Detection of polarization from the E^4\Pi-A^4\Pi system of FeH in sunspot spectra

Here we report the first detection of polarization signals induced by the Zeeman effect in spectral lines of the E^4\Pi-A^4\Pi system of FeH located around 1.6 $\mu$m. Motivated by the tentative detection of this band in the intensity spectrum of late-type dwarfs, we have investigated the full Stokes sunspot spectrum finding circular and linear polarization signatures that we associate with the FeH lines of the E^4\Pi-A^4\Pi band system. We investigate the Zeeman effect in these molecular transitions pointing out that in Hund's case (a) coupling the effective Land\'e factors are never negative. For this reason, the fact that our spectropolarimetric observations indicate that the Land\'e factors of pairs of FeH lines have opposite signs, prompt us to conclude that the E^4\Pi-A^4\Pi system must be in intermediate angular momentum coupling between Hund's cases (a) and (b). We emphasize that theoretical and/or laboratory investigations of this molecular system are urgently needed for exploiting its promising diagnostic capabilities.Comment: 11 pages, 4 figures, accepted for publication in Astrophysical Journal Letter

Uncertainties in the solar photospheric oxygen abundance

The purpose of this work is to better understand the confidence limits of the photospheric solar oxygen abundance derived from three-dimensional models using the forbidden [OI] line at 6300 \AA , including correlations with other parameters involved. We worked with a three-dimensional empirical model and two solar intensity atlases. We employed Bayesian inference as a tool to determine the most probable value for the solar oxygen abundance given the model chosen. We considered a number of error sources, such as uncertainties in the continuum derivation, in the wavelength calibration and in the abundance/strength of Ni. Our results shows correlations between the effects of several parameters employed in the derivation. The Bayesian analysis provides robust confidence limits taking into account all of these factors in a rigorous manner. We obtain that, given the empirical three-dimensional model and the atlas observations employed here, the most probable value for the solar oxygen abundance is $\log(\epsilon_O) = 8.86\pm0.04$. However, we note that this uncertainty does not consider possible sources of systematic errors due to the model choice.Comment: Accepted for publication in Astronomy and Astrophysic

Penumbral thermal structure below the visible surface

$Context$. The thermal structure of the penumbra below its visible surface (i.e., $\tau_5 \ge 1$) has important implications for our present understanding of sunspots and their penumbrae: their brightness and energy transport, mode conversion of magneto-acoustic waves, sunspot seismology, and so forth. $Aims$. We aim at determining the thermal stratification in the layers immediately beneath the visible surface of the penumbra: $\tau_5 \in [1,3]$ ($\approx 70-80$ km below the visible continuum-forming layer). $Methods$. We analyzed spectropolarimetric data (i.e., Stokes profiles) in three Fe \textsc{i} lines located at 1565 nm observed with the GRIS instrument attached to the 1.5-meter solar telescope GREGOR. The data are corrected for the smearing effects of wide-angle scattered light and then subjected to an inversion code for the radiative transfer equation in order to retrieve, among others, the temperature as a function of optical depth $T(\tau_5)$. $Results$. We find that the temperature gradient below the visible surface of the penumbra is smaller than in the quiet Sun. This implies that in the region $\tau_5 \ge 1$ the penumbral temperature diverges from that of the quiet Sun. The same result is obtained when focusing only on the thermal structure below the surface of bright penumbral filaments. We interpret these results as evidence of a thick penumbra, whereby the magnetopause is not located near its visible surface. In addition, we find that the temperature gradient in bright penumbral filaments is lower than in granules. This can be explained in terms of the limited expansion of a hot upflow inside a penumbral filament relative to a granular upflow, as magnetic pressure and tension forces from the surrounding penumbral magnetic field hinder an expansion like this.Comment: 5 pages; 2 figures; accepted for publication in Astronomy and Astrophysics Letter

Estimating the magnetic field strength from magnetograms

A properly calibrated longitudinal magnetograph is an instrument that measures circular polarization and gives an estimation of the magnetic flux density in each observed resolution element. This usually constitutes a lower bound of the field strength in the resolution element, given that it can be made arbitrarily large as long as it occupies a proportionally smaller area of the resolution element and/or becomes more transversal to the observer and still produce the same magnetic signal. Yet, we know that arbitrarily stronger fields are less likely --hG fields are more probable than kG fields, with fields above several kG virtually absent-- and we may even have partial information about its angular distribution. Based on a set of sensible considerations, we derive simple formulae based on a Bayesian analysis to give an improved estimation of the magnetic field strength for magnetographs.Comment: 8 pages, 7 figures, accepted for publication in A&

Analytical maximum likelihood estimation of stellar magnetic fields

The polarised spectrum of stellar radiation encodes valuable information on the conditions of stellar atmospheres and the magnetic fields that permeate them. In this paper, we give explicit expressions to estimate the magnetic field vector and its associated error from the observed Stokes parameters. We study the solar case where specific intensities are observed and then the stellar case, where we receive the polarised flux. In this second case, we concentrate on the explicit expression for the case of a slow rotator with a dipolar magnetic field geometry. Moreover, we also give explicit formulae to retrieve the magnetic field vector from the LSD profiles without assuming mean values for the LSD artificial spectral line. The formulae have been obtained assuming that the spectral lines can be described in the weak field regime and using a maximum likelihood approach. The errors are recovered by means of the hermitian matrix. The bias of the estimators are analysed in depth.Comment: accepted for publication in MNRA

MOLPOP-CEP: An Exact, Fast Code for Multi-Level Systems

We present MOLPOP-CEP, a universal line transfer code that allows the exact calculation of multi-level line emission from a slab with variable physical conditions for any arbitrary atom or molecule for which atomic data exist. The code includes error control to achieve any desired level of accuracy, providing full confidence in its results. Publicly available, MOLPOP-CEP employs our recently developed Coupled Escape Probability (CEP) technique, whose performance exceeds other exact methods by orders of magnitude. The program also offers the option of an approximate solution with different variants of the familiar escape probability method. As an illustration of the MOLPOP-CEP capabilities we present an exact calculation of the Spectral Line Energy Distribution (SLED) of the CO molecule and compare it with escape probability results. We find that the popular large-velocity gradient (LVG) approximation is unreliable at large CO column densities. Providing a solution of the multi-level line transfer problem at any prescribed level of accuracy, MOLPOP-CEP is removing any doubts about the validity of its final results.Comment: 10 pages, 3 figures, accepted for publication in A&