Asteroseismology Of Red Giant Branch Stars In Clusters

Asteroseismology is a powerful tool and method to directly obtain diferentkinds of detailed information about the stellar internal structure and status andthe evolutionary state of stars. It is through the propagation of mechanical wavesin the stellar interior to detect and research the internal structure and status ofstars. The propagation of waves in stellar internal will leads to stars alternatelyexpansion and contraction and further to the change of stellar lightness and theirradial velocities along with time. From the light curve or the radial velocitycurve, the stellar oscillation information, which are dominated by the stellarinternal structure and status, including oscillation frequencies and amplitudes,can be obtained. These oscillation information (oscillation parameters) can beused to determine the stellar fundamental parameters, such as stellar mass M,radius R, age τ, surface gravity g, and mean density ρˉ.Thanks to the space-based observations from instruments, such as WIRE,MOST, CoRoT, and Kepler, more and more stars with solar-like oscillations havebeen observed with an observational mode of high precision and uninterruptedphotometric. This has opened a new research area in which it is possible to studylarge samples of stars which have same properties in certain aspect, i.e., so-calledensemble asteroseismology.Stars in a cluster are usually thought to be formed coevally from the sameinterstellar cloud of gas and dust. They are therefore expected to have manycommon properties which did not exist in ordinary feld stars, such as the samechemical compositions, ages, distances. These common properties strengthen ourability to constrain the theoretical models and/or to determine the cluster fun-damental parameters, such as cluster distance, age, and metallicity. In addition,the stars of diferent masses staying at diferent evolutionary phase, thus all ofthe stars in a cluster compose a completed evolutionary series. Cluster stars aretherefore used to test the theory of stellar evolution. So, we can combine thetheory of stellar structure and evolution with asteroseismology to study cluster stars. These mentioned properties in the above make cluster stars to be of aspecial natural sample.In the present thesis, combining the asteroseismology, the theory of stellarstructure and evolution, and the theory of stellar photometric observations, weobtain a series of new relations. These new relations can be used to interpretthe observational phenomenons which are the correlations between the large fre-quency separations and the frequency of maximum oscillation power and betweenapparent magnitudes and large frequency separations. At the same time, basedon these new relations and combining the common properties of cluster, throughanalyzing the red giant stars of cluster NGC6791and NGC6819, which are ob-served by Kepler, with the method of ensemble asteroseismology, we determinethe cluster fundamental parameters, including their metallicities, distance mod-uli, and RGB masses. In addition, we estimate the interstellar extinctions of thetwo clusters’ stars with asteroseismology.Based on a relation for stars on the Hayashi track (√Tef～gpRq), we obtaina similar relation on the red giant branch respect to stellar efective temperatureTef, mass M, radius R, and metallicity Z from the theory of stellar structure andevolution. Combining the new efective temperature relation with the solar-likeoscillations, we derive a series of new relations respect on ν, νmax, Z, M, R,and g. Based on these new relations, we obtain the following conclusions:Our method provides direct observational evidence to confrm the theoreti-cal argument that the masses of RGB stars in a cluster are the same withintheir uncertainty.The stellar mass M, radius R, and surface gravity g of RGB stars canbe precisely determined from oscillation parameters (large frequency sep-arations ν and the frequency of maximum oscillation power νmax) andnon-oscillation parameter (metallicity Z). Their uncertainties are mainlyfrom the oscillation parameters. In these new relations, mass M, radius R,and surface gravity g are slightly dependent on the metallicity. ·The the relation among△v, vmax, Z, and M can be used to interpret the relation△v=αvmaxβ, which is derived from fitting; observational parameters△v and vmax, and its parameters α and β. The parameter a is dependent on mass M and metallicity Z, i.e., it can be expressed as α(M,Z). The parameter β is a constant.· Based on the new relation△v-vmax, regarding all stars in a cluster as one entity and analyzing them, finally, we derive the clusters metallicities and their RGB masses in asef-consistent way from large frequency separations△v and the frequency of maximum oscillation power vmax, with a lower intrinsic uncertainties.Combining the new effective temperature relation with the solar-like oscilla-tions and the theory of stellar photometric observations, we obtain a new relation respect on the apparent magnitude V, bolometric correction BC, large frequen-cy separation△v, the frequency of maximum oscillation power vmax, distance modulus (m-M)0, and metallicity Z. Based on the new relation, analyzing the RGB stars of NGC6791and NGC6819, we obtain the following conclusions:· The new relation can be used to interpret the correlation between the appar-ent magnitude and large frequency separation, and the different dispersion of correlation between the different bands.· Through regarding all stars in a cluster as one entity and analyzing them, we determine cluster distance modulus of NGC6791and NGC6819, re-spectively.· From the analysis of new relation, we find that the distance modulus is slightly dependent on the metallicity. A change of0.1dex in the metallicity [Fe/H] will lead to a change of about0.06mag in distance modulus.· In addition, the new method presented here could be used as a discrimina-tion tool to determine the membership of cluster stars. Based on the obtained relation V ν in the above, we determine theinterstellar extinctions of cluster stars in NGC6791and NGC6819from largefrequency separations ν and the frequency of maximum oscillation power νmax.Through the deal with of Gaussian smoothing interpolation, we establish a2-Dgrid table along with the right ascension and declination. In the viewing feld ofNGC6791and NGC6819, the interstellar extinction of star can be estimatedfrom the2-D grid table by interpolating.