<p>This study explores the dispersion properties of slow magnetoacoustic (MA) waves in solar coronal loops, emphasizing the combined effects of thermal conduction, thermal misbalance, and waveguide geometry to refine coronal seismological techniques. We analyzed the dispersion relations derived under infinite magnetic field and thin flux tube approximations, introducing characteristic timescales (<InlineEquation ID="IEq1"> <EquationSource Format="MATHML"><math> <msub> <mi>P</mi> <mi mathvariant="normal">cond</mi> </msub> </math></EquationSource> <EquationSource Format="TEX">$P_{\mathrm{cond}}$</EquationSource> </InlineEquation> for conduction-induced transition to isothermal sound speed, <InlineEquation ID="IEq2"> <EquationSource Format="MATHML"><math> <msub> <mi>P</mi> <mi mathvariant="normal">mis</mi> </msub> </math></EquationSource> <EquationSource Format="TEX">$P_{\mathrm{mis}}$</EquationSource> </InlineEquation> for misbalance effects, and <InlineEquation ID="IEq3"> <EquationSource Format="MATHML"><math> <msub> <mi>P</mi> <mi mathvariant="normal">gI</mi> </msub> </math></EquationSource> <EquationSource Format="TEX">$P_{\mathrm{gI}}$</EquationSource> </InlineEquation> for isothermal waveguide dispersion). The timescale <InlineEquation ID="IEq4"> <EquationSource Format="MATHML"><math> <msub> <mi>P</mi> <mi mathvariant="normal">cond</mi> </msub> </math></EquationSource> <EquationSource Format="TEX">$P_{\mathrm{cond}}$</EquationSource> </InlineEquation> is determined solely by plasma parameters and is unrelated to the waveguide size. These scales delineate bands where phase velocities approach adiabatic <InlineEquation ID="IEq5"> <EquationSource Format="MATHML"><math> <msub> <mi>c</mi> <mi mathvariant="normal">S</mi> </msub> </math></EquationSource> <EquationSource Format="TEX">$c_{\mathrm{S}}$</EquationSource> </InlineEquation>, isothermal <InlineEquation ID="IEq6"> <EquationSource Format="MATHML"><math> <msub> <mi>c</mi> <mi mathvariant="normal">SI</mi> </msub> </math></EquationSource> <EquationSource Format="TEX">$c_{\mathrm{SI}}$</EquationSource> </InlineEquation>, misbalance-modified <InlineEquation ID="IEq7"> <EquationSource Format="MATHML"><math> <msub> <mi>c</mi> <mi mathvariant="normal">SQ</mi> </msub> </math></EquationSource> <EquationSource Format="TEX">$c_{\mathrm{SQ}}$</EquationSource> </InlineEquation> sound speeds, or corresponding tube speeds <InlineEquation ID="IEq8"> <EquationSource Format="MATHML"><math> <msub> <mi>c</mi> <mi mathvariant="normal">T</mi> </msub> </math></EquationSource> <EquationSource Format="TEX">$c_{\mathrm{T}}$</EquationSource> </InlineEquation>, <InlineEquation ID="IEq9"> <EquationSource Format="MATHML"><math> <msub> <mi>c</mi> <mi mathvariant="normal">TI</mi> </msub> </math></EquationSource> <EquationSource Format="TEX">$c_{\mathrm{TI}}$</EquationSource> </InlineEquation>, <InlineEquation ID="IEq10"> <EquationSource Format="MATHML"><math> <msub> <mi>c</mi> <mi mathvariant="normal">TQ</mi> </msub> </math></EquationSource> <EquationSource Format="TEX">$c_{\mathrm{TQ}}$</EquationSource> </InlineEquation>. Our analysis also reveals that, depending on the ratio <InlineEquation ID="IEq11"> <EquationSource Format="MATHML"><math> <msub> <mi>P</mi> <mi mathvariant="normal">gI</mi> </msub> <mo stretchy="false">/</mo> <msub> <mi>P</mi> <mi mathvariant="normal">cond</mi> </msub> </math></EquationSource> <EquationSource Format="TEX">$P_{\mathrm{gI}} / P_{\mathrm{cond}}$</EquationSource> </InlineEquation>, the behavior of dispersion curves can change qualitatively. The joint influence of waveguide dispersion and dispersion caused by thermal conduction expands the range of influence of the isothermal regime, which can in particular be expressed in the fact that the phase velocity even in the range of periods corresponding to the adiabatic regime may not reach the speed of sound <InlineEquation ID="IEq12"> <EquationSource Format="MATHML"><math> <msub> <mi>c</mi> <mi mathvariant="normal">S</mi> </msub> </math></EquationSource> <EquationSource Format="TEX">$c_{\mathrm{S}}$</EquationSource> </InlineEquation>, and the tube speed <InlineEquation ID="IEq13"> <EquationSource Format="MATHML"><math> <msub> <mi>c</mi> <mi mathvariant="normal">T</mi> </msub> </math></EquationSource> <EquationSource Format="TEX">$c_{\mathrm{T}}$</EquationSource> </InlineEquation> for this band is a better estimate. Applied to observed hot loop oscillations, the model yields magnetic-field strengths of <InlineEquation ID="IEq14"> <EquationSource Format="MATHML"><math> <mo>∼</mo> <mn>10</mn> <mspace width="0.3em" /> <mi mathvariant="normal">G</mi> </math></EquationSource> <EquationSource Format="TEX">$\sim 10~\mathrm{G}$</EquationSource> </InlineEquation>, matching observed periods and damping times more accurately than adiabatic estimates alone.</p>

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Diagnosing Coronal Magnetic Fields with Slow Magnetoacoustic Waves: The Role of Isothermal Speeds

  • Dmitrii Zavershinskii,
  • Daria Agapova

摘要

This study explores the dispersion properties of slow magnetoacoustic (MA) waves in solar coronal loops, emphasizing the combined effects of thermal conduction, thermal misbalance, and waveguide geometry to refine coronal seismological techniques. We analyzed the dispersion relations derived under infinite magnetic field and thin flux tube approximations, introducing characteristic timescales ( P cond $P_{\mathrm{cond}}$ for conduction-induced transition to isothermal sound speed, P mis $P_{\mathrm{mis}}$ for misbalance effects, and P gI $P_{\mathrm{gI}}$ for isothermal waveguide dispersion). The timescale P cond $P_{\mathrm{cond}}$ is determined solely by plasma parameters and is unrelated to the waveguide size. These scales delineate bands where phase velocities approach adiabatic c S $c_{\mathrm{S}}$ , isothermal c SI $c_{\mathrm{SI}}$ , misbalance-modified c SQ $c_{\mathrm{SQ}}$ sound speeds, or corresponding tube speeds c T $c_{\mathrm{T}}$ , c TI $c_{\mathrm{TI}}$ , c TQ $c_{\mathrm{TQ}}$ . Our analysis also reveals that, depending on the ratio P gI / P cond $P_{\mathrm{gI}} / P_{\mathrm{cond}}$ , the behavior of dispersion curves can change qualitatively. The joint influence of waveguide dispersion and dispersion caused by thermal conduction expands the range of influence of the isothermal regime, which can in particular be expressed in the fact that the phase velocity even in the range of periods corresponding to the adiabatic regime may not reach the speed of sound c S $c_{\mathrm{S}}$ , and the tube speed c T $c_{\mathrm{T}}$ for this band is a better estimate. Applied to observed hot loop oscillations, the model yields magnetic-field strengths of 10 G $\sim 10~\mathrm{G}$ , matching observed periods and damping times more accurately than adiabatic estimates alone.