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Title: Energy loss of solar p modes due to the excitation of magnetic sausage tube waves: Importance of coupling the upper atmosphere

Abstract

We consider damping and absorption of solar p modes due to their energy loss to magnetic tube waves that can freely carry energy out of the acoustic cavity. The coupling of p modes and sausage tube waves is studied in a model atmosphere composed of a polytropic interior above which lies an isothermal upper atmosphere. The sausage tube waves, excited by p modes, propagate along a magnetic fibril which is assumed to be a vertically aligned, stratified, thin magnetic flux tube. The deficit of p-mode energy is quantified through the damping rate, Γ, and absorption coefficient, α. The variation of Γ and α as a function of frequency and the tube's plasma properties is studied in detail. Previous similar studies have considered only a subphotospheric layer, modeled as a polytrope that has been truncated at the photosphere. Such studies have found that the resulting energy loss by the p modes is very sensitive to the upper boundary condition, which, due to the lack of an upper atmosphere, have been imposed in a somewhat ad hoc manner. The model presented here avoids such problems by using an isothermal layer to model the overlying atmosphere (chromosphere, and, consequently, allows us to analyzemore » the propagation of p-mode-driven sausage waves above the photosphere. In this paper, we restrict our attention to frequencies below the acoustic cut off frequency. We demonstrate the importance of coupling all waves (acoustic, magnetic) in the subsurface solar atmosphere with the overlying atmosphere in order to accurately model the interaction of solar f and p modes with sausage tube waves. In calculating the absorption and damping of p modes, we find that for low frequencies, below ≈3.5 mHz, the isothermal atmosphere, for the two-region model, behaves like a stress-free boundary condition applied at the interface (z = –z{sub 0}).« less

Authors:
;  [1];  [2]
  1. Applied Mathematics Department, University of Sheffield, Sheffield S3 7RH (United Kingdom)
  2. JILA and Department of Astrophysical and Planetary Sciences, University of Colorado at Boulder, Boulder, CO 80309-0440 (United States)
Publication Date:
OSTI Identifier:
22365724
Resource Type:
Journal Article
Resource Relation:
Journal Name: Astrophysical Journal; Journal Volume: 789; Journal Issue: 2; Other Information: Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; ABSORPTION; BOUNDARY CONDITIONS; CHROMOSPHERE; COUPLING; ENERGY LOSSES; EXCITATION; FREQUENCY DEPENDENCE; LAYERS; MAGNETIC FIELDS; MAGNETIC FLUX; MAGNETOHYDRODYNAMICS; MHZ RANGE; OSCILLATIONS; PHOTOSPHERE; PLASMA; SUN

Citation Formats

Gascoyne, A., Jain, R., and Hindman, B. W., E-mail: a.d.gascoyne@sheffield.ac.uk, E-mail: r.jain@sheffield.ac.uk. Energy loss of solar p modes due to the excitation of magnetic sausage tube waves: Importance of coupling the upper atmosphere. United States: N. p., 2014. Web. doi:10.1088/0004-637X/789/2/109.
Gascoyne, A., Jain, R., & Hindman, B. W., E-mail: a.d.gascoyne@sheffield.ac.uk, E-mail: r.jain@sheffield.ac.uk. Energy loss of solar p modes due to the excitation of magnetic sausage tube waves: Importance of coupling the upper atmosphere. United States. doi:10.1088/0004-637X/789/2/109.
Gascoyne, A., Jain, R., and Hindman, B. W., E-mail: a.d.gascoyne@sheffield.ac.uk, E-mail: r.jain@sheffield.ac.uk. Thu . "Energy loss of solar p modes due to the excitation of magnetic sausage tube waves: Importance of coupling the upper atmosphere". United States. doi:10.1088/0004-637X/789/2/109.
@article{osti_22365724,
title = {Energy loss of solar p modes due to the excitation of magnetic sausage tube waves: Importance of coupling the upper atmosphere},
author = {Gascoyne, A. and Jain, R. and Hindman, B. W., E-mail: a.d.gascoyne@sheffield.ac.uk, E-mail: r.jain@sheffield.ac.uk},
abstractNote = {We consider damping and absorption of solar p modes due to their energy loss to magnetic tube waves that can freely carry energy out of the acoustic cavity. The coupling of p modes and sausage tube waves is studied in a model atmosphere composed of a polytropic interior above which lies an isothermal upper atmosphere. The sausage tube waves, excited by p modes, propagate along a magnetic fibril which is assumed to be a vertically aligned, stratified, thin magnetic flux tube. The deficit of p-mode energy is quantified through the damping rate, Γ, and absorption coefficient, α. The variation of Γ and α as a function of frequency and the tube's plasma properties is studied in detail. Previous similar studies have considered only a subphotospheric layer, modeled as a polytrope that has been truncated at the photosphere. Such studies have found that the resulting energy loss by the p modes is very sensitive to the upper boundary condition, which, due to the lack of an upper atmosphere, have been imposed in a somewhat ad hoc manner. The model presented here avoids such problems by using an isothermal layer to model the overlying atmosphere (chromosphere, and, consequently, allows us to analyze the propagation of p-mode-driven sausage waves above the photosphere. In this paper, we restrict our attention to frequencies below the acoustic cut off frequency. We demonstrate the importance of coupling all waves (acoustic, magnetic) in the subsurface solar atmosphere with the overlying atmosphere in order to accurately model the interaction of solar f and p modes with sausage tube waves. In calculating the absorption and damping of p modes, we find that for low frequencies, below ≈3.5 mHz, the isothermal atmosphere, for the two-region model, behaves like a stress-free boundary condition applied at the interface (z = –z{sub 0}).},
doi = {10.1088/0004-637X/789/2/109},
journal = {Astrophysical Journal},
number = 2,
volume = 789,
place = {United States},
year = {Thu Jul 10 00:00:00 EDT 2014},
month = {Thu Jul 10 00:00:00 EDT 2014}
}
  • The dissipation depths of Alfven and sound waves in the magnetic structure of the solar chromosphere and corona are obtained with allowance for the decay process and nonlinear phase advance in Alfven and sound waves. In the calculations it was assumed that energy balance occurs in each volume element: The amount of wave energy epsilon/sub dis/ dissipated here is equal to the emission power epsilon/sub emis/. The calculations were made for three mechanisms of losses to emission, namely, in accordance with a) a given population of the second level, b) a Boltzmann distribution by levels, and c) emission at highmore » temperatures in accordance with the results of (D. P. Cox and W. H. Tucker, Astrophys. J. 157, 1157 (1969)). The depths are given in Table I. Sound waves dissipate rapidly both in the chromosphere and in the corona. Under certain conditions, which can be estimated from Eqs. (17) -(19), taking phi/..pi.. and ..mu.. on the order of unity there, Alfven waves penetrate to greater heights, and at the same time the dissipation of these waves in magnetic tubes is still sufficient for the heating.« less
  • A weakly nonlinear fluid wave propagating within a star can be unstable to three-wave interactions. The resonant parametric instability is a well-known form of three-wave interaction in which a primary wave of frequency ω {sub a} excites a pair of secondary waves of frequency ω {sub b} + ω {sub c} ≅ ω {sub a}. Here we consider a nonresonant form of three-wave interaction in which a low-frequency primary wave excites a high-frequency p-mode and a low-frequency g-mode such that ω {sub b} + ω {sub c} >> ω {sub a}. We show that a p-mode can couple so stronglymore » to a g-mode of similar radial wavelength that this type of nonresonant interaction is unstable even if the primary wave amplitude is small. As an application, we analyze the stability of the tide in coalescing neutron star binaries to p-g mode coupling. We find that the equilibrium tide and dynamical tide are both p-g unstable at gravitational wave frequencies f {sub gw} ≳ 20 Hz and drive short wavelength p-g mode pairs to significant energies on very short timescales (much less than the orbital decay time due to gravitational radiation). Resonant parametric coupling to the tide is, by contrast, either stable or drives modes at a much smaller rate. We do not solve for the saturation of the p-g instability and therefore we cannot say precisely how it influences the evolution of neutron star binaries. However, we show that if even a single daughter mode saturates near its wave breaking amplitude, the p-g instability of the equilibrium tide will (1) induce significant orbital phase errors (Δφ ≳ 1 radian) that accumulate primarily at low frequencies (f {sub gw} ≲ 50 Hz) and (2) heat the neutron star core to a temperature of T ∼ 10{sup 10} K. Since there are at least ∼100 unstable p-g daughter pairs, Δφ and T are potentially much larger than these values. Tides might therefore significantly influence the gravitational wave signal and electromagnetic emission from coalescing neutron star binaries at much larger orbital separations than previously thought.« less
  • In the applications of solar magneto-seismology, the ratio of the period of the fundamental mode to twice the period of its first overtone, P{sub 1}/2P{sub 2}, plays an important role. We examine how field-aligned flows affect the dispersion properties, and hence the period ratios, of standing modes supported by magnetic slabs in the solar atmosphere. We numerically solve the dispersion relations and devise a graphic means to construct standing modes. For coronal slabs, we find that the flow effects are significant for the fast kink and sausage modes alike. For the kink ones, they may reduce P{sub 1}/2P{sub 2} bymore » up to 23% compared with the static case, and the minimum allowed P{sub 1}/2P{sub 2} can fall below the lower limit analytically derived for static slabs. For the sausage modes, while introducing the flow reduces P{sub 1}/2P{sub 2} by typically {approx}< 5% relative to the static case, it significantly increases the threshold aspect ratio only above which standing sausage modes can be supported, meaning that their detectability is restricted to even wider slabs. In the case of photospheric slabs, the flow effect is not as strong. However, standing modes are distinct from the coronal case in that standing kink modes show a P{sub 1}/2P{sub 2} that deviates from unity even for a zero-width slab, while standing sausage modes no longer suffer from a threshold aspect ratio. We conclude that transverse structuring in plasma density and flow speed should be considered in seismological applications of multiple periodicities to solar atmospheric structures.« less
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