arXiv subjects

D. O. Gough

Publications and source records attributed to D. O. Gough.

27 records · Page 2Linked to original sources

arXiv2007

Temporal Variations in the Sun's Rotational Kinetic Energy

AIM: To study the variation of the angular momentum and the rotational kinetic energy of the Sun, and associated variations in the gravitational multipole moments, on a timescale of the solar cycle. METHOD: Inverting helioseismic rotational splitting data obtained by the Global Oscillation Network Group and by the Michelson Doppler Imager on the Solar and Heliospheric Observatory. RESULTS: The temporal variation in angular momentum and kinetic energy at high latitudes (>π/4) through the convection zone is positively correlated with solar activity, whereas at low latitudes it is anticorrelated, except for the top 10% by radius where both are correlated positively. CONCLUSION: The helioseismic data imply significant temporal variation in the angular momentum and the rotational kinetic energy, and in the gravitational multipole moments. The properties of that variation will help constrain dynamical theories of the solar cycle.

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arXiv2007

On the seismic age of the Sun

We use low-degree acoustic modes obtained by the BiSON to estimate the main-sequence age $t_\odot$ of the Sun. The calibration is accomplished by linearizing the deviations from a standard solar model the seismic frequencies of which are close to those of the Sun. Formally, we obtain the preliminary value $t_\odot=4.68\pm0.02 $Gy, coupled with an initial heavy-element abundance $Z=0.0169\pm0.0005$. The quoted standard errors, which are not independent, are upper bounds implied under the assumption that the standard errors in the observed frequencies are independent.

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arXiv2007

An Elementary Introduction to the JWKB Approximation

Asymptotic expansion of the second-order linear ordinary differential equation Psi'' + k^2 f(z) Psi = 0, in which the real constant k is large and f = O(1), can be carried out in the manner of Liouville and Green provided f does not vanish. If f does vanish, however, at z_0 say, then Liouville-Green expansions can be carried out either side of the turning point z = z_0, but it is then necessary to ascertain how to connect them. This was first accomplished by Jeffreys, by a comparison of the differential equation with Airy's equation. Soon afterwards, the situation was found to arise in quantum mechanics, and was discussed by Brillouin, Wentzel and Kramers, after whom the method was initially named. It arises throughout classical physics too, and is encountered frequently when studying waves propagating in stars. This brief introduction is aimed at clarifying the principles behind the method, and is illustrated by considering the resonant acoustic-gravity oscillations (normal modes) of a spherical star.

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arXiv2006

On seismic signatures of rapid variation

We present an improved model for an asteroseismic diagnostic contained in the frequency spacing of low-degree acoustic modes. By modelling in a realistic manner regions of rapid variation of dynamically relevant quantities, which we call acoustic glitches, we can derive signatures of the gross properties of those glitches. In particular, we are interested in measuring properties that are related to the helium ionization zones and to the rapid variation in the background state associated with the lower boundary of the convective envelope. The formula for the seismic diagnostic is tested against a sequence of theoretical models of the Sun, and is compared with seismic diagnostics published previously by Monteiro & Thompson (1998, 2005) and by Basu et al. (2004).

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arXiv2006

An asteroseismic signature of helium ionization

We investigate the influence of the ionization of helium on the low-degree acoustic oscillation frequencies in model solar-type stars. The signature in the oscillation frequencies characterizing the ionization-induced depression of the first adiabatic exponent $γ$ is a superposition of two decaying periodic functions of frequency $ν$, with `frequencies' that are approximately twice the acoustic depths of the centres of the Helium I and Helium II ionization regions. That variation is probably best exhibited in the second frequency difference $Δ_2ν_{n,l}\equivν_{n-1,l}-2ν{n,l}+ν_{n+1,l}$. We show how an analytic approximation to the variation of $γ$ leads to a simple representation of this oscillatory contribution to $Δ_2ν$ which can be used to characterize the $γ$ variation, our intention being to use it as a seismic diagnostic of the helium abundance of the star. We emphasize that the objective is to characterize $γ$, not merely to find a formula for $Δ_2ν$ that reproduces the data.

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arXiv2001

Oscillations of alpha UMa and other red giants

There is growing observational evidence that the variability of red giants could be caused by excitation of global modes of oscillation. The most recent evidence of such oscillations was reported for alpha UMa by Buzasi et al.(2000). We address the problem of radial and nonradial mode excitation in red giants from the theoretical point of view. In particular, we present the results of numerical computations of oscillation properties of a model of alpha UMa and of several models of a 2M_sun star in the red-giant phase. In the red giant stars by far most of the nonradial modes are confined to to the deep interior, where they have the g-mode character. Only modes at resonant frequencies of the p-mode cavity have substantial amplitudes in the outer layers. We have shown that such modes can be unstable with the linear growth rates similar to those of corresponding to radial modes. We have been unable to explain the observed oscillation properties of alpha UMa, either in terms of mode instability or in terms of stochastic excitation by turbulent convection. Modes at the lowest frequencies, which exhibit the largest amplitudes and may correspond to the first three radial modes, are found stable if all effects of convection are taken into account. The observed frequency dependence of amplitudes does not agree with what one expects from stochastic excitation. The predicted fundamental mode amplitude is by about two orders of magnitude smaller than those of high frequency modes, which is in stark disagreement with the observations.

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arXiv1999

Amplitudes of stochastically excited oscillations in main-sequence stars

We present estimates of the amplitudes of intrinsically stable stochastically excited radial oscillations in stars near the main sequence. The amplitudes are determined by the balance between acoustical energy generation by turbulent convection (the Lighthill mechanism) and linear damping. Convection is treated with a time-dependent, nonlocal, mixing-length model, which includes both convective heat flux and turbulent pressure in both the equilibrium model and the pulsations. Velocity and luminosity amplitudes are computed for stars with masses between 0.9 M_\sun and 2.0 M_\sun in the vicinity of the main sequence, for various metallicities and convection parameters. As in previous studies, the amplitudes are found to increase with stellar mass, and therefore with luminosity. Amongst those stars that are pulsationally stable, the largest amplitudes are predicted for a 1.6 M_\sun model of spectral type F2; the values are approximately 15 times larger than those measured in the Sun.

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arXiv1998

On Solar Frequency Changes

The structure of the surface layers of the Sun is changed by magnetic activity which, in turn, changes the eigenfrequencies of the acoustic modes. These frequency shifts have been observed both in low- and high-degree data, and are found to be correlated with the solar cycle. Time-distance helioseismology has shown that waves travelling through sunspots suffer time delays. Also it is known that sunspots induce phase shifts between inwardly and outwardly propagating waves. In the present work we show how these phase shifts are related to the observed time delays by treating the scattering of acoustic waves off sunspots as a diffraction problem. These time delays are then related to the frequency shifts of the modes. From this relation we obtain a lower limit for the contribution of sunspots to the observed frequency variations with the solar cycle. Moreover, we predict the frequency dependence of the time delays suffered by rays travelling through a sunspot.

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arXiv1997

On electrostatic screening of ions in astrophysical plasmas

There has been some controversy over the expression for the so-called `interaction energy' due to screening of charged particles in a plasma. Even in the relatively simple case of weak screening, first discussed in the context of astrophysical plasmas by Salpeter (1954), there is disagreement. In particular, Shaviv and Shaviv (1996) have claimed recently that by not considering explicitly in his calculation the complete screening cloud, Salpeter obtained a result for the interaction energy between two nuclei separated by a distance $r$ which in the limit $r \to 0$ is only 2/3 the correct value. It appears that this claim has arisen from a fundamental misconception concerning the dynamics of the interaction. We rectify this misconception, and show that Salpeter's formula is indeed correct.

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