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.     

Power law relating 10.7 cm flux to sunspot number

To investigate the relation between observations of the 10.7 cm flux and the international sunspot number so that a physical unit may be ascribed to historical records, both polynomial and power law models are developed giving the radio flux as a function of sunspot number and vice versa. Bayesian data analysis is used to estimate the model parameters and to discriminate between the models. The effect on the parameter uncertainty and on the relative evidence of normalizing the measure of fit is investigated. The power law giving flux as a function of sunspot number is found to be the most plausible model and may be used to estimate the radio flux from historical sunspot observations.     

Rotational modulation of Ca K flux ratio and sunspot number

The results of daily monitoring of the Ca K flux variations of integrated sunlight during the period 1 July 1979–18 February 1980 are presented, and the data analyzed by both power spectrum and autocorrelation methods. The latter method is found to be superior; in it the autocorrelation function is fit to a model having three parameters, viz. the maximum long-term autocorrelation c ₁, the rotational period ₀ and an effective lifetime ₁. Values of c ₁ = 0.26, ₀ = 25.9 days, and ₁ = 500 days are obtained for the Ca K flux ratio; somewhat different values of c ₁ = 0.77, ₀ = 28.0 days, and ₁ = 89 days are obtained for the sunspot number for the same period. Rotational modulation is clearly evident for the relatively weak chromosphere of the Sun and should be even more easily observed for more active stars.     

Facular models and the sunspot energy deficit

The problem of the energy deficit in a sunspot is shown to be critically related to the depth of a given sunspot model. Recent facular models are discussed and a new model is derived from recent data using a two-dimensional radiative transfer analysis. The excess non-radiative energy required by this and other models is evaluated and it is shown that in some models this may account for a considerable fraction of the sunspot energy deficit. For these models the Alfvén energy travelling along the closed flux loops from the sunspot is insufficient to supply the requirements of the faculae and it is suggested that excess energy flux from below the faculae is also required. These results provide further support for deep as opposed to shallow sunspot models.     

On midrange periodicities in solar radio flux and sunspot areas

Using the Hilbert-Huang transform technique, we investigate the midrange periodicities in solar radio flux at 2800 MHz (F10.7) and sunspot areas (SAs) from February 1, 1947 to September 30, 2016. The following prominent results are found: (1) The quasi-periodic oscillations of both data sets are not identical, such as the rotational cycle, the midrange periodicities, and the Schwabe cycle. In particular, the midrange periodicities ranging from 37.9 days to 297.3 days are related to the magnetic Rossby-type waves; (2) The 1.3-year and 1.7-year fluctuations in solar activity indicators are surface manifestations (from photosphere to corona) of magnetic flux changes generated deep inside the Sun; (3) At the timescale of the Schwabe cycle, the complicated phase relationships in the three intervals (1947–1958, 1959–1988, and 1989–2016) agree with the produced periodicities of the magnetic Rossby-type waves. The findings indicate that the magnetic Rossby-type waves are the possible physical mechanism behind the midrange periodicities of solar activity indicators. Moreover, the significant change in the relationship between photospheric and coronal activity took place after the maximum of solar cycle 22 could be interpreted by the magnetic Rossby-type waves.     

Acoustic wave ducting along magnetic flux tubes in the sunspot regions

The acoustic waves generated in the solar atmosphere propagate globally as well as upwards. These waves interact with the solar magnetic field structures and are ducted upwards. The velocity of these modified acoustic waves is shown to vary in a modelled solar atmosphere. The solar plasma propagating upwards with these waves are likely to alter the observed features of spicules, granules, and supergranules during changing phases of sunspot regions.     

Oscillations of flux tube bundles and the structure of sunspot magnetic fields

Observational aspects of the previously found quasi-hourly oscillations of magnetic fragments in sunspot polar coordinates are investigated. The orientation of the oscillations is shown to be azimuthally anisotropic, with their amplitude reaching a maximum in penumbra at a distance of ～0.8 sunspot radius (the maximum amplitude is estimated to be 3700 km). Based on the detected deviations of the oscillations from the radial direction, we numerically simulate the horizontal configuration of field lines in the region of the major spots in bipolar groups.     

Elaboration of the new magnetohydrostatic sunspot theory (double return flux model)

An extension of the recently formulated Return Flux Sunspot Model is presented. The basic equation for a Double Return Flux Sunspot Model is derived, and a pressure distribution and magnetic field are calculated. The possible topology of the magnetic structure and its thermodynamic consequences are discussed. The paper includes a magnetogram of a single round sunspot (9 August, 1981). The authors attempt to interpret the observational data for the vertical component of magnetic field of this sunspot on the basis of the Double Return Flux Model.     

prior to surface appearance of sunspot flux tubes and magneto-thermal pulsation of the Sun

We found an evidence that the luminosity of the Sun systematically decreased about 20 days before sunspot surface appearance by analysing time-lag correlation of time derivatives of running mean time profiles of the data of the Active Cavity Radiometer Irradiance Monitor (ACRIM) I experiment on board of Solar Maximum Mission (SMM) and of the data of the daily sunspot number. This indicates that sunspot flux tube cooling and heat transport blocking by the flux tubes start to take place in the interior of the solar convection zone well before the sunspot surface appearance. From this finding and our previous finding that the luminosity of the Sun systematically increased and the blocked heat appeared on the surface about 50 days after the sunspot surface appearance, a new view of sunspot formation and dynamics and a new view of the luminosity modulation emerged. (i) Sunspots of a solar cycle are formed from clusters of flux tubes which can be seen in the running mean time profile of the sunspot number as a peak with duration on the order of 100 to 200 days. (ii) Heat flow is blocked by the cluster of sunspot flux tubes inside the convection zone to decrease the luminosity about 20 days before the surface emergence of the sunspot cluster. (iii) The blocked heat appears on the surface about 50 days after the surface emergence of the cluster of sunspot flux tubes to heat up the surface. This appears as a thermal pulse in the running mean time profile of the ACRIM dat in between the peaks of the sunspot running mean time profile. This process of heating the surface makes the temperature gradient less steep and weakens the buoyancy of sunspot flux tubes below the surface. (vi) The radiative cooling of the surface layer by the excess heat release steepens the temperature gradient so that the buoyancy of the sub-surface magnetic flux tubes becomes stronger to cause the next surge of emergence of a cluster of sunspots and other magnetic activities, which creates a peak in the time profile of the sunspot number. We call this peak a magnetic pulse of the Sun and the coupled process of alternating pulsed appearance of heat and sunspots the magneto-thermal pulsation of the Sun.     

Studies of grand minima in sunspot cycles by using a flux transport solar dynamo model

We propose that grand minima in solar activity are caused by simultane- ous fluctuations in the meridional circulation and the Babcock-Leighton mechanism for the poloidal field generation in the flux transport dynamo model. We present the following results： （a） fluctuations in the meridional circulation are more effective in producing grand minima; （b） both sudden and gradual initiations of grand minima are possible; （c） distributions of durations and waiting times between grand minima seem to be exponential; （d） the coherence time of the meridional circulation has an effect on the number and the average duration of grand minima, with a coherence time of about 30 yr being consistent with observational data. We also study the occurrence of grand maxima and find that the distributions of durations and waiting times between grand maxima are also exponential, like the grand minima. Finally we address the question of whether the Babcock-Leighton mechanism can be operative during grand minima when there are no sunspots. We show that an a-effect restricted to the upper portions of the convection zone can pull the dynamo out of the grand minima and can match various observational requirements if the amplitude of this a-effect is suitably fine-tuned.     

Relationship between sunspot numbers during years of sunspot maximum and sunspot minimum

A correlation analysis shows that the sunspot numbers at the peaks of the last eight solar cycles are well-correlated with the sunspot numbers in heliolatitudes 20°–40° (specially in the southern hemisphere) occurring in the solar minimum years immediately preceding the solar maximum years.On leave from Physical Research Laboratory, Ahmedabad, India.     

Cosmological solution with an energy flux

The paper presents some spherically symmetric cosmological Solutions in which the velocity field is shear-free but there is a flux of energy. The solutions are believed to be new and the previous known solutions of this class due to Bergmann and Maiti may be obtained as special cases of our metrics.     

GMS proton flux observation during February 1978

It is suggested that the drop out of the 1.2–4 MeV proton flux, observed by the geostationary satellite GMS, was due to the Earthward shift of the particle boundary in all local time. The particle boundary motions are associated with substorm activities.     

To the description of long-term variations in the solar magnetic flux: The sunspot area index

We show that the Wolf sunspot numbers W and the group sunspot numbers GSN are physically different indices of solar activity and that it is improper to compare them. Based on the approach of the so-called “primary” indices from the observational series of W(t) and GSN(t), we suggest series of yearly mean sunspot areas beginning in 1610 and monthly mean sunspot areas beginning in 1749.     

Cosmic flux of low energy gamma rays

Measurements have been made on the cosmic gamma rays of energy between 0.25 and 4.2 MeV from a balloon experiment made near the geomagnetic equator using a collimated 7.6 cm×7.6 cm NaI(T1) crystal assembly. The depth-intensity curves obtained were used to estimate the contribution due to the diffuse cosmic gamma rays in the above energy interval; an unfolding of the counting rates was then performed to obtain the energy spectrum. It is found that a power law fitted to the present data points has a spectral index of –1.8±0.2. A critical examination is then made of all the observational data between 1 keV and 100 MeV to deduce information on the spectral shape in this energy region. Upper limits on low energy gamma ray fluxes from Sco X-1 and the Galactic centre region are also reported.     

Thermospheric energy flux of the semidiurnal tide

The upward energy flux of the (2,2,2) mode of atmospheric oscillation generated by water vapour and ozone radiational heating is calculated at 125 km for mean January, April, July and October conditions. The values obtained for the global mean flux lie close to 0.05 mW m^?2 with a small reduction in July amounting to 13% of the average for the other 3 months. The effect of semidiurnal tidal heating on exospheric temperature is discussed with reference to the earlier work of Lindzen and Blake (1970) and it is concluded that the semidiurnal tide causes a relatively small increase in exospheric temperature of ～ 33 K.     

A “lost” sunspot observation in 1785

The reconstruction of the solar activity during some years of the 18th century is poorly known because there are scarce sunspot observations. The aim of this short contribution is to present a “lost” sunspot observation realized by the Portuguese scientist Sanches Dorta during his observation of the solar eclipse of 1785 from Rio de Janeiro (Brazil). This record was not included in the database compiled by Hoyt and Schatten (1998). We present new estimations of the solar activity during 1785. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)