arXiv:1702.00545v1 [astro-ph.EP] 2 Feb 2017 ilase l 04.Bnr 9Hrui a ria ec- com- orbital has are Herculis 99 2014; Akeson Binary binaries 0 & centricity 2014). Jensen of al. Misaligned 1998; their et al. Williams component et to Stapelfeldt 1994). each misaligned (e.g. (Hale mon are around axes AU that 40 rotation disks of about axes orbital misalignment than rotation binary greater a spin separations has have with binaries 43 Murray-Clay in 60 IRS & least Chiang around protostar disk at circumbinary 2004; binary The 2012). al. the al. et et Winn Capelo 2004; orbital (e.g. binary the in- to plane is respected that se- with disk precessing pre–main circumbinary and a The clined has 15D systems. 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Dissipation libration (polar nodal binary t node. the undergoes evolve of can it plane binary state, orbital eccentric the an to around dicular disk accretion circumbinary OA LGMN FAPOOLNTR IKAON NECCENTRI AN AROUND DISK PROTOPLANETARY A OF ALIGNMENT POLAR euetredmninlhdoyaia iuain oso that show to simulations hydrodynamical three-dimensional use We ◦ . 6adamslge ersds.Temost The disk. debris misaligned a and 76 Bic ta.21) ansqec stars Main–sequence 2016). al. et (Brinch 1 eateto hsc n srnm,Uiest fNevada, of University Astronomy, and Physics of Department 1. A INTRODUCTION T E tl mltajv 5/2/11 v. emulateapj style X crto,aceindss–bnre:gnrl–hdoyais–p – hydrodynamics – general binaries: – disks accretion accretion, ie:formation lites: 2 pc eecp cec nttt,Blioe D228 US 21218, MD Baltimore, Institute, Science Telescope Space eec .Martin G. Rebecca rf eso coe ,2018 8, October version Draft ABSTRACT 1 n tpe .Lubow H. Stephen and saot60 about binary. oper- is eccentricity, not the low does For of mechanism ate. the eccentricity binaries, orbit the The circular For with mechanism this decreases 2011). which Blundell operates above & angle Doolin misalignment oscillations critical 2010; inclination Laskar with & (Farago together (rather circulation), libration more than nodal ec- undergo is misaligned sometimes a binary situation around centric orbits the particle Test binaries, complicated. eccentric involving tilts rtclagei bu 40 about is angle critical iay nScin4w ics h mlctoso our 5. of Section in implications conclusions the our discuss draw we we eccentric and 4 and results Section misaligned hydrodynamic In a a binary. of around evolution Sec- disk the In consider protoplanetary then stars. we young 3 around rel- tion disks parameters circumbinary for to binary evant eccentric misaligned a around disks. planetary than less of ratio axis aspect rotation and parameter, disk, orbital viscosity cold the the a than with vector binary), (rather disks. the eccentricity binary hole the the black about of the cold precession 2015; examined for observed (2015) disk case al. They al. et eccentric the et Dunhill and Aly to misaligned 2016). 1994; coplanar that Quinn 2013; but & or Lubow Fleming eccentric al. & 2013) Artymowicz et is Facchini the Lai or- (e.g. orbit & 2012; Foucart but binary binary Nixon 2013; the the studied, (e.g. Facchini & either circular circumbi- Lodato been that is misaligned previously assumed bit of typically Lai have dynamics & studies Foucart The disks 2011; al. nary et 2014). vis- Nixon through 2013, (e.g. plane orbital dissipation binary the cous with align to dicted loNxne l 03.I hswr efcso the on focus we work this In which in 2013). regime al. wave–like (see et interactions Nixon violent to also leading regions radial disjoint nScin2w rtreaiets atceorbits particle test reexamine first we 2 Section In pre- been has disk circumbinary misaligned slightly A a ea,LsVgs V814 USA 89154, NV Vegas, Las Vegas, Las ◦ clyfrds asssalrthan smaller masses disk for ically hl o ihreccentricity, higher for while noinainta sperpen- is that orientation an o trsystems. star vle oteperpendicular the to evolves k ftebnr n h asof mass the and binary the of niiilymll misaligned mildly initially an ogtd fteascending the of longitude e 2 ges hseouinhas evolution This egrees. A oesoeae bv a above operates rocess ◦ / α < H/R e . 0 = / α > H/R . aesadsatel- and lanets ,teciia inclination critical the 2, h iktr into tore disk The . BINARY C eeatt proto- to relevant e 0 = . ,the 5, 2

Fig. 1.— Initially circular test particle orbits around an eccentric binary with e = 0.5. Left: Time evolution of the inclination (upper ◦ panel) and the longitude of the ascending node (lower panel) for orbits initially inclined by i0 = 60 to the binary orbit. The initial ◦ separation is d = 5 a (solid lines) and d = 8 a (dashed lines). The initial longitude of the ascending node is φ0 = 90 . Right: The i cos φ − i sin φ plane for orbits with varying initial inclination and longitude of the ascending node. The green lines show orbits close to ◦ ◦ ◦ ◦ prograde with i0 = 10 , i0 = 20 and i0 = 30 with φ0 = 90 in order of increasing size. The blue lines show orbits close to retrograde ◦ ◦ ◦ ◦ ◦ with i0 = 150 , i0 = 160 and i0 = 170 with φ0 = 90 in order of increasing size. The red lines show librating solutions with i0 = 80 , ◦ ◦ ◦ ◦ ◦ i0 = 70 , i0 = 60 , i0 = 50 and i0 = 40 with φ0 = 90 in order of increasing size. The magenta lines show librating solutions with ◦ ◦ ◦ ◦ ◦ ◦ i0 = 80 , i0 = 70 , i0 = 60 , i0 = 50 and i0 = 40 with φ0 = −90 in order of increasing size. 2. INCLINED CIRCUMBINARY TEST PARTICLE OBITS does not affect the motion in this phase portrait, only the In this Section we consider inclined test particle orbits time taken to make a complete orbit. Above a certain around an eccentric binary. The stars have equal mass initial inclination, the particle orbits undergo libration rather than circulation. The centre of the upper librat- M1 = M2 = 0.5 M, where M is the total mass of the ◦ ◦ binary and they orbit with semi–major axis, a. The ec- ing region corresponds to i = 90 and φ = 90 , while the centre of the lower librating region corresponds to i = 90◦ centricity of the binary is e =0.5 and the ◦ 3 and φ = −90 . For higher binary eccentricity, the critical is Porb = 2π/pG(M1 + M2)/a . We work in the frame inclination tilt angle that separates the librating from cir- of the centre of mass of the binary. In Cartesian coordi- culating cases is smaller (see Doolin & Blundell 2011, for nates, with the binary orbit in the x−y plane, the binary more details). When the third body is massive, the nodal begins at periastron separation on the x axis. libration region shrinks (see Fig. 5 in Farago & Laskar The test particle begins in a circular Keplerian orbit 2010). For a body with a mass of the order of a few at position (0, d, 0) with velocity (−Ωp cos i0, 0, Ωp sin i0), percent of the binary mass, the region may be reduced 3 where Ωp = pG(M1 + M2)/d is the Keplerian angular somewhat for the configuration of bodies considered here. velocity about the centre of mass of the binary and i0 is In the next Section we consider the evolution of a mis- the initial particle tilt with respect to the binary orbital aligned low mass circumbinary disk around an eccentric plane. The longitude of the ascending node is measured binary. from the x-axis. These initial conditions correspond to ◦ an initial longitude of the ascending node of φ0 = 90 . 3. CIRCUMBINARY DISK SIMULATIONS The left panel of Fig. 1 shows the test particle orbit ◦ With hydrodynamic disk simulations we now an- evolution for an initial inclination of i0 = 60 for two alyze the evolution of a misaligned circumbinary different initial separations, d = 5 a and d = 8 a. The disk around an eccentric equal mass binary. We upper panel shows the inclination of the orbit, i, and the use the smoothed particle hydrodynamics (SPH; e.g. lower panel shows the longitude of the ascending node, φ. Price 2012) code phantom (Price & Federrath 2010; The semi-major axis of the particle remains close to con- Lodato & Price 2010). phantom has been used to model stant over the orbit. The inclination and the longitude of misaligned accretion disks in binary systems previously the ascending node show synchronous oscillations. The (e.g. Nixon 2012; Nixon et al. 2013; Martin et al. 2014; magnitude of the oscillations does not depend upon the Fu et al. 2015) Table 1 contains a summary of the binary distance of the particle from the centre of mass of the and disk parameters. The binary has equal mass compo- binary. However, the timescale for the oscillations in- nents with total mass M = M1 + M2, and an eccentric creases with distance. orbit in the x-y plane with semi–major axis, a. The ac- The right hand panel of Fig. 1 shows test particle orbits cretion radius for particle removal from the simulation in the i cos φ − i sin φ phase space. The test particles all about each star is 0.25 a. begin at a separation of d =5 a, although the separation The upper panels in Fig. 2 show the initially flat and 3

x-y plane t = 0 Porb x-z plane t = 0 Porb y-z plane t = 0 Porb

2a 2a 2a

x-y plane t = 500 Porb x-z plane t = 500 Porb y-z plane t = 500 Porb

2a 2a 2a Fig. 2.— Upper panels: Initial disk set up for the SPH simulation of a binary (shown by the red circles) with an inclined circumbinary disk. Lower panels: The disk at a time of t = 500 Porb. The color denotes the gas density with yellow regions being about two orders of magnitude larger than the blue. The left panels show the view looking down on to the binary orbital plane, the x − y plane. The middle panels show the x − z plane and the right panels show the y − z plane. In the right hand panels the binary components lie in front of each other and so only one red point is seen.

Fig. 3.— Left panel: Inclination (upper panel) and longitude of the ascending node (lower panel) for a circumbinary disk that is initially ◦ misaligned by i0 = 60 . The solid lines show the disk evolution at a radius of 3 a and the dashed lines show a radius of 5 a. Right panel: The same simulation in the i cos φ − i sin φ plane at a radius of 3 a (solid line) and 5 a (dashed line). 4

TABLE 1 Although we do not present the results here, we have Parameters of the initial circumbinary disk set up for an also examined some different parameters for simulations. eccentric, equal mass binary with total mass, M, and First, we have considered disks with a larger radial ex- separation, a. tent. We find for a disk initially outer truncated at larger Binary and Disk Parameters Symbol Value radius that the evolution is at least initially qualitatively Mass of each binary component M1/M = M2/M 0.5 the same. The disk displays oscillations and moves to- Eccentricity of the binary e 0.5 wards a perpendicular orientation. The oscillations are Accretion radius of the masses Racc/a 0.25 more strongly damped for a disk with a larger radial ex- Initial disk mass Mdi/M 0.001 tent. However, for disks truncated at radius & 10 a, there Initial disk inner radius Rin/a 2 is some damping of the binary eccentricity. Lower binary Initial disk outer radius Rout/a 5 eccentricity reduces the tendency for polar alignment. Disk viscosity parameter α 0.01 There is thus a competition between the timescales for Disk aspect ratio H/R(R = Rin) 0.1 the binary eccentricity damping and the polar alignment. H/R(R = Rout) 0.08 ◦ Furthermore, if the alignment timescale becomes shorter Initial disk inclination i 60 than the sound crossing timescale, then disk warping will occur. circular disk that is tilted to the binary orbital plane We have run the same simulation that is presented by 60◦. The disk has initial mass 10−3 M distributed here, but with a circular binary and find that the align- in 300, 000 equal mass particles. The small disk mass ment proceeds towards the binary orbital plane. We have has a minor dynamical significance on the orbit of the also explored the evolution of a disk that begins close to binary. Disk self-gravity is ignored. The initial surface counter alignment and find that the disk moves closer −3/2 to counter–alignment. We have also considered the ef- density profile has a power law distribution Σ ∝ R fect of a larger disk mass. We find that the accretion of between Rin = 2 a and Rout = 5 a. The inner radius of material from a disk of mass 0.05 M can circularise the the disk is chosen to be close to the radius where a disk binary. Furthermore, for large disk masses, the apsidal is tidally truncated (Artymowicz & Lubow 1994). How- precession timescale of the binary may become shorter ever, misaligned disks feel a weaker binary torque (e.g. than the libration timescale of the disk, in which case Lubow et al.2015; Nixon & Lubow2015; Miranda & Lai the disk more closely follows a circulating solution. Both 2015). The disk is locally isothermal with sound speed of these effects, accretion and precession, can result in −3/4 cs ∝ R and H/R = 0.1 at R = Rin. This choice disk–binary planar alignment, rather than polar align- allows both α and hhi /H to be constant over the ra- ment. If we observe a disk, or a planet, to be in a polar dial extent of the disk (Lodato & Pringle 2007). The orbit, the eccentricity of the binary places constraints on Shakura & Sunyaev (1973) α parameter is taken to be the mass of the circumbinary disk. These effects will all 0.01 (the disk viscosity is implemented in the usual man- be investigated in future work. ner by adapting the SPH artificial viscosity according to The circumbinary disk around the binary in KH 15D Lodato & Price (2010) with αAV = 0.4 and βAV = 2.0). may be subject to the nodal and tilt oscillations described The disk is resolved with shell-averaged smoothing length here. The binary eccentricity is high, 0.68

5. CONCLUSIONS many implications for circumbinary gas disks, circumbi- We have found that a polar alignment mechanism can nary planets, and circumbinary debris disks. operate for inclined disks around an eccentric system. The mechanism operates best for higher binary S.H.L. acknowledges support from NASA grant eccentricity, larger initial disk misalignment angle, and NNX11AK61G. Computing resources supporting this lower disk mass. The inclination of the disk is exchanged work were provided by the UNLV National Supercom- with the longitude of the ascending node. Dissipation puting Institute. We thank Daniel Price for providing within the disk aligns the disk to be perpendicular to the phantom code for SPH simulations and the splash the binary orbital plane with disk rotation axis paral- code (Price 2007) for data analysis and rendering of fig- lel to the binary eccentricity vector. The results have ures.

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