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How to Access Physical Quantities

In order to compute the synthetic spectrum, TARDIS must either be told or must calculate many physical properties of the model. To understand and test the code it can be important to look at these values. One easy way to do this is to run TARDIS in an interactive mode and then inspect the model properties.

Running an interactive Python session

# Download the atomic data
from tardis.io.atom_data import download_atom_data
download_atom_data('kurucz_cd23_chianti_H_He_latest')

# Download the example configuration file
!curl -O https://raw.githubusercontent.com/tardis-sn/tardis/master/docs/tardis_example.yml

Atomic Data kurucz_cd23_chianti_H_He_latest already exists in /home/runner/Downloads/tardis-data/kurucz_cd23_chianti_H_He_latest.h5. Will not download - override with force_download=True.

  % Total    % Received % Xferd  Average Speed   Time    Time     Time  Current
                                 Dload  Upload   Total   Spent    Left  Speed
100   987  100   987    0     0  11919      0 --:--:-- --:--:-- --:--:-- 12036

from tardis import run_tardis

simulation = run_tardis('tardis_example.yml')

Auto-detected Sphinx build environment

Auto-detected Sphinx build environment

Initializing tabulator and plotly panel extensions for widgets to work

Embedding the final state for Jupyter environments

If all goes well, the simulation should run as usual. Afterwards, the information from the simulation will all exist in Simulation and can be examined. Some examples for useful/interesting quantities are given below (but much more information is available: contact us via tardis-sn-users if you need further help).

Examples of finding physical quantities

For example, two of our important quantities are the parameters of the radiation field model, \(T_{\rm rad}\) and \(W\). These exist as numpy.ndarray

Thus simulation.plasma.t_rad will give you a list of the \(T_{\rm rad}\)-values for the model zones in cgs units.

simulation.plasma.t_rad

array([11069.39398096, 11217.36671066, 11332.60184044, 11426.22631754,
       11491.48972523, 11516.91377885, 11462.16807103, 11333.41619011,
       11369.28853392, 11281.15653031, 11196.95437013, 11081.40565856,
       11005.00279487, 10899.22884746, 10800.99123096, 10723.69631975,
       10615.8274979 , 10529.75048763, 10441.74294229, 10354.82768508])

Similarly, the \(W\)-values can be accessed using simulation.plasma.w

simulation.plasma.w

array([0.46662935, 0.35416247, 0.28001569, 0.2281332 , 0.19311512,
       0.16757667, 0.15009942, 0.13811674, 0.12336904, 0.11380625,
       0.10634533, 0.10168536, 0.09617056, 0.09178887, 0.08740182,
       0.08316363, 0.0804724 , 0.07785579, 0.07505503, 0.07241463])

Several important quantities that were setup when the model was defined by the configuration file are located in the model section of the simulation. For example, the inner and outer velocity boundaries of the zones in the model is given by simulation.simulation_state.v_inner.cgs and simulation.simulation_state.v_outer.cgs respectively. These exist as Astropy Quantities.

simulation.simulation_state.v_inner.cgs

$[1.1 \times 10^{9},~1.145 \times 10^{9},~1.19 \times 10^{9},~1.235 \times 10^{9},~1.28 \times 10^{9},~1.325 \times 10^{9},~1.37 \times 10^{9},~1.415 \times 10^{9},~1.46 \times 10^{9},~1.505 \times 10^{9},~1.55 \times 10^{9},~1.595 \times 10^{9},~1.64 \times 10^{9},~1.685 \times 10^{9},~1.73 \times 10^{9},~1.775 \times 10^{9},~1.82 \times 10^{9},~1.865 \times 10^{9},~1.91 \times 10^{9},~1.955 \times 10^{9}] \; \mathrm{\frac{cm}{s}}$

simulation.simulation_state.v_outer.cgs

$[1.145 \times 10^{9},~1.19 \times 10^{9},~1.235 \times 10^{9},~1.28 \times 10^{9},~1.325 \times 10^{9},~1.37 \times 10^{9},~1.415 \times 10^{9},~1.46 \times 10^{9},~1.505 \times 10^{9},~1.55 \times 10^{9},~1.595 \times 10^{9},~1.64 \times 10^{9},~1.685 \times 10^{9},~1.73 \times 10^{9},~1.775 \times 10^{9},~1.82 \times 10^{9},~1.865 \times 10^{9},~1.91 \times 10^{9},~1.955 \times 10^{9},~2 \times 10^{9}] \; \mathrm{\frac{cm}{s}}$

The average density in the zones is given by simulation.simulation_state.density.cgs. These also exist as Astropy Quantities.

simulation.simulation_state.density.cgs

$[7.5428036 \times 10^{-14},~5.728475 \times 10^{-14},~4.3960742 \times 10^{-14},~3.4062874 \times 10^{-14},~2.6631346 \times 10^{-14},~2.0995965 \times 10^{-14},~1.6682872 \times 10^{-14},~1.3353105 \times 10^{-14},~1.0761538 \times 10^{-14},~8.7290848 \times 10^{-15},~7.1236516 \times 10^{-15},~5.8469209 \times 10^{-15},~4.8250928 \times 10^{-15},~4.0023242 \times 10^{-15},~3.3360386 \times 10^{-15},~2.7935404 \times 10^{-15},~2.3495504 \times 10^{-15},~1.9843968 \times 10^{-15},~1.6826769 \times 10^{-15},~1.4322598 \times 10^{-15}] \; \mathrm{\frac{g}{cm^{3}}}$

Many other interesting quantities are stored in the plasma. For example the calculated ion populations and level populations is given by simulation.plasma.ion_number_density and simulation.plasma.level_number_density respectively.

simulation.plasma.ion_number_density

		0	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19
atomic_number	ion_number
8	0	9.816659e+02	4.604150e+02	2.316153e+02	1.226249e+02	6.876536e+01	4.137050e+01	2.811893e+01	2.144973e+01	1.328381e+01	9.865431e+00	7.388643e+00	5.861030e+00	4.455958e+00	3.577868e+00	2.876588e+00	2.266979e+00	1.892041e+00	1.543745e+00	1.276175e+00	1.063504e+00
	1	5.392045e+08	4.093079e+08	3.138516e+08	2.428781e+08	1.895662e+08	1.491939e+08	1.185039e+08	9.496466e+07	7.636813e+07	6.198194e+07	5.060933e+07	4.158729e+07	3.433233e+07	2.850228e+07	2.377296e+07	1.991404e+07	1.675988e+07	1.416038e+07	1.201152e+07	1.022703e+07
	2	2.227084e+05	3.669784e+05	5.361457e+05	7.245227e+05	8.893827e+05	9.599717e+05	8.046942e+05	5.308615e+05	5.936509e+05	4.446343e+05	3.358960e+05	2.273113e+05	1.746121e+05	1.205867e+05	8.492438e+04	6.413167e+04	4.307064e+04	3.115373e+04	2.224782e+04	1.586440e+04
	3	2.647301e-08	1.246274e-07	4.275557e-07	1.192008e-06	2.580870e-06	3.993551e-06	3.210557e-06	1.387352e-06	2.300471e-06	1.357052e-06	8.133745e-07	3.657353e-07	2.262683e-07	1.060832e-07	5.204906e-08	3.038471e-08	1.309125e-08	6.789233e-09	3.394767e-09	1.684833e-09
	4	0.000000e+00	0.000000e+00	0.000000e+00	0.000000e+00	0.000000e+00	0.000000e+00	0.000000e+00	0.000000e+00	0.000000e+00	0.000000e+00	0.000000e+00	0.000000e+00	0.000000e+00	0.000000e+00	0.000000e+00	0.000000e+00	0.000000e+00	0.000000e+00	0.000000e+00	0.000000e+00
...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...
20	16	0.000000e+00	0.000000e+00	0.000000e+00	0.000000e+00	0.000000e+00	0.000000e+00	0.000000e+00	0.000000e+00	0.000000e+00	0.000000e+00	0.000000e+00	0.000000e+00	0.000000e+00	0.000000e+00	0.000000e+00	0.000000e+00	0.000000e+00	0.000000e+00	0.000000e+00	0.000000e+00
	17	0.000000e+00	0.000000e+00	0.000000e+00	0.000000e+00	0.000000e+00	0.000000e+00	0.000000e+00	0.000000e+00	0.000000e+00	0.000000e+00	0.000000e+00	0.000000e+00	0.000000e+00	0.000000e+00	0.000000e+00	0.000000e+00	0.000000e+00	0.000000e+00	0.000000e+00	0.000000e+00
	18	0.000000e+00	0.000000e+00	0.000000e+00	0.000000e+00	0.000000e+00	0.000000e+00	0.000000e+00	0.000000e+00	0.000000e+00	0.000000e+00	0.000000e+00	0.000000e+00	0.000000e+00	0.000000e+00	0.000000e+00	0.000000e+00	0.000000e+00	0.000000e+00	0.000000e+00	0.000000e+00
	19	0.000000e+00	0.000000e+00	0.000000e+00	0.000000e+00	0.000000e+00	0.000000e+00	0.000000e+00	0.000000e+00	0.000000e+00	0.000000e+00	0.000000e+00	0.000000e+00	0.000000e+00	0.000000e+00	0.000000e+00	0.000000e+00	0.000000e+00	0.000000e+00	0.000000e+00	0.000000e+00
	20	0.000000e+00	0.000000e+00	0.000000e+00	0.000000e+00	0.000000e+00	0.000000e+00	0.000000e+00	0.000000e+00	0.000000e+00	0.000000e+00	0.000000e+00	0.000000e+00	0.000000e+00	0.000000e+00	0.000000e+00	0.000000e+00	0.000000e+00	0.000000e+00	0.000000e+00	0.000000e+00

94 rows × 20 columns

simulation.plasma.level_number_density

			0	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19
atomic_number	ion_number	level_number
8	0	0	513.445731	240.317130	120.699354	63.818960	35.755733	21.503678	14.626899	11.177758	6.918919	5.144761	3.857656	3.065011	2.332715	1.875793	1.510194	1.191434	0.995876	0.813525	0.673345	0.561813
		1	301.794933	141.292782	70.978993	37.535838	21.032516	12.649615	8.603512	6.573251	4.069034	3.025174	2.267998	1.801603	1.370966	1.102206	0.887213	0.699841	0.584845	0.477673	0.395292	0.329756
		2	99.703863	46.684336	23.454164	12.404158	6.950783	4.180498	2.843209	2.172054	1.344602	0.999593	0.749354	0.595201	0.452902	0.364085	0.293043	0.231140	0.193141	0.157736	0.130522	0.108874
		3	65.279128	31.396434	16.098614	8.653707	4.903727	2.962089	1.995840	1.491081	0.928849	0.679922	0.502120	0.390556	0.293022	0.230930	0.182412	0.141734	0.115935	0.093056	0.075627	0.061953
		4	1.270507	0.630131	0.330744	0.181135	0.103967	0.063113	0.042073	0.030639	0.019224	0.013825	0.010035	0.007620	0.005626	0.004334	0.003351	0.002559	0.002043	0.001607	0.001280	0.001027
...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...
20	16	0	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000
	17	0	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000
	18	0	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000
	19	0	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000
	20	0	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000

4435 rows × 20 columns

These are stored as Pandas DataFrames. An index can be supplied to obtain the population in a particular zone. E.g., for the ion populations of the innermost zone (index = 0), we will use simulation.plasma.ion_number_density[0]

simulation.plasma.ion_number_density[0]

atomic_number  ion_number
8              0             9.816659e+02
               1             5.392045e+08
               2             2.227084e+05
               3             2.647301e-08
               4             0.000000e+00
                                 ...
20             16            0.000000e+00
               17            0.000000e+00
               18            0.000000e+00
               19            0.000000e+00
               20            0.000000e+00
Name: 0, Length: 94, dtype: float64

Ion populations for a particular ionization stage of a particular element can be accessed by specifying an appropriate tuple (𝑍,𝐶), which identifies the element (via atomic number 𝑍 ) and the charge (via the ion charge 𝐶 ). Thus, simulation.plasma.ion_number_density.loc[14,1] will identify the ion popuations for Si II (𝑍=14,𝐶=1) in all the zones.

simulation.plasma.ion_number_density.loc[14,1]

0     70825.681873
1     31990.969562
2     15613.549042
3      8050.728970
4      4419.989679
5      2626.941022
6      1804.879104
7      1423.919182
8       867.376865
9       658.766974
10      504.180713
11      412.993680
12      320.355705
13      264.989338
14      219.028071
15      176.358495
16      151.869698
17      127.029477
18      107.751281
19       92.134805
Name: (14, 1), dtype: float64

The above examples can be combined to obtain e.g. the Si II population in the innermost zone can be obtained by simulation.plasma.ion_number_density[0].loc[14,1]

simulation.plasma.ion_number_density[0].loc[14,1]

np.float64(70825.68187285573)

The level populations are stored (and can be accessed) in a similar way - a third label can be used to pick out a particular atomic level. E.g., to pull out the population of the ground state (index 0) of Si II we can use simulation.plasma.level_number_density.loc[14,1,0]

simulation.plasma.level_number_density.loc[14,1,0]

0     23978.146383
1     10819.001844
2      5275.816671
3      2718.409555
4      1491.703522
5       886.391767
6       609.267293
7       481.139206
8       293.005484
9       222.682912
10      170.534002
11      139.807671
12      108.506435
13       89.819711
14       74.290737
15       59.849006
16       51.575235
17       43.163557
18       36.633579
19       31.341378
Name: (14, 1, 0), dtype: float64

Notes

• If you prefer to work in SI units, all the Astropy Quantities may instead by accessed with “xxx.si”.

• Information that is not stored as Astropy Quantities (e.g. the ion and level populations used in the example above) are usually stored in cgs units (i.e. cm−3 for the populations).