Equation of the field lines of an axisymmetric multipole with a source surface

Gregory, S. G.

doi:10.1119/1.3549206

Cited by 13 publications

(12 citation statements)

References 37 publications

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“…sin 2 θ where the constant is the maximum radial extent of the dipole loops in the stellar midplane (a result commonly found in the literature e.g. Gregory 2011). …”

Section: It Is Clear Frommentioning

confidence: 65%

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Analytic and numerical models of the 3D multipolar magnetospheres of pre‐main sequence stars

Gregory

Donati

2011

Astron Nachr

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Traditionally models of accretion of gas on to T Tauri stars have assumed a dipole stellar magnetosphere, partly for simplicity, but also due to the lack of information about their true magnetic field topologies. Before and since the first magnetic maps of an accreting T Tauri star were published in 2007 a new generation of magnetospheric accretion models have been developed that incorporate multipole magnetic fields. Three-dimensional models of the large-scale stellar magnetosphere with an observed degree of complexity have been produced via numerical field extrapolation from observationally derived T Tauri magnetic maps. Likewise, analytic and magnetohydrodynamic models with multipolar stellar magnetic fields have been produced. In this conference review article we compare and contrast the numerical field extrapolation and analytic approaches, and argue that the large-scale magnetospheres of some (but not all) accreting T Tauri stars can be well described by tilted dipole plus tilted octupole field components. We further argue that the longitudinal field curve, whether derived from accretion related emission lines, or from photospheric absorption lines, provides poor constrains on the large-scale magnetic field topology and that detailed modeling of the rotationally modulated Stokes V signal is required to recover the true field complexity. We conclude by examining the advantages, disadvantages and limitations of both the field extrapolation and analytic approaches, and also those of magnetohydrodynamic models.

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“…sin 2 θ where the constant is the maximum radial extent of the dipole loops in the stellar midplane (a result commonly found in the literature e.g. Gregory 2011). …”

Section: It Is Clear Frommentioning

confidence: 65%

“…Mohanty & Shu 2008;Gregory et al 2010;Gregory 2011). Furthermore, when the multipole moments are tilted by different amounts relative to the stellar rotation axis, and/or towards different rotation phases, the field structure (i.e.…”

Section: Discussionmentioning

confidence: 99%

Analytic and numerical models of the 3D multipolar magnetospheres of pre‐main sequence stars

Gregory

Donati

2011

Astron Nachr

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“…This paper constructs coordinate systems for magnetic field configurations with a pure dipole component (Section 4), for dipole and octupole contributions (Section 5), and for dipole and radial (split monopole) contributions (Appendix B). The coordinates for a general multipole field can be written in terms of Legendre polynomials, as shown in Result 6 of Appendix A (see also Gregory 2011;Gregory et al 2010). This approach can thus be generalized further to incorporate even more complex magnetic field configurations.…”

Section: Resultsmentioning

confidence: 99%

Magnetically Controlled Accretion Flows Onto Young Stellar Objects

Adams

Gregory

2011

ApJ

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Accretion from disks onto young stars is thought to follow magnetic field lines from the inner disk edge to the stellar surface. The accretion flow thus depends on the geometry of the magnetic field. This paper extends previous work by constructing a collection of orthogonal coordinate systems, including the corresponding differential operators, where one coordinate traces the magnetic field lines. This formalism allows for an (essentially) analytic description of the geometry and the conditions required for the flow to pass through sonic points. Using this approach, we revisit the problem of magnetically controlled accretion flow in a dipole geometry, and then generalize the treatment to consider magnetic fields with multiple components, including dipole, octupole, and split monopole contributions. This approach can be generalized further to consider more complex magnetic field configurations. Observations indicate that accreting young stars have substantial dipole and octupole components, and that accretion flow is transonic. If the effective equation of state for the fluid is too stiff, however, the flow cannot pass smoothly through the sonic points in steady state. For a multipole field of order , we derive a general constraint on the polytropic index, n > + 3/2, required for steady transonic flow to reach free-fall velocities. For octupole fields, inferred on surfaces of T Tauri stars, the index n > 9/2, so that the flow must be close to isothermal. The inclusion of octupole field components produces higher densities at the stellar surface and smaller areas for the hot spots, which occur at higher latitudes; the magnetic truncation radius is smaller (larger) for octupole components that are aligned (anti-aligned) with the stellar dipole. This contribution thus increases our understanding of magnetically controlled accretion for young stellar objects and can be applied to a variety of additional astrophysical problems.

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“…The magnetic field of stars may be complex (e.g., Johns-Krull 2007). However, at large distances from stars, the dipole component often dominates and is responsible for the discmagnetosphere interaction (e.g., Long et al 2007Long et al , 2008Gregory 2011). .…”

Section: Introductionmentioning

confidence: 99%

3D MHD Simulations of Accretion onto Stars with Tilted Magnetic and Rotational Axes

Romanova,

Koldoba,

Ustyugova

et al. 2020

Preprint

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We present results of global three-dimensional (3D) magnetohydrodynamic (MHD) simulations of the accretion onto a magnetized star where both the magnetic and rotational axes of the star are tilted about the rotational axis of the disc. We observed that initially, the inner parts of the disc are warped due to the magnetic interaction between the external regions of the magnetosphere and the inner disc. Subsequently, larger parts of the disc become tilted and precess about the rotational axis of the star. After a few precessional periods, the disc becomes almost aligned with the equatorial plane of the star. This alignment may result from the winding of the magnetic field lines about the rotational axis of the star and the formation of a new magnetic configuration, where the magnetic pressure force acts to align the disc. Another possible explanation of this alignment is the magnetic Bardeen-Petterson effect where a part of the disc, precessing about the rotational axis of the star, settles in the equatorial plane due to the precessional and viscous torques in the disc.

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Equation of the field lines of an axisymmetric multipole with a source surface

Cited by 13 publications

References 37 publications

Analytic and numerical models of the 3D multipolar magnetospheres of pre‐main sequence stars

Analytic and numerical models of the 3D multipolar magnetospheres of pre‐main sequence stars

Magnetically Controlled Accretion Flows Onto Young Stellar Objects

3D MHD Simulations of Accretion onto Stars with Tilted Magnetic and Rotational Axes

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