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

摘要

Context. Spectral lines formed over a limited height rangein either a stellar or planetary atmosphere provide us with informationabout the physical conditions within this height range. In thiscontext, an important quantity is the so-called line formation depth.It is usually determined from numerical calculation of the atmosphericopacity in the line of interest and then converted into geometricaldepth by using atmospheric models. Aims. We develop a radically different approach, which allows usto measure directly line formation depths from spectroscopicobservations without relying on assumptions about an atmospheric model.This method requires spatially resolved observations, which up to nowhave been available only for solar or planetary studies. We apply thismethod to images of the solar granulation. Methods. The method was presented and tested numerically inprevious papers. It is based on the measurement of the perspectiveshift between images at different wavelengths, formed at differentheights, when they are observed away from disk center. Because of theFourier transform properties, this shift gives rise to a deterministiclinear phase term in the cross spectrum of the images. Results. The method is applied to observations of solar quietregions performed with the SOT spectropolarimeter on HINODE in theFe Iline pair at 630.15 and 630.25nm.We derive the difference in formation heights between the two lines andits center-to-limb variations. We show that the high sensitivity of themeasurements allows us to detect variations in the line formationheights between magnetized and non-magnetized regions of the solaratmosphere. Conclusions. Our results are the first direct measurements ofline formation depths in the solar photosphere. Cross spectral analysisprovides us with a new observable quantity, which may be measured withan accuracy well bellow the spatial resolution of the observations. Werecall that the Fe Iline pairat630.15 and630.25nm is often used to determine solarmagnetic fields by spectropolarimetric observations and inversionmethods. The difference in the line formation heights that we measureshould be taken into account in the inversion procedures. Key words: line: formation - techniques: high angular resolution - techniques: spectroscopic - Sun: photosphere