A magnetic mechanism for halting inward protoplanet migration: I. Necessary conditions and angular momentum transfer timescales

A magnetic torque associated with the magnetic field linking a giant, gaseous protoplanet to its host pre-main-sequence star can halt inward protoplanet migration. This torque results from a toroidal magnetic field generated from the star’s poloidal (dipole) field by the twisting differential motion between the star’s rotation and the protoplanet’s revolution. Outside the corotation radius, where a protoplanet orbits slower than its host star spins, this torque transfers angular momentum from the star to the protoplanet, halting inward migration. Necessary conditions for angular momentum transfer include the requirement that the Alfvén speed v _A in the region magnetically linking a protoplanet to its host star exceeds the protoplanet’s orbital speed v _K . In addition, the timescale for Ohmic dissipation τ _D must exceed the protoplanet’s orbital period P to ensure that the protoplanet is magnetically coupled to its host star. For a Jupiter-mass protoplanet orbiting a solar-mass pre-main-sequence star, v _A >v _K and τ _D >P only when the migrating protoplanet approaches within about 0.1 AU of its host star, primarily because of the rapid drop in the strength of the magnetic field with increasing distance from the central star. Because of this restricted reach, inwardly migrating gaseous protoplanets can be expected to “pile up” very close to their central stars, as is indeed observed for extrasolar planets. The characteristic timescale required for a magnetic torque to transfer angular momentum outward from a more rapidly spinning central star to a magnetically coupled protoplanet is found to be comparable to planet-forming disk lifetimes and protoplanet migration timescales.     

Complex structure of the magnetic field of the CP star HD32633

The method of “virtual magnetic charges” is used to analyze the structure of the magnetic field of the CP star HD32633. The phase relation of its magnetic field differs strongly from a sine wave. The structure of the star’s field can be described fairly well by two dipoles located in the opposite regions of the star near its rotation equator. Each of these dipoles produces two pairs of magnetic spots of opposite polarity similar to sunspots. The dipoles are located at a distance of Δa=0.6 R from the center, where R is the radius of the star. The field strength at the poles is equal to ±42 and ±19 kG.     

Modeling of the magnetosphere of Mercury at the time of the first MESSENGER flyby

The MESSENGER spacecraft flyby of Mercury on 14 January 2008 provided a new opportunity to study the intrinsic magnetic field of the innermost planet and its interaction with the solar wind. The model presented in this paper is based on the solution of the three-dimensional, bi-fluid equations for solar wind protons and electrons in the absence of mass loading. In this study we provide new estimates of Mercury’s intrinsic magnetic field and the solar wind conditions that prevailed at the time of the flyby. We show that the location of the boundary layers and the strength of the magnetic field along the spacecraft trajectory can be reproduced with a solar wind ram pressure P_sw = 6.8 nPa and a planetary magnetic dipole having a magnitude of 210 R_M³ − nT and an offset of 0.18 R_M to the north of the equator, where R_M is Mercury’s radius. Analysis of the plasma flow reveals the existence of a stable drift belt around the planet; such a belt can account for the locations of diamagnetic decreases observed by the MESSENGER Magnetometer. Moreover, we determine that the ion impact rate at the northern cusp was four times higher than at the southern cusp, a result that provides a possible explanation for the observed north-south asymmetry in exospheric sodium in the neutral tail.     

The influence of non-uniform solar wind expansion on the angular momentum loss from the Sun

The influence on the rate of angular momentum loss from the Sun of magnetic geometries which are not spherically symmetric is estimated. Departures from spherical symmetry are expected to influence significantly the loss rate by two effects - the presence of closed magnetic field regions with no loss and also the variability in the radial distance to the Alfvénic point, as stressed by Mestel (1968).The loss rate is calculated for an MHD solar wind model with a solar magnetic field whose normal component at the surface is that of a north-south dipole. In contrast to Mestel's work, where the field was assumed dipolar within a certain surface and radial outside, the coupling between the solar wind and magnetic field is here taken into account exactly. For equivalent boundary conditions at the surface, the resulting field configuration yields an angular momentum loss rate which is only 15% of that for the monopole field normally used in angular momentum loss estimates. If, instead of equating boundary conditions at the Sun, one equates the two losses at the equator to that observed at 1 AU by spacecraft, then the ratio of the total loss for the distended dipole to that for the monopole is about 40%.On Leave from the Department of Applied Mathematics, The University, St. Andrews, Scotland.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

Analytical theory of tachocline transport at mid latitudes

We provide a theory of magnetic diffusion, momentum transport, and mixing in the solar tachocline by considering magnetohydrodynamics (MHD) turbulence on a β plane subject to a large scale shear (provided by the latitudinal differential rotation). In the strong magnetic field regime, we find that the turbulent viscosity and diffusivity are reduced by magnetic fields only, similarly to the two-dimensional MHD case (without Rossby waves). In the weak magnetic field regime, we find a crossover scale (L_R) from a Alfvén dominated regime (on small scales) to a Rossby dominated regime (on large scales). For parameter values typical of the tachocline, L_R is larger than the solar radius so that Rossby waves are unlikely to play an important role in the transport of magnetic field and angular momentum. This is mainly due to the enhancement of magnetic back-reaction by shearing which efficiently generates small scales, thus strong currents. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Energy release on the surface of a rapidly rotating neutron star during disk accretion: A thermodynamic approach

The total energy E of a star as a function of its angular momentum J and mass M in the Newtonian theory, E=E(J, M) [in general relativity, the gravitational mass of a star as a function of its angular momentum J and rest mass m, M=M(J, m)], is used to determine the remaining parameters (angular velocity, chemical potential, etc.) in the case of rigid rotation. Expressions are derived for the energy release during accretion onto a cool (with constant entropy), rapidly rotating neutron star (NS) in the Newtonian theory and in general relativity. A separate analysis is performed for the cases where the NS equatorial radius is larger and smaller than the radius of the marginally stable orbit in the disk plane. An approximate formula is proposed for the NS equatorial radius for an arbitrary equation of state, which matches the exact equation of state at J=0.     

Self-excitation of motions in near-convection zones and the generation of solar magnetic field

In view of the recently discovered time variations in rotation velocity within the solar differentially rotating tachocline (Howe et al. 2000), we study conditions for the equilibrium and excitation of motions in nonrigidly rotating magnetized layers of the radiative zones located near the boundaries of the convection zone. The emphasis is on the possible relationship between quasi-periodic tachocline pulsations and the generation of a nonaxisymmetric magnetic field in the convection zone. This field generation is studied under the assumption that it results from a reduction in the expenditure of energy on convective heat transport. The (antisymmetric about the equator) field is shown to increase in strength if there are both a radial gradient in angular velocity and steady-state axisymmetric meridional circulation of matter. The sense of circulation is assumed to change (causing the sign of the generated field to change) after the maximum permissible field strength is reached. This is apparently attributable to the excitation of the corresponding turbulent viscosity of the medium. It is also important that the cyclic field variations under discussion are accompanied by variations in solar-type dipole magnetic field.     

Magnetic field measurement of the star HD 35298

Based on the spectropolarimetric data obtained at the 6-m telescope, a study of the magnetic field and physical parameters of the magnetic He-weak star HD 35298 was performed. A comparison of the results of magnetic field measurements by various methods has been carried out. The star’s magnetic field varies in the range from ?3 to +3 kG. The field geometry is explained in terms of the oblique rotator model. The obtained magnetic field variation curve can be described by a central dipole with the dipole axis inclined to the axis of rotation by β = 60°, and the magnetic field strength at the pole of B _p = 11.5 kG. The data on the variability of spectral lines of some metals are presented, allowing to make an assumption that the stellar surface is heavily spotted.     

Determining the rotation law of the solar convection zone

The condition of minimum total dissipation is used to derive stationary rotation and azimuthal magnetic field distributions in the bulk of the solar convection zone with an upper boundary at which the relative radius is r/R=0.95. General equilibrium con figurations with symmetric and antisymmetric (about the equator) angular-velocity and field components are determined. The calculated rotation law matches the observed one in general parameters, but the decrease in angular velocity at high latitudes in theory is larger than that in observations. Besides, there are additional sharp variations in the rotation and field distributions in the theoretical curves near the generation zone of solar torsional waves. The possible cause of the latter discrepancy is discussed. The change in equilibrium distributions due to the presence of an inverse molecular-weight gradient at the base of the convection zone is also studied. This gradient is known to be produced by accelerated gravitational helium settling in the convection zone.     

The gas content in galactic disks: Correlation with kinematics

We consider the relationship between the total HI mass in late-type galaxies and the kinematic properties of their disks. The mass M_HI for galaxies with a wide variety of properties, from dwarf dIrr galaxies with active star formation to giant low-brightness galaxies, is shown to correlate with the product V_cR₀ (V_c is the rotational velocity, and R₀ is the radial photometric disks cale length), which characterizes the specific angular momentum of the disk. This correlation, along with the decrease in the relative mass of the gas in a galaxy with increasing V_c, can be explained in terms of the previous assumption that the gas density in the disks of most galaxies is maintained at a level close to the threshold (marginal) stability of a gaseous layer to local gravitational perturbations. In this case, the regulation mechanism of the star formation rate associated with the growth of local gravitational instability in the gaseous layer must play a crucial role in the evolution of the gas content in the galactic disk.     

The Shape of the Outer Corona during Cycle 21

The Naval Research Laboratory (NRL) Solwind coronagraph recorded the outer corona at elongations 2_5 R to 10 R during the 6 1/2-year interval from March 1979, before solar maximum, to the beginning of solar minimum in September 1985. During the minimum period, when the solar magnetic field was dipole-like, the observed corona consisted of the equatorial streamer belt that is characteristic of solar minimum, and that is interpreted as an edgewise view of a nearly flat current sheet or coronal disk lying near the plane of the heliographic equator. The observed disk was a radial projection from the magnetic neutral line that was computed for the 2.5 R source surface surrounding the Sun. At earlier times, shortly after solar maximum, the observed corona often consisted of a single coronal disk similar to that at solar minimum, but strongly tilted to the heliographic equator. Again this disk projected from a tilted magnetic neutral line that was computed for the 2.5 R source surface. Solar rotation allowed this coronal disk to be viewed in all aspects. In the edgewise view it appeared as a tilted streamer belt. In the broadside view the more flower-like pattern of solar maximum was observed. The latter view was interpreted as a non-uniform distribution of coronal material in the thin coronal disk. There were many intervals during the declining phase of the solar cycle when the computed magnetic neutral line at 2.5 R remained relatively simple but was not the source of an observable coronal disk. This latter result was probably because of the limitations of plane-of-sky observations, combined with short-term changes in the corona. Altogether, a single coronal disk, either flat or somewhat convoluted, was recognizable during only one third of the year lifetime of the coronagraph.     

Effect of partial mixing of matter on the hydrodynamic angular momentum transport processes in massive main-sequence stars

We consider the evolution of a rotating star with a mass of 16M _⊙ and an angular momentum of 3.25 × 10⁵² g cm² s^?1, along with the hydrodynamic transport of angular momentum and chemical elements in its interiors. When the partial mixing of matter of the turbulent radiative envelope and the convective core is taken into account, the efficiency of the angular momentum transport by meridional circulation in the stellar interiors and the duration of the hydrogen burning phase increase. Depending on the Schmidt number in the turbulent radiative stellar envelope, the ratio of the equatorial rotational velocity to the circular one increases with time in the process of stellar evolution and can become typical of early-type Be stars during an additional evolution time of the star on the main sequence. Partial mixing of matter is a necessary condition under which the hydrodynamic transport processes can increase the angular momentum of the outer stellar layer to an extent that the equatorial rotational velocity begins to increase during the second half of the evolutionary phase of the star on the main sequence, as shown by observations of the brightest stars in open star clusters with ages of 10–25 Myr. When the turbulent Schmidt number is 0.4, the equatorial rotational velocity of the star increases during the second half of the hydrogen burning phase in the convective core from 330 to 450 km s^?1.     

Origin of the solar system

A theory for the origin of the solar system, which is based on ideas of supersonic turbulent convection and indicates the possibility that the original Laplacian hypothesis may by valid, is presented. We suggest that the first stage of the Sun's formation consisted of the condensation of CNO ices (i.e. H₂O, NH₃, CH₄,...) and later H₂, including He as impurity atoms, at interstellar densities to from a cloud of solid grains. These grains then migrate under gravity to their common centre of mass giving up almost two orders of magnitude of angular momentum through resistive interaction with residual gases which are tied, via the ions, to the interstellar magnetic field. Grains rich in CNO rapidly dominate the centre of the cloud at this stage, both giving up almost all of their angular momentum and forming a central chemical inhomogeneity which may account for the present low solar neutrino flux (Prentice, 1976). The rest of the grain cloud, when sufficiently compressed to sweep up the residual gases and go into free fall, is not threatened by rotational disruption until its mean size has shrunk to about the orbit of Neptune. When the central opacity rises sufficiently to halt the free collapse at central density near 10^?13 g cm^?3, corresponding to a mean cloud radius of 10⁴ R _⊙, we find that there is insufficient gravitational energy, for the vaporized cloud to acquire a complete hydrostatic equilibrium, even if a supersonic turbulent stress arising from the motions of convective elements becomes important, as Schatzman (1967) has proposed. Instead we suggest that the inner 3–4% of the cloud mass collapses freely all the way to stellar size to release sufficient energy to stabilize the rest of the infalling cloud. Our model of the early solar nebula thus consists of a small dense quasi-stellar core surrounded by a vast tenuous but opaque turbulent convective envelope. Following an earlier paper (Prentice, 1973) we show how the supersonic turbulent stress \((\rho _t v_t ^2 ) = \beta \rho GM(r)/r\) , where β is called the turbulence parameter, ρ is the gas density andM(r) the mass interior to radiusr causes the envelope to become very centrally condensed (i.e. drastically lowers its moment-of-inertia coefficientf) and leads to a very steep density inversion at its photosurface, as well as causing the interior to rotate like a solid body. As the nebula contracts conserving its angular momentum the ratio θ of centrifugal force to gravitational force at the equator steadily increases. In order to maintain pressure equilibrium at its photosurface, material is extruded outwards from the deep interior of the envelope to form a dense belt of non-turbulent gases at the equator which are free of turbulent viscosity. If the turbulence is sufficiently strong, we find that when θ→1 at equatorial radiusR _e=R₀, corresponding to the orbit of Neptune, the addition of any further mass to the equator causes the envelope to discontinuously withdraw to a new radiusR _e>R₀, leaving behind the circular belt of gas at the Kepler orbitR ₀. The protosun continues to contract inwards, again rotationally stabilizing itself by extruding fresh material to the equator, and eventually abandoning a second gaseous ring at radiusR ₁, and so on. If the collapse occurs homologously the sequence of orbital radiiR _n of the system of gaseous Laplacian rings satisfy the geometric progression $$R_n /R_{n + 1} = [1 + m/Mf]^2 = constant, n = 0, 1,2, \ldots ,$$ analogous to the Titius-Bode Law of planetary distances, wherem denotes the mass of the disposed ring andM the remaining mass of the envelope. Choosing a ratio of surface to central temperature for the envelope equal to about 10^?3 and adjusting the turbulence parameter β～~0.1 so thatR _n/R_n+1 matches the observed mean ratio of 1.73, we typically findf=0.01 and that the rings of gas each have about the same mass, namely 1000M _⊕ of the solar material. Detailed calculations which take into account non-homologous behaviour resulting from the changing mass fraction of dissociated H₂ in the nebula during the collapse do not appreciably disturb this result. This model of the contracting protosun enables us to account for the observed physical structure and mass distribution of the planetary system, as well as the chemistry. In a later Paper II we shall examine in detail the condensation of the planets from the system of gaseous rings.     

Numerical simulations of dissipationless disk accretion

Our goal is to study the regime of disk accretion in which almost all of the angular momentum and energy is carried away by the wind outflowing from the disk in numerical experiments. For this type of accretion the kinetic energy flux in the outflowing wind can exceed considerably the bolometric luminosity of the accretion disk, what is observed in the plasma flow from galactic nuclei in a number of cases. In this paper we consider the nonrelativistic case of an outflow from a cold Keplerian disk. All of the conclusions derived previously for such a system in the self-similar approximation are shown to be correct. The numerical results agree well with the analytical predictions. The inclination angle of the magnetic field lines in the disk is less than 60°, which ensures a free wind outflow from the disk, while the energy flux per wind particle is greater than the particle rotation energy in its Keplerian orbit by several orders of magnitude, provided that the ratio r _A/r ? 1, where r _A is the Alfvénic radius and r is the radius of the Keplerian orbit. In this case, the particle kinetic energy reaches half the maximum possible energy in the simulation region. The magnetic field collimates the outflowing wind near the rotation axis and decollimates appreciably the wind outflowing from the outer disk periphery.     

Differential Rotation of the Solar Corona from Magnetic Field Data

A method for investigating the differential rotation of the solar corona using the coronal magnetic field as a tracer is proposed. The magnetic field is calculated in the potential approximation from observational data at the photospheric level. The time interval from June 24, 1976, to December 31, 2004, is considered. The magnetic field has been calculated for all latitudes from the equator to ±75? with a 5? step at distances from the base of the corona 1.0 R_⊙ to 2.45 R_⊙ near the source surface. The coronal rotation periods at 14 distances from the solar center have been determined by the method of periodogram analysis. The coronal rotation is shown to become progressively less differential with increasing heliocentric distance; it does not become rigid even near the source surface. The change in the coronal rotation periods with time is considered. At the cycleminimumthe rotation has been found to bemost differential, especially at small distances from the solar center. The change in coronal rotation with time is consistent with the tilt of the solar magnetic equator. The results from the magnetic field are compared with those obtained from the brightness of the green coronal Fe XIV 530.3 nm line. The consistency between these results confirms the reliability of the proposed method for studying the coronal rotation. Studying the rotation of the coronal magnetic field gives hope for the possibility of using this method to diagnose the differential rotation in subphotospheric layers.     

Capture radius and synchronization of the white dwarf in the unique magnetic cataclysmic system V1432 Aql

Results from two-color VR photometry of the unique cataclysmic magnetic variable star V1432 Aql and a theoretical model of these data are presented. The accuracy is improved by using the “mean-weighted comparison star” method. The derivative of the rotational period is dP/dt = −1.11(±0.016)·10⁻⁸. The characteristic synchronization time for the rotational and orbital motions of the white dwarf is 96.7±1.5 years, in good agreement with theory for the acceleration of an asynchronous propeller owing to the angular momentum of accreting matter. A third type of minimum detected in the light curve is interpreted in terms of the presence of an arc, or ring, rather than an accretion disk. A theoretical model is developed for determining the capture radius of accreted matter by the magnetic field of the white dwarf using the phase difference between the two types of minima associated with the axial rotation. This parameter is estimated to be 16–28 times the radius of the white dwarf for an inclined column model. A dependence of the main characteristics of the system on the mass of the white dwarf is derived which yields better values for the range of this quantity than those determined by indirect methods. For the assumed masses (M₁ = 0.9 M_⊙ and M₂ = 0.3 M_⊙) the estimated accretion rate is ∼7×10⁻¹⁰ M_⊙. It is shown that in a synchronizing polar the contribution to the change in the period by the variation in the angular momentum of the white dwarf is negligible compared to the accretion torque. In the future multicolor monitoring is needed for studying the spin-orbital synchronization and periodic changes in the accretion structure caused by “spinning” of the white dwarf. __________ Translated from Astrofizika, Vol. 50, No. 1, pp. 135–159 (February 2007).     

Formation of the regular satellites of giant planets in an extended gaseous nebula I: subnebula model and accretion of satellites

We model the subnebulae of Jupiter and Saturn wherein satellite accretion took place. We expect each giant planet subnebula to be composed of an optically thick (given gaseous opacity) inner region inside of the planet’s centrifugal radius (where the specific angular momentum of the collapsing giant planet gaseous envelope achieves centrifugal balance, located at rCJ ∼ 15R_J for Jupiter and rCS ∼ 22R_S for Saturn) and an optically thin, extended outer disk out to a fraction of the planet’s Roche-lobe (R_H), which we choose to be ∼R_H/5 (located at ∼150 R_J near the inner irregular satellites for Jupiter, and ∼200R_S near Phoebe for Saturn). This places Titan and Ganymede in the inner disk, Callisto and Iapetus in the outer disk, and Hyperion in the transition region. The inner disk is the leftover of the gas accreted by the protoplanet. The outer disk may result from the nebula gas flowing into the protoplanet during the time of giant planet gap-opening (or cessation of gas accretion). For the sake of specificity, we use a solar composition “minimum mass” model to constrain the gas densities of the inner and outer disks of Jupiter and Saturn (and also Uranus). Our model has Ganymede at a subnebula temperature of ∼250 K and Titan at ∼100 K. The outer disks of Jupiter and Saturn have constant temperatures of 130 and 90 K, respectively.Our model has Callisto forming in a time scale ∼10⁶ years, Iapetus in 10⁶-10⁷ years, Ganymede in 10³-10⁴ years, and Titan in 10⁴-10⁵ years. Callisto takes much longer to form than Ganymede because it draws materials from the extended, low density portion of the disk; its accretion time scale is set by the inward drift times of satellitesimals with sizes 300-500 km from distances ∼100R_J. This accretion history may be consistent with a partially differentiated Callisto with a ∼300-km clean ice outer shell overlying a mixed ice and rock-metal interior as suggested by Anderson et al. (2001), which may explain the Ganymede-Callisto dichotomy without resorting to fine-tuning poorly known model parameters. It is also possible that particulate matter coupled to the high specific angular momentum gas flowing through the gap after giant planet gap-opening, capture of heliocentric planetesimals by the extended gas disk, or ablation of planetesimals passing through the disk contributes to the solid content of the disk and lengthens the time scale for Callisto’s formation. Furthermore, this model has Hyperion forming just outside Saturn’s centrifugal radius, captured into resonance by proto-Titan in the presence of a strong gas density gradient as proposed by Lee and Peale (2000). While Titan may have taken significantly longer to form than Ganymede, it still formed fast enough that we would expect it to be fully differentiated. In this sense, it is more like Ganymede than like Callisto (Saturn’s analog of Callisto, we expect, is Iapetus). An alternative starved disk model whose satellite accretion time scale for all the regular satellites is set by the feeding of planetesimals or gas from the planet’s Roche-lobe after gap-opening is likely to imply a long accretion time scale for Titan with small quantities of NH₃ present, leading to a partially differentiated (Callisto-like) Titan. The Cassini mission may resolve this issue conclusively. We briefly discuss the retention of elements more volatile than H₂O as well as other issues that may help to test our model.     

Observation of the 1997-03-09 total eclipse at 8.6 mm

COPY THE ORIGINAL Analysis of the total eclipse observation of 1997 March 9 at wavelength 8.6 mm, shows that, at this wavelength, the solar radius is 1.012 R_⊙, the total flux density is 2540 sfu, the mean brightness temperature of the solar disk is 9632 K, and the brightness temperature distribution shows limb brightening at the inner edge of the solar disk, the average brightness at 0.936−0.992 R_⊙ being 9.7% above the central brightness.     

Features of calcium and strontium distribution on the surface of CP star HD49976

Modelling the magnetic field structure in HD49976, we obtained a map of its magnetic field distribution on the surface and its main parameters. Simulating the distribution of Ca and Sr by the phase dependences of the Ca II 3934 Å and Sr II 4215 Å equivalent line widths revealed that their abundances are most likely increased between the magnetic poles. An insufficiently clear result is due to the structure of the magnetic field of HD49976, which proved to be complex, not corresponding to the central dipole. It is modelled by two dipoles, the stronger of them is in the center of the star, and the other, weaker, is at distance of 0.3R _* from the center. The synthetic spectrum method yielded abundances of 28 elements in the moments of magnetic field extrema. The carbon and sulfur abundances proved to be close to the solar values, silicon showed a deficit of 1.0 dex, lithium, calcium, iron and the iron peak elements, strontium, rare earths are in excess, especially significant in the case of rare earths. High-resolution spectropolarimetric observations closely covering the entire rotation period are required to investigate the distribution of chemical elements in complex multi-dipole magnetic configurations, applying the Magnetic Doppler Imaging method.     

The cyclic variation of the outburst recurrence time in GRS 1747–312

We present an analysis of the long-term evolution of outbursts in the neutron star soft X-ray transient GRS 1747–312. Observations taken from ASM/RXTE, in the 1.5–12 keV passband, are utilized. We reveal a cyclic behavior in the residuals of the outburst recurrence time with respect to the mean value of T_C = 136 ± 2 days. The profile of this cycle is approximately sinusoidal; the remaining cycle-to-cycle fluctuations possess a considerably smaller amplitude. We find that, although the peak flux of the outbursts displays a significant scatter at a given phase of the cycle, the most luminous outbursts occur after the longest T_C. The fluence displays a large scatter for the individual outbursts and tends to decrease with time. We argue that although the cycle-length of ～5.4 yr is compatible with that of the presumed magnetic activity of the late-type donor, it cannot be explained by variations of the mass outflow from the donor to the disk. In our interpretation, the stellar activity is translated to variations of T_C via interaction of the magnetic field of the spots on the donor with the magnetic field of the disk. This gives rise to a variable efficiency of the removal of the angular momentum from the quiescent disk during the activity cycle of the donor. This mechanism can be strengthened by accompanying variations of the radius of the optically thin advection-dominated accretion flow in quiescence. We show that the peak mass accretion rate onto the neutron star in the individual outbursts of GRS 1747–312 is considerably more stable than in two other similar systems with frequent outbursts, Aql X-1 and 4U 1608–52; this allows the cyclic modulation of T_C to show itself in GRS 1747–312.