Effects of Dispersion of Wave Packets in the Determination of Lifetimes of High-Degree Solar p Modes from Time – Distance Analysis: TON Data

We use the method of time – distance analysis to measure lifetimes of solar p modes in the range ℓ=100 − 600 and ν=3.0 − 4.5 mHz with data taken with the Taiwan Oscillation Network (TON). The lifetimes of p modes are determined by the changes in the amplitude and width of the cross-correlation function of a wave packet with the number of skips. The amplitude of the cross-correlation function decreases exponentially with the number of skips as in previous work. This decrease has been interpreted as the effect of the finite p-mode lifetime. In this study, we find that the width of the cross-correlation function increases with the number of skips. We interpret this phenomenon as the effect of the dispersion of the wave packet. We include this effect in the determination of the lifetime of the wave packet. The lifetime increases after the dispersion is taken into account. We also study the change in lifetime between solar minimum and maximum.     

Effects of Dispersion of Wave Packets in the Determination of Lifetimes of High-Degree Solar <Emphasis Type="Italic">p</Emphasis> Modes from Time – Distance Analysis: MDI Data

The cross-correlation function of solar p modes in a time – distance analysis changes with travel distance (or travel time). The exponential decrease in the amplitude of the cross-correlation function with travel distance has been interpreted as the dissipation of solar p-mode power and used to determine the lifetimes of high-degree p modes. It is found that the width of the cross-correlation function increases with travel distance. We interpret the increase in width as the dispersion of the wave packet in a time – distance analysis. The dispersion would also cause a decrease in amplitude and affect the determination of lifetimes. We include the dispersion effect in the determination of lifetimes of high-degree p modes in a time – distance analysis and find that the derived lifetime increases significantly compared with the previous study for degree less than 400.     

Surface-Focused Seismic Holography of Sunspots: I. Observations

We present a comprehensive set of observations of the interaction of p-mode oscillations with sunspots using surface-focused seismic holography. Maps of travel-time shifts, relative to quiet-Sun travel times, are shown for incoming and outgoing p modes as well as their mean and difference. We compare results using phase-speed filters with results obtained with filters that isolate single p-mode ridges, and we further divide the data into multiple temporal frequency bandpasses. The f mode is removed from the data. The variations of the resulting travel-time shifts with magnetic-field strength and with the filter parameters are explored. We find that spatial averages of these shifts within sunspot umbrae, penumbrae, and surrounding plage often show strong frequency variations at fixed phase speed. In addition, we find that positive values of the mean and difference travel-time shifts appear exclusively in waves observed with phase-speed filters that are dominated by power in the low-frequency wing of the p ₁ ridge. We assess the ratio of incoming to outgoing p-mode power using the ridge filters and compare surface-focused holography measurements with the results of earlier published p-mode scattering measurements using Fourier?–?Hankel decomposition.     

Interpretation of the solar-like pulsational behaviour of η Bootis

HR 5235, better known as η Bootis, is a bright and well-known star for which very accurate observations have recently enabled Kjeldsen et al. (2003) and Carrier, Bouchy, and Eggenberger (2003) not only to confirm the presence of solar-like oscillations, but also to identify the excitation in the oscillation spectrum of several p-mode frequencies with harmonic degrees l = 0 – 2. Here we show how such observational success, through the calculation and the investigation of theoretical structure models and the comparison of the observed oscillation spectra with the predicted p-mode frequencies of oscillations, permits one to draw conclusions about the actual evolutionary state of this star and on the physical properties of its internal structure. The computation of the structure models is based on the use of updated global parameters and includes overshooting from the convective core. In particular, we consider the effect on the stellar structure, and hence on the theoretical frequencies, of employing different equations of state and different formalisms to describe the convective energy transport.     

Mode Conversion of Solar <Emphasis Type="Italic">p</Emphasis>-Modes in Non-Vertical Magnetic Fields

Sunspots absorb and scatter incident f- and p-modes. Until recently, the responsible absorption mechanism was uncertain. The most promising explanation appears to be mode conversion to slow magnetoacoustic-gravity waves, which carry energy down the magnetic field lines into the interior. In vertical magnetic field, mode conversion can adequately explain the observed f-mode absorption, but is too inefficient to account for the absorption of p-modes. In the first paper of the present series we calculated the efficiency of fast-to-slow magnetoacoustic-gravity wave conversion in uniform non-vertical magnetic fields. We assumed two-dimensional propagation, where the Alfvén waves decouple. In comparison to vertical field, it was found that mode conversion is significantly enhanced in moderately inclined fields, especially at higher frequencies. Using those results, Cally, Crouch, and Braun showed that the resultant p-mode absorption produced by simple sunspot models with non-vertical magnetic fields is ample to explain the observations. In this paper, we further examine mode conversion in non-vertical magnetic fields. In particular, we consider three-dimensional propagation, where the fast and slow magnetoacoustic-gravity waves and the Alfvén waves are coupled. Broadly speaking, the p-mode damping rates are not substantially different to the two-dimensional case. However, we do find that the Alfvén waves can remove similar quantities of energy to the slow MAG waves.     

Solar Wind Statistics at 1 AU: Alfven Speed and Plasma Beta

The phenomenon of MHD wave refraction is useful in interpreting the properties of the magnetic fluctuations in certain parcels of solar wind. In the physics of MHD wave refraction, variations in the Alfvén speed V_Alf play a dominant role. Here, we compile statistics of the 1-min averages of V_Alf at the location of the ACE spacecraft during its first 5 years of operation. We find that monthly distributions of V_Alf are close to log-normal, with standard deviations σ_V as small as 0.11 in the logarithm. Variations in the monthly mean V_Alf are correlated significantly with sunspot number. We also compile monthly distributions of the plasma β parameter. The distributions of both V_Alf and β are significantly narrower than they would be if the various solar wind parameters were statistically independent. In the T_p–V_Alf plane, we find a zone of avoidance at low V_Alf: for V_Alf ≤10 – 15 km/s, there are no samples in the 1-min data that are cooler than T_p = 10 000 – 15 000 K. This feature can be understood in the context of MHD wave refraction, although other explanations are also possible.     

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.     

An Estimate of <Emphasis Type="Italic">P</Emphasis>-Mode Damping by Wave Leakage

High-cadence TRACE observations show that outward-propagating intensity disturbances are a common feature in large, quiescent coronal loops. Analysis of the frequency distribution of these modes shows peaks at both three- and five-minute periods, indicating that they may be driven by the solar surface oscillations (p modes). The energy flux contained within the coronal intensity disturbances is of the order of (1.1±0.4)×10³ ergs cm⁻² s⁻¹. A simple order-of-magnitude estimate of the damping rate of the relevant p modes allows us to put an observational constraint on the damping of p modes and shows that leakage into the overlying coronal atmosphere might be able to account for a significant fraction of p-mode damping.     

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.     

How Good are the Predictions for Oscillation Frequencies

We have used available intermediate degree p-mode frequencies for solar cycle 23 to check the validity of previously derived empirical relations for frequency shifts (Jain et al., 2000). We find that the calculated and observed frequency shifts during the rising phase of cycle 23 are in good agreement. The observed frequency shift from minimum to maximum of this cycle as calculated from MDI frequency data sets is 251±7 nHz and from GONG data is 238±11 nHz. These values are in close agreement with the empirically predicted value of 271±22 nHz.     

A New Way to Model the Solar Oscillation ℓ−ν Power Spectrum

We present a new approach for the precise and accurate forward modeling of the solar oscillation ℓ−ν power spectrum. The approach is designed to provide the basis for a streamlined solar seismic inversion without measurements of the p-mode frequencies. The new strategy represents a paradigm change in how information is extracted from the oscillation spectrum. It also represents a step toward the ideal case of inferring the Sun's properties directly from the raw observations.     

Toward Waveform Heliotomography: Observing Interactions of Helioseismic Waves with a Sunspot

We investigate how helioseismic waves that originate from effective point sources interact with a sunspot. These waves are reconstructed from observed stochastic wavefields on the Sun by cross-correlating photospheric Doppler-velocity signals. We select the wave sources at different locations relative to the sunspot, and investigate the p- and f-mode waves separately. The results reveal a complicated picture of waveform perturbations caused by the wave interaction with the sunspot. In particular, it is found that for waves originating from outside of the sunspot, p-mode waves travel across the sunspot with a small amplitude reduction and slightly higher speed, and wave amplitude and phase get mostly restored to the quiet-Sun values after passing the sunspot. The f-mode wave experiences some amplitude reduction passing through the sunspot, and the reduced amplitude is not recovered after that. The wave-propagation speed does not change before encountering the sunspot and inside the sunspot, but the wavefront becomes faster than the reference wave after passing through the sunspot. For waves originating from inside the sunspot umbra, both f- and p-mode waves show significant amplitude reductions and faster speed for all propagation paths. A comparison of positive and negative time lags of cross-correlation functions shows an apparent asymmetry in the waveform changes for both the f- and p-mode waves. We suggest that the waveform variations of the helioseismic waves interacting with a sunspot found in this article can be used for developing a method of waveform heliotomography, similar to the waveform tomography of the Earth.     

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.     

Realistic Solar Convection Simulations

We report on realistic simulations of solar surface convection that are essentially parameter-free, but include detailed physics in the equation of state and radiative energy exchange. The simulation results are compared quantitatively with observations. Excellent agreement is obtained for the distribution of the emergent continuum intensity, the profiles of weak photospheric lines, the p-mode frequencies, the asymmetrical shape of the mode velocity and intensity spectra, the p-mode excitation rate, and the depth of the convection zone. We describe how solar convection is non-local. It is driven from a thin surface thermal boundary layer where radiative cooling produces low entropy gas which forms the cores of the downdrafts in which most of the buoyancy work occurs. Turbulence and vorticity are mostly confined to the intergranular lanes and underlying downdrafts. Finally, we present some preliminary results on magneto-convection.     

Seismology of the solar convection zone

An attempt is made to infer the structure of the solar convection zone from observedp-mode frequencies of solar oscillations. The differential asymptotic inversion technique is used to find the sound speed in the solar envelope. It is found that envelope models which use the Canuto-Mazzitelli (CM) formulation for calculating the convective flux give significantly better agreement with observations than models constructed using the mixing length formalism. This inference can be drawn from both the scaled frequency differences and the sound speed difference. The sound speed in the CM envelope model is within 0.2% of that in the Sun except in the region withr > 0.99R _⊙. The envelope models are extended below the convection zone, to find some evidence for the gravitational settling of helium beneath the base of the convection zone. It turns out that for models with a steep composition gradient below the convection zone, the convection zone depth has to be increased by about 6 Mm in order to get agreement with helioseismic observations.     

Bianchi type-II space-times with constant deceleration parameter in self creation cosmology

The properties of locally rotationally symmetric Bianchi type-II perfect fluid space-times are analyzed in Barber’s second self-creation theory by using a special law of variation for Hubble’s parameter that yields a constant value of deceleration parameter. By assuming the equation of state p=γ ρ, many new solutions are obtained for different era—Zel’dovich, radiation, vacuum and vacuum energy dominated. The solutions with power-law and exponential expansion are discussed. A detailed study of geometrical and physical parameters is carried out. The nature of singularity is also clarified in each case.     

Frequencies of low-degree solar acoustic oscillations and the phase of the solar cycle

A study of the solar total irradiance data of the Active Cavity Radiometer Irradiance Monitor (ACRIM) on the Solar Maximum Mission (SMM) satellite shows a small but formally significant shift in the frequencies of solar acoustic (p-mode) oscillations between the epochs of maximum and minimum solar activity. Specifically, the mean frequency of the strongest p-mode resonances of low spherical-harmonic degree (l = 0–2) is approximately 1.3 parts in 10⁴ higher in 1980, near the time of sunspot maximum, than in 1985, near sunspot minimum. The observed frequency shift may be an 11-yr effect but the precise mechanism is not clear.     

Distinguishing RBL-like Objects and XBL-Like Objects With thePeak Emission Frequency of the Overall Energy Spectrum

We investigate quantitatively how the peak emission frequency of the overall energy spectrum is at work in distinguishing RBL-like and XBL-like objects. We employ the sample of Giommi et al. (1995) to study the distribution of BL Lacertae objects with various locations of the cutoff of the overall energy spectrum. We find that the sources with the cutoff located at lower frequency are indeed sited in the RBL region of the α_ro-α_oxplane, while those with the cutoff located at higher frequency are distributed in the XBL region. For a more quantitative study, we employ the BL Lacerta esamples presented by Sambruna et al. (1996), where the peak emission frequency, ν_p, of each source is estimated by fitting the data with a parabolic function. In the plot of α_rx -log ν_p we find that, in the four different regions divided by the α_rx = 0.75 line and thelogν_p = 14.7 line, all the RBL-like objects are inside the upper left region, while most XBL-like objects are within the lower right region. A few sources are located in the lower left region. No sources are in the upper right region. This result is rather quantitative. It provides an evidence supporting what Giommi et al. (1995) suggested: RBL-like and XBL-like objects can be distinguished by the difference of the peak emission frequency of the overall energy spectrum. This revised version was published online in July 2006 with corrections to the Cover Date.     

Galaxy Evolution from Deep Field Galaxy Counts

We present deep galaxy number counts and colours of K—band selected galaxy surveys. We argue that primeval galaxies are present within the survey data, but have remained unidentified. There are few objects with the colours of an L ^* elliptical galaxy at a redshift of z ≈ 1, in contradiction to standard luminosity evolution models. We present K—band photometry of the objects in a spectroscopic redshift survey selected at 21 < B < 22.5. The absolute K magnitudes of the galaxies are consistent with the no-evolution or pure luminosity evolution models. The excess faint blue galaxies seen in the B—band number counts at intermediate magnitudes are a result of a low normalization, and do not dominate the population until B ≈ 25. Extreme merging or excess dwarf models are not needed at z < 1. This revised version was published online in July 2006 with corrections to the Cover Date.     

FIRST RESULTS FROM VIRGO,THE EXPERIMENT FOR HELIOSEISMOLOGY AND SOLAR IRRADIANCE MONITORING ON SOHO

First results from the VIRGO experiment (Variability of solar IRradiance and Gravity Oscillations) on the ESA/NASA Mission SOHO (Solar and Heliospheric Observatory) are reported. The observations started mid-January 1996 for the radiometers and sunphotometers and near the end of March for the luminosity oscillation imager. The performance of all the instruments is very good, and the time series of the first 4–6 months are evaluated in terms of solar irradiance variability, solar background noise characteristics and p-mode oscillations. The solar irradiance is modulated by the passage of active regions across the disk, but not all of the modulation is straightforwardly explained in terms of sunspot flux blocking and facular enhancement. Helioseismic inversions of the observed p-mode frequencies are more-or-less in agreement with the latest standard solar models. The comparison of VIRGO results with earlier ones shows evidence that magnetic activity plays a significant role in the dynamics of the oscillations beyond its modulation of the resonant frequencies. Moreover, by comparing the amplitudes of different components ofp -mode multiplets, each of which are influenced differently by spatial inhomogeneity, we have found that activity enhances excitation.