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### C. Kayhan – One of the best experts on this subject based on the ideXlab platform.

• ##### fundamental properties of kepler and corot targets iii tuning scaling relations using the first AdiabaticExponent
Monthly Notices of the Royal Astronomical Society, 2016
Co-Authors: Mutlu Yildiz, Celik Z Orhan, C. Kayhan

Abstract:

So called scaling relations have the potential to reveal the mass and radius of solar-like oscillating stars, based on oscillation frequencies. In derivation of these relations, it is assumed that the first Adiabatic Exponent at the surface (Gamma_1s) of such stars is constant. However, by constructing interior models for the mass range 0.8-1.6 Msun, we show that Gamma_1s is not constant at stellar surfaces for the effective temperature range with which we deal. Furthermore, the well-known relation between large separation and mean density also depends on Gamma_1s. Such knowledge is the basis for our aim of modifying scaling relations. There are significant differences between masses and radii found from modified and conventional scaling relations. However, comparison of predictions of these relations with the non-asteroseismic observations of Procyon A reveals that new scaling relations are effective in determining the mass and radius of stars. In the present study, solar-like oscillation frequencies of 89 target stars (mostly Kepler and CoRoT) were analysed. As well as two new reference frequencies (nu_min1 and nu_min2) found in the spacing of solar-like oscillation frequencies of stellar interior models, we also take into account nu_min0. In addition to the frequency of maximum amplitude, these frequencies have very strong diagnostic potential for determination of fundamental properties. The present study involves the application of derived relations from the models to the solar-like oscillating stars, and computes their effective temperatures using purely asteroseismic methods. There are in general very close agreements between effective temperatures from asteroseismic and non-asteroseismic (spectral and photometric) methods. For the Sun and Procyon A, for example, the agreement is almost total.

• ##### Fundamental properties of Kepler and CoRoT targets – III. Tuning scaling relations using the first AdiabaticExponent
Monthly Notices of the Royal Astronomical Society, 2016
Co-Authors: Mutlu Yildiz, Z. Çelik Orhan, C. Kayhan

Abstract:

So called scaling relations have the potential to reveal the mass and radius of solar-like oscillating stars, based on oscillation frequencies. In derivation of these relations, it is assumed that the first Adiabatic Exponent at the surface (Gamma_1s) of such stars is constant. However, by constructing interior models for the mass range 0.8-1.6 Msun, we show that Gamma_1s is not constant at stellar surfaces for the effective temperature range with which we deal. Furthermore, the well-known relation between large separation and mean density also depends on Gamma_1s. Such knowledge is the basis for our aim of modifying scaling relations. There are significant differences between masses and radii found from modified and conventional scaling relations. However, comparison of predictions of these relations with the non-asteroseismic observations of Procyon A reveals that new scaling relations are effective in determining the mass and radius of stars. In the present study, solar-like oscillation frequencies of 89 target stars (mostly Kepler and CoRoT) were analysed. As well as two new reference frequencies (nu_min1 and nu_min2) found in the spacing of solar-like oscillation frequencies of stellar interior models, we also take into account nu_min0. In addition to the frequency of maximum amplitude, these frequencies have very strong diagnostic potential for determination of fundamental properties. The present study involves the application of derived relations from the models to the solar-like oscillating stars, and computes their effective temperatures using purely asteroseismic methods. There are in general very close agreements between effective temperatures from asteroseismic and non-asteroseismic (spectral and photometric) methods. For the Sun and Procyon A, for example, the agreement is almost total.

### Mutlu Yildiz – One of the best experts on this subject based on the ideXlab platform.

• ##### fundamental properties of kepler and corot targets iii tuning scaling relations using the first AdiabaticExponent
Monthly Notices of the Royal Astronomical Society, 2016
Co-Authors: Mutlu Yildiz, Celik Z Orhan, C. Kayhan

Abstract:

So called scaling relations have the potential to reveal the mass and radius of solar-like oscillating stars, based on oscillation frequencies. In derivation of these relations, it is assumed that the first Adiabatic Exponent at the surface (Gamma_1s) of such stars is constant. However, by constructing interior models for the mass range 0.8-1.6 Msun, we show that Gamma_1s is not constant at stellar surfaces for the effective temperature range with which we deal. Furthermore, the well-known relation between large separation and mean density also depends on Gamma_1s. Such knowledge is the basis for our aim of modifying scaling relations. There are significant differences between masses and radii found from modified and conventional scaling relations. However, comparison of predictions of these relations with the non-asteroseismic observations of Procyon A reveals that new scaling relations are effective in determining the mass and radius of stars. In the present study, solar-like oscillation frequencies of 89 target stars (mostly Kepler and CoRoT) were analysed. As well as two new reference frequencies (nu_min1 and nu_min2) found in the spacing of solar-like oscillation frequencies of stellar interior models, we also take into account nu_min0. In addition to the frequency of maximum amplitude, these frequencies have very strong diagnostic potential for determination of fundamental properties. The present study involves the application of derived relations from the models to the solar-like oscillating stars, and computes their effective temperatures using purely asteroseismic methods. There are in general very close agreements between effective temperatures from asteroseismic and non-asteroseismic (spectral and photometric) methods. For the Sun and Procyon A, for example, the agreement is almost total.

• ##### Fundamental properties of Kepler and CoRoT targets – III. Tuning scaling relations using the first AdiabaticExponent
Monthly Notices of the Royal Astronomical Society, 2016
Co-Authors: Mutlu Yildiz, Z. Çelik Orhan, C. Kayhan

Abstract:

So called scaling relations have the potential to reveal the mass and radius of solar-like oscillating stars, based on oscillation frequencies. In derivation of these relations, it is assumed that the first Adiabatic Exponent at the surface (Gamma_1s) of such stars is constant. However, by constructing interior models for the mass range 0.8-1.6 Msun, we show that Gamma_1s is not constant at stellar surfaces for the effective temperature range with which we deal. Furthermore, the well-known relation between large separation and mean density also depends on Gamma_1s. Such knowledge is the basis for our aim of modifying scaling relations. There are significant differences between masses and radii found from modified and conventional scaling relations. However, comparison of predictions of these relations with the non-asteroseismic observations of Procyon A reveals that new scaling relations are effective in determining the mass and radius of stars. In the present study, solar-like oscillation frequencies of 89 target stars (mostly Kepler and CoRoT) were analysed. As well as two new reference frequencies (nu_min1 and nu_min2) found in the spacing of solar-like oscillation frequencies of stellar interior models, we also take into account nu_min0. In addition to the frequency of maximum amplitude, these frequencies have very strong diagnostic potential for determination of fundamental properties. The present study involves the application of derived relations from the models to the solar-like oscillating stars, and computes their effective temperatures using purely asteroseismic methods. There are in general very close agreements between effective temperatures from asteroseismic and non-asteroseismic (spectral and photometric) methods. For the Sun and Procyon A, for example, the agreement is almost total.

### Juhi Jang – One of the best experts on this subject based on the ideXlab platform.

• ##### Expanding large global solutions of the equations of compressible fluid mechanics
Inventiones mathematicae, 2018

Abstract:

Without any symmetry assumptions on the initial data we construct global-in-time unique solutions to the vacuum free boundary three-dimensional isentropic compressible Euler equations when the Adiabatic Exponent $$\gamma$$ γ lies in the interval $$(1,\frac{5}{3}]$$ ( 1 , 5 3 ] . Our initial data lie sufficiently close to the expanding compactly supported affine motions recently constructed by Sideris and they satisfy the physical vacuum boundary condition.

• ##### Instability theory of the Navier–Stokes–Poisson equations
Analysis & PDE, 2013
Co-Authors: Juhi Jang, Ian Tice

Abstract:

The stability question of the Lane‐Emden stationary gaseous star configurations is an interesting problem arising in astrophysics. We establish both linear and nonlinear dynamical instability results for the Lane‐Emden solutions in the framework of the Navier‐Stokes‐Poisson system with Adiabatic Exponent 6 5 < < 4 3 .

• ##### Instability theory of the Navier-Stokes-Poisson equations
arXiv: Analysis of PDEs, 2011
Co-Authors: Juhi Jang, Ian Tice

Abstract:

The stability question of the Lane-Emden stationary gaseous star configurations is an interesting problem arising in astrophysics. We establish both linear and nonlinear dynamical instability results for the Lane-Emden solutions in the framework of the Navier-Stokes-Poisson system with Adiabatic Exponent $6/5 < \gamma < 4/3$.