Mode Mixing by a Shallow Sunspot

Sunspots are strong absorbers of f and p modes. A possible absorption mechanism is direct conversion to slow magnetoacoustic waves. Calculations based on vertical magnetic field models show that this works well for f modes, but is inadequate for p modes. Using a very simple shallow spot model, in which the effects of the magnetic field are accounted for solely by a surface condition, we investigate the possibility that p modes first scatter into f modes inside the spot, which are then more susceptible to conversion to slow modes. We find that the coupling between an incident p mode and the internal f mode is unlikely to be strong enough to account for the observed absorption, but that the incident modes do couple strongly to the acoustic jacket in some cases, leading to a region immediately around the sunspot where a significant fraction of the surface velocity is due to the jacket modes.     

The Spectral Irradiance Monitor: Scientific Requirements, Instrument Design, and Operation Modes

The Spectral Irradiance Monitor (SIM) is a dual Fèry prism spectrometer that employs 5 detectors per spectrometer channel to cover the wavelength range from 200 to 2700 nm. This instrument is used to monitor solar spectral variability throughout this wavelength region. Two identical, mirror-image, channels are used for redundancy and in-flight measurement of prism degradation. The primary detector for this instrument is an electrical substitution radiometer (ESR) designed to measure power levels ∼1000 times smaller than other radiometers used to measure TSI. The four complementary focal plane photodiodes are used in a fast-scan mode to acquire the solar spectrum, and the ESR calibrates their radiant sensitivity. Wavelength control is achieved by using a closed loop servo system that employs a linear charge coupled device (CCD) in the focal plane. This achieves 0.67 arcsec control of the prism rotation angle; this is equivalent to a wavelength positioning error of δλ/λ = 150 parts per million (ppm). This paper will describe the scientific measurement requirements used for instrument design and implementation, instrument performance, and the in-flight instrument operation modes.     

Helical magnetorotational instability of Taylor‐Couette flows in the Rayleigh limit and for quasi‐Kepler rotation

The magnetorotational instability (MRI) of differential rotation under the simultaneous presence of axial and azimuthal components of the (current‐free) magnetic field is considered. For rotation with uniform specific angular momentum the MHD equations for axisymmetric perturbations are solved in a local short‐wave approximation. All the solutions are overstable for B_z · B_ϕ ≠ 0 with eigenfrequencies approaching the viscous frequency. For more flat rotation laws the results of the local approximation do not comply with the results of a global calculation of the MHD instability of Taylor‐Couette flows between rotating cylinders. – With B_ϕ and B_z of the same order the traveling‐mode solutions are also prefered for flat rotation laws such as the quasi‐Kepler rotation. For magnetic Prandtl number Pm → 0 they scale with the Reynolds number of rotation rather than with the magnetic Reynolds number (as for standard MRI) so that they can easily be realized in MHD laboratory experiments. – Regarding the nonaxisymmetric modes one finds a remarkable influence of the ratio B_ϕ/B_z only for the extrema. For B_ϕ ≫ B_z and for not too small Pm the nonaxisymmetric modes dominate the traveling axisymmetric modes. For standard MRI with B_z ≫ B_ϕ, however, the critical Reynolds numbers of the nonaxisymmetric modes exceed the values for the axisymmetric modes by many orders so that they are never prefered. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Mode Conversion of Solar p Modes in non-Vertical Magnetic Fields – i. two-Dimensional Model

Sunspots absorb incident p modes. The responsible mechanism is uncertain. One possibility is mode conversion to slow magnetoacoustic–gravity waves. In vertical field mode conversion can adequately explain the observed f-mode absorption, but is too inefficient to explain the absorption of p modes. In this investigation we calculate the efficiency of fast-to-slow magnetoacoustic–gravity wave conversion in non-vertical field. We assume two-dimensional propagation where the Alfvén waves decouple. It is found that resultant p-mode absorption is significantly enhanced for moderate inclinations at higher frequencies, whereas for p modes at lower frequencies, and the f mode in general, there is no useful enhancement. However, the enhancement is insufficient to explain the observed p-mode absorption by sunspots. Paper II considers the efficiency of mode conversion in non-vertical field with three-dimensional propagation, where fast and slow magnetoacoustic–gravity waves and Alfvén waves are coupled.     

Modelling p-Mode Interaction with a Spreading Sunspot Field

Sunspots absorb and scatter incident p modes. The dominant mechanism is still uncertain. One possibility, mode conversion to slow magneto-acoustic waves, has been shown to yield results in agreement with observations for the f mode only. Absorption of p modes in simple vertical magnetic field models is too weak by an order of magnitude or more. Here we report on numerical calculations of p modes encountering a simple sunspot model with field which spreads with height. It is found that p-mode absorption is greatly enhanced by field spread, to a level consistent with observations, and it appears that it occurs preferentially in the outer regions of the spot, in line with recent results from acoustic holography.     

IN-FLIGHT PERFORMANCE OF THE VIRGO LUMINOSITY OSCILLATIONS IMAGER ABOARD SOHO

The Luminosity Oscillations Imager (LOI) is a part of the VIRGO instrument aboard the Solar and Heliospheric Observatory (SOHO). The scientific objective of the LOI experiment is to identify and characterize pressure and internal gravity oscillations of the Sun by observing the radiance variations. The LOI is a low-resolution imager with 12 pixels, for the measurement of the radiance distribution over the solar disk at 500 nm. The low resolution capability of the instrument allows the identification of individual azimuthal orders for l = 0 to 7, without suffering the mixing that affects integrated solar disk instruments. The performance, calibrations and instrumental effects of the LOI are described together with the procedures for extracting the solar p modes.     

Low-Order p Modes From Virgo Irradiance Data

Several candidates for low-order p modes (n 5) and possibly g modes were found by applying mode-detection techniques such as multivariate spectral regression analysis and time-frequency analysis to the VIRGO full-disc solar irradiance data. Three out of the candidates for low-order p modes could be confirmed by significant peaks in the un-treated power spectra in good agreement with theoretical predictions. The frequency of a fourth candidate for a low-order p mode lies some 2.8 Hz below the predicted frequency. The candidates found for g modes are less reliable, since none of them could be confirmed neither by significant peaks in the un-treated power spectra nor by the detection of multiplets.     

Analysis of the solar low-ℓ p-mode asymmetries using wavelets

It is presently widely accepted that the solar low p modes show asymmetric profiles when their power spectrum is analysed and that the fact of fitting symmetric profiles yields systematic effects in the obtained frequencies which could affect the results of inversions. In this paper the low p-mode profiles are analysed using wavelets to denoise the power spectra of the modes. This denoising method is applied both to artificial data generated by Kosovichev (the Hare and Hound exercise) and to real data obtained with the GOLF instrument. The asymmetries as well as the frequencies obtained are studied in both cases. The results show that although the obtained p-mode profiles present a slightly negative asymmetry, the use of symmetric profiles to fit the power spectra does not introduce any systematic effect in the obtained frequencies.     

Magnetic Field Vector Retrieval With the Helioseismic and Magnetic Imager

We investigate the accuracy to which we can retrieve the solar photospheric magnetic field vector using the Helioseismic and Magnetic Imager (HMI) that will fly onboard of the Solar Dynamics Observatory by inverting simulated HMI profiles. The simulated profiles realistically take into account the effects of the photon noise, limited spectral resolution, instrumental polarization modulation, solar p modes, and temporal averaging. The accuracy of the determination of the magnetic field vector is studied by considering the different operational modes of the instrument.     

Global Oscillations at Low Frequency from the SOHO mission (GOLF)

The GOLF experiment on the SOHO mission aims to study the internal structure of the sun by measuring the spectrum of global oscillations in the frequency range 10^–7 to 10^–2 Hz. Bothp andg mode oscillations will be investigated, with the emphasis on the low order long period waves which penetrate the solar core. The instrument employs an extension to space of the proven ground-based technique for measuring the mean line-of-sight velocity of the viewed solar surface. By avoiding the atmospheric disturbances experienced from the ground, and choosing a non-eclipsing orbit, GOLF aims to improve the instrumental sensitivity limit by an order of magnitude to 1 mm s^–1 over 20 days for frequencies higher than 2.10^–4 Hz. A sodium vapour resonance cell is used in a longitudinal magnetic field to sample the two wings of the solar absorption line. The addition of a small modulating field component enables the slope of the wings to be measured. This provides not only an internal calibration of the instrument sensitivity, but also offers a further possibility to recognise, and correct for, the solar background signal produced by the effects of solar magnetically active regions. The use of an additional rotating polariser enables measurement of the mean solar line-of-sight magnetic field, as a secondary objective.     

The In-Flight Performance of the SOHO/CDS Grazing Incidence Spectrometer

We present the characteristics, operations history, performance, and calibration of the Grazing Incidence Spectrometer (GIS) of the Coronal Diagnostic Spectrometer onboard SOHO. The GIS sensitivity has been monitored in a direct manner by examining the quiet Sun count rates during 1996 – 2006, nearly a whole solar cycle of observations. Overall, the instrument, with its grazing-incidence optics and microchannel plates, has performed exceptionally well. For most spectral regions, changes in the instrument sensitivity have been very small over a 10-year period. The trends in sensitivities support the use of the radiometric calibration of Del Zanna et al. (Astron. Astrophys. 379, 708, 2001) throughout the mission. The verification of the detector performance over such a long period allows us to point out the spectral lines that can reliably be used for scientific analysis.     

Small-Amplitude Disturbances In A Radiating And Scattering Grey Medium Ii. Solutions Of Given Real Wave Number <Emphasis Type="BoldItalic">k</Emphasis>

We study the fundamental modes of radiation hydrodynamic waves arising from one-dimensional small-amplitude initial fluctuations with wave number k in a radiating and scattering grey medium using the Eddington approximation. The dispersion relation analyzed is the same as that of Paper I (Kaneko et al., 2000), but is solved as a quintic in angular frequency ω while a quadratic in k ² in Paper I. Numerical results reveal that wave patterns of five solutions are distinguished into three types of the radiation-dominated and type 1 and type 2 matter-dominated cases. The following wave modes appear in our problem: radiation wave, conservative radiation wave, entropy wave, Newtonian-cooling wave, opacity-damped and cooling-damped waves, constant-volume and constant-pressure diffusion modes, adiabatic sound wave, cooling-damped and drag–force-damped isothermal sound waves, isentropic radiation-acoustic wave, and gap mode. The radiation-dominated case is characterized by the gap between the isothermal sound and isentropic radiation-acoustic speeds within which there is not any acoustic wave propagating with real phase speed. One of the differences between type 1 and type 2 matter-dominated cases is the connectivity of the constant-volume diffusion mode, which originates from the radiative mode in the former case, while from the Newtonian-cooling wave in the latter case. Analytic solutions are derived for all wave modes to discuss their physical significance. The criterion, which distinguishes between radiation-dominated and type 1 matter-dominated cases, is given by Γ₀ = 9, where Γ₀ = C _p ^(tot)/C _V ^(tot) is the ratio of total specific heats at constant pressure and constant volume. Waves in a scattering grey medium are also analyzed, which provides us some hints for the effects of energy and momentum exchange between matter and radiation.     

Separating E from B

In a microwave background polarization map that covers only part of the sky, it is impossible to separate the E and B components perfectly. This difficulty in general makes it more difficult to detect the B component in a data set. Any polarization map can be separated in a unique way into “pure E”, “pure B” and “ambiguous” components. Power that resides in the pure E(B) component is guaranteed to be produced by E(B) modes, but there is no way to tell whether the ambiguous component comes from E or B modes. A polarization map can be separated into the three components either by finding an orthonormal basis for each component, or directly in real space by using Green functions or other methods.     

Flow around sunspots from it p-mode frequency shift measurements

We use five-day helioseimic data from the Taiwan Oscillation Network to study the flow around a sunspot, NOAA 7887. The p-mode oscillations in an annular region centered at the sunspot are decomposed into the modes propagating toward and away from the sunspot. We find that the frequency of an outgoing mode is greater than that of the corresponding incoming mode. This indicates that the plasma is flowing outward from the sunspot. The outflow velocity is estimated to be about 40–80 m s^-1.     

Influence of Low-Degree High-Order p-Mode Splittings on the Solar Rotation Profile

The solar rotation profile is well constrained down to about 0.25R _⊙ thanks to the study of acoustic modes. Since the radius of the inner turning point of a resonant acoustic mode is inversely proportional to the ratio of its frequency to its degree, only the low-degree p modes reach the core. The higher the order of these modes, the deeper they penetrate into the Sun and thus they carry more diagnostic information on the inner regions. Unfortunately, the estimates of frequency splittings at high frequency from Sun-as-a-star measurements have higher observational errors because of mode blending, resulting in weaker constraints on the rotation profile in the inner core. Therefore inversions for the solar internal rotation use only modes below 2.4 mHz for ?≤3. In the work presented here, we used an 11.5-year-long time series to compute the rotational frequency splittings for modes ?≤3 using velocities measured with the GOLF instrument. We carried out a theoretical study of the influence of the low-degree modes in the region from 2 to 3.5 mHz on the inferred rotation profile as a function of their error bars.     

Analysis of MDI High-Degree Mode Frequencies and their Rotational Splittings

We present a detailed analysis of solar acoustic mode frequencies and their rotational splittings for modes with degree up to 900. They were obtained by applying spherical harmonic decomposition to full-disk solar images observed by the Michelson Doppler Imager onboard the Solar and Heliospheric Observatory spacecraft. Global helioseismology analysis of high-degree modes is complicated by the fact that the individual modes cannot be isolated, which has limited so far the use of high-degree data for structure inversion of the near-surface layers (r>0.97R _⊙). In this work, we took great care to recover the actual mode characteristics using a physically motivated model which included a complete leakage matrix. We included in our analysis the following instrumental characteristics: the correct instantaneous image scale, the radial and non-radial image distortions, the effective position angle of the solar rotation axis, and a correction to the Carrington elements. We also present variations of the mode frequencies caused by the solar activity cycle. We have analyzed seven observational periods from 1999 to 2005 and correlated their frequency shift with four different solar indices. The frequency shift scaled by the relative mode inertia is a function of frequency alone and follows a simple power law, where the exponent obtained for the p modes is twice the value obtained for the f modes. The different solar indices present the same result.     

Magnetohydrodynamic modes of a periodic magnetic medium

The oscillations of a magnetic medium periodic in the x-direction with B parallel to z, have been studied. The case with no gravity and a stepwise profile for B(x), allowing a normal mode analysis, has been examined and dispersion relations have been derived. The dispersion curves in the diagram k _z – display two types of modes, kink and sausage, like in the isolated slab, but the profiles are different and depend on Bloch's number k ₀. Moreover, modes usually absent in the isolated slab (propagating and tunelling) appear here, connecting surface- or body-wave domains. The detectability of this characteristic structure of the diagnostic diagram on the observations is discussed, and prospects for a more realistic analysis including gravity are given.     

Orbits of colliding galaxies

A simple, semi-analytic method is developed for obtaining the orbits of galaxies undergoing fast collisions in which the galaxies are represented by Plummer models. The results are found to agree fairly well with those of N-body simulations.A simple formula for obtaining the angle of deflection is deduced. The maximum angle of deflection is 180° forV _p/V _esc(p)=1.00, about 36° forV _p/V _esc(p)=1.50, and about 18° forV _p/V _esc(p)=2.00, whereV _p is the velocity at closest approachp, andV _esc(p) is the parabolic velocity of escape atp. The angle of deflection of a pair of colliding elliptical galaxies without halos is about twice that for a pair of galaxies with halos for the same relative velocity at infinite separation.     

Thermosolutal instability of compressible hall plasma in porous medium

The thermosolutal instability of a plasma in porous medium in the presence of a vertical magnetic field is considered to include the effects of compressibility and Hall currents. The effects of stable solute gradient and compressibility are found to be stabilizing and the Hall currents have a destabilizing effect. The system is stable for (C _p/g)<1;C _p, , andg denoting specific heat at constant pressure, uniform temperature gradient, and acceleration due to gravity, respectively. In contrast to the non-oscillatory modes in the absence of magnetic field and stable solute gradient, the presence of magnetic field (and, hence, Hall currents) and stable solute gradient introduce oscillatory modes for (C _p/g)>1. The case of overstability is also studied wherein the necessary conditions for the existence of overstability are obtained.     

PAPPA: Primordial anisotropy polarization pathfinder array

The primordial anisotropy polarization pathfinder array (PAPPA) is a balloon-based instrument to measure the polarization of the cosmic microwave background and search for the signal from gravity waves excited during an inflationary epoch in the early universe. PAPPA will survey a 20° × 20° patch at the North Celestial Pole using 32 pixels in 3 passbands centered at 89, 212, and 302 GHz. Each pixel uses MEMS switches in a superconducting microstrip transmission line to combine the phase modulation techniques used in radio astronomy with the sensitivity of transition-edge superconducting bolometers. Each switched circuit modulates the incident polarization on a single detector, allowing nearly instantaneous characterization of the Stokes I, Q, and U parameters. We describe the instrument design and status.