Spectral Characteristics of the He I D3 Line in a Quiescent Prominence Observed by THEMIS
J. Koza J. Rybák P. Gömöry M. Kozák A. López Ariste
astro-ph.SR


  

    

     addressref=aff1, corref, email=koza@astro.sk ]J.Július Koza0000-0002-7444-7046
    
     addressref=aff1 ]J.Ján Rybák0000-0003-3128-8396
     addressref=aff1 ]P.Peter Gömöry0000-0002-0473-4103
     addressref=aff1 ]M.Matúš Kozák
     addressref=aff2,aff3 ]A.Arturo López Ariste

    
    
    
    J. Koza et al.
    Spectral Characteristics of  in a Quiescent Prominence

    
    
    
    [id=aff1]Astronomical Institute, Slovak Academy of Sciences, Tatranská Lomnica, Slovakia
    [id=aff2]Université de Toulouse, UPS-OMP, Institut de Recherche en Astrophysique et Planétologie, Toulouse, France
    [id=aff3]CNRS, Institut de Recherche en Astrophysique et Planétologie, 14 Avenue Edouard Belin, F-31400 Toulouse, France
    
    
    
      
      We analyze the observations of a quiescent prominence acquired
      by the Téléscope Heliographique pour l'Étude du
        Magnetisme et des Instabilités Solaires (THEMIS) in the
      He i 5876 Å () multiplet aiming to measure the
      spectral characteristics of the  profiles and to find for
      them an adequate fitting model.
      
The component characteristics of the
 Stokes I profiles
      are measured by the fitting system approximating them with a
      double Gaussian.
      
      This model yields an  component peak intensity ratio of
      5.5±0.4, which differs from the value of 8 expected in the
      optically thin limit. Most of the measured Doppler velocities
      lie in the interval ±5 , with a standard deviation of
      ±1.7  around the peak value of 0.4 . The wide
      distribution of the full-width at half maximum has two maxima at
      0.25 Å and 0.30 Å for the  blue component and two
      maxima at 0.22 Å and 0.31 Å for the red
      component. The width ratio of the components is
      1.04±0.18. We show that the double-Gaussian model
      systematically underestimates the blue wing intensities. To
      solve this problem, we invoke a two-temperature multi-Gaussian
      model, consisting of two double-Gaussians, which provides a
      better representation of  that is free of the wing
      intensity deficit. This model suggests temperatures of 11.5 kK
      and 91 kK, respectively, for the cool and the hot component of
      the target prominence. The cool and hot components of a typical
       profile have component peak intensity ratios of 6.6 and 8,
      implying a prominence geometrical width of 17 Mm and an optical
      thickness of 0.3 for the cool component, while the optical
      thickness of the hot component is negligible.
      
      These prominence parameters seem to be realistic, suggesting the
      physical adequacy of the multi-Gaussian model with important
      implications for interpreting  spectropolarimetry by
      current inversion codes.

    
    
    
    
    

  
  

  

§ INTRODUCTION


  

  The He i multiplet at 5876 Å, called the D3 line
  (hereafter ), is one of the prime diagnostics used in
  ground-based observations of solar prominences
  <cit.>. The multiplet consists of six
  transitions. In current solar spectropolarimetric observations, a
  combined emission of five transitions is resolved as its stronger
  blue component, while the sixth transition makes the weaker red
  component. Their spectral separation is 343.3 mÅ, giving the line
  its characteristic double-lobed profile. In the limiting case of
  negligible optical thickness in both components and the natural
  excitation of the triplet 3 ^3D term, the blue-to-red ratio of
  the component peak intensities is 8:1
  <cit.>.

  

  The optical thinness of prominence plasma in  has been
  documented convincingly by i) the semi-empirical modeling of
   profiles
  <cit.>, ii) the
  non-LTE radiative modeling of
   <cit.>,
  and iii) the obvious observational fact of the on-disk transparency
  of filaments in . The non-local thermal equilibrium (non-LTE) 2D
  multi-thread modeling by <cit.> and
  <cit.> showed that under realistic conditions
  the prominence plasma never becomes optically thick for
  . Remarkably, these studies also showed that an optically thin
  structure, composed of several optically thin threads, emits the
   profiles with component peak intensity ratios lower than
  8. (We recommend a reader of <cit.> to change
  their Figure 9 for Figure 7.21 in <cit.>.) This
  compatibility of the optical thinness with the ratio of lower than 8
  settles down earlier indications of non-negligible plasma optical
  thickness in  expressed in
  <cit.>;
  and <cit.> in the context of the observed ratios
  ranging from 6 to 7.6.
  
  

  The  emission has been used mainly in spectropolarimetry of
  prominences aiming to measure prominence magnetic fields. The
  pioneering work in this field by <cit.>
  was later followed by the series of studies by J. L. Leroy,
  V. Bommier, and S. Sahal-Bréchot <cit.>. The
  successful measurements made by these authors confirmed that the
  magnetic fields are essentially horizontal and twisted, with average
  field strengths of 10 – 20 G. Horizontal fields were detected in
  the majority of nearly 200 prominences observed from 2012 to 2015
  <cit.>. However, this study reported non-horizontal
  fields in a jet-like structure in an eruptive prominence, with
  inclinations tilted to 50 from the vertical. A recent
  multi-instrumental study involving  by <cit.>
  reported finding a horizontal magnetic field in the legs of a
  tornado-like prominence. <cit.> also found mostly
  horizontal magnetic fields by  in a prominence pillar showing
  signatures of magnetosonic waves propagating transverse to the
  magnetic field with a velocity of about 10 , a period of about
  300 s, and a wavelength of around 2 000 km. The low
  signal-to-noise ratio of the  polarization signatures was
  interpreted in <cit.> as a possible manifestation
  of a turbulent field superimposed on the macroscopic horizontal
  component of the prominence magnetic field. The results of these
  recent studies made use of  spectropolarimetry obtained by the
  Téléscope Heliographique pour l'Étude du Magnetisme
    et des Instabilités Solaires (THEMIS) solar telescope.

  

  Current models of prominences or filaments present them as
  aggregates of thin threads that are weakly or highly twisted into
  flux ropes with the effective volume-filling factor of radiating
  threads on the order of 10^-1-10^-3
  <cit.>. These models stem from
  high-resolution observations showing their fine-thread and knotty
  composition with thread widths down to the resolution limit of
  ≈150 km
  <cit.>. A
  significant advance in modeling the fine structure of prominences
  and filaments has been achieved in the studies by
  <cit.>, which for the first time
  present the whole-prominence and filament fine-structure model and
  their synthetic  images in 3D. This study even presented the
  temporal evolution of prominences and filaments in response to
  changes in the underlying photospheric magnetic flux distribution,
  and it visualized their  appearance as it evolved in time. In an
  earlier study, <cit.> statistically tested the 2D
  multi-thread model of a quiescent prominence comparing the
  integrated intensity, the full-width at half maximum (hereafter FWHM
  or just the width), and the Doppler velocity of the observed and
  synthetic  profiles computed by the model. Of course, upcoming
  or future radiative transfer codes <cit.> and
  multi-thread models of prominences or filaments should allow the
  comparison of observed and synthetic  Stokes
  profiles. <cit.> and <cit.> have
  presented the results of 2D non-LTE modeling of the  line
  taking the atomic fine structure of helium into account.

  

  The aims of this study are twofold: first, to produce solid
  statistics of spectral characteristics of the blue and red component
  of  in a form that allows comparisons with future
   modeling in the fashion applied in <cit.> for
  ; second, to suggest an adequate fitting model for the
   Stokes I profile in accord with contemporary views on
  prominence thermodynamic structure. The definition of these aims is
  motivated by a lack of pertinent studies.

  

§ OBSERVATIONS
  

  A tree-like quiescent prominence occurring on 2 August 2014 at the
  east solar limb at the position angle of
  117 (Figure <ref>) was selected as a target for the
  double-beam spectropolarimetry in the  line by THEMIS operated
  in the MulTi Raies mode at Observatorio del Teide
  <cit.>. The prominence area in the plane of the
  sky, measured in the  broad-band image (Figure <ref>) taken
  at the Kanzelhöhe Solar Observatory
  <cit.>, is 1483 Mm^2. After subtracting
  the off-limb aureole that is due to the scattered photospheric
  light, the prominence relative intensity in the KSO 0.7 Å-wide
   Lyot filter with respect to the disk center is within the range
  from 7% to 27% with a median of 17%, corresponding to a
  radiance of 1.0 W cm^-2 sr^-1, and the prominence
   radiant intensity is about 3.9×10^22 W sr^-1.

  
  
  

  

 §.§ THEMIS Spectropolarimetry

    

  The slit of the THEMIS spectrograph was opened to one arcsecond and
  placed parallel to the limb. The setup involved the Semel mask, i.e. a grid mask with three rectangular windows placed at the F1
  focus of the telescope before the polarization analyzer
  <cit.>. A rationale for its use and
  the necessity of 2D scanning in directions parallel (X) and
  perpendicular (Y) to the slit were clarified in
  <cit.> and
  <cit.>. The 2D scanning of the target prominence
  started close to the limb at 14:59:02 UT and progressed radially
  away from the limb untill about 17:00 UT. It involved one step in
  the X direction with the size of 15 arcsec followed by a step
  in the Y direction. In total, 25 steps separated by 2 arcsec
  were ordered in the Y direction. This provided a field of view
  of 88 arcsec × 50 arcsec, and the top left panel of
  Figure <ref> shows the effective cutout covering the whole
  target prominence. The axes keep the (X, Y) orientation
  defined above. Unlike Figure <ref>, in Figures <ref>,
  <ref>, <ref>, and <ref>, the solar disk and the
  target prominence are rotated about 117 clockwise (the THEMIS
  images; the image provided by the Global Oscillation Network
    Group  network monitor, operated by the National Solar
    Observatory (NSO/GONG); and the images taken by the Atmospheric Imaging Assembly onboard the Solar Dynamic
    Observatory (SDO/AIA)) or counterclockwise (the images taken by
  the Solar TErrestrial RElations Observatory B (STEREO B)) but
  keeping the same heliocentric coordinate system as in
  Figure <ref>. The STEREO B images were then flipped over
  around the Y axis. The white contour in the top left panel of
  Figure <ref> outlines the prominence mask defined in
  Section <ref>.

  One particular THEMIS spectrum at a given slit position is taken
  with the exposure time of 2 s, and overall, the observing procedure
  is the same as in <cit.> and
  <cit.>. We emphasize that in our
  case a modulation cycle of six images, spanning the three
  polarization states with either positive or negative signs, is
  repeated ten times to increase the signal-to-noise ratio. Therefore
  the 2D scanning lasts two hours.  A typical acquisition time of four
  Stokes parameters at one slit position is 144 s, which includes the
  switch time of retarders and a dead time of the system duty cycle.

  

  The spatial and spectral sampling of the obtained spectra is
  0.227 arcsec px^-1 and 11.6 mÅ px^-1,
  respectively. The latter value is determined by the photospheric
  lines  5873.218 Å and  5877.797 Å that are seen in
  the spectra in the scattered photospheric light in the background
  (Figure <ref>). The dispersion of 11.6 mÅ px^-1 is
  used in calculating the spectral characteristics presented in
  Section <ref> and in Figures <ref> – <ref>.

  

  Comparing the average  line profiles with their counterparts
  extracted from the spectral atlas of solar disk-center intensity
  <cit.> and convolved with a Gaussian, we estimate the
  instrumental smearing of the THEMIS spectra. We find that the
  smearing profile can be approximated by a Gaussian with FWHM =
  71 mÅ.

  
  
  

  
  
  

  

 §.§ Morphology, Dynamics, and Evolution of the Target Prominence


  To place the THEMIS observations in context, we make use of data
  provided by NSO/GONG <cit.>, SDO/AIA
  <cit.>, and the Extreme
    Ultraviolet Imager (EUVI), which is a part of the Sun-Earth
    Connection Coronal and Heliospheric Investigation (SECCHI)
  instrument suite onboard the STEREO B spacecraft
  <cit.>. Figure <ref>
  and the movie available in the online edition show the
  slit-reconstructed map of the  peak intensity of the target
  prominence coaligned with the context images taken in the broad-band
   filter of the NSO/GONG monitor at Observatorio del Teide and in
  the AIA  and  passbands during the THEMIS scanning
  overlaid with selected  peak intensity contours (yellow) and
  the  intensity contour (red). The coalignment of the  peak
  intensity image and the  image is approximate relying on
  morphological similarity. The coalignment of the  and AIA images
  is exact; it takes advantage of full-disk images and availability of
  all necessary data. The X-axis represents the position along
  the slit of the THEMIS spectrograph, and the Y-axis
  corresponds to the radial scanning direction. To highlight the
  structure of the target prominence, the top left panel shows a
  smaller field of view than the other panels. The  image
  suggests that the tree-like prominence consists of a central
  vertical pillar spreading out with height on both sides. The
  appearance of the prominence in  (top right panel) corresponds
  to the  peak intensity contours. The middle right panel shows
  the prominence in the AIA  passband as a dark structure
  against the bright background, absorbing the background coronal
  emission. Its “silhouette” agrees approximately with the shapes
  outlined by the  and  contours. However, the prominence
  appears very differently in the AIA  passband, which is shown
  in the middle left panel. It clearly illustrates the large areal
  extent and the horizontal arcades that stretch to the right, which
  are not visible in the previous panels.

  

  Quiescent prominences are often characterized as sheets of plasma
  standing vertically above the polarity inversion line and showing
  fine horizontal or vertical threads <cit.>.
  The attained spatial resolution in the THEMIS and the NSO/GONG
   observations prevents us from resolving any prominence fine
  structures. However, we do see signatures of strands in the AIA
   and particularly in the  images. The bottom panels of
  the movie display plasma flows along the arcades, stretching to the
  right, that are generally parallel to the solar limb, similar to
  those described in <cit.> and
  <cit.>. On the other side of the prominence
  body, one can see clumps of plasma flowing mostly toward the limb
  only in the AIA  passband.

  

  To gain a comprehensive picture of the target prominence, we also
  inspect images taken by the STEREO A and B spacecraft on 2 August
  2014 from 15:00 UT to 17:00 UT. While for STEREO A the prominence
  is invisible beyond the limb, the STEREO B images show it clearly
  at the west limb in all four passbands of the SECCHI/EUVI
  imager. Since the separation angle of the spacecraft with Earth is
  162, the SECCHI/EUVI  and  images of the
  prominence in the bottom panels of Figure <ref> provide almost
  rear views of its dark central pillar and arcades stretching to the
  right, resembling its AIA  counterpart in the middle left
  panel. Different positions of the photospheric limbs in the SDO/AIA
  and STEREO B images are due to different solar disk diameters as
  seen from the vantage points of the spacecraft at heliocentric
  distances of about 1.015 AU and 1.003 AU, respectively.

  

  The post-observation NSO/GONG  image from 3 August 2014 in the
  left panel of Figure <ref> shows that the prominence is still
  bright with a long and prominent arcade. The arrow in the NSO/GONG
  image from the following day (right panel) identifies its probable
  on-disk filamentary counterpart, which occupies a quiet-Sun area far
  from active regions. The SDO/HMI magnetogram (not shown here)
  suggests only an enhanced network in that area. Therefore, we
  classify the prominence as of quiescent type. It seems to be an
  isolated segment of the filament stretching diagonally from the
  lower right corner of the image. On that day, the marked structure
  disappears quickly.

  

§ DATA REDUCTION
 
  

  

  The primary reduction is the same as applied in
  <cit.> and
  <cit.>, and it involves data from all
  ten modulation cycles. The raw THEMIS spectra are reduced using the
  IDL package DeepStokes, whose main characteristics are outlined in
  <cit.>. The data reduction includes geometry
  corrections of inclination and curvature of spectral lines, dark
  current and bias subtraction, flat-field correction, and a careful
  handling of the polarization signals. Since the reduction yields
  Stokes Q, U, V profiles with very small amplitudes, typically
  0.2 – 0.4% of the Stokes I peak intensity, we repeat the
  reduction taking data only from five modulation cycles as in
  <cit.> and
  <cit.>, but without
  improvement. Therefore, we aim the analysis only at the Stokes I profiles. To eliminate the large temporal smearing, we repeat
  the DeepStokes reduction again, but taking data at each slit position
  only from the fifth, i.e. only one modulation cycle, lasting
  about 14 s. Figure <ref> shows an example of the one-cycle
  Stokes I spectra.

  
  
  

  
  
  To extract only prominence-relevant data, we construct the
  prominence mask as a vector of pixel subscripts with the Stokes I peak intensity I_ max greater than or equal to the ad-hoc threshold value 0.2I_ gmax, where I_ gmax is
  the global maximum of the peak intensity over the whole
  prominence. The condition I_ max≥ 0.2I_ gmax is
  fulfilled at the 2983 pixel positions defined in the top left panel
  of Figure <ref> by the white contour representing the
  prominence in Figures <ref> and <ref>. The data gaps due
  to the Semel mask (Figure <ref>) are filled in by linear
  interpolation.

  

§ DOUBLE-GAUSSIAN FIT

          

  

  Prominence models are often constructed and validated by comparing
  spectral characteristics of observed and synthetic line profiles
  <cit.>. The study
  by <cit.> made use of this approach in modeling the
  fine structure of a quiescent prominence by statistically comparing
  the Doppler velocity, the integrated intensity, and the FWHM of
  observed and synthetic  line profiles computed for an array of
  multi-thread prominence models. To provide solid statistics of
  spectral characteristics for the  Stokes I profiles, we
  perform a double-Gaussian fitting of their double-lobe structure
  resolved in the THEMIS spectra (Figure <ref>). The background
  intensity is approximated by a linear fit. The choice of this
  conservative fitting model is justified by the studies of, e.g., <cit.> and
  <cit.>, who claimed that the double Gaussian
  is an adequate representation of the  double-lobed profile.

  
  
  

  

  For the background and double-Gaussian fitting we use the SolarSoft
  function  calling the engine 
  <cit.>. The latter performs
  Levenberg-Marquardt least-squares minimization of the sum of the
  weighted squared differences between the data I_i (i = 1 … N)
  and the user-supplied model function F_i. The relevant merit
  function is defined as χ^2 = 1/ N∑_i=1^
    N(I_i - F_i)^2/σ_i^2, where the weights σ_i
  represent one-sigma uncertainties of the data. Assuming Poisson
  statistics for propagation of the uncertainties, we estimate these
  as the standard deviation of the background intensity variations
  σ_ back outside the spectral lines and rescale them
  using the formula σ_i = σ_ back√(I_i / <
    I_ back>), where σ_i and I_i are the
  uncertainty and intensity at the particular wavelength and <
  I_ back> is the average background intensity outside
  the lines. The definition of the merit function implies that the
  χ^2 values of good fits are about one, meaning that the model
  is within the one-sigma uncertainties of the data.

  

  We approximate the observed  Stokes I profiles with a
  model of two Gaussians superimposed on the first-order polynomial
  representing the background intensity. The model has seven free
  parameters: the peak intensities I_ blue,  red, the
  FWHM_ blue,  red, the spectral position of the blue
  component peak λ_ blue, and the two coefficients of the
  polynomial. The spectral position of the red component peak is tied
  to λ_ blue as λ_ red = λ_ blue +
  343.3 mÅ. This coupling is kept in all models discussed
  below. We also check a six-parameter model with equal widths of the
  components. This model yields component peak intensity ratios that
  are different from the optically thin limit, suggesting radiative
  transfer effects. Therefore, we decide not to tie the widths and to
  adopt the seven-parameter model with the red component width as a
  free parameter.

  

  Figure <ref> shows an example of the fit of a typical profile
  and an average of all 2983 profile fits in the top left and right
  panels, respectively. The corresponding fit parameters are listed in
  columns 1 and 2 of Table <ref>. The bottom subpanels display
  the best-fit residuals (I_i - F_i)/σ_i, normalized by the
  uncertainties of observations σ_i. They show that the
  residuals of typical fits are mostly within the 1σ span. The
  largest residuals of about 3σ occur at Δλ≈
  -0.35 Å, suggesting a systematic excess of the observed blue
  wing intensities over the Gaussian wing profile. We refer to this
  feature in the following as the blue wing excess.
  
  

§ RESULTS OF THE DOUBLE-GAUSSIAN FITTING

  

  

  Figure <ref> shows maps and histograms of χ^2 values and
  spectral characteristics of the observed double-lobed Stokes I
  profiles inferred by the double-Gaussian fitting of the one-cycle
  Stokes I profiles. The χ^2 distribution in the top left
  subpanel has a maximum and median at 1.2 and 1.8, respectively. Most
  of the measured Doppler velocities lie in the interval
  ±5 , and their distribution shows a redshifted median and
  peak at 0.3  and 0.4±1.7 , respectively. The latter
  value and its standard deviation result from the Gaussian fit of the
  distribution. An average of all 2983 pixel positions of blue
  component maxima is taken as a reference for the Doppler velocity.

  

  The bottom panels of Figure <ref> show maps of spatial
  distributions and histograms of the widths of the blue and red
  components. The maps of FWHM_ blue and FWHM_ red
  suggest a frequent occurrence of narrow profiles with component
  widths smaller than 0.3 Å in a compact area in the center of the
  upper part of the prominence body at (X, Y) ≈ (-55,
  980) arcsec. The area coincides approximately with a large island
  of redshifts in the velocity map. The FWHM_ blue histogram
  has not one global maximum, but suggests a double-peaked
  distribution with two local maxima at 0.25 Å and
  0.30 Å. Similarly, the distribution of FWHM_ red has a
  prominent peak at 0.22 Å and a second peak at 0.31 Å. The
  medians of the FWHM_ blue and FWHM_ red histograms are
  at 0.31 Å and 0.29 Å, respectively. A comparison of the two
  histograms suggests an excess of red components narrower than
  0.23 Å and broader than 0.48 Å compared with the blue
  components.

  

  An indicator of the plasma optical thickness in  is the ratio
  of peak intensities and widths of the  double-lobed profile
  <cit.>. The distribution of the peak intensity ratios in
  the lower left subpanel of Figure <ref> has a median and peak
  at 5.4 and 5.5±0.4, respectively.  The latter value and its
  standard deviation result from the Gaussian fit of the distribution,
  which shows an excess of profiles with lower ratios down to 2. The
  distribution of the width ratios in the lower right subpanel has a
  median and peak at 1.03 and 1.04±0.18.
  
  

  We emphasize that the typical observed profile and its fit in the
  left panel of Figure <ref> are chosen to be representative in
  the sense of typical values of χ^2 = 1.72, a blue component
  width of 0.31 Å, and a component peak intensity ratio of
  5.5 (see also the corresponding entries in Tables <ref> and
  <ref>).

  

  Figure <ref> presents pixel-by-pixel comparisons of the blue
  component peak intensities I_ blue with the peak intensity
  ratios (left panel) and the width ratios (right panel) in the form
  of scatter plots supplementing the histograms in
  Figure <ref>. The plots suggest that while the weak profiles
  show a broad range of ratios, the strong profiles with high peak
  intensities I_ blue have peak intensity ratios and width
  ratios of about 5.5±0.4 and 1.04±0.18, respectively. These
  are indicated by the red vertical lines. The shape of the scatter
  plots also suggests that the values 5.5±0.4 and 1.04±0.18
  inferred from the histograms in Figure <ref> are representative
  of weak as well as strong profiles.

  
  
  

  
  
  

  
  
  

  

 §.§ Effects of Temporal and Instrumental Smearing

   

  

  To examine the effect of temporal smearing on the spectral
  characteristics of the target prominence, we calculate them using
  the ten-cycle Stokes I profiles with an effective integration
  time of 144 s. Since this trial yields the same results as those
  presented in Figures <ref> and <ref>, we conclude that the
  dynamics of the target quiescent prominence evolves on a timescale
  longer than two minutes at spatial scales larger than 2 arcsec.

  

  The  profiles analyzed in this section are the convolutions of
  the original emission profiles with the instrumental profile of the
  THEMIS spectrograph, which can be approximated by a Gaussian with
  FWHM = 71 mÅ (see Section <ref>). How much does this
  instrumental smearing bias the results? Could the smearing be
  responsible for the blue wing excess? To answer these questions, we
  deconvolve the typical  profile shown in the left panel of
  Figure <ref> by applying the optimum filter
  <cit.>. The deconvolved  profile is shown
  in the left panel of Figure <ref> by the gray circles, and its
  fit is plotted with the black line. We apply the seven-parameter
  double-Gaussian model in fitting the deconvolved profile. Columns 1
  and 3 of Table <ref> compare the characteristics of the typical
  instrumentally smeared profile with the deconvolved
  profile. Apparently, the instrumental smearing may bias the results
  only insignificantly. Since the optimum filter removes noise, the
  bottom left subpanel of Figure <ref> shows the differences
  Δ I=100(I_i - F_i)/I_i, where I_i represents the
  deconvolved data and F_i is the model function. The left subpanel
  of Figure <ref> demonstrates that the blue wing excess persists
  even after deconvolving the typical profile, because the difference
  Δ I at Δλ≈ -0.33 Å is
  3.3%. Therefore we conclude that the blue wing excess is not due to
  the instrumental smearing. This might suggest inadequacy of the
  double-Gaussian model in representing the typical  profiles
  emitted by the target prominence.

  

§ ALTERNATIVE FITTING MODELS


  In this study we adopt the double-Gaussian fitting model of the
   profiles. An indicator that the fitting model is inadequate is
  not only the value of χ^2, but also the shape of residuals. If
  a model represents data correctly, then the residuals or differences
  Δ I should be featureless with no systematic structure other
  than random excursions reflecting the noise variations. However, the
  residuals in Figure <ref> and differences in the left subpanel
  of Figure <ref> are not featureless, because they show
  quasi-periodic variations, which are particularly apparent in the
  blue wing of the blue component at Δλ≈
  -0.35 Å. This may indicate an inadequacy of the adopted
  seven-parameter double-Gaussian model. The blue wing excess is also
  apparent in the  Stokes I profiles shown in
  <cit.>;
  and <cit.>. Therefore, in the following
  we examine alternative  fitting models with the aim to propose
  a new model that appears to be characterized by small and
  featureless differences Δ I and negligible blue wing excess
  as well.

  
  
  

  

 §.§ Double-Lorentzian Model

  

  Recently, <cit.> applied a
  double-Lorentzian profile in fitting blended components of the
  He i 10 830 Å triplet observed by the GREGOR
    Infrared Spectrograph (GRIS) at the 1.5-meter GREGOR solar
  telescope. Following this approach, we test the seven-parameter
  double-Lorentzian model using the typical profile shown in the left
  panel of Figure <ref>. For this particular profile, the model
  renders much higher χ^2 values and residuals than the
  seven-parameter double-Gaussian model. Moreover, it substantially
  overestimates the observed blue wing intensity of the blue component
  at Δλ≈ -0.35 Å. Hence, the double-Lorentzian
  model renders an inadequate representation of our data and is
  dismissed.

  

 §.§ Double-Voigt Model

  

  Since the double Gaussian underestimates and the double Lorentzian
  overestimates the observed blue wing intensity of the blue
  component, the double-Voigt function might render a natural
  compromise. In fact, the Voigt function has been employed by
  <cit.> and <cit.> in fitting the
   profiles. Therefore, we test a model consisting of two Voigt
  functions normalized to their maxima. The model has seven free
  parameters: the peak amplitudes I_ blue,  red; the damping
  parameter  and FWHM common for both components; the
  spectral position of the blue component peak λ_ blue;
  and two coefficients of the polynomial. The parameters of this model
  for the typical deconvolved profile are given in column 4 of
  Table <ref>. The inferred damping parameter is shown there both
  in wavelength units as _λ and in frequency units as
  the decadic logarithm of _ν.  They are linked by the
  conversion formula _ν = c_λ/λ^2,
  where c is the speed of light and λ is the wavelength of
  . The right panel of Figure <ref> shows the typical
  deconvolved  profile by the gray circles, and its double-Voigt
  fit is represented by the black line. The bottom subpanel
  illustrates that the model is free of the blue wing excess, compared
  with the left subpanel and subpanels in Figure <ref>, and
  renders a satisfactory fit with featureless differences Δ I
  smaller than 2%. Although the model seems to comply with our
  requirements imposed on a new adequate model, we postpone a final
  judgement about its physical adequacy to Section <ref> of the
  Discussion.

  
  
  
  
  

  

 §.§ Multi-Gaussian Model
   
  

  The problem of the enhanced wing emissions in the  and He i 10 830 Å lines was addressed by <cit.>
  and <cit.>, who invoked two-temperature models
  of prominence structure. Inspired by this approach to explain the
  surplus of blue wing emission, we construct a multi-Gaussian model
  consisting of two double-Gaussians with different line widths
  representing the cool and hot components of a prominence. The model
  has nine free parameters: the peak intensities of the blue
  components I_ blue (two parameters); the ratios of the peak
  intensities I_ blue/I_ red constrained by the limit
  values 0.001 and 8 (two parameters); the FWHM common for the blue
  and red components, but different for the cool and hot ones (two
  parameters); the spectral position of the blue component peak
  λ_ blue (one parameter); and two coefficients of the
  polynomial (two parameters). The parameters of this model for the
  typical and average deconvolved profiles are listed in columns 5 and
  6 of Table <ref>, showing the hot component parameters in
  parentheses. It also shows the blue component intensities I_
    blue/I_ max and the kinetic temperatures T of the cool
  and hot components estimated by the formula:
  
  
    T = m_ He/2k{( FWHM/2√(ln2)c/λ)^2 - v^2 } ,

  
  where m_ He is the mass of a helium atom, k is the
  Boltzmann constant, c is the speed of light, λ is the
  wavelength of , and v is the microturbulent velocity of
  5  for both components <cit.>.

  Figure <ref> displays the typical and average  profiles
  free of the instrumental smearing by the gray circles and their
  multi-Gaussian fits, comprising the cool (thin blue and red lines)
  and hot components (thick lines), shown by the black lines. The
  bottom subpanels illustrate that the model is free of the blue wing
  excess when compared with respective subpanels in Figures <ref>
  and <ref>, and renders satisfactory fits with differences
  Δ I smaller than 2%, similar to the double-Voigt
  model. Thus, the multi-Gaussian model also complies with the
  requirements we impose on our new fitting model. We postpone a final
  judgement about its physical adequacy to Section <ref> of the
  following Discussion.

  
  
  

  

§ DISCUSSION


  

 §.§ Small Stokes Q, U, V Amplitudes

  

  An important fact characterizing the target prominence is the
  surprisingly small amplitude of the Stokes Q, U, V profiles,
  typically about 0.2 – 0.4% of the Stokes I peak
  intensities. The previous studies by, e.g.,
  <cit.>;
  and <cit.> reported the Stokes Q, U, V amplitudes
  ranging from 4×10^-3 % to 2.3 %. Is the weak
  polarimetric signal a possible consequence of some inherent feature
  of this particular target prominence? Or is it rather due to
  non-optimal seeing, some technical aspects of the instrument setup,
  and/or an inadequate observing or reduction procedure? An inadequacy
  of the observing or reduction procedure may probably be excluded,
  because decreasing the number of modulation cycles adopted for the
  data reduction from ten to five, as used in
  <cit.> and
  <cit.>, does not bring
  improvement. A very plausible explanation was suggested by
  <cit.>. To quote them: “It has been
  suggested by <cit.> that line-of-sight integration
  or limited spatial resolution might result in a depression of the
  degree of linear polarization of the observed radiation, which would
  be wrongly interpreted in terms of Hanle depolarization by stronger
  fields.” Therefore, we conclude that a combination of non-optimal
  seeing, the long integration time, and THEMIS instrumental
  characteristics very probably caused a degradation of the spatial
  resolution. This is most likely the culprit for the small
  Stokes Q, U, V amplitudes.

  
  
  
  
  

  

 §.§ Spectral Characteristics of the Double-Gaussian Model


  While Table <ref> lists the spectral characteristics of
  the typical and average  profile inferred by three
  different fitting models, Table <ref> summarizes
  statistics of the  spectral characteristics derived from
  the histograms in Figures <ref> and <ref>, which
  represent the double-Gaussian model.

  

  The most important fact characterizing the target prominence is the
  component peak intensity ratio of 5.5±0.4 (Table <ref>),
  which differs from the optically thin limit 8. However, this is not
  a new finding. <cit.> previously reported a peak
  ratio of 6.6±0.4. In a study of eight prominences,
  <cit.> found the  peak intensity ratios ranging
  from 6.1 to 7.6. Finally, <cit.> and
  <cit.> reported peak intensity ratios of 6.8 and
  6, respectively. While the former two studies employed the
  double-Gaussian model, the method of inferring the ratios in the
  latter two articles is unclear. Thus, the measured peak intensity
  ratio of 5.5±0.4 is on the lower limit of the values reported so
  far.

  

  Many of the published Doppler velocity measurements of prominences
  were made in  by the MSDP instrument <cit.>,
  but reports on the  velocity measurements are infrequent. A
  search of the NASA Astrophysics Data System provides us only with
  the study by <cit.>, presenting the line-of-sight
  velocity distribution over a quiescent prominence observed in
   with a standard deviation of 1.8 . This agrees with the
  deviation of 1.7  derived from our measurements. The interval
  of ±5 , presented in the top right panel of
  Figure <ref>, is characteristic for the quiescent type of
  prominences and is fully in line with  <cit.>,
   <cit.>, He i 10 830 Å <cit.>,
  and Mg ii k & h <cit.>
  Doppler-velocity measurements in quiescent prominences.

  

  The sharp lower limit of the measured width FWHM_ blue of the
  dominant  blue component at about 0.23 Å (the bottom panel
  of Figure <ref>) agrees well with the lower limit of Doppler
  widths of  reported by <cit.>. However, they
  reported the upper limit of the observed FWHM at 0.32 Å, while
  the histogram in the bottom panel of Figure <ref> shows a
  continuous distribution of broad profiles beyond this
  value. <cit.> measured a nearly equal FWHM of
  0.28 Å for both components. Similarly, the median of 15 FWHM
  values reported in <cit.> was
  0.27 Å. Most of the  FWHMs measured by
  <cit.> were within the interval from 0.32 Å to
  0.56 Å, in good agreement with our results shown in the bottom
  panel of Figure <ref>.
  
  

  Finally, we find width ratios of the  blue and red components
  of 1.04±0.18 over almost the entire prominence. Their close
  equality was also reported by <cit.> and
  <cit.>. The width equality is a strong confirmation
  that the  multiplet components in the plasma have a common
  origin.
  
  

 §.§ Toward a New Fitting Model


  In the following we examine in detail the physical adequacy of the
  double-Voigt model and the multi-Gaussian model as alternative
  models of .

  

  §.§.§ Double-Voigt Model

  

  We have shown that the double-Voigt model of the typical profile
  requires a damping parameter _λ =
  0.5 Å corresponding to log(_ν [ s^-1]) =
  10.6. How does this observed value compare with the theoretical
  parameter given as the sum of the natural damping parameter
  _ RAD and the collisonal (or Van der Waals) damping
  parameter _ VdW <cit.>?
  The latter parameter represents collisions of the emitting helium
  atoms with the neutral hydrogen atoms. The sum of the relevant
  Einstein coefficients of spontaneous emission A, adopted from the
  National Institute of Standards and Technology Atomic Spectra
  Database <cit.>, gives the value
  log(_ RAD [ s^-1]) = 7.7. Assuming a
  prominence gas pressure of 1 dyn cm^-2 and a temperature of
  11 kK in combination with the line-broadening theory by
  <cit.>, one can estimate for  the value of
  log(_ VdW [ s^-1]) = 4.4. Thus, the
  observed damping parameter is about three orders of magnitudes
  larger than the theoretical parameter. Apparently, this disqualifies
  the double-Voigt model from any further consideration because it is
  physical inadequate. This conclusion is in accord with
  <cit.>, who also dismissed the physical adequacy of
  the Voigt-shaped absorption coefficient for . They inferred the
  broadening parameter
  
  
    a = 2√(ln2)/ FWHMλ^2/c_ν/4π

  
  on the order of magnitude 0.1 corresponding to
  log(_ν [ s^-1]) = 10.3 for FWHM =
  0.27 Å. Because this value was also orders of magnitude
  greater than the values calculated on the basis of commonly
  accepted prominence plasma parameters, they ruled out
  collisional broadening as a realistic solution of the blue
  wing excess. This is in accord with <cit.>, who claimed that
  collisions can be neglected in forming .

  

  §.§.§ Multi-Gaussian Model

  

  Focusing on the typical  profile (the left panel of
  Figure <ref> and column 5 in Table <ref>), we assess the
  multi-Gaussian model, which is similar to the two-temperature model
  of  applied in <cit.> and <cit.>.
  
  The medians of 32 FWHM values, reported in Table 2 of
  the latter study for the cool and hot components, are about
  0.22 Å and 0.59 Å, respectively, and thus smaller than
  the equivalent FWHMs 0.28 Å and 0.65 Å inferred by the
  typical profile.
  
  Remarkably, the temperatures 11.5 kK and 91 kK of the cool
  and hot components of the multi-Gaussian model agree very well
  with the central and boundary temperatures of 10 kK and
  100 kK for the 2D model of prominence fine structure applied
  in <cit.> and <cit.>. This
  may be evidence of the physical adequacy of the multi-Gaussian
  model.

  

  While the component peak intensity ratio of 8 of the hot component
  (Table <ref>) implies its negligible optical thickness, the
  ratio of 6.6 of the cool component can be interpreted in terms of
  the prominence geometrical width and optical thickness based on the
  2D multi-thread prominence model by <cit.>. Figures 7.21
  and 7.22 in <cit.> present the  component peak
  intensity ratio as a function of the number of 1.2 Mm wide
  prominence threads and their total optical thickness for the
  temperatures 8 kK and 17 kK. Taking the temperature 11.5 kK of
  the cool component of the target prominence and the ratio of 6.6,
  one can estimate by interpolating the values in these figures that
  the target prominence is composed from of 14 threads with a total
  geometrical width of 17 Mm and an optical thickness of
  0.3. Remarkably, the width, corresponding to 23 arcsec, is
  comparable with the typical width of a filament (see the right panel
  of Figure <ref>). However, the optical thickness of 0.3 is
  about an order of magnitude greater than the thicknesses reported in
  <cit.>; and <cit.>. In this
  context, <cit.> commented on their method and
  results by stating: “The computed line shapes are relatively
  insensitive to the τ_0i because of the smallness of these
  quantities.” For this reason, we may conclude that the prominence
  parameters inferred by the typical profile support the physical
  adequacy of the multi-Gaussian model with important implications for
  the interpretation of  spectropolarimetry by current inversion
  codes.

  

§ SUMMARY AND CONCLUSIONS


  

  In this study we analyze the observations of a quiescent, tree-like
  prominence scanned by the THEMIS spectrograph on 2 August 2014 in
  the  multiplet. In a broad-band  image the distribution of
  its relative intensity with respect to the disk center has the
  median at 17%.

  

  The double-Gaussian model of the  Stokes I profiles shows
  wide distributions of the FWHM with two maxima at 0.25 Å and
  0.30 Å for the  blue component and at 0.22 Å and
  0.31 Å for the red component. The FWHM distributions have
  medians at 0.31 Å and 0.29 Å for the blue and red component,
  respectively. We find width ratios of the  components of
  1.04±0.18 over almost over the entire prominence. The width
  equality is a strong confirmation of the common origin of the
  multiplet components in the plasma. This model yields a
   component peak intensity ratio of 5.5±0.4, which differs
  from the value of 8 expected in the optically thin limit. Most of
  the measured Doppler velocities are from the interval
  ±5  with a standard deviation of ± 1.7  around
  the peak value of 0.4  (Section <ref>). The
  pixel-by-pixel comparisons of the  spectral characteristics in
  Figure <ref> and their values in Tables <ref> and
  <ref> may become valuable in future modeling of . However,
  we have shown that the double-Gaussian model fails to reproduce the
  observed  blue wing intensities and leads to quasi-periodic
  residuals with more than one-sigma amplitudes
  (Section <ref>).

  

  We demonstrate that the blue wing excess persists even after
  correcting the typical  profile for the instrumental profile of
  the THEMIS spectrograph, suggesting the inadequacy of the
  double-Gaussian model (Section <ref>). To investigate this
  issue we test the double-Lorentzian and the double-Voigt model
  showing that the former produces unsatisfactory fits and the latter
  is physically invalid (Sections <ref>, <ref>, and
  <ref>).

  
  
  With the goal of identifying an adequate fitting model, we examine
  the multi-Gaussian model consisting of two double-Gaussians with
  different line widths, representing the cool and hot components of
  the prominence. This model adequately reproduces the typical
   profile, indicating temperatures for the cool and hot
  components of about 11.5 kK and 91 kK, respectively. The cool and
  hot components of the typical  profile have component peak
  intensity ratios of 6.6 and 8, implying a prominence geometrical
  width of 17 Mm and an optical thickness of 0.3 for the cool
  component, while the optical thickness of the hot component is
  negligible (Sections <ref> and <ref>). These
  prominence parameters seem to be realistic, which supports the
  physical adequacy of the multi-Gaussian model. This has important
  implications for the interpretation of  spectropolarimetry
  using current inversion codes.

  

  These conclusions are based on data taken during a non-optimal
  seeing period, which is most likely the culprit for the observed
  small amplitudes of the Stokes Q, U, V profiles, which
  typically reach only 0.2 – 0.4% of the Stokes I peak
  intensities (Sections <ref> and <ref>). A statistically
  larger sample of data, taken under more favorable seeing conditions,
  is needed to confirm these conclusions.

  
    
    We thank an anonymous referee for valuable comments, which
    improved the article substantially. J. Koza is grateful to
    P. Heinzel and E. Dzifčáková for fruitful
    discussions, comments, and suggestions. J. Koza and M. Kozák
    would like to thank B. Gelly, the director of the THEMIS solar
    telescope, and the technical team for their support during their
    THEMIS observing campaign. The authors thank M. Saniga for
    language corrections of the article.
    
    This work was supported by the Science Grant Agency project VEGA
    2/0004/16. The THEMIS observations were taken within the
    EU-7FP-SOLARNET Transnational Access and Service Programme (High
    Resolution Solar Physics Network -
    FP7-INFRAS­TRUCTURES-2012-1). This article was created by the
    realization of the project ITMS No. 26220120029, based on the
    supporting operational Research and development program financed
    from the European Regional Development Fund. 
    
    This work uses GONG data obtained by the NSO Integrated Synoptic
    Program (NISP), managed by the National Solar Observatory, which is
    operated by the Association of Universities for Research in Astronomy
    (AURA), Inc. under a cooperative agreement with the National Science
    Foundation. The AIA data used here are courtesy of SDO (NASA) and the
    AIA consortium. The STEREO B data used here were produced
    by an international consortium of the Naval Research Laboratory (USA),
    Lockheed Martin Solar and Astrophysics Lab (USA), NASA Goddard Space
    Flight Center (USA), Rutherford Appleton Laboratory (UK), University
    of Birmingham (UK), Max-Planck-Institut for Solar System Research
    (Germany), Centre Spatiale de Liege (Belgium), Institut d'Optique
    Theorique et Appliquee (France), and Institut d'Astrophysique Spatiale
    (France).
    
    This research has made use of NASA Astrophysics Data System.
 
       
    Disclosure of Potential Conflicts of Interest The authors
    declare that they have no conflicts of interest.
  

75

#1ISBN #1#1#1#1#1#1#1#1#1#1#1#1#1#1#1#1#1#1#1#1#1#2et al.#1#1#1#1#1#1#1#1#1#1#1#1#1#1#1#1#1#1#1#1#1#1#1#1#1#1http://dx.doi.org/#1#1http://arxiv.org/abs/#1#1http://adsabs.harvard.edu/abs/#1#1<><#>1#1#1#1#1#1#1#1#1#1#1 

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