1 Scientifc goals
This proposal follows previous proposals (2007, 2009) devoted to in-depth" investigations of the 3D structure of the photosphere through application of a Differential Cross-correlation Technique (DCT). At present, three scientific papers have been published in A&A applying the DCT to SOT/SP data ( Faurobert et al. 2009, 2012, 2013), another one is presently submitted, and two more are still in preparation.
In the last two papers, we used December 19, 2007 data from the irradiance survey program, as it turned out that the pole-to-pole scans with full spatial resolution (0.16"/px) were very well suited to our scientific objectives.
In Faurobert et al. (2013) we could measure the temperature depth-gradient in the photosphere of the quiet Sun and we found that it is significantly lower than in the standard FALC model. It seems to us that some of the assumptions used to solve the pseudohydrostatic equilibrium in semi-empirical models are probably at fault, and that some physical mechanisms at play in the solar photosphere could be missing. For example, the magnetic pressure due to ubiquitous mixed polarity magnetic fields at small scales, revealed in particular by Hinode high resolution polarization measurements, is not considered in such models.
To go further it would be very interesting to measure the temperature depth-gradient in the photosphere with the same technics over the solar activity cycle. Unfortunately, since 2008 the irradiance survey program has been performed with a lower spatial resolution (0.32"/px), this would degrade the sensitivity of the DCT method. The December 2007 data were taken at a minimum of the activity cycle, we are now at a maximum of the
cycle, so it would be very valuable for this program to perform the same observing run as on December 19, 2007, i.e. pole-to-pole scans with the full spatial resolution of SOT/SP.
We also recently expanded the scope of our studies towards the magnetic structure of the quiet photosphere. The 3D spatial distribution of the photospheric magnetic fields still remains an open question that may be investigated with the DCT method. As a first step we have examined the cross-correlation of polarization images obtained in the two FeI lines with images of the granulation observed in the continuum and of the reversed granulation observed at line centers. In a paper presently submitted to A& A, we argue that we observe the signatures of two spatially separated populations of magnetic regions, one is correlated with the granulation (i.e. it lies mainly over the bright granules), whereas the other one is anti-correlated (located in the inter-granular lanes). We also show that we are able to measure the formation height of the polarization signals arising from the inter-granular lanes: we determine that the polarization is formed at altitudes between 100 km and 120 km above the continuum formation layer. The method seems very promising and various detailed investigations are now carried out on the cross-correlation of polarization signals observed along the line profiles.
Let us now recall the principles of the DCT.
2. Differential cross-correlation technique.
The experiment is based on the fact that photospheric structures observed at different wavelength positions along a spectral line will appear horizontally displaced if one observes away from disc center. The displacementÉ√is proportional to the difference of depth ÉĘh between the formation depths of the radiation at the considered wavelengths and to the projected distance r from the solar disk center, of the form É√ = ÉĘhĀ~r/R_s=ÉĘhĀ~sinÉ∆, where É∆ is the heliocentric angle. It is important that the spectrograph slit is orientated radially and that spectrograms are corrected for the Doppler shifts arising from granular velocity fields. Expected displacements can be very small, ~200 km between the continuum and the line, and much smaller (a few tens of km) if we cross-correlate images obtained for nearby positions in wavelength inside the line, or at the two line centers.
We emphasize that the displacements between structures we seek to measure are not limited by diffraction. The signal to noise ratio of the experiment is the only limiting factor. Indeed, a well-known result of astrometry is that it is clearly possible to measure a displacement of an unresolved object far below the resolution of the telescope. However, good spectral resolution is required in order to correct the spectrograms for the Doppler effects of granular velocities. In our approach, the displacement is derived from the phase of the cross-spectrum of images at two different wavelengths. For a displacement " between the two patterns, the phase takes the linear form 2ÉőÉ√u, where u is the angular frequency. This information may be alternatively derived from the cross-correlations of the images. This technique was first proposed by Beckers & Hege (1982) and later developed for stellar applications (Aime, 1984; 1986). The technique we use makes it possible to increase the SNR by averaging cross spectra using many images.
First results using this method were obtained with the 90 cm ground-based telescope THEMIS, using the non-magnetic 557.6 nm Fe i line (Grec et al., 2007).
3. Importance of HINODE facilities for this program
With HINODE we are able to measure the phase of the spectrograms cross-spectra over a broad range of spatial frequencies up to the diffraction limit of the telescope, without the limitation due to seeing. This dramatically increases the SNR of the experiment. The very good spectral resolution of SOT/SP is another crucial advantage for implementing the DCT method. It allows us to correct the spectrograms for Doppler effects due to granular velocities in order to construct images of the solar granulation at constant opacity levels over the granules and the inter-granular lanes. Figure 1 shows examples of the cross-spectrum phase for images at successive levels in the FeI 630.15 nm line wing and line core, taken at cos(É∆) = 0:776 (É∆ denotes the heliocentric angle). For these two examples the measured perspective shifts are 13 km and 10 km, respectively!
The high sensitivity of the DCT method together with the high SNR of SOT data is necessary to reach the required accuracy.
Aime, C. 1974, Journal of the Optical Society of America (1917-1983), 64, 1129
Aime, C., Martin, F., Petrov, R., Ricort, G., & Kadiri, S. 1984, A&A, 134, 354
Beckers, J. M. & Hege, E. K. 1982, in ASSL Vol. 92: IAU Colloq. 67: Instrumentation for Astronomy with Large Optical Telescopes, ed. C. M. Humphries, 199, 206
Faurobert, M., Aime, C., Perini, C., Uitenbroek, H., Ricort, G., Arnaud, J., "Direct measurement of the formation height difference of the 630 nm FeI solar lines", 2009, A& A 507, L29
Faurobert, M., Ricort, G., Aime, C., "A cross-correlation method for measuring line formation heights in the solar photosphere", 2012, A& A 548, 80
Faurobert, M., Ricort, G., Aime, C., "Empirical determination of the temperature stratification in the photosphere of the quiet Sun", 2013, A& A 554, 116
Grec, C., Aime, C., Faurobert, M., Ricort, G., & Paletou, F. 2007, A&A, 463, 1125