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1.
Semiempirical models of the photosphere of an Ellerman bomb in the NOAA 11024 active region were obtained using profiles of Stokes parameters I, Q, U, and V of photospheric lines. Spectropolarimetric observations were conducted using the French–Italian THEMIS telescope (Tenerife, Spain). The SIR inversion code [28] was used in the modeling. The models have two components: a magnetic flux tube and nonmagnetic surroundings. The dependences of temperature, magnetic field strength, inclination of the magnetic field vector, and line-of-sight velocity in the tube on the optical depth were obtained. The models demonstrate that the thermodynamic parameters of the Ellerman bomb photosphere differ considerably from those of the quiet photosphere. The temperature in the tube model varied nonmonotonically with height and deviated by up to 700–900 K from its values for the quiet photosphere. Downflows were observed in the lower and the upper photospheric layers. The line-of-sight velocity in the upper layers of the photosphere was as high as 17 km/s. The magnetic field strength in the models varied from 0.1–0.13 T in the lower photospheric layers to 0.04–0.07 T in the upper ones. The physical state of the photosphere did change in the course of observations.  相似文献   

2.
The results of the analysis of the full Stokes profiles of the photospheric lines Fe I λ 630.15 nm and Fe I λ 630.25 nm in a region of chromospheric dual flows appearance in the vicinity of a small pore are presented. The analysis is based on the spectropolarimetric observations of the active region NOAA 11024 with the THEMIS French–Italian telescope (Tenerife Island, Spain). The temporal variations in the high-resolution Stokes parameters I, Q, U, and V were considered for each pixel. It was found that the dual chromospheric flows appeared in the region of the abnormal Stokes profiles of the photospheric lines. Most of the Stokes profiles Q, U, and V have a complex shape and vary greatly from pixel to pixel, which indicates strong inhomogeneities in the structure of the magnetic field in that region. The amplitude and shape of the Stokes profiles were rapidly changing during the observations. A change in the polarity of the photospheric magnetic field took place during the observations in the region of a bright chromospheric point. The evidence of the emergence of a new small-scale magnetic flux of the opposite polarity is obtained; this could lead to magnetic reconnections, appearance of dual chromospheric flows, and occurrence of a microflare.  相似文献   

3.
This study based on longitudinal Zeeman effect magnetograms and spectral line scans investigates the dependence of solar surface magnetic fields on the spectral line used and the way the line is sampled to estimate the magnetic flux emerging above the solar atmosphere and penetrating to the corona from magnetograms of the Mt. Wilson 150-foot tower synoptic program (MWO). We have compared the synoptic program λ5250 Å line of Fe?i to the line of Fe?i at λ5233 Å since this latter line has a broad shape with a profile that is nearly linear over a large portion of its wings. The present study uses five pairs of sampling points on the λ5233 Å line. Line profile observations show that the determination of the field strength from the Stokes V parameter or from line bisectors in the circularly polarized line profiles lead to similar dependencies on the spectral sampling of the lines, with the bisector method being the less sensitive. We recommend adoption of the field determined with the line bisector method as the best estimate of the emergent photospheric flux and further recommend the use of a sampling point as close to the line core as is practical. The combination of the line profile measurements and the cross-correlation of fields measured simultaneously with λ5250 Å and λ5233 Å yields a formula for the scale factor δ ?1 that multiplies the MWO synoptic magnetic fields. By using ρ as the center-to-limb angle (CLA), a fit to this scale factor is δ ?1=4.15?2.82sin?2(ρ). Previously δ ?1=4.5?2.5sin?2(ρ) had been used. The new calibration shows that magnetic fields measured by the MDI system on the SOHO spacecraft are equal to 0.619±0.018 times the true value at a center-to-limb position 30°. Berger and Lites (2003, Solar Phys. 213, 213) found this factor to be 0.64±0.013 based on a comparison using the Advanced Stokes Polarimeter.  相似文献   

4.
Five sky areas about the radio sources ICRS 1254+571, ICRS 1345+125, ICRS 1641+399, ICRS 1732+389, and ICRS 1807+698 were observed with the aim to identify reliably the extragalactic radio sources in these areas with bright infrared objects and objects in the optical range. The test CCD observations were made in the U, V, and R bands of the Johnson system with the 2-meter telescope of the Terskol Peak Observatory (North Caucasus, Russian Federation). The U, V, and B magnitudes and the equatorial coordinates α and δ in the USNO-A2.0 catalog system were determined for objects down to V ≈ 23m in 8.5′ × 8.5′ areas, and these objects were identified with stars and infrared objects in the 2MASS catalog. The CCD image processing realized within the MIDAS/ROMAFOT program package on the basis of a new method for flat-field elimination is briefly described.  相似文献   

5.
We present our long-term photometric and spectroscopic observations of a high-latitude B supergiant with an infrared excess—the protoplanetary nebula IRAS 18062+2410. OurU BV observations in 2000–2006 have confirmed the rapid irregular photometric variability of the star with a maximum amplitude as high as 0 . m 4 in V that we found previously. The B—V and U—B color indices vary with amplitudes as high as 0 . m 10 and 0 . m 25, respectively, and show no clear correlation with the brightness. Our V-band CCD observations on 11 nights in 2006 have revealed brightness trends during the night. The variability of IRAS18062+2410 is similar in pattern to the light variations in other hot post-AGB objects and some of the nuclei of young planetary nebulae. We assume that pulsations and a variable stellar wind can be responsible for the variability of these stars. In addition to the rapid variability, our 12-year-long observations have revealed a systematic decline in the mean brightness of IRAS 18062+2410. This may be related to a rise in the temperature of the star at constant luminosity as a result of its evolution. Low-resolution spectroscopic observations have shown a systematic increase in the equivalent widths of the Hα, Hβ, [NII]λ6584 Å, OI λ8446 Å, and [OII] λ7320–7330 Å emission lines. The changes in the star’s emission line spectrum are probably caused by an increase in the degree of ionization of the gas shell due to a rise in the temperature of the ionizing star. Our photometric and spectroscopic observations of IRAS 18062+2410 confirm the previously made assumptions that the star evolves very rapidly to the region of planetary nebulae.  相似文献   

6.
Based on a self-consistent solution of the equations of gas dynamics, kinetics of hydrogen atomic level populations, and radiative transfer, we analyze the structure of a shock wave that propagates in a partially ionized hydrogen gas. We consider the radiative transfer at the frequencies of spectral lines by taking into account the effects of a moving medium in the observer's frame of reference. The flux in Balmer lines is shown to be formed behind the shock discontinuity at the initial hydrogen recombination stage. The Doppler shift of the emission-line profile is approximately one and a half times smaller than the gas flow velocity in the Balmer emission region, because the radiation field of the shock wave is anisotropic. At Mach numbers M1?10 and unperturbed gas densities σ1=10?10 g cm?3, the Doppler shift is approximately one third of the shock velocity U1. The FWHM of the emission-line profile δ ? is related to the shock velocity by δ ? ≈ k ? U1, where k ? = 1, 0.6, and 0.65 for the Hα, Hβ, and Hγ lines, respectively.  相似文献   

7.
The results of analyzing variations in the line-of-sight (LOS) velocities in the solar loop at photospheric and chromospheric levels in the region of emerging magnetic flux for the evolving active region NOAA 11024 are reported. The analysis combines the data of multiwave spectropolarimetric observations that were carried out on July 4, 2009, (Tenerife, Spain) using THEMIS solar telescope and the data obtained with GOES, SOHO, and STEREO cosmic satellites. A complex sequence of active events has been studied: formation of the Ellerman bomb, B1 X-ray microflare, and four chromospheric surges that were formed as a result of magnetic reconnection caused by new emerging magnetic flux. The Ellerman bomb was formed in the vicinity of a growing pore. Variations in the velocity V LOS of the EB had an oscillation character for chromosphere and photosphere. Before the microflare, the average velocities of the upward and downward plasma fluxes in one leg of the magnetic loop were nearly the same—26 km/s. During the microflare, the velocity V LOS of the ascending and descending flows increased up to ?33 and 50 km/s, respectively. Variations in line-of-sight velocity of a plasma in the second leg of the magnetic loop correlated well with variations of V LOS in the region of microflare, but they occurred 1.5 minutes later. During the time of observations, four chromospheric ejections of matter were formed and three of them occurred in the region of Ellerman’s bomb formation. Sharp variations in the soft X-ray intensity occurred during these ejections. At photospheric level, variations in the line-of-sight velocity of plasma in the legs of the loop occurred in the opposite direction. In the region of the first leg, velocity V LOS diminished from ?1.8 to ?0.4 km/s, while the velocity increased from ?0.6 to ?2.6 km/s in the region of the second leg.  相似文献   

8.
Optical spectra taken in 1997–2008 are used to analyze the spectral peculiarities and velocity field in the atmosphere of the peculiar supergiant 3 Pup. The profiles of strong Fe II lines and of the lines of other iron-group ions have a specific shape: the wings are raised by emissions, whereas the core is sharpened by a depression. The latter feature becomes more pronounced with the increasing line strength, and the increasing wavelength. Line profiles are variable: the magnitude and sign of the absorption asymmetry, and the blue-to-red emission intensity ratios vary from one spectrum to another. The temporal Vr variations are minimal for the forbidden emissions and sharp shell cores of the absorption features of FeII(42), and other strong lines of iron-group ions. The average velocity for the above lines can be adopted as the systemic velocity: Vsys = 28.5 ± 0.5 km/s. The weakest photospheric absorptions and photospheric MgII, Si II absorptions exhibit well-defined day-to-day velocity variations of up to 7 km/s. Quantitative spectral classification yields the spectral type of A2.7±0.3 Ib. The equivalent widths and profiles of Hδ and Hγ, and the equivalent width of the OI 7774 Å triplet yield an absolute magnitude estimate of Mv=?5.5m ± 0.3m, implying the heliocentric distance of 0.7 kpc.  相似文献   

9.
We consider stars with radial velocities, proper motions, and distance estimates from the RAVE4 catalogue. Based on a sample of more than 145 000 stars at distances r < 0.5 kpc, we have found the following kinematic parameters: \({\left( {U,{\kern 1pt} V,{\kern 1pt} W} \right)_ \odot }\) = (9.12, 20.80, 7.66) ± (0.10, 0.10, 0.08) km s?1, Ω0 = 28.71 ± 0.63 km s?1 kpc?1, and Ω0 ’ = ?4.28 ± 0.11 km s?1 kpc?2. This gives the linear rotation velocity V 0 = 230 ± 12 km s?1 (for the adopted R 0 = 8.0 ± 0.4 kpc) and the Oort constants A = 17.12 ± 0.45 km s?1 kpc?1 and B = ?11.60 ± 0.77 km s?1 kpc?1. The 2D velocity distributions in the UV, UW, and VW planes have been constructed using a local sample, r < 0.25 kpc, consisting of ~47 000 stars. A difference of the UV velocity distribution from the previously known ones constructed from a smaller amount of data has been revealed. It lies in the fact that our distribution has an extremely enhanced branch near the Wolf 630 peak. A previously unknown peak at (U, V) = (?96, ?10) km s?1 and a separate new feature in the Wolf 630 stream, with the coordinates of its center being (U, V) = (30, ?40) km s?1, have been detected.  相似文献   

10.
We study the variability of the Hγ, Hβ, and Hα line profiles in the spectrum of the supergiant κ Cas. The variability pattern proved to be the same for all the lines considered: their profiles are superimposed by blueshifted, central, and redshifted emission. For Hγ the positions of the emissions coincide with the positions of the corresponding emissions for He I λλ 5876, 6678 Å lines, and are equal to about ?135 ± 30.0 km s?1, ?20 ± 20 kms?1, and 135 ± 30.0 kms?1, respectively, whereas the three emissions in the Hβ profiles are fixed at about ?170.0 ± 70.0 kms?1, 20 ± 30 kms?1, and 170.0 ± 70.0 km s?1, respectively. The positions of the blueshifted and central emissions for Hα are the same as for Hβ, with additional blueshifted emission at ?135.0 ± 30.0 kms?1, whereas no traces of emission can be seen in the red wing of the line. These emissions show up more conspicuously in wind lines, however, their traces can be seen in all photospheric lines. When passing from wind lines to photospheric lines the intensity of superimposed emission components decreases and the same is true for the absolute values of their positions in line wings expressed in terms of radial velocities. The V/R variations of the lines studied found in the spectrum of κ Cas and the variability of the Hα emission indicate that the star is a supergiant showing Be phenomenon.  相似文献   

11.
We analyze the spectra of DR Tau in the wavelength range 1200 to 3100 Å obtained with the GHRS and STIS spectrographs from the Hubble Space Telescope. The profiles for the C IV 1550 and He II 1640 emission lines and for the absorption features of some lines indicate that matter falls to the star at a velocity ～300 km s?1. At the same time, absorption features were detected in the blue wings of the N I, Mg I, Fe II, Mg II, C II, and Si II lines, suggesting mass outflow at a velocity up to 400 km s?1. The C II, Si II, and Al II intercombination lines exhibit symmetric profiles whose peaks have the same radial velocity as the star. This is also true for the emission features of the Fe II and H2 lines. We believe that stellar activity is attributable to disk accretion of circumstellar matter, with matter reaching the star mainly through the disk and the boundary layer. At the time of observations, the accretion luminosity was Lac ? 2L⊙ at an accretion rate ?10?7M⊙ yr?1. Concurrently, a small (<10%) fraction of matter falls to the star along magnetospheric magnetic field lines from a height ～R*. Within a region of size ?3.5R*, the disk atmosphere has a thickness ～0.1R* and a temperature ?1.5 × 104 K. We assume that disk rotation in this region significantly differs from Keplerian rotation. The molecular hydrogen lines are formed in the disk at a distance <1.4 AU from the star. Accretion is accompanied by mass outflow from the accretion-disk surface. In a region of size <10R*, the wind gas has a temperature ～7000 K, but at the same time, almost all iron is singly ionized by H I L α photons from inner disk regions. Where the warm-wind velocity reaches ?400 km s?1, the gas moves at an angle of no less than 30° to the disk plane. We found no evidence of regions with a temperature above 104 K in the wind and leave open the question of whether there is outflow in the H2 line formation region. According to our estimate, the star has the following set of parameters: M* ? 0.9M⊙, R* ? 1.8R⊙, L* ? 0.9L⊙, and \(A_V \simeq 0\mathop .\limits^m 9\). The inclination i of the disk axis to the line of sight cannot be very small; however, i≤60°.  相似文献   

12.
We used high-resolution echelle spectra with high signal-to-noise ratio to determine with a high degree of accuracy some atmospheric parameters (T eff, log g and [Fe/H]) for 68 non-variable supergiants of types F, G, and K and 26 classical Cepheids in 302 pulsation phases. Very accurate effective temperatures, with errors of only 10–30 K, were determined by the line-depth ratio method. We found that the observed intrinsic color indices (B ? V)0 can be related to these parameters: (B ? V)0 = 57.984? 10.3587(log T eff)2 + 1.67572(log T eff)3 ? 3.356 log g+ 0.321 V t + 0.2615[Fe/H] + 0.8833log g(log T eff). With this empirical relation, the intrinsic colors of individual supergiants and classical Cepheids of spectral types F0-K0 and of luminosity classes I and II can be estimated with an accuracy as high as 0.05 m , which is comparable to the accuracy of the most elaborate photometric procedures. In view of large distances to supergiants, the method we propose here allows a large-scale mapping of interstellar extinction with an accuracy of 0.1–0.2 m in a quite large region of the Galaxy.  相似文献   

13.
A series of highly accurate photoelectric observations of the eclipsing binary MZ Lac was obtained with a 48-cm AZT-14 reflector at the Tien-Shan High-Altitude Station of the Sternberg Astronomical Institute from 1985 to 2004 to study its apsidal motion. We constructed a consistent system of physical and geometrical parameters of the components and the binary’s orbit: we determined their masses (M1 = 1.50M⊙, M2 = 1.29M⊙), radii (R1 = 1.86R⊙, R2 = 1.35R⊙), luminosities (L1 = 0.79L⊙, L2 = 0.45L⊙), surface gravities (logg1 = 4.06, logg2 = 4.27), age (t = 1.9 × 109 yr), and the distance to the binary (d = 510 pc). The binary exhibits apsidal motion with the period Uobs = 480 ± 40 yr, while its theoretically expected value is Uth = 450 ± 40 yr. Spectroscopic studies of MZ Lac and calculations of the absolute parameters of the components are required to test our conclusions.  相似文献   

14.
The following conclusions about the kinematics and parameters of the gas in the vicinity of TW Hya have been drawn from an analysis of optical and ultraviolet line profiles and intensities. The accreting matter rises in the magnetosphere to a distance z>R* above the disk plane and falls to the star near its equator almost perpendicular to its plane. The matter outflows from a disk region with an outer radius of ≤0.5 AU. The [OI], [SII], and H2 lines originate in the disk atmosphere outside the outflow region, where the turbulent gas velocity is close to the local speed of sound. In the formation region of the forbidden lines, T?8500 K and Ne?5×106 cm?3, and the hydrogen is almost neutral: xe<0.03. The absorption features observed in the blue wings of some of the ultraviolet lines originate in the part of the wind that moves almost perpendicular to the disk plane, i.e., in the jet of TW Hya. The V z gas velocity component in the jet decreases with increasing distance from the jet axis from 200 to 30 km s?1. The matter outflowing from the inner disk boundary, moves perpendicular to the disk plane in the formation region of blue absorption line components, at a distance of ～0.5 AU from the axis of symmetry of the disk. This region of the wind is collimated into the jet at a distance of <3 AU from the disk plane. The gas temperature in the formation region of absorption components is ?2×104 K, and the gas density is <3×106 cm?3. This region of the jet is on the order of several AU away from the disk plane, while free recombination in the jet begins even farther from the disk. The mass-loss rate for TW Hya is \(\dot M_w < 7 \times 10^{ - 10} M_ \odot yr^{ - 1}\), which is a factor of 3lower than the mean accretion rate. The relative abundance of silicon and aluminum in the jet gas is at least an order of magnitude lower than its standard value.  相似文献   

15.
We study the sources and components of the solar-wind spatial stream structure at the maximum of the solar cycle 23. In our analysis, we use several independent sets of experimental data: radio-astronomical observations of scattered radiation from compact sources with the determination of the distance from the Sun to the inner boundary of the transonic-flow transition region (Rin); calculated data on the magnetic-field intensity and structure in the solar corona, in the solar-wind source region, obtained from optical measurements of the photospheric magnetic-field intensity at the Stanford Solar Observatory (USA); and observations of the white-light corona with the LASCO coronograph onboard the SOHO spacecraft. We show that at the solar maximum, low-speed streams with a transition region located far from the Sun dominate in the solar-wind structure. A correlation analysis of the location of the inner boundary Rin and the source-surface magnetic-field intensity |B R | on a sphere R=2.5RS (RS is the solar radius) has revealed the previously unknown lowest-speed streams, which do not fit into the regular relationship between the parameters Rin and |B R |. In the white-light corona, the sources of these streams are located near the dark strip, a coronal region with a greatly reduced density; the nonstandard parameters of the streams probably result from the interaction of several discrete sources of different types.  相似文献   

16.
We have measured the interstellar extinction in the region of ultradeep Galactic-field observations by the Chandra telescope (l II, b II) ≈ 0.1–1.42 using photometric data from the 2MASS infrared allsky survey. The angular resolution of our interstellar extinction map is 1′.8. We show that the interstellar extinction has a minimum, A V ～ 3.4, near the center of the Chandra field of view and increases to A V ～ 5.8–6 at the edge of the field of view. In addition, we show that the bulk of the extinction is gained in the Galactic disk and is approximately the same for all bulge stars. Our results will be subsequently used to process the Chandra data and to estimate the properties of the stellar population in this region.  相似文献   

17.
Using the high-resolution spectra obtained at the 6-meter telescope of the SAO RAS over 2002–2013, we studied the spectral features of the lines of interstellar medium. The radial velocities of the Na I 5890 Å, Na I 5896 Å, Ca II 3934 Å and Ca II 3968 Å absorption lines were analyzed. Seven diffuse interstellar bands 4964, 5780, 5797, 6196, 6203, 6379 Å were identified in the optical spectrum of IRAS01005+7910. Radial velocities Vr and equivalent widths Wλ of these DIBs were measured, for which the values of the interstellar reddening EB?V and column density of neutral hydrogen log [N(H)] were calculated.  相似文献   

18.
We present the results of our UBV and JHKLM photometry for the semiregular pulsating variable V1027 Cyg, a supergiant with an infrared excess, over the period from 1997 to 2015 (UBV) and in 2009–2015 (JHKLM). Together with the new data, we analyze the photometric observations of V1027 Cyg that we have obtained and published previously. Our search for a periodicity in the UBV brightness variations has led to several periods from P = 212d to 320d in different time intervals. We have found the period P = 237d based on our infrared photometry. The variability amplitude, the lightcurve shape, and themagnitude of V1027 Cyg atmaximum light change noticeably from cycle to cycle. The deepest minimum was observed in 2011, when the amplitudes of brightness variations in the star reached the following values: ΔU = 1 . m 28, ΔB = 1 . m 10, ΔV = 1 . m 05, ΔJ = 0 . m 30, ΔH = 0 . m 35, ΔK = 0 . m 32, ΔL = 0 . m 26, and ΔM = 0 . m 10. An ambiguous correlation of the B ? V and U ? B colors with the brightness has been revealed. For example, a noticeable bluing of the star was observed during the deep 1992, 2008, and 2011 minima, while the variations with smaller amplitudes show an increase in B ? V at the photometric minima. The spectral energy distribution for V1027 Cyg from our photometry in the range 0.36 (U)–5.0 (M) μm corresponds to spectral types from G8I to K3I at different phases of the pulsation cycle. Low-resolution spectra of V1027 Cyg in the range λ4400–9200 ?A were taken during 16 nights over the period 1995–2015. At the 1995 and 2011 photometric minima the star’s spectrum exhibited molecular TiO bands whose intensity corresponded to spectral types M0–M1, while the photometric data point to a considerably earlier spectral type. We hypothesize that the TiO bands are formed in the upper layers of the extended stellar atmosphere. We have measured the equivalent widths of the strongest absorption lines, in particular, the infrared Ca II triplet in the spectrum of V1027 Cyg. The calcium triplet (Ca T) with W λ(Ca T) = 20.3 ± 1.8 ?A as a luminosity indicator for supergiants places V1027 Cyg in the region of the brightest G–K supergiants. V1027 Cyg has been identified with the infrared source IRAS 20004+2955 and is currently believed to be a candidate for post-AGB stars. The evolutionary status of the star and its difference from other post-AGB objects are discussed.  相似文献   

19.
Highly accurate W BV R photometric measurements of the eclipsing binary HP Aur were performed in 2002–2003 with the 48-cm AZT-14 reflector at the Tien-Shan High-Altitude Observatory to determine the rate of apsidal motion. A consistent system of physical and geometrical parameters of the components and the binary as a whole has been constructed for the first time by analyzing these new measurements together with other published data: we determined their radii (R1 = 1.05R⊙, R2 = 0.82R⊙) and luminosities (L1 = 1.10L⊙, L2 = 0.46L⊙), spectral types (G2V + G8V) and surface gravities (log g1 = 4.38, log g2 = 4.51), age (t = 9.5 × 109 yr), and the distance to the binary (d = 197 pc). We detected an ultraviolet excess in the spectra of both components, \(\Delta (W - B) \simeq - 0\mathop .\limits^m 25\), that is probably attributable to a metal deficiency in the atmospheres of these stars. In this system of two solar-type stars, we found a third body with the mass M3 sin i 3 3 = 0.17M⊙ that revolved with the period P3 = 13.7 yr around the eclipsing binary in a highly eccentric elliptical orbit: e3 = 0.70 and A3 sin i3 ? 7 AU. The orbit of the eclipsing binary itself was shown to be also elliptical, but with a low eccentricity (e = 0.0025(5)), while apsidal motion with a period Uobs > 80 yr was observed at a theoretically expected period Uth ≈ 92 yr. At least 20 to 30 more years of photoelectric measurements of this star will be required to reliably determine Uobs.  相似文献   

20.
Speckle-interferometric observations of FU Ori are performed with the 6-m telescope of the Special Astrophysical Observatory with 600/40 nm and 800/100 nm (central bandwidth/halfwidth) filters. The companion star FU Ori S that was recently discovered at λ >-1.25µm was recorded in observations with the λ/Δλ==800/100 nm filter. The positional parameters and magnitude difference of the companion in the filter considered are found to be θ = (163.9 ± 1.0)°, ρ = (0.493 ± 0.007)″, Δm = 3.96 ± 0.28. An analysis of the spectral energy distribution of the companion implies that for the extinction A V toward FU Ori to be greater than about 1.6 m , i.e., the minimum value required by the available models of the fuor, the spectral type of the companion star must be no later than K3. The reliability of this conclusion and the possible ways for obtaining more accurate estimates of A V are discussed.  相似文献   

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