new circumstellar and circumbinary disks in eccentric stellar binary...

Circumstellar and Circumbinary Disksin Eccentric Stellar Binary Systems

Bárbara S. Pichardo (IAUNAM/México)Linda S. Sparke (U. of Wisconsin)

Luis A. Aguilar (IAUNAM/México)

Extrasolar Planets

After a very intense search and some false starts, in 1995 M. Mayor and D. Quelozannounced the discovery of the first planet outside the Solar System.

M. Mayor y D. Queloz (1995)Nature, V. 378, p. 355

Star: 51 Pegasi G5V 1.06 MO dist: 15.36 pcPlanet: p: 4.23 d a: 0.05 A.U. e: 0.01 M*sen(i): 0.46 Mj v: 54.99 m/s

Extrasolar Planets

To date, more than 150 extrasolar planets have been found.

Hardly any of the planetary systems found looks like the Solar System.This is due to the Doppler technique used to find most of them, that is most sensitivefor massive planets in tight orbits.

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!vr = mp / a

Binary Stars

Most of stars, however, lie in binary or multiple systems

From a solar neighbourhood sample, weknow that the majority of stars are part ofbinary or multiple star systems (Duquennoyand Mayor, 1991).

Around 70% of stars in binary systems have aseparation up to 400 A.U.This is less than the typical size of circumstellardisks in single stars (Mundi et al., 1996, Wilner,Ho and Rodriguez, 1996).

Heacox & Gathright (1994) AJ 108, 1101.

Binary Stars

Most of stars, however, lie in binary or multiple systems

Working with a local sample of halo stars,Carney et al., (2001) have found a binaryfraction similar to that of the galactic disk.

The sample of Carney et al. contains binaries withperiods up to 7,500 days, spanning the wholeinterval where their identification technique issensitive.If we assume a total mass of one solar mass, theseparations are smaller than ~10 A.U.

Carney, Aguilar, Latham & Laird (2004) AJ.

Binary Stars

We know that tidal effects can be important for close binaries

The plot of period vs. eccentricity shows acircularization effect for binaries whoseperiods are shorter than 10 days.

We may then wonder, can thegravitational influence of a stellarcompanion inhibit planet formation?

Duquennoy & Mayor (1991) AA 248, 485.

Planet Formation in Binary Stars

Up to now, no planets have been discovered in close binary systems.

Some planets have been discovered aroundstars that are part of a binary system: 16Cygni-B, τ Bootis, 55 ρ Cancri, etc.; however,in all cases the separation between the binarystars is larger than 100 A.U.

Is there observational evidence for theformation of planets within binaries atcloser separations?

Cochran & Hatzes (1997) ApJ 483, 457.

16 Cygni-B M*Sin(i): 1.5 MJ, e: 0.63 a: 1.6 A.U.

Circumstellar Disks around CloseBinary Stars

A different strategy is to search in the millimeter region of the spectrum,the hot dust emission of a viscuous protoplanetary disk

Akeson, Koerner & Jensen (1998) ApJ 505, 358.

In 1998, Akeson, Koerner and Jensen announcedthe discovery of a circumstelar disk around thenorth companion of T-Tauri.

The observations were made at λ=3mm using the BIMAarray. The external radius of the disk is 41(+26,-14) A.U.This is smaller than the projected separation with T-tauri(S), which is 100 A.U., in which no disk emissioncould be detected. The estimated mass for the detecteddisk is around 1% of the star’s mass.


A different strategy is to search in the millimeter region of the spectrum,the hot dust emission of a viscuous protoplanetary disk

Rodriguez et al. (1998) Nature 395, 355.

Also in 1998, with only 4 days of difference inthe publication date, Rodriguez et al. announcedthe discovery of circumstellar disks around eachcomponent of a binary system in the IRS5 sourcein L1551

In this case, the observations were made at λ=7mm usingthe VLA. Both disks are of similar size (~10 A.U.), muchsmaller than the projected separation of 45 A.U. betweenthe stars. The estimated mass for the disks is 0.06 and0.03 MO, although these numbers are uncertain by up to afactor of 4, due to possible contamination due to free-freeemission from ionized gas in the bipolar flow.


In both observational studies, the authors note that the sizes of thecircumstellar disks found, are smaller than that expected from the

projected separations between the stars.

Rodriguez et al., also comment that the mm emission of isolated T-Tauri stars islarger than those that form part of a binary system with a separation of less than100 A.U. They interpret this as evidence for less massive disks in the latter case,presumably due to the gravitational perturbation of the stellar companion.


What is the mechanism responsible for the truncation of circumstellardisks in a binary system?



One possibility is the Roche Lobe that forms around each star

Orbital rotation produces a centrifugal barrier in the Jacobi energy in the corotatingframe



One possibility is the Roche Lobe that forms around each star

The centrifugal barrier and the effective potential give rise to the lobes, which can notbe crossed by particles whose Jacobi energy is not sufficient to surmount them


The Roche lobes, however, can not explain the circumstellar disks in L1551 IRS-5, since the disks are much smaller than the star’s separation

Some additional mechanism, presumably of dynamical origin, must be responsiblefor truncating these disks.

Orbits in Stationary Potentials

In a stationary potential, like that of a binary system in circular orbit seen in thecorotating frame, it is the closed, stable orbits, the ones that form the scaffoldingof the orbital structure supported by the potential.

In this case, particles follow paths whose shape isinvariant in time.

A necessary, but not sufficient condition, for apotential to allow the formation of a gaseousaccretion disk, is that it should allow the existence ofclosed, stable, non self intersecting orbits.

Orbits in Non Stationary Potentials

The case of an eccentric binary system, however, is qualitatively different to thecircular case, since in the first case there is no frame of reference where thepotential is time invariant

If the potential is time dependent,then the particle trajectories will varywith time.

What is then the basis forthe orbits that gas mayfollow?

Orbits in Non Stationary Potentials

In 1997, W. Maciejewski and L. Sparke introduced the concept of loops withinthe context of the dynamics of barred galaxies.

These authors were interested in the orbitalstructure of galaxies that have two nested barsof different size.The observational evidence indicates that thebars spin at different rates, so there is no frameof reference where the combined potential isstatic.

Erwin & Sparke (1999) ApJ 521, L37

What orbits follow the gas in thesegalaxies?

The concept of "Loops" in time dependentpotentials

Maciejewski and Sparke discovered the existence of closed contours, whoseshape change with orbital phase in a periodic manner, and which contain thesame particles all the time.

A "loop" is not an orbit in the sense that it is the pathfollowed by a given particle, but rather, it is asnapshot of a set of particles that belong to a givenorbit.

As the particles move around along their paths, thecontour delineated by them gets distortedcontinuously. When a full period is completed, allparticles return to the initial contour, but notnecessarily to the same point on it.

The concept of "Loops" in time dependentpotentials

In their study of double bar potentials, Maciejewski and Sparkefound families of "loops" that get distorted and come back to theinitial shape, when the two bars come back to the same relativeorientation.

Gas can “park” in these loops if they are not self-intersecting at anygiven moment.

The Concept of "Loops" in Eccentric BinarySystems

In this work we have extended the concept of “loops” to the problem ofdetermining the size of circumstellar and circumbinary disks in an eccentric

binary system

For this we have made a systematic search for non self-intersecting loops in the planar,three-body problem.

We have used an Adams "predictor-corrector" integrator (NAG library) of variable order and step.The maximum error in the conservation of the Jacoby energy in the circular case is of one part in107 for an integration of 104 periods.


The search for loops is done automaticallyby a program that moves inward throughthe circumbinary disk and outwardsthrough the circumstellar disks.

The search is made along the line that joinsthe stars at apoastron and it is restricted topaths that cross this line orthogonally.

At a set of gridpoints in the line, the searchis started at the Keplerian velocity. Thealgorithm adjusts the initial tangentialvelocity looking for a minimum in radialposition and velocity dispersions, when thetrajectory is within a 5 degree sectoraround the initial line.


There are 2 parameters that define eachstudied case: the mass ratio (q) defined asthe ratio of the secondary star to the totalmass, and the eccentricity (e) of their orbit.

We have considered the following cases:q: 0.001, 0.1, 0.2, 0.3, 0.4 and 0.5e: 0.0, 0.2, 0.4, 0.6 and 0.8

In each case, we have found the externalradius of the circumstellar disks and theinternal radius of the circumbinary disk.

Circumbinary disk Circumstellar disks

Binary system orbit

Results

CIRCULAR ORBITS

When making the search within thecircumstellar disks, one encountersfirst a region (black) where loops donot intersect each other. One thenencounters a region where theyintersect previous loops (magenta).Finally, one reaches a region whereno loops can be found.We take as external border for thecircumstellar disks the borderbetween the black and magentaregions (blue line).

q=0.3

Results

CIRCULAR ORBITS

In this case, the size of the centralhole of the circumbinary disk remainsroughly constant, when varying themass ratio.

q=0.5 q=0.4

q=0.2 q=0.1

Results

CIRCULAR ORBITS


The size of the circumstellar disksvary with the size of the Roche lobes,although they are always smaller thanthe lobes.

q=0.5 q=0.4

q=0.2 q=0.1

Results

CIRCULAR ORBITS


The size of the circumstellar disksvary with the size of the Roche lobes,although they are always smaller thanthe lobes.

Results

ECCENTRIC ORBITS

In the eccentric case, the effect on thesize of the central hole of thecircumbinary disk is dramatic,growing by a factor of 1.75 when theeccentricity goes from 0.0 to 0.8

e=0.4

e=0 e=0.2

e=0.8

q=0.5

Results

ECCENTRIC ORBITS


The circunestellar disks are stronglyaffected as well.

e=0 e=0.2

e=0.4 e=0.8

q=0.5

Results

ECCENTRIC ORBITS


The circunestellar disks are stronglyaffected as well.

Results

In this sequence, we canappreciate the magnitude of theeffect in the sizes of the disksproduced by the orbitaleccentricity.

e=0 e=0.2

e=0.4 e=0.8

Results

In this sequence, we canappreciate the magnitude of theeffect in the sizes of the disksproduced by the orbitaleccentricity.

It is quite clear that the orbitaleccentricity is a very importantfactor in setting the relative sizesof the circumstellar andcircumbinary disks.

e=0 e=0.2

e=0.4 e=0.8

Results

In the source IRS5 in L1551, there is a projectedseparation between the stars of 45 A.U. Thedetected circumstellar disks have roughly thesame size, 10 A.U., and there is no information onthe size of the circumbinary disk.

Assuming that the stellar masses are the same, andtaking their separation in the sky as the properscale length to scale our results, we conclude thatthe orbital eccentricity of the system must be less,or about equal, to 0.2

The case of L1551 IRS5

Results

We have also studied the case of α Centauri Aand B. This binary system has a G2V star (1.1 MO

) and a K1V star (0.9 MO), in an orbit whosesemimajor axis is 23.4 A.U. and with an orbitaleccentricity of 0.52Quintana et al. (2002) have made numericalsimulations of planet formation in this systemusing the “planetesimal” hypothesis. Due to itslarge eccentricity, this system is a challenge forplanet formation. These authors have onlyconsidered orbits within 2 A.U. of the primarystar.

The case of α Centauri A and B

Our results indicate that a protoplanetary disk is possible up to 3.5 A.U.

Conclusions

We have applied the concept of "loops" to find dynamicallystable regions where gas can settle, or planets can be formed,around each star of an eccentric binary system, or surroundingboth stars.

The size of the circumstellar disks, and that of the central holeof the circumbinary disk, depend strongly on the orbitaleccentricity, and to a much lesser degree, on the mass ratio ofthe stars.

In the case of the source IRS5 in L1551, we predict an orbitaleccentricity less than 0.2

Even in high eccentricity systems like α-Centauri A and B, planet formation is possible.

Pichardo et al. (2005) MNRAS 359, 521

new circumstellar and circumbinary disks in eccentric stellar binary...

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