SPECTRUM: Synthetic Spectral Calculations for Global Space Plasma Modeling

J. Szente , E. Landi, W. B. Manchester, IV, G. Toth , B. van der Holst , and T. I. GombosiClimate and Space Sciences and Engineering Department, University of Michigan, Ann Arbor, MI 48109, USA; judithsz@umich.edu

Received 2019 January 8; revised 2019 April 3; accepted 2019 April 4; published 2019 May 1

Abstract

High-resolution spectroscopy is the most accurate tool for measuring the properties of the solar corona. However,interpreting measured line intensities and line profiles emitted by the optically thin solar corona is complicated byline-of-sight (LOS) integration, which leads to measuring weighted averages of the plasma properties along theLOS. LOS integration effects can be removed by combining CHIANTI spectral emissivities with a 3D globalmodel of the solar corona to calculate the contribution of all structures along the LOS to the measured intensities.In this paper, we describe SPECTRUM, a postprocessing tool that can calculate the emission from the opticallythin solar corona by combining 3D magnetohydrodynamic (MHD) space plasma simulation results with theCHIANTI database. Doppler-shifted, nonthermal line broadening due to low-frequency Alfvén waves andanisotropic proton and isotropic electron temperatures can be individually taken into account during calculations.Synthetic spectral calculations can then be used for model validation, for interpretation of solar observations, andfor forward modeling purposes. SPECTRUM is implemented within the Space Weather Modeling Framework(SWMF) and is therefore publicly available. In this paper, we describe the SPECTRUM module and show itsapplications by comparing synthetic spectra using simulation data by the 3D MHD Alfvén Wave Solar Model withobservations done by the Hinode/Extreme-ultraviolet Imaging Spectrometer during Carrington rotations 2063and 2082.

Key words: line: profiles – magnetohydrodynamics (MHD) – Sun: corona – techniques: spectroscopic

1. Introduction

The outer solar atmosphere (corona) is of critical importancefor the relationship of the Sun with its own planetary system. Infact, it is the place where the solar wind is accelerated and themost energetic electromagnetic radiation is emitted, both due toits multimillion degree temperature whose origin we still do notunderstand. Furthermore, all the major solar activity eventsdriving space weather—coronal mass ejections (CMEs), flares,high-speed streams, and solar energetic particles—take place inthe solar corona.

The most physically revealing vehicle to study the solarcorona is high-resolution spectroscopy. Measuring the inten-sities and the profiles of the spectral lines emitted by coronalplasmas at all temperatures provides a wealth of information onthe emitting plasma temperature and density structure, on itselemental and charge-state composition, on the bulk motions aswell as on the subresolution dynamics taking place in it (e.g.,Phillips et al. 2008). An enormous amount of literature hasflourished that utilizes X-ray, extreme ultraviolet (EUV), andUV radiation to measure the properties of solar plasmas duringand outside quiescence (e.g., Del Zanna & Mason 2018 andreferences therein). More recently, interest has been renewedon coronal emission in the visible wavelength range thanks tothe eclipse observations of Shadia Habbal and co-workers (e.g.,Ding & Habbal 2017; Boe et al. 2018, and references therein)and the advent of the Daniel K. Inouye Solar Telescope(DKIST) observatory, leading to renewed interest in visibleradiation diagnostic techniques (Landi et al. 2016).

However, the diagnostic use of the emission of the solarcorona is affected by a fundamental limitation. In fact, the solarcorona is optically thin, so the radiation that we measure is thesum of the radiation emitted along the entire line of sight(LOS). This causes two problems: first, any measurement of aphysical quantity made using line intensities or line profiles is a

weighted average of the values of such quantity along the LOS;second, it is very difficult to understand where, along the LOS,any structure that can be seen is located.There are three possible solutions to this problem. From the

observational point of view, simultaneous observations frommultiple view points allow the reconstruction of the 3Ddistribution of coronal plasmas (Aschwanden 2009). However,with the only exception of the Solar Terrestrial RelationsObservatory (STEREO) satellites, no other instrument has beenavailable to carry out this type of observation; furthermore,STEREO/Sun Earth Connection Coronal and HeliosphericInvestigation (SECCHI; Howard et al. 2008) did not includespectrometers. Another possibility is to use the Sun’s rotationto provide multiple views of long-lived structures and apply atomographic analysis for the reconstruction of the 3Ddistribution of the coronal emission. This approach, spear-headed by Frazin et al. (2009), can be used for all types ofcoronal emission and allows for plasma diagnostics to becarried out in individual voxels (Vásquez et al. 2010).Tomography has also been used with spectroscopic data forthe 3D reconstruction of plasma emissivity (Panasyuk 1999).The need of series of observations much longer than thetimescales of the evolution of coronal structures, such as activeregions, limit the applicability of tomography to large-scalequiescent structures only.The third approach is to use a forward model of the solar

corona to reconstruct the relevant plasma properties (electrondensity, electron and ion temperatures, and bulk and sub-resolution dynamics) necessary to calculate line intensities andprofiles across the entire corona and integrate them along auser-defined LOS. The recent development of sophisticatedfirst-principle models able to predict plasma properties in 3Dacross the entire corona makes it possible to predict localcoronal emission everywhere and to integrate it along any user-defined LOS. This approach has the advantage that it allows

The Astrophysical Journal Supplement Series, 242:1 (17pp), 2019 May https://doi.org/10.3847/1538-4365/ab16d0© 2019. The American Astronomical Society. All rights reserved.

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users to understand where the bulk of the emission comes from,in order to interpret spectroscopic diagnostics of the solarcorona; furthermore, when applied to high-resolution spectra, itprovides a formidable tool to validate those models and toguide their improvement with an accuracy that is simply notpossible with narrowband imagers.

An interactive data language (IDL) program has beendeveloped recently to calculate synthetic observations, includ-ing but not limited to high-resolution spectra: FORWARD(Gibson 2015; Gibson et al. 2016). However, this tool isfocused toward providing forward modeling of magnetic fieldmeasurements, in preparation to the upcoming ground-basedvisible light observatories, the Upgraded Coronal Multi-channel Polarimeter (UCoMP) and DKIST. In the presentwork, we have developed an entirely independent code,SPECTRUM, as a module for the Space Weather ModelingFramework (SWMF; Tóth et al. 2012), which is publiclyavailable at thehttp://csem.engin.umich.edu/Tools/SWMFwebsite. SPECTRUM is written in Fortran (it isoptional to run in parallel). Its purpose is to act as apostprocessing tool to calculate coronal spectra along anyuser-defined LOS and at any user-defined resolution utilizingthe results of the 3D magnetohydrodynamic (MHD) AlfvénWave Solar Model (AWSoM) code (van der Holst et al. 2014),which is the inner solar corona component of the SWMF. Thus,the SPECTRUM module fulfills two main purposes. First, itprovides SWMF with the capability to calculate line emissionfor in-house model validation and LOS disentangling. Second,AWSoM relies on Alfvén wave turbulence to heat andaccelerate the solar corona and the solar wind: SPECTRUMallows one to identify and utilize spectral observables to testand validate the AWSoM model for example by studying thepresence, propagation, and damping of Alfvén waves in orderto explain how they heat the corona to over a million degreesand accelerate the solar wind.

In Section 2, we describe the processes of line formation,and the algorithms we used to implement them in SPEC-TRUM. Section 3 briefly describes the AWSoM solar coronamodel, and in Section 4, we show some examples ofSPECTRUM applications, including the comparison withHinode/Extreme-ultraviolet Imaging Spectrometer (EIS)high-resolution spectra. Section 5 summarizes this paper.

2. Synthetic Spectral Calculation

SPECTRUM uses the results of the AWSoM code as aninput: plasma density, bulk velocity vector components,magnetic field vector components, plasma pressure or temper-ature (which can be proton temperature alone, proton andelectron temperatures, or anisotropic proton and isotropicelectron temperatures), backward and forward propagatingAlfvén wave energy densities, and the matrix that describes therotation that transforms the coordinate system of the simulationdomain into the coordinate system aligned with the observer’sLOS. (Any number of observers’ positions can be described inthe command that saves the extracted data files during the solarcorona simulation. Carrington map reconstruction as in Li et al.2000 can therefore be efficiently be obtained in one singleAWSoM run.)

The synthetic spectra is calculated for emissions occurringabove temperatures of 100,000K based on CHIANTI (Dereet al. 1997; Del Zanna et al. 2015) emissivities. The user cancontrol the parameters of spectral calculations via editing the

commands of an input text file. In AWSoM, the corona isdescribed in a physically self-consistent manner based on theAlfvén wave dissipation (see van der Holst et al. 2014).SPECTRUM can calculate nonthermal broadening of spectrallines based on the local Alfvén wave energy density, whichallows testing and/or validating the Alfvén wave heatingtheory against observations. AWSoM can simulate single-temperature plasmas, two-temperature plasmas (electron andproton temperatures), and three-temperature plasmas (isotropicelectron and anisotropic proton temperatures; Meng et al.2015); SPECTRUM can utilize AWSoM results obtained witheither one-, two- or three-temperature plasmas.Synthetic spectra based on the AWSoM model have been

studied using isotropic proton and electron temperatures byOran et al. (2017), showing good agreement with line widthsand fluxes of a few spectral lines measured by the SolarUltraviolet Measurements of Emitted Radiation on board theSolar and Heliospheric Observatory (SoHO/SUMER; Wil-helm et al. 1995), suggesting that the change in the effectivevelocity (the rms of thermal and nonthermal velocities) as afunction of the radial distance is indeed due to wave damping.While the work of Oran et al. (2017) was focused on a fewspectral lines calculated with an ad-hoc program, SPECTRUMallows the user to select any spectral range and focus on anyspectral line available in the CHIANTI database.

2.1. Total Line Intensity

In this paper, we consider the mechanisms creating the solarcoronal spectrum as discussed in Phillips et al. (2008). Becausethe AWSoM coronal model simulates the solar atmospherefrom temperatures of 50,000 K and above (the low-transitionregion), the following calculations are performed on opticallythin and collisionally excited (including cascades) coronalplasmas. However, this approximation is not valid for severalions emitting below 100,000K that have low ionizationpotential, as plasmas under this temperature are not opticallythin. The present version of SPECTRUM does not calculatecontinuum emission and does not include resonant scattering(which can be important in case of some higher-temperaturelines, such as O VI) and photoexcitation; these processes will beadded in the next version. It is also assumed that the plasma isin ionization equilibrium, which means that sudden energeticprocesses, such as flares, need to be modeled separately. Also ithas been observed that, even in the quiet corona, the solar windplasma departs from ionization equilibrium at low coronalheights depending on the outflow speed (Landi et al. 2012).Consider volume element dV at distance d from the observer

along the LOS. Let N Xjm+( ) denote the density of ion m of

element X in the bound level j, which emits at frequency νij dueto the transition between excitation levels j to i. Thecorresponding emitted flux (energy reaching the observer perunit area and unit time) can be written as

dFd

N X A h dV1

4, 1j

mji ij2pn= +( ) ( )

where Aji is the Einstein coefficient of the spontaneous radiativedecay rate for the transition, d is the distance between theobserver and the emitting volume, and h is the Planck constant.Finally, the total flux reaching the observer is the integral of theemission from the individual volume elements along the LOS(assuming d is much larger than the thickness of the emitting

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plasma along the LOS):

Fd

N X A h dV1

4. 2

Vj

mji ij2 òpn= +( ) ( )

The density of the emitting ions N Xjm+( ) can be written as

the product of the relative level population,N X

N Xj

m

m

+

+

( )( )

(calculatedfrom the balance between excitation and de-excitationprocesses relative to level i, assuming equilibrium); the relativeion population, N X

N X

m+( )( )

(obtained from solving the equationsdescribing the ionization-recombination processes, assumingionization equilibrium); the element’s abundance relative tohydrogen, N X

N H

( )( )

(based on observations); the ratio of hydrogen

to free electrons, N H

Ne

( ) (which is about 0.83 due to the electronsoriginating from heavy ions and completely ionized H and Heat the temperatures covered by AWSoM); and the electrondensity, Ne. Defining the contribution function as

G T NN X

N X

N X

N X

N X

N H

N H

N

A

Nh, , 3e e

jm

m

m

e

ij

eijn=

+

+

+( )

( )( )

( )( )

( )( )

( ) ( )

the observed flux can be written simply as

Fd

G T N N dV1

4, . 4

Ve e e2

2òp= ( ) ( )

The F integral for each line along the LOS has to be calculatedto obtain the full synthetic spectra of the simulation results.SPECTRUM performs that calculation at every volumeelement dV along the user-defined LOS by using the plasmaparameters predicted by AWSoM to calculate both G T N,e e( )and Ne

2. At each volume element, SPECTRUM distributes thepredicted flux over the spectral line profile as a function ofwavelength λ. Finally, the total intensity component for the lineis calculated:

I N G dx1

4. 5etotal

2intòp

=-¥

¥( )

2.2. Line Profile

The sum of all emitted photons by thermal ions results in aline profile that can be approximated with a Gaussian (fordetails see Phillips et al. 2008). Within each dV volumeelement, the profile of the emission line centered at wavelengthλ0 with line width Δλcan be written as

e1

2. 6

0 2

2 2f lp l

=D

- l l

l

-

D( ) ( )( )

( )

Hence

I I e1

2, 7total 2

Dist2

2lp l

=D

-l

lD( ) ( )

where λDist=λshifted−λ is the distance between λ and theactual Doppler-shifted wavelength and Δλ is the line broad-ening—both are components we discuss next. Note that thedefinition of line broadening is a factor 2 of what iscommonly used in the community (for example, Hassler et al.1990). The thermal, nonthermal, and instrumental componentsof line broadening, defined below, are changed by this factoraccordingly for consistency.

Due to bulk plasma motions along the LOS direction, theline center is Doppler-shifted relative to λ0:

v

c1 , 8shifted

los0l l= -⎜ ⎟⎛

⎝⎞⎠ ( )

where ulos is the bulk plasma velocity’s LOS component,positive is toward the observer, and c is the speed of light invacuum. By explicitly including Doppler shifts from bulkmotions at every point along the LOS, SPECTRUM correctlyincludes the effects of bulk velocity fields in differentdirections at different positions along the LOS in the linebroadening.The total line broadening is calculated as the sum of thermal,

nonthermal, and instrumental components:

v v

c, 92 2 th

2nth2

2 instrument2l l lD =

++ D ( )

where instrument2lD is instrumental broadening, and vth and vnth

are the thermal and nonthermal random velocities. The thermalbroadening component is calculated taking into accounttemperature anisotropy:

vk T

m A, 10

p Xth2 B LOS= ( )

where kB is the Boltzmann constant; the LOS temperature iscalculated as T T Tsin cosLOS perp

2par

2a a= + , where α is theangle between the LOS and the magnetic field directions; mp isthe proton mass; and AX is the atomic mass of the emitting ionX. This way, temperature anisotropy is explicitly included inthe calculations.The nonthermal broadening is caused by the Alfvén wave

turbulence. For Alfvén waves, the kinetic and magneticenergies of the fluctuations v1

22rd and B1

22

0d

mare approximately

of the same magnitude, so

u B u

z z

1

2

1

2

1

4, 11

2

0

2 2

2 2

rdm

d rd

w w r

+ =

= + = ++ - + -( ) ( )

where ρ is plasma mass density, μ0 is vacuum permeability, z±are the Elsässer variables for forward- and backward-propagating waves with energy densities, ω±. The nonthermalbroadening due to low-frequency Alfvén waves in the twotransverse directions can be calculated as

v v

z z

1

4sin

1

4sin

1

16sin . 12

nth2 2 2 2

2 2 2

d aw w

ra

a

= á ñ =+

= +

+ -

+ -( ) ( )

See Oran et al. (2017) for further details on line broadening.After the above calculations are carried out for each volumeelement along the LOS, we add up the calculated line profilesfor every voxel as discretized LOS integration.

2.3. SPECTRUM Implementation

Due to its flexibility, it is easy for SPECTRUM to predictboth high-resolution spectra or narrowband images by

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prescribing the wavelength intervals and the wavelengthresolution of the instrument to be used. The contributionfunction values (Equation (3)) needed for emission calculations(Section 2.1) are obtained by an IDL script that uses proceduresfrom the CHIANTI package. The logarithms of contributionfunction values are stored on a logarithmic density–temperaturegrid in an ASCII file. Both the tabulated values and the IDLprogram used to generate the table are available in the SWMF,so that it is not necessary to regenerate the tabulated values foreach spectral calculation. The CHIANTI table of G(Te, Ne)values is calculated using a prescribed abundance for eachelement X: N X

N H

( )( )

. In the following examples, we use theabundance file Sun_coronal_1992_feldman.abund stored in

SolarSoft’s CHIANTI package based on Feldman et al. (1992).In future versions of SPECTRUM, we will implement thepossibility of including variable abundances along the LOS(e.g., open versus closed field regions) to better account for thefirst ionization potential (FIP) effect (Laming 2015) in differentplasma structures along the LOS.The calculation is done in the following way: for each

spectral line stored in the table containing the contributionfunction values, we loop over the whole data domain providedby the AWSoM simulation result and cell-by-cell calculate theline intensity profile and store these profiles by each cell (bothLOS and transverse directions of the final image). The datadomain used by SPECTRUM is a 3D subdomain of theAWSoM simulation, which is predefined and saved in advance

Figure 1. AWSoM steady-state simulation results of CR2063 (left) and CR2082 (right), showing the electron density in the top row and the radial bulk speed in thebottom one in the plane of the sky viewed from the LOS direction. The contour-colored 1.002 solar radii spherical surface of the solar body also shows the electrondensity (top) and the radial bulk speed (bottom).

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Figure 2. AWSoM steady-state simulation results of CR2063 (left) and CR2082 (right), respectively, showing parallel proton (top row), perpendicular proton(middle row), and electron temperatures (bottom row) in the plane of the sky viewed from the LOS direction. The contour-colored 1.002 solar radii spherical surface ofthe solar body also shows parallel proton (top row), perpendicular proton (middle row), and electron temperatures (bottom row).

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of calculating synthetic spectra. Then we move to the nextlines, and finally, when looped over the whole table, we sumthe contribution from each cell along the LOS direction.

In the input file, the user can choose whether to includeDoppler shift due to bulk plasma motion, and/or nonthermalbroadening due to Alfvén waves. The instrumental broadeningterm instrument

2lD( ) can also be added to the calculation. The

Figure 3. From top to bottom: model validation of AWSoM steady-state simulation results of CR2063 and CR2082, respectively, comparing LOS SoHO/EITobservations to synthetic images.

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user can directly prescribe the wavelength interval(s) of interestalong with the wavelength resolution. To calculate the Dopplershift, the wavelength intervals are extended by 10% in casesome lines would shift outside or into the specified wavelengthrange. During the process of line profile calculation, theGaussians are truncated at±5σ for efficiency.

For the sake of computational speed, the lines can bedistributed over many CPU cores, and the calculations can beperformed in parallel. SPECTRUM output files contain the 1D,2D, or 3D spectrum data (depending on the input file from theAWSoM simulation result), where the first dimension is thewavelength, and the second and third ones are spatial

dimensions of the plane of the sky. For testing and diagnosticspurposes, it is also possible to restrict the calculations to oneline or to one cell only.An important feature of SPECTRUM is that line formation

can be studied by separating thermal (including temperatureanisotropy) and nonthermal (Alfvénic turbulence) line broad-ening Doppler shifts from bulk motions and, most importantly,from the LOS effects. In this way, SPECTRUM provides aformidable tool to interpret spectral observations in terms of theproperties of different plasmas located at different places alongthe LOS.We tested SPECTRUM performances in individual voxels,

(assumed to have homogeneous temperatures and densities)against CHIANTI 8.0 uniform plasma calculations. Thesynthetic spectra in CHIANTI was generated by the SolarSoftprogram ch_ss.pro with several temperatures, electron numberdensities, wavelength ranges, and resolution inputs. In eachcase, we obtained perfect match with the CHIANTI results,verifying the correctness of the implementation.

3. Solar Corona Model

The SPECTRUM postprocessing tool uses AWSoM simula-tion results as input data for synthetic spectral calculations.Different versions of AWSoM have been successfully used tomodel solar wind plasma from the transition region to beyondMars for space weather purposes and for studying both quiet(Huang et al. 2012; Jin et al. 2012; Nuevo et al. 2013) anddynamic (Jin et al. 2013, 2017a, 2017b; Szente et al. 2017)processes on the Sun, using the Block Adaptive Tree Solar-wind Roe-type Upwind Scheme (BATS-R-US; Powell et al.1999; Tóth et al. 2012). The results in this paper are producedwith the three-temperature AWSoM model, which is describedin detail in van der Holst et al. (2014). This model can solve foranisotropic proton and isotropic electron temperatures. Thisfeature can be very important for calculating high-resolutionsynthetic spectra based on the local electron temperature andtaking into account the LOS direction relative to the localmagnetic field direction.In the global solar corona simulations we present, the

magnetic boundary conditions are based on synoptic magneto-grams produced by the National Solar Observatory from theGlobal Oscillation Network Group. We performed simulationsof Carrington rotations (CR) 2063 (CR 2063, between 2007November 4 and December 1) and 2082 (CR 2082, between2009 April 5 and May 3). These two CRs have been chosen asthey occurred during the cycle 24 solar minimum, thusreducing uncertainties due to CMEs occurring during thoseperiods. Running the three-temperature AWSoM model for60,000 iterations with the fifth-order accurate scheme by Chenet al. (2016), we obtain the steady-state solar wind solution onthe domain (from the transition region to 24 solar radii).Figure 1 shows the steady-state solution for the density andradial speed, while Figure 2 shows the three temperaturesmodeled by AWSoM. Both figures show results obtained in themeridional cut plane perpendicular to the LOS direction. Theplasma boundary in both simulations is set to n=3×1010

cm−3 and T=5×104 K at 1.001Re.While, at the base of the domain, the plasma is isotropic due

its high density, there is a strong temperature anisotropy wherecollisions are not sufficient to equate the temperatures. Theparallel proton temperature exceeds the perpendicular protontemperature near the heliospheric current sheet and streamer

Figure 4. From top to bottom: model validation of AWSoM steady-statesimulation results of CR2063 and CR2082, respectively, comparing OMNI1au in situ plasma measurements (red) with simulated data sampled at thesame location of the domain (black).

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top where the parallel proton plasma beta is high. This is adirect consequence of the energy partitioning used in theAWSoM model (van der Holst et al. 2014). Such anisotropy isalready significant at heights that can be reached by past andcurrently available high-resolution EUV spectrometers. TheSPECTRUM code currently assumes ionization equilibrium,which breaks down at a similar height where the protontemperature becomes anisotropic.

4. Comparison with Observations

As standard model validation, we compare the simulationresults to LOS narrowband imager observations and also with1au solar wind plasma measurements. Here we use observa-tions by the Extreme-ultraviolet Imaging Telescope (EIT)aboard SoHO (Delaboudinière et al. 1995), and OMNI (King &Papitashvili 2005) composite data set, respectively. Figure 3shows the steady-state solution compared to respectiveobservations using 2D narrowband images. The images weretaken with the Al+1 filter, using 12 s and 13 s exposure times.The synthetic images are brighter than the observed ones, andthis difference is usually interpreted as the density predicted bythe model is too high. However, the overall coronal structure iswell reproduced in both cases. Figure 4 shows in situ datacomparison for plasma observations taken at 1au. This currentmodel run is optimized to predict 1au plasma data, and this is

why there is a better match in the heliospheric data compared tothe coronal observations.The AWSoM simulations of these two CRs have been fed

into SPECTRUM to predict high-resolution spectra that iscompared with observations from the Hinode/EIS high-resolution spectrometer (Culhane et al. 2007). We used threedifferent observations from the end of solar cycle 23 and fromthe beginning of solar cycle 24. The first two observations arefrom CR2063: one in a closed magnetic field region on thesolar west limb taken at 2007 November 4 19:12:27 UT, andone in an open magnetic field region above the north coronalhole measured at 2007 November 12 12:32:02 UT. The thirdobservation was taken during CR2082 in the open magneticfield region of the south coronal hole, collected at 2009 April23 12:08:15 UT. These are the same observation sites analyzedby Hahn et al. (2012). The slit positions in each of the threeobservations are superimposed to the narrowband images takenby SoHO/EIT in Figure 5. The Hinode/EIS spectral resolutionis 0.0223Å in two wavelength bands (170–210Å and250–290Å). All three observations were done with the 2″ slitin raster mode.The input data is extracted for SPECTRUM from the steady-

state plasma solutions at the locations corresponding to theHinode/EIS observational sites as Cartesian boxes. Each site iscentered at the plane of sky and is extend from −1.5 to 1.5

Figure 5. SoHO/EIT narrowband images of the solar disk for the times of the observations were taken: CR2063 (left and middle) and CR2082 (right). The whiteboxes show the Hinode/EIS observation sites.

Figure 6. From left to right: The rectangular boxes represent the three data boxes where the MHD solution data were extracted for synthetic spectral calculationscorresponding to observation sites of CR2063 and CR2082 with field of view 0.8 solar radii. Each box stretches out to 3 solar radii in the LOS direction. Magentacolor indicates the part of the LOS in front of the plane of the sky, the semitransparent color indicates the portion behind the plane of the sky.

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solar radii in the LOS direction of the observer, as shown inFigure 6. The integration is limited to the box of a three solarradii length because plasma outside this interval provided nosignificant contribution to the total intensity; furthermore, sucha restriction saves a significant amount of computationalresources when performing the calculations.

In the following, we show a representative sample ofSPECTRUM data outputs. The first two observations will bediscussed as comparisons of spectra produced in open andclosed magnetic flux regions, and the third observation will beused to calculate the nonthermal velocity distribution as afunction of the radial distance for selected emission lines. Asmentioned by Hahn et al. (2012), the effective velocity trendsare insensitive to the assumption of position-varying or fixedinstrumental widths, so we used fixed instrumental broadeningof 0.06Å for both wavelength intervals, which is an estimatedaverage for both EIS channels.

4.1. Spectral Comparisons

Figure 7–12 show the comparison between SPECTRUMpredictions of the spectra in several small windows of the EISwavelength range (green lines) with observations (black lines)for the two data sets of CR2063. In these figures, lines fromFeIX–XIV, SiX, and SX are shown. Observed spectra havebeen obtained by taking the median of the observations in

selected off-disk wavelength ranges: for the coronal hole, werestricted the median to a slit position and to limit the decreaseof the electron density with the distance along the selectedheight range. In the case of the west limb observation, weaveraged along most of the slit (pixels 0–500) as the slit isparallel to the limb itself, so the density decrease was minimal.Figures 7–12 provide information to assess the performance

of AWSoM in reproducing coronal plasmas and demonstratesthe power of high-resolution spectroscopy for model valida-tion. The first thing to notice is that most of the spectral linesshown in those figures are not well reproduced by the model,although the discrepancies are normally smaller than a factor of2, which is a remarkable feat for a first principles model basedon CR-long magnetograms that make it impossible toreproduce the short-term evolution of the solar corona. Also,discrepancies are different in the two regions, indicatingspecific issues with each of them.

4.1.1. The West Limb Spectrum

If we consider the west limb spectra, we immediately noticethat the predicted intensities of Fe X–XI and Si X are in goodagreement with observations, while those of Fe IX are too low,and those of Fe XII–XIV are too high. This indicates that thepredicted temperature distribution along the LOS for thisregion is skewed too much toward high temperatures.Furthermore, Figures 7–12 include a few line pairs that canbe used to measure the plasma electron density: Fe XI 192.8/

Figure 7. Synthetic spectral line profiles of FeIX 189.941, FeX 190.037,FeXI 189.711, and FeXI 190.382 Å obtained by SPECTRUM (green)compared to Hinode/EIS observation (black) for the west limb (top) and thenorth polar (bottom) observations of CR2063.

Figure 8. Synthetic spectral line profile of Fe X 174.532 Å obtained bySPECTRUM (green) compared to Hinode/EIS observation (black) for the westlimb (top) and the north polar (bottom) observations of CR2063.

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189.7 and 192.8/201.7, Fe X 190.0/193.7, Fe XII 186.8/193.5,and Fe XIII 201.1/202.0. In all cases, the predicted ratio is veryclose to the observed one, indicating that the LOS-averageddensity predicted by the model is approximately the same asthe observed one. This result indicates that the excessiveintensity of the EIT 195 and 284Å narrowband images islikely not due to an excess predicted electron density, but ratherto a too large electron temperature. This explanation holds alsofor the EIT 171Å channel, which is nominally made ofemission from the Fe IX ion, which is underestimated by themodel due to the low density at that temperature. In fact, theemission observed by EIT in that channel is actually mainlycomposed of Fe X–XI emission (e.g., Landi & Miralles 2014),which Figures 7–12 show to be either well reproduced oroverestimated by AWSoM. It is also interesting to note thatdensity sensitivity ratios from the colder ions of Fe VIII andFe X lines indicate that the model’s predicted average density isclose to the observed one. In the comparison with densitiesusing emission measures, we implicitly assumed that the fillingfactor is one in the corona, although it is observed to befilamentary (Raymond et al. 2014; DeForest et al. 2018). As faras the line profile is concerned, the west limb spectrum showsthat, for all ions, the predicted and observed line widths areapproximately the same. This means that the combination ofbroadening due to ion temperature (which is assumed to be thecombination of proton parallel and perpendicular temperaturesin this version of the AWSoM model, see Equation (10)) and

Alfvén waves is able to provide a line width that is inagreement with observations. Furthermore, predicted spectralline profiles are centered at the same wavelengths as in theobserved spectra, which are essentially the same as the restwavelengths of each transition, indicating that no bulk flowsare present along the LOS. The few exceptions (e.g., 189.7Å)are likely due to inaccuracies in the CHIANTI rest wavelength.

4.1.2. The Coronal Hole Spectrum

Results for the coronal hole show a different story. First, aquick inspection of line profiles shows that the predicted onesare broader than the observed ones. This indicates that eitherthe ion temperature or the Alfvén wave broadening, or both, areoverpredicted. The amount of excess width seems to be largerfor the hotter ions, and it is unclear if the larger disagreement isdue to hotter ions being more heated by the AWSoM model orby the observed profiles being broader due to instrumentaleffects, such as instrument-scattered light.Line intensities, on the contrary, show a different mix of

results. Lines from Fe IX–XI are a bit underpredicted, whilethose for Fe XII–XIV, as well as Si X, are either in agreement oroverpredicted by the model. However, this comparison ismisleading for two reasons.

Figure 9. Synthetic spectral line profile of FeXI 192.813 and FeXII 193.509 Åobtained by SPECTRUM (green) compared to Hinode/EIS observation (black)for the west limb (top) and the north polar (bottom) observations of CR2063.

Figure 10. Synthetic spectral line profile of FeXI 201.734 and FeXIII 201.121and 202.044 Å obtained by SPECTRUM (green) compared to Hinode/EISobservation (black) for the west limb (top) and the north polar (bottom)observations of CR2063. CHIANTI does not include any line at201.5–201.6 Å, which explains the missing peak at that interval in thesynthetic spectrum.

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First, the elemental abundances used to calculate these linesare coronal, meaning that the abundances of Si and Fe arelarger by a factor of ≈3 than typical coronal hole values. Thismeans that the model, had the right abundance been used,likely underpredicts all line intensities. The fact that lowerstages of ionization of iron are more underpredicted than thehigher one likely reflects the same problem as that found in thewest limb spectrum—namely that the predicted plasmatemperature distribution is shifted toward values that aretoo high.

Second, all line intensities are predicted under the assump-tion of ionization equilibrium. However, solar wind expansionand acceleration causes all ions in the solar wind to be out ofequilibrium, resulting in a charge-state composition shiftedtoward lower values than the equilibrium values at the localtemperature (e.g., Landi et al. 2012). Such a shifted distribu-tion, if taken into account in the present calculation, would tendto increase the predicted intensities of the lower ionizationstages and decrease those of the higher ionization stages,bringing both closer to the observations. However, such acalculation is not yet implemented in SPECTRUM or AWSoM.

The comparison of the coronal hole emission with the EITimages is also misleading for two reasons. First, theSPECTRUM calculations have been carried out with the twofundamental limitations discussed above; second, the coronal

hole count rates of the EIT images are affected by instrument-scattered light (Shearer et al. 2012), and thus they are anoverestimate of the real emission of coronal holes. Theselimitations prevent us from drawing any conclusions from thecomparison with EIT.Finally, we assumed that the kinetic proton and ion

temperatures are equal. However, in the region of the dataextraction, the proton temperature anisotropy, T⊥/TP, isbetween 1 and 1.3. In regions where there is temperatureanisotropy, the kinetic proton and ion temperatures are notequalized by Coulomb collisions.

4.1.3. Sulfur

The total intensity of the S X 264.2Å line is significantlyunderestimated in both models even if lines formed at similartemperatures are in agreement with observations for the westlimb. The reason for this discrepancy is likely due to theassumed abundance of sulfur. The values adopted in this studyare photospheric, but the abundance of this element isnotoriously difficult to determine because sulfur behaves inan anomalous way with regard to the FIP effect. In fact,sometimes it can behave as a high-FIP element, and sometimesas a low-FIP element, depending on the properties of the region

Figure 11. Synthetic spectral line profile of SX 264.232 and FeXIV264.787 Å obtained by SPECTRUM (green) compared to Hinode/EISobservation (black) for the west limb (top) and the north polar (bottom)observations of CR2063.

Figure 12. Synthetic spectral line profile of SiX 261.058 and FeXIII261.743 Å obtained by SPECTRUM (green) compared to Hinode/EISobservation (black) for the west limb (top) and the north polar (bottom)observations of CR2063. The observed line at 261.4 Å might correspond to anFeIX transition, which has an uncertain wavelength that is only a part of theCHIANTI table as “unobserved/theoretical” line.

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where it is emitted (Laming 2015, and references therein).Therefore, while the comparison of the predicted intensity ofthis element is expected to follow the behavior of the other ionsformed at similar temperatures (e.g., Fe XI–XII), the uncertain-ties in the element abundances make its interpretation moredifficult.

4.2. Narrowband and Spectral Imaging

SPECTRUM has the capability to apply instrument effectiveareas on the calculated intensities and to create 2D narrowbandimages, such as those observed by SoHO/EIT or the SolarDynamic Observatory/Atmospheric Imaging Assembly (SDO/AIA). To obtain such images, we need to save the 3D datadomain surrounding the Sun. Then we calculate syntheticspectra for each pixel, weighting it by the effective area of theinstrument and calibration factors. Figure 13 was created basedon a box with sides of 3 Re in length, with 200 cells along eachside. SPECTRUM calculated the full spectra from 165 to 350Åfor each cell within the box and convolved them with the

instrument’s response function to obtain the observed datanumber count (DN) measured with the imager. The top leftpanel in Figure 13 shows the simulated plasma conditions ofthe solar corona as observed from Earth on 2007 November 419:12:27 UT, the top right panel corresponds to 2007November 12 12:32:02 UT, and the bottom one is at 2009April 23 13:13:36 UT, corresponding to the closest time to thespectral observations when narrowband observations weretaken at the 195Å wavelength. The interpolation from thespherical grid onto the low-resolution Cartesian box results inconcentric circles on the images. This method of generatingsynthetic narrowband images is less efficient than the one usedto obtain Figure 3, where we integrate on the original grid, andthe instrument’s response function is calculated using differ-ential emission measure (DEM) distribution along the LOS (seedetails in Downs et al. 2010).The main feature of SPECTRUM is that it makes it possible

to calculate LOS images of individual spectral line properties:intensity, centroid, and line width. These images can be directly

Figure 13. Synthetic images of the solar corona during CR2063 (top row) and CR2082 (bottom row), calculated using synthetic spectra obtained from SPECTRUMin the wavelength range of 165–350 Å and the instrumental response function from SoHO/EIT 195 Å. (The concentric circles at the center of the disk are an artifactdue to the interpolation from a spherical to low-resolution Cartesian grid when calculating the images.)

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compared with 2D images measured by high-resolutionspectrometers rastering their slit across a solar region.Figure 14 shows an example, based on the strong Fe XIII202.044Å line for CR2082, that is easily observable with theEIS spectrometer. In the top left panel, the line intensity mapclearly shows the presence of a coronal hole at the south poleand the presence of more active areas. The contrast between thecoronal hole and the surrounding quiet areas is larger thannormally observed by EIS; this discrepancy is due to thepresence of instrument-scattered light in disk observations ofcoronal holes (Wendeln & Landi 2018).

The top right panel of Figure 14 shows the line’s FWHM.This quantity indicates the combination of the effects of theion’s temperature (assumed to be the same as the anisotropicproton temperature) and of the Alfvén wave motions along theLOS. As expected, this image shows the large increase in thenonthermal motions in the off-limb corona where open fieldlines are found, due to the effects of waves on the acceleratingsolar wind. On the contrary, line widths on the disk and inclosed field regions are much smaller. These effects can bedirectly compared with observations of the line width to assessthe performance of the model when accounting for these twophysical quantities in both open and closed field regions.

The bottom panel shows the Doppler shift resulting from theintegration along the LOS. While very small LOS velocities arepredicted to occur in the closed field corona, there aresignificant velocities in the open field regions, which are theresult of solar wind acceleration. The LOS integration effectsare immediately evident in the Doppler shifts. For example, thedisk portion of the coronal hole at the south pole shows largeblueshifts, indicating that the solar wind is strongly acceleratedtoward the observer; still, immediately above the limb, theseshifts turn to the red, indicating the presence of wind that ismoving away from the observer. This occurs because denser,redshifted wind plasma is present in the south pole regionwhose emission dominates over the blueshifted one, resultingafter the LOS integration in an overall redshifted emission.Figure 14 predicts the emission that should be observable

from the Earth as a product of LOS integration. However,SPECTRUM allows the calculation of the emission everywherein the 3D corona, so that the emission (intensity, line width andDoppler shift) from every volume element along the LOS canbe retrieved, effectively allowing one to analyze whichstructures are contributing to the emission. Figure 15 showsan example by displaying the Fe XIII 202.044Å line para-meters from the point of view 90° clockwise from Figure 14. In

Figure 14. 2D synthetic maps of intensity in the logarithmic scale (top left), FWHM (top right), and Doppler shift (bottom) of line Fe XIII 202.044 Å from theobserver’s LOS from CR2082.

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this figure, the FWHM and Doppler shifts are calculated alongthe direction of the Earth (the x-axis, with the Earth on theright); in this way, the contribution to the final shifts of all thepoints along the LOS can be seen. In particular, it is possible tosee that the large blueshifts predicted on the disk at the southpole turn to redshifts right outside the limb because of thepresence of strongly redshifted plasma closer to the surface,hence brighter, than the blueshifted one.

Figure 16 shows the effects of structures at differentdensities along the LOS. It shows the line intensity, FWHM,and Doppler shift cut from Figure 15 at the south pole. Theobserver, again, is placed at the right of the figure, along the x-axis. In this figure, only the areas responsible for a total of 80%of the emission are shown, and the rest are painted in black.Figure 16 shows that, above 1.2 solar radii, the emissionobserved from the x-axis is formed around the plane of the sky(X= 0 in that figure), but below that height, a denser structuresignificantly behind the plane of the sky is actually responsiblefor most of the coronal emission. This explains, for example,the sudden change in the FWHM and Doppler shifts seen inFigure 14, at the south pole along the central meridian.

4.3. Effective Velocity Width

The third observation site is a quiet-Sun coronal hole ofCR2082, which has been used by Hahn et al. (2012) to showevidence of significant Alfvén wave damping in the lowcorona. The effective velocity change as a function of the radialdistance in the solar atmosphere is a widely discussed and well-observed phenomenon. While some observations support thetheory of significant Alfvén wave dissipation happening in thelow corona (e.g., Bemporad & Abbo 2012; Hahn et al. 2012),others contradict this (e.g., Banerjee et al. 1998, 2009; Doyleet al. 1998). With SPECTRUM, it is possible to obtainsynthetic spectra of the regions studied in these works and tolook for signatures of wave damping. The effective velocitiesare calculated from measuring the FWHM of the lines:

cv

c

k T

MvFWHM 8 ln 2 8 ln 2 . 13i0

eff2 0 B

nth2l l

= = +⎜ ⎟⎛⎝

⎞⎠ ( )

Here we assumed that the ion temperatures are equal to theproton temperature up to the 1.4 solar radii distance, althoughthis assumption may not be valid over this range of heights in

Figure 15. Point of view 90° clockwise from Figure 14: the observer is in the positive X direction. These 2D synthetic maps of intensity in the logarithmic scale (top,left), FWHM (top, right), and velocity component in the X direction (bottom) of line FeXIII 202.044 Å from the observer’s LOS from CR2082. The velocity iscalculated toward the observer direction, which is the LOS direction in Figure 14.

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coronal holes according to UltraVioletCoronagraph Spectrometer (UVCS) observations, whichshowed that ion effective velocities depart from the hydrogenone between 1.34 and 1.5 solar radii heliocentric distances incoronal holes (Kohl et al. 1999). The predicted FWHM for thesame region studied by Hahn et al. (2012) is shown inFigure 17, calculated including (top) and excluding (bottom)the effects of Alfvén wave broadening. Figure 18 instead showsthe effective velocity determined from the FWHM, to bedirectly compared with Hahn et al. (2012).

There are two main results that can be deduced fromFigures 17 and 18. First, the presence of Alfvén wavesproduces a significant broadening of the line profile detectableby the EIS spectrometer. So, synthetic spectra do need toinclude such an effect, and other line widths observed by EIScan indeed be used to investigate Alfvén wave damping. Thesecond result is that no decrease of the line width is predictedby AWSoM, which is in stark contrast to the observationsreported by Hahn et al. (2012). Even if different lines increasein widths at a different rate (especially below 1.2 solar radii),no hint of decrease is predicted by the model.

This discrepancy might be due to several causes. Hahn et al.(2012) discuss several possible effects that could contaminatethe line width of the coronal lines they used: instrument-scattered light, photoexcitation, broadening due to motionsalong the LOS, and the presence of different plasma structuresalong the LOS. The latter two effects are automatically takeninto account from SPECTRUM, so they are likely not the cause

of the discrepancy, especially in a relatively unstructuredregion, such as a polar coronal hole where possible errors in theplasma morphology by AWSoM should be minimized.Photoexcitation is not taken into account by SPECTRUM,but Hahn et al. (2012) rule it out, essentially, based on atomicphysics arguments. Instrument-scattered light was also dis-missed by Hahn et al. (2012) as they showed that even if itaccounted for ≈50% of the observed emission—much largerthan anticipated based on estimates of scattered light providedby the EIS team—it still would have no effect on line widths.This leaves the option open that the AWSoM heating by

Alfvén waves is incorrect, damping energy at a much largerheight than indicated by the EIS measurements of Hahn et al.(2012). This is possible, but it leaves the question open aboutthe amount of energy damped in the inner corona (below 1.4solar radii, the height range was investigated by Hahn et al.2012), which would leave insufficient energy to heat the higherlayers of the corona itself.Further investigation of this problem is postponed to a future

article; here we only note that, again, for the first time,SPECTRUM allows us to directly connect high-resolutionspectral measurements, such as those taken by Hinode/EIS,directly to the physics of coronal heating and solar windacceleration, something that the narrowband imaging compar-ison utilized so far for model-observations comparisons did notallow.

Figure 16. Side view of the center of the observational site presented in Figure 14. These are 2D synthetic maps of the intensity (top), FWHM (middle), and velocity(bottom) of line Fe XIII 202.044 Å from the observer’s LOS from CR2082. The velocity is calculated toward the observer direction, which is the LOS direction inFigure 14. The areas are colored where 80% of the emission is coming from; the rest of the domain is left blank.

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5. Summary

SPECTRUM, a new postprocessing tool available within theSWMF that performs synthetic spectral calculations, has beenpresented in this paper. SPECTRUM calculates spectral line

emission based on simulated MHD data using CHIANTI-tabulated emission rates. We have shown that synthetic spectrarepresent a valuable diagnostics for interpreting solar observa-tions, providing the ability to study the 3D distribution ofplasma properties that high-resolution spectrometers can onlyinfer from LOS-averaged radiation. SPECTRUM can also beused for validating global simulations, and it can help toachieve a more realistic solar wind model for space weatherpredictions. In this paper, we have shown examples ofapplication of SPECTRUM predictions to EIS observationstaken during CR 2063 and 2082.In the future, we plan to implement an automated process

that distinguishes the open and closed magnetic field regions,so the difference between element abundances can be takeninto account during the calculations. We also plan to extend thecalculations in SPECTRUM with resonant scattering andphotoexcitation, which would enable more realistic estimatesof coronal line emission in the visible range observed byground-based instruments (such as the upcoming DKIST andUCoMP) and during eclipses. The inclusion of visible lines willallow coronal examination and model validation at heightslarger than observed by most space-based EUV instrumentation(SoHO/SUMER is a notable exception) and will provide betterpredictive capabilities, so SPECTRUM could be used not onlyfor upcoming missions but also for space weather forecasting(Habbal et al. 2014; Landi et al. 2016; Tomczyk et al. 2016). Inaddition, AWSoM is currently being developed into a multi-fluid MHD global solar corona model, and SPECTRUM willbe developed to take the multi-fluid solutions into account.

The authors would like to thank the anonymous reviewer’scomments and recommendations from which the manuscriptbenefited greatly.Hinode is a Japanese mission developed and launched by

ISAS/JAXA, collaborating with NAOJ as a domestic partner,NASA and UKSA as international partners. Scientific operationof the Hinode mission is conducted by the Hinode science teamorganized at ISAS/JAXA. This team mainly consists ofscientists from institutes in the partner countries. Support forthe post-launch operation is provided by JAXA and NAOJ(Japan), UKSA (UK), NASA, ESA, and NSC (Norway).This work utilizes data obtained by the Global Oscillation

Network Group (GONG) program, managed by the NationalSolar Observatory, which is operated by AURA, Inc. under acooperative agreement with the National Science Foundation.The data were acquired by instruments operated by the BigBear Solar Observatory, the High Altitude Observatory, theLearmonth Solar Observatory, the Udaipur Solar Observatory,the Instituto de Astrofisica de Canarias, and the Cerro TololoInteramerican Observatory.SoHO/EIT observational data were provided by The Virtual

Solar Observatory, Solar Data Analysis Center (http://virtualsolar.org).CHIANTI is a collaborative project involving George Mason

University, the University of Michigan (USA), and theUniversity of Cambridge (UK).The work of E.L. and J.S. was supported by NSF grant AGS-

1408789, as well as NASA grants NNX16AH01G andNNX17AD37G.Our team also acknowledges high-performance computing

support from Pleiades, operated by NASA’s Advanced Super-computing Division.

Figure 17. FWHM for spectral lines of selected ions that have nonthermaleffects included (top) and excluded (bottom) from the line profile calculation.The difference between the top and bottom panels shows that nonthermalbroadening has a significant effect on line widths.

Figure 18. Effective velocity of selected spectral lines along the radial distancein the coronal hole of the CR2082 observation shows little or no wavedamping compared to what was observed by Hahn et al. (2012). The FeXIIIline shows different behavior below 1.2 solar radii than the other ions, becausein that region, the emission originates mainly from a hotter structure along theLOS, see Figure 16.

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ORCID iDs

J. Szente https://orcid.org/0000-0002-9465-7470G. Toth https://orcid.org/0000-0001-8459-2100B. van der Holst https://orcid.org/0000-0001-5260-3944T. I. Gombosi https://orcid.org/0000-0001-9360-4951

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