The appearance of a radio-pulsar magnetosphere from a vacuum with a strong magnetic field. Accumulation of particles     

Ya. N. Istomin  D. N. Sob’yanin 《Astronomy Reports》2010,54(4):355-366

The motion of electrons and positrons in the vacuum magnetosphere of a neutron star with a surface magnetic field of B ≈ 10¹² G is considered. Particles created in the magnetosphere or falling into it from outside are virtually instantaneously accelerated to Lorentz factors γ ≈ 10⁸. After crossing the force-free surface, where the projection of the electric field onto the magnetic field vanishes, a particle begins to undergo ultra-relativistic oscillations. The particle experiences a regular drift along the force-free surface simultaneous with this oscillatory motion.  相似文献   

A new model of a magnetar     

I. F. Malov  G. Z. Machabeli  V. M. Malofeev 《Astronomy Reports》2003,47(3):232-239

A new model is put forward to explain the observed features of anomalous X-ray pulsars (AXPs) and soft gamma-ray repeaters (SGRs). It is shown that drift waves can be excited in the magnetosphere of a neutron star with a rotational period of P～0.1 s, surface magnetic field B_s～10¹² G, and angle between the rotational axis and magnetic moment β<10°. These waves lead to the formation of radiation pulses with a period of P_dr～10 s. The rate of loss of rotational energy by such a star (～10³⁷ erg/s) is sufficient to produce the observed increase in the period \((\dot P \sim 10^{ - 10} )\), the X-ray luminosities of AXPs and SGRs (～10³⁴–10³⁶ erg/s), and an injection of relativistic particles into the surrounding supernova remnant. A modulation of the constant component of the radiation with a period of P～0.1 s is predicted. In order for SGRs to produce gamma-ray bursts, an additional source of energy must be invoked. Radio pulsars with periods of P_obs>5 s can be described by the proposed model; in this case, their rotational periods are considerably less than P_obs and the observed pulses are due to the drift waves.  相似文献   

The pulsar J1852+0040 in Kes 79 and the nature of central compact objects in supernova remnants     

I. F. Malov 《Astronomy Reports》2009,53(5):472-476

A possible model for the pulsar PSR J1852+0040 associated with the supernova remnant Kes 79 and detected in place of a central compact object in this remnant is discussed. The main observational properties of the pulsar can be understood as consequences of its weak surface magnetic field (B _s < 3 × 10¹¹ G) and short rotational period (P ～ 0.1 s). Its X-ray emission is thermal, and is generated in a small region near the surface of the neutron star due to cooling of the surface as the surface accretes matter from a relict disk surrounding the pulsar. The radio emission is generated in the outer layers of the pulsar magnetosphere by the synchrotron (cyclotron) mechanism. The optical luminosity of J1852+0040 is estimated to be L _opt < 10²⁸ erg/s. If the spectral features in another central compact object, 1E 1207.4+5209, are interpreted as electron cyclotron lines, this provides evidence for a weak surface magnetic field for this neutron star as well (B < 6 × 10¹⁰ G). The hypothesis that all central compact objects have weak surface fields makes it possible to explain the number of detected central compact objects, the absence of pulsar-wind nebulae associated with these objects, and the fact that no pulsar has yet been detected at the position of SN 1987a. We suggest that, after the supernova remnant has dissipated, the central compact object becomes a weak X-ray source (XDINS), whose weak emission is also due to the weakness of its magnetic field.  相似文献   

Effect of the pulsar-tube radius on the gamma-ray curvature radiation from the polar regions of radio pulsars with non-dipolar magnetic fields     

D. P. Barsukov  P. I. Polyakova  A. I. Tsygan 《Astronomy Reports》2009,53(1):86-94

The effect of the radius of the tube of open magnetic-field lines on the gamma-ray curvature radiation from the polar regions of a radio pulsar with a non-dipolar magnetic field is analyzed. The pulsar is considered in a polar-cap model with free electron emission from the neutron-star surface. The effect of the non-dipolar magnetic field on the radius of curvature of the field lines and the field intensity is taken into account. In connection with the creation of electron-positron pairs, we take into account only the birth of pairs by curvature radiation in the magnetic field. The small non-dipolarity of the field enables the radio pulsar not to turn off, even after a considerable decrease in the pulsar-tube radius. For instance, with a 20% non-dipolarity (ν = 0.2), a pulsar with B = 10¹³ G and P = 0.5 s can still operate even for a fivefold decrease in the pulsar-tube radius. A maximum is observed in the dependence of the electrostatic potential in the diode on the non-dipolarity parameter ν at ν ～ 0.5–0.7. The pulse profile in non-thermal X-ray emission for ν ～ 0.5–0.7 may look virtually the same as for ν ～ 0.1–0.2. Decreases in the pulsar-tube radius could be due to a structure of currents in the magnetosphere that results in the pulsar diode on the neutron-star surface occupying only a small fraction of the pulsar tube, with the remainder of the tube containing an outer annular gap. The pulsar-tube size is also affected by the presence of a circum-pulsar disk. A change in the pulsar-tube radius could also be due to an external magnetic field, associated with either a magnetic white dwarf or a circum-pulsar disk.  相似文献   

The magnetic-field structure in a stationary accretion disk     

M. Yu. Piotrovich  N. A. Silant’ev  Yu. N. Gnedin  T. M. Natsvlishvili  S. D. Buliga 《Astronomy Reports》2016,60(5):486-497

The magnetic-field structure in regions of stationary, planar accretion disks around active galactic nuclei where general-relativistic effects can be neglected (from 10 to 200 gravitational radii) is considered. It is assumed that the magnetic field in the outer edges of the disk, which forms in the magnetosphere of the central black hole during the creation of the relativisitic jets, corresponds to the field of a magnetic dipole perpendicular to the plane of the disk. In this case, the azimuthal field component B_φ in the disk arises due to the presence of the radial field B_ρ and the azimuthal velocity component U_φ. The value of the magnetic field at the inner radius of the disk is taken to correspond to the solution of the induction equation in a diffusion approximation. Numerical solutions of the induction equation are given for a number of cases.  相似文献   

Seyfert nuclei as sources of ultrahigh-energy cosmic rays     

A. V. Uryson 《Astronomy Reports》2004,48(2):81-88

Particles can be accelerated to ultrahigh energies E≈10²¹ eV in moderate Seyfert nuclei. This acceleration occurs in shock fronts in relativistic jets. The maximum energy and chemical composition of the accelerated particles depend on the magnetic field in the jet, which is not well known; fields in the range ～5–1000 G are considered in the model. The highest energies of E≈10²¹ eV are acquired by Fe nuclei when the field in the jet is B≈16 G. When B～(5–40) G, nuclei with Z<10 are accelerated to E≤10²⁰ eV, while nuclei with Z≥10 acquire energies E≥2×10²⁰ eV. Only particles with Z≥23 acquire energies E≤10²⁰ eV when B～1000 G. Protons are accelerated to E<4×10¹⁹ eV, and do not fall into the range of energies of interest for any magnetic field B. The particles lose a negligible amount of their energy in interactions with infrared photons in the accretion disk; losses in the thick gas-dust torus are also negligible if the luminosity of the galaxy is L≤10⁴⁶ erg/s and the angle between the normal to the galactic plane and the line of sight is sufficiently small, i.e., if the axial ratio of the galactic disk is comparatively high. The particles do not lose energy to curvature radiation if their deviations from the jet axis do not exceed 0.03–0.04 pc at distances from the center of R≈40–50 pc. Synchrotron losses are small, since the magnetic field frozen in the galactic wind at R≤40–50 pc is directed (as in the jet) primarily in the direction of motion. If the model considered is valid, the detected cosmic-ray protons could be either fragments of Seyfert nuclei or be accelerated in other sources. The jet magnetic fields can be estimated both from direct astronomical observations and from the energy spectrum and chemical composition of cosmic rays.  相似文献   

The X-ray emission of magnetars     

I. F. Malov  G. Z. Machabeli 《Astronomy Reports》2005,49(6):459-462

It is shown that cyclotron radiation by electrons near the surface of a neutron star with a magnetic field of ～10¹² G can easily provide the observed quiescent radiation of magnetars (Anomalous X-ray Pulsars and Soft Gamma-ray Repeaters). Pulsed emission is generated by the synchrotron mechanism at the periphery of the magnetosphere. Short-time-scale cataclysms on the neutron star could lead to flares of gamma-ray radiation with powers exceeding the power of the X-ray emission by a factor of 2γ², where γ is the Lorentz factor of the radiating particles. It is shown that an electron cyclotron line with an energy of roughly 1 MeV should be generated in the magnetar model. The detection of this line would serve as confirmation of the correctness of this model.  相似文献   

The distribution of space velocities of radio pulsars     

I. F. Malov  Yu. A. Baurov 《Astronomy Reports》2007,51(10):830-835

The distribution of the directions of the space velocities of 67 radio pulsars is shown to be strongly anisotropic. This anisotropy cannot be explained by the structure of our Galaxy or by various types of solar motions. Pulsars with stronger surface magnetic fields B have higher velocities V. The mean value of V for B < 10¹⁰ G is 108 km/s, while 〈V〉 = 340 km/s for B > 10¹⁰ G. These results must be taken into account when identifying a mechanism to explain the observed pulsar velocities and their anisotropy.  相似文献   

Possible reasons for the frequency splitting of the harmonics of type II solar radio bursts     

V. G. Eselevich  M. V. Eselevich  I. V. Zimovets 《Astronomy Reports》2016,60(1):163-173

AIA/SDO data in the 193 Å channel preceding a coronal mass ejection observed at the solar limb on June 13, 2010 are used to simultaneously identify and examine two different shock fronts. The angular size of each front relative to the CME center was about 20°, and their propagation directions differed by ≈25° (≈4° in position angle). The faster front, called the blast shock, advanced the other front, called the piston shock, by R ≈ (0.02-0.03)R⊙ (R⊙ is the solar radius) and had a maximum initial speed of V_B ≈ 850 km/s (with V_P ≈ 700 km/s for the piston shock). The appearance and motion of these shocks were accompanied by a Type II radio burst observed at the fundamental frequency F and second harmonic H. Each frequency was split into two close frequencies f₁ and f₂ separated by Δf = f₂ - f₁ ? F, H. It is concluded that the observed frequency splitting Δf of the F and H components of the Type II burst could result from the simultaneous propagation of piston and blast shocks moving with different speeds in somewhat different directions displaying different coronal-plasma densities.  相似文献   

Spectral-temporal evolution of low-frequency pulsations in the microwave radiation of solar flares     

V. V. Zaitsev  A. G. Kislyakov  S. Urpo  A. V. Stepanov  E. I. Shkelev 《Astronomy Reports》2003,47(10):873-882

Low-frequency pulsations of 22 and 37 GHz microwave radiation detected during solar flares are analyzed. Several microwave bursts observed at the Metsähovi Radio Observatory are studied with time resolutions of 100 and 50 ms. A fast Fourier transformation with a sliding window and the Wigner-Ville method are used to obtain frequency-time diagrams for the low-frequency pulsations, which are interpreted as natural oscillations of coronal magnetic loops; the dynamical spectra of the pulsations are synthesized for the first time. Three types of low-frequency fluctuations modulating the flare microwave radiation can be distinguished in the observations. First, there are fast and slow magneto-acoustic oscillations with periods of 0.5–0.8 s and 200–280 s, respectively. The fast magneto-acoustic oscillations appear as trains of narrow-band signals with durations of 100–200 s, a positive frequency drift dν/dt=0.25 MHz/min, and frequency splitting δν=0.01–0.05 Hz. Second, there are natural oscillations of the coronal magnetic loops as equivalent electrical circuits. These oscillations have periods of 0.5–10 s and positive or negative frequency drift rates dν/dt=8×10^?3 Hz/min or dν/dt=?1.3×10^?2 Hz/min, depending on the phase of the radio outburst. Third, there are modulations of the microwave radiation by short periodic pulses with a period of 20 s. The dynamical spectra of the low-frequency pulsations supply important information about the parameters of the magnetic loops: the ratio of the loop radius to its length r/L≈0.1, the plasma parameter β≈10^?3, the ratio of the plasma densities outside and inside the loop ρ_e/ρ_i≈10^?2, and the electrical current flowing along the loop I≈10¹² A.  相似文献   

Nonlinear radial pulsations of Wolf-Rayet stars     

Yu. A. Fadeev 《Astronomy Reports》2008,52(8):645-655

The evolution of Population I stars with initial masses 60 M _⊙ ≤ M _ZAMS ≤ 120 M _⊙ is computed up to the Wolf-Rayet stage, when the central helium abundance decreases to Y _c ≈ 0.05. Several models from evolutionary sequences in the core helium-burning stage were used as initial conditions when solving the equations of radiative hydrodynamics for self-exciting stellar radial pulsations. The low-density envelope surrounding the compact core during the core helium burning is unstable against radial oscillations in a wide range of effective temperatures extending to T _eff ～ 10⁵ K. The e-folding time of the amplitude growth is comparable to the dynamical time scale of the star, and, when the instability ceases growing, the radial displacement of the outer layers is comparable to the stellar radius. Evolutionary changes of the stellar radius and luminosity are accompanied by a decrease in the amplitude of radial pulsations, but, at the effective temperature T _eff ≈ 10⁵ K, the stellar oscillations are still nonlinear, with a maximum expansion velocity of the outer layers of about one-third the local escape velocity. The period of the radial oscillations decreases from 9 hr to 4 min as stellar mass decreases from M = 28 M _⊙ to M = 6 M _⊙ in the course of evolution. The nonlinear oscillations lead to a substantial increase of the radii of the Lagrangian mass zones compared to their equilibrium radii throughout the instability region. The instability of Wolf-Rayet stars against radial oscillations is due to the action of the κ mechanism in the iron-group ionization zone, which has a temperature of T ～ 2 × 10⁵ K.  相似文献   

The space velocities of radio pulsars     

A. A. Loginov  E. B. Nikitina  I. F. Malov 《Astronomy Reports》2016,60(2):193-203

Known models proposed to explain the high space velocities of pulsars based on asymmetry of the transport coefficients of different sorts of neutrinos or electromagnetic radiation can be efficient only in the presence of high magnetic fields (to 10¹⁶ G) or short rotation periods for the neutron stars (of the order of 1 ms). This current study shows that the observed velocities are not correlated with either the pulsar periods or their surface magnetic fields. The initial rotation periods are estimated in a model for the magnetedipolar deceleration of their spin, aßsuming that the pulsar ages are equal to their kinematic ages. The initial period distribution is bimodal, with peaks at 5 ms and 0.5 s, and similar to the current distribution of periods. It is shown that asymmetry of the pulsar electromagnetic radiation is insufficient to give rise to additional acceleration of pulsars during their evolution after the supernova explosion that gave birth to them. The observations testify to deceleration of the motion, most likely due to the influence of the interstellar medium and interactions with nearby objects. The time scale for the exponential decrease in the magnetic field τ_D and in the angle between the rotation axis and magnetic moment τ_ß are estimated, yielding τ_β = 1.4 million years. The derived dependence of the transverse velocity of a pulsar on the angle between the line of sight and the rotation axis of the neutron star corresponds to the expected dependence for acceleration mechanisms associated with asymmetry of the radiation emitted by the two poles of the star.  相似文献   

Magnetic fields and the $$\dot P - P$$ diagram for radio pulsars     

I. F. Malov 《Astronomy Reports》2001,45(5):389-394

Various mechanisms for the loss of angular momentum of neutron stars are analyzed. Theoretical predictions about the evolution of the period are compared with the observed distribution of pulsars on the log\(\dot P\)log(P) diagram. Pulsars with short periods (P≤0.1 s) cannot be fit well by any of the models considered. Their braking index is n=?1, which requires the development of a new braking mechanism. The evolution of pulsars with P>1.25 s is described by the law \(\dot P \propto P^2\), probably due to processes internal to the neutron stars. The observational data for pulsars with 0.1<P≤1.25 s can be fit with a hybrid model incorporating internal processes and magnetic-dipole losses. The magnetic fields in pulsar catalogs should be recomputed in accordance with the results obtained. For example, the magnetic fields obtained for two magnetars with P=5.16 s and P=7.47 s are B _s =1.7×10¹³ and 2.9×10¹³ G, which are lower than the critical field B_cr=4.4×10¹³ G. For a substantial fraction of pulsars, their characteristic ages \(\tau = P/2\dot P\) cannot serve as measures of their real ages.  相似文献   

A “tsunami” in the protoplanetary disk of SV Cep     

V. I. Shenavrin  V. P. Grinin  A. N. Rostopchina-Shakhovskaya  T. V. Demidova  D. N. Shakhovskoi  S. P. Belan 《Astronomy Reports》2017,61(1):38-46

The results of ~15 years of photometric observations of the UX Ori star SV Cep in the near-infrared (JHKL) are presented. They demonstrate the presence of a cyclic component with a period of ~7 years in the variations of the IR fluxes. This is clearly seen in all four IR bands, but is absent in the optical. The variation amplitude is highest in the K band: ΔK ≈ 0.68 ^m . The shape of the variations differs slightly in the transition from J to L. However, it is reproduced with good accuracy during two cycles, suggesting a periodic process is observed. If the periodic perturbations in the circumstellar disk of SV Cep are due to a companion’s orbitalmotion, the orbital semi-major axis should be ~5AU, foramass of SVCep of 2.6M _⊙. The absence of a seven-year period in the optical light curve of SV Cep means that the observed period cannot be due to variations in the circumstellar extinction. The IR brightness variations could be due to the companion’s motion along an eccentric orbit, resulting in a periodic modulation of the rate of accretion onto the star.  相似文献   

Magnetic field models for HD 116458 and HD 126515     

Yu. V. Glagolevskii 《Astronomy Reports》2005,49(12):1001-1008

We have modeled the magnetic fields of the slowly rotating stars HD 116458 and HD 126515 using the “magnetic charge” technique. HD 116458 has a small angle between its rotation axis and dipole axis (β = 12°), whereas this angle is large for HD 126515 (β = 86°). Both stars can be described with a decentered-dipole model, with the respective displacements being r = 0.07 and r = 0.24 in units of the stellar radius. The decentered-dipole model is able to satisfactorily explain the phase relations for the effective field, B_e(P), and the mean surface field, B_s(P), for both stars, along with the fact that the B_e(P) phase relation for HD 126515 is anharmonic. We discuss the role of systematic measurement errors possibly resulting from instrumental or methodical effects in one or both of the phase relations. The displacement of the dipole probably reflects real asymmetry of the stellar field structure, and is not due to measurement errors. Using both phase relations, B_e(P) and B_s(P), in the modeling considerably reduces the influence of the nonuniform distribution of chemical elements on the stellar surface.  相似文献   

Comparison of the magnetic properties of leading and following spots and the overlying ultraviolet emission     

Yu. S. Zagainova  V. G. Fainshtein  V. N. Obridko  G. V. Rudenko 《Astronomy Reports》2017,61(6):533-549

SDO/HMI and SDO/AIA data for the 24th solar-activity cycle are analyzed using a quicker and more accurate method for resolving π ambiguities in the transverse component of the photospheric magnetic field, yielding new results and confirming some earlier results on the magnetic properties of leading and following magnetically connected spots and single spots. The minimum inclination of the field lines to the positive normal to the solar surface α _min within umbrae is smaller in leading than in following spots in 78% of the spot pairs considered; the same trend is found for the mean angle 〈α〉 in 83% of the spot pairs. Positive correlations between the α _min values and the 〈α〉 values in leading and following spots are also found. On average, in umbrae, the mean values of 〈B〉, the umbra area S, and the angles α _min and 〈α〉 decrease with growth in the maximum magnetic field B _max in both leading and following spots. The presence of a positive correlation between B _max and S is confirmed, and a positive correlation between 〈B〉 and S in leading and following spots has been found. Themagnetic properties of the umbrae of magnetically connected pairs of spots are compared with the contrast of the He II 304 emission above the umbrae, C ₃₀₄. Spots satisfying certain conditions display a positive correlation between C _304?L and 〈α _L 〉 for the leading (L) spots, and between C _304?L /C _304?F and l _L /l _F , where l _L (l _F ) are the lengths of the field lines connecting leading (L) or following (F) spots from the corresponding spot umbrae to the apex of the field line.  相似文献   

Dualistic distribution coefficients of trace elements in the system mineral–hydrothermal solution. III. precious metals (Au and Pd) in magnetite and manganmagnetite     

V. L. Tauson  D. N. Babkin  T. M. Pastushkova  N. V. Smagunov  S. V. Lipko  I. Yu. Voronova  V. I. Men’shikov  N. V. Bryanskii  K. Yu. Arsent’ev 《Geochemistry International》2016,54(2):149-166

Distribution coefficients D of Au and Pd between magnetite (manganmagnetite) and ammonium chloride hydrothermal solution and the structural D^str and surface-related D^sur terms of these coefficients were determined at 450 and 500°С and a pressure of 1 kbar using internal sampling techniques. Quantitative data on the speciation of precious metals are obtained using the technique of statistical selections of analytical data on single crystals SSADSC and compared with LA-ICP-MS data. Both Pd and Au are elements compatible with magnetite and its manganoan variety: D^str is ≈3 for Pd and ≈1 for Au, although Au seems to weakly enrich fluid at 500°C: D^str ≈ 0.5–0.8. The trends of postmagmatic Pd and Au fractionation can thus strongly depend on the presence of spinel-group minerals, first of all, magnetite and its solid solutions. The dualistic nature of the distribution coefficients provides sound grounds to believe that both elements are highly compatible, with regard not only for the structural but also for the surface-related modes of their occurrence (D^sur ≈ 17 and ≈50–70 for Au and Pd, respectively). The maximum concentrations of structural modes of the elements are 5.3 ppm for Au and 5.1 ppm for Pd and were found in the solid solution whose jacobsite mole fractions were 0.82 and 0.49, respectively. The principal distribution patterns of the elements in crystals are confirmed by LA-ICP-MS data. Data on this system testify that the distribution coefficients of minor and trace elements are geochemically dualistic because of the abnormal absorption properties of nanometer-sized nonautonomous phases on the surface of ore minerals, and this dualism plays an important geochemical role.  相似文献   

Photometry and spectroscopy of the system V4641 sagittarii in quiescence     

V. P. Goranskij  E. A. Barsukova  A. N. Burenkov 《Astronomy Reports》2003,47(9):740-749

We present the results of our CCD photometric and moderate-dispersion spectroscopic observations of the binary system V4641 Sgr, which contains a black hole of mass ≈9.5M_⊙ and a normal B9III star. The photometric light curve reveals an ellipticity effect with very high amplitudes in V and R, 0.40^m and 0.37^m, and the color curve shows that the surface temperature is nonuniform. All this testifies to tidal distortion of the normal star's surface due to the massive companion and to a high inclination of the orbit to the line of sight. In June and July 2002, during quiescence, we obtained data during three flares with amplitudes up to 0.26^m. In particular, spectroscopic observations were acquired near the time of the black hole's inferior conjunction. One hour before conjunction, a depression by EW=0.5 Å was observed in the red wing of the Hα absorption line, interpreted as absorption by gas flowing in the direction from the observer toward the normal star. This flow is apparently associated with a rarefied gas disk around the black hole, and the conjunction grazes the stellar surface if the orbital inclination is close to 70.7°. The maximum velocity along a circular Keplerian orbit is 650 km/s at a distance of R=0.15–0.20a from the black hole (where a is the component separation). Thus, we find the mass of the black hole to be M _BH =7.1–9.5M_⊙, confirming the model of Orosz et al. (2001).  相似文献   

Segregation of Calcium Isotopes in the Atmospheres of CP Stars as a Consequence of Light-Induced Drift     

A. I. Parkhomenko  A. M. Shalagin 《Astronomy Reports》2018,62(6):383-395

  相似文献   

Radial pulsations of helium stars and a model for BX CIR     

Yu. A. Fadeev  M. F. Novikova 《Astronomy Reports》2003,47(1):68-74

The results of hydrodynamical calculations of radially pulsating helium stars with masses 0.5M_⊙≤M≤0.9M_⊙, bolometric luminosities 600L_⊙≤5×10³L_⊙, and effective temperatures 1.5×10⁴ K≤T_eff≤3.5×10⁴ K are presented. The pulsation instability of these stars is due to the effects of ionization of iron-group elements in layers with temperatures T～2×10⁵ K. The calculations were carried out using opacities for the relative mass abundances of hydrogen and heavy elements X=0 and Z=0.01, 0.015, and 0.02. Approximate formulas for the pulsation constant Q over the entire range of pulsation instability of the hot helium stars in terms of the mass M, radius R, effective temperature T_eff, and heavy-element abundance Z are derived. The instability of BX Cir to radial pulsations with the observed period Π=0.1066 d occurs only for a mass M≥0.55M_⊙, effective temperature T_eff≥23000 K, and heavy-element abundance Z≥0.015. The allowed mass of BX Cir is in the range 0.55M_⊙≤M≤0.8M_⊙, which corresponds to luminosities 800L_⊙≤M≤1400L_⊙ and mean radii 1.7R_⊙?R?2.1R_⊙.  相似文献