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Author name code: christopoulou
ADS astronomy entries on 2022-09-14
author:"Christopoulou, E.B." 

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Title: Planets In Your Hand (2017-2019)
Authors: Palafouta, Sofia; Gazeas, Kosmas; Christopoulou, Elena;
   Karampotsiou, Efsevia; Athanasopoulos, Dimitrios; Konstantinou, Anna;
   Tzouganatos, Lefteris; Kefala, Kyriaki; Papadami, Argiro; Trivyza,
   Marilia; Skliris, Vasilis; Chliaras, Vangelis
2019EPSC...13.1816P    Altcode:
  The Planets In Your Hand project was granted by Europlanet in the
  frame of Public Engagement Funding Scheme in 2017. It consists of a
  portable interactive exhibition of planetary surface models, embedded
  in square frames. The project offers the visitors a chance to see,
  learn and understand the diversity of the planetary surfaces in our
  Solar System, including the different conditions such as temperature,
  wind and atmosphere. Since the beginning of the project, the planetary
  surfaces have been presented to a wide range of audience, including
  visually impaired people, preliminary school and high school students
  as well as university researchers.

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Title: 120 Minima timings of eclipsing binaries
Authors: Palafouta, S.; Gazeas, K.; Christopoulou, E.; Bakogianni,
   V.; Dervou, M.; Loukaidou, G.
2017IBVS.6218....1P    Altcode:
  We present 120 times of minima of 8 eclipsing binaries.

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Title: Modeling of Detached Binary Systems in LMC from OGLE III
Authors: Theodosiou, A.; Christopoulou, E.; Papageorgiou, A.
2013hell.confQ..46T    Altcode:
  Using BVI data from OGLE II and OGLE III survey, we analyze light curves
  for detached binary systems with nearly circular orbits in the Large
  Magellanic Cloud (LMC). We make use of orbital periods, classification,
  empirical relations as well as the distance to the LMC to present
  light curve solutions with the software PHOEBE. The assumptions made
  for the procedure of light curve solution are thoroughly discussed
  and compared with previously determined global stellar parameters of
  other detached binaries in LMC from spectroscopic and photometric data.

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Title: The first comprehensive photometric study of the overcontact
    binary TY Boo
Authors: Christopoulou, E.
2012hell.conf...25C    Altcode:
  New precision BVRI light curves of the overcontact binary TY Boo have
  been obtained using the 35.5 cm Schmidt-Cassegrain telescope at the
  University of Patras, Observatory equipped with an SBIG ST-10XME CCD
  made during 2010 and 2011. The complete light curves are analyzed with
  the Wilson-Devinney code (PHOEBE) and new geometric and photometric
  elements are derived. A period investigation based on all available data
  spanning 85 years, shows that there exists a cyclic variation overlaying
  a secular period decrease. The presence of a third body is investigated
  but also spotted models as resulting from magnetic activity.

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Title: CCD photometric study of the misclassified binary system
    V380 Cas
Authors: Papageorgiou, A.; Christopoulou, E.
2012hell.confQ..29P    Altcode:
  A photometric study of the eclipsing binary V380 Cas is presented for
  the first time with the 35.5cm Schmidt-Cassegrain telescope at the
  University of Patras, Observatory from June 2009 to July 2010. The
  BVRI light curves were observed and 7 new minima were calculated. No
  secondary minimum has been detected, indicating that its original
  period was wrong. The complete light curves are analyzed with the
  Wilson-Devinney code (PHOEBE) and the first photometric solution is
  derived. The system is probably a detached one with equal components
  and double period, contrary to its previous classification as Algol
  type. The first O-C analysis of the system based on all timings of
  minima is presented and the first precision ephemeris is estimated. Also
  the probability of third light is examined from both O-C and photometric
  solution.

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Title: Promises and Pitfalls of Solar Hα Zeeman Spectropolarimetry
Authors: Balasubramaniam, K. S.; Christopoulou, E. B.; Uitenbroek, H.
2004ApJ...606.1233B    Altcode:
  Zeeman spectropolarimetry of the solar disk in the Hα line is a
  daunting, yet promising diagnostic for measuring solar chromospheric
  magnetic fields. As a demonstration of its potential we used the
  National Solar Observatory (NSO)/High Altitude Observatory (HAO)
  Advanced Stokes Polarimeter to obtain simultaneous measurements
  of polarimetric signals from the photosphere in the Fe I 6301.5,
  6302.5 Å lines and from the chromosphere in Hα. With these
  measurements, we explore the promises and pitfalls of Hα Zeeman
  spectropolarimetry. Remarkable features observed in Hα include
  a reversal of Zeeman polarity in the emission core across flaring
  active regions and highly redshifted and smeared Stokes V profiles in
  prominences. We reproduce the Hα Zeeman reversals using radiative
  transfer diagnostics, and we compare photospheric and chromospheric
  line-of-sight magnetic fields.

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Title: Wavelet Analysis of Umbral Oscillations
Authors: Christopoulou, E. B.; Skodras, A.; Georgakilas, A. A.;
   Koutchmy, S.
2003ApJ...591..416C    Altcode:
  We study the temporal behavior of the intensity and velocity
  chromospheric umbral oscillations, applying wavelet analysis techniques
  to four sets of observations in the Hα line and one set of simultaneous
  observations in the Hα and the nonmagnetic Fe I (5576.099 Å) line. The
  wavelet and Fourier power spectra of the intensity and the velocity at
  chromospheric levels show both 3 and 5 minute oscillations. Oscillations
  in the 5 minute band are prominent in the intensity power spectra; they
  are significantly reduced in the velocity power spectra. We observe
  multiple peaks of closely spaced cospatial frequencies in the 3 minute
  band (5-8 mHz). Typically, there are three oscillating modes present:
  (1) a major one near 5.5 mHz, (2) a secondary near 6.3 mHz, and (3)
  oscillations with time-varying frequencies around 7.5 mHz that are
  present for limited time intervals. In the frame of current theories,
  the oscillating mode near 5.5 mHz should be considered as a fingerprint
  of the photospheric resonator, while the other two modes can be better
  explained by the chromospheric resonator. The wavelet spectra show a
  dynamic temporal behavior of the 3 minute oscillations. We observed
  (1) frequency drifts, (2) modes that are stable over a long time
  and then fade away or split up into two oscillation modes, and (3)
  suppression of frequencies for short time intervals. This behavior
  can be explained by the coupling between modes closely spaced in
  frequency or/and by long-term variations of the driving source of the
  resonators. <P />Based on observations performed on the National Solar
  Observatory/Sacramento Peak Observatory Richard B. Dunn Solar Telescope
  (DST) and on the Big Bear Solar Observatory Harold Zirin Telescope.

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Title: Chromospheric Evershed flow
Authors: Georgakilas, A. A.; Christopoulou, E. B.; Skodras, A.;
   Koutchmy, S.
2003A&A...403.1123G    Altcode:
  We studied the chromospheric Evershed flow from filtergrams obtained
  at nine wavelengths along the Hα profile. We computed line-of-sight
  velocities based on Becker's cloud model and we determined the
  components of the flow velocity vector as a function of distance
  from the center of the sunspot, assuming an axial symmetry of both
  the spot and the flow. We found that the flow velocity decreases
  with decreasing height and that the maximum of the velocity shifts
  towards the inner penumbral boundary. The flow related to some fibrils
  deviates significantly from the average Evershed flow. The profile of
  the magnitude of the flow velocity as a function of distance from the
  spot center, indicates that the velocity attains its maximum value in
  the downstream part of the flow channels (assumed to have the form of a
  loop). This behavior can be understood in terms of a critical flow that
  pass from subsonic to supersonic near the apex of the loop, attains
  its higher velocity at the downstream part of the loop and finally
  relaxes to subsonic through a tube shock. We computed the average flow
  vector from segmented line-of-sight velocity maps, excluding bright
  or dark fibrils alternatively. We found that the radial component of
  the velocity does not show a significant difference, but the magnitude
  of the vertical component of the velocity related to dark fibrils is
  higher than that related to bright fibrils. <P />Based on observations
  performed on the NSO/SPO Richard B. Dunn Solar Telescope (DST).

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Title: Temporal Behavior of the Evershed Effect
Authors: Georgakilas, A. A.; Christopoulou, E. B.
2003ApJ...584..509G    Altcode:
  We study the Evershed flow in the photosphere and the reverse Evershed
  flow in the chromosphere from simultaneous observations, giving
  emphasis to the temporal evolution of the phenomena. We compute the
  components of the velocity vector as a function of distance from the
  center of the sunspot, assuming an axial symmetry of both the spot and
  the flow. A five-minute oscillatory pattern is obvious in the penumbra
  at photospheric level. Our results verify that the velocity of the
  Evershed flow has a maximum above the penumbra in the photosphere and
  well outside the penumbra in the chromosphere. We find evidence of
  temporal variations prominent in the radial component of the average
  photospheric velocity with a characteristic timescale of 25 minutes. We
  consider a transient siphon flow or a wave superimposed on a steady flow
  as possible explanations for the temporal behavior of the photospheric
  Evershed flow. The radial component of the chromospheric reverse
  Evershed flow shows a repetitive temporal variation with a typical
  timescale of 15 minutes. The variation consists of enhanced velocity
  amplitudes that propagate to an opposite direction from the flow with a
  velocity of about 5-6 km s<SUP>-1</SUP>. This behavior cannot be easily
  explained in the frame of a transient flow and strongly suggests that it
  is related to the propagation of a wave. We examine the possibility of
  its being associated with the propagation of running penumbral waves
  in the superpenumbra. The temporal evolution of the line-of-sight
  velocity across superpenumbral fibrils presents alterations that can
  be associated with a time-dependent flow. However, we also observe
  propagating velocity packets that can be associated with a wave. <P
  />Based on observations performed on the NSO/SPO Richard B. Dunn Solar
  Telescope (DST).

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Title: Simultaneous Chromospheric and Photospheric Spectropolarimetry
    of a Sunspot
Authors: Balasubramaniam, K. S.; Christopoulou, E. B.; Uitenbroek, H.
2003ASPC..286..227B    Altcode: 2003ctmf.conf..227B
  No abstract at ADS

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Title: Ultraviolet Observations of Periodic Annular Intensity
    Fluctuations Propagating around Sunspots
Authors: Georgakilas, A. A.; Muglach, K.; Christopoulou, E. B.
2002ApJ...576..561G    Altcode:
  We analyze UV observations of an isolated sunspot taken with the
  Transition Region and Coronal Explorer. We produced “space/time
  slice images,” which reveal periodic, inward-propagating, intensity
  fluctuations in the inner photospheric penumbra and periodic,
  outward-propagating, annular intensity fluctuations in the outer
  penumbra and the area around the sunspot. The average propagation
  velocity of the inward- and outward-propagating intensity flows is about
  0.5 and 1 km s<SUP>-1</SUP>, respectively, and the distance between
  subsequent crests is about 2500 km. Using observations obtained with
  the Michelson Doppler Imager, we found propagating magnetic field
  enhancements that present a spatial and temporal coherence with the
  UV intensity fluctuations. We have not observed any waves similar or
  related to the chromospheric 5 minute waves. Based on observations
  taken with the Transition Region and Coronal Explorer and the Michelson
  Doppler Imager (MDI) on board the Solar and Heliospheric Observatory.

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Title: Multi-wavelength study of Network Bright Points near the limb*
Authors: Georgakilas, A. A.; Christopoulou, E. B.; Koutchmy, S.
2001SoPh..202..241G    Altcode:
  We analyze the morphology of network bright points (NBPs), their
  relation to fine dark mottles and their temporal variations,
  using observations of a quiet region near the polar solar limb,
  obtained during the solar minimum. For our analysis we used an
  image-processing method for the selection and identification of
  NBPs. Further we constructed 'maximum power frequency' maps computing
  the power spectrum for each pixel of a field and selecting the frequency
  of maximum spectral power as the most representative oscillating
  frequency for this pixel. The morphological analysis of our data
  indicates that the enhancement of NBPs is part of a complicated process
  that is responsible for the formation of mottles. The analysis of the
  lifetimes of NBPs indicates that although the general patterns of NBPs
  remain constant for time intervals larger than an hour, the lifetime
  of individual bright points is of the order of 16 min. Furthermore,
  our results indicate an association of the lifetime of NBPs with that
  of mottles. From the analysis of temporal variations we confirm that the
  power of NBPs is smaller than the corresponding power for intra-network
  points at both the 3-min and the 5-min oscillating modes and in both
  the Mg b<SUB>1</SUB>−0.4 Å and the continuum. Our analysis revealed
  enhanced power in the 7-min range, which is theoretically considered
  a candidate frequency for transverse waves related to NBPs at the base
  of the chromosphere (Kalkofen, 1997). However, we consider more likely
  that this period is related to the evolution of individual NBPs.

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Title: Oscillations and running waves observed in
    sunspots. III. Multilayer study
Authors: Christopoulou, E. B.; Georgakilas, A. A.; Koutchmy, S.
2001A&A...375..617C    Altcode:
  We continue our study of waves and oscillations observed in sunspots
  using an improved method for enhancing the waves, giving the opportunity
  to identify them and determine their properties in far Hα wings. We
  found that the running penumbral waves are observable at least up to
  the formation height of the Hα +/- 0.5 Å line, but not in the Hα +/-
  0.75 Å or the Fe I+/-0.12 Å. We found a time lag between the waves
  in the blue and the red wing of the Hα line corresponding to a phase
  shift of 180<SUP>o</SUP>, that indicates a pure Doppler shift of the
  line. There is a lag in the propagation of the waves seen at Hα center
  and at Hα wings. Also there is a lag in the variation of the umbral
  oscillations as they are observed from lower to higher atmospheric
  layers. The correlation between umbral oscillations at various
  atmospheric heights and running penumbral waves strongly indicates
  that the latter are excited by photospheric umbral oscillations and
  not the chromospheric ones. We found a new category of photospheric
  waves that originate at approximately 0.7 of the distance between the
  umbra and the penumbra boundary and propagate beyond the outer penumbra
  boundary with a velocity of the order of 3-4 km s<SUP>-1</SUP>. Further,
  we found 3 min penumbral oscillations apparent in the inner penumbra
  at lower chromospheric layers (far Hα wings). Based on observations
  performed on the NSO/SPO Richard B. Dunn Solar Telescope (DST)

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Title: Polar surges and macrospicules. II. Dynamics of an eruptive
    event from off-limb observations
Authors: Georgakilas, A. A.; Koutchmy, S.; Christopoulou, E. B.
2001A&A...370..273G    Altcode:
  We continue our study of polar surges and macrospicules at the
  period of solar minimum, analyzing high resolution multiwavelength
  limb observations that provide a clearer picture of the dynamical
  phenomena occurring well above the chromosphere of a polar cap. The
  time sequence of an erupting and impulsive polar event is examined
  from the low chromosphere to coronal heights, deriving both proper
  motions and Doppler velocities. Our observations suggest that there is
  a close association of polar surges with explosive events, supporting
  the hypothesis that magnetic reconnection triggered by emerging flux
  provides the accelerative mechanism for this polar region event.

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Title: Fine Structure of the Magnetic Chromosphere: Near-Limb Imaging,
    Data Processing and Analysis of Spicules and Mottles
Authors: Christopoulou, E. B.; Georgakilas, A. A.; Koutchmy, S.
2001SoPh..199...61C    Altcode:
  The origin and the dynamical evolution of spicules and mottles continue
  to be a highly interesting research subject. Using high-resolution
  Hα observations obtained with the Dunn Solar Telescope of the
  Sacramento Peak Observatory and an image processing technique for
  the enhancement of near-limb solar images, we study the dynamics of
  spicules and mottles as well as their relation. Our image-processing
  technique is based on the correction for the limb darkening and the
  use of a directionally sensitive operator, the `MadMax'. The temporal
  evolution of characteristic cases of spicules, dark and bright mottles,
  indicates an association between them and supports the suggestion that
  the magnetic field and probably related forces play a fundamental
  role in their generation and dynamics. We present characteristic
  cases of fine bright mottles, observable in the Hα far wings, that
  appear in close juxtaposition to dark mottles. The phenomenon appears
  to be common, suggesting that the velocities derived from marginal
  resolution spectroscopic observations could be underestimated. Typical
  examples of individual mottles crossing the solar limb further
  support the association between spicules and mottles. Finally we
  show images of arch-shaped mottles above the limb and especially on
  the disk, confirming the existence of chromospheric small loops. Our
  image-processing method substantially enhances near-limb observations
  and permits an insight into the studies of the very fine chromospheric
  structures.

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Title: Oscillations and running waves observed in sunspots: Analysis
    of an extended sample of sunspots
Authors: Georgakilas, A. A.; Christopoulou, E. B.; Zirin, H.
2000AAS...197.5109G    Altcode: 2000BAAS...32Q1489G
  Sunspots show oscillatory behavior, identifiable as intensity and
  velocity variations in photospheric and chromospheric lines. In
  the chromospheric layers 3 min standing oscillations are dominant
  in the umbra (umbral oscillations), while 5 min running waves are
  dominant in the penumbra and superpenumbra. Penumbral waves (RPW)
  were first observed in Hα by Zirin and Stein (1972) and independently
  by Giovanelli (1972). Since their discovery a number of authors have
  tried to determine the physical properties of umbral oscillations
  and running penumbral waves (like the frequency and the propagation
  velocity) and to identify their nature, as well as the relation between
  them. In order to clarify discrepancies, due to the analysis of limited
  number of sunspots, we present comprehensive results from the study of
  8 sunspots observed from the Big Bear Solar Observatory (BBSO) during
  1999 and 2000. Our results show that RPW are propagating with a mean
  velocity of the order of 15 km s<SUP>-1</SUP>. The fourier analysis
  of 'time slice images' (created taking cross sections of every image
  of a time series) indicates that there is not a clear relationship
  between umbral oscillations and running penumbral waves. This work
  was supported by NSF grant ATM-9726147.

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Title: Oscillations and running waves observed in
    sunspots. II. Photospheric waves
Authors: Georgakilas, A. A.; Christopoulou, E. B.; Koutchmy, S.
2000A&A...363..306G    Altcode:
  To continue our study of waves related to sunspots in the photosphere,
  we analyzed CCD, high resolution sunspot observations obtained
  in the Fe i 557.6 nm line. We produced “time slice images" which
  reveal inward slow propagating waves in the photospheric penumbra and
  outward propagating waves in the area around the sunspot. The phase
  velocity of the waves is near 0.5 km s<SUP>-1</SUP> in both cases and
  their horizontal wavelength about 2500 km. The waves could be related
  either to solar p-modes or to the subphotospheric layer large-scale
  convection. Based on observations performed on the NSO/SPO Dunn's
  Solar Telescope (DST).

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Title: Oscillations and running waves observed in sunspots
Authors: Christopoulou, E. B.; Georgakilas, A. A.; Koutchmy, S.
2000A&A...354..305C    Altcode:
  In order to study umbral oscillations, running penumbral waves and
  the relationship between them, we analyzed CCD, high resolution,
  sunspot observations obtained at center and the wings of the Hα line
  and the Fe I 5576 Ä line. The UBF filter was used in order to produce
  high cadence sequences of filtergrams. Images were processed to remove
  the sharp intensity gradient between the umbra and the penumbra. They
  show the waves to start out around umbral oscillating elements and to
  propagate outwards forming concentric cycles around the elements. The
  waves appear to propagate beyond the outer edge of the photospheric
  penumbra, in the superpenumbra, where they dilute. Comparing images
  in 9 wavelengths along the Hα profile we found out that the waves
  are definitely better observed near the Hα center and near the blue
  wing -0.35 Ä. This indicates a possible vertical upward mass motion
  in the oscillating penumbral structure and that the oscillation is not
  symmetric about zero. We found different oscillating modes. Standing
  umbral oscillations are dominant in the umbra and inner penumbra;
  their frequency is around 6.5 mHz. Similar oscillations are observed
  in the penumbra - superpenumbra boundary but with considerably lower
  frequency (2 mHz). Oscillations are absent or have reduced magnitude
  in the central part of the penumbra. Penumbral waves are running waves
  propagating with a constant phase velocity around 13 km s<SUP>-1</SUP>;
  their frequency is remaining constant over the whole penumbra, in the
  band of 3 mHz. We produced “time slice images" which show, that there
  is not a clear relationship between umbral oscillations and running
  penumbral waves.

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Title: Multiwavelength Observations of Ellerman Bombs
Authors: Georgakilas, A. A.; Christopoulou, E. B.; Koutchmy, S.
1999ESASP.448..279G    Altcode: 1999mfsp.conf..279G; 1999ESPM....9..279G
  No abstract at ADS

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Title: Fine Structure of the Solar Chromosphere: Dynamics of Spicules
    and Fine Dark Mottles
Authors: Georgakilas, A. A.; Christopoulou, E. B.; Koutchmy, S.
1999ESASP.448..285G    Altcode: 1999mfsp.conf..285G; 1999ESPM....9..285G
  No abstract at ADS

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Title: New Results about Running Penumbral Waves
Authors: Christopoulou, E. B.; Georgakilas, A. A.; Koutchmy, S.
1999ESASP.448..245C    Altcode: 1999mfsp.conf..245C; 1999ESPM....9..245C
  No abstract at ADS

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Title: Chromospheric Mass Motions Associated with an Emerging
    Flux Region
Authors: Christopoulou, E. B.; Georgakilas, A. A.; Koutchmy, S.
1999ESASP.448..593C    Altcode: 1999ESPM....9..593C; 1999mfsp.conf..593C
  No abstract at ADS

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Title: Dynamics and Nature of Macrospicules
Authors: Georgakilas, A. A.; Koutchmy, S.; Christopoulou, E. B.
1999ESASP.448..291G    Altcode: 1999mfsp.conf..291G; 1999ESPM....9..291G
  No abstract at ADS

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Title: Running Penumbral Waves in Sunspots
Authors: Christopoulou, E. B.; Georgakilas, A. A.; Koutchmy, Serge
1999ASPC..184..103C    Altcode:
  In order to study running penumbral waves, we analyzed high resolution
  sunspot observations obtained at the center and the wings of the
  Hα line. The sharp intensity gradient between the umbra and the
  penumbra has been removed by using an image processing technique. The
  processed images show the waves to start out from the umbral oscillating
  elements and to propagate outwards forming concentric circles around the
  elements. The propagation velocity is between 6 to 18 km s<SUP>1</SUP>;
  and the average period is about 190 sec.

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Title: Two dimensional distribution of physical parameters in dark
    mottles assuming constant and non-constant source function
Authors: Tsiropoula, G.; Madi, G.; Christopoulou, E.; Alissandrakis,
   G.; Schmieder, B.; Preka-Papadema, P.
1997jena.confE..60T    Altcode:
  Observations of a rosette region consisting of several dark mottles
  located almost at the solar disk centre (N5, W5) were made with the
  Multichannel Double Pass (MSDP) spectrograph mounted on the 50 cm
  “Tourelle” refractor of the Pic du Midi Observatory, on June 17,
  1986. The MSDP having 11 channels provides at every point of the field
  of view the profile of the H-alpha line, which is reconstructed from
  11 values. The observed contrast profiles of the dark features as a
  function of the wavelength are used in terms of Beckers' cloud model
  (e.g. assuming that the source function is constant throughout the
  feature) in order to derive 4 parameters: the line-of-sight velocity,
  the optical depth at line centre, the Doppler width and the source
  function. The computation of the four parameters was carried out by an
  iterative least square procedure for non linear functions. Allowing
  the source function to have a parabolic variation with the optical
  depth and using the same iteration procedure the source function at
  the centre of the feature and the source function variation factor
  are determined. Comparison of the values of the physical parameters
  derived under these two different assumptions concerning the source
  function is performed. These values are also compared with the values
  obtained from multilevel non-LTE models.

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Title: Comparison of line-of-sight velocities of chromospheric
    structures derived by three different methods
Authors: Tsiropoula, G.; Christopoulou, E.; Madi, C.; Dialetis, D.;
   Mein, P.; Mein, N.
1997jena.confE..61T    Altcode:
  We have used three different methods to derive line-of-sight velocities
  in dark fibrils forming the superpenumbra of an isolated regular sunspot
  located near the centre of the solar disk (NOOA/AR 7783). The present
  observations were obtained on October 3, 1994. They were performed
  with the Multichannel Subtractive Double Pass (MSDP) spectrograph which
  operates in H-alpha and it is installed at the focus of the Vacuum Tower
  Telescope (VTT) at Tenerife (Canary Islands). This instrument records
  a two dimensional field of view on the solar surface with good spatial
  and temporal resolution. The observations were made simultaneously in 9
  wavelengts, 0.3AA apart in the H-alpha profile. At every pixel of the
  2D field of view the line profile can be restored from the measured
  values of the intensity in the 9 channels and a third degree spline
  interpolation. These profiles were used for the computation of the
  line-of-sight velocity by three different methods: (a) the Doppler
  shift method, (b) the photographic subtraction method expressing the
  “Doppler signal” and (c) the classical Beckers' cloud model. 2D
  maps of the velocity are computed, comparison of the values derived
  by the 3 different methods is performed and the conditions governing
  the validity of the 3 methods are stated.