The behavior of hydrogen-line brightness variations, depending on the prominence-velocity changes were investigated. By solving the NON-Local thermodynamic equilibrium (LTE) problem for hydrogen researchers determine quantitatively the effect of Doppler brightening and/or Doppler dimming (DBE, DDE) in the lines of Lyman and Balmer series. It is demonstrated that in low-density prominence plasmas, DBE in H alpha and H beta lines can reach a factor of three for velocities around 160 km/sec, while the L alpha line exhibits typical DDE. L beta brightness variations follow from a combined DBE in the H alpha and DDE in L alpha and L beta itself, providing that all relevant multilevel interlocking processes are taken into account

Heinzel, P.

Rompolt, B.

English

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. o
N87-20895
NON-LTE HYDROGEN-LINE FORMATION IN MOVING PROMINENCES
P. Heinzel
Astronomical Institute, 251 65 Ond_ejov, Czechoslovakia
B.-Rompolt *
High Altitude Observatory, NCAR, Boulder, CO 80307, U.S.A.
ABSTRACT
We investigate the behaviour of hydrogen-line brightness variations, depending
on the prominence-velocity changes. By solving the non-LTE problem for hydrogen
we determine quantitatively the effect of Doppler brightening and/or Doppler dimming
(DBE, DDE) in the lines of Lyman and Balmer series.It is demonstrated that in low-den-
sity prominence plasmas, DBE in Ha and HB lines can reach a factor of three for veloci-
ties around 160 km/sec, while the La line exhibits typical DDE. LB brightness variations
follow from a combined DBE in the Ha and DDE in La and L B itself,providing that
all relevant multilevel interlocking processes are taken into account.
INTRODUCTION
In the present paper we investigate the problem of hydrogen emission
emergent from prominence structures moving in the corona. In fact, there exists
a vast literature concerning the formation of emission lines in quiescent
prominences (see the review by Hirayama, 1985 or Heinzel et al., 1986), but
the influence of the prominence macroscopic motions on the amount of the emitt-
ed line radiation has not been studied yet in greater detail. Considering
the hydrogen spectrum, only Rompolt (1980 a, b) has made some calculations
of brightness variations in Balmer lines caused by velocity changes, assuming
a two-level atom undergoing radiative transitions. Since there exist several
observational indications of, at least, Ha brightness variations in different
moving structures, which can be explained in terms of the so-called Doppler
brightening and/or Doppler dimming effect (DBE, DDE) (see Rompolt, 1967; Hyder
and Lites, 1970; Labonte, 1979; Kawaguchi et al., 1984), we address this study
to a detailed non-LTE treatment of hydrogen-line formation in moving prominen-
ces. We try to assess the prominence brightness variations caused by the macro-
scopic-velocity changes, keeping other prominence parameters fixed for the
moment. As a result, we present here the first quantitative estimates of DBE
and DDE in hydrogen lines and briefly discusse the influence of various promi-
nence-plasma parameters on such brightness variations.
On leave from the Wroclaw University Observatory, Poland
163
https://ntrs.nasa.gov/search.jsp?R=19870011462 2020-03-20T11:52:05+00:00Z
NON-LTE RADIATIVE TRANSFER IN A MOVING PROMINENCE
For the purpose of this rather exploratory work we use a simplified one-di-
mensional geometry where the prominence is represented by a plane-parallel
slab of finite thickness and its motion is simply simulated by determining
the velocity-dependent boundary conditions. This schematic approach avoids
complicated multidimensional solutions, still keeping the basic non-LTE physics
of the problem. For a five-level model atom of hydrogen we solve simultaneously
the radiative transfer equations in all Lyman transitions and in the Ha line
(the radiation field in the remaining transitions is fixed by the external
solar radiation), together with the equations of statistical equilibrium and
particle and charge conservation equations. The corresponding numerical procedu-
re is the same as that applied by Heinzel et al. (1986) for quiescent prominen-
ces. As the basic iteration loop we use a linearization scheme similar to
that of Mihalas et al. (1975), supplemented by several equivalent-two-level-atom
iterations in order to accelerate the convergence. Hydrostatic equilibrium
is treated iteratively. We use all hydrogen opacity sources which are important
in low-density prominence plasmas; the hydrogen atomic data were compiled
from different sources (inelastic collisional rates are computed according
to Mihalas et al., 1975).
As a result, we obtain the overall excitation and ionization balance
for hydrogen in the moving prominence, depending on the velocity v, height
H above the solar surface and on the basic input parameters M, T, p, v_ M
• • • _i
is the total column mass along the line of sight, T is the kznetlc temperature
of the plasma, p represents the total gas pressure and vt characterizes the
mean microturbulent velocity. To obtain the correct gas density structure,
the prominence is assumed to be composed of helium and hydrogen with the abun-
dance ratio equal to 0.1 (a contribution of helium ionization to the total
electron density is negligible under typical prominence conditions).
Photospheric and chromospheric line radiation fields incident at the
prominence at a given height determine (i) the velocity-dependent radiative
rates for all optically-thin lines, and (ii) the velocity-dependent surface
boundary conditions for all line transitions treated explicitely (i. e. Lyman
lines and Ha). Both these quantities have been precomputed for a given grid
of velocities using the method described by Heinzel (1983). The incident radia-
tion fields used here are identical to those described in Heinzel et al. (1986)
and also the continua are treated in a similar way.
In this paper we use the complete frequency redistribution for all lines,
but we cannot rule out possible effects of quasi-coherent scattering in L_
and LB line wings on the velocity-dependent level populations (for higher
velocities, most of the incident L_ and LB radiation is absorbed in the wings).
NUMERICAL RESULTS AND DISCUSSION
From the velocity-dependent level populations we computed the emergent
integrated intensities for all lines of interest and for radial velocities
in the range of 0 - 240 km/sec. To demonstrate the effect of the prominence
motion on the hydrogen-line emission, we define here the relative intensity
or brightness W = E(v)/E(O), where E is the velocity-dependent integrated
intensity. For the sake of illustration, we have selected one representative
isothermal-isobaric model with parameters H=50000 km, M=1.2xlO -s g/cm 2, T=SSOOK,
p=O.l dyn/cm 2, vt=O km/sec (the geometrical thickness amounts about 650 km).
164
The resulting electron density n generally depends on the velocity, but fore
velocities up to about 200 km/sec thls dependence is very weak and n can
be regarded as nearly constant - this fact allows us to estimate the importance
of various MHD-processes leading to density variations.
The behaviour of W for our schematic model is displayed in Fig. 1 for
Lyman and Balmer lines.
5_
_.0
3_
2.0
H-_
/
/
/
/
/
/
/
/
/
/
10 L_
RAD_L VEL_ES VO_/S)
Figure 1
Brightness variations for Lyman and Balmer lines as computed for the model
described in the text. Full lines correspond to multilevel non-LTE solution,
dashed line corresponds to a two-level model atom without collisions.
165
Due to a decrease of the second-level population for higher velocities, the
La brightness decreases as demonstrated in Fig. I thls decrease represents
typical DDE. A more complicated situation occurs for third level, the popula-
tion of which depends on three factors: DDE in La , a similar effect in
and an important DBE in H_ line. The rate of radiative excitation in these
lines is roughly proportional to velocity-dependent incident line radiation
so that the third-level population inside the prominence body remarkably increa-
ses for velocities up to about 160 km/sec (DBE in Ha is dominant), and then
decreases due to the action of DDE in La and LB itself. Since the third level
of the hydrogen atom represents a common upper state for both LB and Ha lines,
the behaviour of the brightness variations in these two lines is similar except
for higher velocities, where the optically-thin Ha line still exhibits DBE
while the surface emission of L B is strongly affected by DDE in LB itself
(see Fig. I). DBE in Ha takes place for velocities up to about 160 km/sec
which is in qualitative agreement with the results of Hyder and Lites (1970).
A similar behaviour was also found for the HE line, while Hy exhibits a less
pronounced DBE, reaching only a factor of two. Finally, in Fig. I we compare
our "exact" Ha brightness variations with those following from a two-level-atom
approximation without collisions (see Rompolt, 1980 a, b). The significant
difference between these two curves is the consequence of the multilevel inter-
locking (including the effect of continua) and the appropriate DDE in La and
LB which are not accounted for by the two-level-atom model.
To obtain a more complete picture of the various interdependences, we
have also computed some examples using other values of T, vt and p. An increase
of T or vf generally leads to a prominence brightening, namely for lower veloci-
ties. For_high velocities, the changes in T or v_ do not affect DBE significant-
ly. Cas pressure p determines the plasma density and, consequently, also the
electron density which controls the rate of collisional transitions. As could
be expected, for higher n we arrived at much less pronounced DBE in Balmer
e
lines since the source functzon becomes collisionally-dominated. For ne of
the order I_3 we observe practically no velocity effects on the line source
functions (the model discussed above led to n = 2.43 x I0 i° cm _ ).
e
Our non-LTE modelling of a moving prominence can equally be applied to
other coronal structures like limb flares, cool coronal loops, various types
of prominence ejecta and transient Ha- phenomena. If the hydrostatic equilibri-
um used here is replaced by more realistic MHD-equilibria, the present approach
can serve as a basis for further development of adequate spectral diagnostics
of the prominence plasma and deeper understanding of the relevant radiation-hyd-
rodynamical processes.
The authors are indebted to NASA for its financial support which enabled them
to participate in the CPP-Workshop.
166
REFERENCES
Heinzel, P.,1983, "Resonance Scattering of Radiation in Solar Prominences",
Bull. Astron. Inst. Czechosl., 34 (I).
Heinzel, P., Couttebroze, P., Vial, 3. C., 1986, "Partial Redistribution
Effects in the Formation of Hydrogen Lines in Quiescent Prominences", this
volume.
Hirayama, T., 1985, "Modern Observations of Solar Prominences", Sol. Phys.,
tO0 (415).
Hyder, Ch. L., Lites, B., 1970, "Ha Doppler Brightening and Lyman-a Doppler
Dimming in Moving HaProminenees", So1. Phys., 14 (147).
Kawaguchi, I., Nakai, Y., Funakoshi, Y., Kim, K. P., 1984, "Brightening Phenomena
in Prominences at the Center of the Haline", Sol. Phys., 91 (87).
Labonte, B., 1979, "Activity in the Quiet Sun", Sol. Phys., 61 (283)
Mihalas, D., Heasley, 3. N., Auer, L. H., 1975, "A Non-LIE Model Stellar Atmo-
sphere Computer Program", NCAR Technical Note, NCAR-TN/STR-I04.
Rompolt, B., 1967, "The Ha Radiation Field in the Solar Corona for Moving
Prominences", Acta Astron., 17 (329).
Rompolt, B., 1980 a, "Doppler Brightening Effect in Ha Line for Optically
Thin Moving Prominences", Hvar Obs. Bull., 4 (39).
Rompolt, B., 1980 b, "Doppler Brightening of Active Prominences in Hydrogen
Balmer Lines", Hvar Obs. Bull., 4 (49).
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Non-LTE hydrogen-line formation in moving prominences

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