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I. INTRODUCTION
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The envir nment f a binary star system may c ntain tw circumstellar disks,ne rbiting each f the stars, and a circumbinary disk rbiting ab ut the entire
binary. The disk structure and ev luti n are m dified by the presence f the bi-nary. Res nances emit waves and pen disk gaps. The binary’s t tal mass andmass rati as well as rbital elements can be m dified by the disks. Signatures fthese interacti ns pr vide bservati nal tests f the dynamical m dels. The inter-acti n f y ung planets with pr t planetary disks circularizes the rbits f Jupiter-mass planets and may pr duce much m re massive extras lar planets n eccentricrbits.
[731]
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Space Telescope Science Institute
Stockholm Obser atory
Hubble Space Telescope
INTERACTIONS OF YOUNG BINARIES WITH DISKS
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STEPHEN H. LUBOW
and
PAWEL ARTYMOWICZ
The study f the interacti n f y ung binary stars with disks is m tivatedby tw fact rs: the high frequency f binarity in y ung stars and the highfrequency f disks ar und y ung stars. M st stars, including y ung stars,are f und in binary star systems. Alth ugh the binary f rmati n pr cessis as yet n t well underst d (see B denheimer et al. 1993; the chapter byB denheimer et al., this v lume), binarity appears t be established am ngthe y ungest bserved stars (Ghez et al. 1993; Mathieu 1994).
General arguments suggest that disks are an inevitable c nsequencef the star f rmati n pr cess. The standard picture f single-star f rmati n
inv lves the c llapse f a r tating cl ud (Shu et al. 1987). A disk is anatural pr duct f the c llapse, because centrifugal f rces prevent muchf the cl ud material fr m falling directly nt the central star. Instead, the
material settles nt a centrifugally supp rted disk, fr m which accreti ncan ccur nt the central star (Lynden-Bell and Pringle 1974).
C nsiderable bservati nal evidence n w exists f r the presence fdisks ar und y ung stars. Observati nally determined disk frequencies instar-f rming regi ns exceed 50% (see review by Sargent and Beckwith1994). The images f disks taken with the (HST)
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II. GENERAL DISK PROPERTIES
A. Disk Configuration
732 S. H. LUBOW AND P. ARTYMOWICZ
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pr vide verwhelming evidence f r the existence f disks (e.g., McCaugh-rean and O’Dell 1996; Burr ws et al. 1996). Res lved circumbinary disksare n w directly bserved (e.g., Dutrey et al. 1994; R ddier et al. 1996).
The scale f a typical binary star separati n is ab ut 30–50 AU f rfield stars (Duquenn y and May r 1991), which is less than the typicalT Tauri disk size f a few hundred AU. C nsequently, ne expects thatbinary star systems will usually interact str ngly with disks (Beckwith etal. 1990). Except f r the sh rtest-peri d systems (peri ds less than ab ut8 days), binaries are eccentric with typical eccentricity f ab ut 0.3 (seeMathieu 1994).
These interacti ns give rise t several phen mena imp rtant in ev lu-ti nary and bservati nal c ntexts. In this review we emphasize the recentthe retical results btained after the publicati n f a previ us extensive re-view by Lin and Papal iz u (1993).
There are tw types f disks in a binary envir nment: circumstellar (CS)disks, which surr und nly ne star, and circumbinary (CB) disks, whichsurr und the entire binary. Tw CS disks, ne ar und each star, and neCB disk can be present in a binary. The CS and CB disks are separated bya tidally pr duced gap (e.g., Lin and Papal iz u 1993; Artym wicz andLub w 1994).
The exact size f the gap depends n several fact rs, including thebinary eccentricity, disk turbulent visc sity, and s und speed, as will bedescribed later. Subject t certain assumpti ns, the inner edge f the CBdisk is typically 1 8 t 3 , f r binary semimaj r axis . The circumpri-mary and circumsec ndary disk uter edges have typical radii f 0 35t 0 5 and 0 2 t 0 3 , respectively, f r a binary with a mass ratif 3:1.
Supp rt f r this picture c mes fr m studies f millimeter (and submil-limeter) emissi n f y ung binary systems, which is characteristic f ma-terial at several tens f AU fr m a central star. F r binaries with (pr jected)separati ns f that scale, there is a systematic deficit f emissi n (Beck-with et al. 1990; Jensen and Mathieu 1997). On the ther hand, near-IRemissi n, characteristic f regi ns cl se t each star, ften d es n t sh wa c rresp nding deficit. This result is suggestive f gaps pr duced n thesize scale f the binary.
The m st direct evidence f r gaps in disks c mes fr m bservati nsf binaries GG Tauri and UY Aurigae. In each case f these tw systems,
b th millimeter interfer metry and IR imaging clearly sh w the existencef a CB disk and a depleti n f material near the central regi ns where the
binary is l cated (Duvert et al. 1998; Cl se et al. 1998). F r b th binaries,
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B. Evolutionary State
INTERACTIONS OF YOUNG BINARIES WITH DISKS 733
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there are bservati nal signatures f circumstellar disks and accreti n ntthe stars (Hartigan et al. 1995; Hartmann et al. 1998).
An imp rtant related issue is whether these gaps are c mpletely clearf material r whether material might fl w thr ugh the gap and influence
the ev luti n f the binary (secti n III.F)In m st cases, this review will assume that the disks are c planar
with the binary rbit. Alth ugh this assumpti n is a natural ne, giventhe ge metry f a simple-minded cl ud c llapse m del, it need n t actu-ally be realized. Recent the retical and bservati nal results suggest thatn nc planarity s metimes ccurs (cf. secti n III.E)
In the earliest phases f stellar ev luti n (Classes 0 and I f Lada and Shu1990), a y ung pr t binary might be expected t be embedded in its parentcl ud. Cl ud material accretes nt the binary and the disks. The infallingmaterial affects the disk structure and accreti n pr perties (e.g., Cassenand M sman 1981).
M deling binary ev luti n in this early phase has emphasized theev luti n f the binary rbit and mass rati , assuming the binary rbitremains circular at all times. The main result is that the binary mass ra-ti resp nds t the specific angular m mentum (angular m mentum perunit mass) f the accreting cl ud material, relative t the specific angu-lar m mentum f the binary (Artym wicz 1983; Bate and B nnell 1997).If the material falls in with l w specific angular m mentum (l wer thanappr ximately the binary specific angular m mentum), then it is accretedpreferentially nt the primary star. The reas n is that the matter falls in-ward t ward the deeper p tential well. With high-angular-m mentum ac-creti n, the material preferentially accretes nt the sec ndary star. Thehigh angular m mentum f the material h lds it at larger radii, where itcan m re easily enc unter the sec ndary (f r a physical argument see sec-ti n III).
The semimaj r axis ev luti n f a circular- rbit binary is d minatedby gravitati nal t rques f the accreting material and the advecti n f an-gular m mentum carried by the accreting material. Gravitati nal t rquescause the rbit t shrink. Generally, it is f und that the advecti n f angu-lar m mentum d minates ver gravitati nal t rques. S the verall sensef the rbit ev luti n is that the rbit shrinks when material with l w spe-
cific angular m mentum is accreted, and the rbit expands when materialwith high specific angular m mentum is accreted.
Figure 1 displays a set f sm thed particle hydr dynamics (SPH)results f the accreti n fl w f r different values f specific angular m -mentum in the infl wing material. The embedding cl ud that supplies ma-terial is likely t have its specific angular m mentum increase with radiusin rder t be stable dynamically. C nsequently, the specific angular m -mentum f material supplied t the binary will likely increase in time,
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734 S. H. LUBOW AND P. ARTYMOWICZ
Figure 1. SPH simulati ns f the accreti n nt the pr t binary star f mass rati0.2 f r different values f specific angular m mentum in the infl wing material,
, determining the partiti ning f the fl w between the circumstellar disks (andstars). (Taken fr m Bate and B nnell 1997.)j
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as material c llapses nt the binary fr m greater and greater distances.The frames in Fig. 1 can then be c nsidered t represent a sequence intime.
Starting with the l west-angular-m mentum infl w (earliest times),the sequence reveals that a B ndi-H yle (B ndi and H yle 1944) accreti n
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C. Accretion and Decretion Disks
D. Disk Viscosity Mechanisms
INTERACTIONS OF YOUNG BINARIES WITH DISKS 735
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c lumn devel ps ab ut each star, f ll wed by the devel pment f disksar und first the primary star and then the sec ndary star. F r infl w withs mewhat higher specific angular m mentum, a circumbinary disk f rms,but the angular m mentum is still l w en ugh t drive an infl w int thebinary. Ong ing bservati nal w rk n embedded s urces will pr videm re c nstraints n this early ev luti nary phase (e.g., L ney et al. 1997).
F r sufficiently high specific angular m mentum, the disk settles intKeplerian rbits that surr und the entire binary. Subsequent ev luti n c-curs n the visc us timescale f the disk.
At later times, the binary c nsists f T Tauri ( r Herbig Ae/Be) starsand is n l nger surr unded by the cl ud (Class II). Remnant disks arepresent in the system. The system may have a circumbinary disk, as seenin the last frame f Fig 1. In additi n, remnant circumstellar disks may bepresent, which may have been f rmed during a phase f accreti n f l werspecific angular m mentum, as seen in the middle frames f Fig. 1. Tdate, m re attenti n has been given t the pr perties f binary systems atthis state, because such systems are m re easily bserved. The remainderf this review will c ncentrate n such systems.
There are tw types f disks that are relevant t the binaries: accreti ndisks and decreti n disks. The circumstellar disks are essentially standardaccreti n disks. Material fl ws inward as angular m mentum fl ws ut-ward by means f turbulent visc sity. The angular m mentum is carriedt the uter edge f the circumstellar disk, where it is rem ved thr ughtidal t rques n the binary.
Decreti n disks are less well kn wn. F r such disks, the central t rquepr vided by the binary prevents material fr m accreting. Instead, the bi-nary l ses angular m mentum t the disk, and the disk then expands ut-ward as the binary c ntracts (Lin and Papal iz u 1979; Pringle 1991;Lub w and Artym wicz 1996).
A circumbinary disk can in principle behave as a decreti n disk. H w-ever, initially, during a transient stage, the circumbinary disk can behaveas an accreti n disk until the disk density pr file adjusts t that appr pri-ate f r a decreti n disk. An ther effect is that material might penetratethe gap surr unding the binary and s accrete. Such an effect appears intw -dimensi nal simulati ns f disks (Artym wicz and Lub w 1996 ). Inpractice, a circumbinary disk might then be intermediate between a pureaccreti n and a pure decreti n disk.
The m dels f r disks described here are based n a simple effective vis-c sity prescripti n. The disk visc sity is c nsidered t be an an mal usvisc sity resulting fr m turbulence (see review by Pringle 1981). The diskturbulence c uld be due t gravitati nal instability (e.g., Lin and Pringle1987). The T mre criteri n f r gravitati nal instability in a Keplerian
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III. EFFECTS OF A BINARY ON DISKS
A. Gravitational Interactions
736 S. H. LUBOW AND P. ARTYMOWICZ
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disk can appr ximately be expressed as ( / ) , f r a disk f mass, thickness-t -radius rati / , surr unding a binary r single star f
mass . Gravitati nal instabilities are alm st certainly imp rtant duringthe earliest phases f star f rmati n, because f the rapid mass buildup fthe disk. H wever, f r parameters f s me bserved systems such as GGTauri (Dutrey et al. 1994), gravitati nal instability is als p ssible.
An ther pr mising mechanism f r pr ducing this turbulence is a mag-netic shearing instability (Balbus and Hawley 1991). Since this instabilityrelies n the effects f a magnetic field, the exact nature f this instabilityis c mplex, and the use f a simple visc sity is a simplificati n. Dynam smay play a r le, as well as vari us ther magnetic instabilities (T ut andPringle 1992; Hawley et al. 1996).
In applicati n t pr t stellar disks, this instability depends n the diskbeing s mewhat i nized. It appears p ssible that pr t stellar disks ares metimes n t sufficiently i nized t be turbulent thr ugh ut. Instead, theturbulence may be restricted t the upper layers f the disk that are suffi-ciently i nized (Gammie 1996; Glassg ld et al. 1997).
F r the present purp ses, these c mplicati ns will be ign red, anda simple turbulent visc sity will be assumed. The level f disk turbu-lence is characterized by the Shakura-Sunyaev dimensi nless parameter
/ , where is the kinematic turbulent visc sity, is the diskthickness, and is the disk s und speed (Shakura and Sunyaev 1973).
The tidal f rces caused by the binary generally act t dist rt a disk fr mits circular f rm. Since m st binaries are eccentric, they bring ab ut time-dependent dist rti ns that ccur at the binary frequency and its harm nics.At special l cati ns in the disk that are res nance p ints, str ng interac-ti ns between the binary and disk ften ccur. It is these res nant interac-ti ns that usually d minate.
The the ry f res nances f r disks has been devel ped as a result fw rk by G ldreich and Tremaine (1980). Fr m this linear the ry, analyticexpressi ns f r the t rques exerted at res nances can be btained. T un-derstand h w res nances arise in the the ry, c nsider a dec mp siti n fthe binary p tential int a sum f rigidly r tating F urier c mp nents:
( ) ( )c s( ) (1)
where cylindrical c rdinates ( ) are centered n the binary center fmass in the inertial frame, and is 2 divided by the binary rbitalperi d.
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B. Wave Propagation
INTERACTIONS OF YOUNG BINARIES WITH DISKS 737
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F r a circular- rbit binary, nly diag nal (i.e., ) terms aren nzer . Setting in equati n (1), we see that the p tential is staticin the frame f the binary, where is a c nstant. In this dec m-p siti n, n ndiag nal (i.e., ) elements arise nly t the extent thatthe binary is eccentric, which is typically the case. The magnitude fscales with eccentricity as . At res nances, waves are launched,which exert t rques n disk material as they damp.
Tw types f res nances are relevant:
1. Lindblad res nances ccur where ( ) /( 1). F rtheir primary effect is t truncate disks. F r , they are calledeccentric Lindblad res nances. They can truncate a disk and usuallyincrease the binary eccentricity.
2. C r tati nal res nances ccur where ( ) / . They generallydamp binary eccentricity. (Technical n te: The dynamical effects fc r tati nal res nances depend n the radial derivative f disk v rtic-ity divided by surface density, . The sign f this quantity might seemill determined, because the distributi n f is n t kn wn. H wever,in the case f a disk with a gap, the steep gradient in the density at thedisk edge determines the sign f the effects f the c r tati nal res -nance. The edges generally pr duce the d minant c r tati nal t rquesand act t damp eccentricity.)
At Lindblad res nances (LRs), waves are launched that carry energy andangular m mentum fr m the binary. The disk experiences changes in itsangular m mentum in regi ns f space where the waves damp. Severalmechanisms have been pr p sed that cause wave damping. The detailedc nditi ns in the disk (which vary ver time) determine which mechanismd minates.
Sh cks pr vide ne mechanism f wave damping (Spruit 1987; Yuanand Cassen 1994; Sav nije et al. 1994). This f rm f damping may play ar le, because a disk is ften f und in simulati ns t be truncated near res-nances that pr duce str ng waves. Waves that are mildly n nlinear near
a res nance might steepen as they pr pagate away fr m the res nance andthen sh ck. Such effects are likely t be m re imp rtant f r c lder disks.Circumstellar disks that surr und pr t stars may be warm en ugh that se-vere damping by this mechanism d es n t ccur. Sh cks c uld pr vides me accreti n ver a br ad regi n f a pr t stellar disk.
Turbulent disk visc sity may act as a dissipati n s urce. H wever, thelevel f damping it pr duces is highly uncertain, especially if magneticstresses play an imp rtant r le in pr viding the turbulence. It is unclearwhether the damping f waves due t magnet hydr dynamic (MHD) tur-bulence can be pr fitably described thr ugh a visc sity. An ther c mpli-cati n is that the eddy turn ver timescale f r the largest turbulent eddies
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C. Gap Formation
738 S. H. LUBOW AND P. ARTYMOWICZ
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may be l nger than the wave peri d, resulting in a reduced effective diskturbulent visc sity (e.g., Lub w and Ogilvie 1998).
S und waves can l se energy by radiative damping (Cassen andW lum 1996). In the absence f radiative damping, the waves w uldinduce adiabatic density fluctuati ns and pr pagate with ut energy l ss.When effects f radiative l sses are included in the cycle f wave c m-pressi n and dec mpressi n, there is a net l ss f energy. The wave radialdamping length is r ughly equal t the disk thickness times the rati fthe disk c ling time t the l cal rbit peri d in the disk. The range fplausible pr t stellar disk c nditi ns permits rapid r sl w decay t ccurby this pr cess.
Nearly all studies f waves in disks have regarded the disk as tw -dimensi nal. That is, dynamical effects in the vertical directi n are ftenign red r simplified. In many circumstances, disks are likely t be p-tically thick in the vertical directi n, and substantial vertical temperaturevariati ns c uld ccur. F r these c nditi ns, c nventi nal wisd m was thats und waves ( m des) w uld be launched at a Lindblad res nance, justas in the vertically is thermal case. The waves w uld then experience apr pagati n speed that varies with height. As a result, the waves w uldrefract up int the disk atm sphere, where they w uld sh ck, ver a radialdistance scale f the rder f the disk thickness (e.g., Lin et al. 1990).
H wever, recent semianalytic 3D results pr vide a different picture.F r a disk having a midplane temperature that is large c mpared t thedisk surface temperature, -m de waves are launched by Lindblad res -nances (Lub w and Ogilvie 1998). The waves are naturally c nfined ver-tically by the increasing vertical gravity with height fr m the disk planeand d n t pr pagate vertically (the wave is vertically evanescent). As them de pr pagates radially away fr m the res nance, it behaves like a sur-
face gravity wave. The wave energy bec mes increasingly c nfined (chan-neled) cl se t the disk surface. The wave amplitude gr ws, and wavedamping by sh cks can s metimes ccur (Ogilvie and Lub w 1999).
As a c nsequence f the damping mechanisms described ab ve, itappears plausible that the waves launched fr m res nances are dampedl cally, s mewhat near the res nance in pr t stellar circumbinary disks.N nlinear simulati ns pr vide s me supp rt f r l cal damping (e.g., Arty-m wicz and Lub w 1994). (H wever, numerical artifacts may be playinga r le.) We will ften assume l cal damping in the discussi n bel w.
Where wave damping ccurs, the angular m mentum f the disk mate-rial changes. This pr cess leads t the pening f a gap in the disk (Linand Papal iz u 1979; G ldreich and Tremaine 1980). Gap clearing is b-served in astr physical disks, am ng thers in planetary rings perturbedby satellites (e.g., Lissauer et al. 1981). Visc us effects in the disk act tfill the gaps. The criteri n f r gap pening at any radius in a visc us disk is
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0 .2 .4 .6 .8 1
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circumbinary disk with z/r=0.03
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INTERACTIONS OF YOUNG BINARIES WITH DISKS 739
Figure 2. The size f a gap ar und a binary system with eccentricity , in termsf binary semimaj r axis , f r different parameters f r visc sity f the disk
(numbers give l g ).
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that the visc us t rque (which acts t sm th density variati ns) must beless than the res nant t rque. B th t rques are typically evaluated usinglinear the ry. In the case f an eccentric binary with m derate , manyres nances are present, but nly ne r tw d minate. The gap peningcriteri n has been f und t agree with the results f SPH simulati ns feccentric binaries (Artym wicz and Lub w 1994).
If ne assumes that the res nant t rque is exerted l cally near the res-nance, the disk edge l cati n is determined by the l cati n f the weak-
est res nance f r which the res nant t rque equals r exceeds the visc ust rque. If waves are damped n nl cally, then the visc sity-balancing res -nance is still the l cati n where the disk is effectively truncated, alth ughthe verall maximum density f the disk may be f und farther away fr mthe perturber (Takeuchi et al. 1996). In the extreme case f negligible vis-c sity and little ther wave damping, there w uld nly be a minimal gap(due t rbit cr ssing). In any case, c nsiderati n f the ptical depth fthe disk is needed t predict the p siti n f the edge bserved in a partic-ular wavelength band. As a rule, the disks are sufficiently paque t makethe t rque-balance definiti n f the gap size useful.
Figure 2 sh ws the expected l cati ns f the inner edge f a typical CBdisk f r vari us values f binary eccentricity and disk turbulent visc sity.The d minant res nance resp nsible f r disk truncati n in a binary sys-tem having 0 2 and 0 01 is typically the 2, 1 uter
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D. Generation of Disk Eccentricity and Features
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740 S. H. LUBOW AND P. ARTYMOWICZ
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Lindblad res nance (LR). All the barlike, 2 gravitati nal field har-m nics decrease sl wly with distance, in c mparis n with 2 harm n-ics. The n neccentric ( ) (2 2) LR is s str ng that it easily clearsthe gas fr m its vicinity.
The imp rtance f the next-str ngest (2,1) LR is c nnected with thefact that binaries with 0 2–0.5 spend relatively much time near apas-tr n, where their angular speed decreases t /(1 ) /2. Thisgives rise t a str ng 1 harm nic, which r tates unif rmly at the speed
/ /2. Whenever that res nance is t str ng c mpared withvisc sity, as happens at intermediate and high eccentricity f the binary,the disk recedes further t the regi ns f higher- LRs with 1.
Pl ts similar t Fig. 2, sh wing the expected disk sizes f r circumpri-mary and circumsec ndary disks (Artym wicz and Lub w 1994), dem n-strate that as the eccentricity increases, the 2 inner eccentric LRswith increasing number ( 2) play a d minant r le in CS disk trunca-ti n.
Jensen et al. (1996) and Jensen and Mathieu (1997) have successfullyfit the infrared spectral energy distributi ns f pre-main-sequence (PMS)binaries with a simple m del f disks with gaps. The standard pr t stellardisks are sharply truncated at radii c rresp nding t the t rque balance.Excepti nal cases, such as AK Sc rpii, require, h wever, that the gap bepartially filled with dust, pr bably embedded in gas fl wing thr ugh thegap fr m a CB disk (see the chapter by Mathieu et al., this v lume).
A disk can bec me eccentric as a result f its interacti n with the binary.The eccentricity can arise as an instability in a system with a binary incircular rbit r thr ugh direct driving by an eccentric binary.
One example f an eccentric instability is that which ccurs in CSdisks f superhump binaries (Whitehurst 1988). The instability ccursthr ugh a pr cess f m de c upling and relies n the effects f the 3:1 res-nance in the disk (Lub w 1991). F r this instability t perate, the binary
mass rati must be fairly extreme, greater than 5:1. On the ther hand, itcann t be t extreme, r the instability will be damped by visc sity. Thisr ther m de-c upling instabilities in principle c uld als perate in a CB
disk at the 1:3 res nance [see equati n (35) f Lub w 1991, with 1].An eccentric binary with unequal stellar masses drives eccentricity in
an initially nearly axisymmetric CB disk via its ne-armed bar p tentialwith ( ) (1 0). The disk disturbance f ll ws the sl w apsidal m ti nf the binary (Artym wicz and Lub w 1996 ). The ne-sidedness f disk
f rcing has a tw f ld effect. Initially the eccentricity f the disk’s edge,den ted as , gr ws as
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INTERACTIONS OF YOUNG BINARIES WITH DISKS 741
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where and are the binary’s semimaj r axis and eccentricity, is thesemimaj r axis f the disk inner edge, and is the binary mass parameter(sec ndary mass divided by t tal mass). The l ngitude f periastr n fdisk rbits, with respect t the stellar periastr n, is den ted as . Typi-cally, disk eccentricity gr ws significantly in a few hundred rbital peri ds
f the binary, while c nstant. During this phase, is l cked at astable value 3 /2, c rresp nding t the perpendicular relative ri-entati n f the tw (disk and binary) apsidal lines. H wever, as gr ws,the l cking acti n f the l psided p tential weakens, and the standardpr grade precessi n f the disk (due t the quadrup le m ment f thed uble star) d minates. B th the analytical and SPH results sh w that thedisk edge begins t precess ar und the binary when / 0 2–0.7. Af-terwards, eccentricity scillates with a precessi nal peri d ( 10 –10 ),driven up and d wn by the sin fact r in equati n (3). In numericalcalculati ns, the CB disk typically attains / 0.5–1. In additi n tthe direct driving described by equati n (2), eccentric instabilities mayplay a r le. M de-c upling instabilities appear t saturate in the endstate f the SPH simulati ns, which, apart fr m the peri dic driving,resembles the free 1 m de studied by Hir se and Osaki (1993).In this m de, pressure gradients between adjacent rings synchr nizetheir precessi n, c unteracting the differential quadrup le-induced pre-cessi n.
Figure 3 presents the eccentric disk ev luti n in snapsh ts fr m avery l ng SPH simulati n f a CB disk ar und a binary with 0 8 and
0 3. The upper left panel f the figure illustrates the initial gr wthf , while the remaining three panels sh w a quasistati nary ( scillating)
eccentricity f the dense, precessing, disk edge. The binary itself is alwayssh wn at periastr n and, because f its very high eccentricity, is n t wellres lved in this figure.
Streamlike features emanating fr m the disk edge t ward the ther-wise empty circumbinary gap are n nres nant in rigin. They are seennly n the receding part f the gas traject ries, f ll wing the periastr n,
when the perturbati n by the binary is greatest. Since the binary is rev lv-ing much faster than the disk material, its main ( ) harm nics createdisturbances that are later enhanced by the kinematics f rbits cr ssingat caustics. These disturbances lead t l cal sh cking f gas al ng thefeathery features that are c lliding with the disk rim. The sh cks ccurbef re the material starts descending t ward the binary al ng the ellipticutline f the disk edge (hence the asymmetry between the tw halvesf the elliptic edge). The cuspy features at the disk rim are p tentiallybservable. Their number c ntains inf rmati n ab ut the mean gap size,
/ , and the mean binary separati n (which may n t be easy t es-tablish therwise fr m bservati ns f wide binaries). They als act asp tential sites f r the streams f gas fl wing nt the binary, describedlater.
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E. Noncoplanar Disks
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742 S. H. LUBOW AND P. ARTYMOWICZ
Figure 3. T p views f an SPH simulati n f an eccentric binary ( 0 8) withmass rati 3:7. Axes are scaled in units f , and time is given in binary rbitalperi ds . Sl w precessi n and ev luti n f disk eccentricity are apparent, aswell as the transient features generated at the disk edge by the binary.
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The binary tidal field might be expected t f rce a disk t c planarity be-cause f differential precessi n. Differential precessi n ccurs because thedisk n dal precessi n rate varies with radius. C nsider a disk as a c llec-ti n f ballistic rbits that initially all have the same tilt and line f n des,s the disk is f a tilted planar f rm. Over time, different annuli in the diskw uld devel p different n dal phasing, and the disk c herence w uld bel st. F r a fluid disk, ne might expect that the str ng n nplanar shear-ing m ti ns w uld give rise t str ng dissipati n (Papal iz u and Pringle1983), which w uld lead t c planarity with the rbit plane f the binary.
F r a fluid disk, there is als the p ssibility that the disk c uld actas a c herently precessing b dy. The ry (Papal iz u and Terquem 1995)and simulati ns (Larw d et al. 1996) suggest that this is indeed p ssible,pr vided that the radial s und cr ssing time in the disk is sh rter than thetimescale f r differential precessi n. F r c nditi ns in binaries, c herentprecessi n typically requires that the rati f the disk thickness t radiusbe greater than ab ut 0.05. When the rati lies in the range f 0.05 t 0.1,
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F. Mass Flow through Gaps
INTERACTIONS OF YOUNG BINARIES WITH DISKS 743
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mildly warped structures devel p. F r much thinner disks, with thicknessrati f 0.02 r less, there is a str ng disrupti n f the disk structure bydifferential precessi n.
The rigin f the n nplanarity is unclear. It may be established bystar f rmati n in widely separated pairs. Observati ns f visual binariessuggest that n nalignment f the stellar spin axes ccurs f r separati nsgreater than ab ut 40 AU (Hale 1994). The stellar spin axis directi n mayreflect the rientati n f a preexisting surr unding disk, which was sub-sequently accreted. C nsequently, widely separated binaries might wellhave f rmed with misaligned disks.
A recent HST image f HK Tau pr vides evidence f r a misaligned,tidally truncated disk in a binary system (Stapelfeldt et al. 1998). Alth ughthe disk’s rientati n is clear fr m the image (nearly edge- n), the binary’srientati n is unkn wn. Fr m statistical arguments c ncerning the binaryrbit, the bserved disk size suggests that the disk is tidally truncated.
With m derate binary eccentricity ( 0 5), the degree f misalignmentis likely t be at least 20 degrees.
F r this system, the disk thickness-t -radius rati appears t be in therange f r c herent precessi n with warping. Furtherm re, the disk preces-si n peri d is plausibly f the rder f the age f the binary (several milli nyears). The expected warping might then be related t the bserved asym-metries.
F r y ung stars f high lumin sity (mass exceeding a few M ,greater than 10 L ) the radiati n fr m the central star can induce a warpinstability in a CS disk (Armitage and Pringle 1997). The warp is str ngestin the inner parts f the disk but may bec me significant in the uter parts.
Until the mid-1990s, the c nsensus, based in part n numerical case stud-ies, was that there is essentially n fl w f gas fr m the CB disk nt thecentral binary. Theref re the ev luti n f CS disks was th ught t be in-dependent f the CB disk. One f the natural c nsequences w uld be afaster depleti n f the CS disks in binaries, because f their sh rter vis-c us ev luti n time. H wever, the evidence fr m the accreti n rates ntPMS spectr sc pic binary stars (presumably fr m the CS disks) was indisagreement with naive expectati ns (Mathieu 1994).
It n w appears that stars in single and binary systems may accretesimilar am unts f mass fr m surr unding disks. Tw -dimensi nal simu-lati ns f disks in binary-disk systems with m derately thin and visc usdisks have revealed the presence f a fl w thr ugh the gap fr m the CBdisk, generally in the f rm f tw gas streams (Artym wicz and Lub w1996 ). One reas n the ld paradigm was inadequate was its reliancen a ne-dimensi nal appr ximati n f r the physical quantities. The mass
density, res nant t rque, and visc us t rque were treated as functi ns fradius nly, by c nsidering their azimuthal averages. The tw -dimensi nal
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744 S. H. LUBOW AND P. ARTYMOWICZ
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studies sh wed that at certain l cati ns in azimuth, the c nditi ns may besuch as t permit mass t penetrate the gap.
The fl w pr cess f r m derately eccentric binaries can be underst din terms f an effective p tential. The inner edge f the CB disk is main-tained by the uter Lindblad res nance f the “simplified p tential” r thec mbined ( ) (0 0) and (2 1) p tential (see Artym wicz and Lub w1996 f r c mparative simulati ns with the full and the simplified p ten-tials). This bisymmetric p tential is static in a frame that r tates at the rate
/2, r ne-half the mean angular speed f the binary. Its effective p ten-tial (gravitati nal p tential plus centrifugal barrier) has tw saddle p ints,which are unstable t small perturbati ns. They c rresp nd cl sely t thec llinear Lagrange p ints L2 and L3 in the circular restricted three-b dypr blem f celestial mechanics. Free particles that have a small inwardvel city w uld fl w inward as a stream fr m the saddle p ints, similar twhat ccurs in a classical R che verfl w pr cess. The finite enthalpy fthe disk gas pr vides an expanding fl w that pr duces the tw streams,which are directed t ward the stars. We have pr p sed that an “efficient”fl w f gas fr m the CB disk can s metimes ccur. (An efficient fl w isne that pr duces an inward mass fl w rate that is c mparable t the rate
that w uld be pr duced in the absence f the binary.)The CB disk is typically truncated just utside the (2,1) LR by the
res nant t rques it pr duces. In this case, the gas passes thr ugh the vicin-ity f p ints at which penetrati n inward is easiest (i.e., the saddle p intsc r tating with the simplified p tential), l cated inside the LR. An effi-cient fl w requires (and results fr m) the Bern ulli c nstant f the gas atthe disk edge being sufficient t verc me the effective p tential barrierbetween the LR and c r tati n p int. This c nditi n can be satisfied indisks which are sufficiently warm (larger enthalpy) r visc us (disk edgecl ser t the center and end wed with larger effective energy). We havef und such fl ws in SPH simulati ns f disks with relative thickness rati
/ / 0 05 and 10 .Figure 4 sh ws the snapsh ts fr m ne SPH simulati n, m deling a
binary system with nearly equal masses (mass parameter 0 44) andeccentricity 0 5. The cr sses den te the saddle p ints f the (0 0)(2 1) p tential, and the added line segments indicate the preferred direc-ti n al ng which gas fl ws thr ugh these p ints. The directi n is deter-mined by taking int acc unt the underlying p tential and the C ri lisf rce, but neglecting gas enthalpy and vel city bef re the passage (cf.Lub w and Shu 1975). We see that the simplified binary p tential indeeddetermines the number f streams, their r tati n at ne-half the mean bi-nary rate, and the pitch angle f the streamlike features.
The mismatch f the streams’ angular vel city with that f the binarycauses a marked time dependence f the mass accreti n rate nt the stars( r their CS disks). Alth ugh the binary pulls n the disk m st str ngly
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INTERACTIONS OF YOUNG BINARIES WITH DISKS 745
Figure 4. Circumbinary disk with half-thickness / / 0 05 transfer-ring mass nt the central eccentric ( 0 5) binary with nearly equal c mp -nents (mass rati 11:14).
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at apastr n, the material d es n t impact the binary in Fig. 4 until ap-pr ximately periastr n. The pr files f ( ) depend sensitively n thebinary’s rbital elements, making the variability a valuable t l in analyz-ing the pr perties f unres lved PMS systems (Artym wicz and Lub w1996 ).
Near the stars, in the case f m derate rbital eccentricity, the clas-sical R che effective p tential (which c r tates with the mean m ti n fthe binary) exerts c ntr l ver the fl w. The fl w is channeled by this p -tential in the vicinity f the classical uter Lagrange p ints L2 and L3.The L3 p int ( n the side f the less massive c mp nent) all ws easierpenetrati n because its effective p tential barrier is l wer. The L3 p inttheref re pr duces a higher accreti n rate than the L2 p int [as f und byArtym wicz (1983) and by Bate and B nnell (1997)]. Tw maj r c nse-quences f this fl w are (i) accreti n rate reversal, which may cause theless massive star t bec me m re lumin us (due t a higher accreti nal lu-min sity), and (ii) mass equalizati n. The imp rtance f these effects f rinterpretati n f bservati ns is n t yet clear (Clarke 1996). In principle,there are implicati ns f r the distributi n f mass rati s and the bserved
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IV. EFFECTS OF DISKS ON A BINARY
746 S. H. LUBOW AND P. ARTYMOWICZ
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binary frequency am ng all types f stars, because actively accreting starswith small c mpani ns may be easier t detect as binaries.
Several bservati ns, summarized bel w, supp rt the existence f amass fl w thr ugh gaps in CB disks.
Near-IR images f classical T Tauri binaries GG Tau and UY Aur(R ddier et al. 1996; Cl se et al. 1998) revealed the inner edges f the CBdisks. The inner edge l cati ns based n millimeter bservati ns (Dutreyet al. 1994; Duvert et al. 1998) agree with the IR imaging and the reticalexpectati ns, and the disk r tati n is c nsistent with Keplerian. The IRbservati ns pr vide weak evidence f r the presence f material in the
central gap. A high-vel city feature may be ass ciated with gas streamsin UY Aur.
A d uble-lined cTTS cl se binary, DQ Tau, d es n t have much spacef r CS disks, yet it sh ws all the signs f active accreti n, presumablythr ugh the CB gap. C ntinuum and line fluxes underg m dulati ns nthe peri d f the binary (Mathieu et al. 1997; Basri et al. 1997). The high-est fluxes ccur near binary periastr n, a behavi r c nsistent with the SPHsimulati ns, if the enhanced emissi n is due t the gas stream impact ntthe stars r very small CS disks. The dynamical m del is c nsistent withthe variability f spectral features, which pr vides an independent testf r the m del.
Spectral energy distributi ns f several PMS binaries (Jensen andMathieu 1997) sh w n evidence f r a binary-pr duced gap. This mayindicate that the dust emissi n fr m the material fl wing thr ugh the gapmasks its presence.
Observati ns f 144 G and K dwarfs in Pleiades (B uvier et al. 1997)sh wed n significant differences in the r tati nal vel city distributi nsf r single and binary stars. This suggests that accreti n nt b th types fstars is similar and, in the case f binaries, likely pr ceeds fr m a CB disk.
Embedded IR c mpani ns t T Tauri stars (K resk et al. 1997; Meyeret al. 1997) are plausibly interpreted in terms f the mass fl w fr m CBdisks nt the sec ndary c mpani ns. Cases in which the m re massivestar is apparently accreting m re gas are c mm n (M nin et al. 1998).
The gravitati nal interacti n f the bulk f the disk with the binary changesits rbital elements. Gas streams can als change the rbital elements, b thby gravitati nal t rque c ntributi ns and by direct impact (advecti n fmass, energy, and angular m mentum). The p tentially imp rtant effectsf gas streams depend n the still unkn wn details f where and with what
vel city the streams hit the CS disks r stars, in the highly dynamic envi-r nment f an eccentric binary. (H wever, in secti n V we menti n pre-liminary w rk n pr t planets, treated as binaries with l w eccentricities
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INTERACTIONS OF YOUNG BINARIES WITH DISKS 747
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and extreme mass rati s.) In this secti n we describe the l ng-range effectsf the disks, which d n t include effects f gas streams.
In a binary with mass parameter 0 3 and eccentricity 0 1, stud-ied by Artym wicz et al. (1991), by far m st f the semimaj r axis andeccentricity driving is due t an uter LR f the ( ) (2 1) p ten-tial c mp nent (which als keeps the disk edge in equilibrium). In sucha case, the gravitati nal t rque is equal t the axisymmetric visc ust rque, 3 , evaluated at radius in the disk just utside fthe edge regi n (maximum wave damping regi n). This relati nship pr -vides a means f estimating the rate f decrease f the binary semimaj raxis (cf. Lub w and Artym wicz 1996):
6 ( / )(3)
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where / quantifies the disk-binary mass rati , and isthe t tal mass f the binary. This r bust f rmula is c nsistent with thenumerical results rep rted by Artym wicz et al. (1991), giving /
10 f r the binary with 0 3 and eccentricity 0 1.The eccentricity ev luti n f a binary is d minated by the effects f
the CB disk. In general, eccentricity gr ws at a rate
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This equati n implies that a CB disk shepherded by the (2,1) p tential ina l w eccentricity binary has /(2 ), in g d agreement with theSPH results f Artym wicz et al. (1991).
The numerical rati between rates / and / was analyzed byLub w and Artym wicz (1996), wh c ncluded that the rati f theserates increases linearly with up t a maximum f und at 0 03 (f rtheir assumed disk parameters), then decreases as 1/ . The maximumdriving c rresp nds t a sh rt timescale f r d ubling eccentricity, f therder f several hundred binary rbit peri ds.
At higher values f eccentricity, many res nances are excited, includ-ing res nances that damp eccentricity (eccentric inner LRs and c r ta-ti nal res nances). At an eccentricity f ab ut 0.5 t 0.7, these res nancesnearly cancel, and the mean rate f gr wth f eccentricity diminishes c n-siderably (Lub w and Artym wicz 1993).
In additi n, in systems with eccentric disks, the disk f rces the bi-nary eccentricity t scillate n the relative precessi nal timescale. Thisccurs because f the disk’s (1,0) ne-sided f rcing, which is similar in
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748 S. H. LUBOW AND P. ARTYMOWICZ
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basic physics t the reverse influence f the eccentric binary n the disk,discussed previ usly. It is n t unc mm n t find in SPH simulati ns thatthis leads t temp rary (n nsecular) eccentricity damping peri ds in manybinary-disk systems.
A paradigm in the planet f rmati n the ry was that a planet (specificallyJupiter) st ps accreting gas when it pens a gap in the prim rdial nebula(e.g., Lin and Papal iz u 1993). Artym wicz and Lub w (1996 ) sug-gested that this d es n t n rmally happen (cf. Artym wicz 1998 f r asample SPH calculati n). Instead, simulati ns suggest that matter fl wsthr ugh an therwise nearly evacuated gap, much as in the case f a bi-nary star (alth ugh the dynamics may be different). This may pr vide ameth d f f rmati n in standard s lar nebulae f r the “superplanets,” rplanets with masses 5 M (Jupiter masses) r greater. Newly disc v-ered extras lar planets ar und 14 Herculis, 70 Virginis, Gl 876, and HD114762 may fall in this mass range. This s mewhat arbitrary mass def-initi n f r superplanets assumes a s lar-mass c mpani n. In the the ry,the mass rati , rather than the mass, is relevant. C nsequently, the dy-namical pr perties we ascribe t superplanets may be appr priate t 70Vir, since its minimum mass rati is in the range f r superplanets. Mutu-ally c mpatible results supp rting this general scenari have since beenbtained with five m dern hydr dynamical schemes in eight implementa-
ti ns (Artym wicz et al. 1999; Kley 1999; Bryden et al. 1999; Lub w et al.1999; chapter by Lin et al., this v lume). Results sh w that there is n fun-damental impediment in the gr wth pr cess f a giant pr t planet via diskaccreti n t bec me a superplanet r p ssibly even a br wn dwarf-massb dy (alth ugh n t a br wn dwarf acc rding t f rmative and structuraldefiniti n). The difficulties are m re “practical”: The mass f the gas inthe disk r its l ngevity may be insufficient, r the disk may have t littlevisc sity r pressure t supply efficient fl w. F r instance, relatively thinand l w-visc sity disks tend t prevent the gr wth f superplanets (seethe chapter by Lin et al., this v lume). Sufficiently high-mass perturbersmay limit further accreti n by tidal effects. F r standard m derate-massnebulae (with mass several times the minimum s lar nebula, visc sity pa-rameter 10 –10 , and / 0 05) ne finds that Jupiter c uldeasily d uble its mass within a few Myr. Present masses f the s lar sys-tem giant planets may thus indicate that they f rmed late in the life f thes lar nebula and c uld n t capture the dwindling supply f mass. An ap-parent lack f their large-scale inward migrati n supp rts speaks f thesame. That may n t be a universal utc me, h wever.
C l r Plate 12 dem nstrates the fl w, simulated with the PPM (piece-wise parab lic meth d) f r a disk with 0 004 and a Jupiter-masspr t planet in circular rbit. A t p view f a fragment f the 2D disk withembedded Jupiter-mass planet is sh wn. Tw wakes, which are sh ck
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waves, penetrate the gap. Disk gas hitting restricted secti ns f the wakescl se t the Lagrange p ints delimiting the R che l be (white val) isbr ught t a near-standstill in the frame c r tating with the planet andfalls t ward the planet.
An intriguing c rrelati n between the mass (rati ) f the planet and itsrbital eccentricity exists am ng the currently c nfirmed radial-vel city
planetary candidates (Mazeh et al. 1997; Marcy and Butler 1998). Werepr duce in Fig. 5 the distributi n f extras lar planets and s lar systemplanets, including the pulsar planets, in the - plane. This distributi n,unless an artifact caused by small statistics, sh ws that superplanets av idcircular rbits and that the maj rity f Jupiter-class and smaller planetsprefer circularity.
In the case f planets, the gaps are much smaller than in the case fbinary stars, and the tidally disturbed material experiences many m re res-nances fr m the higher- c mp nents f the planet’s p tential. Still, at
s me critical mass (called the cr ss ver mass) the (2,1) p tential harm nicd minates (the gap must extend t at least the 1:2 and 2:1 c mmensurabil-ities), and the same mechanism as described f r stars may rapidly def rmthe initially nearly circular (super)planet rbits int ellipses f intermedi-ate ( 0 2). On the ther hand, planets unable t pen gaps, typicallyless massive than Neptune, suffer str ng and m del-independent eccen-tricity damping by c rbital Lindblad res nances (Ward 1986; Artym w-icz 1993). In additi n, the Jupiter-class planets that pen a m dest gap areals circularized by c r tati nal t rques (G ldreich and Tremaine 1980).Thus, alth ugh the value f the cr ss ver mass (which likely depends ndisk temperature and visc sity) has yet t be determined in high-res luti ncalculati ns taking int acc unt mass fl ws, its existence is well estab-lished. Based n early SPH calculati ns f nly the gravitati nal interac-ti ns, the cr ss ver mass in a standard s lar nebula was determined t be
10 M (Artym wicz 1992). In m re recent w rk, we f und evidencethat gas infl ws such as seen in C l r Plate 12 generally damp eccentrici-ties. Since the fl w is inefficient at masses exceeding 10 Jupiter masses(in a standard s lar nebula), the cr ss ver mass may indeed be cl se tthat value. H wever, given the diversity f nebular pr perties, we d n texpect a unique ( ) functi nal dependence. Rather, a pure disk-planetinteracti n in an ensemble f systems w uld result in a switch fr m veryl w t m derately high eccentricities ver a finite range f masses, pr b-ably centered near 10 M . Sh uld such a mass-eccentricity patternbe c nfirmed by future, impr ved statistics, it w uld str ngly argue f r theimp rtance f binary-disk interacti ns in shaping the rbits f ex planets.C nversely, a large percentage f Jupiter-like r smaller planetary candi-dates f und n high- rbits ar und single stars w uld require a c mple-mentary mechanism f r eccentricity generati n: planet-planet interacti n(e.g., Weidenschilling and Marzari 1996; Lin and Ida 1997; Levis n et al.1998).
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Figure 5. The - c rrelati n vs. the predicti ns f the disk-planet interacti nthe ry, in which the eccentricity is damped by pr t planetary disks at masssmaller than appr ximately 10 Jupiter masses and rapidly gr ws at largermasses. P tentially tidally circularized c mpani ns have been mitted (cf.Artym wicz 1998; Artym wicz et al. 1999).
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Independent evidence f disk-planet interacti n in extras lar systems,resulting in migrati n, is pr vided by the sh rt-peri d “h t” Jupiters (Linet al. 1996; chapter by Lin et al., this v lume).
Disks play an imp rtant r le in the ev luti n f y ung binaries. At theearliest phases f ev luti n, m st f the material accreted by a sufficientlycl se binary (semimaj r axis less than ab ut 20 AU) passes thr ugh a cir-cumbinary disk (see Fig. 1). The ev luti n ccurs in the dynamical c l-lapse timescale f ab ut 10 years. During the later T Tauri phase, theev luti n ccurs n a visc us timescale f the disk. The binary underg eseccentricity excitati n because f its interacti ns with the disk.
Many aspects f disk-binary interacti ns are directly bservable andpr vide a p tentially p werful diagn stic t l. Res nances emit spiralwaves and clear gaps (Fig. 2). Simulati ns and analytic the ry indicatethat circumbinary disks s metimes bec me eccentric as a result f theirinteracti ns with the central binaries (Fig. 3). Small-scale features at thedisk edge result fr m interacti ns with an eccentric binary.
Mass s metimes fl ws as gas streams fr m the circumbinary disk,thr ugh the central gap, nt the binary (see Fig. 4). This fl w can causethe sec ndary star t appear t be the m re lumin us (lumin sity reversal)and can cause the sec ndary t accrete m re mass than the primary (tend-ing t ward mass equalizati n). The fl w has additi nal c nsequences nthe rbital ev luti n f the binary that remain t be determined. There areseveral bservati nal indicati ns f the existence f these fl ws.
The analysis f binary-disk interacti ns can be extended t the case fplanet-disk interacti ns. Mass fl w nt a y ung Jupiter can ccur despitethe presence f a gap (C l r Plate 12). It appears p ssible that s me plan-ets can gr w t mass rati s with their stars c mparable with r larger thanthe minimum mass rati s f the newly disc vered extras lar superplanets,such as th se in 70 Vir r 14 Her. Unlike planet-planet interacti n, planet-disk interacti ns may pr duce substantial eccentricity f r high-massplanets and l w eccentricity f r l w-mass planets. Current bservati nspr vide s me supp rt f r this c rrelati n, but the sample size is small (Fig.5). The pattern f p pulati n f the mass-eccentricity plane by ex planetssh uld be indicative f which pr cess is typically resp nsible f r the shapef their rbits.
This w rk was supp rted by NASA GrantsNAGW-4156 and NAG5-4310. S. L. ackn wledges supp rt fr m TheIsaac Newt n Institute f r Mathematical Sciences f Cambridge Univer-sity. P. A. ackn wledges the STScI visit r pr gram and Swedish NaturalScience Research C uncil research grants. We thank the referee, MatthewBate, f r c mments.
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