HOP 0143

abstract of observational proposal

The solar photosphere is a boundary layer where physical quantities show very sharp depth variations and where structures such as the granulation are present on small scales. The modeling of this complex layer requires 3D hydrodynamical simulations of magneto-convection. Very efficient numerical calculations are developed (Voegler et al. 2005). They allow the formation of different solar spectral lines to be simulated (see Orozco Suarez et al., 2007). However, comparison of the simulations with high vertical resolutionobservations are quite rare. One aim of this proposal is to carry out such an "in-depth" in-vestigation of the 3D structure of the photosphere by using a Differential Cross-correlation Technique (DCT) similar to the one described in Grec et al. (2007, 2009).

This proposal aims at applying the DCT to measure the depths of formation of the two FeI lines at 630.1 and 630.2 nm. Those two lines are extensively used in order to determine the photospheric magnetic field. However, Martinez et al (2006) pointed out
that spurious results may be obtained from this set of lines due to the ignored fact that they have different formation depths. DCT can provide a direct measurement of the difference between the two line formation depths.

We already obtained observing time on SOT/SP for this project in October 2007. The Level-1 calibrated data have been available only this spring, because of some accidental problems in the calibration procedures for our observations which have fortunately been solved. The quality of the spectrograms in the two FeI lines is excellent and we could derive the difference between the line formation depths with a high accuracy. A letter has recently been submitted to Astronomy & Astrophysics, and is accepted with minor revisions. We show that the line formation depth difference varies with the latitude, between 100 km to 60 km typically and that it is very sensitive to the presence of magnetic fields. Furthermore, we find some evidence of an asymmetry between the values measured in the North and in the South solar hemispheres. This unexcepted result could be due to asymmetries in the quiet sun magnetic fields, this has to be confirmed by further observations.

Let us now recall the principles of the DCT. They are also briefly described and illustrated in the Letter than we join to this proposal.

request to SOT

We propose to perform SOT observations, using SP and simultaneous BFI in the G-band. The first results we obtained with SOT/SP show a dependence of the line formation depths with respect to the latitude and to the presence of magnetic fields. We now wish to investigate further these effects. In order to get continuous coverage in latitudes, the slit has to be oriented along the North-South axis and successively positioned in thirteen different positions which are given in Fig. 1. Furthermore, we need to have the solar equator at the center of the disk image, meaning that we wish to observe at a date when the inclinaison angle of the solar polar axis, B0, is near zero (polar axis in the plane of the sky). Therefore the right period for our observations would be the first two weeks of December when B0 is below 1°in absolute value.

We also wish to perform measurements with the slit orientated radially along the　solar equator, at seven positions in the west-east direction (see Fig. 1). As we are at the beginning of the rising solar magnetic cycle we do not except to see active regions along the equator. The measurements along the equator will give access to the line formation depth variations over network and intranetwork regions at latitude zero, which cannot be measured in any other radial direction (the perpective effect vanishes when the heliocentric angle is zero).

We will use SP in the Normal map single side mode and simultaneously BFI in the G-band in order to get 2D images of the context at each slit position.

･ Normal scans: Scan of 13 regions of 164 arcsec x 4.8 arcsec each, along the North-South polar axis.
For each region, a scan should take about 2.5 minutes. The same observation is run 16 times, which amounts to a total of 40 minutes for a given region. The center of the slit for the 13 scans is positioned from center to limb on the North-South axis at the Center, North 152 ", 304", 456", 608", 760" and 912" (with a small overlap of 12" between two successive positions) and at symetrical positions in the southern hemisphere. as shown in Fig. 1. The objective is to achieve a good polarimetric accuracy for studies of the magnetic field effects. Estimated total time for 13 positions: 520 minutes

･ Normal scans: Scan of 7 regions of 164 arcsec x 4.8 arcsec each, along the East-West equator The 7 scans are positioned at disk center, ±304", ±608" and ±912" along the equator and the slit is orientated along the equator. For each region, a scan should take about 2.5 minutes. The same observation is run 16 times, which amounts to a total of 40 minutes for a given region. Estimated total time for 7 positions: 280 minutes

･ BFI in G-band at each slit position with 211"x 111" FOV and a cadence of 5 minutes (one image every two scans)
The overall requested observing time is 800 minutes. The data volume is 20x16x[30x(1024x112x1x4)]= 9 GBits for the SP data and 20x8x[2048x1024]= 670 MBits for the BFI data.

remarks

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 outside the disc center. The displacement " is proportional to the difference of depth Δh 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 ε = Δh × r/R_s = Δh × sin θ, where θ is the heliocentric angle. For that the spectrograph slit is orientated radially and spectrograms are corrected from the Doppler effect due to 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 close-by 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, it is clearly possible to measure a displacement of an unresolved object far below the resolution of the telescope, as we know it from astrometry. However a good spectral resolution is required in order to correct the spectrograms for the Doppler effects of granular velocities (see Grec at al. 2009). In our approach, the displacement is derived from the phase of the cross-spectrum of images at two different wavelengths. For a displacement ε between the two patterns, the phase takes the linear form 2πεu, 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). Numerical simulations of the DCT applied on the FeI pair of lines at 630 nm is presented in Grec et al. (2009 in press).

3 Importance of HINODE facilities for this program

With HINODE we are able to measure the phase of the spectrograms cross-spectra overa 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 and allows us to investigate the magnetic effects on the line formations depths. We find that, typically, the line formation depth difference is about 10 km smaller in the network than in the inter-network regions. The high sensitivity of the DCT method together with the high SNR of SOT data is necessary to reach the required accuracy.

We also intend to enlarge our studies towards the magnetic structure of the quiet photosphere. It seems now well established that mainly vertical strong fields are detected in the intergranular lanes whereas weaker fields with variable orientations are found over the granules. However the depth variation of the photospheric magnetic field still remains an open question. In a first step, we propose to study whether the polarization images obtained in the two FeI lines outside the disk center do show slightly displaced similarstructures. An analysis of the cross-correlations of polarization images (or of cross-spectra) seems to be an adequate tool for this kind of study.