arXiv subjects

Paul S. Cally

Publications and source records attributed to Paul S. Cally.

At least 19 recordsLinked to original sources

arXiv2024

MHD waves in homogeneous and continuously stratified atmospheres

The basic equations, concepts, and modes of linear, ideal, MHD waves -- slow, Alfvén and fast -- are set out and generalised to gravitationally-stratified atmospheres. Particular attention is devoted to mode conversion, wherein the local behavior of a global wave changes from one mode to another in passing through particular atmospheric layers. Exact solutions are explored where available. Eikonal methods -- WKBJ and ray theory -- are described. Although our emphasis is on the theoretical underpinning of the subject, the solar atmospheric heating implications of fast/slow and fast/Alfvén conversions are discussed in detail.

astro-ph.SR↗

arXiv2023

Efficiency of MHD Wave Generation in Weakly Ionized Atmospheres

Generation of Alfvén and slow magneto-acoustic waves in weakly ionized atmospheres by excitation of the charges-only component of the two fluid (charges and neutrals) plasma is shown to be more or less efficient depending on the energy fraction initially allocated to the three stationary "flow differential" modes which characterize the inter-species drift. This is explained via detailed analysis of the full ten-dimensional spectral description of two-fluid linear magnetohydrodynamics. Excitation via the velocity of the charges only is found to be very inefficient, in accord with previous results, whilst excitation via the magnetic field perturbation alone is highly efficient. All ten eigenvalues and eigenvectors are presented analytically in the high collision frequency regime.

astro-ph.SR↗

arXiv2021

On the Fragility of Alfvén waves in a Stratified Atmosphere

Complete asymptotic expansions are developed for slow, Alfvén and fast magnetohydrodynamic waves at the base of an isothermal three-dimensional (3D) plane stratified atmosphere. Together with existing convergent Frobenius series solutions about $z=\infty$, matchings are numerically calculated that illuminate the fates of slow and Alfvén waves injected from below. An Alfvén wave in a two-dimensional model is 2.5D in the sense that the wave propagates in the plane of the magnetic field but its polarization is normal to it in an ignorable horizontal direction, and the wave remains an Alfvén wave throughout. The rotation of the plane of wave propagation away from the vertical plane of the magnetic field pushes the plasma displacement vector away from horizontal, thereby coupling it to stratification. It is shown that potent slow-Alfvén coupling occurs in such 3D models. It is found that about 50% of direction-averaged Alfvén wave flux generated in the low atmosphere at frequencies comparable to or greater than the acoustic cutoff can reach the top as Alfvén flux for small magnetic field inclinations $θ$, and this increases to 80% or more with increasing $θ$. On the other hand, direction-averaged slow waves can be 40% effective in converting to Alfvén waves at small inclination, but this reduces sharply with increasing $θ$ and wave frequency. Together with previously explored fast-slow and fast-Alfvén couplings, this provides valuable insights into which injected transverse waves can reach the upper atmosphere as Alfvén waves, with implications for solar and stellar coronal heating and solar/stellar wind acceleration.

astro-ph.SR↗

arXiv2021

Conversion and Smoothing of MHD Shocks in Atmospheres with Open and Closed Magnetic Field and Neutral Points

Planar acoustically dominated magneto\-hydro\-dynamic waves are initiated at the high-$β$ base of a simulated 2D isothermal stratified atmosphere with potential magnetic field exhibiting both open and closed field regions as well as neutral points. They shock on their way upward toward the Alfvén-acoustic equipartition surface $a=c$, where $a$ and $c$ are the Alfvén and sound speeds respectively. Expanding on recent 1.5D findings that such shocks mode-convert to fast shocks and slow smoothed waves on passing through $a=c$, we explore the implications for these more complex magnetic geometries. It is found that the 1.5D behaviour carries over to the more complex case, with the fast shocks strongly attracted to neutral points, which are disrupted producing extensive fine structure. It is also observed that shocks moving in the opposite direction, from $a>c$ to $a<c$, split into fast and slow components too, and that again it is the slow component that is smoothed.

astro-ph.SR↗

arXiv2019

Smoothing of MHD Shocks in Mode Conversion

Shock waves are simulated passing through the Alfvén-acoustic equipartition layer in a stratified isothermal magneto-atmosphere. The recent ray-theoretic calculations of Núñez (2019) predicted smoothing of the shock through this layer, causing both the fast and slow components to emerge as continuous waves. However, it is found that the partial mode conversion expected from linear theory for oblique incidence of the shock on the magnetic field is accompanied by a smoothing of the slow-shock only, whilst the fast-shock persists. Explanations are presented based on MHD mode conversion and shock theory.

astro-ph.SR↗

arXiv2017

Sensitivity of Coronal Loop Sausage Mode Frequencies and Decay Rates to Radial and Longitudinal Density Inhomogeneities: A Spectral Approach

Fast sausage modes in solar magnetic coronal loops are only fully contained in unrealistically short dense loops. Otherwise they are leaky, losing energy to their surrounds as outgoing waves. This causes any oscillation to decay exponentially in time. Simultaneous observations of both period and decay rate therefore reveal the eigenfrequency of the observed mode, and potentially insight into the tubes' nonuniform internal structure. In this article, a global spectral description of the oscillations is presented that results in an implicit matrix eigenvalue equation where the eigenvalues are associated predominantly with the diagonal terms of the matrix. The off-diagonal terms vanish identically if the tube is uniform. A linearized perturbation approach, applied with respect to a uniform reference model, is developed that makes the eigenvalues explicit. The implicit eigenvalue problem is easily solved numerically though, and it is shown that knowledge of the real and imaginary parts of the eigenfrequency is sufficient to determine the width and density contrast of a boundary layer over which the tubes' enhanced internal densities drop to ambient values. Linearized density kernels are developed that show sensitivity only to the extreme outside of the loops for radial fundamental modes, especially for small density enhancements, with no sensitivity to the core. Higher radial harmonics do show some internal sensitivity, but these will be more difficult to observe. Only kink modes are sensitive to the tube centres. {Variation in internal and external Alfvén speed along the loop is shown to have little effect on the fundamental dimensionless eigenfrequency, though the associated eigenfunction becomes more compact at the loop apex as stratification increases, or may even displace from the apex.

astro-ph.SR↗

arXiv2016

Alfvén Waves in the Structured Solar Corona

A simple model of a periodic ensemble of closely packed flux tubes sitting atop a vertically stratified layer reveals that an incident fast wave from below preferentially converts almost immediately to Alfvén waves in the flux tubes, with kink waves restricted to at most a very few Fourier modes. This suggests that observations of coronal kink modes in such structured systems may greatly underestimate the net wave energy flux being transported into and through the corona, much of which may reside in harder-to-observe Alfvén waves. The processes of mode conversion/resonant absorption and Alfvén phase mixing are implicated. It is suggested that the Sun's internal p-mode field -- the 5-minute oscillations -- may contribute substantially to the process by supplying incident fast waves in the chromosphere that scatter and mode-convert in the tube ensemble.

astro-ph.SR↗

arXiv2015

3D simulations of realistic power halos in magneto-hydrostatic sunspot atmospheres: linking theory and observation

The well-observed acoustic halo is an enhancement in time-averaged Doppler velocity and intensity power with respect to quiet-sun values which is prominent for weak and highly inclined field around the penumbra of sunspots and active regions. We perform 3D linear wave modelling with realistic distributed acoustic sources in a MHS sunspot atmosphere and compare the resultant simulation enhancements with multi-height SDO observations of the phenomenon. We find that simulated halos are in good qualitative agreement with observations. We also provide further proof that the underlying process responsible for the halo is the refraction and return of fast magnetic waves which have undergone mode conversion at the critical $a=c$ atmospheric layer. In addition, we also find strong evidence that fast-Alfvén mode conversion plays a significant role in the structure of the halo, taking energy away from photospheric and chromospheric heights in the form of field-aligned Alfvén waves. This conversion process may explain the observed "dual-ring" halo structure at higher ($> 8 $ mHz) frequencies.

astro-ph.SR↗

arXiv2015

Fast-to-Alfvén Mode Conversion Mediated by Hall Current. I. Cold Plasma Model

The photospheric temperature minimum in the Sun and solar-like stars is very weakly ionized, with ionization fraction $f$ as low as $10^{-4}$. In galactic star forming regions, $f$ can be $10^{-10}$ or lower. Under these circumstances, the Hall current can couple low frequency Alfvén and magneto\-acoustic waves via the dimensionless Hall parameter $ε=ω/Ω_\text{i}f$, where $ω$ is the wave frequency and $Ω_\text{i}$ is the mean ion gyrofrequency. This is analysed in the context of a cold (zero-$β$) plasma, and in less detail for a warm plasma. It is found that Hall coupling preferentially occurs where the wave vector is nearly field-aligned. In these circumstances, Hall coupling in theory produces a continual oscillation between fast and Alfvén modes as the wave passes through the weakly ionized region. At low frequencies (mHz), characteristic of solar and stellar normal modes, $ε$ is probably too small for more than a fraction of one oscillation to occur. On the other hand, the effect may be significant at the far higher frequencies (Hz) associated with magnetic reconnection events. In another context, characteristic parameters for star forming gas clouds suggest that $\mathcal{O}(1)$ or more full oscillations may occur in one cloud crossing. This mechanism is not expected to be effective in sunspots, due to their high ion gyrofrequencies and Alfvén speeds, since the net effect depends inversely on both and therefore inverse quadratically on field strength.

astro-ph.SR↗

arXiv2015

IAU commission 10 "Solar Activity": Legacy report and triennial report for 2012-2015

After more than half a century of community support related to the science of "solar activity'', IAU's Commission 10 was formally discontinued in 2015, to be succeeded by C.E2 with the same area of responsibility. On this occasion, we look back at the growth of the scientific disciplines involved around the world over almost a full century. Solar activity and fields of research looking into the related physics of the heliosphere continue to be vibrant and growing, with currently over 2,000 refereed publications appearing per year from over 4,000 unique authors, publishing in dozens of distinct journals and meeting in dozens of workshops and conferences each year. The size of the rapidly growing community and of the observational and computational data volumes, along with the multitude of connections into other branches of astrophysics, pose significant challenges; aspects of these challenges are beginning to be addressed through, among others, the development of new systems of literature reviews, machine-searchable archives for data and publications, and virtual observatories. As customary in these reports, we highlight some of the research topics that have seen particular interest over the most recent triennium, specifically active-region magnetic fields, coronal thermal structure, coronal seismology, flares and eruptions, and the variability of solar activity on long time scales. We close with a collection of developments, discoveries, and surprises that illustrate the range and dynamics of the discipline.

astro-ph.SR↗

arXiv2015

Multiple Scattering of Seismic Waves from Ensembles of Upwardly Lossy Thin Flux Tubes

Our previous semi-analytic treatment of f- and p-mode multiple scattering from ensembles of thin flux tubes (Hanson and Cally, Astrophys. J. 781, 125; 791, 129, 2014) is extended by allowing both sausage and kink waves to freely escape at the top of the model using a radiative boundary condition there. As expected, this additional avenue of escape, supplementing downward loss into the deep solar interior, results in substantially greater absorption of incident f- and p-modes. However, less intuitively, it also yields mildly to substantially smaller phase shifts in waves emerging from the ensemble. This may have implications for the interpretation of seismic data for solar plage regions, and in particular their small measured phase shifts.

astro-ph.SR↗

arXiv2015

MHD wave refraction and the acoustic halo effect around solar active regions - a 3D study

An enhancement in high-frequency acoustic power is commonly observed in the solar photosphere and chromosphere surrounding magnetic active regions. We perform 3D linear forward wave modelling with a simple wavelet pulse acoustic source to ascertain whether the formation of the acoustic halo is caused by MHD mode conversion through regions of moderate and inclined magnetic fields. This conversion type is most efficient when high frequency waves from below intersect magnetic field lines at a large angle. We find a strong relationship between halo formation and the equipartition surface at which the Alfvén speed $a$ matches the sound speed $c$, lending support to the theory that photospheric and chromospheric halo enhancement is due to the creation and subsequent reflection of magnetically dominated fast waves from essentially acoustic waves as they cross $a=c$. In simulations where we have capped $a$ such that waves are not permitted to refract after reaching the $a=c$ height, halos are non-existent, which suggests that the power enhancement is wholly dependent on returning fast waves. We also reproduce some of the observed halo properties, such as a dual 6 and 8 mHz enhancement structure and a spatial spreading of the halo with height.

astro-ph.SR↗

arXiv2014

The scattering of $f$- and $p$-modes from ensembles of thin magnetic flux tubes - An analytical approach

Motivated by the observational results of Braun (1995), we extend the model of Hanson & Cally (2014) to address the effect of multiple scattering of f and p-modes by an ensemble of thin vertical magnetic flux tubes in the surface layers of the Sun. As in observational Hankel analysis we measure the scatter and phase shift from an incident cylindrical wave in a coordinate system roughly centred in the core of the ensemble. It is demonstrated that, although thin flux tubes are unable to interact with high order fluting modes individually, they can indirectly absorb energy from these waves through the scatters of kink and sausage components. It is also shown how the distribution of absorption and phase shift across the azimuthal order m depends strongly on the tube position, as well as on the individual tube characteristics. This is the first analytical study into an ensembles multiple scattering regime, that is embedded within a stratified atmosphere.

astro-ph.SR↗

arXiv2014

Helioseismology with Solar Orbiter

The Solar Orbiter mission, to be launched in July 2017, will carry a suite of remote sensing and in-situ instruments, including the Polarimetric and Helioseismic Imager (PHI). PHI will deliver high-cadence images of the Sun in intensity and Doppler velocity suitable for carrying out novel helioseismic studies. The orbit of the Solar Orbiter spacecraft will reach a solar latitude of up to 21 deg (up to 34 deg by the end of the extended mission) and thus will enable the first local helioseismology studies of the polar regions. Here we consider an array of science objectives to be addressed by helioseismology within the baseline telemetry allocation (51 Gbit per orbit, current baseline) and within the science observing windows (baseline 3 x 10 days per orbit). A particularly important objective is the measurement of large-scale flows at high latitudes (rotation and meridional flow), which are largely unknown but play an important role in flux transport dynamos. The full range of Earth-Sun-spacecraft angles provided by the orbit will enable helioseismology from two vantage points by combining PHI with another instrument: stereoscopic helioseismology will allow the study of the deep solar interior and a better understanding of the physics of solar oscillations in both quiet Sun and sunspots. We have used a model of the PHI instrument to study its performance for helioseismology applications. As input we used a 6 hr time-series of realistic solar magneto-convection simulation (Stagger code) and the SPINOR radiative transfer code to synthesize the observables. The simulated power spectra of solar oscillations show that the instrument is suitable for helioseismology. In particular, the specified point spread function, image jitter, and photon noise are no obstacle to a successful mission.

astro-ph.SR↗

arXiv2014

Sensitivity of helioseismic travel-times to the imposition of a Lorentz force limiter in computational helioseismology

The rapid exponential increase in the Alfvén wave speed with height above the solar surface presents a serious challenge to physical modelling of the effects of magnetic fields on solar oscillations, as it introduces a significant CFL time-step constraint for explicit numerical codes. A common approach adopted in computational helioseismology, where long simulations in excess of 10 hours (hundreds of wave periods) are often required, is to cap the Alfvén wave speed by artificially modifying the momentum equation when the ratio between Lorentz and hydrodynamic forces becomes too large. However, recent studies have demonstrated that the Alfvén wave speed plays a critical role in the MHD mode conversion process, particularly in determining the reflection height of the upward propagating helioseismic fast wave. Using numerical simulations of helioseismic wave propagation in constant inclined (relative to the vertical) magnetic fields we demonstrate that the imposition of such artificial limiters significantly affects time-distance travel times unless the Alfvén wave-speed cap is chosen comfortably in excess of the horizontal phase speeds under investigation.

astro-ph.SR↗

arXiv2013

An Analytical Approach to Scattering Between Two Thin Magnetic Flux Tubes in a Stratified Atmosphere

We expand on recent studies to analytically model the behavior of two thin flux tubes interacting through the near- and acoustic far-field. The multiple scattering that occurs between the pair alters the absorption and phase of the outgoing wave, when compared to non-interacting tubes. We have included both the sausage and kink scatter produced by the pair. It is shown that the sausage mode's contribution to the scattered wave field is significant, and plays an equally important role in the multiple scattering regime. A disparity between recent numerical results and analytical studies, in particular the lack of symmetry between the two kink modes, is addressed. This symmetry break is found to be caused by an incorrect solution for the near-field modes.

astro-ph.SR↗

arXiv2013

Seismology of the Wounded Sun

Active regions are open wounds in the Sun's surface. Seismic oscillations from the interior pass through them into the atmosphere, changing their nature in the process to fast and slow magneto-acoustic waves. The fast waves then partially reflect and partially mode convert to upgoing and downgoing Alfvén waves. The reflected fast and downgoing Alfvén waves then re-enter the interior through the active regions that spawned them, infecting the surface seismology with signatures of the atmosphere. Using numerical simulations of waves in uniform magnetic fields, we calculate the upward acoustic and Alfvénic losses in the atmosphere as functions of field inclination and wave orientation as well as the Time-Distance `travel time' perturbations, and show that they are related. Travel time perturbations relative to quiet Sun can exceed 40 seconds in 1 kG magnetic field. It is concluded that active region seismology is indeed significantly infected by waves leaving and re-entering the interior through magnetic wounds, with differing travel times depending on the orientation of the wave vector relative to the magnetic field. This presages a new directional-time-distance seismology.

astro-ph.SR↗

arXiv2013

Near- and Far-Field Response to Compact Acoustic Sources in Stratified Convection Zones

The role of the acoustic continuum associated with compact sources in the Sun's interior wave field is explored for a simple polytropic model. The continuum produces a near-field acoustic structure -- the so-called `acoustic jacket' -- that cannot be represented by a superposition of discrete normal modes. Particular attention is paid to monochromatic point sources of various frequency and depth, and to the surface velocity power that results, both in the discrete f- and p-mode spectrum and in the continuum. It is shown that a major effect of the continuum is to heal the surface wave field produced by compact sources, and therefore to hide them from view. It is found that the continuous spectrum is not a significant contributor to observable inter-ridge seismic power.

astro-ph.SR↗