Probing sunspot magnetic fields with p-mode absorption and phase shift data

Long-standing observations of incoming and outgoing f- and p-modes in annuli around sunspots reveal that the spots partially absorb and substantially shift the phase of waves incident upon them. The commonly favoured absorption mechanism is partial conversion to slow magneto-acoustic waves that disappear into the solar interior channelled by the magnetic field of the sunspot. However, up until now, only f-mode absorption could be accounted for quantitatively by this means. Based on vertical magnetic field models, the absorption of p-modes was insufficient. In this paper, we use the new calculations of Crouch & Cally for inclined fields, and a simplified model of the interaction between spot interior and exterior. We find excellent agreement with phase shift data assuming field angles from the vertical in excess of 30° and Alfvén/acoustic equipartition depths of around 600–800 km. The absorption of f-modes produced by such models is considerably larger than is observed, but consistent with numerical simulations. On the other hand, p-mode absorption is generally consistent with observed values, up to some moderate frequency dependent on radial order. Thereafter, it is too large, assuming absorbing regions comparable in size to the inferred phase-shifting region. The excess absorption produced by the models is in stark contrast with previous calculations based on a vertical magnetic field, and is probably due to finite mode lifetimes and excess emission in acoustic glories. The excellent agreement of phase shift predictions with observational data allows some degree of probing of subsurface field strengths, and opens up the possibility of more accurate inversions using improved models. Most importantly, though, we have confirmed that slow mode conversion is a viable, and indeed the likely, cause of the observed absorption and phase shifts.     

Imaging bright-spots in the accretion flow near the black hole horizon of Sgr A*

Solar active regions are distinguished by their strong magnetic fields. Modern local helioseismology seeks to probe them by observing waves which emerge at the solar surface having passed through their interiors. We address the question of how an acoustic wave from below is partially converted to magnetic waves as it passes through a vertical magnetic field layer where the sound and Alfvén speeds coincide (the equipartition level), and find that (i) there is no associated reflection at this depth, either acoustic or magnetic, only transmission and conversion to an ongoing magnetic wave; and (ii) conversion in active regions is likely to be strong, though not total, at frequencies typically used in local helioseismology, with lower frequencies less strongly converted. A simple analytical formula is presented for the acoustic-to-magnetic conversion coefficient.     

Acoustic Imaging of Solar Active Regions – (Invited Review)

Acoustic imaging is a new method to construct the acoustic signal at a point on the solar surface or in the solar interior with the signals measured at the solar surface. The constructed signals contain both intensity information and phase information. The intensity is computed by summing the squared amplitude of the constructed signal over time. The phase of constructed signals can be studied by the cross-correlation function between the time series constructed with ingoing waves and outgoing waves. The location of the envelope peak of the cross-correlation function and the phase of the cross-correlation function contain different information on the physical conditions of the plasma along the wave path. From the constructed signals, one can form the two-dimensional outgoing intensity map, absorption map, phase-shift map, and envelope-shift map of a target region at different focal depths. The perturbed physical conditions caused by the magnetic fields of active regions manifest in these maps. The outgoing intensity is lower in magnetic regions than the quiet Sun. The group travel time and phase travel time are smaller in magnetic regions than in the quiet Sun. In this paper, we review the studies of active regions, including emerging flux regions, with acoustic imaging.     

Propagation of magnetically guided acoustic shocks in the solar chromosphere

We study the propagation of a train of acoustic shocks guided by diverging magnetic fields through a static model of the solar chromospheric network and transition region. Our results show that for initial flux densities of the order 10⁶ ergs cm^–2 s^–1 in the lower chromosphere, the local efficiency of acoustic transmission into the corona can be much higher than calculated for a plane parallel atmosphere. Thus acoustic energy will tend to be deposited at higher chromospheric levels in diverging magnetic fields, and magnetic guiding may well influence the temperature profile of the network and plages. But the total flux that can be transmitted into the corona along such diverging fields is severely limited, since the magnetic elements occupy a small fractional area of the photosphere, and the transmission efficiency is a rapidly decreasing function of initial acoustic flux density. We conclude that diverging magnetic fields and a varying ratio of specific heats are not likely to allow high frequency shocks to dissipate high enough in a static atmosphere, to contribute significantly to the coronal energy balance. This result strengthens the view that acoustic waves do not heat the solar corona. However, the conclusion may be sensitive to the influence of observed mass motions, such as spicules.     

Magneto-gravity waves and the heating of the solar corona

It is generally believed that the heating of the solar corona is caused by waves originating in the photosphere and propagating into the corona where their energy is dissipated. The medium through which these waves propagate is in general permeated by magnetic fields complicating the behaviour of this propagation considerably. We have therefore analysed the wave motions in a plasma permeated by constant magnetic and gravitational fields. In general, three waves modes were found, which we called the + mode, –mode, and the Alfvén mode. Each mode was found to be strongly coupled to each of the three kinds of motion; acoustic, gravity, and hydromagnetic. However, the Alfvén mode was found to be separable from the dispersion relation, and therefore independent of compressibility and gravity. The local dispersion relation is derived and expressed in nondimensional form independent of the constants that describe a particular atmosphere. From the dispersion relation one can show that rising waves propagate either with a constant or a growing wave amplitude depending on the magnitudes and directions of the gravitational field, magnetic field, and the wave vector. The variation of the density with height is taken into account by a generalized W.K.B. method. Equations are found which give the height at which wave reflection occurs, giving the upper bound for possible wave propagation.Work supported by the National Aeronautics and Space Administration under Research Grant NGR-29-001-016.On leave of absence from the Desert Research Institute and Department of Physics, University of Nevada, Reno, Nevada, U.S.A.     

The Effect of Abnormal Granulation on Acoustic Wave Travel Times and Mode Frequencies

Observations indicate that in plage areas (i.e. in active regions outside sunspots) acoustic waves travel faster than in the quiet Sun, leading to shortened travel times and higher p-mode frequencies. Coupled with the 11-year variation of solar activity, this may also explain the solar cycle variation of oscillation frequencies. While it is clear that the ultimate cause of any difference between the quiet Sun and plage is the presence of magnetic fields of order 100 G in the latter, the mechanism by which the magnetic field exerts its influence has not yet been conclusively identified. One possible such mechanism is suggested by the observation that granular motions in plage areas tend to be slightly “abnormal”, dampened compared to the quiet Sun. In this paper we consider the effect that abnormal granulation observed in active regions should have on the propagation of acoustic waves. Any such effect is found to be limited to a shallow surface layer where sound waves propagate nearly vertically. The magnetically suppressed turbulence implies higher sound speeds, leading to shorter travel times. This time shift Δ τ is independent of the travel distance, while it shows a characteristic dependence on the assumed plage field strength. As a consequence of the variation of the acoustic cutoff with height, Δ τ is expected to be significantly higher for higher frequency waves within the observed regime of 3 – 5 mHz. The lower group velocity near the upper reflection point further leads to an increased envelope time shift, as compared to the phase shift. p-mode frequencies in plage areas are increased by a corresponding amount, Δ ν/ν=ν Δ τ. These characteristics of the time and frequency shifts are in accordance with observations. The calculated overall amplitudes of the time and frequency shifts are comparable to, but still significantly less than (by a factor of 2 to 5), those suggested by measurements.     

Accretion onto stars with octupole magnetic fields: Matter flow, hot spots and phase shifts

Recent measurements of the surface magnetic fields of classical T Tauri stars (CTTSs) and magnetic cataclysmic variables show that their magnetic fields have a complex structure. Investigation of accretion onto such stars requires global three-dimensional (3D) magnetohydrodynamic (MHD) simulations, where the complexity of simulations strongly increases with each higher-order multipole. Previously, we were able to model disc accretion onto stars with magnetic fields described by a superposition of dipole and quadrupole moments. However, in some stars, like CTTS V2129 Oph and BP Tau, the octupolar component is significant and it was necessary to include the next octupolar component. Here, we show results of global 3D MHD simulations of accretion onto stars with superposition of the dipole and octupole fields, where we vary the ratio between components. Simulations show that if octupolar field strongly dominates at the disc-magnetosphere boundary, then matter flows into the ring-like octupolar poles, forming ring-shape spots at the surface of the star above and below equator. The light-curves are complex and may have two peaks per period. In case where the dipole field dominates, matter accretes in two ordered funnel streams towards poles, however the polar spots are meridionally-elongated due to the action of the octupolar component. In the case when the fields are of similar strengths, both, polar and belt-like spots are present. In many cases the light-curves show the evidence of complex fields, excluding the cases of small inclinations angles, where sinusoidal light-curve is observed and ‘hides’ the information about the field complexity.We also propose new mechanisms of phase shift in stars with complex magnetic fields. We suggest that the phase shifts can be connected with: (1) temporal variation of the star’s intrinsic magnetic field and subsequent redistribution of main magnetic poles; (2) variation of the accretion rate, which causes the disc to interact with the magnetic fields associated with different magnetic moments. We use our model to demonstrate these phase shift mechanisms, and we discuss possible applications of these mechanisms to accreting millisecond pulsars and young stars.     

Wave heating of the solar chromosphere

The nonmagnetic interior of supergranulation cells has been thought since the 1940s to be heated by the dissipation of acoustic waves. But all attempts to measure the acoustic flux have failed to show sufficient energy for chromospheric heating. Recent space observations with TRACE, for example, have found 10% or less of the necessary flux. To explain the missing energy it has been speculated that the nonmagnetic chromosphere is heated mainly by waves related to the magnetic field. If that were correct, the whole chromosphere, magnetic as well as nonmagnetic, would be heated mainly by waves related to the magnetic field. But contrary to expectation, the radiation emerging from the nonmagnetic chromosphere shows none of the signatures of magnetic waves, only those of acoustic waves. Nearly all the heating of the nonmagnetic chromosphere must therefore be due to acoustic waves. In the magnetic network on the boundary of supergranulation cells, on the other hand, the small filling factor of the magnetic field in the photosphere implies that only a small fraction of the wave flux that travels upward to heat the chromosphere can be channeled by the magnetic field. Hence, while some of the energy that is dissipated in the magnetic network is in the form of magnetic waves, most of it must be in the form of acoustic waves. Thus, the quiet solar chromosphere, instead of being heated mainly by magnetic waves throughout, must be heated mainly by acoustic waves throughout. The full wave flux heating the quiet chromosphere must travel through the photosphere. In the nonmagnetic medium, this flux is essentially all in the form of acoustic waves; TRACE registers at most 10% of it, perhaps because of limited spatial resolution.     

The effect of q-distributed ions during the head-on collision of dust acoustic solitary waves

The head-on collision of dust acoustic solitary waves are studied in a dusty plasma composed of dust and nonextensive distributed ions by using the extended version of Poincaré-Lighthill-Kuo (PLK) method. The effect of the nonextensivity on the phase shift is studied. It is found that the presence of nonextensive distributed ions plays a significant role on the collision of dust acoustic solitary waves.     

Modeling helioseismic modes in the magnetic atmosphere of the Sun

The pulsation of the solar surface is caused by acoustic waves traveling in the solar interior. Thorough analyses of observational data indicate that these f and p helioseismic oscillation modes are not bounced back completely at the surface but they partially penetrate into the atmosphere. Atmospheric effects and their possible observational application are investigated in one‐dimensional magnetohydrodynamic models. It is found that f and p mode frequencies are shifted of the order of μHz due to the presence of an atmospheric magnetic field. This shift varies with the direction of the wave propagation.Resonant coupling of global helioseismic modes to local Alfvén and slow waves reduce the life time of the global modes. The resulting line width of the frequency line is of the order of nHz, and it also varies with propagation angle. These features enable us to use helioseismic observations in magnetic diagnostics of the lower atmosphere. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Hydromagnetic waves in structured magnetic fields

Although the inhomogeneous nature of solar magnetic fields is now well established, most theoretical analyses of hydromagnetic wave propagation assume infinite homogeneous fields. Here we reformulate the hydromagnetic wave problem for magnetic fields which vary in one direction perpendicular to the field. The permitted modes of small amplitude hydromagnetic oscillations are considered, first in the case of a single interface between semi-infinite magnetic and non-magnetic compressible regions, and secondly for a magnetic flux sheath of given thickness imbedded in a nonmagnetic region. It is shown that, for small values of R (the ratio of the Alfvén to the sound speed), an acoustic or p-mode wave front passes through the flux sheath with only minor deformation. However, for large R, the transmitted acoustic wave is attenuated and, depending upon the thickness of the flux sheath and the angle of incidence, a hydromagnetic wave may be effectively trapped and guided along the flux sheath. It is also shown that, for the symmetric vibration of the flux sheath in the absence of incident acoustic waves, only slow mode type waves are permitted. Thus, in compressible regions for which R > 1 the Alfvénic-type fast mode is not a permitted mode of free vibration of a flux sheath.     

磁场中p模/s模的转换及黑子对声波的吸收

在柱坐标下将黑子周围的环形区域（黑子除外）内的振荡分解为朝向黑子传播的（入射的）波和离开黑子传播的（出射的）波。对无黑子的环形区域内的振荡也进行了同样的分解。将黑子周围的入射波看成是被黑子磁流管磁化了的介质（介质内的磁场基本是水平的）中的波。而无黑子区的入射波看成是非磁化介质中的波。比较这两种波在固定波数下功率随频率的分布发现，在磁化介质中不同径向除ｎ的声波（ｐ模）频率系统降低，同时功率也降低，降低的功率最高达非磁化介质中波的功率的３０％。而比较在固定频率下功率随波数的分布发现，磁场中ｆ模及ｎ＝１，２，３的ｐ模的脊向高波数方向位移，功率的降低受频率调制，即声波在某些有限的频带中被吸收。这些观测表明，在磁场中ｐ模与磁声重力波（ＭＡＧ）产生了模式混合或耦合。模式混合的存在支持了模式转换作为ｐ模式被黑子吸收的机制的解释。此外，本文还分析了转换的ＭＡＧ波进入黑子磁流管（其中的磁场基本上是垂直的）后进一步被吸收，吸收的功率最高达ＭＡＧ波的２０％。在磁流管内没有进一步观测到模式的转换     

On mode conversion and wave reflection in magnetic Ap stars

We investigate the effect of a strong large-scale magnetic field on the reflection of high-frequency acoustic modes in rapidly oscillating Ap stars. To that end, we consider a toy model composed of an isothermal atmosphere matched on to a polytropic interior and determine the numerical solution to the set of ideal magnetohydrodynamic equations in a local plane-parallel approximation with constant gravity. Using the numerical solution in combination with approximate analytical solutions that are valid in the limits where the magnetic and acoustic components are decoupled, we calculate the relative fraction of energy flux that is carried away in each oscillation cycle by running acoustic waves in the atmosphere and running magnetic waves in the interior. For oscillation frequencies above the acoustic cut-off, we show that most energy losses associated with the presence of running waves occur in regions where the magnetic field is close to vertical. Moreover, by considering the depth dependence of the energy associated with the magnetic component of the wave in the atmosphere we show that a fraction of the wave energy is kept in the oscillation every cycle. For frequencies above the acoustic cut-off frequency, such energy is concentrated in regions where the magnetic field is significantly inclined in relation to the local vertical. Even though our calculations were aimed at studying oscillations with frequencies above the acoustic cut-off frequency, based on our results we discuss what results may be expected for oscillations of lower frequency.     

Probing solar convection

In the solar convection zone, acoustic waves are scattered by turbulent sound speed fluctuations. In this paper the scattering of waves by convective cells is treated using Rytov's technique. Particular care is taken to include diffraction effects, which are important, especially for high-degree modes that are confined to the surface layers of the Sun. The scattering leads to damping of the waves and causes a phase shift. Damping manifests itself in the width of the spectral peak of p-mode eigenfrequencies. The contribution of scattering to the linewidths is estimated and the sensitivity of the results to the assumed spectrum of the turbulence is studied. Finally, the theoretical predictions are compared with recently measured linewidths of high-degree modes.     

On the propagation of magneto-acoustic-gravity waves

An analysis of magneto-acoustic-gravity waves in the case of an isothermal atmosphere permeated by a uniform magnetic field is presented. The general solution is expressed in terms of generalized hypergeometric functions. It can be used in numerical simulation of oscillations in a magnetic atmosphere.

It is shown that the elliptically polarized magneto-acoustic-gravity waves consist of a pair of surface waves and a pair of body waves above the cut-off frequency. The body waves along the magnetic field are similar to acoustic waves in an atmosphere and their cut-off frequency is unaffected by magnetic field. The transverse oscillation decreases with height. For the usual boundary condition, the longitudinal oscillation decreases with height; however, in some cases, it may contain terms that increase with height. The solution is singular on a family of ellipses in the frequency - horizontal wave number plane. Near these ellipses, the wave components grow indefinitely.     

Detailed analysis of flares,magnetic fields and activity in the sunspot group of Sept. 13–26, 1963

We analyze large-scale H-alpha movies of the large spot group of Sept. 13–26, 1963, together with radio, ionospheric and magnetic field data as well as white light pictures. The evolution of the group and associated magnetic fields is followed, and the positions of solar flares relative to the fields are noted, along with their morphology. Although the magnetic field is deformed in time, characteristic field structures may be traced through the deformation as the seat of recurrent homologous flares.We find that most flares are homologous, and some are triggered by disturbances elsewhere in the region. We note events produced by surges falling back to the surface, and one flare initiated by a bright bead seen to fly across the region. In almost every case of an isolated type III radio burst, a corresponding H-alpha brightening could be found, but not all flares produced bursts. Flares close to the sunspots are most likely to produce radio bursts. Flare surface waves in the region all travel out to the west, because of more open magnetic field structure there. In one case (Sept. 25) a wave is turned back by the closed field structure to the east.In almost all cases the time association of radio or ionospheric events is with the beginning of the flare or with the flash phase.Several morphological classes of flares are noted as recurrent types.     

Vertical velocities and horizontal wave propagation in the solar photosphere

We used the Sacramento Peak Doppler-Zeeman Analyzer to study the velocity and magnetic fields in 60 × 300 areas on the solar disk. We map the steady component of the line-of-sight velocity and longitudinal magnetic fields and compare them with the coarse Ca⁺ network. The collective phase behavior of the 5-min oscillations is studied in detail. We find large scale phase coherence, including waves with typical horizontal phase velocities of 100 km/sec which can be followed up to 50 000 km. The important oscillatory features are interpreted in terms of the properties of modified sound waves. We find no apparent relationship between the steady and oscillatory fields.     

Wave propagation in a magnetically structured atmosphere

The solar atmosphere, from the photosphere to the corona, is structured by the presence of magnetic fields. We consider the nature of such inhomogeneity and emphasis that the usual picture of hydromagnetic wave propagation in a uniform medium may be misleading if applied to a structured field. We investigate the occurrence of magnetoacoustic surface waves at a single magnetic interface and consider in detail the case where one side of the interface is field-free. For such an interface, a slow surface wave can always propagate. In addition, a fast surface wave may propagate if the field-free medium is warmer than the magnetic atmosphere.     

关于磁声重力波传播性质的探讨

本文对充满垂直均匀磁场的等温大气内的磁声重力波做了严格的解析分析,并将其通解表述成广义超几何函数的形式。该解可用于对磁大气内振荡现象的进一步数值模拟研究。对解的分析澄清了若干磁声重力波的传播性质。     

The effect of retardation on the stability of current filaments

We investigate the influence of the finite Alfvén velocity on the evolution of an active region filament. In general, variations of a current result in variations of the magnetic fields which spread around with the Alfvén velocity. As a consequence of the fact that a magnetic field can only change with the Alfvén velocity, a filament will experience the photospheric boundary conditions as these were at an Alfvén travel time back in time. The inclusion of this retardation effect in the momentum equation of a filament leads effectively to an extra force term. This force contribution acts in the direction in which the filament moves and has therefore a destabilizing effect on the filament. Because a moving filament acts as an antenna of Alfvén waves, the filament loses energy by the emission process. This leads to a radiative damping term in the equation of motion of the filament. In general, the radiative damping will be sufficiently strong to counteract the retardation instability. Numerical simulations show that during the energy build-up phase a filament follows the van Tend-Kuperus equilibrium curve. After the van Tend-Kuperus equilibrium has disappeared the filament goes through a transient phase moving with a sub-Alfvénic velocity upward. At greater heights the repulsive Lorentz force of the photospheric surface current magnetic field is balanced by the radiative damping, resulting in a decreasing filament velocity.Parts of this paper were presented at the 4th CESRA Workshop in Ouranopolis (Greece) in 1991.