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An Open Source, Massively Parallel Code for Non-LTE Synthesis and Inversion of Spectral Lines and Zeeman-induced Stokes Profiles

H. Socas-Navarro, J. de la Cruz Rodriguez, A. Asensio Ramos, J. Trujillo Bueno, B. Ruiz Cobo

arXiv:1408.6101v2astro-ph.SR

TL;DR

Growing chromospheric observations and more complex simulations call for diagnostic tools that bridge the two. NICOLE provides non-LTE spectral-line synthesis and inversion, including Zeeman polarization, and has been tested in LTE and NLTE Stokes-profile inversions and large-scale profile synthesis.

  • Problem

    Chromospheric observations and increasingly complex simulations require diagnostic tools to bridge observations and models.

    Source: §1 · p. 1

  • Method

    NICOLE performs non-LTE spectral-line synthesis and inversion, including Zeeman polarization, and uses a parallel 1.5D scheme for large datasets.

    Source: §1 · p. 1

  • Results

    NICOLE has been tested in LTE and NLTE Stokes-profile inversions and in synthesizing large numbers of profiles in 3D atmospheric models.

    Source: §9 · p. 9

  • Takeaways & Limitations

    NICOLE is a publicly released code for massive radiative-transfer calculations, with use spanning solar or stellar models and observations.

    Source: §9 · p. 9

    Meaningful results require users to understand the underlying physics, numerical procedures, and data products; NICOLE should not be used as a black box.

    Source: §9 · p. 9

Abstract

from arXiv · show

With the advent of a new generation of solar telescopes and instrumentation, the interpretation of chromospheric observations (in particular, spectro-polarimetry) requires new, suitable diagnostic tools. This paper describes a new code, NICOLE, that has been designed for Stokes non-LTE radiative transfer, both for synthesis and inversion of spectral lines and Zeeman-induced polarization profiles, spanning a wide range of atmospheric heights, from the photosphere to the chromosphere. The code fosters a number of unique features and capabilities and has been built from scratch with a powerful parallelization scheme that makes it suitable for application on massive datasets using large supercomputers. The source code is being publicly released, with the idea of facilitating future branching by other groups to augment its capabilities.

1. Introduction

Growing chromospheric observations and increasingly complex solar simulations call for diagnostic tools that bridge the two. NICOLE provides non-LTE synthesis and inversion for spectral lines and Zeeman polarization, with parallel processing for large datasets and an openly released source code.

1. Introduction

  • NICOLE performs non-LTE spectral-line calculations for chromospheric lines and their Zeeman-regime polarization profiles.It supports both synthesis and inversion.Source: §1 · p. 1
  • Synthesis from simulation datacubes, including the instrumental profile, enables direct comparison with observations; inversion of observed spectra infers atmospheric parameters for comparison with simulations.Examples of inferred parameters include temperature, magnetic-field vector, and Doppler velocity.Source: §1 · p. 1
  • An MPI master-slave scheme and 1.5D treatment make NICOLE suitable for massive datasets and supercomputers with over a thousand processors.Each model column is treated as a horizontally infinite atmosphere, enabling almost ideal parallelization.Source: §1 · p. 1
  • NICOLE can provide flux-calibrated late-type stellar spectra, invert stellar spectra, and invert abundances for solar or stellar composition studies.The stellar-spectrum inversion follows work on the MISS code.Source: §1 · pp. 1–2
  • Released under the GPL, NICOLE may be copied, altered, redistributed, and branched to add or improve features.The authors encourage users to develop and distribute their own versions.Source: §1 · p. 2

2. Code description

NICOLE combines radiative-transfer and inversion approaches informed by earlier codes with several explicit approximations and implementation choices. Its scope includes flexible line calculations and a 1.5D treatment, while some physical effects are excluded or simplified.

2. Code description

  • NICOLE's inversion structure resembles SIR, its NLTE module resembles MULTI, and its iterative core implements a previously described method.The inversion module also follows the approach of Socas-Navarro et al. (1998, 2000).Source: §2 · p. 2
  • Statistical equilibrium assumes instantaneous balance among transitions, neglecting time-dependent ionization; complete redistribution is suitable for some lines but can differ near the cores of Ca II H and K.The text notes that statistical equilibrium may be less adequate in other situations.Source: §2 · p. 2
  • Zeeman-induced polarization is included, but scattering polarization and Hanle effects are not; NLTE populations are computed without magnetic fields.The text identifies Stokes I and V, or all Stokes profiles in sufficiently strong fields, as the more suitable applications.Source: §2 · p. 2
  • Hydrostatic equilibrium is used only in inversion mode to compute the density scale, while blends enter the final polarized formal solution but not the NLTE population calculation.The hydrostatic approximation mainly affects optical-to-geometrical depth conversion and, to some extent, background opacities.Source: §2 · p. 2
  • In 1.5D, columns are treated independently; this works well in LTE and for strong NLTE lines, whose core photons have short mean free paths.The approximation therefore confines population control for strong-line cores to immediate surroundings.Source: §2 · p. 2
  • Users can include hyperfine structure at a performance cost, place inversion nodes flexibly, and use Bezier formal solvers designed for greater robustness and stability.Flexible nodes can be concentrated where observations carry more information.Source: §2 · p. 2

3. The equation of state

NICOLE offers several equation-of-state routes, from a full molecular-equilibrium calculation to faster approximations and neural-network methods. Its molecular-hydrogen ANN avoids iteration, while pressure-retrieval ANNs trade accuracy for speed.

3. The equation of state

  • The equation of state relates plasma parameters; NICOLE can accept them as inputs or derive the remaining quantities from temperature and one supplied density or pressure variable.With hydrostatic equilibrium imposed, temperature stratification and an upper-boundary electron pressure are sufficient; this is the inversion-mode approach.Source: §3 · pp. 2–3

3.1. Full ICE solution

  • Full ICE solves atomic ionization and molecular chemical equilibrium using 273 molecules, but its 273-equation nonlinear system is demanding and can occasionally fail to converge.Faster, more stable alternatives are also implemented.Source: §3.1 · p. 3

3.2. Restricted ICE solution

  • Restricted ICE considers only H2 and H+2, making it faster and more stable than full ICE, although it can rarely fail and remains slower than the NICOLE option.Source: §3.2 · p. 3

3.3. The NICOLE method

  • The NICOLE method avoids iteration and is perfectly stable and faster; its ANN reaches a validation standard deviation of about 5×10^-3.Training is restricted to the region where molecular hydrogen is nontrivial, and the full ICE calculation supplies the training data.Source: §3.3 · p. 3

3.4. The Wittman procedure

  • The Wittmann method computes Pg directly from (T, Pe) using only H molecules, while retrieving Pe from (T, Pg) requires iteration and may fail to converge.It is a good approximation in most conditions, except very cool plasmas such as sunspot umbrae, where other molecules may matter.Source: §3.4 · p. 3

3.5. Artificial Neural Networks

  • The pressure-retrieval ANN has an error of about 15% in log Pe, but provides direct solutions in both directions and is fastest if that accuracy trade-off is acceptable.Spectral lines are described as less sensitive to density or gas pressure than to temperature.Source: §3.5 · p. 3, Figure 2 · p. 4

3.6. NICOLE EoS

  • The NICOLE EoS uses an ANN to determine molecular hydrogen and the Saha equation for other atomic populations; the reverse Pg-from-(T, Pe) calculation iterates.Source: §3.6 · p. 3

4. Background opacities

NICOLE supplies multiple packages for background opacity calculations, with separate treatments for visible/infrared and ultraviolet wavelengths. The ultraviolet packages address metal photoionization contributions that vary with wavelength and atmospheric conditions.

4. Background opacities

  • Background opacity arises from continuum absorption, and NICOLE treats ultraviolet separately from visible/infrared at a boundary of 400 nm.Source: §4 · p. 4

4.1. Visible and infrared opacities

  • NICOLE has three visible/infrared opacity packages that account for nearly the same physical processes but differ in details such as tabulated values and coding.Source: §4.1 · p. 4

4.1.1. The Wittmann package

  • The Wittmann package includes continuum absorption by H−, neutral H, He−, H−2, and H+2, photoionization of Ca, Na, and Mg, and several scattering processes.It includes Rayleigh scattering by neutral H, H2, and neutral He, plus Thomson scattering by electrons.Source: §4.1.1 · p. 4

4.1.2. The SOPA package

  • The SOPA package includes photoionization from selected Si, C, Mg, Al, and Fe levels, but is disabled by default and supported only through a special compile-time switch.It was not brought to NICOLE coding standards, to avoid compile problems or hardware incompatibilities.Source: §4.1.2 · p. 4

4.1.3. The NICOLE package

  • NICOLE’s independent visible/infrared package computes opacity from neutral H, H−, and Mg, with scattering by H, H2, and free electrons.Figures 3 and 4 compare the three packages under two sets of atmospheric conditions.Source: §4.1.3 · p. 4

4.2. Ultraviolet opacities

  • Ultraviolet opacity is complicated by photoionization from numerous metals, which can matter despite low abundances, and no single species dominates above 91 nm across conditions.NICOLE therefore includes two additional packages specifically for ultraviolet opacity, beyond SOPA.Source: §4.2 · p. 4

4.2.1. The Dragon-Mutschlecner package

  • The Dragon-Mutschlecner package uses tabulated photoionization cross-sections for neutral Mg, Al, Si, and Fe levels with analytical expressions that approximate many practical situations.Source: §4.2.1 · p. 5

4.2.2. The TIP-TOP package

  • Under photospheric conditions, TIP-TOP produces many metal photoionization peaks while the other two ultraviolet packages give smoother approximations; chromospheric opacity is mostly Thomson scattering except at the shortest wavelengths.NICOLE preloads cross-sections on a 0.1 nm wavelength grid and weights them by abundance, ionization fraction, and level excitation when calculating total opacity.Source: §4.2.2 · p. 5

5. Formal solutions

NICOLE solves the unpolarized NLTE problem in each vertical column using short-characteristics formal solutions, then computes Zeeman-induced Stokes profiles. Its Bezier-based approach controls overshooting, and the tested local operator converges in fewer iterations.

5. Formal solutions

  • Each vertical column is treated as a 1D plane-parallel NLTE problem with isotropic scattering and complete frequency redistribution.Population densities assume statistical equilibrium and unpolarized light; Zeeman sublevels are equally populated, excluding quantum interference.Source: §5 · pp. 5–6
  • Figures 3–4 compare Wittmann, NICOLE, and SOPA background opacities under photospheric (T=5600 K, Pe=10 dyn cm−2, Pg=8×105 dyn cm−2) and chromospheric (T=9000 K, Pe=0.05 dyn cm−2, Pg=0.15 dyn cm−2) conditions; all packages’ scattering curves agree within plot line thickness.Source: Figure 3 · p. 6, Figure 4 · p. 6

5.1. Formal solutions and the NLTE problem

  • The short-characteristics solution integrates the transfer equation over a depth interval after approximating the source function with a polynomial interpolant.The depth-grid subscripts denote upwind, central, and downwind points.Source: §5.1 · pp. 6–7
  • NICOLE offers parabolic interpolation with linear fallback for overshooting, or Bezier splines that control overshooting while retaining high-order accuracy.Parabolic interpolation is known to overshoot on irregular grids.Source: §5.1 · p. 7
  • The tested local operator Λ*=β̂+γ̂ achieves convergence in fewer iterations.The authors find this choice optimal for the second formal-solution formalism.Source: §5.1 · p. 7
  • For Method 2, the control point is constrained to prevent source-function overshooting, with a downwind check improving stability and enforcing monotonic approach to the central point.The downwind-interval refinement is attributed to Štěpán & Trujillo Bueno (2013).Source: §5.1 · p. 7
  • Method 1 can flip-flop when switching between parabolic and linear solutions, typically requiring more iterations than the Bezier alternative.The comparison is at a similar convergence threshold.Source: §5.1 · p. 7

5.2. Formal solution of the polarized transfer equations

  • After calculating populations, NICOLE computes the emerging Stokes vector for Zeeman-induced polarization using several available polarized-transfer solvers.Options include quadratic and cubic DELO-Bezier, DELO-Linear, DELO-Parabolic, and Hermitian methods.Source: §5.2 · p. 7

6. Hyperfine structure

Hyperfine structure splits fine-structure levels into F levels, which can mix under magnetic fields when Zeeman splittings approach their separation. NICOLE represents the resulting magnetic sublevels by diagonalizing a block-diagonal Hamiltonian and derives allowed transition strengths from dipole matrix elements.

6. Hyperfine structure

  • When Zeeman splittings approach the separation between hyperfine F levels, intermediate Paschen–Back effects can strongly perturb Zeeman patterns and emergent Stokes profiles.The hyperfine splitting is usually much smaller than the fine-structure splitting.Source: §6 · p. 7
  • The hyperfine energy splitting of the F levels relative to the original J level (the fine-structure level without hyperfine structure) is given, with very good approximation, by Casimir (1963); K = F(F + 1) − I(I + 1) − J(J + 1).Source: §6 · p. 8
  • When fine-structure separations greatly exceed typical Zeeman splittings, the Hamiltonian can focus on hyperfine–magnetic coupling and is block-diagonal.The magnetic term uses the Bohr magneton μ0, field strength B, and level Landé factor gJ.Source: §6 · p. 8
  • The magnetic sublevel quantum number MF remains good, but the Hamiltonian mixes levels with different F; numerical diagonalization yields the MF sublevel energies.Allowed transitions have ΔMF = 0, ±1, and component strengths follow squared electric-dipole matrix elements.Source: §6 · p. 8

7. Abundance inversions

NICOLE can invert element abundances as nodes, but simultaneous abundance and atmosphere inversion is meaningful only when multiple-element lines constrain both. A simulated O, Ni, and Sc test recovered reference abundances in a subset of trials, with reported uncertainties limited to inversion error under a prescribed atmosphere.

7. Abundance inversions

  • Simultaneous abundance and atmospheric-parameter inversion is meaningful only when lines from multiple elements can unambiguously constrain both.The authors advise determining the atmospheric model independently, or approximating it well, before abundance inversion.Source: §7 · p. 8
  • Only 8/30 simulated inversions converged to the correct O, Ni, and Sc abundances, with successful fits reaching the 5×10−4 noise level.The fit shown is representative of those solutions; the tests used reference abundances 8.83, 6.25, and 3.17, respectively.Source: Figure 8 · p. 8, §7 · p. 8
  • The reported abundance uncertainties represent inversion error alone because the simulated test prescribes and knows the atmospheric model.Uncertainty in the atmospheric model would add systematic errors that are likely much larger.Source: §7 · p. 8

8. Parallelization

NICOLE distributes spatial-pixel calculations through a master–slave MPI scheme for large synthesis and inversion workloads. In tests on a 3D MHD snapshot, CPU time followed ideal parallel scaling without saturation through 200 processors, provided computation dominates input reading.

8. Parallelization

  • Each slave computes for a spatial pixel while the master handles input, dispatch, result collection, and output, avoiding interprocess disk-access conflicts.The scheme targets large spectral or spectro-polarimetric scans and simulation datacubes.Source: §8 · p. 8
  • CPU time followed ideal parallel scaling with no saturation through 200 processors in the Ca II 8542 Å tests.The plotted comparison is CPU time versus inverse processor count against the ideal-parallelization line.Source: Figure 9 · p. 9, §8 · p. 9
  • The benchmark computed intensity and polarization profiles for the 8542 Å line using a six-level Ca II atom on each simulation column.It used a BIFROST 3D MHD snapshot and a subset of 204 cluster cores.Source: §8 · p. 9
  • Ideal scaling holds when computation time is much longer than input-reading time; the MPI setup generally uses one master process alongside N worker threads.Compilation and execution require a working MPI installation.Source: §8 · p. 9

9. Conclusions

NICOLE is presented as a public, documented code for massive radiative-transfer calculations across LTE and NLTE applications, including profile inversions and model conversions. Prior publications demonstrate LTE and NLTE Stokes inversion and large-scale synthesis, while the authors caution that meaningful use requires understanding the underlying physics and numerical procedures.

9. Conclusions

  • NICOLE is a public, documented, user-friendly code for massive radiative-transfer calculations, with permission to modify and redistribute it under the GNU public license.It can be applied to solar or stellar models and observations, including LTE or NLTE calculations, depth conversions, and profile inversions.Source: §9 · p. 9
  • The authors expect NICOLE-like codes to matter as chromospheric-magnetometry instruments produce large NLTE datasets and realistic 3D simulations become available.Polarized synthesis in simulation datacubes is described as necessary for detailed comparison with observations.Source: §9 · p. 9
  • Published tests demonstrate NICOLE in LTE and NLTE Stokes-profile inversion and in synthesis of large numbers of profiles in 3D atmospheric models.The cited examples include Socas-Navarro (2011), de la Cruz Rodríguez et al. (2012, 2013b), Leenaarts et al. (2014), and Socas-Navarro (2014).Source: §9 · p. 9
  • Meaningful results require understanding the physics, numerical procedures, and data products; NICOLE should not be treated as a black box.Source: §9 · p. 9
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