Chromospheric polarimetry through multi-line observations of the 850 nm spectral region III: Chromospheric jets driven by twisted magnetic fields
C. Quintero Noda, H. Iijima, Y. Katsukawa, T. Shimizu, M. Carlsson, J. de la Cruz Rodríguez, B. Ruiz Cobo, D. Orozco Suárez, T. Oba, T. Anan, M. Kubo, Y. Kawabata, K. Ichimoto, Y. Suematsu
aa r X i v : . [ a s t r o - ph . S R ] A p r MNRAS , 1–14 (2018) Preprint 22 April 2019 Compiled using MNRAS L A TEX style file v3.0
Chromospheric polarimetry through multi-lineobservations of the 850 nm spectral region III:Chromospheric jets driven by twisted magnetic fields
C. Quintero Noda, , , ⋆ H. Iijima, Y. Katsukawa, T. Shimizu, M. Carlsson, , J. de la Cruz Rodr´ıguez, B. Ruiz Cobo, , D. Orozco Su´arez, T. Oba, T. Anan, M. Kubo, Y. Kawabata, , K. Ichimoto, , Y. Suematsu Institute of Space and Astronautical Science, Japan Aerospace Exploration Agency, Sagamihara, Kanagawa 252-5210, Japan Rosseland Centre for Solar Physics, University of Oslo, P.O. Box 1029 Blindern, N-0315 Oslo, Norway Institute of Theoretical Astrophysics, University of Oslo, P.O. Box 1029 Blindern, N-0315 Oslo, Norway Institute for Space-Earth Environmental Research, Nagoya University, Furocho, Chikusa-ku, Nagoya, Aichi 464-8601, Japan National Astronomical Observatory of Japan, 2-21-1 Osawa, Mitaka, Tokyo 181-8588, Japan Institute for Solar Physics, Dept. of Astronomy, Stockholm University, Albanova University Center, SE-10691 Stockholm, Sweden Instituto de Astrof´ısica de Canarias, E-38200, La Laguna, Tenerife, Spain. Departamento de Astrof´ısica, Univ. de La Laguna, La Laguna, Tenerife, E-38205, Spain Instituto de Astrof´ısica de Andaluc´ıa (CSIC), Glorieta de la Astronom´ıa, 18008 Granada, Spain National Solar Observatory, 22 Ohi’a Ku, Makawao, HI 96768, USA Department of Earth and Planetary Science, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan Kwasan and Hida Observatories, Kyoto University, Kurabashira Kamitakara-cho, Takayama-city, 506-1314 Gifu, Japan
Accepted XXX. Received YYY; in original form ZZZ
ABSTRACT
We investigate the diagnostic potential of the spectral lines at 850 nm for under-standing the magnetism of the lower atmosphere. For that purpose, we use a newlydeveloped 3D simulation of a chromospheric jet to check the sensitivity of the spectrallines to this phenomenon as well as our ability to infer the atmospheric informationthrough spectropolarimetric inversions of noisy synthetic data. We start comparingthe benefits of inverting the entire spectrum at 850 nm versus only the Ca ii ii Key words:
Sun: chromosphere – Sun: magnetic fields – techniques: polarimetric
This is the third study of a series of publications investi-gating the properties of the spectral lines belonging to the850 nm window. In the first paper, we examined their diag-nostic potential for inferring the atmospheric parameters atphotospheric and chromospheric layers with semi-empirical ⋆ E-mail: [email protected] models and more complex atmospheres as the 3D enhancednetwork simulation (Carlsson et al. 2016) generated with the bifrost code (Gudiksen et al. 2011). We concluded that, al-though the Ca ii c (cid:13) C. Quintero Noda et al.
Figure 1.
From left to right, spatial distribution of temperature, line-of-sight velocity, and the vertical component of the magneticfield at log τ = −
5, respectively. Negative LOS velocities correspond to material moving upwards with respect to the solar surface. Thehighlighted location is examined later. upper atmospheric layers (see, for instance, the comparativework by Socas-Navarro et al. 2000a).In the second study of this series, we examined the two-dimensional simulation of a magnetic flux tube presented inKato et al. (2016). In this case, the atmosphere inside themagnetic concentration periodically changes due to the so-called magnetic pumping process. We determined that thisvariation of the atmospheric conditions leaves a characteris-tic imprint in the Stokes profiles of photospheric and chro-mospheric spectral lines through large Dopplershifts and in-tensity fluctuations (Quintero Noda et al. 2017a). Also, weconcluded both publications mentioning that we need to per-form additional studies to understand better our capabilitiesfor inferring the atmospheric information from spectropo-larimetric observations. In particular, to assess the accuracyof the inferred atmospheric parameters through non-localthermodynamic equilibrium (NLTE) inversions of multiplespectral lines with a different height of formation (see, forinstance, the recent studies by da Silva Santos et al. 2018;Leenaarts et al. 2018). Our target is to pave the road forwhen chromospheric polarimetric observations are routinelyperformed in the future. Something that will happen soonwhen ground-based telescopes such as DKIST (Keil et al.2011) or EST (Collados et al. 2013), as well as balloon mis-sions such as the Sunrise solar balloon-borne observatory(Barthol et al. 2011; Berkefeld et al. 2011; Gandorfer et al.2011), start performing observations.In this publication, we focus on the MHD simulation ofa chromospheric jet with complex plasma flows and twistedmagnetic field lines by Iijima (2016); Iijima & Yokoyama(2017). In this simulation, the thermal convection near thesolar surface excites various MHD waves and generates chro-mospheric jets rooted in magnetic field concentrations. Also,the magnetic field lines that define the jet are entangled atchromospheric heights, which helps the chromospheric jet tobe driven by the Lorentz force.The primary target of this study is to examine the di-agnostic potential of the 850 nm spectral lines for inferringthe physical information of the chromospheric jet throughnumerical NLTE inversions of noisy synthetic spectra. Tothis purpose, we analyse one of the dynamic events of thesimulation where large gradients dominate the atmospheric parameters, and we propose an inversion set-up that opti-mally works when performing simultaneous inversions of thephotospheric and chromospheric spectral lines belonging tothe 850 nm window.
Iijima & Yokoyama (2017) developed a 3D radiation MHDsimulation with the numerical code RAdiation Magne-tohydrodynamics Extensive Numerical Solver ( ramens ,Iijima & Yokoyama 2015) that extends from the upper con-vection zone to the lower corona, i.e. from -2 to 14 Mm abovethe solar surface. The setup of this simulation is explained inIijima & Yokoyama (2017) although we describe below someof its properties for the sake of clarity.The horizontal domain of the simulation covers 9 × with a uniform grid size of 41.7 km, i.e. a spatialresolution of around 80 km. However, the effective spatialresolution is slightly larger than twice the grid size (typically3-6 grid zones, or 120-240 km in this case). This reduction ofthe effective resolution is caused by the numerical diffusion ofthe MHD scheme. Therefore, the effective spatial resolutionis comparable to the values that can be achieved with current1 m or larger telescopes (i.e. Sunrise, SST (Scharmer et al.2003), GST (Goode et al. 2003), or Gregor (Schmidt et al.2012)) and indeed will be attained by future large 4 m tele-scopes as DKIST and EST. As an illustrative example, SSTcan achieve, observing the 850 nm window, a spatial resolu-tion of 0.2 arc sec at diffraction limit, i.e. around 150 km.The vertical domain comprises 16 Mm with a constantstep size of 29.6 km. Horizontal boundary conditions areperiodic while the top and bottom boundaries are opento flows. In addition, the computation is done in multiplestages although we only analyse the simulation results cor-responding to the last 30 minutes of the run. Figure 1 de-picts an example of the whole simulation horizontal domainat log τ = −
5, where τ is the optical depth at 500 nm.The temperature panel shows a complex scenario coveredby ubiquitous thin and hot structures surrounded by coolareas. In the case of the line-of-sight (LOS) velocity panel,we can see a dynamic pattern with upflows and downflowsof more than 16 km/s in a few locations with, in general, the MNRAS , 1–14 (2018) olarimetry through multi-line observations III former associated with hot areas. If we move to the longi-tudinal component of the magnetic field, we can detect twomain concentrations of the same polarity with opposite signmagnetic fields in between them. In both cases, the longitu-dinal component of the magnetic field shows values close to100 G while it is weaker outside those concentrations beinglower than 10 G.We focus on the region enclosed by a box (see Fig-ure 1) that is centred on the chromospheric jet studied inIijima & Yokoyama (2017). This feature has a maximumheight of 10 Mm, and its core is hotter than its surroundingsat chromospheric layers. Also, it shows an intricate magneticstructure with entangled and twisted magnetic field lines(see Figure 8 of the mentioned work). The method used in the present study is similar to the oneemployed in Quintero Noda et al. (2017b,a). We generatethe full Stokes vector for the 850 nm window shown in Fig-ure 1 of the first publication of this series. Inside this spectralwindow, there are several lines of interest, with the most im-portant ones being the photospheric Fe i transitions at 8468and 8514 ˚A. They show high sensitivity to the magnetic field(comparable to, e.g., Fe i ii triplet at8498 and 8542 ˚A that are sensitive to the atmospheric pa-rameters up to the middle chromosphere, around 1000 kmabove the visible surface.We perform synthesis of these spectral lines withthe nicole code (Socas-Navarro et al. 2000b, 2015). Thisis done with column-by-column forward modelling, i.e.each column is treated independently, and the non-localthermodynamic equilibrium atomic populations are solvedfor the Ca ii line transitions assuming a plane-parallelatmosphere. This approximation is appropriate for theCa ii lines where horizontal scattering does not rep-resent a dominant contribution (Leenaarts et al. 2009;de la Cruz Rodr´ıguez et al. 2012). Also, the code works un-der the field-free approximation (Rees 1969), i.e. the statisti-cal equilibrium equations are solved neglecting the presenceof a magnetic field (see also Bruls & Trujillo Bueno 1996;Trujillo Bueno & Landi Degl’Innocenti 1996, for more de-tails).The spectral sampling used is the same as well, i.e.∆ λ = 40 m˚A. Therefore, the full spectrum of interest wouldfit in a hypothetical sensor of 2000 pixels (for instance, Kat-sukawa et al. in preparation). The simulation’s vertical do-main is shortened to z = [ − , µ = 1 (where µ = cos θ , and θ is the angle of the ray with respect tothe normal of the atmosphere). We deactivate the default“velocity free” option because we believe it would produceless accurate results in this simulation where strong LOSvelocity gradients are dominant. We switch on the keyword“optimise grid” that interpolates the initial atmosphere to adifferent grid of points in height. The resulting atmosphereis the one used in any plot of this manuscript, including thatof Figure 1. We start the initial guess for the atomic popula- Figure 2.
Comparison between the solar atlas (black) andthe spatially averaged intensity profile for different simulations(colour). tions assuming LTE populations using the multi (Carlsson1986) approach (see nicole ’s manual for more information).Also, line broadening owing to collisions by neutral hydro-gen atoms is applied to all the spectral lines following thetheory of Barklem et al. (1998).To simulate the effect of a general spectral point spreadfunction, we degrade the spectra employing a Gaussian pro-file with a full width at half maximum of 1.0 km/s, andwe use the original spatial sampling, i.e. no spatial degra-dation. We also simulate the presence of noise in observa-tions adopting similar conditions to those expected for theSunrise Chromospheric Infrared spectro-Polarimeter (SCIP,Katsukawa et al. in preparation) instrument under develop-ment for the third flight of the Sunrise balloon. In this re-gard, the nominal observing mode of SCIP integrates longerthan 10 s per slit position and aims to achieve a noise level forthe polarisation Stokes profiles of the order of ± × − of I c . Thus, this is the noise value we assume for Stokes ( Q , U , V ). In the case of Stokes I , there are always systematic errorsin the post-processing of the signals that prevent achievingso low noise levels. Therefore, we tentatively choose a ran-dom noise with a standard deviation of ± × − of I c .Those noise signals are different for each spectral point, eachStokes profile, and each spatial pixel. Leenaarts et al. (2009) explained that current numericalsimulations do not contain sufficient heating and small-scalemotions to match the observed intensities and widths ofchromospheric lines. Moreover, if the line core intensity pro-file is narrower and deeper than expected, this could induceunrealistic polarisations signals (de la Cruz Rodr´ıguez et al.2012). Therefore, we follow the steps of the first two pub-lications of this series examining first the intensity profilespatially averaged over the whole simulation box presentedin Figure 1, synthesised using a null microturbulence value.The results are depicted by the dashed line in Figure 2, whilesolid corresponds to the solar atlas (Delbouille et al. 1973),dashed-dotted line displays the results from the spatiallyaveraged profile of snapshot 385 of the enhanced network
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C. Quintero Noda et al.
Figure 3.
Each panel shows the spatial distribution, from left to right column, of temperature, LOS velocity, horizontal and verticalcomponents of the magnetic field at the optical depths log τ = [0 , − , − simulation (Carlsson et al. 2016) using a microturbulence of3 km/s, and dots represent the averaged profile computedusing the 2D flux sheath simulation (Kato et al. 2016) anda null microturbulence.The intensity profile produced by the chromospheric jetsimulation (dashed) is broad, showing a line core width atfull width half maximum of 423 m˚A, close to the value dis-played by the solar atlas, i.e. 574 m˚A, and the results of ad-ditional studies (for instance, Cauzzi et al. 2009, obtaineda line core width ranging between 450-550 m˚A). Therefore,in this case, we do not need to introduce an additional mi-croturbulence contribution. Finally, although the width ofthe line is sufficiently broad to avoid using an artificial mi-croturbulence, we can still detect intensity differences in theouter wings of the line, e.g. at 8540 and 8544 ˚A. We guessthat this could be caused because none of those simulationsaims to represent strictly quiet Sun conditions. We are interested in the enclosed region highlighted in Fig-ure 1. In particular, we examine the spatial distributionof different atmospheric parameters at selected heights inthe atmosphere. We focus on the temperature, LOS veloc- ity, horizontal ( B h = p B x + B y ) and vertical ( B z ) com-ponents of the magnetic field (see columns in Figure 3) atthree selected optical depths, i.e. log τ = [0 , − , − i ii x and y coordinates equal to (2.2,4.0) Mm, definedby a cool intergranular region. Moving on to upper layers(middle row), we detect areas with enhanced temperature,with a localised hot point at the roots of the chromosphericjet, but also a cool patch at around (1.6,4.6) Mm. Higher inthe atmosphere (bottom row), there is a thin hot “thread”surrounding the core of the jet. Additional cool areas can befound at different spatial locations, for instance, close to thecentre of the jet at (1.9,4.2) Mm.Concerning the LOS velocity, the granulation patternis also discernible. At log τ = − MNRAS , 1–14 (2018) olarimetry through multi-line observations III Figure 4.
Panels show the spatial distribution of maximum linear (top) and circular (bottom) polarisation signals for selected spectrallines. From left to right, Fe i ii infrared lines at 8498 and 8542 ˚A, respectively. We display the inferred averagemagnetic field azimuth with headless arrows in the top panel for those pixels with an amplitude larger than 3 × − of I c . The magnitudeof the linear polarisation signals gives the length of each arrow. jet. This also takes place at higher layers, bottom panel,where a similar pattern now occupies broader areas.In the case of the horizontal component of the magneticfield (third column), it is concentrated in a narrow regionin the lower photosphere with values larger than 300 G atsome points, e.g. (2.3,4.0) Mm. This region expands occupy-ing wider areas at log τ = −
2, and the field strength dropsto values in between 250 −
300 G. In the chromosphere (bot-tom), the spatial distribution shows almost null values in thesame spatial location of the core of the jet, i.e. (2.2,4.3) Mm,with a field strength of the order of tens of Gauss.The longitudinal magnetic field (rightmost column),displays a similar behaviour as B h , i.e. localised concentra-tions at lower layers that expand with height. In addition,in the case of the jet, a single polarity component dominateslower layers. At higher heights, i.e. log τ = −
5, there are twomain components of opposite polarity, a positive one thatcorresponds to the core of the jet at around (2.2,4.0) Mm(label A), and a negative one located near the jet (labelB) that extends towards the right side beyond the selectedfield-of-view. Also, the interface between those two oppo-site polarity regions is comprised by almost null B z values,co-spatial with areas of larger B h (see the bottom panel inthe third column). In this regard, if we look at Figure 8 ofIijima & Yokoyama (2017) the A region is associated to thecentral spine of the jet while the B labelled area correspondsto the almost isolated magnetic field lines that, after twist-ing around the jet, extend beyond it (see sky blue lines inthe cited figure around Z =1 Mm). We plan to study in this section the properties of theStokes profiles that can reveal information about the jet.In particular, the magnetic field azimuth and its longi-tudinal component. The former one can be inferred us-ing the ratio of the synthetic Stokes Q and U pro-files through the following equation (see, for instance,Landi Degl’Innocenti & Landolfi 2004) φ = 12 arctan (cid:18) UQ (cid:19) . (1)The wavelength position used corresponds to the spectralpoint with maximum Q ( λ ) or U ( λ ) signals. The results forthe azimuth are displayed in the top row of Figure 4 overthe spatial distribution of the maximum total linear polari-sation ( LP = p Q max + U max ) for three spectral lines fromthe 850 nm window. To simplify the analysis, we picked aphotospheric line sensitive to the magnetic field at lower lay-ers (Fe i ii lines that aremost sensitive to the atmospheric parameters at slightly dif-ferent heights in the chromosphere. In this regard, headless(we do not solve the 180 degrees ambiguity) arrows showthe inferred average magnetic field azimuth weighted withthe strength of the linear polarisation signals. Starting withthe photosphere, we can detect the presence of twist aroundthe jet with lines that circle it, see (2.2,4.0) Mm. This typeof pattern can also be recognised at higher layers in the at-mosphere indicating that the magnetic field configurationdescribed in Iijima & Yokoyama (2017) leaves a characteris-tic imprint in the linear polarisation profiles above the addednoise signals. MNRAS , 1–14 (2018)
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Regarding the longitudinal component of the magneticfield, we study its spatial distribution by plotting the maxi-mum Stokes V signals (see the bottom row of Fig. 4). Thereis a strong concentration at lower heights (leftmost panel)that occupies larger areas as we examine lines that formhigher in the atmosphere. Moreover, there is a thin regionthat corresponds to magnetic field lines that extend beyondthe core of the jet (see sky blue lines at the left part ofthe structure presented in Figure 8 of Iijima & Yokoyama(2017)). This thin region is located further from the centreof the jet when we scan higher heights. Finally, linear polar-isation signals are situated outside the strong longitudinalfield concentrations, in agreement with the spatial distribu-tion of the atmospheric parameters presented in Figure 3. We perform NLTE inversions of the full Stokes vec-tor synthesised with the nicole code after adding anoise signal. In this regard, computing the Stokes pro-files, adding noise, and then inverting them, is some-thing that has been done in the past by various au-thors with photospheric (e.g. Orozco Su´arez et al. 2010;Riethm¨uller & Solanki 2019) and chromospheric (amongothers, de la Cruz Rodr´ıguez et al. 2012, 2016; Felipe et al.2018; da Silva Santos et al. 2018; Mili´c & van Noort 2018)lines (see also the reviews of del Toro Iniesta & Ruiz Cobo2016; de la Cruz Rodr´ıguez & van Noort 2017). In our case,we aim to complement those mentioned works focusing onthe advantages of inverting multiple spectral lines versus asingle chromospheric line.
We mentioned in previous publications of this series thatadding spectral lines that form at different heights and havedifferent sensitivity to the atmospheric parameters helps tounderstand the solar phenomena. This argument was basedon various studies like the spatial distribution of polarisationsignals or the response functions to changes in different at-mospheric parameters. However, we have not studied so farthe benefits of inverting the full spectrum at 850 nm versus,for instance, only fitting the Ca ii nicole distribution. In both cases, we initialisethe inversion using the HSRA (Gingerich et al. 1971) at-mosphere as a guess model with a constant magnetic fieldof 200 G, 30 degrees of inclination and azimuth, and anull microturbulence velocity. The atmospheric model con-tains 41 points in height with a constant optical depthstep of ∆ log τ = 0 . τ = [ − , ii ii τ = 0, as well as, the core of thejet with a downflow surrounded by material moving upwards(see (2.2,4) Mm) at log τ = −
2. In the case of upper layers,the multi-line inversion continues increasing the accuracy ofthe results, i.e. we recover the downflow at (2.2,4) Mm andthe upflowing region that extends towards the right side at(2.5,4.6) Mm. However, in both cases, some areas are poorlyfitted, mainly at log τ = −
2, where even the velocity sign iswrong in most of the locations outside the jet.Concerning the horizontal component of the magneticfield, we obtain wrong values for the inversions of the Ca ii ii MNRAS , 1–14 (2018) olarimetry through multi-line observations III Figure 5.
Comparison between the input atmospheric parameters, the inferred parameters from the inversion of Ca ii τ =[0,-2,-5], respectively.MNRAS , 1–14 (2018) C. Quintero Noda et al.
In the previous section, we found that inverting multiplelines shows an improvement on the inferred atmospheric pa-rameters, mainly at lower heights. However, we also men-tioned that the results were sometimes incorrect, even forthe multi-line inversions. We stated that the reason couldbe a non-optimised inversion configuration. Thus, in thissection, we aim to improve it. We focus mainly on two ele-ments. On the one hand, the weight the Stokes parameters,as well as the weight different spectral regions of the spec-trum, have on the computation of the goodness of the fit( χ ). On the other hand, the number of nodes used in theinversion process.Starting with the first part, we write below a generaldefinition (more specific expressions can be found in the re-view of del Toro Iniesta & Ruiz Cobo 2016) of the goodnessof the fit to explain the role of the weight on its computation, χ = X k =1 M X i =1 h I obsk ( λ i ) − I synk ( λ i ) i × w k ( λ i ) , (2)where the index i stands for the wavelength points while k defines the four components of the Stokes vector. The labels“obs” and “syn” refer to the observed and synthetic data,respectively. Finally, w k ( λ i ) is the mentioned weight that iswavelength and Stokes parameter dependent.Since early works on inversions assuming LTE condi-tions, for instance, Ruiz Cobo & del Toro Iniesta (1992), itis customary to use weights that are Stokes parameter de-pendent. The reason is that the signals of the polarisationprofiles are always lower than that of the intensity. Thus,when computing the χ , a relative error of the same ampli-tude in Stokes I and V , will have a weaker impact in thelatter case as its amplitude is lower. Later on, having inmind the scenarios where some part of the spectrum needsto be removed, e.g. telluric lines in ground-based observa-tions, those weights became wavelength dependent too (see nicole ’s manual). Moreover, when performing inversions ofmultiple spectral bands, one sometimes needs to weight moreone region of interest than others. This was done, for in-stance, in the recent work of da Silva Santos et al. (2018)where the continuum wavelengths observed with ALMA(Wootten & Thompson 2009) were of particular importance.In our case, we face the task of inverting together multi-ple photospheric and chromospheric lines, where wavelengthdependent weights could play an important role. For in-stance, if we have two photospheric lines that we aim toinvert simultaneously, although their intensity signals areequivalent, the polarisation signals they produce can displaydifferent amplitude. This can be due to different sensitivityto the magnetic field or the spectral properties of each line.Still, the deviations on the amplitude of those polarimetricsignals for traditional lines are in the order of a factor twoor smaller, e.g. the Fe i
630 nm or the Fe i
525 nm line pairs.However, in the case of chromospheric lines, the differencesin polarisation signals respect to those generated by photo-spheric lines could be larger than a factor 10 (see the barscale of the different panels of Figure 4). That large ampli-tude disparity inevitably reduces the impact they have onthe computation of the χ . That is, an error in the fit of theCa ii Figure 6.
Wavelength dependent weights used for the inversionof the Stokes profiles. We use three different configurations, i.e.same weight for all the spectrum (not included here), larger weightfor chromospheric lines (top), and more weight for the line corewavelengths of chromospheric lines than the wings (bottom). Inthe two cases presented here, the photospheric Fe i lines at 8468and 8514 ˚A are weighted more than the rest of the spectrum. lower than that of the Fe i g eff =2.5) signals whensetting the same weight for both spectral lines. Therefore,when inverting two extreme cases like those represented bythe two mentioned spectral lines one must be sure that theirimpact on the computation of the goodness of the fit is prop-erly balanced.In this section, we perform a study to verify the impor-tance of the wavelength dependent weights on the inversionresults. We choose different sets of weights, and we run theinversion process with the same configuration used in theprevious section. The target is to estimate what could bea reasonable configuration for future instruments that ob-serve the 850 nm window or similar multi-line observationsthat combine photospheric and chromospheric lines. In thisregard, we use three sets of wavelength-dependent weights.In all cases, the weight ratio among Stokes parameters isthe same where we put more weight on the Stokes param-eters that show weaker polarisation signals, i.e. (1, 50, 50,10) for ( I , Q , U , V ), respectively. The first wavelength de-pendent weight configuration is the default of the code, i.e.identical weight for all the wavelengths (the same that weused in the previous section). The second and third weightconfigurations we use are presented in Figure 6. The formerprovides larger values for the entire spectra covered by thechromospheric lines (250 times larger than the continuum),including the wings and the photospheric lines blended with MNRAS , 1–14 (2018) olarimetry through multi-line observations III Figure 7.
Inversion results for different weight configurations. From left to right, input atmosphere and the inferred physical parametersusing the weights setting 1, 2, and 3, respectively. From top to bottom, the horizontal and vertical component of the magnetic field atlog τ = [0 , − , − them. The latter configuration gives 250 times more weightto the line core wavelengths and 50 times more weight to thespectral wings than the continuum. Moreover, in both cases,we weight 10 times more the Fe i lines at 8468 and 8514 ˚Abe-cause they are the most sensitive ones to the magnetic fieldat the photosphere.We present the results of this comparison in Figure 7.We focus only on the horizontal and vertical component ofthe magnetic field at different heights to simplify the visu- alisation. We can see that the first configuration producesincorrect results in general for both magnetic field compo-nents (second column from the left). In the case of the secondconfiguration (third column from the left), there is an im-provement in all layers and for both components of the mag-netic field. Finally, with the third configuration (rightmostcolumn) we obtain accurate results in higher layers althoughlower heights show a worse match than that obtained withthe second configuration of weights. Moreover, this same be- MNRAS , 1–14 (2018) C. Quintero Noda et al.
Figure 8.
Comparison between the input atmospheric parameters and those obtained from the inversion of the spectral lines at the850 nm window using the weight configuration number 2. We plot one after the other, from top to bottom, at log τ = [0 , − , − haviour is reproduced by the LOS velocity results (not shownhere) where the second configuration is the one that yieldsbetter results at all atmospheric layers. Therefore, we pickthe second configuration to test our capabilities to extractthe physical information of the simulated atmosphere fromnoisy polarimetric spectra.We mentioned at the beginning of this section that wealso study the impact the number of nodes has on the inver- sion results. In this regard, starting with the configurationof weights number 2 we examined different combinationsof nodes for different atmospheric parameters. However, wedid not find a noticeable improvement from the results ob-tained with the current setup. Therefore, we opt to use thecurrent one as best option to study our capabilities for un-derstanding the physics of the present simulation, and we MNRAS , 1–14 (2018) olarimetry through multi-line observations III Figure 9.
Comparison between the input (black) and the inferred (colour) atmosphere for two selected pixels. From left to right, weshow the temperature, LOS velocity, the horizontal and vertical component of the magnetic field. Top row corresponds to a pixel closeto the “A” labelled region while the bottom pixel belongs to the area labelled as “B” in Figure 3. Dotted lines designate the heights usedin the comparison presented in Figure 8, i.e. log τ = [0 , − , − leave that comparison results outside to reduce the contentof this work.We repeat the inversion done with the second weightconfiguration and the same number of nodes but increas-ing the number of random inversions up to 10. The aimis to slightly reduce the characteristic salt-and-pepper pat-tern that sometimes appears on the inversion results (seein Figure 7, for instance, the inferred longitudinal field atlog τ = − stic (de la Cruz Rodr´ıguez et al. 2018).Figure 8 shows the comparison between the input atmo-sphere and that inferred with nicole using the “optimised”inversion configuration. We can see again that the temper-ature results at lower layers are very similar to the originalones. At higher atmospheric layers, we still have some dis-crepancies in the coldest areas, although the code matchessome of them this time. We are not entirely sure about thereasons for these differences, but we try to explain themin the discussion section. Regarding the LOS velocities, thespatial distribution resembles (better than in the first re-sults shown in Figure 5) that of the input atmosphere at allheights. However, we are not able to achieve a good accuracyat log τ = −
2, mainly outside the core of the chromosphericjet, something that we do not understand either. We guessthat a computation of the RF in those areas could revealmore information, but we leave that for future studies. Inthe case of the horizontal component of the magnetic field,we also detect an improvement with respect to previous in-versions and a similar spatial distribution to the input one.Finally, concerning the longitudinal magnetic field, we haveexcellent results, even at the highest layers where the weak,in order of 50 G, opposite polarity field (label B) is wellreproduced as well as the core of the jet (label A).
Based on the results presented in Figure 8 we can say thatthe inferred parameters match in general the input atmo-sphere at the selected heights. Those heights were chosenbased on previous studies on the RF to changes in the phys-ical parameters for the lines of interest using the FALC at-mosphere. In particular, the continuum and “weak”, in termsof low-intensity depression, spectral lines show a peak atbottom layers close to log τ = 0. The core of stronger pho-tospheric lines shows the same peak in the RF at aroundlog τ = −
2, while the core of the Ca ii τ = −
5. It is important tobear in mind that, as the RF depend on the atmosphericmodel used, the mentioned results do not necessarily satisfythe present case. However, we assumed that the said layerscould be a good reference point for this work. This raises thequestion of whether we can reproduce the small scale vari-ations of the simulated atmosphere as well. In other words,if we choose a different set of optical depths, would we finda good correlation too?The answer to this question is no, and for illustratingpurposes, we plot in Figure 9 the vertical stratification ofthe atmospheric parameters for two selected pixels. Thosepixels are located close to the areas labelled as A and B,respectively, and they show good results for the longitudi-nal field at log τ = −
5. If we examine the inferred atmo-spheres (colour), we find that the inversion is not able toreproduce the steep variations that take place in the simula-tion at short height scales. However, it follows the tendencyconcerning gradients, absolute value and sign of the atmo-spheric parameters. Most importantly, when examining theregions highlighted with dotted lines (the same heights usedin Figure 8), we can see that there is where the code usuallygets closer to the original atmosphere. Hence the reason why
MNRAS , 1–14 (2018) C. Quintero Noda et al. we obtained a good agreement in previous sections. We be-lieve that the cause for this behaviour is that the RF of thewhole set of spectral lines is large at those optical depths. Inother words, when analysing future observations of this setof spectral lines (or a similar combination), we can representthe results at discrete layers like the ones used here. Also,we could even believe the general properties, concerning gra-dients, absolute values, and the sign of the atmospheric pa-rameters at heights in between those layers.
We ascertained that the coldest regions in the upper layersare systematically hotter in the inversion results. If we re-visit the work of de la Cruz Rodr´ıguez et al. (2012), we canfind a similar problem where the inferred temperatures areconsistently lower at higher layers. They explained that thisis because the synthesis was done assuming 3D with multi (Carlsson 1986; Leenaarts & Carlsson 2009) while the in-version was performed in 1D with nicole . However, in ourcase, we cannot use the same argument as we did both theforward modelling and the inversion with nicole . Thus, weshould look for additional explanations.One option could be that, as the temperature in thesimulation at chromospheric layers is low, the Ca ii lines,the ones that form at those heights, are not sensitive to thesmall temperature variations we see in the plots. To verifythis assumption, we show in Figure 10 the temperature atlog τ = − . ii I c , at around (2,4) Mm that indeed resemblethe input atmosphere. At the same time, there are enhancedpatches at (1.5,4) and (2.5,3.7) Mm that do not correspondto any hot feature in the simulation. Moreover, those en-hanced areas are reproduced in the recovered temperaturestratification (see Figure 8). Therefore, this leads us to adifferent possibility; the line core intensity and consequentlythe inferred temperature that fits it, could correspond to agiven range of optical depth layers instead of a single height.Thus, if we average the temperature, for instance betweenlog τ = [ − . , − .
8] we should find a similar pattern betweenthe averaged input and inferred atmospheres. We displaythis comparison in Figure 11 where we can see that indeed,the temperature spatial distribution is similar, both showingthe enhancements found in the line core intensity. It is truethat the central part still shows cool areas, something thatit is barely perceptible in the inversion results, so we shouldcontinue investigating the reason of the lack of accuracy forthe inferred temperature at higher layers. One option thatwe want to test in the future is to manually increase thedensity of nodes, for instance, between log τ = [ − . , − . Figure 10.
Comparison between the input temperature from thesimulation (top) and the line core intensity for the Ca ii mospheric parameters at selected optical depth layers wherethe RF have a significant value. We examined the properties of the simulation presented inIijima & Yokoyama (2017) that contains a chromospheric jetthat, in its emerging phase, extends several Mm above thesolar surface. At the low atmosphere, the temperature at thecore of the structure is higher than its surroundings, and itis dominated by downward velocities, while outer areas arecolder and display upward motions. Regarding the magneticfield, the core of the structure shows a strong longitudinalcomponent of positive sign encompassed by horizontal fieldsand a weaker longitudinal field of opposite polarity.The next step we took was to examine the syntheticStokes profiles. The amplitude of linear polarisation sig-nals for chromospheric lines is around 1 × − of I c whileten times more significant for the case of circular polarisa-tion signals. The latter means that with average integrationtimes, assuming diffraction limit, modern telescopes shouldbe able to achieve those signals. The twist of the jet governsthe magnetic field azimuth derived from the linear polarisa-tion signals with field lines that move away from the core ofthe structure, arching and bending around it. In the case ofthe circular polarisation signals, they are strong in the cen-tral part of the magnetic feature and show rounded shapessimilar to that of the simulated longitudinal magnetic com-ponent. MNRAS , 1–14 (2018) olarimetry through multi-line observations III Figure 11.
Comparison between the input atmosphere (top) andthe one inferred from the inversions (bottom) when averaging overthe optical depth range comprehended by log τ = [ − . , − . We took a step further, and we employed the inversioncode nicole aiming to comprehend the diagnostic potentialof the 850 nm window for inferring the atmospheric infor-mation of the chromospheric jet through NLTE inversions.We started with a simple study to corroborate that the in-version of multiple spectral lines with different height of for-mation provides better results than when fitting a singlespectral line. We, thus, inverted the synthetic Ca ii ii χ , the latterhave an impact in the order of 10 or 100 times lower than theformer for the polarisation Stokes parameters. Also, this isindependent of where the lines form, and where their max-imum sensitivity lies. Therefore, we tested this hypothesis with different wavelength dependent weight configurationswhere chromospheric lines were weighted more than the restof spectral lines. The results revealed that there is an im-provement in all the inferred atmospheric parameters lead-ing to a better resemblance to the input atmosphere.We conclude then that multi-line inversions benefit fromthe predicted increase of sensitivity and height coverage ofthe RF mentioned in previous works of this series. But theuser should be aware that the computation of the χ requiresadditional fine-tuning not needed when performing singleline inversions. Hence the possibility of choosing wavelengthdependent weights in the modern NLTE codes like nicole , snapi or stic . Besides that, we can close this work sayingthat the Ca ii ACKNOWLEDGEMENTS
C. Quintero Noda acknowledges the support of theISAS/JAXA International Top Young Fellowship (ITYF)and the JSPS KAKENHI Grant Number 18K13596.H. Iijima is supported by MEXT/JSPS KAKENHI GrantNumber JP15H05816. This work was supported by the fund-ing for the international collaboration mission (SUNRISE-3) of ISAS/JAXA and the JSPS KAKENHI Grant Number18H03723 and 18H05234, and by the Research Council ofNorway through its Centres of Excellence scheme, projectnumber 262622. J. de la Cruz Rodr´ıguez is supported bygrants from the Swedish Research Council (2015-03994), theSwedish National Space Board (128/15) and the SwedishCivil Contingencies Agency (MSB). This project has re-ceived funding from the European Research Council (ERC)under the European Union’s Horizon 2020 research and in-novation programme (SUNMAG, grant agreement 759548).This work has also been supported by Spanish Ministry ofEconomy and Competitiveness through the project ESP-2016-77548-C5-1-R. D. Orozco Su´arez also acknowledges fi-nancial support through the Ram´on y Cajal fellowships.
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