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1.
A study of cluster characteristics and internal kinematical structure of the middle-aged Pleiades open star cluster is presented. The individual star apexes and various cluster kinematical parameters including the velocity ellipsoid parameters are determined using both Hipparcos and Gaia data. Modern astrometric parameters were taken from the Gaia Data Release 1 (DR1) in combination with the Radial Velocity Experiment Fifth Data Release (DR5). The necessary set of parameters including parallaxes, proper motions and radial velocities are used for \(n=17\) stars from Gaia DR1+RAVE DR5 and for \(n=19\) stars from the Hipparcos catalog using SIMBAD data base. Single stars are used to improve accuracy by eliminating orbital movements. RAVE DR5 measurements were taken only for the stars with the radial velocity errors not exceeding \(2~\mbox{km}/\mbox{s}\). For the Pleiades stars taken from Gaia, we found mean heliocentric distance as \(136.8 \pm 6.4\) pc, and the apex position is calculated as: \(A_{CP}=92^{\circ }.52\pm 1^{\circ }.72\), \(D_{CP}=-42^{\circ }.28\pm 2^{\circ }.56\) by the convergent point method and \(A_{0}=95^{\circ }.59\pm 2^{\circ }.30\) and \(D_{0}=-50^{\circ }.90\pm 2^{\circ }.04\) using AD-diagram method (\(n=17\) in both cases). The results are compared with those obtained historically before the Gaia mission era.  相似文献   

2.
To investigate the \(M_\bullet -\sigma \) relation, we consider realistic elliptical galaxy profiles that are taken to follow a single power-law density profile given by \(\rho (r) = \rho _{0}(r/ r_{0})^{-\gamma }\) or the Nuker intensity profile. We calculate the density using Abel’s formula in the latter case by employing the derived stellar potential; in both cases. We derive the distribution function f(E) of the stars in the presence of the supermassive black hole (SMBH) at the center and hence compute the line-of-sight (LoS) velocity dispersion as a function of radius. For the typical range of values for masses of SMBH, we obtain \(M_{\bullet } \propto \sigma ^{p}\) for different profiles. An analytical relation \(p = (2\gamma + 6)/(2 + \gamma )\) is found which is in reasonable agreement with observations (for \(\gamma = 0.75{-}1.4\), \(p = 3.6{-}5.3\)). Assuming that a proportionality relation holds between the black hole mass and bulge mass, \(M_{\bullet } =f M_\mathrm{b}\), and applying this to several galaxies, we find the individual best fit values of p as a function of f; also by minimizing \(\chi ^{2}\), we find the best fit global p and f. For Nuker profiles, we find that \(p = 3.81 \pm 0.004\) and \(f = (1.23 \pm 0.09)\times 10^{-3}\) which are consistent with the observed ranges.  相似文献   

3.
We aim to probe the dynamic structure of the extended Solar neighborhood by calculating the radial metallicity gradients from orbit properties, which are obtained for axisymmetric and non-axisymmetric potential models, of red clump (RC) stars selected from the RAdial Velocity Experiment’s Fourth Data Release. Distances are obtained by assuming a single absolute magnitude value in near-infrared, i.e. \(M_{Ks}=-1.54\pm0.04\) mag, for each RC star. Stellar orbit parameters are calculated by using the potential functions: (i) for the MWPotential2014 potential, (ii) for the same potential with perturbation functions of the Galactic bar and transient spiral arms. The stellar age is calculated with a method based on Bayesian statistics. The radial metallicity gradients are evaluated based on the maximum vertical distance (\(z_{max}\)) from the Galactic plane and the planar eccentricity (\(e_{p}\)) of RC stars for both of the potential models. The largest radial metallicity gradient in the \(0< z_{max} \leq0.5\) kpc distance interval is \(-0.065\pm0.005~\mbox{dex}\,\mbox{kpc}^{-1}\) for a subsample with \(e_{p}\leq0.1\), while the lowest value is \(-0.014\pm0.006~\mbox{dex}\,\mbox{kpc}^{-1}\) for the subsample with \(e_{p}\leq0.5\). We find that at \(z_{max}>1\) kpc, the radial metallicity gradients have zero or positive values and they do not depend on \(e_{p}\) subsamples. There is a large radial metallicity gradient for thin disc, but no radial gradient found for thick disc. Moreover, the largest radial metallicity gradients are obtained where the outer Lindblad resonance region is effective. We claim that this apparent change in radial metallicity gradients in the thin disc is a result of orbital perturbation originating from the existing resonance regions.  相似文献   

4.
5.
We show the possibility of existence of a self-gravitating spherically-symmetric equilibrium configuration for a neutral matter with neutron-like density, small mass \(M \ll M_{\odot }\), and small radius \(R \ll R_{\odot }\). We incorporate the effects of both the special and general theories of relativity. Such object may be formed in a cosmic cataclysm, perhaps an exotic one. Since the base equations of hydrostatic equilibrium are completed by the equation of state (EoS) for the matter of the object, we offer a novel, interpolating experimental data from high-energy physics, EoS which permits the existence of such compact system of finite radius. This EoS model possesses a critical state characterized by density \(\rho_{c}\) and temperature \(T_{c}\). For such an object, we derive a radial distribution for the super-dense matter in “liquid” phase using Tolman–Oppenheimer–Volkoff equations for hydrostatic equilibrium. We demonstrate that a stable configuration is indeed possible (only) for temperatures smaller than the critical one. We derive the mass-radius relation (adjusted for relativistic corrections) for such small (\(M \ll M_{\odot }\)) super-dense compact objects. The results are within the constraints established by both heavy-ion collision experiments and theoretical studies of neutron-rich matter.  相似文献   

6.
It is shown that a number of superfast, with periods \(< 2\) d, exoplanets revolve around parent stars with periods, near-commensurate with \(P_{E}\) and/or \(2 P_{E} / \pi\), where the exoplanet resonance timescale \(P_{E}=9603(85)\) s agrees fairly well with the period \(P_{0}= 9600.606(12)\) s of the so-called “cosmic oscillation” (the probability that the two timescales would coincide by chance is near \(3 \times10^{-4}\); the \(P_{0}\) period was discovered first in the Sun, and later on—in other objects of Cosmos). True nature of the exoplanet \(P_{0}\) resonance is unknown.  相似文献   

7.
This addendum uses an alternate fit for the electron density distribution \(N(r)\) (see Figure 1) and estimates the coronal magnetic field using the new model. We find that the estimates of the magnetic field are in close agreement using both the models.
We have fit the \(N(r)\) distribution obtained from STEREO-A/COR1 and SOHO/LASCO-C2 using a fifth-order polynomial (see Figure 1). The expression can be written as
$$\begin{aligned} N_{\text{cor}}(r) &= 1.43 \times 10^{9} r^{-5} - 1.91 \times 10^{9} r^{-4} + 1.07 \times 10^{9} r^{-3} - 2.87 \times 10^{8} r^{-2} \\ &\quad {} + 3.76 \times 10^{7} r^{-1} - 1.91 \times 10^{6} , \end{aligned}$$
(1)
where \(N_{\text{cor}}(r)\) is in units of cm?3 and \(r\) is in units of \(\mathrm{R}_{\odot}\). The background coronal electron density is enhanced by a factor of 5.5 at 2.63 \(\mathrm{R}_{\odot}\) during the coronal mass ejection (CME). The estimated coronal magnetic field strength (\(B\)) using radio data indicates that \(B(r) \approx(0.51\text{\,--\,}0.48) \pm 0.02\ \mathrm{G}\) in the range \(r \approx2.65\text{\, --\,}2.82\ \mathrm{R}_{\odot}\). The field strengths for STEREO-A/COR1 and SOHO/LASCO-C2 are ≈?0.32 G at \(r \approx 3.11\ \mathrm{R}_{\odot}\) and ≈?0.12 G at \(r \approx 4.40\ \mathrm{R}_{\odot}\), respectively.
  相似文献   

8.
We investigate the parameters of global solar p-mode oscillations, namely damping width \(\Gamma\), amplitude \(A\), mean squared velocity \(\langle v^{2}\rangle\), energy \(E\), and energy supply rate \(\mathrm{d}E/\mathrm{d}t\), derived from two solar cycles’ worth (1996?–?2018) of Global Oscillation Network Group (GONG) time series for harmonic degrees \(l=0\,\mbox{--}\,150\). We correct for the effect of fill factor, apparent solar radius, and spurious jumps in the mode amplitudes. We find that the amplitude of the activity-related changes of \(\Gamma\) and \(A\) depends on both frequency and harmonic degree of the modes, with the largest variations of \(\Gamma\) for modes with \(2400~\upmu\mbox{Hz}\le\nu\le3300~\upmu\mbox{Hz}\) and \(31\le l \le60\) with a minimum-to-maximum variation of \(26.6\pm0.3\%\) and of \(A\) for modes with \(2400~\upmu\mbox{Hz}\le\nu\le 3300~\upmu\mbox{Hz}\) and \(61\le l \le100\) with a minimum-to-maximum variation of \(27.4\pm0.4\%\). The level of correlation between the solar radio flux \(F_{10.7}\) and mode parameters also depends on mode frequency and harmonic degree. As a function of mode frequency, the mode amplitudes are found to follow an asymmetric Voigt profile with \(\nu_{\text{max}}=3073.59\pm0.18~\upmu\mbox{Hz}\). From the mode parameters, we calculate physical mode quantities and average them over specific mode frequency ranges. In this way, we find that the mean squared velocities \(\langle v^{2}\rangle\) and energies \(E\) of p modes are anticorrelated with the level of activity, varying by \(14.7\pm0.3\%\) and \(18.4\pm0.3\%\), respectively, and that the mode energy supply rates show no significant correlation with activity. With this study we expand previously published results on the temporal variation of solar p-mode parameters. Our results will be helpful to future studies of the excitation and damping of p modes, i.e., the interplay between convection, magnetic field, and resonant acoustic oscillations.  相似文献   

9.
This study’s objective was to exploit infrared VVV (VISTA Variables in the Via Lactea) photometry for high latitude RRab stars to establish an accurate Galactic Centre distance. RRab candidates were discovered and reaffirmed (\(n=4194\)) by matching \(K_{s}\) photometry with templates via \(\chi ^{2}\) minimization, and contaminants were reduced by ensuring targets adhered to a strict period-amplitude (\(\Delta K_{s}\)) trend and passed the Elorietta et al. classifier. The distance to the Galactic Centre was determined from a high latitude Bulge subsample (\(|b|>4^{\circ}\), \(R_{\mathit{GC}}=8.30 \pm 0.36\) kpc, random uncertainty is relatively negligible), and importantly, the comparatively low color-excess and uncrowded location mitigated uncertainties tied to the extinction law, the magnitude-limited nature of the analysis, and photometric contamination. Circumventing those problems resulted in a key uncertainty being the \(M_{K_{s}}\) relation, which was derived using LMC RRab stars (\(M_{K_{s}}=-(2.66\pm 0.06) \log {P}-(1.03\pm 0.06)\), \((J-K_{s})_{0}=(0.31\pm 0.04) \log {P} + (0.35\pm 0.02)\), assuming \(\mu _{0,\mathit{LMC}}=18.43\)). The Galactic Centre distance was not corrected for the cone-effect. Lastly, a new distance indicator emerged as brighter overdensities in the period-magnitude-amplitude diagrams analyzed, which arise from blended RRab and red clump stars. Blending may thrust faint extragalactic variables into the range of detectability.  相似文献   

10.
By systematically searching the region of far infrared loops, we found a number of huge cavity-like dust structures at \(60\,\mu \hbox {m}\) and \(100\,\mu \hbox {m}\) IRIS maps. By checking these with AKARI maps (\(90\,\mu \hbox {m}\) and \(140\,\mu \hbox {m}\)), two new cavity-like structures (sizes \(\sim \) \( 2.7\,\hbox {pc} \times 0.8\,\hbox {pc}\) and \(\sim \) \( 1.8\,\hbox {pc} \times 1\,\hbox {pc}\)) located at R.A. (\(\hbox {J}2000)=14^{h}41^{m}23^{s}\) and Dec. \((\hbox {J}2000)=-64^{\circ }04^{\prime }17^{{\prime }{\prime }}\) and R.A. \((\hbox {J}2000)=05^{h}05^{m}35^{s}\) and Dec. \((\hbox {J}2000)=-\,69^{\circ }35^{\prime } 25^{{\prime }{\prime }}\) were selected for the study. The difference in the average dust color temperatures calculated using IRIS and AKARI maps of the cavity candidates were found to be \(3.2\pm 0.9\,\hbox {K}\) and \(4.1\pm 1.2\,\hbox {K}\), respectively. Interestingly, the longer wavelength AKARI map gives larger values of dust color temperature than that of the shorter wavelength IRIS maps. Possible explanation of the results will be presented.  相似文献   

11.
This paper deals with the photo-gravitational restricted four-body problem (PR4BP) with variable mass. Following the procedure given by Gascheau (C. R. 16:393–394, 1843) and Routh (Proc. Lond. Math. Soc. 6:86–97, 1875), the conditions of linear stability of Lagrange triangle solution in the PR4BP are determined. The three radiating primaries having masses \(m_{1}\), \(m_{2}\) and \(m_{3}\) in an equilateral triangle with \(m_{2}=m_{3}\) will be stable as long as they satisfy the linear stability condition of the Lagrangian triangle solution. We have derived the equations of motion of the mentioned problem and observed that there exist eight libration points for a fixed value of parameters \(\gamma (\frac{m \ \text{at time} \ t}{m \ \text{at initial time}}, 0<\gamma\leq1 )\), \(\alpha\) (the proportionality constant in Jeans’ law (Astronomy and Cosmogony, Cambridge University Press, Cambridge, 1928), \(0\leq\alpha\leq2.2\)), the mass parameter \(\mu=0.005\) and radiation parameters \(q_{i}, (0< q_{i}\leq1, i=1, 2, 3)\). All the libration points are non-collinear if \(q_{2}\neq q_{3}\). It has been observed that the collinear and out-of-plane libration points also exist for \(q_{2}=q_{3}\). In all the cases, each libration point is found to be unstable. Further, zero velocity curves (ZVCs) and Newton–Raphson basins of attraction are also discussed.  相似文献   

12.
We report the discovery of gamma-ray detection from the Large Magellanic Cloud (LMC) B0443-6657 using the Large Area Telescope (LAT) on board the Fermi Gamma-ray Space Telescope. LMC B0443-6657 is a flat-spectrum radio source, possibly associated with a supernova remnant in the Large Magellanic Cloud (LMC N4). Employing the LAT data of 8 years, our results show a significant excess (\(>9.4\sigma \)) of gamma rays in the range of 0.2–100 GeV above the gamma-ray background. A power-law function is found to adequately describe the 0.2–\(100\mbox{ GeV}\)\(\gamma \)-ray spectrum, which yields a photon flux of \(3.27\pm 0.53\ \text{photon}\,\mbox{cm}^{2}\,\mbox{s}^{-1}\) with a photon index of \(2.35\pm 0.11\), corresponding to an isotropic gamma-ray luminosity of \(5.3\times 10^{40}~\mbox{erg}\,\mbox{s}^{-1}\). The hadronic model predicts a low X-ray and TeV flux while the leptonic model predicts an observable flux in these two energy bands. The follow-up observations of the LMC B0443-6657 in X-ray or TeV band would distinguish the radiation models of gamma rays from this region.  相似文献   

13.
On 27 June 2012, an eruptive solar prominence was observed in the extreme ultraviolet (EUV) and radio wavebands. At the Aalto University Metsähovi Radio Observatory (MRO) it was observed at 37 GHz. It was the first time that the MRO followed a radio prominence with dense sampling in the millimetre wavelengths. This prompted us to study the connection of the 37 GHz event with other wavelength domains. At 37 GHz, the prominence was tracked to a height of around \(1.6~\mathrm{R}_{\odot}\), at which the loop structure collapsed. The average velocity of the radio prominence was \(55 \pm 6~\mbox{km}\,\mbox{s}^{-1}\). The brightness temperature of the prominence varied between \(800 \pm 100\) K and \(3200 \pm 100\) K. We compared our data with the Solar Dynamic Observatory (SDO)/Atmospheric Imaging Assembly (AIA) instrument’s 304 Å EUV data, and found that the prominence behaves very similarly in both wavelengths. The EUV data also reveal flaring activity nearby the prominence. We present a scenario in which this flare works as a trigger that causes the prominence to move from a stable stage to an acceleration stage.  相似文献   

14.
We have studied the variability of S5 0716+714 at radio 15 GHz and \(\gamma\)-ray band using three different methods. A possible periodicity of \(P_{15~\text{GHz}}=266.0\pm11.5\) and \(P_{\gamma}=344.0 \pm16.4\) days are obtained for radio 15 GHz and \(\gamma\)-ray light curves, respectively. The variability may be related to the intrinsically emission mechanism. The difference between the variability timescales of radio 15 GHz and \(\gamma \)-ray may be due to that the emission of radio 15 GHz is produced via the synchrotron process, while the \(\gamma\)-ray is produced by both the SSC and EC processes.  相似文献   

15.
We study the solar-cycle variation of subsurface flows from the surface to a depth of 16 Mm. We have used ring-diagram analysis to analyze Dopplergrams obtained with the Michelson Doppler Imager (MDI) Dynamics Program, the Global Oscillation Network Group (GONG), and the Helioseismic and Magnetic Imager (HMI) instrument. We combined the zonal and meridional flows from the three data sources and scaled the flows derived from MDI and GONG to match those from HMI observations. In this way, we derived their temporal variation in a consistent manner for Solar Cycles 23 and 24. We have corrected the measured flows for systematic effects that vary with disk positions. Using time-depth slices of the corrected subsurface flows, we derived the amplitudes and times of the extrema of the fast and slow zonal and meridional flows during Cycles 23 and 24 at every depth and latitude. We find an average difference between maximum and minimum amplitudes of \(8.6 \pm0.4~\mbox{m}\,\mbox{s}^{-1}\) for the zonal flows and \(7.9 \pm0.3~\mbox{m}\,\mbox{s}^{-1}\) for the meridional flows associated with Cycle 24 averaged over a depth range from 2 to 12 Mm. The corresponding values derived from GONG data alone are \(10.5 \pm0.3~\mbox{m}\,\mbox{s}^{-1}\) for the zonal and \(10.8 \pm0.3~\mbox{m}\,\mbox{s}^{-1}\) for the meridional flow. For Cycle 24, the flow patterns are precursors of the magnetic activity. The timing difference between the occurrence of the flow pattern and the magnetic one increases almost linearly with increasing latitude. For example, the fast zonal and meridional flow appear \(2.1 \pm 0.6\) years and \(2.5\pm 0.6\) years, respectively, before the magnetic pattern at \(30^{\circ}\) latitude in the northern hemisphere, while in the southern hemisphere, the differences are \(3.2 \pm 1.2\) years and \(2.6 \pm 0.6\) years. The flow patterns of Cycle 25 are present and have reached \(30^{\circ}\) latitude. The amplitude differences of Cycle 25 are about 22% smaller than those of Cycle 24, but are comparable to those of Cycle 23. Moreover, polynomial fits of meridional flows suggest that equatorward meridional flows (counter-cells) might exist at about \(80^{\circ}\) latitude except during the declining phase of the solar cycle.  相似文献   

16.
In this paper, we explore the possibility of accreting primordial black holes as the source of heating for the collapsing gas in the context of the direct collapse black hole scenario for the formation of super-massive black holes (SMBHs) at high redshifts, \(z\sim \) 6–7. One of the essential requirements for the direct collapse model to work is to maintain the temperature of the in-falling gas at \(\approx \)10\(^4\) K. We show that even under the existing abundance limits, the primordial black holes of masses \(\gtrsim \)10\(^{-2}M_\odot \), can heat the collapsing gas to an extent that the \(\mathrm{H}_2\) formation is inhibited. The collapsing gas can maintain its temperature at \(10^4\) K till the gas reaches a critical density \(n_{{c}} \,{\approx }\, 10^3~\hbox {cm}^{-3}\), at which the roto-vibrational states of \(\mathrm{H}_2\) approaches local thermodynamic equilibrium and \(\mathrm{H}_2\) cooling becomes inefficient. In the absence of \(\mathrm{H}_2\) cooling, the temperature of the collapsing gas stays at \(\approx \)10\(^4\) K even as it collapses further. We discuss scenarios of subsequent angular momentum removal and the route to find collapse through either a supermassive star or a supermassive disk.  相似文献   

17.
In this study, we present CCD UBV photometry of poorly studied open star clusters, Dolidze 36, NGC 6728, NGC 6800, NGC 7209, and Platais 1, located in the first and second Galactic quadrants. Observations were obtained with T100, the 1-m telescope of the TÜB?TAK National Observatory. Using photometric data, we determined several astrophysical parameters such as reddening, distance, metallicity and ages and from them, initial mass functions, integrated magnitudes and colours. We took into account the proper motions of the observed stars to calculate the membership probabilities. The colour excesses and metallicities were determined independently using two-colour diagrams. After obtaining the colour excesses of the clusters Dolidze 36, NGC 6728, NGC 6800, NGC 7209, and Platais 1 as \(0.19\pm0.06\), \(0.15\pm0.05\), \(0.32\pm0.05\), \(0.12\pm 0.04\), and \(0.43\pm0.06\) mag, respectively, the metallicities are found to be \(0.00\pm0.09\), \(0.02\pm0.11\), \(0.03\pm0.07\), \(0.01\pm0.08\), and \(0.01\pm0.08\) dex, respectively. Furthermore, using these parameters, distance moduli and age of the clusters were also calculated from colour-magnitude diagrams simultaneously using PARSEC theoretical models. The distances to the clusters Dolidze 36, NGC 6728, NGC 6800, NGC 7209, and Platais 1 are \(1050\pm90\), \(1610\pm190\), \(1210\pm150\), \(1060\pm90\), and \(1710\pm250\) pc, respectively, while corresponding ages are \(400\pm100\), \(750\pm150\), \(400\pm100\), \(600\pm100\), and \(175\pm50\) Myr, respectively. Our results are compatible with those found in previous studies. The mass function of each cluster is derived. The slopes of the mass functions of the open clusters range from 1.31 to 1.58, which are in agreement with Salpeter’s initial mass function. We also found integrated absolute magnitudes varying from ?4.08 to ?3.40 for the clusters.  相似文献   

18.
Analysis of the radial velocities based on spectra of high (near the H α line) and moderate (4420–4960 Å) resolutions supplemented by the published radial velocities has revealed the binarity of a bright member of the young open star cluster χ Per, the star V622 Per. The derived orbital elements of the binary show that the lines of both components are seen in its spectrum, the orbital period is 5.2 days, and the binary is in the phase of active mass exchange. The photometric variability of the star is caused by the ellipsoidal shape of its components. Analysis of the spectroscopic and photometric variabilities has allowed the absolute parameters of the binary’s orbit and its components to be found. V622 Per is shown to be a classical Algol with moderate mass exchange in the binary. Mass transfer occurs from the less massive (\({M_1} = 9.1 \pm 2.7{M_ \odot }\)) but brighter (\(\log {L_1} = 4.52 \pm 0.10{L_ \odot }\)) component onto the more massive (\({M_2} = 13.0 \pm 3.5{M_ \odot }\)) and less bright (\(\log {L_2} = 3.96 \pm 0.10{L_ \odot }\)) component. Analysis of the spectra has confirmed an appreciable overabundance of CNO-cycle products in the atmosphere of the primary component. Comparison of the positions of the binary’s components on the T eff–log g diagram with the age of the cluster χ Per points to a possible delay in the evolution of the primary component due to mass loss by no more than 1–2Myr.  相似文献   

19.
In present paper higher harmonic electrostatic ion-cyclotron (EIC) parallel flow velocity shear instability in presence of perpendicular inhomogeneous DC electric field with the ambient magnetic field has been studied, in different regions of the magnetosphere of Saturn. Dimensionless growth rate variation of EIC waves has been observed with respect to \(k_{ \bot } \rho _{i}\) for various plasma parameters. Effect of velocity shear scale length (\(A_{i}\)), temperature anisotropy (\(T_{ \bot } /T_{\|}\)), magnetic field (\(B\)), electric field (\(E\)), inhomogeneity (\(P/a\)), angle of propagation (\(\theta \)), ratio of electron to ion temperature (\(T_{e}/T_{i}\)) and density gradient (\(\varepsilon _{n}\rho _{i}\)) on the growth of EIC waves in the inner magnetosphere of Saturn has been studied and analyzed. The mathematical formulation for dispersion relation and growth rate has been done by using the method of characteristic solution and kinetic approach. This theoretical analysis has been done taking the data from the Cassini in the inner magnetosphere of Saturn in the extended region where ion cyclotron waves have been observed. The change in the growth of these waves due to the presence of Enceladus has been analyzed.  相似文献   

20.
Pulsation period changes in Mira type variables are investigated using the stellar evolution and nonlinear stellar pulsation calculations. We considered the evolutionary sequence of stellar models with initial mass \({M_{ZAMS}} = \;3{M_ \odot }\) and population I composition. Pulsations of stars in the early stage of the asymptotic giant branch are shown to be due to instability of the fundamental mode. In the later stage of evolution when the helium shell source becomes thermally unstable the stellar oscillations occur in either the fundamental mode (for the stellar luminosuty \(L < 5.4 \times {10^3}{L_ \odot }\)) or the first overtone (\(L > 7 \times {10^3}{L_ \odot }\)). Excitation of pulsations is due to the κ-mechanism in the hydrogen ionization zone. Stars with intermediate luminosities \(5.4 \times {10^3}{L_ \odot } < L < 7 \times {10^3}{L_ \odot }\) were found to be stable against radial oscillations. The pulsation period was determined as a function of evolutionary time and period change rates \(\dot \Pi \) were evaluated for the first ten helium flashes. The period change rate becomes the largest in absolute value \((\dot \Pi /\Pi \approx - {10^{ - 2}}y{r^{ - 1}})\) between the helium flash and the maximum of the stellar luminosity. Period changes with rate \(\left| {\dot \Pi /\Pi } \right| \geqslant - {10^{ - 3}}y{r^{ - 1}}\) take place during ≈500 yr, that is nearly one hundredth of the interval between helium flashes.  相似文献   

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