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Register a new userSensitivity of low-degree solar p modes to active and ephemeral regions: frequency shifts back to the Maunder Minimum
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We explore the sensitivity of the frequencies of low-degree solar p-modes to near-surface magnetic flux on different spatial scales and strengths, specifically to active regions with strong magnetic fields and ephemeral regions with weak magnetic fields. We also use model reconstructions from the literature to calculate average frequency offsets back to the end of the Maunder minimum. We find that the p-mode frequencies are at least three times less sensitive (at 95% confidence) to the ephemeral-region field than they are to the active-region field. Frequency shifts between activity cycle minima and maxima are controlled predominantly by the change of active region flux. Frequency shifts at cycle minima (with respect to a magnetically quiet Sun) are determined largely by the ephemeral flux, and are estimated to have been $0.1,rm mu Hz$ or less over the last few minima. We conclude that at epochs of cycle minimum, frequency shifts due to near-surface magnetic activity are negligible compared to the offsets between observed and model frequencies that arise from inaccurate modelling of the near-surface layers (the so-called surface term). The implication is that this will be the case for other Sun-like stars with similar activity, which has implications for asteroseismic modelling of stars.
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The Maunder minimum (MM) of greatly reduced solar activity took place in 1645-1715, but the exact level of sunspot activity is uncertain as based, to a large extent, on historical generic statements of the absence of spots on the Sun. Here we aim, using a conservative approach, to assess the level and length of solar cycle during the Maunder minimum, on the basis of direct historical records by astronomers of that time. A database of the active and inactive days (days with and without recorded sunspots on the solar disc respectively) is constructed for three models of different levels of conservatism (loose ML, optimum MO and strict MS models) regarding generic no-spot records. We have used the active day fraction to estimate the group sunspot number during the MM. A clear cyclic variability is found throughout the MM with peaks at around 1655--1657, 1675, 1684 and 1705, and possibly 1666, with the active day fraction not exceeding 0.2, 0.3 or 0.4 during the core MM, for the three models. Estimated sunspot numbers are found very low in accordance with a grand minimum of solar activity. We have found, for the core MM (1650-1700), that: (1) A large fraction of no-spot records, corresponding to the solar meridian observations, may be unreliable in the conventional database. (2) The active day fraction remained low (below 0.3-0.4) throughout the MM, indicating the low level of sunspot activity. (3) The solar cycle appears clearly during the core MM. (4) The length of the solar cycle during the core MM appears $9pm 1$ years, but there is an uncertainty in that. (5) The magnitude of the sunspot cycle during MM is assessed to be below 5-10 in sunspot numbers; A hypothesis of the high solar cycles during the MM is not confirmed.
In this work, we analysed the physical parameters of the spotless actives regions observed during solar minimum 23 - 24 (2007 - 2010). The study was based on radio maps at 17~GHz obtained by the Nobeyama Radioheliograph (NoRH) and magnetograms provided by the Michelson Doppler Imager (MDI) on board the Solar and Heliospheric Observatory (SOHO). The results shows that the spotless active regions presents the same radio characteristics of a ordinary one, they can live in the solar surface for long periods (>10 days), and also can present small flares.
Here we present a systematic study of force-free field equation for simple axisymmetric configurations in spherical geometry. The condition of separability of solutions in radial and angular variables leads to two classes of solutions: linear and non-linear force-free fields. We have studied these linear solutions Chandrasekhar (1956) and extended the non-linear solutions given in Low & Lou (1990) to the irreducible rational form $n= p/q$, which is allowed for all cases of odd $p$ and to cases of $q>p$ for even $p$. We have further calculated their energies and relative helicities for magnetic field configurations in finite and infinite shell geometries. We demonstrate here a method here to be used to fit observed magnetograms as well as to provide good exact input fields for testing other numerical codes used in reconstruction on the non-linear force-free fields.
We present an adaptation of the rotation-corrected, m-averaged spectrum technique designed to observe low signal-to-noise-ratio, low-frequency solar p modes. The frequency shift of each of the 2l+1 m spectra of a given (n,l) multiplet is chosen that maximizes the likelihood of the m-averaged spectrum. A high signal-to-noise ratio can result from combining individual low signal-to-noise-ratio, individual-m spectra, none of which would yield a strong enough peak to measure. We apply the technique to GONG and MDI data and show that it allows us to measure modes with lower frequencies than those obtained with classic peak-fitting analysis of the individual-m spectra. We measure their central frequencies, splittings, asymmetries, lifetimes, and amplitudes. The low-frequency, low- and intermediate-angular degrees rendered accessible by this new method correspond to modes that are sensitive to the deep solar interior down to the core and to the radiative interior. Moreover, the low-frequency modes have deeper upper turning points, and are thus less sensitive to the turbulence and magnetic fields of the outer layers, as well as uncertainties in the nature of the external boundary condition. As a result of their longer lifetimes (narrower linewidths) at the same signal-to-noise ratio the determination of the frequencies of lower-frequency modes is more accurate, and the resulting
A revision is presented of the sunspot observations made by Charles Malapert from 1618 to 1626, studying several documentary sources that include those observations. The revised accounting of the group numbers recorded by Malapert for that period shows new information unavailable in the current sunspot group database. The average solar activity level calculated from these revised records of Malapert is by almost one third greater than that calculated from his records included in the current group database. Comparison of the sunspot observations made by Malapert and by other astronomers of that time with regard to the number of recorded groups and sunspot positions on the solar disk shows good agreement. Malapert reported that he only recorded one sunspot group in each sunspot drawing presented in Austriaca Sidera Heliocyclia (the documentary source which includes most of the sunspot records made by Malapert), although he sometimes observed several groups. Therefore, the sunspot counts obtained in this present work on Malaperts sunspot observations represents the lower limit of the solar activity level corresponding to those records.
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