July 31, 2014

Measuring the Sun’s diameter

In the 17 th century, Jean Picard performed a precise series of measurements of the Sun’s diameter to determine the eccentricity of Earth’s orbit (as the apparent diameter varies if the orbit is elliptical). These measurements were made at a time when Earth’s climate was especially cold during a period known as the Maunder minimum, when very few sunspots were observed. Later analysis of Picard’s measurements revealed the Sun’s diameter was probably a half arcsecond larger than at the end of the Maunder minimum (Ribes et al., 1987). Measurements of the solar constant since 1978 have been modelled from sunspots and faculae and this model applied to past observations has enabled total solar irradiance (TSI) to be reconstructed. The results show a remarkable correlation between TSI and variations in mean temperature (Lean et al., 1995), particularly in the 17 th century, except in periods of intense volcanic activity (Figure 1). Carbon dioxide levels deduced from polar ice cores have shown that a reduced greenhouse effect cannot explain the cold climate during this period. Such a well-documented climatic event is therefore very significant, and at that time the Sun’s diameter was different to what it is today, meaning that it was in a unique configuration. 

Measurements continued after Picard, but it’s difficult to establish a secular trend due to the diversity of instruments used. Different methods were used and still are today, but the results are not consistent. These include Meridian circle, Mercury transits, astrolabes, imaging telescopes and helioseismology. Measurements were acquired at different periods and in varying spectral domains that contain Fraunhofer lines likely to vary as a result of activity in the chromosphere. So, what can we conclude from all this? 

Certain measurements indicate no variation in diameter (Brown and Christensen-Dalsgaard, 1998), while other observations over the same period (Ulrich and Bertello, 1995) show a variation in solar activity. Measuring the time taken by Mercury to transit in front of the Sun enables the value of the Sun’s diameter to be deduced. These measurements show a periodic variation related to the Gleissberg cycle (Parkinson, 1980, 1983), which spans 90 years or so. Diameter variations measured during eclipses of the Sun (Sofia et al., 1983, 1985) show an anti-correlation with solar activity, as Picard’s measurements suggested. However, recent measurements are not consistent with each other. The longest series has been obtained with the Danjon astrolabe on the Calern plateau (Laclare et al., 1996), revealing an anti-correlation between solar activity and diameter that declined in the 2000s and then was apparent again more recently (Delmas and Laclare, 2002). But the same instrument in Santiago shows a variation in phase with solar activity and an amplitude five times larger than at Calern (Noël, 2004). Clearly, ground-based measurements are affected by photons coming through the atmosphere, where scattering, turbulence and absorption could explain these inconsistent results. Certain measurements show a constant diameter and others an anti-correlation or correlation with solar activity, so measurements outside the atmosphere are needed to determine if the diameter varies with solar activity or not. The Solar Disk Sextant instrument (Sofia et al., 1994a, b) measured the Sun’s diameter and oblateness from a stratospheric balloon. Four flights were completed, showing an anti-correlation with the solar cycle and agreement with the measurements from Calern. However, conclusions cannot be drawn from such a small number of flights. The MDI instrument on the SOHO spacecraft is studying the Sun’s internal structure by observing oscillation modes (Kosovichev et al., 1997). Among those observed, f-modes enable deduction of the radius of the sphere inside which these oscillations propagate (Schou et al., 1997). By adjusting the expected oscillation frequencies with a model to those observed, we can deduce the radius of the sphere, called the ‘seismic radius’, and its altitude at between 5,000 and 10,000 km below the photosphere. The results show a tiny variation in the radius at this depth. Depending on the processing methods used, we obtain no variation at all (Dziembowski et al., 2000; Antia et al. 2003), a correlation (Dziembowski et al., 1998) or an anti-correlation (Antia et al., 2000; Antia et al., 2001 ; Dziembowski et al., 2001) with solar activity. However, MDI has recorded images in the solar continuum that can be used to deduce the Sun’s diameter and its variations. Taken together, all measurements acquired since 1995 show a variation in the diameter for which significant instrumental effects can be seen. After instrument corrections, the secular variation would be less than 15 mas per year (Emilio et al., 2000; Kuhn et al., 2004). A detailed survey of results obtained by different methods of measuring the diameter has been conducted by Thuillier et al., 2005.