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1.
Recently, Juckett and Wolff (Solar Phys.
252, 247, 2008) showed that the timing and longitude of sunspot patterns has some correspondence with a model based on coupled g modes. The model maximizes the nonlinear coupling of those g modes sharing harmonic degree ℓ to generate a “set(ℓ)” that assists its own excitation by locally enhancing nuclear burning. Each set(ℓ) has oscillatory power concentrated at two longitudes, on opposite sides of the Sun and drifts slowly retrograde within the
radiative zone (RZ) at a rate that depends on ℓ. When the strong longitudes of two or more sets overlap, wave dissipation adds extra energy to that locality at the base
of the convective envelope increasing convection and then sunspot activity. We compare the main subdecadal sunspot frequencies
with the intersections of sets derived from ℓ=2 – 11 and G, where G represents unresolvable high-ℓ modes that rotate similarly to the RZ. After determining the set(ℓ) spatial phases, we show that 17 subdecadal oscillations with periods in the range 0.6 to 7.0 years (4.5 to 50 nHz), generated
by 23 unique intersections of the 11 sets, are synchronous with 17 corresponding frequencies in the sunspot time series. After
optimizing parameters, we find a mean correlation of 0.96 for synchrony among the 17 waveform pairs. These 17 frequencies
constitute the bulk of the non-noise subdecadal frequency domain of the sunspot variation. We conclude that the sunspot series
contains oscillatory components with the same temporal phases and frequencies as various set(ℓ) intersections spanning the past ≈ 100 years. This additional evidence for the role of coupled g modes in sunspot dynamics suggests that more of sunspot variability can be understood with nonmagnetic fluid mechanics than
popularly thought. 相似文献
2.
Results are presented from a study of various sunspot contrast parameters in broadband red (672.3 nm) Cartesian full-disk
digital images taken at the San Fernando Observatory (SFO) over eight years, 1997 – 2004, of the twenty-third sunspot cycle.
A subset of over 2700 red sunspots was analyzed and values of average and maximum sunspot contrast as well as maximum umbral
contrast were compared to various sunspot parameters. Average and maximum sunspot contrasts were found to be significantly
correlated with sunspot area (r
s=− 0.623 and r
s=− 0.714, respectively). Maximum umbral contrast was found to be significantly correlated with umbral area (r
s=− 0.535). These results are in agreement with the works of numerous other authors. No significant dependence was detected
between average contrast, maximum contrast, or maximum umbral contrast during the rising phase of the solar cycle (r
s=0.024, r
s=0.033, and r
s=0.064, respectively). During the decay phase, no significant correlation was found between average contrast or maximum contrast
and time (r
s=− 0.057 and r
s=0.009, respectively), with a weak dependence seen between maximum umbral contrast and cycle (r
s=0.102). 相似文献
3.
We examine daily records of sunspot group areas (measured in millionths of a solar hemisphere or μHem) for the last 130 years
to determine the rate of decay of sunspot group areas. We exclude observations of groups when they are more than 60° in longitude
from the central meridian and only include data when at least three days of observations are available following the date
of maximum area for a group’s disk passage. This leaves data for over 18 000 measurements of sunspot group decay. We find
that the decay rate increases linearly from 28 μHem day−1 to about 140 μHem day−1 for groups with areas increasing from 35 μHem to 1000 μHem. The decay rate tends to level off for groups with areas larger
than 1000 μHem. This behavior is very similar to the increase in the number of sunspots per group as the area of the group
increases. Calculating the decay rate per individual sunspot gives a decay rate of about 3.65 μHem day−1 with little dependence upon the area of the group. This suggests that sunspots decay by a Fickian diffusion process with
a diffusion coefficient of about 10 km2 s−1. Although the 18 000 decay rate measurements are lognormally distributed, this can be attributed to the lognormal distribution
of sunspot group areas and the linear relationship between area and decay rate for the vast majority of groups. We find weak
evidence for variations in decay rates from one solar cycle to another and for different phases of each sunspot cycle. However,
the strongest evidence for variations is with latitude and the variations with cycle and phase of each cycle can be attributed
to this variation. High latitude spots tend to decay faster than low latitude spots. 相似文献
4.
R. P. Kane 《Solar physics》2007,243(2):205-217
For many purposes (e.g., satellite drag, operation of power grids on Earth, and satellite communication systems), predictions of the strength of
a solar cycle are needed. Predictions are made by using different methods, depending upon the characteristics of sunspot cycles.
However, the method most successful seems to be the precursor method by Ohl and his group, in which the geomagnetic activity
in the declining phase of a sunspot cycle is found to be well correlated with the sunspot maximum of the next cycle. In the
present communication, the method is illustrated by plotting the 12-month running means aa(min ) of the geomagnetic disturbance index aa near sunspot minimum versus the 12-month running means of the sunspot number Rz near sunspot maximum [aa(min ) versus Rz(max )], using data for sunspot cycles 9 – 18 to predict the Rz(max ) of cycle 19, using data for cycles 9 – 19 to predict Rz(max ) of cycle 20, and so on, and finally using data for cycles 9 – 23 to predict Rz(max ) of cycle 24, which is expected to occur in 2011 – 2012. The correlations were good (∼+0.90) and our preliminary predicted
Rz(max ) for cycle 24 is 142±24, though this can be regarded as an upper limit, since there are indications that solar minimum
may occur as late as March 2008. (Some workers have reported that the aa values before 1957 would have an error of 3 nT; if true, the revised estimate would be 124±26.) This result of the precursor
method is compared with several other predictions of cycle 24, which are in a very wide range (50 – 200), so that whatever
may be the final observed value, some method or other will be discredited, as happened in the case of cycle 23. 相似文献
5.
Jiangtao Su Yu Liu Jihong Liu Xinjie Mao Hongqi Zhang Hui Li Xiaofan Wang Wenbin Xie 《Solar physics》2008,252(1):55-71
Zhao and Kosovichev (Astrophys. J.
591, 446, 2003) found two opposite sub-photospheric vortical flows in the depth range of 0 – 12 Mm around a fast rotating sunspot. So far
there is no theoretical model explaining such flow motions. In this paper, we try to explain this phenomenon from the point
of view of magnetic flux tubes interacting with large-scale vortical motions of plasma. In the deeper zone under the photosphere,
the magnetic force may be less than the nonmagnetic force of plasma. The vortical flow located there twists the flux tube
and magnetic free energy is built up in the tube. In the shallower zone under the photosphere, the magnetic force may be greater
than the nonmagnetic force. Thus, part of the stored magnetic free energy is released to drive the plasma to rotate in two
opposite directions, e.g., in the depth ranges of 0 – 3(5) and 9 – 12 Mm. In addition, we also define a vector of nonpotential magnetic stress τ, which can be related to flare occurrence. It is calculated for the active region NOAA 10930 on 11 December 2006. We find
that: i) the integral of its line-of-sight (LOS) stress successively increases around the magnetic neutral line (MNL) prior to and
during the flare and decreases to a minimum after the flare; ii) the integral of its transverse stress exceeds the integral of its LOS component by one order of magnitude over the whole
field of view; iii) the transverse stress first points toward the MNL, then along it, and finally it points away from it. We need other data
to verify whether or not the magnetic energy is transported in the horizontal direction to the neutral line, and then partly
changes into the energy in LOS direction before and during the flare. 相似文献
6.
Based on the extended Greenwich – NOAA/USAF catalogue of sunspot groups, it is demonstrated that the parameters describing
the latitudinal width of the sunspot generating zone (SGZ) are closely related to the current level of solar activity, and
the growth of the activity leads to the expansion of the SGZ. The ratio of the sunspot number to the width of the SGZ shows
saturation at a certain level of the sunspot number, and above this level the increase of the activity takes place mostly
due to the expansion of the SGZ. It is shown that the mean latitudes of sunspots can be reconstructed from the amplitudes
of solar activity. Using the obtained relations and the group sunspot numbers by Hoyt and Schatten (Solar Phys.
179, 189, 1998), the latitude distribution of sunspot groups (“the Maunder butterfly diagram”) for the eighteenth and the first half of
the nineteenth centuries is reconstructed and compared with historical sunspot observations. 相似文献
7.
Using the Greenwich Photoheliographic Results for the years 1874–1976 the daily rotational velocities for 955 recurrent and
13169 non-recurrent sunspot groups from the first day of their appearance and during their evolution have been determined.
The rotational velocities were divided in six latitude strips with a width of five degrees and grouped according to the age
of the groups. It was established that the rotational velocities of recurrent and non-recurrent sunspot groups decrease with
time in all studied latitude strips. At their birth the recurrent spot groups rotate faster by about 0.15° day−1 than the non-recurrent ones and settle, within the errors of measurements, to an about 0.5° day−1 slower velocity value during the second disc passage. A comparison of our results with helioseismology measurements indicates
that in the frame of the anchoring hypothesis, the recurrent sunspot groups at their birth could be coupled to the fast rotating
layer at about r=0.93 R
⊙. 相似文献
8.
In the previous study (Dabas et al. in Solar Phys.
250, 171, 2008), to predict the maximum sunspot number of the current solar cycle 24 based on the geomagnetic activity of the preceding
sunspot minimum, the Ap index was used which is available from the last six to seven solar cycles. Since a longer series of the aa index is available for more than the last 10 – 12 cycles, the present study utilizes aa to validate the earlier prediction. Based on the same methodology, the disturbance index (DI), which is the 12-month moving
average of the number of disturbed days (aa≥50), is computed at thirteen selected times (called variate blocks 1,2,…,13; each of them in six-month duration) during the
declining portion of the ongoing sunspot cycle. Then its correlation with the maximum sunspot number of the following cycle
is evaluated. As in the case of Ap, variate block 9, which occurs exactly 48 months after the current cycle maximum, gives the best correlation (R=0.96) with a minimum standard error of estimation (SEE) of ± 9. As applied to cycle 24, the aa index as precursor yields the maximum sunspot number of about 120±16 (the 90% prediction interval), which is within the 90%
prediction interval of the earlier prediction (124±23 using Ap). Furthermore, the same method is applied to an expanded range of cycles 11 – 23, and once again variate block 9 gives the
best correlation (R=0.95) with a minimum SEE of ± 13. The relation yields the modified maximum amplitude for cycle 24 of about 131±20, which
is also close to our earlier prediction and is likely to occur at about 43±4 months after its minimum (December 2008), probably
in July 2012 (± 4 months). 相似文献
9.
R. P. Kane 《Solar physics》2007,246(2):471-485
Many methods of predictions of sunspot maximum number use data before or at the preceding sunspot minimum to correlate with
the following sunspot maximum of the same cycle, which occurs a few years later. Kane and Trivedi (Solar Phys. 68, 135, 1980) found that correlations of R
z(max) (the maximum in the 12-month running means of sunspot number R
z) with R
z(min) (the minimum in the 12-month running means of sunspot number R
z) in the solar latitude belt 20° – 40°, particularly in the southern hemisphere, exceeded 0.6 and was still higher (0.86)
for the narrower belt > 30° S. Recently, Javaraiah (Mon. Not. Roy. Astron. Soc.
377, L34, 2007) studied the relationship of sunspot areas at different solar latitudes and reported correlations 0.95 – 0.97 between minima and maxima of sunspot areas at low latitudes
and sunspot maxima of the next cycle, and predictions could be made with an antecedence of more than 11 years. For the present
study, we selected another parameter, namely, SGN, the sunspot group number (irrespective of their areas) and found that SGN(min) during a sunspot minimum year at latitudes > 30° S had a correlation
+0.78±0.11 with the sunspot number R
z(max) of the same cycle. Also, the SGN during a sunspot minimum year in the latitude belt (10° – 30° N) had a correlation +0.87±0.07 with the
sunspot number R
z(max) of the next cycle. We obtain an appropriate regression equation, from which our prediction for the coming cycle 24 is R
z(max )=129.7±16.3. 相似文献
10.
One goal of helioseismology is to determine the subsurface structure of sunspots. In order to do so, it is important to understand
first the near-surface effects of sunspots on solar waves, which are dominant. Here we construct simplified, cylindrically-symmetric
sunspot models that are designed to capture the magnetic and thermodynamics effects coming from about 500 km below the quiet-Sun
τ
5000=1 level to the lower chromosphere. We use a combination of existing semi-empirical models of sunspot thermodynamic structure
(density, temperature, pressure): the umbral model of Maltby et al. (1986, Astrophys. J. 306, 284) and the penumbral model of Ding and Fang (1989, Astron. Astrophys. 225, 204). The OPAL equation-of-state tables are used to derive the sound-speed profile. We smoothly merge the near-surface properties
to the quiet-Sun values about 1 Mm below the surface. The umbral and penumbral radii are free parameters. The magnetic field
is added to the thermodynamic structure, without requiring magnetostatic equilibrium. The vertical component of the magnetic
field is assumed to have a Gaussian horizontal profile, with a maximum surface field strength fixed by surface observations.
The full magnetic-field vector is solenoidal and determined by the on-axis vertical field, which, at the surface, is chosen
such that the field inclination is 45° at the umbral – penumbral boundary. We construct a particular sunspot model based on
SOHO/MDI observations of the sunspot in active region NOAA 9787. The helioseismic signature of the model sunspot is studied
using numerical simulations of the propagation of f, p
1, and p
2 wave packets. These simulations are compared against cross-covariances of the observed wave field. We find that the sunspot
model gives a helioseismic signature that is similar to the observations. 相似文献
11.
R. P. Kane 《Solar physics》2008,249(2):369-380
The sunspot number series at the peak of sunspot activity often has two or three peaks (Gnevyshev peaks; Gnevyshev, Solar Phys.
1, 107, 1967; Solar Phys.
51, 175, 1977). The sunspot group number (SGN) data were examined for 1997 – 2003 (part of cycle 23) and compared with data for coronal
mass ejection (CME) events. It was noticed that they exhibited mostly two Gnevyshev peaks in each of the four latitude belts
0° – 10°, 10° – 20°, 20 ° – 30°, and > 30°, in both N (northern) and S (southern) solar hemispheres. The SGN were confined
to within latitudes ± 50° around the Equator, mostly around ± 35°, and seemed to occur later in lower latitudes, indicating
possible latitudinal migration as in the Maunder butterfly diagrams. In CMEs, less energetic CMEs (of widths < 71°) showed
prominent Gnevyshev peaks during sunspot maximum years in almost all latitude belts, including near the poles. The CME activity
lasted longer than the SGN activity. However, the CME peaks did not match the SGN peaks and were almost simultaneous at different
latitudes, indicating no latitudinal migration. In energetic CMEs including halo CMEs, the Gnevyshev peaks were obscure and
ill-defined. The solar polar magnetic fields show polarity reversal during sunspot maximum years, first at the North Pole
and, a few months later, at the South Pole. However, the CME peaks and gaps did not match with the magnetic field reversal
times, preceding them by several months, rendering any cause – effect relationship doubtful. 相似文献
12.
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. 相似文献
13.
R. P. Kane 《Solar physics》2007,245(2):415-421
The occurrence of double peaks near the maximum of sunspot activity was first emphasized by Gnevyshev (Solar Phys.
1, 107, 1967) for the peak years of solar cycle 19 (1954 – 1964). In the present analysis, it is shown that double peaks in sunspot numbers
were clearly visible in solar latitudes 10 – 30° N but almost absent in the southern latitudes, where some single peaks were
observed out of phase by several months from any of the peaks in the northern latitudes. The spacing between the double peaks
increased from higher to lower northern latitudes, hinting at latitudinal migration. In the next cycle 20 (1965 – 1976), which
was of about half the strength of cycle 19, no clear-cut double peaks were seen, and the prominent peak in the early part
of 1967 in the northern latitudes was seen a few months later in the southern latitudes. A direct relationship of Gnevyshev
peaks with changes in the solar polar magnetic fields seems to be dubious. The commencements do not match. 相似文献
14.
David A. Juckett 《Solar physics》2010,262(1):3-17
Wolff (Astrophys. J.
193, 721, 1974) introduced the concept of g-mode coupling within the solar interior. Subsequently, Wolff developed a more quantitative model invoking a reciprocal interaction
between coupled g modes and burning in the solar core. Coupling is proposed to occur for constant values of the spherical harmonic degree [ℓ] creating rigidly rotating structures denoted as sets(ℓ). Power would be concentrated near the core and the top of radiative zone [RZ] in narrow intervals of longitude on opposite
sides of the Sun. Sets(ℓ) would migrate retrograde in the RZ as function of ℓ and their intersections would deposit extra energy at the top of the RZ. It is proposed that this enhances sunspot eruptions
at particular longitudes and at regular time intervals. Juckett and Wolff (Solar Phys.
252, 247, 2008) detected this enhancement by viewing selected spherical harmonics of sunspot patterns within stackplots twisted into the
relative rotational frames of various sets(ℓ). In subsequent work, the timings of the set(ℓ) intersections were compared to the sub-decadal variability of the sunspot cycle. Seventeen sub-decadal intersection frequencies
(0.63 – 7.0 year) were synchronous with 17 frequencies in the sunspot time-series with a mean correlation of 0.96. Six additional
non-11-year frequencies (periods of 8.0 to 28.7 year) are now shown to be nearly synchronous between sunspot variability and
the model. Two additional intersections have the same frequency as the solar cycle itself and peak during the rising phase
of the solar cycle. This may be partly responsible for cycle asymmetry. These results are evidence that some of the solar-cycle
variability may be attributable to deterministic components that are intermixed with a broad-spectrum stochastic and long-term
chaotic background. 相似文献
15.
Using Greenwich data (1879–1976) and SOON/NOAA data (1977–2002) on sunspot groups we found the following results: (i) The
Sun's mean (over all the concerned cycles during 1879–1975) equatorial rotation rate (A) is significantly larger (≈0.1%) in the odd-numbered sunspot cycles (ONSCs) than in the even-numbered sunspot cycles (ENSCs).
The mean rotation is significantly (≈10%) more differential in the ONSCs than in the ENSCs. North–south difference in the
mean equatorial rotation rate is larger in the ONSCs than in the ENSCs. North–south difference in the mean latitude gradient
of the rotation is significant in the ENSCs and insignificant in the ONSCs. (ii) The known very large decrease in A from cycle 13 to cycle 14 is confirmed. The amount of this decrease in the mean A was about 0.017 μrad s−1. Also, we find that A decreased from cycle 17 to cycle 18 by about 0.008 μrad s−1 and from cycle 21 to cycle 22 by about 0.016 μrad s−1. From cycle 13 to cycle 14 the decrease in A was more in the northern hemisphere than in the southern hemisphere, it is opposite in the later two epochs. The time gap
between the consecutive drops in A is about 44 years, suggesting the existence of a `44-yr' cycle or `double Hale cycle' in A. The time gap between the two large drops, viz., from cycle 13 to cycle 14 and from cycle 21 to cycle 22, is about 90 years
(Gleissberg cycle). We predict that the next drop (moderate) in A will be occurring from cycle 25 to cycle 26 and will be followed by a relatively large-amplitude `double Hale cycle' of sunspot
activity. (iii) Existence of a 90-yr cycle is seen in the cycle-to-cycle variation of the latitude gradient (B). A weak 22-yr modulation in B seems to be superposed on the relatively strong 90-yr modulation. (iv) The coefficient A varies significantly only during ONSCs and the variation has maximum amplitude in the order of 0.01 μrad s−1 around activity minima. (v) There exists a good anticorrelation between the mean variation of B during the ONSCs and that during the ENSCs, suggesting the existence of a `22-yr' periodicity in B. The maximum amplitude of the variation of B is of the order of 0.05 μrad s−1 around the activity minima. (vi) It seems that the well-known Gnevyshev and Ohl rule of solar activity is applicable also
to the cycle-to-cycle amplitude modulation of B from cycle 13 to cycle 20, but the cycles 12 (in the northern hemisphere, Greenwich data) and 21 (in both hemispheres, SOON/NOAA
data) seem to violate this rule in B. And (vii) All the aforesaid statistically significant variations in A and B seem to be related to the approximate 179-yr cycle, 1811–1989, of variation in the Sun's motion about the center of mass
of the solar system. 相似文献
16.
Longitudinal distributions of the photospheric magnetic field studied on the basis of National Solar Observatory (Kitt Peak)
data (1976 – 2003) displayed two opposite patterns during different parts of the 11-year solar cycle. Helio-longitudinal distributions
differed for the ascending phase and the maximum of the solar cycle on the one hand and for the descending phase and the minimum
on the other, depicting maxima around two diametrically opposite Carrington longitudes (180° and 0°/360°). Thus the maximum
of the distribution shifted its position by 180° with the transition from one characteristic period to the other. Two characteristic
periods correspond to different situations occurring in the 22-year magnetic cycle of the Sun, in the course of which both
global magnetic field and the magnetic field of the leading sunspot in a group change their sign. During the ascending phase
and the maximum (active longitude 180°) polarities of the global magnetic field and those of the leading sunspots coincide,
whereas for the descending phase and the minimum (active longitude 0°/360°) the polarities are opposite. Thus the observed
change of active longitudes may be connected with the polarity changes of Sun’s magnetic field in the course of 22-year magnetic
cycle. 相似文献
17.
In the present study, the short-term periodicities in the daily data of the sunspot numbers and areas are investigated separately
for the full disk, northern, and southern hemispheres during Solar Cycle 23 for a time interval from 1 January 2003 to 30
November 2007 corresponding to the descending and minimum phase of the cycle. The wavelet power spectrum technique exhibited
a number of quasi-periodic oscillations in all the datasets. In the high frequency range, we find a prominent period of 22 – 35
days in both sunspot indicators. Other quasi-periods in the range of 40 – 60, 70 – 90, 110 – 130, 140 – 160, and 220 – 240
days are detected in the sunspot number time series in different hemispheres at different time intervals. In the sunspot area
data, quasi-periods in the range of 50 – 80, 90 – 110, 115 – 130, 140 – 155, 160 – 190, and about 230 days were noted in different
hemispheres within the time period of analysis. The present investigation shows that the well-known “Rieger periodicity” of
150 – 160 days reappears during the descending phase of Solar Cycle 23, but this is prominent mainly in the southern part
of the Sun. Possible explanations of these observed periodicities are delivered on the basis of earlier results detected in
photospheric magnetic field time series (Knaack, Stenflo, and Berdyugina in Astron. Astrophys.
438, 1067, 2005) and solar r-mode oscillations. 相似文献
18.
V. A. Sheminova 《Solar physics》2009,254(1):29-50
The properties of solar magnetic fields on scales less than the spatial resolution of solar telescopes are studied. A synthetic
infrared spectropolarimetric diagnostic based on a 2D MHD simulation of magnetoconvection is used for this. Analyzed are two
time sequences of snapshots that likely represent two regions of the network fields with their immediate surroundings on the
solar surface with unsigned magnetic flux densities of 300 and 140 G. In the first region from the probability density functions
of the magnetic field strength it is found that the most probable field strength at log τ
5=0 is equal to 250 G. Weak fields (B<500 G) occupy about 70% of the surface, whereas stronger fields (B>1000 G) occupy only 9.7% of the surface. The magnetic flux is −28 G and its imbalance is −0.04. In the second region, these
parameters are correspondingly equal to 150 G, 93.3%, 0.3%, −40 G, and −0.10. The distribution of line-of-sight velocities
on the surface of log τ
5=−1 is estimated. The mean velocity is equal to 0.4 km s−1 in the first simulated region. The average velocity in the granules is −1.2 km s−1 and in the intergranules it is 2.5 km s−1. In the second region, the corresponding values of the mean velocities are equal to 0, −1.8, and 1.5 km s−1. In addition the asymmetry of synthetic Stokes V profiles of the Fe i 1564.8 nm line is analyzed. The mean values of the amplitude and area asymmetry do not exceed 1%. The spatially smoothed
amplitude asymmetry is increased to 10% whereas the area asymmetry is only slightly varied. 相似文献
19.
Radiative transfer (RT) problems in which the source function includes a scattering-like integral are typical two-points boundary
problems. Their solution via differential equations implies making hypotheses on the solution itself, namely the specific
intensity I (τ; n) of the radiation field. On the contrary, integral methods require making hypotheses on the source function S(τ). It seems of course more reasonable to make hypotheses on the latter because one can expect that the run of S(τ) with depth is smoother than that of I (τ; n). In previous works we assumed a piecewise parabolic approximation for the source function, which warrants the continuity
of S(τ) and its first derivative at each depth point. Here we impose the continuity of the second derivative S′′(τ). In other words, we adopt a cubic spline representation to the source function, which highly stabilizes the numerical
processes. 相似文献
20.
We study the relationship between the brightness (I) and magnetic field (B) distributions of sunspots using 272 samples observed at the San Fernando Observatory and the National Solar Observatory,
Kitt Peak, whose characteristics varied widely. We find that the I – B relationship has a quadratic form for the spots with magnetic field less than about 2000 G. The slope of the linear part
of the I – B curve varies by about a factor of three for different types of spots. In general the slope increases as the spot approaches
disk center. The I – B slope does not have a clear dependency on the spot size but the lower limit appears to increase as a function of the ratio
of umbra and penumbra area. The I – B slope changes as a function of age of the sunspots. We discuss various sunspot models using these results. 相似文献