On Novel Methods to Determine Areas of Sunspots from Photoheliograms

Two novel methods of measuring umbral and penumbral areas of sunspots and of complex sunspot groups are described. Both methods comprise the digitization of photoheliograms by a frame grabber and the computation of intensity histograms of selected areas of activity. The first method, called cumulative histogram method, in principle determines the intensity boundaries umbra–penumbra and penumbra–photosphere from the intersections of linear fits into the corresponding parts of the cumulative histograms of sunspots. The second method, called maximum gradient method, marks image pixels of a given intensity level ±2 units wide as a white isophote on a display. Interactive variation of this level makes it easy to visually select the contour line fitting the boundary penumbra–photosphere (or umbra–penumbra) best. At the same level usually the width of the contour line is smallest. In both cases the summation of the pixel numbers above the corresponding intensity levels yields the umbral and the total sunspot areas, respectively. Some limitations of the two methods are discussed.     

Dynamic phenomena in the chromospheric layer of a sunspot

We have studied running penumbral waves, umbral oscillations, umbral flashes and their interrelations from H observations of a large isolated sunspot. Using a subtraction image processing technique we removed the sharp intensity gradient between the umbra and the penumbra and enhanced the low contrast, fine features. We observed running penumbral waves which started in umbral elements with a size of a few arcseconds, covered the umbra and subsequently propagated through the penumbra. The period of the waves was 190 s and the mean propagation velocity was about 15 km s^–1. We detected intense brightenings, located between umbral elements from where waves started, which had the characteristics of umbral flashes. There are indications that umbral flashes are related to the propagation of the waves through the umbra and their coupling. The subtraction images also show considerable fine structure in the chromospheric umbra, with size between 0.3 and 0.8.     

Statistical survey of planetary nebulae: Distances,masses, and distribution in the galaxy

On the basis of empirical (D)-dependency at the frequency of 5 GHz constructed using 15 planetary nebulae with the independently measured distances (10^–171×10^–20 W m^–2 Hz^–1 ster^–1), we evaluated distances of 335 objects. Independent evidence of the correctness of the accepted scale are given. Then(D)-dependency is constructed and it is shown that atD<0.08 pc the mean electron density is higher than the one determined by the Seaton method. We showed that the filling factor diminishes with the increase of the PN diameter (1 atD0.08 pc and 0.2 atD0.4 pc). the ionized mass of 33 PNs is determined. With the diameter increase the ionized mass grows and atD0.4 pc reaches the valueM0.07M . We used the new distance scale when investigating the space distribution of PNs. The mean scale height =130±15 pc and the mean gradient of the change of surface densitym=0.37, which allowed us to estimate the total number of nebulae in the GalaxyN4×10⁴. We divided the PNs according to their velocities (withV _LSR>35 km s^–1 andV _LSR<35 km s^–1) and permitted us to confirm that the PN belong to different sub-systems of the Galaxy. The estimated local formation rate of PNs [=(4.6±2.2)×10^–12 pc^–3 yr^–1] is a little higher than the one of the white dwarfs. That can be explained by a large number of PNs having binary cores, which used in our sample. The statistical estimation of PN expansion velocity showed thatV _ex increases from 5–7 km s^–1 (atD0.03 pc) to 40–50 km s^–1 (atD0.8 pc).     

A refined measurement of the sunspot radiative flux deficit

New measurements of the radiative flux deficits of two large sunspots are presented, based on detailed isophotometric maps. Results are given separately for umbrae and penumbrae. The umbral and penumbral deficits are 4–5 × 10¹⁰ and 1–1.5 × 10¹⁰ erg cm^–2 s^–1 respectively, the larger figures ref to the larger spot. Over limited areas centered on the umbral cores the deficits for the two spots amount to 76 and 86% of the photospheric flux.     

Photospheric and chromospheric umbral dots in a decaying sunspot

Time-sequenced H filtergrams and narrow-band blue filtergrams (₀ = 4308 Å, = 10 Å) of umbral dots in a decaying sunspot were studied. The results are: (a) Photospheric umbral dots have lifetimes of about 40 min. (b) Two types of proper motion were found for photospheric umbral dots. Umbral dots born in the umbra or in the light bridge show virtually no proper motion. On the other hand, umbral dots of penumbral origin move inward to the umbra with speeds of about 0.4 km s ^–1. (c) Chromospheric umbral dots, which have dimensions of 0.6 × 1.2 in the mean, were more numerously found than photospheric umbral dots. (d) Photospheric umbral dots were observed to be associated with chromospheric umbral dots. Thus umbral dots are not phenomena confined to photospheric levels but also extend to chromospheric levels. (e) Some of the chromospheric umbral dots are unrelated to the photospheric umbral dots. They may be excited by the infalling matter from the umbral corona.Contribution from the Kwasan and Hida Observatories, University of Kyoto, No. 266.     

Almost stable regions for an area-preserving mapping

The area preserving mapping x = x + a(y – y ³), y = y – a(x – x³), for 0.3 a 2.0 has been studied to locate approximately the x-axis points bounding almost stable regions. For each value of a, these are fixed points with variational trace just greater than 2.0. Transition to chaos can occur rapidly as a increases (with n/k fixed).     

RKRV Potential Energy Curves, Dissociation Energies, γ-Centroids And Franck-Condon Factors Of YO, CrO, BN, ScO, SiO And AlO Molecules

The potential energy curves for the electronic ground states of astrophysically important YO, CrO, BN, ScO, SiO and AlO molecules are constructed techniques using the five-parameter Hulburt-Hirschfelder function. The estimated dissociation energies are 7.235±0.15, 4.337 ± 0.09, 3.917 ± 0.09, 6.899 ± 0.14, 8.181 ± 0.17 and 5.202 ± 0.11 eV for YO, CrO, BN, ScO, SiO and AlO, respectively. The estimated D₀ values are in reasonably good agreement with literature values. The r-Centroids and Franck-Condon factors for the bands of B^{2 +} – X^{2 +} of YO, B⁵ –X⁵ > of CrO, A³ – X³ of BN, B^{2 +} –X^{2 +} of ScO, E^{1 +} – X^{1 +} of SiO and D^{2 +} – X^{2 +} and B^{2 +} –X^{2 +} of AlO molecules have been determined. The Franck-Condon factors are evaluated by the approximate analytical method of Jarmain and Fraser. The absence of the bands in these systems is explained.     

Large-amplitude low-frequency electromagnetic waves in pulsar magnetospheres

Nonlinear propagation of strong low-frequency waves, as emitted by pulsars or compact galactic nuclei at their rotation frequencies, in a magnetized plasma is investigated. It is shown that even rather small amplitude waves can drive electrons to ultrarelativistic energies. In the limit when the electrons are ultrarelativistic but the ions are immobile, two types of circularly polarized waves (i.e., ^± modes) are excited. In the wave zone of the Crab pulsar, both the electric field ( 3 V m^–1) and the wavelength (10⁸ m) of the ^- mode are larger, by an order of magnitude, than those of the ⁺ wave mode. Both ^± modes can become modulationally unstable due to their nonlinear interaction with density fluctuations induced by the electrostatic waves.     

Umbral oscillations and penumbral waves in Hα

We present examples of umbral oscillations observed on Big Bear H filtergram movies and investigate the relation between umbral oscillations and running penumbral waves occurring in the same sunspot. Umbral oscillations near the center of the umbra are probably physically independent of the penumbral waves because the period of these umbral oscillations (150 s) is shorter than the penumbral wave period (270 s) but not a harmonic. We also report dark puffs which emerge from the edge of the umbra and move outward across the penumbra, and which have the same period as the running penumbral waves. We interpret these dark puffs to be the extension of chromospheric umbral oscillations at the edge of the umbra. It is suggested that the dark puffs and the running penumbral waves have a common source: photospheric oscillations just inside the umbra.     

Dynamics of Blinkers

The relative Doppler and non-thermal velocities of quiet-Sun and active-region blinkers identified in Ov with CDS are calculated. Relative velocities for the corresponding chromospheric plasma below are also determined using the Hei line. Ov blinkers and the chromosphere directly below, have a preference to be more red-shifted than the normal transition region and chromospheric plasma. The ranges of these enhanced velocities, however, are no larger than the typical spread of Doppler velocities in these regions. The anticipated ranges of Doppler velocities of blinkers are 10–15 km s^–1 in the quiet Sun (10–20 km s^–1 in active regions) for Hei and 25–30 km s^–1 in the quiet Sun (20–40 km s^–1 in active regions) for Ov. Blinkers and the chromosphere below also have preferentially larger non-thermal velocities than the typical background chromosphere and transition region. Again the increase in magnitude of these non-thermal velocities is no greater than the typical ranges of non-thermal velocities. The ranges of non-thermal velocities of blinkers in both the quiet Sun and active regions are estimated to be 15–25 km s^–1 in Hei and 30–45 km s^–1 in Ov. There are more blinkers with larger Doppler and non-thermal velocities than would be expected in the whole of the chromosphere and transition region. The recently suggested mechanisms for blinkers are revisited and discussed further in light of the new results.     

The proper motion VS redshift relation for superluminal radio sources

Two models for superluminal radio sources predict sharp lower bounds for the apparent velocities of separation. The light echo model predicts a minimum velocityv _min=2c, and the dipole field model predictsv _min=4.446c. Yahil (1979) has suggested that, if either of these models is correct, thenv _min provides a standard velocity which can be used to determine the cosmological parametersH andq ₀. This is accomplished by estimating a lower envelope for the proper motion vs redshift relation. Yahil also argued that the procedure could easily be generalized to include a nonzero cosmical constant . We derive the formulas relating the proper motion to the redshiftz in a Friedmann universe with a nonzero . We show that the determination of a lower envelope for a given sample of measured points yields an estimate of the angle of inclination _i for each source in the sample. We formulate the estimation of the lower envelope as a constrained maximum likelihood problem with the constraints specified by the expected value of the largest order statistic for the estimated _i . We solve this problem numerically using an off-the-shelf nonlinearly constrained nonlinear optimization program from the NAg library. Assuming =0, we apply the estimation procedure to a sample of 27 sources with measured values , using both the light echo and the dipole field models. The fits giveH=103 km s^–1 Mpc^–1 for the light echo model andH=46 km s^–1 Mpc^–1 for the dipole field model. In both cases the fits giveq ₀=0.4, but the uncertainty in this result is too large to rule out the possibility thatq ₀>0.5. When is allowed to be a free parameter, we obtainH=105 km s^–1 Mpc^–1 for the light echo model andH=47 km s^–1 Mpc^–1 for the dipole field model. In both cases the fits giveq ₀=–1 and /H ₀ ² =6.7, but no significance can be attached to these results because of the paucity of measured data at hight redshifts. For all of the fits, we compute the corresponding estimates of the _i and compare the cumulative distribution of these values with that expected from a sample of randomly oriented sources. In all cases we find a large excess of sources at low-inclination angles (high apparent velocities). The expected selection effect would produce such an excess, but the excess is large enough to suggest a strong contamination of the sample by relativistic beam sources which would only be seen at low inclination angles.Applied Research Corporation     

Imaging Spectropolarimetry of Ti I 2231 nm in a Sunspot

Spectro-polarimetric observations at 2231 nm were made of NOAA 10008 near the west solar limb on 29 June 2002 using the National Solar Observatory McMath–Pierce Telescope at Kitt Peak and the California State University Northridge – National Solar Observatory infrared camera. Scans of spectra in both Stokes I and Stokes V were collected; the intensity spectra were processed to remove strong telluric absorption lines, and the Stokes V umbral spectra were corrected for instrumental polarization. The sunspot temperature is computed using the continuum contrast and umbral temperatures down to about 3700 K are observed. A strong Tii line at 2231.0 nm is used to probe the magnetic and velocity fields in the spot umbra and penumbra. Measurements of the Tii equivalent width versus plasma temperature in the sunspot agree with model predictions. Zeeman splitting measurements of the Stokes I and Stokes V profiles show magnetic fields up to 3300 G in the umbra, and a dependence of the magnetic field on the plasma temperature similar to that which was seen using Fei 1565 nm observations of the same spot two days earlier. The umbral Doppler velocity measurements are averaged in 16 azimuthal bins, and no radial flows are revealed to a limit of ±200 m s^–1. A Stokes V magnetogram shows a reversal of the line-of-sight magnetic component between the limb and disk center sides of the penumbra. Because the Tii line is weak in the penumbra, individual spectra are averaged in azimuthal bins over the entire penumbral radial extent. The averaged Stokes V spectra show a magnetic reversal as a function of sunspot azimuthal angle. The mean penumbral magnetic field as measured with the Stokes V Zeeman component splitting is 1400 G. Several weak spectral lines are observed in the sunspot and the variation of the equivalent width versus temperature for four lines is examined. If these lines are from molecules, it is possible that lines at 2230.67, 2230.77, and 2231.70 nm originate from OH, while the line at 2232.21 nm may originate from CN.     

Periodic and non-periodic phenomena in a sunspot region

We have studied running penumbral waves, the homogeneous Evershed effect, and the spatial relation between intensity and Doppler velocity penumbral features of a chromospheric sunspot. The observations were obtained with the multichannel subtractive double-pass spectrograph (MSDP) operating in H at the Vacuum Tower Telescope (VTT) installed at Tenerife (Canary Islands). We derived intensity and Doppler velocity maps at H ± 0.3 Å over a two-dimensional field of view. We have computed the components of the velocity vector (radial, azimuthal, vertical) as a function of distance from the center of the spot under the assumption of axial symmetry. The results show the well-known, from previous observations, general large-scale characteristics of the chromospheric Evershed flow. Our measurements show that the axes along the discrete structures, where the Evershed flow is confined, are not spatially related to the axes along H ± 0.3 Å intensity features, and we suggest that either the flow is confined in flow channels or that it takes place along sheared magnetic field lines. We also detected, for the first time in velocity images, running penumbral waves, which started in the outer 0.3 of the umbral radius and propagated through the penumbra with propagation velocities 13–24 km s^–1. The propagation velocity, as well as the velocity amplitude, is greater for the waves closer to the center of the spot and diminishes as one moves outward.     

Understanding Solar Flare Waiting-Time Distributions

The observed distribution of waiting times t between X-ray solar flares of greater than C1 class listed in the Geostationary Operational Environmental Satellite (GOES) catalog exhibits a power-law tail (t) for large waiting times (t>10hours). It is shown that the power-law index varies with the solar cycle. For the minimum phase of the cycle the index is =–1.4±0.1, and for the maximum phase of the cycle the index is –3.2±0.2. For all years 1975–2001, the index is –2.2±0.1. We present a simple theory to account for the observed waiting-time distributions in terms of a Poisson process with a time-varying rate (t). A common approximation of slow variation of the rate with respect to a waiting time is examined, and found to be valid for the GOES catalog events. Subject to this approximation the observed waiting-time distribution is determined by f(), the time distribution of the rate . If f() has a power-law form for low rates, the waiting time-distribution is predicted to have a power-law tail (t)^–(3+) (>–3). Distributions f() are constructed from the GOES data. For the entire catalog a power-law index =–0.9±0.1 is found in the time distribution of rates for low rates (<0.1hours ^–1). For the maximum and minimum phases power-law indices =–0.1±0.5 and =–1.7±0.2, respectively, are observed. Hence, the Poisson theory together with the observed time distributions of the rate predict power-law tails in the waiting-time distributions with indices –2.2±0.1 (1975–2001), –2.9±0.5 (maximum phase) and –1.3±0.2 (minimum phase), consistent with the observations. These results suggest that the flaring rate varies in an intrinsically different way at solar maximum by comparison with solar minimum. The implications of these results for a recent model for flare statistics (Craig, 2001) and more generally for our understanding of the flare process are discussed.     

The Splitting Or Disappearance of the Solar 160-Min Mode?

The CrAO-WSO-network experiment was designed for detection of low-degree oscillations of the Sun representing either its normal g -modes or those driven by, e.g., rapid (hypothetical) rotation of the central solar core. The Doppler-shift measurements were made in 1974–1995 at both sites during about 13600 hr, in all. Taking into account the upper limit (0.08 m s^-1) for amplitudes of potential g-modes, attention is paid to the Sun's behaviour at frequencies near the 9th daily harmonic (period P 160.The two main issues follow from analysis of the combined CrAO-WSO data: (a) in 1974–1982 the primary period of solar pulsation was P ₀160.0099 ± 0.0016 ± 0.0016 min, but (b) during the last 13 yr it attained a new value, P ₁ 159.9654 ± 0.0010 min, which happens to be a near-annual sidelobe of P ₀. We find therefore that the phase stability of the 160-min mode is no longer present: it appears to be splitted at least into a pair of oscillations,P ₀ and P ₁, having perhaps different physical origins. But the most striking is the fair coincidence of the strongest peaks in the two data sets: CrAO (1974–1995): P = 159.9662 ±0.0006 min, WSO (1977–1994): P = 159.9663 ± 0.0007 min. The existence of two frequencies,P ^-1 ₀ and P ^-1 ₁, with their separation corresponding to 1-yr period, seems to be difficult to explain in terms of gravity g modes.     

SERTS-97 Measurements Of Relative Wavelength Shifts In Coronal Emission Lines Across A Solar Active Region

We used slit spectra from the 18 November 1997 flight of Goddard Space Flight Center's Solar EUV Rocket Telescope and Spectrograph (SERTS-97) to measure relative wavelength shifts of coronal emission lines as a function of position across NOAA active region 8108. The shifts are measured relative to reference wavelengths derived from spectra of the region's nearby quiet surroundings (not necessarily at rest) because laboratory rest wavelengths for the coronal EUV lines have not been measured to sufficient accuracy for this work. An additional benefit to this approach is that any systematic uncertainties in the wavelength measurements are eliminated from the relative shifts by subtraction. We find statistically significant wavelength shifts between the spatially resolved active region slit spectra and the reference spectrum. For He ii 303.78 Å the maximum measured relative red shift corresponds to a Doppler velocity +13 km s^–1, and the maximum relative blue shift corresponds to a Doppler velocity –3 km s^–1. For Si x 347.40 Å, Si xi 303.32 Å, Fe xiv 334.17 Å, and Fe xvi 335.40 Å the corresponding maximum relative Doppler velocities are +19 and –14, +23 and –7, +10 and –10, and +13 and –5 km s^–1, respectively. The active region appears to be divided into two different flow areas; hot coronal lines are predominantly red-shifted in the northern half and either blue-shifted or nearly un-shifted in the southern half. This may be evidence that material flows up from the southern part of the region, and down into the northern part. Qualitatively similar relative wavelength shifts and flow patterns are obtained with SOHO/CDS spectra.     

The Coronal Mass Ejection Waiting-Time Distribution

The distribution of times t between coronal mass ejections (CMEs) in the Large Angle and Spectrometric Coronagraph (LASCO) CME catalog for the years 1996–2001 is examined. The distribution exhibits a power-law tail (t) with an index –2.36±0.11 for large waiting times (t>10 hours). The power-law index of the waiting-time distribution varies with the solar cycle: for the years 1996–1998 (a period of low activity), the power-law index is –1.86±0.14, and for the years 1999–2001 (a period of higher activity), the index is –2.98±0.20. The observed CME waiting-time distribution, and its variation with the cycle, may be understood in terms of CMEs occurring as a time-dependent Poisson process. The CME waiting-time distribution is compared with that for greater than C1 class solar flares in the Geostationary Operational Environmental Satellite (GOES) catalog for the same years. The flare and CME waiting-time distributions exhibit power-law tails with very similar indices and time variation.     

An Erupting Active Region Filament: Three-Dimensional Trajectory and Hydrogen Column Density

From 15:33 through 16:02 UT on 13 June 1998, observations of an erupting filament as it crossed solar disk center were obtained with the NSO/KPVT and SOHO/CDS instruments as part of the SOHO Joint Observing Program 70. Context observations show that this event was the eruption of the north-east section of a small active region filament associated with NOAA 8237, that the photospheric magnetic field was changing in this active region between 12–14 June 1998, and that a coronal Moreton-wave disk event occurred, as well as a white-light CME off the south-west solar limb. The NSO/KPVT imaging spectroscopy data covered 512 × 512 arc sec of the disk center and were spectrally centered at the Hei 1083 nm line and captured ±1.0 nm of surrounding solar spectrum. The Hei absorption line is seen blue-shifted to velocities of between 200 and 300 km s^–1. The true solar trajectory of the eruption is obtained by using the projected solar coordinates and by integrating the Doppler velocity. The filament travels with a total velocity of about 300 km s^–1 along a path inclined roughly 49 deg to the solar surface and rises to a height of just over 1.5 solar radii before it becomes too diffuse to follow. The filament also shows internal motions with multiple Doppler components shifted by ±25 km s^–1. Finally, the KPVT data show no Stokes V profiles in the Doppler-shifted Hei 1083.03 nm absorption to a limit of roughly 3×10^–3 times the continuum intensity. The SOHO/CDS scanned the center of the KPVT FOV using seven EUV lines; Doppler-shifted filament emission is seen in lines from Hei 58.4 nm, Heii 30.4 nm, Oiv 55.5 nm, Ov 63.0 nm, Nevi 56.3 nm, and Mgx 61.0 nm representing temperatures from about 2×10⁴K through 1×10⁶K. Bound-free continuum absorption from Hi, without confusion from foreground emission and line emission, is seen as the filament obscures underlying chromospheric emission. A fit to the wavelength dependence of the absorption from five lines between 55.5 to 63.0 nm yields a column density _H I =4.8±2.5×10¹⁷ cm^–2. Spatial maps show that this filament absorption is more confined than the regions which show emission.     

The spatial distribution and birth-rate of pulsars

The distribution of pulsars in the wide range of observed luminosities has been obtained. It is shown that the function of luminosity (FL) within 3×10²⁶L2×10³⁰ erg s^–1 conforms to the power law dN/dL–c ₁ L ^–, where =1.76±0.06. ForL3×10²⁶ erg s^–1, FL changes its inclination and may be approximated as , where ₁ = 0.7±0.2. On the basis of statistical selection, including all pulsars withL>3×10²⁸ erg s^–1, the distribution of pulsars has been investigated as a function of the distance to the centreR and galactic planeZ.The obtained laws of the radial andZ-distribution of pulsars and galactic supernova remnants and also the radial distribution of types I and II supernovae in the models Sb and Sc support the hypothesis of their origin from the objects of the flat subsystem of Population I. Since there are some arguments in favour of a possible connection between supernovae I and the objects of the intermediate component of the Galaxy, one cannot exclude the possibility of supernovae explosions at the end of the evolution of stars with masses of 1.5–2M . It is also shown that pulsars and supernovae are evidently objects that are connected genetically, and, within the limits of statistical error, they have a similar birth-rate.The empirical law of the evolution of a pulsar's luminosity as a function of its true age has been obtained, according to whichL=c ₂ t ^–, wherec ₂=(3.69±3.4)×10³⁵, =1.32±0.11.     

Pulsars: Observational parameters and a discussion on dispersion measures

The relevant data for the known 147 pulsars are presented in graphical and tabular forms. Various data correlations are discussed, and a detailed analysis of pulsar dispersion measures and distances is given. The range of the electron densities in the diffuse interstellar medium is found to be 0.01 cm^–3n _e0.1 cm^–3, and n _e0.03 cm^–3. The dispersion scale height for pulsars is found to be 5.9±0.7 pc cm^–3 implying a linear scale height of 200 pc, which is much smaller than the electron scale height of our Galaxy.Astrophysics and Space Science Review Paper.