Evolved Stars
Planets orbiting the other stellar systems: Giant Stars White Dwarfs??? No. 1, 2010 RETIRED A STARS AND THEIR COMPANIONS. III. 397
Table 1 Planetary-Mass Companions to Evolved Intermediate-Mass Stars with M > 1.5 M ∗ "
Star M SpT R MP sin i aeReference ∗ ∗ (M )(R )(MJup)(AU) " " HD 13189 2–6 K2 II 8–20 1.5–2.2 0.27 (0.06) 1, 2 ··· ! Tau 2.7(0.1) K0III 13.7(0.6) 7.6(0.2) 1.93(0.03) 0.151(0.023) 3 NGC 2423 No. 3 2.4 (0.2) 10.6 2.10 0.21 (0.07) 4 ··· ··· 81 Cet 2.4 (2.0–2.5) G5 III: 11 (10–13) 5.3 2.5 0.206 (0.029) 5 HD 104985 2.3 G9 III 11 8.3 0.95 0.090 (0.009) 6, 7 18 Del 2.3 G6 III 8.5 10.3 2.6 0.08 (0.01) 6 HD 17092 2.3 (0.3) K0 III 10.9 (2.8) 4.6 (0.3) 1.29 (0.05) 0.166 (0.052) 8 ξ Aql 2.2 K0 III 12 2.8 0.68 0.0 (fixed) 6 14 And 2.2 (2.0–2.3) K0 III 11 (10–12) 4.8 0.83 0.0 (fixed) 5 HD 81688 2.1 K0III-IV 13 2.7 0.81 0.0 (fixed) 6 HD 173416 2.0 (0.3) G8 III 13.5 (0.9) 2.7 (0.3) 1.16 (0.06) 0.21 (0.04) 9 HD 11977 1.91 (0.21) G5 III 10.09 (0.32) 6.54 1.93 0.40 (0.07) 10, 11 HD 102272 1.9 (0.3) K0 III 10.1 (4.6) 5.9 (0.2) 0.614 (0.001) 0.05 (0.04) 12 ””””2.6(0.4)1.57(0.05)0.68(0.06)12 β Gem 1.86, 1.7 (0.4) K0 III 8.8 (0.1) 2.9 (0.3) 1.69 (0.03) 0.06 (0.04) 13, 14, 15, 16 HD 89744 1.86 (0.18) F7 IV 2.08 (0.06) 7.2 0.88 0.70 (0.02) 17, 18 HD 210702 1.85 (0.13) K1 IV 4.45 (0.07) 1.97 (0.11,0.18) 1.20 (0.02,0.03) 0.036 (<0.106) 19, 20 κ CrB 1.84 (0.13) K0 IV 4.71 (0.08) 2.01 (0.11,0.17) 2.80 (0.07,0.08) 0.044 (<0.123) 21, 20 6Lyn 1.82(0.13) K0IV 5.2(4.9–5.6) 2.21(0.11,0.16) 2.18(0.05,0.06) 0.059(<0.125) 20, 5 HD 167042 1.72 (0.12) K1 IV 4.30 (0.07) 1.70 (0.09,0.12) 1.32 (0.03,0.04) 0.089 (0.028,0.065) 21, 20, 5 HD 192699 1.69 (0.12) G8 IV 3.90 (0.06) 2.40 (0.15,0.21) 1.15 (0.02,0.03) 0.129 (0.029,0.060) 19, 20 HD 175541 1.65 (0.12) G8 IV 3.80 (0.09) 0.70 (0.06,0.08) 1.03 (0.02,0.03) 0.083 (<0.283) 19 HD 5319 1.59 (0.18) G5 IV 3.26 (0.50,0.41) 1.94 1.75 0.12 (0.08) 22
Notes. HD 47536 b is omitted because the most likely stellar mass is between 1.0 and 1.5 M (Setiawan et al. 2003b). γ Cep A b (Hatzes et al. 2003)isomitted " because the stellar mass estimate was revised to 1.4 M (Neuhauser¨ et al. 20072 ). The minimum mass of the companion to 11 Comae is 19.4 MJup (Liu et al. 2008) and is therefore probably a brown dwarf. References are" for planet discoveries and host-star physical properties. Additionally, HD 90043 and HD 200964 are IM planet-hosting stars, but do not yet have unique orbit solutions and so were omitted from this table. post-main sequence engulfment. References. (1) Hatzes et al. 2005; (2) Schuler et al. 2005; (3) Sato et al. 2007; (4)3.0 Lovis & Mayor 2007; (5) Sato et al. 2008b; (6) Sato et al. 2008a;(7)SatoThe observed semimajor axis distribution can also be et al. 2003;(8)Niedzielskietal.2007; (9) Liu et al. 2009;(10)Setiawanetal.2005; (11) da SilvaSemimajor et al. 2006 Axis;(12)Niedzielskietal. Distribution 2009;(13)Hatzesetal.All references bellow2006explained; as a result of inward orbital migration com- (14) Nordgren et al. 2001; (15) Prieto & Lambert 1999; (16) Reffert et al. 2006; (17) Korzennik2.5 et al. 2000;(18)Valenti&Fischer2005; (19) Johnson et al. 2007bbined; with mass-dependent disk dispersal lifetime. The (20) this work; (21) Johnson et al. 2008;(22)Robinsonetal.2007. Johnson et al. (2011) Johnson et al. (2010) rocky progenitors of Jovian planets (∼10 M⊕ cores) can shown in Figure 1 and a summary of known planets around IM 2.0 form at distances ! 8AUforstellarmassesbetween stars is presented in Table 1. Planet Desert ∼Bowler et al. (2010), 709, ApJ, 396 1.5-3 M! (Kennedy & Kenyon 2008). Currie (2009) performed Monte Carlo simulations of Jovian planet for- There are several explanations for this observational result. (M ) 1.5 * mation and migration around IM stars and, using sim- One possibility is that the swollen radii of evolved stars have M ple stellar mass-dependent gas disk lifetime relations engulfed or tidally disrupted short-period planets. The current 1.0 census of IM exoplanet-host stars mostly consists of red clump (Kennedy & Kenyon 2009) and Type II migration mod- Hot Planets Period Valley els (Ida & Lin 2004), was able to successfully reproduce giants (core helium and hydrogen shell burning post-red giant 0.5 branch (RGB) stars) and subgiants (stars with contracting inert the observed dearth of short-period planets. In this sce- helium cores and hydrogen-burning shells). Planet-hosting stars nario inward migration is halted once rapid disk dispersal 0.0 occurs, stranding migrating planets at semimajor axes in the clump giant phase have radii between 8and14R 0.01 0.10 1.00 10.00 that depend on stellar mass. ( 0.03–0.06 AU) so any planets orbiting inside∼ 0.1 AU will" a (AU) ∼ ∼ An alternative explanation was offered by Kretke et al. likely have been engulfed by an expanding radius during (2008). They found that the protoplanetary disks of post-main-sequence stellar evolution. However, a tidal torqueFig. 1.— The semimajor axis distribution of exoplanets within 200 pc. The data are compiled from the literature and are main- young IM stars will develop a maximum surface density from an expanding stellar surface can also decay the orbitstained by the California & Carnegie Planet Search team. Planet- at ∼ 1AUasaresultofmagnetrotationalinstabilityof of short-period planets. Sato et al. (2008a)numericallytracehosting stars with masses less than 1.5 M! are shown as open the inner disk, leading to a trapping and accumulation of the semimajor axis evolution of short-period planets aroundsquares, while planet-hosting stars with higher masses are shown as solids that can then grow to form rocky cores and Jovian evolving RGB stars and show that, in their past, IM clumpfilled diamonds.Sato et al. (03,07,08); For solar-type Lovis & stars, Mayor planets (07); Niedzielski can be groupe et al. (07,09);dinto Liu (09); two populations:Figure 1. Semimajor “hot planets” axis distribution located at of distances exoplanets within0.1 200 AU pc. and The dataplanets. are This formation scenario provides a mechanism Setiawan et al. (05); Hatzes et al. (06); Johnson et al.(07,08,11);! Reffert et al. (06) giants may have engulfed or disrupted the orbits of planets out tolonger periodcompiled planets from the located literature at and distance are maintained" 1AU.Betweenthese by the California & Carnegiefor in situ formation of Jovian planets interior to the ice 0.5 AU. With radii between 2and5R ( 0.01–0.02 AU),two groupsPlanet lies Search a relative team. Planet-hostingdearth of planets stars with in a masses region less known than 1.5as theM are shown " line, which is located near 3 AU at 10 Myr for a 2 M! ∼planets orbiting IM subgiants∼ are the least" affected∼ by stellar“periodas valley.” open squares, No planets while planet-hosting have been discoveredstars with higher with masses semim areajor shown as filled axes < diamonds.0.6 AU for For stellar solar-type masses stars,> planets1.5 M can!,creatinga“planet be grouped into two populations:star (Kennedy & Kenyon 2008). evolution. Stellar evolution may therefore explain the lack ofdesert” in“hot that planets” region. located Planets at distances with semimajor0.1 AU and axes longer" period5AUare planets locatedModels of Jovian planet formation around IM stars short-period planets around IM clump giants, but the same result ! limited byat distance the current"1AU.Betweenthesetwogroupsliesarelativedearthofplanets baseline of radial velocity observations. make few quantitative predictions that can be obser- for IM subgiants suggests that the observed trend is not due to in a region known as the “period valley.” No planets have been discovered withvationally tested. Simple disk depletion plus migration semimajor axes <0.6 AU for stellar masses >1.5 M ,creatinga“planetdesert” post-main-sequence engulfment. one survey is targeting their main sequence" progenitors models for IM planet hosts (1.5-3.0 M!)byCurrie(2009) The observed semimajor axis distribution can also be ex- in that region. Planets with semimajor axes "5 AU are limited by the current (Gallandbaseline et al. of radial 2005; velocity Lagrange observations. et al. 2009a). predict occurrence rates for Jovian planets with semi- plained as a result of inward orbital migration combined with Recently Johnson et al. (2007b) showed that planets major axes < 0.5 AU to be " 1.5% and for Jovian mass-dependent disk dispersal lifetime. The rocky progeni-orbiting&Kenyon evolved A-type2008). Currie stars have (2009 large) performed semimajor Monte axes Carlo sim-planets with semimajor axes > 0.5 AU to be ! 7.5%. tors of Jovian planets ( 10 M cores) can form at distancescomparedulations to planets of Jovian around planet solar-type formation stars. and migration This trend around IMKennedy & Kenyon (2008) use a semianalytic model of ∼ ⊕ !8AUforstellarmassesbetween 1.5 and 3 M (Kennedyhas becomestars and, even using stronger simple stellar with the mass-dependent discovery of gas more disk lifetimeprotoplanetary disk evolution to study snow line loca- ∼ " planets orbiting IM stars (Sato et al. 2008a). Specifi- tions and planet formation rates around stars of vary- cally, over 20 planets have been discovered around stars ing masses. For stellar masses between 1.5-2.0 M!, with minimum masses > 1.5 M! but none have semi- their models predict that Jovian planet occurrence rates major axes < 0.6 AU. This “planet desert” is shown in reach frequencies of ∼10-15%. Kretke et al. (2008) sug- Figure 1 and a summary of known planets around IM gest that multiple planetary systems may form more ef- stars is presented Table 1. ficeintly around IM stars compared to other stellar mass There are several explanations for this observational regimes. result. One possibility is that the swollen radii of evolved The semimajor axis distribution of planets with mini- stars have engulfed or tidally disrupted short-period mum masses between ∼ 2-10 MJup orbiting IM stars is planets. The current census of IM exoplanet-host stars beginning to be better constrained by observations, but mostly consists of red clump giants (core helium and little is known about planets with masses < 1.5 MJup. hydrogen shell burning post-RGB stars) and subgiants This poor understanding is a direct result of the dearth (stars with contracting inert helium cores and hydrogen- of low-mass planets currently known, with only one hav- burning shells). Planet-hosting stars in the clump giant ing a minimum mass below 1.5 MJup (HD 175541b with phase have radii between ∼ 8-14 R! (∼ 0.03-0.06 AU) MPsini =0.70MJup). It is unclear, however, whether so any planets orbiting inside ∼ 0.1 AU will likely have this scarcity is a result of a detection bias caused by been engulfed by an expanding radius during post-main higher jitter levels in IM stars or whether it reflects an sequence stellar evolution. However, a tidal torque from intrinsic shortage of low-mass planets. Unfortunately, an expanding stellar surface can also decay the orbits models of planet formation in this stellar mass regime of short period planets. Sato et al. (2008a) numerically have made few predictions about low-mass planetary trace the semimajor axis evolution of short-period plan- companions. For solar-type stars, Mayor et al. (2009) ets around evolving RGB stars and show that, in their estimate the frequency of Neptune-mass planets with pe- past, IM clump giants may have engulfed or disrupted the riods < 50 days to be at least 30%. This raises the excit- orbits of planets out to ∼ 0.5 AU. With radii between ∼ ing possibility that low-mass planets could be abundant 2-5 R! (∼ 0.01-0.02 AU), planets orbiting IM subgiants around IM stars, especially in light of recent studies sug- are the least affected by stellar evolution. Stellar evolu- gesting that the frequency of Jovian-mass planets scales tion may therefore explain the lack of short-period plan- with stellar mass (Johnson et al. 2007a). Testing these ets around IM clump giants, but the same result for IM theories requires an understanding of the detection limits subgiants suggests that the observed trend is not due to of radial velocity surveys. L84 VILLAVER & LIVIO Vol. 705 orbital radius inside of which planets will be engulfed by the star at the end of the RGB evolution. We find that the evolution of the star alone can quantitatively explain the observed lack of close-in planets around evolved stars even allowing for the uncertainties associated with mech- anisms such as mass loss along the RGB or tidal-interaction theory. A mechanism such as the one invoked by Currie (2009; i.e., a lifetime stellar-mass dependency of the gas in the planet- forming disk that can halt migration) is not needed, although it might still be present. We find that given an initial distance at which tidal capture is possible, the more massive the planet, the earlier it will be captured by the RGB envelope. Observationally, it appears that giant stars host more-massive planets than MS stars (e.g., Johnson et al. 2007b;Lovis&Mayor2007). Since we find that more-massive planets are expected to be engulfed earlier in the RGB evolution, the fact that they are more frequently observed may point toward a planet-formation mechanism that favors the formation of more-massive planets around intermediate-mass stars. This would be consistent with a scenario in which the disk mass scales with the stellar mass, and more-massive disks produce more-massive planets (see also Kennedy & Kenyon 2008). Along similar lines, since we find a high probability of tidal capture of the planet by evolved stars, the higher frequency of planets observed around intermediate-mass stars (Lovis & Figure 3. Same as Figure 2 butforastarwithaMSmassof3 M .Inthebottom Mayor 2007;Johnsonetal.2007b)seemstoimplythatthe panel, the star reaches the RGB maximum radius. ! efficiency of planet formation must be considerably higher for more-massive stars, compared to their solar analogous. Table 1 Assef et al. (2009)estimatedtheprobabilityofdetecting Minimum Orbital Radius to Avoid Tidal Capture transits of planetary companions to giant stars to be !10 % for max M R (AU) amin (AU) several of the known systems. Since tidal orbital decay decreases ∗ ∗ Mp MJ Mp 3 MJ Mp 5 MJ the initial orbital distance, it may increase the probability for the = = = 1 M 1.10 3.00 3.40 3.70 planet to be observed in transit. 2 M! 0.84 2.10 2.40 2.50 Our results suggest that many planets may be accreted by their Red Giant Branch 3 M! 0.14 0.18 0.23 0.25 host star (see also Siess & Livio 1999a, 1999b). Although so far 5 M! 0.31 0.45 0.55 0.60 ! the results are based on a fairly limited sample, it appears that giant stars hosting planets have the same metallicity distribution as giant stars without planets (Pasquini et al. 2007). On the other aJupiter-massplanetiscapturedbya2M star if it starts at an hand, we should note that if a giant star engulfs a close-in planet ! initial orbit of 2.1 AU while a 5 MJ planet will be engulfed by early in the RGB, it will appear to be a giant star without a planet. the star if it has an initial orbit ao < 2.5AU.Second,thetidal This mechanism might perhaps provide for a partial explanation capture radius decreases with increasing stellar mass; for a 5 MJ for the lack of correlation with metallicity. max planet theTidal initial orbit capture has to be larger more than ao 3 R to Finally, stars that have accreted planets may show a higher ≈ × ∗ avoid tidal capture around a 2 M star, while it has to be larger spin rate, as the planet’s orbital angular momentum is transferred max ! than ao important2 R to avoid tidal for: capture around a 5 M star. to the star (e.g., Livio & Soker 2002). This phenomenon has been ≈ × ∗ ! investigated by Massarotti (2008)andCarlbergetal.(2009), •4.Less DISCUSSION massive AND CONCLUSIONS stars where they estimate the probability of finding rapid rotators among evolved stars. Our quantification of the tidal capture Our main goal has been to determine whether stellar evolution radius may help refine these calculations. could explain•More the observed massive distribution planets of the semimajor axes of planetary orbits around evolved stars (i.e., semimajor axis > 0.5 AU). We found that when the details of the orbital evolution We are very grateful to Lionel Siess, who used his stellar are accurately calculated, tidal interactions constitute a quite evolution code to calculate the stellar models used in the powerful mechanism, capable of capturing close-in planets into calculations of the orbital evolution. the envelope of evolved stars. To date, there are 20 exoplanets discovered around giant REFERENCES stars with M>1.5 M∼ .Thehoststarshaveradiiintherange 0.02 AU 2. The evolution of the habitable zone From a biological point of view and given the limits of our present knowledge, the existence of life is strongly associated with the presence ofliquidwater(Brack1993).Inthis respect the “habitable zone” is currently defined as the rangeofdistancesfromastarwithin which a planet may contain liquid water at its surface. Several evaluations of the inner and outer limits of the habitable zone have been proposed, as discussed in the review of Forget (1998). A conservative estimate, minimizing the width of thehabitablezone(Forget1998), assumes that around our own Sun the habitable zone currently ranges from 0.95 to 1.67 AU. The inner limit of this conservative estimate is set by an atmospheric water loss effect occurring in the stratosphere of a planet, provided water vapor is injected into it from the planet’s surface (KastingHabitable et al. 1993, Kasting Zone 1998). Thearound outer limit isgiants set by the lowest temperature at which the liquid/solid phase change of water occurs. The estimate of this outer limit assumes the existence of a greenhouse effect involving CO2 and H2Ogas(Kasting et al. 1993). A less conservatively defined “habitable zone” extends the outer edge of the limit of the habitableLower zone mass to as largeplanets as 2.4 have AU, dependingmore chances radiative of properties survival of the CO2 ice clouds. An optically thick condensing CO2 atmosphere with particles having radii larger than 6-8 µmhasaveryestar´s evolutionfficient greenhouse effect that maintains the surface temperature above the freezing point of water (Forget & Pierrehumbert 1997, Mischna et al. 2000). HZ moves outward as the star moves into de subgiant In this paperand we giant investigate phases, the evolution at a given of the location transit of the the duration habitable zoneof as a consequence of stellar evolution. A convenient way of estimating the inner and outer limit 8 of the habitablehabitable zone at diff erentconditions stages of can stellar be evolutio largernistoassumethattheplanet than 10 yr. behaves as a gray-bodyWithin with 30 pc: albedo, 44 ALuminosity,andwithperfectheatconductivity(implyingthe class III, 94 LC IV temperature is uniform over the planet’s surface). Its radiative equilibrium temperature, Tp, is then determined by : 2 0.25 Tp =[(1− A)L!/(16πσd )] (1) where L! is the luminosity of the star, σ is the Stefan-Boltzmann constant, and d is the distance from the center of the star to the planet. Typically avalueofapproximately0.2is chosen for the albedo to be representative of an earth-like planet. For these calculations we determine the temperature at the limits of the habitable zone, and from this we calculate the inner and outer distances for a given star. If the albedo iswavelengthindependent,then terms due to the albedo cancel out of the calculation. In the following calculations we use both the conservative limits of the habitable zone and the less conservative limit around our Sun (Forget 1998, Forget and Pierrehumbert 1997, Mischna et al. 2000). For the conservative limit, we assume an effective equilibrium –28– Table 3. Luminosity Class III Stars Within 30 pc Name Alt. Name Type RA J(2000) Dec J(2000) B V Spec. Type Parallax α Phe HD 2261 SB 00 26 17.05 -42 18 21.5 3.46 2.37 K0 42.1 β Cet HD 4128 V 00 43 35.37 -17 59 11.8 3.06 2.04 K0 34.0 χ Cet HD 11171 Ds 01 49 35.10 -10 41 11.1 4.981 4.66 F3 42.4 α Ari HD 12929 V 02 07 10.41 +23 27 44.7 3.15 2.00 K2 49.5 ι Hyi HD 21024 03 15 57.66 -77 23 18.4 5.914 5.51 F4 34.0 γ Dor HD 27290 Pu 04 16 01.59 -51 29 11.9 4.55 4.20 F4 49.3 α Tau HD29139 V 043555.24 +163033.5 2.39 0.85 K5 50.1 HD 29883 04 43 35.44 +27 41 14.6 8.92 8.01 K5 44.7 67 Eri HD 33111 V 05 07 50.99 -05 05 11.2 2.92 2.79 A3 36.7 HD 290054 05 14 48.13 +00 39 43.1 11.1 9.9 K2 38.1 α Aur HD 34029 RS 05 16 41.36 +45 59 52.8 0.88 0.08 G5 77.3 CAL 42 HD 36705 Ro 05 28 44.83 -65 26 54.9 7.73 6.93 K1 66.9 β Col HD 39425 05 50 57.59 -35 46 05.9 4.28 3.12 K2 37.9 SV* ZI 543 HD 47205 V 06 36 41.04 -19 15 21.2 5.01 3.96 K1 50.4 α Cha HD 71243 08 18 31.55 -76 55 11.0 4.436 4.06 F5 51.4 qPup HD63744 081833.31 -363933.4 4.657 4.44 A7 14.4 SV LMi HD 82885 RS 09 35 39.50 +35 48 36.5 6.18 5.41 G8 89.5 46 LMi HD 94264 V 10 53 18.71 +34 12 53.5 4.87 3.83 K0 33.4 UCar HD94510 V 105329.66 -585111.4 4.713 3.79 K1 33.7 η Cru HD 105211 Ds 12 06 52.90 -64 36 49.4 4.462 4.14 F2 50.8 γ Cru HD 108903 V 12 31 09.96 -57 06 47.6 3.22 1.63 M3.5 37.1 Targets δ Mus HD 112985 SB 13 02 16.26 -71 32 55.9 4.80 3.62 K2 35.9 GJ9427 SAO63355 130735.06 +342406.1 10.53 9.30 K3 41.9 HD 118036 13 34 16.26 -00 18 49.6 8.27 7.38 K4 41.0 α Boo HD 124897 V 14 15 39.67 +19 10 56.7 1.19 -0.04 K1.5 88.9 γ Boo HD 127762 dS 14 32 04.67 +38 18 29.7 3.23 3.00 A7 38.3 107 Vir HD 129502 14 43 03.62 -05 39 29.5 4.26 3.90 F2 53.5 HD 130322 14 47 32.73 -00 16 53.3 8.80 8.05 K0 33.6 β TrA HD141891 155508.56 -632550.6 3.14 2.85 F2 81.2 26 Sco HD 151680 V 16 50 09.81 -34 17 35.6 3.44 2.29 K2.5 49.9 κ Oph HD 153210 V 16 57 40.10 +09 22 30.1 4.35 3.20 K2 38.0 α Oph HD 159561 V 17 34 56.07 +12 33 36.1 2.23 2.10 A5 69.8 60 Oph HD 161096 V 17 43 28.35 +04 34 02.3 3.967 2.77 K2 39.8 10 Sgr HD 165135 V 18 05 48.49 -30 25 26.7 3.99 2.99 K0 33.9 111 Her HD 173880 Ds 18 47 01.27 +18 10 53.5 4.477 4.34 A5 35.2 38 Sgr HD 176687 Ds 19 02 36.71 -29 52 48.4 2.704 2.60 A2 36.6 HD 187237 19 48 00.88 +27 52 10.3 7.51 6.88 G2 38.4 HD 195627 20 35 34.85 -60 34 54.3 5.031 4.75 F1 36.3 ε Cyg HD 197989 20 46 12.68 +33 58 12.9 3.49 2.50 K0 45.3 ν Oct HD 205478 SB 21 41 28.65 -77 23 24.2 4.76 3.76 K0 47.2 δ Cap HD 207098 Al 21 47 02.45 -16 07 38.2 3.16 2.87 A7 84.6 HD 216448 22 52 00.55 +57 43 00.9 9.05 8.02 K5 41.2 γ Tuc HD219571 231725.77 -581408.6 4.369 4.00 F1 45.4 λ And HD 222107 RS 23 37 33.84 +46 27 29.3 4.90 3.82 G8 38.7 –28– Table 3. Luminosity Class III Stars Within 30 pc Name Alt. Name Type RA J(2000) Dec J(2000) B V Spec. Type Parallax α Phe HD 2261 SB 00 26 17.05 -42 18 21.5 3.46 2.37 K0 42.1 β Cet HD 4128 V 00 43 35.37 -17 59 11.8 3.06 2.04 K0 34.0 χ Cet HD 11171 Ds 01 49 35.10 -10 41 11.1 4.981 4.66 F3 42.4 α Ari HD 12929 V 02 07 10.41 +23 27 44.7 3.15 2.00 K2 49.5 ι Hyi HD 21024 03 15 57.66 -77 23 18.4 5.914 5.51 F4 34.0 γ Dor HD 27290 Pu 04 16 01.59 -51 29 11.9 4.55 4.20 F4 49.3 α Tau HD29139 V 043555.24 +163033.5 2.39 0.85 K5 50.1 HD 29883 04 43 35.44 +27 41 14.6 8.92 8.01 K5 44.7 67 Eri HD 33111 V 05 07 50.99 -05 05 11.2 2.92 2.79 A3 36.7 HD 290054 05 14 48.13 +00 39 43.1 11.1 9.9 K2 38.1 α Aur HD 34029 RS 05 16 41.36 +45 59 52.8 0.88 0.08 G5 77.3 CAL 42 HD 36705 Ro 05 28 44.83 -65 26 54.9 7.73 6.93 K1 66.9 β Col HD 39425 05 50 57.59 -35 46 05.9 4.28 3.12 K2 37.9 SV* ZI 543 HD 47205 V 06 36 41.04 -19 15 21.2 5.01 3.96 K1 50.4 α Cha HD 71243 08 18 31.55 -76 55 11.0 4.436 4.06 F5 51.4 qPup HD63744 081833.31 -363933.4 4.657 4.44 A7 14.4 SV LMi HD 82885 RS 09 35 39.50 +35 48 36.5 6.18 5.41 G8 89.5 46 LMi HD 94264 V 10 53 18.71 +34 12 53.5 4.87 3.83 K0 33.4 UCar HD94510 V 105329.66 -585111.4 4.713 3.79 K1 33.7 η Cru HD 105211 Ds 12 06 52.90 -64 36 49.4 4.462 4.14 F2 50.8 γ Cru HD 108903 V 12 31 09.96 -57 06 47.6 3.22 1.63 M3.5 37.1 δ Mus HD 112985 SB 13 02 16.26 -71 32 55.9 4.80 3.62 K2 35.9 GJ9427 SAO63355 130735.06 +342406.1 10.53 9.30 K3 41.9 HD 118036 13 34 16.26 -00 18 49.6 8.27 7.38 K4 41.0 α Boo HD 124897 V 14 15 39.67 +19 10 56.7 1.19 -0.04 K1.5 88.9 γ Boo HD 127762 dS 14 32 04.67 +38 18 29.7 3.23 3.00 A7 38.3 107 Vir HD 129502 14 43 03.62 -05 39 29.5 4.26 3.90 F2 53.5 HD 130322 14 47 32.73 -00 16 53.3 8.80 8.05 K0 33.6 β TrA HD141891 155508.56 -632550.6 3.14 2.85 F2 81.2 26 Sco HD 151680 V 16 50 09.81 -34 17 35.6 3.44 2.29 K2.5 49.9 κ Oph HD 153210 V 16 57 40.10 +09 22 30.1 4.35 3.20 K2 38.0 α Oph HD 159561 V 17 34 56.07 +12 33 36.1 2.23 2.10 A5 69.8 60 Oph HD 161096 V 17 43 28.35 +04 34 02.3 3.967 2.77 K2 39.8 10 Sgr HD 165135 V 18 05 48.49 -30 25 26.7 3.99 2.99 K0 33.9 111 Her HD 173880 Ds 18 47 01.27 +18 10 53.5 4.477 4.34 A5 35.2 38 Sgr HD 176687 Ds 19 02 36.71 -29 52 48.4 2.704 2.60 A2 36.6 HD 187237 19 48 00.88 +27 52 10.3 7.51 6.88 G2 38.4 HD 195627 20 35 34.85 -60 34 54.3 5.031 4.75 F1 36.3 ε Cyg HD 197989 20 46 12.68 +33 58 12.9 3.49 2.50 K0 45.3 ν Oct HD 205478 SB 21 41 28.65 -77 23 24.2 4.76 3.76 K0 47.2 δ Cap HD 207098 Al 21 47 02.45 -16 07 38.2 3.16 2.87 A7 84.6 HD 216448 22 52 00.55 +57 43 00.9 9.05 8.02 K5 41.2 γ Tuc HD219571 231725.77 -581408.6 4.369 4.00 F1 45.4 λ And HD 222107 RS 23 37 33.84 +46 27 29.3 4.90 3.82 G8 38.7 AGB Mass-loss: orbital expansion R /R MMS Rmax f o [AU] [AU] 1 1,6 1,8 1.5 2,4 2,5 2 3,0 3,2 2.5 3,3 3,8 3.5 4,2 4,9 5 5,3 5,5 Villaver & Livio (2007) 2 Agol Orbital Period There are several important consequences of the 5 hr 10 hr 20 hr 40 hr White dwarf effective temperature (10 WDHZ and CHZ. First, the range of white dwarf tem- M =0.6 MO • ; H atmosphere WD 3 10 peratures in the portion of the CHZ within the WDHZ 10 -4.5 10 LO • 4 is that of cool white dwarfs, ≈3000–9000 K (right hand Too cold 5 axis in Figure 1), similar to the Sun. At the hotter end -4.0 10 LO • higher ultraviolet flux might affect the retention of an WDHZ atmosphere, these planets would need to form a sec- ondary atmosphere, as occurred on Earth. Excluding 6 higher temperature white dwarfs only slightly modifies Tidal disruption -3.5 the CHZ since they spend little time at high temper- 10 LO • 7 ature. Cool white dwarfs are photometrically stable White dwarf age (yr) a Too hot R 8 109 (Fontaine & Brassard 2008), which is critical for find- Too short 9 ing planets around them. Second, for white dwarfs 3 10 K) with temperatures !4500 K, the WDHZ is exterior to the Roche limit (tidal disruption radius), aR = 0.004 0.01 0.04 −1/3 1/3 Planet orbital distance (AU) 0.0054AU(ρp/ρ⊕) (MWD/0.6M!) ,whereρp,⊕ are White Dwarfs the mass densities of the planet and of Earth. Conse- Fig. 1.— WDHZ for MWD =0.6M! vs. white dwarf age and planet orbital distance. Blue region denotes the WDHZ. Dashed quently, the 3 Gyr CHZ lies between aR White dwarf age (yr) Too hot DETECTION OF PLANETS IN THE WHITE DWARF a White dwarf mass (M R 8 109 (Fontaine0.4 & Brassard 2008), which is critical for find- HABITABLE ZONE Too short 9 ing planets around them. Second, for white dwarfs 3 K) with temperatures !4500 K, the WDHZ is exterior I plot example light curves of planets in the WDHZ in 10 ≈ to0.2 the Roche limit (tidal disruption radius), aR = Figure 3 for sizes within a factor of 2 of Earth orbiting a 0.004 0.01 0.04 0.004 −1/30.01 1/3 0.04 white dwarf near the peak of the white dwarf luminosity Planet orbital distance (AU) 0.0054AU(ρp/ρ⊕) (MWD/0.6M!) ,whereρp,⊕ are the mass densitiesPlanet of theorbital planet distance and (AU) of Earth. Conse- function. The transits last ≈2 minutes, and have a max- Fig. 1.— WDHZ for MWD =0.6M! vs. white dwarf age and planet orbital distance. Blue regionAgol denotes2008, theApJ, WDHZ. 731, DashL 31ed Fig.quently, 2.— CHZ the vs. 3 white Gyr CHZ dwarf lies mass between and planetaR ) star will have a permanent day, while the far side will • O zone” (CHZ) as the range of planet orbital distances, a, so for every 100 Earths orbiting white dwarfs at 0.01 AU that arehave habitable a permanent for night.a minimum The planet duration, will orbittmin stably(Figure as 0.8 it cannot raise a tide on the compact white dwarf. Radi- with random orientations, on average one will be seen to CHZ: 2). I choose a minimum duration of tmin = 3 Gyr, which t =3 Gyr; H atmosphere ation drag will not cause the orbit to decay, but magnetic transit. min results in a CHZ within a<0.02 AU: a planet that or- Tidal disruption field drag might, depending on the planet’s conductivity Idefineη⊕ to be the number of planets with 0.1M⊕ < 0.6 bits within(Li et al. this 1998). distance spends at least 3 Gyr within the Mp < 10M⊕ in the 3 Gyr CHZ (a<0.02 AU). To mea- WDHZ. From 0.4 to 0.9 M! with tmin=3 Gyr the outer 3. DETECTION OF PLANETS IN THE WHITE DWARF sure η⊕ to an accuracy of ≈33% requires detecting ≈9 White dwarf mass (M boundary of the CHZ always falls within 10% of 0.02 − 0.4 HABITABLE ZONE ≈ 3 1 AU for hydrogen and helium atmospheres (Figure 2). To planets, so one must survey 10 η⊕ white dwarfs. check theI plot sensitivity example light to the curves white of planets dwarf coolingin the WDHZ compu- in ≈ 4. 0.2 tations,Figure I have 3 for also sizes withincomputed a factor the of WDHZ2 of Earth with orbiting BASTI a SURVEY STRATEGY 0.004 0.01 0.04 white dwarf near the peak of the white dwarf luminosity ± × −3 Planet orbital distance (AU) models (Salaris et al. 2010),≈ for which I find a slightly The local density of white dwarfs is (4.7 0.5) 10 function. The transits last 2 minutes, and have a max- −3 longer tHZ. I have also computed the CHZ for atmo- pc (Harris et al. 2006). For a survey out to Dmax < Fig. 2.— CHZ vs. white dwarf mass and planet orbital distance. imum depth of 10%—100%; these events can be detected spheresat a with 100 pctmin distance= 1 Gyr with and a 1 m 5 ground-based Gyr which shifts telescope. the 200 pc, the white dwarfs should be nearly isotropically Green region is the CHZ for tHZ >tmin=3 Gyr, H-atmosphere. 3 2 Left solid line is Roche limit for Earth-density planets. TheotherouterTo boundary detect planets of the in CHZ the CHZ outward/inward one must monitor by a a sample factor spaced on the sky at one per ≈2(100pc/Dmax) deg . lines show how the CHZ outer boundary changes for tmin=1 Gyrof ≈1.5/0.7of white (Figure dwarfs for 2). the duration of the orbital period at This exceeds the field of view of most telescopes, so each (dotted line), for tmin=5 Gyr (dash-dotted line), or for an He at- 0.02 AU, and planets present in edge-on orbits will be mosphere with tmin=3Gyr(dashedline).Horizontallineindicates the most common white dwarf mass of 0.6 M!,plottedinFigure seen to transit their host stars. The transit probability 1. is R /R⊕ + R /0.013R! p =1.0% p WD , (1) WDHZ limits, I next define the “continuously habitable trans ! a/0.01AU " zone” (CHZ) as the range of planet orbital distances, a, that are habitable for a minimum duration, t (Figure so for every 100 Earths orbiting white dwarfs at 0.01 AU min with random orientations, on average one will be seen to 2). I choose a minimum duration of tmin = 3 Gyr, which results in a CHZ within a<0.02 AU: a planet that or- transit. bits within this distance spends at least 3 Gyr within the Idefineη⊕ to be the number of planets with 0.1M⊕ < Mp < 10M⊕ in the 3 Gyr CHZ (a<0.02 AU). To mea- WDHZ. From 0.4 to 0.9 M! with tmin=3 Gyr the outer ≈ ≈ boundary of the CHZ always falls within 10% of 0.02 sure η⊕ to an accuracy of 33% requires detecting 9 ≈ 3 −1 AU for hydrogen and helium atmospheres (Figure 2). To planets, so one must survey 10 η⊕ white dwarfs. check the sensitivity to the white dwarf cooling compu- 4. tations, I have also computed the WDHZ with BASTI SURVEY STRATEGY models (Salaris et al. 2010), for which I find a slightly The local density of white dwarfs is (4.7 ± 0.5) × 10−3 −3 longer tHZ. I have also computed the CHZ for atmo- pc (Harris et al. 2006). For a survey out to Dmax < spheres with tmin = 1 Gyr and 5 Gyr which shifts the 200 pc, the white dwarfs should be nearly isotropically 3 2 outer boundary of the CHZ outward/inward by a factor spaced on the sky at one per ≈2(100pc/Dmax) deg . of ≈1.5/0.7 (Figure 2). This exceeds the field of view of most telescopes, so each A more general planet search around WDs TABLE 1. Statistics of nearby white dwarfs ∗ † 3 ∗∗ 3 ‡ ∗∗ ‡ Vabs WD space d13 [pc] d15 [pc] vol50,13 [pc ] vol100,15 [pc ] N50,13 N100,15 density [pc−3] 8-9 1.698× 10−6 79.4 199.5 5.236 × 105 4.189 × 106 17 9-10 1.076× 10−5 50.1 125.9 5.236 × 105 4.189 × 106 645 10 - 11 1.380 × 10−4 31.6 79.4 1.325 × 105 2.099 × 106 18 290 11 - 12 5.222 × 10−4 20.0 50.1 3.327 × 104 5.273 × 105 17 275 12 - 13 7.087 × 10−4 12.6 31.6 8.358 × 103 1.325 × 105 694 13 - 14 1.044 × 10−3 7.9 20.0 2.099 × 103 3.327 × 104 235 14 - 15 1.269 × 10−3 5.0 12.6 5.273 × 102 8.358 × 103 111 15 - 16 1.119 × 10−3 3.2 7.9 1.325 × 102 2.099 × 103 02 16 - 17 7.460 × 10−5 2.0 5.0 3.327 × 101 5.273 × 102 00 Tot 4.888 × 10−3 51 759 ∗ distance corresponding to an apparent magnitude V=13 † distance corresponding to an apparent magnitude V=15 ∗∗ d≤50, V≤13 ‡ d≤100, V≤15 Silvotti et al.2010 complete and the densities are corrected for incompleteness. For the hottest objects with absolute magnitude 8 DISCUSSION As shown in Table 1 and Figure 1, GAIA will be able to verify the presence of Jovian planets (down to 0.7 MJup or ∼200 MEarth)around∼50 bright (V<13) white dwarfs within 50 pc from the Sun. For magnitudes fainter than V&13, the GAIA performances start to decrease (Lindegren 2010). However, considering e.g. a larger sample of about 750 white dwarfs with V<15 and d<100 pc, GAIA will still be able to detect giant planets and brown dwarfs with masses larger than 2 MJup. Poluted WDs The Astrophysical Journal,732:90(9pp),2011May10 Melis et al. Metal Rich WDs: 25%DA WDs contain heavy elements (Zuckerman et al.03). Asteroids or comets are scattered on to orbits that approach close to the star 8 (JuraA. 03; Bonsor Debes & et Sigurdsson al. 2002). Planetesimals must survive the star´s evolution. Figure 4. Elements identified in the HIRES spectra of GALEX1931. Aluminum is tentatively identified, and the indicated abundance is suggested as an upper limit. Higher S/N spectra in this region or ultravioletGALEX spectra could confirm J193156.8+011745; the detection of Al. Wavelengths Mellis are in the vacuumet al. heliocentric (2011) reference frame. Smooth, red curves are model fits with the indicated abundances by number. (A color version of this figure is available in the online journal.) Table 3 17 CircumstellarGALEX1931+0117 MetalDebris Pollution Disks: Z log[n(Z)/n(H)] τ (days)a [n(Z)/n(Fe)] b [n(Z)/n(Fe)] c M /(107 gs 1)d measured diff accreted CI ˙ acc − C e.g. Gänsicke< 4.85 5.811et al.; Jura<0.0712 et al.; 0Kilic.8912 et al.;<3.15 − O 3.68 0.10e 3.534 1.7338 8.7096 102.0 − ± ZuckermanMg 4.10 0.10 et al., 4.532 Farihi 0. 5140et al., von 1.2022 Hippel 46.1 et. − ± Al < 5.85 5.336 <0.0077 0.0954 <0.772 − Si 4.35 0.11 4.542 0.2884 1.1481 29.8 − ± Ca 5.83 0.10R< 2.730 0.01 0.0158 AU 0.0691 2.34 − ± Ti < 7.00 2.960 <0.0010 0.0027 <0.174 − Cr 5.92 0.14 2.560 0.0137 0.0151 2.55 − ± Mn 6.26 0.15 2.292 0.0070 0.0104 2.64 − ±DAZ white dwarfs: Fe 4.10 0.10 2.329 1.00 1.00 205.0 − ± Ni < 5.60 1.982 <0.0371 0.0549 <8.04 see e.g. −Becklin et al. , Jura et al., Gänsicke et Notes. Bonsor, Mustill & Wyatt (2011) a Diffusion constants; see Koester (2009) and Section 4. b Parent body abundances relative to Fe; see Section 4 and Figure 6. Figure 7. Left panel:The accretion rate calculated using Eq. 7 and Eq.c CI chondrite8foroursimulations,with data from Lodders (2003). See also Figure 6. Mpl =1M⊕ (crosses and solid line), d Macc(Z) Menv(Z)/τdiff (Z), where Menv(Z) is the mass of element Z in GALEX1931’s envelope assuming M M ˙ = 1 Nep (asterisks and dotted line) and 1 J (triangles and dashedthe line). hydrogen-dominated A range envelope of mass belt is 9.4 10 masses16 g (Koester 2009 are; D. Koester calcu 2010,lated private communication). using the population e × models of (Bonsor & Wyatt 2010), but only the median value is plottedThe O abundance here, is derived with from upper the equivalent and widths reported lower in Vennes limits et al. (2010 for); see Section the3.1 1.MNep case shown by the arrows. Each test particle that is scattered in is plotof theted synthetic with O i lines a are discrete then compared value to the Vennes of M˙ et.Astraightlineisthenfittedtothesedata al. with that reported in Vennes et al. (2010, 2011). New elements (2010)measuredvaluestoderivetheabundancereportedin discovered in the HIRES data are chromium identified from points. Right panel: The accretion rates for a population ofTablediscs3.AbundancemeasurementsforCa,Si,andOarein with randomly selected initial belttwo Cr mass, II lines and radius, manganese coo identifiedling from age one and Mn II stellar line properties, using the smoothed fit to the stochastic accretiagreementon process, with those reported as determined in Vennes et al. (2010 in, 2011 the), not left-hand(Figure 4 panel,). Aluminum but may for be present eachindividualdisc in the HIRES data as withstanding the significant Teff difference between our white well (Figure 4); however, the signal-to-noise ratio (S/N) of the mass. These are compared to observed heavy element accretiodwarf parametersnratesfromFarihietal.(2009)(redasterisks). and theirs. The revised Mg abundance quoted detection is marginal so we report Al only as an upper limit in Vennes et al. (2011)islessabundantby 0.3 dex due entirely (Table 3). Abundances for all elements identified to date in the to the Vennes et al. (2011) inclusion of pressure≈ broadening and atmosphere of GALEX1931 are reported in Table 3 as well as non-LTE effects. We find an Fe abundance higher than Vennes upper limits for other elements of interest (see Section 4). et al. (2010, 2011)by 0.4 dex. It is noted that fits to the Fe lines It is noted that the GALEX NUV and FUV measurements ≈ accreting onto the star. Hence, the mass that willassuming be ac- a Teff of 21,000accretion K yield an Fe abundance rates consistent onto theappear star. discrepant If the with pollution the white dwarf is parameters produced derived by creted onto the star is given by: the disruption of a large5 individual body, as suggested by, amongst others, Jura et al. (2009); Debes et al. (2011) then M ∼ f × f × f × M , (7) acc acc TD SI belt alowerscatteringratethanpredictedbythesesimulations where fSI = MSI/Mbelt is the fraction of the initial belt is required. mass defined as ‘scattered in’. MSI can either be the total Using this formulation and these assumptions, we cal- mass that is scattered in, and then Macc is the total mass culated the accretion rate from each individual scattering that is accreted over the white dwarf lifetime, or alterna- event. The timescale for scattering, dt in Eq. 8 is calculated tively the mass scattered in within a time interval dt,in as the mean of the time between the current scattering event which case Macc is the mass accreted in the time interval and those immediately preceding and following it. Proper- dt. ties of the disc were selected randomly from the main se- Spitzer near-infrared observations of white dwarfs are quence population of debris discs around A stars, and the used to determine dust masses for the observed discs. Since collisionally evolved mass at the end of the main sequence discs are opaque, this is a minimum disc mass and it is un- determined, according to the models of Wyatt et al. (2007) clear how it relates to the total disc mass or the mass that and Bonsor & Wyatt (2010). The mass left in the disc af- must be disrupted into order to produce such an observation. ter our initial simulations was equated with the collisionally We, therefore, chose to compare the results of our simula- evolved mass at the end of the main sequence. Collisional tions to the heavy element accretion rates calculated from evolution of the disc mass in the white dwarf phase is negli- observed abundances of metals in the white dwarf atmo- gible (Bonsor & Wyatt 2010). The left-hand panel of Fig. 7 sphere. These are calculated from observed Ca abundances, shows these accretion rates as a function of time, for a belt an assumption that the accretion is in steady state and that truncated by a 1M⊕ (crosses), 1MNep (asterisks) and 1MJ the abundance of Ca in the accreting material is approxi- (triangles) planet. Only the belt with the median mass at mately solar. the end of the main sequence is displayed, whilst the arrows Assuming that mass must be supplied to the disc at show the highest and lowest mass belt in the population, for least at the rate at which it accretes onto star, the results of the 1MNep case. these simulations can be interpreted in terms of the obser- As anticipated, early in the white dwarf phase many vations. The rate at which mass is scattered inwards onto particles are scattered, whilst at later times, the number of star-grazing orbits, or the predicted accretion rate, is given particles scattered as a function of time, and thus the ac- by: cretion rate, decreases. This happens slightly more slowly Macc for the lower mass planets, since scattering times decrease M˙ acc ∼ , (8) ∆t with increasing planet mass. The difference between the dif- where ∆t is the time interval over which a mass Macc is ferent planet masses, however, is small, compared to the scattered. This assumes that the accretion is a continuous range of accretion rates for different initial belt properties, process and that the accretion rate is determined by the or the other assumptions that went into this plot. In order scattering rate rather than viscous timescales in the close-in to convert this stochastic process into a smooth decrease disc. These accretion rates could, however, be considered a with time, a straight line was fitted to the data for each belt minimum for the rate at which material must be supplied to mass. These are shown for the belt with median mass by the disc in order to reproduce the observed heavy element the solid (1M⊕), dotted (1MNep)anddashed(1MJ )lines. !c 0000 RAS, MNRAS 000,000–000 GAIA 15 μas 50pc V<13 3 σ 5 yr 0.6MWD FIGURE 1. Exoplanet discovery space for the GAIA mission based on double-blind tests (Casertano et Silvottial. 2010). et al.2010 Detectability curves are defined on the basis of a 3! criterion for signal detection. The upper and lower curves are for GAIA astrometry with !A =15µas (where !A is the single-measurement astrometric precision), assuming a 0.59-M! WD primary at 100 pc (V<15) and 50 pc (V<13), respectively. Survey duration is set to 5 yr. (Pink) dots indicate the inventory of Doppler-detected exoplanets as of May 2010. Transiting systems are shown as (light-blue) filled diamonds, while the (red) hexagons and the (dark- green) squares are planets detected by microlensing or timing respectively. When the inclination of the system is not known, in particular for the (pink) dots and the (dark-green) squares, we used the minimum mass. Solar System planets are shown as (light-green) pentagons. The small (yellow) dots represent a theoretical distribution of masses and final orbital semi-major axes from Ida & Lin (2008). The colors are visible only in the electronic version of the paper.