates have passed through a phase of common envelope evolution. Any surviving planets in such systems will be of the circumbinary type (i.e., the planets will orbit both stars). For RD/WD systems, the WD atmosphere is often polluted with material captured from the wind of the RD (see, e.g., Zuckerman et al. 2003, Section 4.7). Also, in spatially unresolved systems, Ca ii K-line emission from the RD oftentimes overwhelms K-line absorption in the photosphere of the WD. Because of these effects it is difficult or impossible to use spectroscopy to study planetary systems around very close RD/WD pairs. Perhaps in some such cases planetary system material could find its way onto the WD in measurable quantities (e.g., Farihi et al. 2010), but these would involve careful consideration that is well beyond the scope of the present Letter.

To avoid such uncertainties, we consider only WD stars in cpm binary systems where the unevolved secondary star is so far (>120 AU, see below) from the WD that there is essentially no chance that the wind of the secondary will pollute the atmosphere of the WD. Many such systems are known to exist (e.g., Table 1 in Silvestri et al. 2005 and in Holberg et al. 2013), but for only relatively few have the atmosphere of the WD been examined for Ca with a high-resolution spectrometer on a large telescope such as Keck or the VLT. Indeed, so few (perhaps zero) WDs in wide binary systems have been observed in the UV with COS that we use only Ca in our analysis described below. Our choice of wide separation binaries pretty much guarantees that any planetary system that is discovered orbits only the WD and is not circumbinary.

In Table 1 and Figure 1 we gather together data from the literature for WDs in binary systems that, with a few exceptions, have been observed for the Ca ii K-line with Keck and/or the VLT. As mentioned in Sections 1 and 2, the presence of this line in the spectrum serves as a proxy for the existence of an orbiting planetary system that contains both a debris disk and at least one major planet, all with semi-major axes of at least a few AU. The abscissa, the separation on the sky of the two stars in a given binary, is on average slightly smaller than the semi-major axis of the system.

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Table 1. White Dwarfs in Common Proper Motion Binary Systems

WD	Name	Type	V	Teff	Ca EW	[Ca/H(e)]	Separation	Ref.
			(mag)	(K)	(mÅ)		(arcsec; AU)
0119−004	LP 587-44	DB	16.3	16540	<60	< −8.8	9       990	7,8
0120−024	NLTT 4615	DA	17.0	5840	<450	< −10.0	44     1850	9,11
0148+641	G244-36	DA	14.0	6100(?)	<5	< −12.1	12      200	1
0204−306	NLTT 7051	DA	16.2	5640	<500	< −10.0	73     2190	9,11
0250−007	LP 591-177	DA	16.4	8400	<90	< −9.6	27     1020	5,7
0415−594	Ret B	DA	12.5	15310		< −9.0	12.8     240	6
0433+270	G39-27	DA	15.6	5430(?)	<30	< −12.2	124    2230	1
0615−591	L182-61	DB	14.0	16710	<30	< −9.4	41     1540	7,8
0625+100	G105-B2B	DZ	16.5				127    7880	2
0642−285	LP895-41	DA	15.2	9370	<70	< −9.3	16      510	5,7
0738−172	LHS 235	DZA	13.0	7650	6000	−10.9	21.4     200	13
0751−252	SCR0753-2524	DC	16.3	5080			396    7740	14
0845−188	LP786-6	DB	15.7	17450	<15	< −9.2	31     8740	3
1004+665	LP 62-35	DZ	14.7				112    7050	10
1009−184	LHS 2033B	DZ	15.4	9940			400    6870	4
1105−048	NLTT 26379	DA	13.1	16110	<10	< −8.5	279    7200	5,7
1147+255	G121-22	DA	15.6	10260	<15	< −9.9	36     1980	1
1209−060	LP 674-29	DA	17.3	6400	<60	< −10.3	203    9170	9,11
1327−083	LHS 354	DA	12.3	14570	<7	< −8.9	503    9070	5,7
1336+123	LP 498-26	DB	14.8	16780	<25	< −9.5	87     4440	7,8
1345+238	LHS 361	DA	15.6	4700	<40	< −12.8	198    2400	1
1348−272	LP 856-53	DA	14.5	9830	<40	< −9.6	9       280	5,7
1422+095	GD165	DAV	14.4	12440	<20	< −8.8	3.7      120	1,5
1425+540	G200-040	DBAZ	15.0	14750	150	−9.3	60     3480	3
1542−275	LP 916-27	DB	15.4	10800	<30	< −11.8	54     2800	7,8
1544−377	LTT 6302	DA	12.8	11270	<3	< −10.3	15      240	1
1555−089	G152-B4A	DA	14.7	14530	<30	< −8.1	11      560	5,7
1619+123	PG	DA	14.7	17150	<30	< −7.5	62     3220	5,7
1716+020	Wolf 672	DA	14.3	13620	<20	< −8.5	13      460	1
1911+135	G142-B2A	DA	14.2	13780	<30	< −8.3	19      630	5,7
1917−077	LTT 7658	DBQA	12.3	10200	<15	< −12.1	27      310	7,8
1932−136	L852-37	DA	15.9	16930	<30	< −7.4	29     3080	5,7
2051+095	LP 516-13	DA	16.0	15670	<30	< −8.1	10     1030	5,7
2129+000	G26-10	DB	14.7	14000	<7	< −11.1	133    6020	3
2253−081	NLTT 55288	DA	16.5	6770	<100	< −10.0	42     1540	5,7
2253+803	HS2253+8023	DBAZ	16.1	14400	4700	−7.0	39     2730	12
2318+126	LP 522-34	DA	15.9	14020	<30	< −8.7	35     3050	5,7
2341+322	LP 347-4	DA	12.9	12577	<5	< −9.5	175    3080	1

Notes. Ca EW refers to the equivalent width of the Ca ii K-line. [Ca/H(e) is the logarithm of the ratio by number of Ca atoms to either H or He atoms depending on which is the dominant constituent of the white dwarf atmosphere. 1 = Zuckerman et al. (2003); 2 = Aannestad & Sion (1985); 3 = Zuckerman et al. (2010); 4 = Subasavage et al. (2007); 5 = Koester et al. (2009); 6 = Farihi et al. (2011); 7 = D. Koester (2014, private communication); 8 = Voss et al. (2007); 9 = Kawka & Vennes (2012); 10 = Holberg et al. (2013); 11 = A. Kawka (2014, private communication); 12 = Klein et al. (2011); 13 = Dufour et al. (2007); 14 = Subasavage et al. (2008).

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Given the multiple sources of data that were accessed to construct Table 1, it is not possible to control entirely against biases. Toward this goal, inclusion of a WD in the table was subject to various constraints: (1) V magnitude brighter than 17.3; (2) effective temperature (T_eff) < 17,500 K; and (3) for cool DC and DQ WDs, unambiguous indication in at least one published paper that the region of the Ca ii H- and K-lines had been examined with at least a moderate resolution spectrometer. The first two constraints relate to sensitivity to detection of the Ca K-line (more difficult for faint or hot stars). The third constraint is to avoid inclusion of DC- and DQ-type WDs that have never been observed at wavelengths shorter than 4000 Å and whose atmospheres might thus actually contain calcium notwithstanding their current classifications. (WDs with atmospheric calcium include the letter Z in their classification; see the third column in Table 1.)

Although one is contending with small number statistics, tentative conclusions regarding wide orbit planetary systems in binary star systems may be drawn from Figure 1. First, for cpm binary systems composed of a WD and a main sequence star with separations less than about 2500 AU, the WD stars contain a smaller percentage of wide-orbit planetary systems—1/21 (5%)—than do single WDs, for similar WD temperature ranges. Due to the expansion of orbits during mass-losing phases of the WD progenitor, current star–star separations are typically two to three times the separations when the WD was on the main sequence (see, e.g., Farihi et al. 2013). Thus Figure 1 suggests that in a main sequence binary star system with semi-major axis ⩽1000 AU and where the primary is an A- or F-type star, then extended planetary systems in orbit around the primary star are less common than around single A- and F-type stars.

Another conclusion that may be drawn from Figure 1 is that in main sequence binary systems with semi-major axes larger than about 1000 AU, the frequency of wide-orbit planetary systems around primary A- and F-type stars may well be comparable to the frequency around single stars. That is, for the separation bins from 2500 to 9250 AU the Ca detection frequency is 5/17 (30%), essentially the same as measured for single WDs in the same temperature regime (Section 2).

As mentioned above, our aim is to investigate the frequency of planetary systems that orbit one but not both members of a binary system (i.e., are not circumbinary planets). Therefore, in construction of Table 1 and Figure 1, we avoided binary systems where calcium, if seen in absorption in the spectrum of the WD, might be due to a circumbinary planetary system. For sufficiently well-separated stars there is little chance that a planetary system will be circumbinary. As noted just above, mass loss will cause expansion of orbits, typically by a factor of 2–3. A dynamically stable circumbinary planetary system will have an orbital semi-major axis at least 3.5 times the semi-major axis of the stellar binary (Holman & Wiegert 1999). Thus, any dynamically stable circumbinary planetary system, when on the main sequence, typically would have to have had a semi-major axis at least somewhat larger than the current semimajor axis of a WD/main sequence binary. The smallest apparent separation of any of the stars in Table 1 is the GD 165 system (120 AU separation). Based on the semi-major axes of the few directly imaged planetary systems (e.g., Marois et al. 2010) and of dusty debris disks in binary star systems (Section 4), only circumbinary planetary systems with unusually extreme (large) semi-major axes could encircle any of the systems listed in Table 1.

To date, the most successful planet discovery methods have been stellar transits and PRVs but with semi-major axes typically well less than an astronomical unit for the former and less than about 5 AU for the latter technique (e.g., Figure 1 in Roell et al. 2012). The calculations of Holman & Wiegert (1999) indicate that, depending on the binary mass ratio and eccentricity, a planet in orbit around the primary star could be stable if its semi-major axis was not more than about 20% that of the semi-major axis of the secondary star. However, Figure 4 in Roell et al. illustrates that for actual binary and triple star systems with known planets, the typical ratio of planet/host star separation to star–star separation is much less than 20%—more like 1%.

Typically, PRV measurements are not undertaken for binary systems with separations <2 arcsec (J. Wright 2014, private communication). Since the distance to a typical star targeted with the PRV technique is 50 pc or greater, one anticipates projected linear separations >100 AU between primary and secondary star, in agreement with the distribution of points on the abscissa in Figure 4 in Roell et al. (2012). In Figure 2 we plot the distribution of semi-major axes of planets detected with PRV (upper line) and the subset that orbit one star in a binary system (lower line). The data are from Wright et al. (2011). There does not appear to be any obvious difference in shape between the two lines. This suggests that—contrary to the situation outside of a few astronomical units that is probed by WD studies—inside of a few astronomical units planetary orbits are not significantly disrupted by a companion star with semi-major axis between a few hundreds of astronomical units and about 10,000 AU (Figure 4 in Roell et al. 2012). However, some orbital characteristics that are not delineated in Figure 2, for example, planetary eccentricities (e.g., Kaib et al. 2013) might differ between binary and single star systems. Also, unlike Figure 1, Figure 2 does not delineate star–star separations. Although well beyond the scope of the present Letter, a system by system examination of those plotted in red in Figure 2 might reveal a planet occurrence frequency that is sensitive to star–star separation.

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Most material accreted onto WD stars is dry and rocky, suggestive of asteroidal material that originated inside the snow line (Klein et al. 2011; Xu et al. 2014 and references therein). For A- and F-type stars, this line will lie within a few tens of astronomical units of the star. Based on Figure 1, and as noted in Section 3, heavy element pollution in WDs in binary systems appears unlikely for star–star semi-major axes up to ∼1000 AU when the WD progenitor was on the main sequence. The ratio of snow line radius to 1000 AU is similar to the 1% ratio mentioned two paragraphs above for planets close to their host stars. Simulations by Kaib et al. (2013) in their analysis of properties of planets studied with the PRV technique suggest that a distant stellar companion can have "dramatic" effects on a planetary system, strongly perturbing the system dynamically, increasing planet orbital eccentricities, and even causing outer planet ejection.

Spatially resolved images of dusty debris disks around A- and F-type main sequence stars sometimes reveal narrow dust rings suggestive of shepherding planets with semi-major axes sometimes as large as ∼100 AU, and even in some multiple star systems (e.g., HR 4796, Fomalhaut, and Figure 9 in Rodriguez & Zuckerman 2012). It remains to be determined whether the dusty debris is a definite signpost for planets and, since stars with debris disks tend to be young, whether disappearance of the dust for older systems is related to the presence and characteristics of a secondary star. The study of Rodriguez & Zuckerman (2012) indicated that debris disks are less common around stars in multiple systems than they are around single stars. Herschel data will enable improved statistics on dusty debris in multiple star systems (D. Rodriguez et al., in preparation).

To date, roughly 50 planets have been discovered through microlensing, a few of which are in binary systems (e.g., Gould et al. 2014). However, because of certain biases in the first generation surveys, binaries were discriminated against. Revisions in the observational procedures should eliminate these biases and, in the near future, microlensing should become a good method for detection of planets in binary star systems (A. Gould 2014, private communication). For a number of reasons, microlensing is more sensitive to planets that orbit late G- through M-type stars than to the earlier type stars that are probed by studies of externally polluted WDs. And microlensing has good sensitivity to planets with semi-major axes in the vicinity of the snow line, so it and the WD technique should complement each other.

The occurrence of heavy elements, most notably calcium or silicon, in the atmospheres of white dwarf stars can be used to determine the relative frequency of wide-orbit (>few astronomical units) planets around main sequence single stars and members of binary systems. We used Ca ii K-line data from the published literature to conclude that, for main sequence binaries with A- and F-type primaries and with semi-major axes ⩽1000 AU, the presence of a second star appears to suppress the formation and/or long term orbital stability of wide-orbit planets around the primary star—even planets that have semi-major axes much smaller than that of the secondary. For main sequence binaries with separations ⩾1000 AU the presence of a second star does not seem to diminish the likelihood of wide-orbit planetary systems.

The published data employed to construct Figure 1 were not collected with a view toward understanding the frequency of binary star planets. Thus, the statistics presented here can be much improved by a dedicated spectroscopic campaign to measure, with large ground-based telescopes and with HST, white dwarfs in binary systems.

I thank Drs. D. Koester, A. Kawka, J. Wright, and Ms. L. Vican for their generous assistance, Drs. B. Klein, A. Gould, G. Marcy, and S. Xu for helpful advice, and the referee for suggestions that improved the Letter. This research was supported by NASA grants to UCLA.