arXiv subjects

G. J. Savonije

Publications and source records attributed to G. J. Savonije.

17 recordsLinked to original sources

arXiv2025

The tidal interaction of an orbiting giant planet with a star near the Kraft break: the excitation of $r$-modes and the retention of orbital and spin angular momenta misalignment

In this paper we extend the previous work of Papaloizou \& Savonije on tidal interactions between a solar mass star and a closely orbiting giant planet which is such that the orbital and stellar spin angular momentum directions are misaligned. Here we consider the situation when the central star has a mass of $1.3 M_{\odot}$ and is in the vicinity of the Kraft break. We find and determine the properties of the lowest order $r$ modes and the tidal response arising from the secular non axisymmetric forcing associated with a misaligned orbit. We find that the response of the thin convective envelope, as well as the shift of $r$ mode frequencies from the low rotation frequency, limit can be understood by adopting a vertically averaged model that is similar to the well known one governed by the Laplace tidal equation for an incompressible ocean. From our results we are able to estimate lower bounds on realignment time scales for hot Jupiter systems with orbital periods in the range $2.8-5 d$ and rotation periods in the range $5-31 d$ that indicate the process is indeed markedly less effective than for a solar type star. This is on account of there being less dissipation in a relatively smaller convective envelope as well as the generally faster rotation and hence larger spin angular momentum expected for the more massive star.

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arXiv2023

The tidal excitation of r modes in a solar type star orbited by a giant planet companion and the effect on orbital evolution II: The effect of tides in the misaligned case

We extend the study of Papaloizou & Savonije of the tidal interactions of close orbiting giant planets with a central solar type star to the situation where the spin axis of the central star and the orbital angular momentum are misaligned. We determine the tidal response taking into account the possibility of the excitation of r modes and the effect of tidal forcing due to potential perturbations which have zero frequency in a non rotating frame. Although there is near resonance with r modes with degree l' = 1 and orders m = 1 or -1 , half widths turn out to be sufficiently narrow so that in practice dissipation rates are found to be similar to those produced by non resonant potential perturbations. We use our results to determine the evolution of the misalignment for the full range of initial inclination angles taking account of the spin down of the central star due to magnetic braking. Overall we find the rate of tidal evolution to be unimportant for a one Jupiter mass planet with orbital period of about 3.7d over a main sequence lifetime. However, it becomes significant for higher mass planets and shorter orbital periods, approximately scaling as the square of the planet mass and the inverse fourth power of the orbital period.

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arXiv2023

The tidal excitation of r modes in a solar type star orbited by a giant planet companion and the effect on orbital evolution I: The aligned case

It has been suggested that tidal interaction is important for shaping the orbital configurations of close orbiting giant planets. The excitation of propagating waves and normal modes (dynamical tide) will be important for estimating time scales for orbital evolution. We consider the tidal interaction of a Jupiter mass planet orbiting a solar type primary. Tidal and rotational frequencies are assumed comparable making the effect of rotation important. Although centrifugal distortion is neglected, Coriolis forces are fully taken into account. We focus in detail on the potentially resonant excitation of $r$ modes associated with spherical harmonics of degrees three and five. These are mostly sited in the radiative core but with a significant response in the convective envelope where dissipation occurs. Away from resonance significant orbital evolution over the system lifetime is unlikely. However, tidal interaction is enhanced near resonances and the orbital evolution accelerated as they are passed through. This speed up may be sustained if near resonance can be maintained. For close orbits with primaries rotating sufficiently rapidly, this could arise from angular momentum loss and stellar spin down through a stellar wind bringing about significant orbital evolution over the system lifetime.

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arXiv2013

Visibility of unstable oscillation modes in a rapidly rotating B star

Space missions like CoRoT and Kepler have provided numerous new observations of stellar oscillations in a multitude of stars by high precision photometry. This work compares the observed rich oscillation spectrum of the rapidly rotating B3 IV star HD 43317 with the first results obtained by a new method to calculate unstable oscillation modes in rapidly rotating stars in order to see whether some of the observed modes can be identified. The new numerical method consists of two parts. We first search for modes resonant with a prescribed forcing symmetry by moving through relevant regions of complex frequency space and monitoring any increase of the stellar response to the applied forcing and zooming in onto the resonance. These resonant non-adiabatic 2D-solutions are then fed into a 2D relaxation code with the same equations but without forcing terms. The complex oscillation frequency used in the forcing is now no longer prescribed, but added as an extra unknown. The corresponding free oscillation mode is usually obtained after a few ($<10$) iterations with only minor adjustment of the complex oscillation frequency. To compare with the observed light variations we calculate the `visibility' of the found unstable oscillation modes, taking into account the cancellation of the various parts of the radiating oscillating stellar surface as seen by the observer. The frequencies of unstable axisymmetric g-modes, which have the highest visibility, appear to nearly coincide with the observed largest amplitude photometric variations of HD 43317, making an identification of the latter oscillations as $m$=0 modes plausible. The identification of $m$=1 g-modes is less straightforward, while many of the unstable even $m$=2 g-modes may correspond to observed weaker photometric variations.

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arXiv2007

Non-radial oscillations of the rapidly rotating Be star HD 163868

We study the pulsational stability of the rapidly rotating Be star HD 163868 using a newly developed 2D oscillation code which takes the Coriolis force fully into account and compare our results with observations (MOST) and recent other stability analyses of this ~ 6 Msun star. We find both prograde and retrograde overstable modes (although more prograde than retrograde modes) and confirm the existence of low degree odd r-modes destabilised by the kappa-mechanism. The ultra-low frequency modes that could not be explained in a previous analysis are interpreted as high degree, retrograde m=1 modes. A reasonably good fit to the observed oscillation spectrum is possible if we assume that only even modes are observed. This requires a nearly equator-on view of the observed star, consistent with the measured high v sin i value of 250 km/s.

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arXiv2006

One-armed oscillations in Be star discs

In this paper we study the effect of the quadrupole-term in the gravitational potential of a rotationally deformed central Be star on one armed density waves in the circumstellar disc. The aim is to explain the observed long-term violet over red (V/R) intensity variations of the double peaked Balmer emission-lines, not only in cool Be star systems, but also in the hot systems like gamma Cas. We have carried out semi-analytic and numerical studies of low-frequency one armed global oscillations in near Keplerian discs around Be stars. In these we have investigated surface density profiles for the circumstellar disc which have inner narrow low surface density or gap regions, just interior to global maxima close to the rapidly rotating star, as well as the mode inner boundary conditions. Our results indicate that it is not necessary to invoke extra forces such as caused by line absorption from the stellar flux in order to explain the long-term V/R variations in the discs around massive Be stars. When there exists a narrow gap between the star and its circumstellar disc, with the result that the radial velocity perturbation is non-zero at the inner disc boundary, we find oscillation (and V/R) periods in the observed range for plausible magnitudes for the rotational quadrupole term.

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arXiv2005

Unstable quasi g-modes in rotating main-sequence stars

This paper studies the oscillatory stability of uniformly rotating main-sequence stars of mass 3-8 M_sun by solving the linearized non-adiabatic, non-radial oscillation equations with a forcing term and searching for resonant response to a complex forcing frequency. By using the traditional approximation the solution of the forced oscillation equations becomes separable, whereby the energy equation is made separable by approximation. It is found that the kappa-mechanism in rotating B-stars can destabilize not only gravity- or pressure modes, but also a branch of low frequency retrograde (in corotating frame) oscillations in between the retrograde g-modes and toroidal r-modes. These unstable quasi g-modes (or `q-modes') hardly exhibit rotational confinement to the equatorial regions of the star, while the oscillations are always prograde in the observer's frame, all in contrast to g-modes. The unstable q-modes occur in a few narrow period bands (defined by their azimuthal index m), and seem to fit the oscillation spectra observed in SPB stars rather well. The unstable q-mode oscillation spectrum of a very rapidly rotating 8 M_sun star appears similar to that of the well studied Be-star mu Cen. The unstable q-modes thus seem far better in explaining the observed oscillation spectra in SPB-stars and Be-stars than normal g-modes.

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arXiv2002

Tidal interaction of a rotating 1 Msun star with a binary companion

We calculate the tidal torque on a uniformly rotating 1 Msun star at various stages of core hydrogen burning by an orbiting companion. We apply the `traditional approximation' and solve the radial part of the tidal perturbations by matrix inversion of the set of finite difference equations on a very fine grid. We have identified resonances with gravity- and quasi-toroidal modes with up to 1000 radial nodes in the more evolved stellar models. For low forcing frequencies we find significant tidal response due to viscous damping of inertial modes in the convective envelope of the solar-type star. We conclude that effects due to stellar rotation (including resonance locking) may considerably enhance the speed of tidal evolution in solar-type stars.

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arXiv2002

The evolution of naked helium stars with a neutron-star companion in close binary systems

The evolution of helium stars with masses of 1.5 - 6.7 M_sun in binary systems with a 1.4 M_sun neutron-star companion is presented. Such systems are assumed to be the remnants of Be/X-ray binaries with B-star masses in the range of 8 - 20 M_sun which underwent a case B or case C mass transfer and survived the common-envelope and spiral-in process. The orbital period is chosen such that the helium star fills its Roche lobe before the ignition of carbon in the centre. We distinguish case BA (in which mass transfer is initiated during helium core burning) from case BB (onset of Roche-lobe overflow occurs after helium core burning is terminated, but before the ignition of carbon). We found that the remnants of case BA mass transfer from 1.5 - 2.9 M_sun helium stars are heavy CO white dwarfs. This implies that a star initially as massive as 12 M_sun is able to become a white dwarf. CO white dwarfs are also produced from case BB mass transfer from 1.5 - 1.8 M_sun helium stars, while ONe white dwarfs are formed from 2.1 - 2.5 M_sun helium stars. Case BB mass transfer from more-massive helium stars with a neutron-star companion will produce a double neutron-star binary. We are able to distinguish the progenitors of type Ib supernovae (as the high-mass helium stars or systems in wide orbits) from those of type Ic supernovae (as the lower-mass helium stars or systems in close orbits). Finally, we derive a "zone of avoidance" in the helium star mass vs. initial orbital period diagram for producing neutron stars from helium stars.

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arXiv2001

The origin of the runaway high-mass X-ray binary HD153919/4U1700-37

Based on its Hipparcos proper motion, we propose that the high-mass X-ray binary HD153919/4U1700-37 originates in the OB association Sco OB1. At a distance of 1.9 kpc the space velocity of 4U1700-37 with respect to Sco OB1 is 75 km/s. This runaway velocity indicates that the progenitor of the compact X-ray source lost about 7 Msun during the (assumed symmetric) supernova explosion. The system's kinematical age is about 2 +/- 0.5 million years which marks the date of the supernova explosion forming the compact object. The present age of Sco OB1 is <8 Myr; its suggested core, NGC 6231, seems to be somewhat younger (~5 Myr). If HD153919/4U1700-37 was born as a member of Sco OB1, this implies that the initially most massive star in the system terminated its evolution within <6 million years, corresponding to an initial mass >30 Msun. With these parameters the evolution of the binary system can be constrained.

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arXiv2000

Spin-Orbit Couplings in X-ray Binaries

We discuss the influence of tidal spin-orbit interactions on the orbital dynamics of close intermediate-mass X-ray binaries. In particular we consider here a process in which spin angular momentum of a contracting RLO donor star, in a synchronous orbit, is converted into orbital angular momentum and thus helps to stabilize the mass transfer by widening the orbit. Binaries which would otherwise suffer from dynamically unstable mass transfer (leading to the formation of a common envelope and spiral-in evolution) are thus shown to survive a phase of extreme mass transfer on a sub-thermal timescale. Furthermore, we discuss the orbital evolution prior to RLO in X-ray binaries with low-mass donors, caused by the competing effects of wind mass loss and tidal effects due to expansion of the (sub)giant.

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arXiv2000

Formation of Millisecond Pulsars with Heavy White Dwarf Companions - Extreme Mass Transfer on Sub-Thermal Timescales

We have performed detailed numerical calculations of the non-conservative evolution of close X-ray binary systems with intermediate-mass (2.0-6.0 M_sun) donor stars and a 1.3 M_sun accreting neutron star. We calculated the thermal response of the donor star to mass loss, in order to determine its stability and follow the evolution of the mass transfer. Under the assumption of the "isotropic re-emission model" we demonstrate that in many cases it is possible for the binary to prevent a spiral-in and survive a highly super-Eddington mass-transfer phase (1 << M_dot/M_Edd < 10^5) on a sub-thermal timescale, if the convective envelope of the donor star is not too deep. These systems thus provide a new formation channel for binary millisecond pulsars with heavy CO white dwarfs and relatively short orbital periods (3-50 days). However, we conclude that to produce a binary pulsar with a O-Ne-Mg white dwarf or P_orb ~1 day (e.g. PSR B0655+64) the above scenario does not work, and a spiral-in phase is still considered the most plausible scenario for the formation of such a system.

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arXiv1999

Formation of millisecond pulsars. I. Evolution of low-mass X-ray binaries with P > 2 days

We have performed detailed numerical calculations of the non-conservative evolution of close binary systems with low-mass (1.0-2.0 M_sun) donor stars and a 1.3 M_sun accreting neutron star. Rather than using analytical expressions for simple polytropes, we calculated the thermal response of the donor star to mass loss, in order to determine the stability and follow the evolution of the mass transfer. Tidal spin-orbit interactions and Reimers wind mass-loss were also taken into account. We have re-calculated the correlation between orbital period and white dwarf mass in wide binary radio pulsar systems. Furthermore, we find an anti-correlation between orbital period and neutron star mass under the assumption of the "isotropic re-emission" model and compare this result with observations. We conclude that the accretion efficiency of neutron stars is rather low and that they eject a substantial fraction of the transferred material even when accreting at a sub-Eddington level. The mass-transfer rate is a strongly increasing function of initial orbital period and donor star mass. For relatively close systems with light donors (P < 10 days and M_2 < 1.3 M_sun) the mass-transfer rate is sub-Eddington, whereas it can be highly super-Eddington by a factor of 10^4 for wide systems with relatively heavy donor stars (1.6 - 2.0 M_sun) as a result of their deep convective envelopes. We briefly discuss the evolution of X-ray binaries with donor stars in excess of 2 M_sun. Based on our calculations we present evidence that PSR J1603-7202 evolved through a phase with unstable mass transfer from a relatively heavy donor star and therefore is likely to host a CO white dwarf companion.

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arXiv1999

Tidal evolution of eccentric orbits in massive binary systems; a study of resonance locking

We study the tidal evolution of a binary system consisting of a 1.4 Msun compact object in elliptic orbit about a 10 Msun uniformly rotating main sequence star for various values of the initial orbital parameters. We apply our previously published results of 2D non-adiabatic calculations of the non-radial g- and r-mode oscillations of the uniformly rotating MS star, and include the effects of resonant excitation of these modes in the tidal evolution calculations. A high orbital eccentricity enhances the effectiveness of the tidal interaction because of the large number of harmonic components of the tidal potential and the reduced orbital separation near periastron. By including the evolution of the MS star, especially of its rotation rate, many resonance crossings occur with enhanced tidal interaction. We analyse the phenomenon of resonance locking whereby a particular tidal harmonic is kept resonant with a stellar oscillation mode. Resonance locking of prograde g-modes appears an effective mechanism for orbital circularization of eccentric orbits. We consider the orbital evolution of the binary pulsar PSR J0045-7319 and conclude that resonance locking could explain the observed short orbital decay time of this system if the B-star spins in the direction counter to the orbital motion.

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arXiv1998

The dynamical tide in a rotating 10 Msun main sequence star

We study the linear, but fully non-adiabatic tidal response of a uniformly rotating, somewhat evolved X_c=0.4, 10 Msun main sequence star to the dominant l=2 components of its binary companion's tidal potential. This is done numerically with a 2D implicit finite difference scheme. We assume the spin vector of the 10 Msun star to be aligned perpendicular to the orbital plane and calculate the frequency and width of the resonances with the prograde and retrograde gravity (g) modes as well as the resonances with quasi-toroidal rotational (r) modes for varying rotation rates of the main sequence star. For all applied forcing frequencies we determine the rate of tidal energy and angular momentum exchange with the companion. In a rotating star tidal energy is transferred from l=2 g-modes to g-modes of higher spherical degree (l=4,6,8,...) by the Coriolis force. These latter modes have shorter wavelength and are damped more heavily, so that the l=2 resonant tidal interaction tends to be reduced for large stellar rotation rates. On the other hand, the density of potential resonances (a broad l spectrum) increases. We find several inertially excited unstable l>4 g-modes, but not more than one (retrograde) unstable l=2 g-mode and that only for rapid rotation. Our numerical results can be applied to study the tidal evolution of eccentric binaries containing early type B-star components.

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arXiv1997

Non-adiabatic tidal forcing of a massive, uniformly rotating star II: The low frequency, inertial regime

We study the fully non-adiabatic tidal response of a uniformly rotating unevolved 20 Msun star to the dominant l=m=2 component of the companion's perturbing potential. This is done numerically with a 2D implicit finite difference scheme. We assume the star is rotating slowly, so that the centrifugal force can be neglected, but the Coriolis force is taken fully into account. We study the low frequency `inertial' regime where the tidal oscillation frequency in the frame corotating with the star is less than twice the stellar spin rate. In this frequency range inertial modes are excited in the convective core which can interact with rotationally modified g- or r-modes in the radiative envelope and cause significant strengthening of the tidal interaction. Resonant interaction with quasi-toroidal (r-)modes in slightly super-synchronous stars causes efficient spin down towards corotation.

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arXiv1997

Non-adiabatic tidal forcing of a massive, uniformly rotating star III: Asymptotic treatment for low frequencies in the inertial regime

We describe a generalization of the asymptotic calculation of the tidal torques experienced by a massive star as a result of a companion in circular orbit originally considered by Zahn (1975,1977) to the case of a rotating star when the forcing frequency is small and in the inertial regime, that is it is less than twice the rotation frequency in magnitude. The results confirm the presence of a strong toroidal mode resonance feature for retrograde forcing and also, with a simple description of the convective core, the presence of some core inertial mode features in the response. These were found numerically by Savonije and Papaloizou (astro-ph/9706186).

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