Solar Diameter Measurements Research Articles

Analysis of Solar Diameter Measurements Made at the Basilica of San Petronio during and after the Maunder Minimum

Abstract A series of measurements of the solar diameter taken in the meridian line of the Basilica of San Petronio (Bologna, Italy) between 1655 and 1736 has been analyzed. This series is of interest because the measurement period includes the Maunder Minimum (1645–1715; hereafter MM) when solar activity was abnormally low. Some authors have suggested an increase of the solar diameter during the MM. Trying to detect these changes, statistical analyses comparing measurements taken in San Petronio during the MM (1655–1715) and other ones taken in a subsequent period (1716–1736) have been performed. Mann–Whitney U tests and Student’s t-tests indicate that there is no statistically significant difference in the medians and averages of the solar diameter in both periods. In fact, we have found differences around 0.″6 in the medians and the averages, which are below the mean accuracy of the instrument. Therefore, we conclude that there is no difference between the solar diameter value measured during the MM (1655–1715) and that for the subsequent period 1716–1736. This implies that there has not been an increase in the solar diameter of several arcseconds during the MM as has been speculated by some authors.

Solar diameter measurements from eclipses as a solar variability proxy

AbstractThe widths of total solar eclipse paths depends on the diameter of the Sun, so if observations are obtained near both the northern and southern limits of the eclipse path, in principle, the angular diameter of the Sun can be measured. Concerted efforts have been made to obtain contact timings from locations near total solar eclipse path edges since the mid 19th century, and Edmund Halley organized a rather successful first effort in 1715. Members of IOTA have been making increasingly sophisticated observations of the Baily's bead phenomena near central solar eclipse path edges since 1970.

Geometrical information on the solar shape: high precision results with SDO/HMI

AbstractThe uncertainty of measurement of solar diameter is depending on the observational time scale. Full-disc images of SDO/HMI and the images from ground observations in Huairou Solar Observing Station have been analyzed to get the values of solar diameter. The satellite observations reach a very high precision, but the absolute image scale still need to be calibrated. The solar oblateness is a more challenging measurement than the diameter, since the signal amplitude is a few milli-arcseconds. It is a relative measurement, then not affected by the pixel scale calibration required by the diameter measurement. But the results are strongly dependent on the state of instrument such as focus plane deformation and on the calculation process.

Rights and wrongs of the temporal solar radius variability

From time immemorial men have strived to measure the size of celestial bodies. Among them, the diameter of the Sun was a source of curiosity and study. Tackled by Greek astronomers from a geometric point of view, an estimate, although incorrect, has been first determined, not truly called into question for several centuries. One must wait up to the XVIIth century to get the first precise determinations made by the French school of astronomy. Gradually, as the techniques were more and more sophisticated, many other solar diameter measurements were carried out, notably in England, Germany, Italy and US. However, even with instruments at the cutting edge of progress, no absolute value of the solar diameter has been provided yet, even if the community has adopted a canonical radius of 959.″63, given in all ephemeris since the end of the XIXth century. One of the major difficulties is to define a correct solar diameter. Another issue is the possible temporal variability of the size of the Sun, as first advocated at the end of the XIXth century by the Italian school. Today, this question is just on the way to being solved in spite of considerable efforts developed on ground-based facilities or on board space experiments. We will here give a review of some of the most remarkable techniques used in the past, emphasising how incorrect measurements have driven new ideas, leading to develop new statements for the underlying physics. On such new grounds, it can be speculated that the roundness of the Sun is not perfect, but developing a thin “cantaloupe skin” in periods of higher activity, with departures from sphericity being inevitably bounded by a few kilometers (around 80 km or 10 to 15 mas).

The Measurement of Solar Diameter and Limb Darkening Function with the Eclipse Observations

The Total Solar Irradiance varies over a solar cycle of 11 years and maybe over cycles with longer period. Is the solar diameter variable over time too? We introduce a new method to perform high resolution astrometry of the solar diameter from the ground, through the observations of eclipses by reconsidering the definition of the solar edge. A discussion of the solar diameter and its variations must be linked to the Limb Darkening Function (LDF) using the luminosity evolution of a Baily's Bead and the profile of the lunar limb available from satellite data. This approach unifies the definition of solar edge with LDF inflection point for eclipses and drift-scan or heliometric methods. The method proposed is applied for the videos of the eclipse in 15 January 2010 recorded in Uganda and in India. The result shows light at least 0.85 arcsec beyond the inflection point, and this suggests to reconsider the evaluations of the historical eclipses made with naked eye.

Atmospheric fluctuations below 0.1 Hz during drift-scan solar diameter measurements

Measurements of the power spectrum of the seeing in the range 0.001–1 Hz have been performed in order to understand the criticity of the transits method for solar diameter monitoring.

Historical records of solar grand minima: a review

AbstractKnowing solar activity during the past centuries is of great interest for many purposes. Historical documents can help us to know about the behaviour of the Sun during the last centuries. The observation of aurorae and naked-eye sunspots provides us with continuous information through the last few centuries that can be used to improve our knowledge of the long-term solar activity including solar Grand Minima. We have more or less detailed information on only one Grand minimum (the Maunder minimum in the second half of 17th century), which serves as an archetype for Grand minima in general. Telescopic sunspot records and measurements of solar diameter during Maunder minimum are available. In this contribution, I review some recent progress on these issues.

The development of the Heliometer of the Observatório Nacional

AbstractThe Observatório Nacional at Rio de Janeiro has developed a new heliometer to perform accurate measurements of the solar diameter. The equipment makes use of split parabolic mirrors, rather than split achromatic lenses as objective. In its first campaign this reflector heliometer generated a few thousands of images of the Sun through which we evaluate the precision of the solar diameter measurements as been 5 mas. The mechanical and thermal stability of the instrument is guaranteed by the use of a telescope tube manufactured in carbon fiber. The tube firmly holds the heliometric mirrors and the CCD camera that collects the images. The perfect lodging between the two half-mirrors over its supporting plate defines the angular instrumental separation between the two images of the sun. The heliometric mirrors and supporting plate have been made in ceramic material in order to ensure the stability of the optical configuration and to maintain the two images of the solar disk displaced by a fixed angle in relation to each other. To verify the stability of the instrument we designed the procedures of collimation and comparison. The collimation consists of using the heliometer for measuring the diameter of an artificial solar image specifically created for this purpose. The comparison is performed by measuring the residual unfold of a punctual image after been unfold by two opposed heliometers. The heliometric approach allows the measurement of the solar diameter at any heliolatitude and can be undertaken as often as desired. Computer programs have been developed for automated image acquisition and analysis. The optical and mechanical design has been performed by using 3D computer aided design software.

A solar cycle lengthwise series of solar diameter measurements

AbstractThe measurements of the solar photospheric diameter rank among the most difficult astronomic observations. Reasons for this are the fuzzy definition of the limb, the SNR excess, and the adverse daytime seeing condition. As a consequence there are very few lengthy and consistent time series of such measurements. Using modern techniques, just the series from the IAG/USP and from Calern/OCA span more than one solar cycle. The Rio de Janeiro Group observations started in 1997, and therefore in 2008 one complete solar cycle time span can be analyzed. The series shares common principles of observation and analysis with the ones afore mentioned, and it is complementary on time to them. The distinctive features are the larger number of individual points and the improved precision. The series contains about 25,000 single observations, evenly distributed on a day-by-day basis. The typical error of a single observation is half an arc-second, enabling us to investigate variations at the expected level of tens of arc-second on a weekly basis. These features prompted to develop a new methodology for the investigation of the heliophysical scenarios leading to the observed variations, both on time and on heliolatitude. The algorithms rely on running averages and time shifts to derive the correlation and statistical incertitude for the comparison of the long term and major episodes variations of the solar diameter against activity markers. The results bring support to the correlation between the diameter variation and the solar activity, but evidentiating two different regimens for the long term trend and the major solar events.

Solar Radius Determination from Total Solar Eclipse Observations on 29 March 2006

Solar diameter measurements have been made nearly continuously through different techniques for more than three centuries. They were obtained mainly with ground-based instruments except for some recent estimates deduced from space observations. One of the main problems in such space data analysis is that, up to now, it has been difficult to obtain an absolute value owing to the absence of an internally calibrated system. Eclipse observations provide a unique opportunity to give an absolute angular scale to the measurements, leading to an absolute value of the solar diameter. However, the problem is complicated by the Moon limb, which presents asphericity because of the mountains. We present a determination of the solar diameter derived from the total solar eclipse observation in Turkey and Egypt on 29 March 2006. We found that the solar radius carried back to 1 AU was 959.22±0.04 arcsec at the time of the observations. The inspection of the compiled 19 modern eclipses data, with solar activity, shows that the radius changes are nonhomologous, an effect that may explain the discrepancies found in ground-based measurements and implies the role of the shallow subsurface layers (leptocline) of the Sun.

A Comparison among Solar Diameter Measurements Carried Out from the Ground and outside Earth's Atmosphere

The solar diameter has been measured since the 17th century, using different methods and instruments, and without a clear strategy of measurement, which could explain the lack of coherence between the results obtained. The present study confirms that the discrepancies between solar diameter measurements are mostly due to differences in instrumental characteristics, the spectral domain of observation of each investigation, and atmospheric turbulence for ground measurements. We show that correcting the measurements for the effects introduced by the properties of each instrument reduces the differences between the radius measurements to the level of uncertainty of each instrument. This study makes use of simulated and real data. For the simulated data, we use an empirical model of the solar limb shape, and for observations, we use measurements carried out with the Solar Disk Sextant experiment, the CCD solar astrolabe of Calern Observatory, and the Michelson Doppler Imager on board SOHO.

Processing Method Effects on Solar Diameter Measurements: Use of Data Gathered by the Solar Disk Sextant

To determine the apparent diameter of the Sun, it is first necessary to measure the shape of the intensity profile of the solar limb with an imaging optical system (hereafter denoted as a solar-limb profile). The inflection point of the limb profile is usually used as a reference for calculating the diameter. Because this point may be difficult to determine in the presence of noise, it is necessary to define an appropriate filtering process that eliminates noise while preserving the position of the inflection point. In this paper we study two filtering techniques, one based on the compact wavelet transform and the other on the finite Fourier transform definition, that meet these requirements. The application of these two techniques to data gathered by the Solar Disk Sextant experiment shows that the solar radius increased from 1992 to 1996 by about 197 mas. However, a previous analysis of the same data and our present analysis provide a difference in the measured radii of about 92 mas. We show that this difference is entirely traced to the filtering process.

Solar apparent radius variability: a new statistical approach to astrolabe multisite observations

The results of the analysis of solar diameter measurements obtained by means of the astrolabe have been inconclusive so far. Temporal variations are found, but they differ in amplitude and phase. This paper presents the results of a new statistical approach to compare and analyse the astrolabe data obtained during the period 1998-2003 in Brazil, Chile, France and Turkey. We show that different time series can be considered as extracted from the same statistical population following the Gaussian law. As following on a variographic analysis, the series do not seem to be autocorrelated at small scale (40 d) and present the characteristics of a highly disorganized phenomenon. At medium scale (6 yr), a 1-yr periodicity can be seen. It could be the residual trace of a temporal latitudinal variability. At large scale (up to 30 yr, using only French and Chilean data available, respectively, from 1975 and 1990), a faint 11-yr component in the signal can be pointed out. As an 11-yr periodicity has been found in the stratospheric data, we have explored the possibility of a relationship between the measured radii and stratospheric phenomena. This would explain the discrepancy in amplitudes, the sign of the crossed correlation coefficients, and the apparent disorganized behaviour of the data. Therefore, a complementary non-determinist analysis has been done in order to distinguish a chaotic signal from a random noise. The Hurst exponent establishes the persistence of the series. It can be concluded that the solar measurements from astrolabes are not purely randomly distributed, but show the character of a deterministic series for which (i) the observations need to be far more accurate, as it is only possible if obtained from space or in real-time together with a seeing monitor; (ii) supposing that it is indeed possible to extract a solar component, data must be studied considering their heliographic latitude and (iii) data show the variability of the upper atmospheric conditions (maybe Quasi-Biennial Oscillations) and the stratospheric 11-yr periodicity, for which the modulation is caused by the solar irradiance.

Solar diameter measurements at São Paulo Observatory

In this work we describe solar radius measurements made from 1972 with the Sao Paulo astrolabe. We find values of 959.52 ± 0.03 arcsec for the visual data and 959.61 ± 0.05 arcsec for the CCD data using a modified data acquisition system. We compare our results with other astrolabe measurements and with SOHO-MDI. Observations of the solar radius show contradictory results when we try to correlate changes in the diameter with the solar cycle. Our series is not correlated with the solar cycle but it shows a period of 13.4 ± 2.2 yr. We have also compared our time series with other long-term measurements of solar radius along solar cycle 21 and analysed our measurements as a function of heliographic latitude. We do not find a significant solar oblateness.

Spectral analysis of solar diameter measurements recorded at Calern Observatory astrolabe during two solar cycles

Solar diameter measurements performed with the Calern Observatory astrolabe (O.C.A - France) during more than two solar cycles show temporal variations. Due to the weather, seasonal effects and instrumental characteristics, recorded solar data are non uniformly sampled and present temporal gaps. Thus, to analyze these data, diameter measurements averaged over one or more months have generally been considered. This limits the accessible harmonic terms to a low frequency range. To determine short-term periodicities from the observed variations, all daily solar data need to be considered and also corrected from the zenithal distance. In the present work, we use two methods to analyze solar diameter measurements recorded at Calern Observatory astrolabe during the observation period 1975-1996. They are based on least square fits and deconvolution of the observation window function. Results deduced from the analysis confirm harmonic terms already found by other authors but also reveal new higher frequencies.

Measurements of the Apparent Solar Diameter with Astrolabe at Observatório Nacional—1997/2000

The metrological qualities render the modified CCD solar astrolabe a very reliable instrument for the difficult conditions of solar diameter measurements. At O.N. an average value of 959”.04 ± 0”.01 is found, for λ = 563.5nm, and an effective bandpass of 168nm. To improve the signal to noise ratio, the images are treated for flat field. This includes distortions brought about by the COHU 4710 camera, the astrolabe optics, and by the system of filters that cut down the incoming solar light. The extensive series observed (over 12000 independent measures) is examined, using a CLEAN periodogram algorithm. The outcome shows periods reconcilable with the solar activity and geometry of observation.

The Error in Solar-Diameter Measurements Induced by Atmospheric Turbulence

Diameter measurements performed with the solar astrolabe are affected by atmospheric effects. In order to deduce significant astrophysical results, it is necessary to know how these effects contribute to the error of diameter measurement. For this purpose, a numerical simulation was developed leading to a law of error behaviour with observing conditions. In order to validate these results, recorded data obtained at the Calern observatory astrolabe (France) during the period 1996 – 1997 are used. A good agreement is observed with the simulation, which permit salso to give access to daily atmospheric time constants. (Co-author is A. Irbah, Algeria.)

Analysis of Diameter Measurements Performed at Calern Observatory Astrolabe

Solar diameter measurements performed at Calern Observatory astrolabe during more than two solar cycles show variations at various time scales in a broad range. Due to seasonal effects and instrumental characteristics, the recorded data are not sampled uniformly and present some gaps during these years. This time series has been analyzed by means of a deconvolution of the window function, as an alternative method to the standard least square fits of harmonic functions. The results show an extremely important improvement of the power spectrum. Harmonic terms already found by other authors are confirmed but new frequencies are also revealed by this analysis.

Error due to atmospheric turbulence effects on solar diameter measurements performed with an astrolabe

Diameter measurements performed with the solar astrolabe are affected by instrumental and atmospheric effects. The problem is to know how these effects contribute to the error on diameter measurements. Thus, a numerical simulation is developed to bring some responses to this problem. For this purpose, synthetic images of the Sun similar to the ones obtained by the instrument through the Earth atmosphere are simulated. A fractal model is used to generate randomly perturbed wavefronts and therefore optical response of the whole system, atmosphere and instrument. Many sequences of solar images are then simulated for various observation conditions (Fried's parameter r0, spatial coherence outer scale L0 and atmospheric characteristic times). They are used to define the time of contact of the direct and reflected solar images which is fundamental in the solar astrolabe experiment. It is then studied as a function of the observation conditions relatively to the experimental characteristics (exposure time).

Solar diameter measurements with Calern Observatory astrolabe and atmospheric turbulence effects

In order to deduce significant astrophysical results from solar diameter measurements it is necessary to take an accurate account of instrumental and atmospheric effects. This paper presents a comparison between visual and CCD camera measurements performed by means of the Calern Observatory solar astrolabe during the last 4 years; this allows us to evaluate visual measurements done previously (from 1975 to 1989). Then, a study of atmospheric effects is developed. From CCD measurements, the image quality, expressed by Fried's seeing parameter,r0, is estimated and related to the errors occurring in solar diameter measurements. A statistical analysis gives about 0.26 arc sec (or 0.13 arc sec for the semi-diameter) as the lowest value that this error may reach at Calern Observatory. One conclusion of this work is that it is important in the future to have image quality observations, obtained using a dedicated monitor, in order to evaluate and classify the measurements. A survey of the seeing might so lead to improve the precision of the results by weighting each diameter estimation and eventually to schedule the observations.