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HINODE Operation Plan (HOP)

accepted on


 HOP No.

 HOP title

HOP 0239

Super resolving analysis of photospheric layers using adifferential cross-correlation technique

plan term


@ @


 name : Faurobert, Aime, Ricort, Lites @  e-mail : marianne.faurobert[at]unice.fr

contact person in HINODE team

 name : Lites @  e-mail : lites[at]ucar.edu

 abstract of observational proposal
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 displacementis proportional to the difference of depth h 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 = h~r/R_s=h~sin, where 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 2΃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() = 0:776 ( 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.

5 Bibliography

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

 request to SOT
4 Outline of observations

We propose to perform SOT observations, using SP. The slit has to be oriented along the North-South axis and successively positioned at twenty positions allowing us to scan the solar polar axis from the south to the north pole, as in the regular irradiance program.

The heliocentric angle can be identified to the solar latitude only if the solar equator is at the center of the disk image, i.e. at a date when the inclination angle of the solar polar axis, B0, is near zero (polar axis in the plane of the sky). Therefore the best period for our observations would be the first two weeks of December when B0 is below 1 deg in absolute value. However this is not a decisive condition, the DCT method can be used for any inclination of the solar equator, but for programs related to the magnetic field distribution it would be interesting to explore both solar hemispheres in a symmetrical way.

The objectives are to achieve a good polarimetric accuracy, a good statistical sample of different granular structures, and coverage of the range of latitudes away from disk center. Solar activity should be avoided, so the data should be taken during a period when no significant activity exists along the central meridian.

The proposed program will resemble closely the ongoing SP irradiance program. We propose a program of 11 SP maps, each having the following properties:

. Eleven deep-mode SP maps: five each in the northern and southern hemispheres along the central meridian, distributed symmetrically with respect to disk center, and sampling quiet Sun continuously between 0.25 and 0.85 solar radii, plus one map at disk center. As in the irradiance program, there should be a small overlap in latitude between each of the maps except that at disk center.

. Deep mode integration time: 9.6 seconds with bit-shifting in Stokes I to avoid possible digital wraparound

. Full-resolution pixel sampling along the slit (unbinned)

. Slit scan interval of 0.16"
. Single-sided (downlink only one side of the CCD)
. Map 190 steps wide (190 steps of 0:16")
. Sample 816 pixels along the slit (same window as standard irradiance, but unlike the standard case, no binning along the slit)

TIMING: Each map should require about 35 minutes to execute. Maps should be planned in periods free of the South Atlantic Anomaly.
DATA VOLUME: The raw data load of the standard SP irradiance program is about 1.5 Gbits. Together with the pole-to-pole FG irradiance program, about 3 Gbits are generated for downlink. There are 20 SP maps in the typical standard irradiance program.

Each of the proposed maps will have two times the number of pixels of the standard irradiance program, but there are only about half the number of maps, so the proposed program with 11 maps will produce only very slightly more data than the standard SP irradiance program (half of the combined SP+FG irradiance program, or 1.5 Gbits).

Therefore, like the standard irradiance program, it should fit easily within one planning day.

POINTING COORDINATES: The planning tool for the irradiance program may be used to generate pointing coordinates, and unwanted map positions near the equator and poles may be eliminated from the plan.

 request to XRT

 request to EIS

 other participating instruments


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