Advanced Binary Evolution

Transcription

1 Massive Stars in Interacting Binaries ASP Conference Series, Vol. 367, 2007 N. St-Louis & A.F.J. Moffat Advanced Binary Evolution N. Langer & J. Petrovic Astronomical Institute, Utrecht University Abstract. We discuss recent progress in the modeling and understanding of the mass-transfer process in massive close binary systems and its consequences for their advanced evolution. We thenhighlight the spin evolution ofboth binary components and its dependence on accretion, mass loss and internal angularmomentum transport processes. In particular, we consider the influence of an internal magnetic field, which appears to be required on observational and theoretical grounds. We find that while magnetic fields lead to an agreement of predicted with observed rotation frequencies of white dwarfs and neutron stars, accretion does not always lead to rapidly spinning cores as they are required within the collapsar model for gamma-ray bursts. 1. Introduction The evolution of a star in a binary system can differ significantly from that of an isolated star with the same mass and chemical composition. The physical processes that enter binary evolution are the gravitational and radiation field from the companion, as well as the centrifugal force arising from the rotation of the system. But, most important, it is the evolution of the more massive component that will influence dramatically the evolution of the system. In certain evolutionary phases, mass transfer from one star toanothercanoccur, changing the fundamental properties of both stars as well as their future evolution. The rotational properties of binary components may play a key role in this respect. The evolution of massive single stars can be strongly influenced by rotation (e.g., Heger & Langer 2000; Meynet & Maeder 2000), and evolutionary models of rotating stars are now available for many masses and metallicities. While the treatment of the rotational processes in these models is not yet in a final stage (e.g., magnetic dynamo processes are just being included; Heger et al. 2004, Maeder & Meynet 2004), they provide first ideas of what rotation can really do to a star. Effects of rotation, as important as they are in single stars, can be much stronger in the components of close binary systems: Estimates of the angular momentum gain of the accreting star in mass transferring binaries show that critical rotation may be reached quickly (Packet 1981; Langer et al. 2000, Yoon & Langer 2004a). In order to investigate this, we need binary evolution models which include a detailed treatment of rotation in the stellar interior, as in recent single-star models. However, in binaries, tidal processes as well as angular momentum accretion need to be considered at the same time. Some first such models are now available and are discussed below. Angular momentum accretion and the subsequent rapid rotation of the mass gainer may be essential for some of the most exciting cosmic phenomena, which 359

2 360 Langer & Petrovic may occur exclusively in binaries: Type Ia supernovae, the main producers of iron and cosmic yardstick to measure the accelerated expansion of the universe (Yoon & Langer 2004a,b) and gamma-ray bursts from collapsars, which the most recent stellar models with rotation and magnetic fields preclude to occur in single stars (Heger et al ; Petrovic et al. 2005a). For both Type Ia supernova progenitors and gamma-ray burst progenitors, it is essential to understand how efficientthe mass-transfer process is and on which physical properties it depends. 2. Mass and Angular Momentum Transfer 2.1. How Much Mass Transfer? Dessart et al. (2003) investigated to what extent the radiation and stellar wind momenta in a massive close binary system can remove part of the matter flowing from one star towards the other star during a mass-transfer phase. They performed radiation-hydrodynamics simulations in the co-rotating frame of a binary system made-up of two main sequence stars of 27 M and 26 M in a 4 day orbit. They studied the interaction of the winds of both stars, and of their photons, with the accretion stream originating from the Roche-lobe filling component, adopting a mass transfer rate of M yr 1, a mid-point in the range of values during massive binary-star evolution. Dessart et al. found that even for such moderate transfer rates, the wind and radiative momenta cannot alter the dynamics of the accretion stream which follows essentially ballistic trajectories. By identifying the rather high density in the accretion stream as the main reason for this, a similar behavior can be expectedat largermass-transfer rates. Onlywhen the accretionstream densityis comparable to the density of the stellar wind close to the surface of the accreting star can one expect radiation and wind momenta to affect the stream How Much Accretion? While in the previous section it was argued that the mass-transfer process per se can be considered as very efficient in massive close binaries, we analyze here how much of the accreted matter can actually be retained by the accreting star. Binary evolution models have been constructed using the code of Wellstein et al. (2001), but including the physics of rotation as in the single-star models of Heger et al. (2000) for both components. In addition, spin-orbit coupling according to Zahn (1977) has been added, and rotationally enhanced winds are implemented as in Langer (1998). The specific angular momentum of the accreted matter is assumed to be that of Kepler rotation at the stellar equator in the case of disk accretion, and determined by integrating the equation of motion of a test particle in the Roche potential in case the accretion stream impacts directly on the secondary star (Wellstein 2001). The generation of magnetic fields and the angular momentum transport due to magnetic torques is included as described in Heger et al. (2005). The accretion induced spin-up can bring the secondary close to critical rotation and thus strong rotationally enhanced mass-loss sets in. The difference between the mass overflow rate Ṁ1 and the wind mass loss-rate of the secondary is what we consider as the net accretion rate Ṁ 2 of the secondary

3 Advanced Binary Evolution 361 Figure 1. For a 16M + 15M system with an initial orbital period of 3 days: mass transfer rate ( Ṁ1; solid line) and mass accretion rate of the secondary (Ṁ2; dotted line) as function of the total amount of mass which has already been transferred. Four discrete mass-transfer phases can be distinguished: rapid Case A ( Ṁ1 > 10 4 M yr 1, M 1 8.7M ), slow Case A ( M 1 > 10 7 M yr 1, M 1 0.8M ), Case AB ( Ṁ1 > 10 5 M yr 1, M 1 3.8M ), and Case ABB ( M 1 > 10 4 M yr 1, M 1 1.2M ). star. Fig. 1 shows that during much of the rapid Case A mass transfer in a 16 M + 15 M binary during which the accreting star increases its mass from 15 M to 23 M, it is Ṁ1 = Ṁ2. This is possible due to two factors: 1) During direct impact accretion, the specific angular momentum of the accreted material is only a fraction of the respective Keplerangular momentum. 2) As the secondary star fills a significant fraction of its Roche volume, tidal coupling removes part of the accreted angular momentum and feeds it into the orbit. As the orbit widens significantly during the later evolution, the specific angular momentum of the accreted matter increases and tidal forces weaken. Thus, while the accretion efficiency is close to 1 during Case A, it is less than 0.1

4 362 Langer & Petrovic Figure 2. Time averaged mass accretion efficiency β for various binaryevolution sequences (symbols) and different physical assumptions as a function of the initial orbital period for 16M + 15M systems. Triangles mark systems which have been calculated using rotational physics and the tidal model as proposed by Zahn (1977), which in systems marked by squares has been assumed to be one order of magnitude more efficient. Star symbols designate models by Wellstein et al. (2001) which have been computed without rotational physics and assumedto evolve conservatively unless a contact situation occurs. The dotted vertical line separates Case A systems (to the left) from Case B systems. later, resulting in a time average over the whole evolution of For systems which start out with awiderorbit, we find alow accretionefficiencythroughout (Fig. 2). For 16 M + 15 M systems, we find a critical initial period of 8 d beyond which the secondary accretes only little. These models imply that, despite the angular momentum problem for the accretion star (Packet 1981), quasi-conservative evolution of massive close binaries is possible. However, already in early Case B systems, the accretion efficiency may be strongly reduced compared to binary models without rotation. Petrovic et al. (2005b), in an attempt to reconstruct the evolutionary history of several Galactic Wolf-Rayet binaries, computed systems with initial primary masses in the range M, but for initial mass ratios as low as 0.5. The result was that, due to the very high achieved mass-transfer rates, the Case A evolution of these systems turns out to be very non-conservative, with time averaged mass-accretion efficiencies of β 0.1 (see Fig. 3 for an example). We conclude that only those close binaries can evolve quasi-conservatively which have a short initial orbital period and an initial mass ratio close to one.

5 Advanced Binary Evolution 363 Figure 3. Kippenhahn-diagram for the accreting component of a 56M + 33M binary system with an initial period of 6 days. Fast Case A, slow Case A, and Case AB mass transfer can be distinguished. Various types of internal mixing processes (convection, semi-convection and thermohaline mixing as indicated, rationally induced mixing as dark shading), and nuclear burning (as indicated) are shown. 3. Spins of Compact Objects It appears as if most stars above 2 M start out with a specific angular momentum of about j cm 2 s 1 (implying a core value of about j cm 2 s 1 ) and end at j cm 2 s 1 independently of whether they become white dwarfs or neutron stars (cf. Table 1). A specific angular momentum of cm 2 s 1 is (logarithmically) about half way between local angular momentum conservation and completely rigid rotation. The recently obtained rotating evolutionary models (Table 2) produce typically stellar remnants which rotate one to two orders of magnitude faster. The inclusion of rotationally enhanced magnetic fields in the evolution of massive single stars (Heger et al., 2004, 2005; Petrovic et al. 2005a) has improved the agreement between observed ( ms) and predicted ( > 5 ms) spin periods of young neutron stars. Recent models of a rotating 3 M star including the magnetic torques (Suijs et al. 2005) has brought a similar result for intermediate mass stars: the magnetic fields result in white dwarf rotation rates which do not violate observational constraints.

6 364 Langer & Petrovic Table 1. Orderofmagnitudeofthespecificangular momentum, andofthe spin periodor rotational velocity insingle stars ofintermediate orhigh mass, young pulsars (cf. Heger et al. 2004), and white dwarfs (cf. Kawaler 2004), compared to accreting white dwarfs (Starrfield et al. 2004) and millisecond pulsars. object j/cm 2 s 1 P or v rot single stars in v rot 200 kms 1 young pulsars P = ms isol. WDs < v rot < 20 kms 1 accr. WDs (CVs) kms 1 MSP Table 2. Final core specific angular momenta of recent single-star evolution models, with (B 0) and without (B = 0) considering angular-momentum transport due to internal magnetic fields. single stars: B = 0 3 M j WD cm 2 s 1 Langer et al. (1999) M j NS cm 2 s 1 Heger et al. (2000) Hirschi et al. (2004) 40 M j BH cm 2 s 1 Hirschi et al. (2004) Petrovic et al. (2005a) single stars: B 0 3 M j WD cm 2 s 1 Suijs et al. (2005) M j NS cm 2 s 1 Heger et al. (2004) Heger et al. (2005) 40 M j BH < cm 2 s 1 Petrovic et al. (2005a) While these lines of evidence support the idea of considering the angular momentum transport due to magnetic torques in the evolution of stars, it has the consequence that obtaining gamma-ray bursts from black-hole formation in single stars (collapsars; Woosley & Heger 2004) seems difficult at present. In order to hit the centrifugal barrier during the collapse, a massive iron core needs to have a specific angular momentum in excess of cm 2 s 1. Also the initially more massive stars in massive close binaries are unlikely to produce a gamma-ray burst. First of all, they lose so much mass that even stars with a very large initial mass may not even form a black hole but rather a neutron star (see also Wellstein & Langer 1999). And secondly, these stars are drastically spun down as a consequence of their heavy mass loss. The 16 M star in the computed binary system is expected to produce a neutron star with an initial spin period of more than one second! The only way to avoid both drawbacks is to employ Case C evolution, which leads to a core evolution as in single stars. However, even then the CO-core of the star needs to be spun-up significantly to produce a collapsar and a gammaray burst a possibility suggested by Brown et al. (1999, 2001) in the context ofcommon-envelope evolutionand spiral-in. No detailedmodels for this scenario exist at present.

7 Advanced Binary Evolution 365 Figure 4. Internal specific angular momentum profiles of a star of initially 33M which accretes matter from a star of initially 55M (cf. Fig. 3). The initially less-massive star in a massive binary, on the other hand, accretes large amounts of angular momentum and may thus acquire a larger core spin than a corresponding single star. The effects of magnetic torques might help to transport part of the accreted angular momentum into the stellar core. In an attempt to explore this possibility, Petrovic et al. (2005a) computed massive binary systems including magnetic fields. Fig. 4 shows the evolution of the internal specific angular momentum profiles of the accreting component of a 55 M +33 M system with an initial orbital period of 6 days. It can be seen that the accretion of 4.5 M during the fast Case A mass transfer indeed enhances the core specific angular momentum much above the initial level. However, during the later evolution the magnetic torques lead to a much stronger decrease of the core specific angular momentum, as shown in Fig.4 and as concluded from a non-magnetic comparison model (Petrovic et al. 2005a). We conclude that, within the collapsar model, GRBs at near solar metallicity either need to be produced in rather exotic binary channels, or the magnetic effects in our models are currently overestimated. The first is not implausible, since reverse mass transfer from the original secondary star onto the primary star duringits Wolf-Rayet phase (cf. Wellsteinetal. 2001), orlate stellarmerger may leadto an efficientcore spin-up. However, the realizationfrequencyof such events, even though it is difficult to estimate, may be small. The latter would require a significant angular-momentum loss of iron cores which form neutron

8 366 Langer & Petrovic stars, either during collapse and supernova explosion, or shortly thereafter, in order to explain the relatively slow rotation rates of young pulsars, and would require an additional, so far unknown, mechanism to slow down the cores of intermediate mass white dwarf progenitors. References Brown, G.E., Lee, C.-H., Bethe, H.A. 1999, New Astron., 4, 313 Brown, G.E., Heger, A., Langer, N., Lee, C.-H., Wellstein, S., Bethe, H.A. 2001, New Astron., 6, 457 Dessart, L., Petrovic, J., Langer, N. 2003, A&A, 404, 991 Heger, A., Langer, N. 2000, ApJ, 544, 1016 Heger, A., Langer, N., Woosley, S.E. 2000, ApJ, 528, 368 Heger, A., Woosley, S.E., Langer, N., Spruit, H.C. 2004, in: Stellar Rotation, Proc. IAU-Symp. 215, A. Maeder & P. Eenens, eds, p. 591 Heger, A., Woosley, S.E., Spruit, H.C. 2005, ApJ, 626, 350 Hirschi, R., Meynet, G., Maeder, A. 2004, A&A, 425, 649 Kawaler, S., 2004, in: Stellar Rotation, Proc. IAU-Symp. 215, A. Maeder & P. Eenens, eds, p.561 Langer, N. 1998, A&A, 329, 551 Langer, N., Heger, A., Wellstein, S., Herwig, F. 1999, A&A, 346, L37 Langer, N., Deutschmann, A., Wellstein, S., Höflich, P. 2000, A&A, 362, 1046 Maeder, A., Meynet, G. 2004, A&A, 422, 225 Meynet, G., Maeder, A. 2000, A&A, 361, 101 Packet, W. 1981, A&A, 102, 17 Petrovic, J., Langer, N., Yoon, S.-C., Heger, A. 2005a, A&A, 435, 247 Petrovic, J., Langer, N., van der Hucht, K. 2005b, A&A, 435, 1013 Starrfield, S., Sion, E.M., Szkody, P. 2004, in: Stellar Rotation, Proc. IAU-Symp. 215, A. Maeder & P. Eenens, eds, p. 551 Suijs, M. et al. 2005, in preparation Wellstein, S. 2001, PhD thesis, Potsdam University Wellstein, S., Langer, N. 1999, A&A, 350, 148 Wellstein, S., Langer, N., Braun, H. 2001, A&A, 369, 939 Woosely, S.E., Heger, A. 2004, in: Stellar Rotation, Proc. IAU-Symp. 215, A. Maeder & P. Eenens, eds, p. 601 Yoon, S.-C., Langer, N. 2004a, A&A, 419, 623 Yoon, S.-C., Langer, N. 2004b, A&A, 419, 645 Zahn, J.-P. 1977, A&A, 57, 383

9 Advanced Binary Evolution 367 Discussion Gloria Koenigsberger: If I understand correctly, you start out with a weak magnetic field in a differentially rotating star, and after some time, the star no longer rotates differentially because of the magnetic torques. It is rotating as a rigid body. Is this correct? Norbert Langer: There are two things to clarify this. We do not calculate the growth of the magnetic field, the winding-up, because that occurs so fast that we cannot actually resolve it in time. But we assume that the magnetic field is always in equilibrium between continued formation and continued destruction by the instabilities. So we assume there is an equilibrium present. The second thing is, this magnetic fields leads the star close to rigid rotation on the main sequence. However, it s not strictly rigid rotation. And in the post main sequence phases, it s very far from rigid rotation. Gloria Koenigsberger: But what is the timescale for the diffusion of the magnetic field? Is it long enough that you will retain this magnetic field once it reaches the post main-sequence stage? Norbert Langer: Well, the idea is that, whenever you have a little seed field, very quickly you would reach this equilibrium field strength which Hank Spruit calculates for us, because the timescale for differential rotation is very, very short. Ken Gayley: I noticed in your binary model where you had the mass coming across, that you had a big jump in the rotational speed at the surface and then it very quickly spikes downward. What is causing that rapid drop? Norbert Langer: Well, we have a very rapidly rotating star, i.e. close to break-up. And what we assume is, as I said, that there is something like an Ω limit, so the mass-loss rate from the star goes up very strongly when it reaches critical rotation. Ken Gayley: But is that a spherically symmetric mass-loss rate or is it bipolar? Norbert Langer: It is a 1D calculation so I think that in reality it wouldn t be spherically symmetric. But of course in our models we peel off layers from the outside in. Ken Gayley: I m just pointing out that a bipolar mass-loss rate might spin the star up rather than down. Norbert Langer: Well I know, of course, all the discussion about that. But I have strong doubts because if one has mass loss occurring just from the poles, then what happens to the material at the equator? It has to fall into the potential which is created by the hole at the pole but it cannot because it has too high specific angular momentum. So there must be strong currents inside the star which redistribute angular momentum and all this is not taken into account

10 368 Langer & Petrovic by anybody. And so we are, I think, very far from understanding what happens if we have a very non-isotropic mass loss. Sergey Marchenko: What happens if the star exceeds the break- up velocity? It will change the orbital parameters. Norbert Langer: The definition in our models is that it cannot exceed the break-up velocity because the mass-loss rate tends to go to infinity as break-up is approached. Sergey Marchenko: Yes but it will dramatically change the orbital parameters of the system itself. Norbert Langer: Well, the orbital parameters depend more on the total amount of mass lost than on the mass-loss rate. And, if the mass-loss rate is very high only for a short time, then it just matters how much mass is lost in this phase. What we do consider then, of course, is that the material which leaves the system is carrying the specific angular momentum of the orbit of the star. And so, I forgot perhaps to point out that the angular momentum lost is also self-consistently considered with such a model, so there is no free parameter, such as that called α in the binary community, which describes the angular-momentum loss from the system. Sergey Marchenko: Can it explain the knot-like structures seen in the jets in some systems? Norbert Langer: I think we are a bit far from that. We wish we could be predicting these nice things. In reality, it may be that things go through jets, especially if magnetic fields are involved, but we are not going into that level of detail yet. Karel van der Hucht: I was struck by your suggestion that perhaps WN8 stars could be progenitors of gamma-ray bursts. I think the problem with WN8 stars is that they have relatively low wind terminal-velocities of 1000 km/s and that the long-duration gamma-ray burst afterglows require a high wind-velocity Wolf-Rayet progenitor. WO stars do have terminal velocities up to 5000 km/s. Norbert Langer: First of all, I think the low wind-velocities could support this idea because it may mean that the effective escape velocity from the surface of the star is small. The WN stars won t explode tomorrow and what we see connected to the gamma-ray bursts are WC stars. So we still peel off material which may expose layers which are further processed. And during this process we know that at least the envelope of the star must spin down. And so you might then have higher wind velocities as well. But the question, of course, which is very much still open, is whether the core in this situation might maintain enough rotation. Anyway, this idea is just out of the spur of the moment. I m picking it up and maybe we can discuss it further.

11 Advanced Binary Evolution 369 George Sonneborn: I was wondering about the efficiency of mixing of the transferred material in the envelope of the mass-gaining star, and if you ve looked at the history of the metallicity in the surface. Norbert Langer: Well, you ve seen in one of my plots that typically we would get salt-finger instabilities, which would mix the material, at least on rather short timescales throughout the envelope of the star. This is even aided perhaps by differential rotation or mixing processes associated with it. So the mixing time-scales are of the order of years or so. Norbert Langer