Letter to the Editor

Direct measurement of the formation height difference of the 630 nm Fe I solar lines

¹ UMR 6525 H. Fizeau, Université de Nice Sophia Antipolis, CNRS, Observatoire de la Côte d'Azur, Campus Valrose, 06108 Nice, France e-mail: [marianne.faurobert;claude.aime;jean.arnaud;gilbert.ricort]@unice.fr
² National Solar Observatory/Sacramento Peak, PO Box 62, Sunspot, NM88349, USA e-mail: huitenbroek@nso.edu
³ Institut d'Astrophysique Spatiale, Bâtiment 121, Université Paris XI, 91405 Orsay Cedex, France e-mail: catherine.grec@ias.u-psud.fr

Received: 21 September 2009
Accepted: 21 October 2009

Abstract

Context. Spectral lines formed over a limited height range in either a stellar or planetary atmosphere provide us with information about the physical conditions within this height range. In this context, an important quantity is the so-called line formation depth. It is usually determined from numerical calculation of the atmospheric opacity in the line of interest and then converted into geometrical depth by using atmospheric models.

Aims. We develop a radically different approach, which allows us to measure directly line formation depths from spectroscopic observations without relying on assumptions about an atmospheric model. This method requires spatially resolved observations, which up to now have been available only for solar or planetary studies. We apply this method to images of the solar granulation.

Methods. The method was presented and tested numerically in previous papers. It is based on the measurement of the perspective shift between images at different wavelengths, formed at different heights, when they are observed away from disk center. Because of the Fourier transform properties, this shift gives rise to a deterministic linear phase term in the cross spectrum of the images.

Results. The method is applied to observations of solar quiet regions performed with the SOT spectropolarimeter on HINODE in the Fe i line pair at 630.15 and 630.25 nm. We derive the difference in formation heights between the two lines and its center-to-limb variations. We show that the high sensitivity of the measurements allows us to detect variations in the line formation heights between magnetized and non-magnetized regions of the solar atmosphere.

Conclusions. Our results are the first direct measurements of line formation depths in the solar photosphere. Cross spectral analysis provides us with a new observable quantity, which may be measured with an accuracy well bellow the spatial resolution of the observations. We recall that the Fe i line pair at 630.15 and 630.25 nm is often used to determine solar magnetic fields by spectropolarimetric observations and inversion methods. The difference in the line formation heights that we measure should be taken into account in the inversion procedures.