Opacity for realistic 3D MHD simulations of cool stellar atmospheres

The first paper of Andrea Perdomo Garcia is just submitted for publication in Astronomy & Astrophysics, and out on arxiv.org/abs/2306.03744. The paper is all about computing the opacities for realistic modelling of cool stellar atmospheres. It is divided in three unities. First (Section 3) it describes the computation of detailed monochromatic opacity including millions of atomic and molecular spectral lines and millions of wavelength points. For this the code SYNSPEC (Hubeny and Lanz, 2011, 2017a, b) is used. Then (Section 4) the monochromatic opacities are used to construct opacity distribution function which reduces the number of wavelength points from millions to thousands. The results are compared in detail with ones produced by Kurucz. Some striking similarities and some warning differences are found. Finally (Section 5), the opacity distribution function to construct opacity bins. This method, originally proposed by Nordlund (1982) is the key ingredient for realistically simulating stellar atmospheres in 3D as it reduced the problem further, from thousands of wavelength points to only a few. However, the method depends on a choice of some free parameters. In our paper the possible choices are carefully analyzed and some interesting conclusions are offered. 

In Sect.3 there are two figures (Figs.2 and 3) that I find very useful and illustrative. The monochromatic opacity (Fig.2) and the radiative heating rate (Fig.3) are shown as 2D functions of wavelength (X-axis) and height in the atmosphere (Y-axis) for four different cool stars (all with solar metalicity). Optical depths in the continuum and continuum+lines are overplotted.

(Andrea is the final year PhD student at Instituto de Astrofisica de Canarias and Univeridad de La Laguna, supervised by Manolo Collados Vera and myself. Stay tuned, more cool stuff is coming out from her research this year.)

Robert Jelle Rutten (1942 - 2022)

So long, my teacher and friend. You will be hugely missed.

Three-dimensional simulations of solar magneto-convection including effects of partial ionization

Astronomy & Astrophysics Volume 618 (October 2018) is just out with a figure from our paper on the cover!

The paper (Khomenko, Vitas, Collados & de Vicente 2018: A&A, ADS) describes the effects of the partial ionization on the structure, dynamics and energy balance of the low chromosphere.

How to display magnetic field lines in IDL?

It is a common problem in visualization of magnetic fields. If we assume that the potential $A$ of the magnetic field is knows, the field lines are, by definition, iso-$A$ curves. The quickest way to display them is by using the CONTOUR procedure. If the potential field is given as a 2D variable potential, then:

IDL> CONTOUR, potential, levels = levels, /xs, /ys

gives:




However, the information here is not complete without showing the actual direction of the field along the lines. It is easy to do it in IDL:

IDL> CONTOUR, potential, levels = levels, /xs, /ys
IDL> CONTOUR, potential, levels = levels, /xs, /ys, path_xy = c
IDL> FOR i = 1, N_ELEMENTS(c)/2-1, 50 DO $     ARROW, c[0, i-1], c[1, i-1], c[0, i], c[1, i], /norm, /solid, hsize = 5         


produces:

It is much better now, but the arrow heads from different field lines make it crowded. If we are interested in individual field lines, we can add color to this:

Deep-learning about horizontal velocities at the solar surface

The velocity fields are of great importance for understanding dynamics and structure of the solar atmosphere. The line of sight velocities are coded in the wavelength shifts of the spectral lines, thanks to the Doppler effect, and relatively easy to measure. On the other hand, the orthogonal ("horizontal") components of the velocity vector are impossible to measure directly.

The most popular method for estimating the horizontal velocities is so-called local correlation tracking (LCT, November & Simon, 1988). It is based on comparing successive images of the solar surface in the continuum light and transforming their differences into information about the horizontal fields. However, the LCT algorithm suffers from several limitations.

In a paper by Andres Asensio Ramos and Iker S. Requerey (with a small contribution from my side) accepted by A&A and published on Arxiv some weeks ago (2017arXiv170305128A) this problem is tackled by the deep-learning approach. A deep fully convolutional neural network is trained on synthetic observations from 3D MHD simulations of the solar photosphere and then applied to the real observation with the IMaX instrument on board the SUNRISE balloon (Martinez Pillet et al, 2011; Solanki, 2010). The method is validated using simulation snapshots of the quiet sun produced with the MANCHA code that I have been developing in the last couple of years.

First observation of linear polarization in the forbidden [OI] 630.03 nm line

In a new paper (de Wijn, Socas-Navarro & Vitas, 2017, ApJ, 836, 29D) we present the first results of our observations of a sunspot and an active region using the SP/SOT instrument on board the Hinode satellite. The novelty in our observation is a trick that we used to double the standard wavelength range observed by the instrument. Thanks to that, we were able to see the sun not only in the two iron lines at 630.2 nm, but also in four other lines. One of those is particularly interesting: the forbidden ground-based line of neutral oxygen ([OI] 630.03 nm). It is one of only few oxygen lines in the solar spectrum and probably the best diagnostics of the solar oxygen abundance. For the first time ever we observed the linear polarization in this line! As an M2 (magnetic dipole) transition, it is predicted by the theory (Landi degl'Innocenti and Landi, 2004, Section 6.8) that this line produces the linear polarization signal with the opposite sign to the lines produced by E2 transitions. It is also the first time that linear polarization in M2 and nearby E2 lines is measured simultaneously, so that the flip in sign is obvious (see the left-most spectral line in the red circle in the Figure; in linear polarization it has "W" shape, while all other lines in the wavelength range have "M" shapes). This result may bring new light to the ongoing debate on the solar oxygen crisis.

  

More details of this unique observation will appear soon in a follow-up publication.

1D Solar Atmosphere Models in IDL: Penumbra by Ding & Fang (1989)

Plane-parallel atmosphere in hydrostatic equilibrium published by Ding & Fang (1989, "A semi-empirical model of sunspots penumbra", 1989A&A...225..204D). Statistical equilibrium for hydrogen model-atom with 12 levels plus continuum. The model is produced by fitting observations of penumbra in  2 lines of H and 5 lines of Ca. The observations were carried out on McMath telescope at Kitt Peak National Observatory. The observed sunspot was small, rounded and close to the disk center. The field strength in the umbra was around 1.25 kG and 560 G in the penumbra.

It is interesting to note their Fig.2 (see it below). In the deep photosphere, the temperature in this model is similar to the temperature in the model of Yun et al. (1981). However, between the optical depths -3 and -4 it becomes close to the VALC model (Vernazza et al, 1981).

Equation of state: Vardya - Mihalas - Wittmann

These are my notes on equation of state derived initially by Vardya (1965), described by Mihalas (1967) and popularized by Wittmann (1974). It is widely used (or at least present as an option) in spectral synthesis codes like SIR or NICOLE. It is also prepared for the MANCHA code with several modifications and additionally computed quantities. However, the equation is derived in this particular form to be solvable on computing resources half a century ago. From today's perspective, this formulation is rather obsolete. While the results of the VMW EOS are still largely reliable, various tricks introduced to control numerical stability limit its usability to rather restricted range of the pressure and temperature.

Here I derive a simple equation of state for the solar atmosphere following the classical work of Vardya (1965), Mihalas (1967) and Wittmann (1974). The EOS is based on the Saha ionisation equilibrium and the instanteneous chemical equilibrium for the molecules. The main ingredient is hydrogen. It's included as atomic hydrogen (H), negative hydrogen ion (H-), positive hydrogen ion (H+), and as H2 and H2+ molecules. For all other atoms the neutral and the first two ionisation stages are included.

The equations were first published by Vardya (1967). Mihalas (1967) gave a simple numerical algorithm for an efficient solution of the system. Wittmann (1974) copied the equations and add a corrective factor that provides numerical stability at high temperature.

The derivation here follows Mihalas. However, in the original derivation there is a couple of inconsistencies that obscure the procedure. Here I write the equations in a correct and consistent way.

Definitions

Let's first define the pressures:
$p_{\mathrm{H}}$ - partial pressure of the neutral H atoms;
$p_{\mathrm{H^+}}$ - partial pressure of the positive H ions (protons);

Kurucz' Atlas in GNU Linux

I have just found about great effort made by Sbordone, Bonifacio & Castelli to make the Atlas code of Bob Kurucz available at GNU Linux.

There is a webpage: http://atmos.obspm.fr/ providing the code and the documentation.

1D Solar Models in IDL: Spruit's Convection Model

The semi-empirical models of the solar atmosphere rely on the observed intensities and, therefore, they cannot say much about the invisible convection zone below the surface. Spruit (1974SoPh...34..277S) constructed a 1D model of the solar convection zone using the mixing-length theory with 4 free parameters. The model is constructed so that it matches the HSRA model (Gingerich et al, 1971SoPh...18..347G) of the solar atmosphere. The model of Spruit is sometimes used to initiate the convection simulations with 3D numerical codes.

Fig 1. The HSRA model atmosphere (dashed) and Spruit's model of convective zone (solid). This is reproduced after Fig.3 of Spruit's paper.

1D Solar Atmosphere Models in IDL: Gingerich et al (HSRA)

The Harvard-Smithsonian Reference Atmosphere (HSRA) by Gingerich et al (1971, 1971SoPh...18..347G) is another widely used semi-empirical model of the idealized plane-parallel solar atmosphere in hydrostatic equilibrium. This model also includes the chromosphere where the hydrogen ionization is solved using the statistical equilibrium equations. The model is still often used as the reference solar atmosphere in 1D and its number of citations steadily grows (> 820 so far). The paper is very clearly written and it's a very recommendable reading especially if you use this model. Beside the model itself, there is several tables with computed intensities, brightness temperature, optical depths at different wavelengths, etc.

1D Solar Atmosphere Models in IDL: Maltby et al (MACKKL)

Here I add files containing the one-dimensional models of the solar atmosphere from the famous paper of Maltby et al (1986, 1986ApJ...306..284M). There is a quiet sun model and three models of the sunspot atmosphere (L, M, E corresponding to the late, mid and early cycle of the solar activity). For the details of these models please check the paper.

The data in the files comes directly from Tables 7, 8, 9 and 11 of Maltby et al. The variables stored in the original models are:

• geometrical height scale, 
• column mass scale, 
• optical depth at 5000 A, 
• temperature, 
• turbulent velocity, 
• number density of hydrogen, 
• electron density, 
• total pressure, 
• ratio of gas pressure to total pressure, 
• density.

Fig. The temperature stratification of the three sunspot models (remake of Fig.8 of Maltby et al)