The cooling of a sunspot

This paper considers the recent criticism by Mullan (1973) of sunspot models and the cooling mechanism which I have proposed in Papers I, II and III of this series. The discussion of the cooling produced by an idealized flow cycle has been extended to include vertical temperature gradients which are consistent with a convectively unstable atmosphere. This leads to an expression for Mullan's parameter f (the ratio in which estimates of the energy flux based on an idealized Carnot cycle should be reduced) which is appropriate to this situation. It is shown that, for a cycle similar to that of Paper III, f = 0.82, while for one which has a vertical extent of order 5 Mm, f= 0.4. Hence the energy flux which, in principle, can be transported away from a sunspot by such a cycle is conservatively estimated to be 1.1 × 10²⁹ erg s^?1 compared with a typical sunspot energy deficit of 2.2 × 10²⁹ erg s^?1. Other criticisms relating to the magnetic field amplification and the ‘cool one’ model are discussed. It is concluded that the essential features of these models remain valid and that the modifications suggested by Mullan's criticism greatly increase their applicability to the sunspot problem.     

Relative flow of H+ and O+ ions in the topside ionosphere at mid-latitudes

Theoretical results on the daily variation of O⁺ and H⁺ field-aligned velocities in the topside ionosphere are presented. The results are for an L = 3 magnetic field tube under sunspot minimum conditions at equinox. They come from calculations of time-dependent O⁺ and H⁺ continuity and momentum balance in a magnetic field tube which extends from the lower F2 region to the equatorial plane (Murphy et al., 1976).There are occasions when ion counterstreaming occurs, with the O⁺ velocity upward and H⁺ velocity downward. The conditions causing this counterstreaming are described: the H⁺ layer is descending whilst O⁺ is supplied from below either to increase the O⁺ concentration at fixed heights or to replace O⁺ ions lost by charge exchange with neutral H. It is suggested that the results of observations at Arecibo by Vickrey et al. (1976) of O⁺ and H⁺ concentrations and counterstreaming velocities are significantly affected by $\text{E}\text{×}\text{B}$ drift.     

The effect of a meridional E × B drift on the thermal plasma at L = 1.4

A fully time dependent mathematical model of the thermal plasma at L = 1.4 is described. In the mathematical model account is taken of a quiet-time E × B drift in the meridional plane. Atmospheric conditions appropriate to equinox at sunspot minimum and at sunspot maximum are considered. Results of the model calculations are presented. Emphasis is placed on the effects on the thermal plasma of a quiet-time E × B drift in the meridional plane. A comparison of the model calculations which include an E × B drift with those in which there is no E × B drift shows than an E × B drift significantly affects the plasma concentration and temperature distributions during the day at both sunspot minimum and sunspot maximum; the effects at night are very small. An upward E × B drift during the day increases both NmF2 and hmF2 and decreases the plasma temperature. The decrease in plasma temperature is due primarily to the increase in plasma concentration. It is more pronounced in the electron temperature than in the ion temperature and it varies considerably with altitude, time and atmospheric conditions. The changes in plasma concentration and temperature brought about by an E × B drift also change the O⁺-H⁺ transition height and the O⁺ and H⁺ tube contents. For the E × B drifts considered the O⁺-H⁺ transition height is raised during the morning and lowered during the afternoon. The changes in O⁺ tube content roughly follow the changes in NmF2. The changes in H⁺ tube content, however, are small since the H⁺ tube content is controlled by the H⁺ concentration at the higher altitudes of the tube of plasma and these concentration values are only slightly affected by the E × B drifts considered.     

Nighttime proton fluxes at Millstone Hill

Incoherent scatter measurements of electron density and vertical O⁺ fluxes over Millstone Hill (42.6°N, 71.5°W) previously have been used to study the exchange of plasma between the ionosphere and the magnetosphere. During the daytime there is usually an upward flux of O⁺ ions above about 450 km that can be measured readily and equated to the escaping proton flux. At night the O⁺ fluxes usually are downwards everywhere owing to the decay of the F-layer, and it becomes difficult to detect effects due an arriving proton flux. In a new study of the nighttime fluxes, appeal was made to the estimated abundance of the H⁺ ions in the upper F-region which can be extracted from the observations. From a study of the behavior on 25 days over the interval 1969–1973, we conclude that in the daytime the flux always is upwards and close to its limiting value. This situation persists throughout the night in summer at times of high sunspot activity (e.g., 1969). There is a period of downward flux prior to ionospheric sunrise on winter nights whose duration increases with decreasing sunspot number. As sunspot minimum is approached (e.g., in 1973) downward fluxes are encountered for a brief period prior to ionospheric sunrise in summer also. Thus, over most parts of sunspot cycle, it appears that the protonosphere supplies ionization to the winter night ionosphere, while being maintained from the summer hemisphere. This helps explain the smallness of the day-to-night variations reported for the electron content of magnetospheric flux tubes near L = 4 in the American sector.     

Solar flare induced D-region ionospheric perturbations evaluated from VLF measurements

The results of very low frequency (VLF) wave amplitude measurements carried out at the low latitude station Varanasi (geom. lat. 14^°55′N, long. 154^°E), India during solar flares are presented for the first time. The VLF waves (19.8 kHz) transmitted from the NWC-transmitter, Australia propagated in the Earth-ionosphere waveguide to long distances and were recorded at Varanasi. Data are analyzed and the reflection height H′ and the sharpness factor β are evaluated. It is found that the reflection height decreases whereas sharpness factor increases with the increase of solar flare power. The H′ is found to be higher and β smaller at low latitudes than the corresponding values at mid and high latitudes. The sunspot numbers were low during the considered period 2011–2012, being the rising phase of solar cycle 24 and as a result cosmic rays may impact the D-region ionosphere. The increased ionization from the flare lowers the effective reflecting height, H′, of the D-region roughly in proportion to the logarithm of the X-ray flare intensity from a typical mid-day unperturbed value of about 71–72 km down to about 65 km for an X class flare. The sharpness (β) of the lower edge of the D-region is also significantly increased by the flare but reaches a clear saturation value of about 0.48 km^?1 for flares of magnitude greater than about X1 class.     

A method for the determination of the lithium abundance in sunspots: Observations for 2011

Sunspot spectra for LiI 6708Å lines and for several FeI and CaI lines were obtained. Observations were performed in January and in August, 2011 using the TST-2 telescope with a charge-coupled camera at the Crimean Astrophysical Observatory. The sunspot models were calculated by using the observing profiles of FeI and CaI lines. Lithium abundance was determined by using the calculated sunspot models and LiI 6708Å observed profiles; this equals log(N _Li) = 0.98 and 0.95 (in the scale logA(H) = 12.0).     

Basic properties of sunspots: equilibrium,stability and long-term eigen oscillations

A number of fundamental questions as regards the physical nature of sunspots are formulated. In order to answer these questions, we apply the model of a round-shaped unipolar sunspot with a lower boundary consisting of cool plasma and with strong magnetic field at the depth of about 4 Mm beneath the photosphere, in accordance with the data of local helioseismology and with certain physically sound arguments (the shallow sunspot model). The magnetic configuration of a sunspot is assumed to be close to the observed one and similar to the magnetic field of a round solenoid of the appropriate size. The transverse (horizontal) and longitudinal (vertical) equilibria of a sunspot were calculated based on the thermodynamic approach and taking into account the magnetic, gravitational, and thermal energy of the spot and the pressure of the environment. The dependence of the magnetic field strength in the sunspot center, B ₀, on the radius of the sunspot umbra a is derived theoretically for the first time in the history of sunspot studies. It shows that the magnetic field strength in small spots is about 700 Gauss (G) and then increases monotonically with a, tending asymptotically to a limit value of about 4000 G. This dependence, B ₀(a) includes, as parameters, the gravity acceleration on the solar surface, the density of gas in the photosphere, and the ratio of the radius of the spot (including penumbra), a _p, to the radius of its umbra a. It is shown that large-scale subsurface flows of gas in the sunspot vicinity, being the consequence but not the cause of sunspot formation, are too weak to contribute significantly to the pressure balance of the sunspot. Stability of the sunspot is provided by cooling of the sunspot plasma and decreasing of its gravitational energy due to the vertical redistribution of the gas density when the geometric Wilson depression of the sunspot is formed. The depth of a depression grows linearly with B ₀, in contrast to the quadratic law for the magnetic energy. Therefore, the range of stable equilibria turns out to be limited: large spots, with radius a larger than some limit value (about 12–18 Mm, depending on the magnetic field configuration), are unstable. It explains the absence of very large spots on the Sun and the appearance of light bridges in big spots that divide the spot into a few parts. The sunspots with B ₀≈2.6÷2.7 kilogauss (kG) and a≈5 Mm are most stable. For these spots, taken as a single magnetic structure, the period of their vertical eigen oscillations is minimal and amounts, according to the model, to 10–12 hours. It corresponds well to the period derived from the study of long-term oscillations of sunspots using SOHO/MDI data.     

Cyclic and Long-Term Variation of Sunspot Magnetic Fields

Measurements from the Mount Wilson Observatory (MWO) were used to study the long-term variations of sunspot field strengths from 1920 to 1958. Following a modified approach similar to that presented in Pevtsov et al. (Astrophys. J. Lett. 742, L36, 2011), we selected the sunspot with the strongest measured field strength for each observing week and computed monthly averages of these weekly maximum field strengths. The data show the solar cycle variation of the peak field strengths with an amplitude of about 500?–?700 gauss (G), but no statistically significant long-term trends. Next, we used the sunspot observations from the Royal Greenwich Observatory (RGO) to establish a relationship between the sunspot areas and the sunspot field strengths for cycles 15?–?19. This relationship was used to create a proxy of the peak magnetic field strength based on sunspot areas from the RGO and the USAF/NOAA network for the period from 1874 to early 2012. Over this interval, the magnetic field proxy shows a clear solar cycle variation with an amplitude of 500?–?700 G and a weaker long-term trend. From 1874 to around 1920, the mean value of magnetic field proxy increases by about 300?–?350 G, and, following a broad maximum in 1920?–?1960, it decreases by about 300 G. Using the proxy for the magnetic field strength as the reference, we scaled the MWO field measurements to the measurements of the magnetic fields in Pevtsov et al. (2011) to construct a combined data set of maximum sunspot field strengths extending from 1920 to early 2012. This combined data set shows strong solar cycle variations and no significant long-term trend (the linear fit to the data yields a slope of ??0.2±0.8 G?year^?1). On the other hand, the peak sunspot field strengths observed at the minimum of the solar cycle show a gradual decline over the last three minima (corresponding to cycles 21?–?23) with a mean downward trend of ≈?15 G?year^?1.     

Solar cycle 24 from the standpoint of solar paleoastrophysics

The predictions of the maximum yearly mean sunspot number in the current cycle 24 made by means of the astrophysical approach (by analyzing the instrumental data on solar activity and using various dynamo models) and the paleoastrophysical approach (by analyzing the paleoreconstructions of solar activity spanning the interval from 8555 BC to 1605 AD) are compared. The paleoastrophysical predictions are shown to be considerably more accurate. The amplitude of the next cycle 25 is predicted. It is shown that from the standpoint of solar paleoastrophysics, cycle 25 will most likely be of medium power, R ^max(25) = 85.0 ± 30.5.     

The cosmic age crisis and the Hubble constant in a non-expanding universe

The present paper outlines a cosmological paradigm based upon Dirac’s large number hypothesis and continual creation of matter in a closed static (nonexpanding) universe. The cosmological redshift is caused by the tired-light phenomenon originally proposed by Zwicky. It is shown that the tired-light cosmology together with continual matter creation has a universal Hubble constant H ₀=(512π ²/3)^1/6(GC ₀)^1/3 fixed by the universal rate C ₀ of matter creation, where G is Newton’s gravitational constant. It is also shown that a closed static universe has a finite age τ ₀=(243π ⁵/8GC ₀)^1/3 also fixed by the universal rate of matter creation. The invariant relationship H ₀ τ ₀=3π ²6^1/2 shows that a closed static universe is much older (≈one trillion years) than any expanding universe model based upon Big-Bang cosmology. It is this property of a static universe that resolves any cosmic age crisis provided that galaxy formation in the universe is a continual recurring process. Application of Dirac’s large number hypothesis gives a matter creation rate C ₀=4.6×10^?48 gm?cm^?3?s^?1 depending only on the fundamental constants of nature. Hence, the model shows that a closed static universe has a Hubble constant H ₀=70 km?s^?1?Mpc^?1 in good agreement with recent astronomical determinations of H ₀. By using the above numerical value for H ₀ together with observational data for elongated cellular-wall structures containing superclusters of galaxies, it is shown that the elongated cellular-wall configurations observed in the real universe are at least one hundred billion years old. Application of the microscopic laws of physics to the large-scale macroscopic universe leads to a static eternal cosmos endowed with a matter-antimatter symmetry. It is proposed that the matter-antimatter asymmetry is continuously created by particle-antiparticle pair annihilation occurring in episodic cosmological gamma-ray bursts observed in the real universe.     

Measurements of positive ion conversion and removal reactions relating to the Jovian ionosphere

Measured rates are presented for the reaction of He⁺ ions with H₂ (and D₂) molecules to form H⁺, H₂⁺, and HeH⁺ ions, as well as for the subsequent reactions of H⁺ and HeH⁺ ions with H₂ to form H₃⁺. The neutralization of H₃⁺ (and H₅⁺) ions by dissociative recombination with electrons is shown to be fast. The reaction He⁺ + H₂ is slow (k = 1.1 × 10^?13 cm³/sec at300°K) and produces principally H⁺ by the dissociative charge transfer branch. It is concluded that there may be a serious bottleneck in the conversion of two of the primary ions of the upper Jovian ionosphere, H⁺ and He⁺ (which recombine slowly), to the rapidly recombining H₃⁺ ion (α[H₃⁺]?3.4 × 10^?7 cm³/sec at 150°K).     

The Greenwich Photo-heliographic Results (1874 – 1976): Procedures for Checking and Correcting the Sunspot Digital Datasets

Attention is drawn to the existence of errors in the original digital dataset containing sunspot data extracted from certain sections of the printed Greenwich Photo-heliographic Results (GPR) 1874?–?1976. Calculating the polar coordinates from the heliographic coordinates and comparing them with the recorded polar coordinates reveals that there are both isolated and systematic errors in the original sunspot digital dataset, particularly during the early years (1874?–?1914). It should be noted that most of these errors are present in the compiled sunspot digital dataset and not in the original printed copies of the Greenwich Photo-heliographic Results. Surprisingly, many of the errors in the digitised positions of sunspot groups are apparently in the measured polar coordinates, not the derived heliographic coordinates. The mathematical equations that are used to convert between heliographic and polar coordinate systems are formulated and then used to calculate revised (digitised) polar coordinates for sunspot groups, on the assumption that the heliographic coordinates of every sunspot group are correct. The additional complication of requiring accurate solar ephemerides in order to solve the mathematical equations is discussed in detail. It is shown that the isolated and systematic errors, which are prevalent in the sunspot digital dataset during the early years, disappear if revised polar coordinates are used instead. A comprehensive procedure for checking the original sunspot digital dataset is formulated in an Appendix.     

North–south asymmetry of different solar activity features during solar cycle 23

A study on north–south (N–S) asymmetry of different solar activity features (DSAF) such as solar proton events, solar active prominences [total, low (?40°) and high (?50°) latitudes], Hα flare indices, soft X-ray flares, monthly mean sunspot areas and monthly mean sunspot numbers carried out from May 1996 to October 2008. Study shows a southern dominance of DSAF during this period. During the rising phase of the cycle 23 the number of DSAF approximately equals on both, the northern and the southern hemispheres. But these activities tend to shift from northern to southern hemisphere during the period 1998–1999. The statistical significance of the asymmetry time series using a χ²-test of goodness of fit indicates that in most of the cases the asymmetry is highly significant, meaning thereby that the asymmetry is a real feature in the N–S distribution of DSAF.     

Recurrent magnetic activity,sunspot number and its rate of decline

Power spectral densities computed from low-latitude horizontal intensity of the Earth's magnetic field over two-year periods of declining phases of solar cycles 16 to 19 show a close relationship with the maximum relative sunspot number of the following solar cycles. The maximum sunspot number shows an exponential rise with the power density near 1/27 cd^?1; maximum R _z,however, increases linearly with power density near 1/14 cd^?1. It is also shown that the rate of decline of sunspot number in a solar cycle is almost exactly related, linearly, to power spectral density for the preceding solar cycle. Power densities near 1/27 and 1/14 cd^?1 in declining phase of solar cycle appear to be satisfactory indices for the maximum relative sunspot number of the following cycle and its rate of decline thereafter.     

A Curious History of Sunspot Penumbrae

Daily records of sunspot group areas compiled by the Royal Observatory, Greenwich, from May of 1874 through 1976 indicate a curious history for the penumbral areas of the smaller sunspot groups. On average, the ratio of penumbral area to umbral area in a sunspot group increases from 5 to 6 as the total sunspot group area increases from 100 to 2000 μHem (a μHem is 10^?6 the area of a solar hemisphere). This relationship does not vary substantially with sunspot group latitude or with the phase of the sunspot cycle. However, for the sunspot groups with total areas <?100 μHem, this ratio changes dramatically and systematically through this historical record. The ratio for these smallest sunspots is near 5.5 from 1874 to 1900. After a rapid rise to more than 7 in 1905, it drops smoothly to less than 3 by 1930 and then rises smoothly back to more than 7 in 1961. It then returns to near 5.5 from 1965 to 1976. The smooth variation from 1905 to 1961 shows no indication of any step-like changes that might be attributed to changes in equipment or personnel. The overall level of solar activity was increasing monotonically during this time period when the penumbra-to-umbra area ratio dropped to less than half its peak value and then returned. If this history can be confirmed by other observations (e.g. Mt. Wilson or Kodaikanal), it may impact our understanding of penumbra formation, our dynamo models, and our estimates of historical changes in the solar irradiance.     

The use of abnormal quiet days in Sq(H) for predicting the magnitude of sunspot maximum at the time of preceding sunspot minimum

The previously established connection between the occurence of AQDs (“abnormal quiet days” when the phase of the solar diurnal variation of horizontal magnetic field, Sq(H), at a mid-latitude northern hemisphere station is anomalous) at sunspot minimum and the magnitude of the following sunspot maximum is examined in the light of our recent improved understanding of the nature and cause of AQDs. A small contribution to the relationship is found to arise from variations from cycle to cycle in the additional northward field which is characteristic of AQDs and leads to a reduced Sq(H) amplitude at stations poleward of the Sq focus. However, the main factor which determines the connection is a variation from one sunspot minimum to another of the amplitude of the small southward bay-like field perturbations which constitute the AQD events, and evidence is presented which suggests that this parameter may be quantitatively related to the extent of southward swing of the B_z component of the interplanetary magnetic field which determines the energy transfer from the solar wind into the magnetospheric tail. It thus appears that the magnitude of southward swing in B_z might be another solar parameter which anticipates the size of a forthcoming sunspot cycle during its build-up over the declining phase of the previous cycle and at the minimum.     

SID flares and sunspot morphology

The degree of association between geoeffective (SID producing) flares (hereafter called SID flares) and sunspot morphology is examined. It is found that: (1) the frequency of SID flares associated with sunspot groups is linear function of sunspot area and rate of change in area; (2) the SID flare intensity is dependent on the sunspot area and on the magnetic morphology (field geometry); (3) the probability of a sunspot group being magnetically complex (henceforth called complex ratio) is a linear function of spot area, the larger this area the more likely a group is in the βγ or δ magnetic class; (4) the complex ratio exhibits the greatest degree of association to SID flare frequency. We conclude from these results that a higher frequency of D-region ionizing flares (emitting a soft X-ray flux >2 × 10^?3 erg cm^?2 s^?1) is likely to accompany the disk transit of large area, complex spot groups. This combination of morphological factors reflects a shearing of the associated force-free magnetic field, with accumulation of free magnetic energy to power SID flares. Mutual polarity intrusion would be one observational signature of the pre-flare energy storing process.     

Occurrence of AlO Molecular Lines in Sunspot Umbral Spectra

Aluminium monoxide (AlO) is widely known for its astrophysical significance. An analysis of the prominent lines of the (2,3;3,2;3,4;4,5;4,3;5,6;6,7) bands of the B ²Σ⁺?X ²Σ⁺ transition with those of sunspot umbral spectral lines suggests that the AlO molecule appears to be a non-negligible component of sunspot umbrae. Results of a recent (2008) rotational analysis were used to carry out the study. The effective rotational temperature determined for the above lines in the sunspot umbral spectrum is found to be of the order of 2900 K. The radiative-transition parameters that include Franck–Condon (FC) factors, r-centroids, electronic-transition moment, Einstein coefficient, absorption–band oscillator strength, and radiative lifetime have been estimated for the experimentally known vibrational levels using the Rydberg–Klein–Rees (RKR) potential.     

Interhemispheric flow of thermal plasma in a closed magnetic flux tube at mid-latitudes under sunspot minimum conditions

The coupled H⁺ and O⁺ time-dependent continuity and momentum equations are solved within a region of the L = 3 magnetic flux tube lying between (and including) the F2-layers of conjugate hemispheres. The method of solution is an extended and modified version of the Murphy et al. (1976) method. The model is used to study the coupling between the F2-layers of conjugate hemispheres during magnetically quiet periods.The results of the calculations strongly indicate that the protonosphere acts as a reservoir, with variable H⁺ content, which prevents direct coupling between the F2-layers of conjugate hemispheres. However there is generally a significant interhemispheric flow of plasma. This flow is caused by conditions in the summer and winter topside ionospheres and it maintains continuity in the plasma concentration within the protonosphere. There are times when the direction of flow is from the winter hemisphere to the summer hemisphere. It is suggested that maintenance of the winter F2-layer at night is not assisted directly by the F2-layer of the conjugate summer hemisphere.It is shown that during the first few days of protonosphere replenishment after a magnetic storm there is an upflow of H⁺ in the topside ionosphere at all times in the summer hemisphere. There is also an upflow of H⁺ during the daytime in both hemispheres. A comparison with the results obtained when the interhemispheric H⁺ flux is held permanently at zero shows that both F2-layers are little affected by the interhemispheric H⁺ flux. Nevertheless both F2-layers are affected by the H⁺ tube content of the protonosphere. When the H⁺ flux at 1000 km in one hemisphere is much greater than the H⁺ flux at 1000 km in the conjugate hemisphere, there is a corresponding signature in the interhemispheric H⁺ flux.The results suggest that there is insufficient time between magnetic storms for complete replenishment of the protonosphere to occur.