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Register a new userFrequency ratio method for seismic modeling of Gamma Doradus stars
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A method for obtaining asteroseismological information of a Gamma Doradus oscillating star showing at least three pulsation frequencies is presented. This method is based on a first-order asymptotic g-mode expression, in agreement with the internal structure of Gamma Doradus stars. The information obtained is twofold: 1) a possible identification of the radial order n and degree l of observed frequencies (assuming that these have the same l), and 2) an estimate of the integral of the buoyancy frequency (Brunt-Vaisala) weighted over the stellar radius along the radiative zone. The accuracy of the method as well as its theoretical consistency are also discussed for a typical Gamma Doradus stellar model. Finally, the frequency ratios method has been tested with observed frequencies of the Gamma Doradus star HD 12901. The number of representative models verifying the complete set of constraints (the location in the HR diagram, the Brunt-Vaisala frequency integral, the observed metallicity and frequencies and a reliable identification of n and l) is drastically reduced to six.
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Context. gamma Doradus (gamma Dor) are late A and F-type stars pulsating with high order gravity modes (g-modes). The existence of different evolutionary phases crossing the gamma Dor instability strip raises the question of the existence of pre-main sequence (PMS) gamma Dor stars. Aims. We intend to study the differences between the asteroseismic behaviour of PMS and main sequence (MS) gamma Dor pulsators as it is predicted by the current theory of stellar evolution and stability. Methods. We explore the adiabatic and non-adiabatic properties of high order g-modes in a grid of PMS and MS models covering the mass range 1.2 Msun < Mstar < 2.5 Msun. Results. We derive the theoretical instability strip (IS) for the PMS gamma Dor pulsators. This IS covers the same effective temperature range as the MS gamma Dor one. Nevertheless, the frequency domain of unstable modes in PMS models with a fully radiative core is larger than in MS models, even if they present the same number of unstable modes. Moreover, the differences between MS and PMS internal structures are reflected on the average values of the period spacing as well as on the dependence of the period spacing on the radial order of the modes, opening the window to the determination of the evolutionary phase of gamma Dor stars from their pulsation spectra.
We present a spectroscopic survey of known and candidate $gamma$,Doradus stars. The high-resolution, high signal-to-noise spectra of 52 objects were collected by five different spectrographs. The spectral classification, atmospheric parameters (teff, $log g$, $xi$), $vsin i$ and chemical composition of the stars were derived. The stellar spectral and luminosity classes were found between G0-A7 and IV-V, respectively. The initial values for teff and logg were determined from the photometric indices and spectral energy distribution. Those parameters were improved by the analysis of hydrogen lines. The final values of teff, logg and $xi$ were derived from the iron lines analysis. The teff values were found between 6000,K and 7900,K, while logg,values range from 3.8 to 4.5,dex. Chemical abundances and $vsin i$ values were derived by the spectrum synthesis method. The $vsin i$ values were found between 5 and 240,km,s$^{-1}$. The chemical abundance pattern of $gamma$,Doradus stars were compared with the pattern of non-pulsating stars. It turned out that there is no significant difference in abundance patterns between these two groups. Additionally, the relations between the atmospheric parameters and the pulsation quantities were checked. A strong correlation between the $vsin i$ and the pulsation periods of $gamma$,Doradus variables was obtained. The accurate positions of the analysed stars in the H-R diagram have been shown. Most of our objects are located inside or close to the blue edge of the theoretical instability strip of $gamma$,Doradus.
The hot $gamma$~Doradus stars have multiple low frequencies characteristic of $gamma$~Dor or SPB variables, but are located between the red edge of the SPB and the blue edge of the $gamma$~Dor instability strips where all low-frequency modes are stable in current models of these stars. Though $delta$~Sct stars also have low frequencies, there is no sign of high frequencies in hot $gamma$~Dor stars. We obtained spectra to refine the locations of some of these stars in the H-R diagram and conclude that these are, indeed, anomalous pulsating stars. The Maia variables have multiple high frequencies characteristic of $beta$~Cep and $delta$~Sct stars, but lie between the red edge of the $beta$~Cep and the blue edge of the $delta$~Sct instability strips. We compile a list of all Maia candidates and obtain spectra of two of these stars. Again, it seems likely that these are anomalous pulsating stars which are currently not understood.
We report on observational results obtained for 78 objects originally classified as bona-fide or candidate gamma Doradus stars. For the southern objects, we gathered echelle spectra with the CORALIE spectrograph attached to the Euler telescope in 1998-2003 and/or Johnson-Cousins B,V,Ic observations with the MODULAR photometer attached to the 0.5-m SAAO telescope in 1999-2000. For the northern objects, we obtained Geneva U,B,B1,B2,V,V1,G observations with the P7 photometer attached to the 1.2-m MERCATOR telescope in 2001-2004. At least 15 of our objects are binaries, of which 7 are new. For 6 binaries, we determined the orbit for the first time. At least 17 objects show profile variations and at least 12 objects are multiperiodic photometric variables. Our results allow us to upgrade 11 objects to bona-fide gamma Doradus stars and to downgrade 8 objects to constant up to the current detection limits. Mode identification is still ongoing, but so far, only l = 1 and 2 modes have been identified.
Seismic inverse modeling is a common method in reservoir prediction and it plays a vital role in the exploration and development of oil and gas. Conventional seismic inversion method is difficult to combine with complicated and abstract knowledge on geological mode and its uncertainty is difficult to be assessed. The paper proposes an inversion modeling method based on GAN consistent with geology, well logs, seismic data. GAN is a the most promising generation model algorithm that extracts spatial structure and abstract features of training images. The trained GAN can reproduce the models with specific mode. In our test, 1000 models were generated in 1 second. Based on the trained GAN after assessment, the optimal result of models can be calculated through Bayesian inversion frame. Results show that inversion models conform to observation data and have a low uncertainty under the premise of fast generation. This seismic inverse modeling method increases the efficiency and quality of inversion iteration. It is worthy of studying and applying in fusion of seismic data and geological knowledge.
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