Basilio Ruiz Cobo

Observation of Convective Collapse and Upward-moving Shocks in the Quiet Sun

We present spectropolarimetric evidence of convective collapse and destruction of magnetic flux by upward-moving fronts in the quiet Sun. The observational material consists of time series of the full Stokes vector of two infrared spectral lines emerging from regions associated with Ca II K network points. The amplitude of the circular polarization profiles of a particular spatial point is seen to increase while the profiles are redshifted. It then decreases during a much shorter phase characterized by large blueshifts. Inspection of the data indicates that the blueshift occurs because of the sudden appearance of a new, strongly displaced Stokes V profile of the same polarity. The amplification of the magnetic signal takes place in a time interval of about 13 minutes, while blueshifts and the concomitant decreasing Stokes V amplitudes last for only 2 minutes. An inversion code based on the thin flux-tube scenario has been applied to the data in order to derive the thermal, magnetic, and dynamic structures of the atmosphere. According to our results, the field strength undergoes a moderate increase from 400 to 600 G at z = 0 km during the phase in which redshifts are present. The observed redshifts are produced by internal downflows of up to 6 km s-1 at z = 0 km. After ~13 minutes, the material falling down inside the tube appears to bounce off in the deeper layers, originating an upward-propagating front whose manifestation on the Stokes V profiles is a large blueshift. The front moves with a speed of 2.3 km s-1 and has a downflow-to-upflow velocity difference of about 7 km s-1 initially and some 4 km s-1 after 2 minutes. It strongly weakens the magnetic field strength and may be responsible for the complete destruction of the magnetic feature. The observed behavior is in general agreement with theoretical predictions of flux expulsion, convective collapse, and development of shocks within magnetic flux tubes.

Chemical abundances from inversions of stellar spectra: Analysis of solar-type stars with homogeneous and static model atmospheres

Spectra of late-type stars are usually analyzed with static model atmospheres in local thermodynamic equilibrium (LTE) and a homogeneous plane-parallel or spherically symmetric geometry. The energy balance requires particular attention, as two elements that are particularly difficult to model play an important role: line blanketing and convection. Inversion techniques are able to bypass the difficulties of a detailed description of the energy balance. Assuming that the atmosphere is in hydrostatic equilibrium and LTE, it is possible to constrain its structure from spectroscopic observations. Among the most serious approximations still implicit in the method is a static and homogeneous geometry. In this paper, we take advantage of a realistic three-dimensional radiative hydrodynamical simulation of the solar surface to check the systematic errors incurred by an inversion assuming a plane-parallel horizontally-homogeneous atmosphere. The thermal structure recovered resembles the spatial and time average of the three-dimensional atmosphere. Furthermore, the abundances retrieved are typically within 10% (0.04 dex) of the abundances used to construct the simulation. The application to a fairly complete data set from the solar spectrum provides further confidence in previous analyses of the solar composition. There is only a narrow range of one-dimensional thermal structures able to fit the absorption lines in the spectrum of the Sun. With our carefully selected data set, random errors are about a factor of 2 smaller than systematic errors. A small number of strong metal lines can provide very reliable results. We foresee no major difficulties in applying the technique to other similar stars, and obtaining similar accuracies, using spectra with λ/δλ ~ 5 × 104 and a signal-to-noise ratio as low as 30.

Model Photospheres for Late-Type Stars from the Inversion of High-Resolution Spectroscopic Observations: The Sun

An inversion technique has been developed to recover LTE, one-dimensional, model photospheres for late-type stars from very high resolution, high signal-to-noise ratio stellar line profiles. It is successfully applied to the Sun by using a set of clean Ti I, Ca I, Cr I, and Fe I normalized line profiles with accurate transition probabilities, taking advantage of the well-understood collisional enhancement of the wings of the Ca I line at 6162 A. Line and continuum center-to-limb variations, continuum flux, and wings of strong metal lines are synthesized by means of the model obtained and are compared with solar observations, as well as with predictions from other well-known theoretical and empirical solar models, showing the reliability of the inversion procedure. The prospects for and limitations of the application of this method to other late-type stars are discussed.

Model Photospheres for Late-Type Stars from the Inversion of High-Resolution Spectroscopic Observations: Groombridge 1830 and ϵ Eridani

An inversion technique to recover LTE one-dimensional model photospheres for late-type stars, which was previously applied to the Sun by Allende Prieto et al. in 1998, is now employed to reconstruct, semiempirically, the photospheres of cooler dwarfs: the metal-poor Groombridge 1830 and the active star of solar metallicity Eridani. The model atmospheres we find reproduce satisfactorily all the considered weak-to-moderate neutral lines of metals, satisfying in detail the excitation equilibrium of iron, the wings of strong lines, and the slope of the optical continuum. The retrieved models show a slightly steeper temperature gradient than flux-constant model atmospheres in the layers where log τ ≤ -0.5. We argue that these differences should reflect missing ingredients in the flux-constant models and point to granular-like inhomogeneities as the best candidate. The iron ionization equilibrium is well satisfied by the model for Gmb 1830, but not for Eri, for which a discrepancy of 0.2 dex between the logarithmic iron abundance derived from neutral and singly ionized lines may signal departures from LTE. The chemical abundances of calcium, titanium, chromium, and iron derived with the empirical models from neutral lines do not differ much from previous analyses based on flux-constant atmospheric structures.

Inversion of the radiative transfer equation for polarized light

Since the early 1970s, inversion techniques have become the most useful tool for inferring the magnetic, dynamic, and thermodynamic properties of the solar atmosphere. Inversions have been proposed in the literature with a sequential increase in model complexity: astrophysical inferences depend not only on measurements but also on the physics assumed to prevail both on the formation of the spectral line Stokes profiles and on their detection with the instrument. Such an intrinsic model dependence makes it necessary to formulate specific means that include the physics in a properly quantitative way. The core of this physics lies in the radiative transfer equation (RTE), where the properties of the atmosphere are assumed to be known while the unknowns are the four Stokes profiles. The solution of the (differential) RTE is known as the direct or forward problem. From an observational point of view, the problem is rather the opposite: the data are made up of the observed Stokes profiles and the unknowns are the solar physical quantities. Inverting the RTE is therefore mandatory. Indeed, the formal solution of this equation can be considered an integral equation. The solution of such an integral equation is called the inverse problem. Inversion techniques are automated codes aimed at solving the inverse problem. The foundations of inversion techniques are critically revisited with an emphasis on making explicit the many assumptions underlying each of them.Since the early 1970s, inversion techniques have become the most useful tool for inferring the magnetic, dynamic, and thermodynamic properties of the solar atmosphere. Inversions have been proposed in the literature with a sequential increase in model complexity: astrophysical inferences depend not only on measurements but also on the physics assumed to prevail both on the formation of the spectral line Stokes profiles and on their detection with the instrument. Such an intrinsic model dependence makes it necessary to formulate specific means that include the physics in a properly quantitative way. The core of this physics lies in the radiative transfer equation (RTE), where the properties of the atmosphere are assumed to be known while the unknowns are the four Stokes profiles. The solution of the (differential) RTE is known as the direct or forward problem. From an observational point of view, the problem is rather the opposite: the data are made up of the observed Stokes profiles and the unknowns are the solar physical quantities. Inverting the RTE is therefore mandatory. Indeed, the formal solution of this equation can be considered an integral equation. The solution of such an integral equation is called the inverse problem. Inversion techniques are automated codes aimed at solving the inverse problem. The foundations of inversion techniques are critically revisited with an emphasis on making explicit the many assumptions underlying each of them.

Lagrangian and Eulerian Stratifications of Acoustic Oscillations through the Solar Photosphere

We evaluate the stratification of acoustic oscillations in the solar photosphere in both the Lagrangian (comoving) frame of reference and the Eulerian (inertial) frame of reference, from a temporal sequence of model atmospheres in an optical depth scale obtained after a quasi-non-LTE inversion of the radiative transfer equation applied to spectral observations of the K I 7699 A line. Our results suggest that, to first order, the photosphere moves up and down as a whole with amplitudes ranging from ~8 km in deep layers (around 0 km) to ~19 km in the upper layers (around 640 km). In Lagrangian coordinates, we observe numerous short-lived, local temperature and velocity amplitude enhancements in medium-high layers, together with asymmetric waveforms in the oscillation of these two physical quantities. The Lagrangian temperature oscillation clearly shows two nodes associated with sharp phase jumps of about 180°, whereas the velocity amplitude shows the well-known increase with geometrical height, at nearly constant phase. In Eulerian coordinates, the perturbations are dominated by the coherent oscillation of the entire photosphere.

Persistent magnetic vortex flow at a supergranular vertex

Photospheric vortex flows are thought to play a key role in the evolution of magnetic fields. Recent studies show that these swirling motions are ubiquitous in the solar surface convection and occur in a wide range of temporal and spatial scales. Their interplay with magnetic fields is poorly characterized, however. We study the relation between a persistent photospheric vortex flow and the evolution of a network magnetic element at a supergranular vertex. We used long-duration sequences of continuum intensity images acquired with Hinode and the local correlation-tracking method to derive the horizontal photospheric flows. Supergranular cells are detected as large-scale divergence structures in the flow maps. At their vertices, and cospatial with network magnetic elements, the velocity flows converge on a central point. One of these converging flows is observed as a vortex during the whole 24 h time series. It consists of three consecutive vortices that appear nearly at the same location. At their core, a network magnetic element is also detected. Its evolution is strongly correlated to that of the vortices. The magnetic feature is concentrated and evacuated when it is caught by the vortices and is weakened and fragmented after the whirls disappear. This evolutionary behavior supports the picture presented previously, where a small flux tube becomes stable when it is surrounded by a vortex flow.

New Strategies on the Analysis of Spectral Lines

We analyze different methods to obtain information about gradients of physical quantities in stellar atmospheres. We show that, to this aim, response functions are more useful tools than contribution functions, although both of them may produce erroneous results when are evaluated in a model different from the real one. This apparent loop (the need of knowing a priori the quantities that we want to estimate) is solved by inversion methods. We classify these methods according to the solution they adopt to solve the main problems appearing in an inversion in practise.