The VAL database

Grid of models

We constructed a new grid of semi-empirical models of the solar photosphere and chromosphere to study the effects of various thermal stratifications on spectral lines. The grid of models was constructed keeping the number of free parameters as low as possible. We scaled the existing set of semi-empirical 1D hydrostatic models VAL A–F (Vernazza et al. (1981)), which describe the solar atmosphere from intranetwork to bright network features, by changing independently the temperature (T) and column-mass (m) stratifications. Adopting the column mass as an independent variable makes it possible to conserve the condition of hydrostatic equilibrium in the scaled models. The construction of the grid is explained in more details by Abbasvand et al. (2020a)

The used NLTE radiative-transfer code, written by Petr Heinzel, is based on the Multi-level Accelerated Lambda Iterations technique (MALI, Rybicki and Hummer 1991) with standard partial frequency redistribution (PRD). The hydrogen version of the code (with PRD in Lyman lines) computes the ionization structure and populations of hydrogen levels using a 5-level plus continuum atomic model. It re-computes the complete scaled atmospheric models and calculates synthetic profiles of the Lα, Lβ, Lγ, Hα, Hβ, Hγ, Pα, Pβ, Bα lines and Lyman continuum. As a next step, the calcium version of the MALI code (with PRD in the H and K lines) is used to get synthetic profiles of the Ca II H, K and IR triplet (849.7, 854.2 and 866.2 nm) lines and continuum. The Mg II version (with PRD in the k and h lines) is run to calculate synthetic profiles of the Mg II k, h and UV triplet (279.08, 279.79 and 279.80 nm) lines and continuum.

We used the models VAL A–F as the initial ones and changed their temperature and column-mass stratifications using two parameters: mp – column-mass parameter and tp – temperature parameter. For example, all VAL models can be well reproduced by scaling the VAL C model and, similarly, this can be done with any other initial VAL model. After changing T and m, the other model quantities are re-calculated using the NLTE radiative-transfer code. For each of the initial VAL models we calculate a grid of 2989 models using a combination of 49 values of mp and 61 values of tp. For each model in the grid, synthetic line profiles, contribution functions (CFs), and net radiative cooling rates (radiative losses) are calculated. In Figure 1, we show that the models VAL A–F can be reproduced by scaling the model VAL C.

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Figure 1: Temperature versus column mass plots of the VAL A–F models scaled from the model VAL C. Red and black lines show the scaling results and the original VAL models, respectively. The symbols denote sampling of the models

The synthetic profiles, models, radiative losses, and contribution functions are ordered by tp and mp:

tp = –0.03+k*0.001       k=0–60;    61 values in the range –0.03,...,0,...,0.03
mp = 0.2+j*0.1              j=0–48;    49 values in the range 0.2,...,1,...,5.

There is a file 'ordering.dat' in the "Programs" directory with columns: k, j, tp, mp, ID1, kk, jj, ID2 and ID3, which shows the details of ordering. ID1 (ID number = 49*k+j) is calculated by increasing a counter used in the model scaling. The last four columns are identical with k, j and ID1 to check for errors.
For example, the original initial VAL model is at the position k=30 (tp=0), j=8 (mp=1), i.e., 49*30+8 = 1478 of the range 0–2988. The synthetic profiles, radiative losses, and contribution functions are ordered in the same way.

For few scaled models, the MALI code does not converge, so that the synthetic profile, radiative losses, and contribution functions are not computed and contain NaNs (not-a-numbers).

Details concerning the model files, synthetic profiles, radiative losses, and contribution functions are described in 'model_files.txt', 'profile_files.txt', 'radlos_files.txt', and 'contrib_functions.txt' in the "Programs" directory, respectively.

Examples of temperature stratifications and radiative losses of quiet Sun and a plage

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Figure 2: Left: examples of quiet-Sun temperature stratifications with height (black) at positions along the top white line in the inset image of the Hα line-core intensity. Red-to-orange temperature curves correspond to positions from left to right along the bottom white line that crosses the plage. Right: total net radiative cooling rates vs. height in quiet Sun (black) and the plage (red–orange) at the same positions.


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Figure 3: Net radiative cooling rates vs. height in quiet Sun (black) and the plage (red–orange) for the main contributors: hydrogen (left), Ca II (middle) and Mg II (right) at the same positions as in figure 2.

Examples of contribution functions

Below we present plots of contribution functions of Hα, Hβ, Ca II H, and Mg II k lines calculated for the initial VAL A–F models. We have to note that the contribution-functions data for all models and lines take up a large volume of 26 GB.


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Figure 4: Contribution functions of the Hα and Hβ lines in the initial models VAL A-F together with corresponding synthetic line profiles (red lines). The colors change from light orange to black in ten logarithmic steps between the minimum and maximum.


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Figure 5: Same as in figure 4 for the Ca II K and Mg II k lines.


Database structure

The database consists of data files in ASCII format, stored in the directories "Models", "Profiles", "Radiative_Losses", and "Contrib_Functions". Due to the large volume of data, the latter directory contains compressed (.tar.gz) files with contribution functions of hydrogen, Ca II, and Mg II lines, which should be unpacked before use.
These data can be selected, read and plotted using the IDL routines "read_model_id[tm].pro", "read_profile_id[tm].pro", "readradlos_id[tm].pro", and "readcf_id[tm].pro" stored in the directory "Programs" together with the explanatory text files. The "id" and "tm" versions differ only in input parameters: in the version "id", the ID number is used, while in the version "tm" the model is identified using tp and mp. All program input and output parameters, including initial-model and spectral-line selection, are described in comments at the beginning of the IDL routines. The routines contain also relative paths to data files.

To use the database, copy the programs to your working directory and download the data to the subdirectories "Models", "Profiles", and "Radiative_Losses". The easiest way would be to download the compressed files "Models.tar.gz", "Profiles.tar.gz", and "Radiative_Losses.tar.gz" from the "Programs" directory and unpack them directly in your working directory.
To retrieve the contribution functions, unpack the compressed files "Contrib_Functions/*.tar.gz" into a new subdirectory "Contrib_Functions" that you have to create earlier in your working directory. The total volume of the data is 28 GB, of which 26 GB are taken up by contribution functions.


The links are as follows:

Programs
Models
Profiles
Radiative_Losses
Contrib_Functions



Comments and questions are welcome: michal.sobotka@asu.cas.cz
                   vahid.abbasvand.azar@asu.cas.cz

This work was supported by the Czech Science Foundation grant 18-08097J and by the project SOLARNET that has received funding from the European Union Horizon 2020 research and innovation programme under grant agreement No. 824135.