VECTOR MAGNETIC FIELDS IN PROMINENCES III: He I D 3 Stokes Profile Analysis for Quiescent and Eruptive Prominences R. GRANT ATHAY and CHARLES W. QUERFELD* High Altitude Observatory, National Center for Atmospheric Research** RAYMOND N. SMARTT Sacramento Peak Observatory EGIDIO LANDI DEGL'INNOCENTI Instituto di Astronomia Universitd di Firenze and VERONIQUE BOMMIER Observatoire de Paris (Received 21 June, 1983) Abstract. Observations of linear polarization in two resolved components of He I D 3 are interpreted using the Hanle effect to determine vector magnetic fields in thirteen prominences. As in all vector magnetic field measurements, there is a two-fold ambiguity in field direction that is symmetric to a 180 ~ rotation about the line-of-sight. The polar angles of the fields show a pronounced preference to be close to 90 ~ from the local solar radius, i.e., the field direction is close to horizontal. Azimuth angles show internal consistency from point to point in a given prominences, but because of the rotational symmetry, the fields may be interpreted, in most cases, as crossing the prominence either in the same sense as the underlying photospheric fields or in the opposite sense. An exceptionally well observed large prominence of approximately planar geometry exhibits no measur- able change in the vector magnetic field either with height or with location along the prominence axis. A second well observed large prominence overlying a sharply curved magnetic neutral line, when interpreted assuming that the prominence field has the same sense as the photospheric field, shows a rotation in the azimuth angle of the field relative to the observer by about 150 ~ and relative to the local plane of the prominence by about 65 ~ In the alternative interpretation in which the prominence field has the opposite sense of the photospheric field, the field still rotates by 150 ~ relative to the observer but remains essentially constant with respect to the plane of the prominence. This prominence erupted shortly after the extended observations. One good quality observation during the course of the eruption gives a vector field fully consistent with the pre-eruption field in the same segment of the prominence. 1. Introduction Measurements of magnetic fields in prominences can be grouped in three classes according to the nature of the observations: (1)circular polarization from Zeeman * Currently at Ball Aerospace Systems Division, Boulder, Colo., U.S.A. ** The National Center for Atmospheric Research is Operated by the University Corporation for Atmospheric Research under sponsorship of the National Science Foundation. Solar Physics 89 (1983) 3-30. 0038-0938/83/0891-0003504.20. 1983 by D. Reidel Publishing Company.
Transcript
VECTOR MAGNETIC F I E L D S IN P R O M I N E N C E S
III: He I D 3 Stokes Profile Analysis for Quiescent and Eruptive Prominences
R. G R A N T A T H A Y and C H A R L E S W. Q U E R F E L D *
High Altitude Observatory, National Center for Atmospheric Research**
R A Y M O N D N. SMARTT
Sacramento Peak Observatory
E G I D I O L A N D I D E G L ' I N N O C E N T I
Instituto di Astronomia Universitd di Firenze
and
V E R O N I Q U E B O M M I E R
Observatoire de Paris
(Received 21 June, 1983)
Abstract. Observations of linear polarization in two resolved components of He I D 3 are interpreted using the Hanle effect to determine vector magnetic fields in thirteen prominences. As in all vector magnetic field measurements, there is a two-fold ambiguity in field direction that is symmetric to a 180 ~ rotation about the line-of-sight. The polar angles of the fields show a pronounced preference to be close to 90 ~ from the local solar radius, i.e., the field direction is close to horizontal. Azimuth angles show internal consistency from point to point in a given prominences, but because of the rotational symmetry, the fields may be interpreted, in most cases, as crossing the prominence either in the same sense as the underlying photospheric fields or in the opposite sense.
An exceptionally well observed large prominence of approximately planar geometry exhibits no measur- able change in the vector magnetic field either with height or with location along the prominence axis. A second well observed large prominence overlying a sharply curved magnetic neutral line, when interpreted assuming that the prominence field has the same sense as the photospheric field, shows a rotation in the azimuth angle of the field relative to the observer by about 150 ~ and relative to the local plane of the prominence by about 65 ~ In the alternative interpretation in which the prominence field has the opposite sense of the photospheric field, the field still rotates by 150 ~ relative to the observer but remains essentially constant with respect to the plane of the prominence. This prominence erupted shortly after the extended observations. One good quality observation during the course of the eruption gives a vector field fully consistent with the pre-eruption field in the same segment of the prominence.
1. Introduction
Measurements of magnetic fields in prominences can be grouped in three classes according to the nature of the observations: (1)circular polarization from Zeeman
* Currently at Ball Aerospace Systems Division, Boulder, Colo., U.S.A. ** The National Center for Atmospheric Research is Operated by the University Corporation for Atmospheric Research under sponsorship of the National Science Foundation.
Solar Physics 89 (1983) 3-30. 0038-0938/83/0891-0003504.20. �9 1983 by D. Reidel Publishing Company.
4 R. GRANT ATHAY ET AL.
splitting; (2) broad band linear polarization; and (3) narrow band Stokes profiles giving both linear and circular polarization. The first is the classical magnetograph technique used by Rust (1966), Harvey (1969), Tandberg-Hanssen (1970), and others. The second method has been used extensively by Leroy (1977, 1978) and Leroy etal. (1983) to observe the Hanle effect in HeI D3, and has provided the first sound information on field direction. The broad band method is limited, however, in that it produces only two observed parameters, viz., amplitude and direction of linear polarization. Thus, it is insufficient for determining the full vector field. Leroy (1978) has circumvented this shortcoming by assuming that the field direction is always in the plane perpendicular to the solar radius, which reduces the vector field description to the field strength and a single azimuth angle. The assumption made by Leroy (1978) appears to be eminently reasonable, but needs observational verification.
Narrow band Stokes polarimetry in the D 3 multiplet was carried out by the High Altitude Observatory and Sacramento Peak Observatory for an extended period during 1978, 1979, and 1980. The instrument is described by Baur etaL (1980, 1981). The observations typically give well-defined /, Q, and U profiles describing the linear polarization in both the central group of five unresolved lines and the resolved line approximately 340 m~, to the red of the main component. Since in these observations the average Doppler width of D 3 in quiescent prominences is near 150 mA, the wing component is easily resolved. Occasionally the circularly polarized V profile in D 3 is sufficiently intense to provide a usable signal, also.
Since the narrow band data give four linear polarization parameters (two for each component), they fully define the vector magnetic field, apart from symmetry ambi- guities. If the V profile is usable, it provides an independent check on the results from the linear polarization.
The appropriate theoretical framework for using the Hanle effect to interpret the linear polarization in broad band D 3 profiles has been developed by Bommier (1980) and Bommier etal. (1981), and in narrow band, spectrally resolved profiles by Landi Degl'Innocenti (1982). The latter work also includes the theoretical basis for interpreting the circularly polarized V profiles. Preliminary analyses of limited data sets from the narrow band Stokes profile observations have been given by House and Smartt (1982), and the analysis of the V profile for a single observation is given by Landi Degl'Innocenti (1982). A more detailed analysis of two prominences is given by Querfeld et aL (1983).
Leroy's (1977, 1978) early results from broad band observations for 82 quiescent prominences may be summarized as giving average field strengths of 6.5 G and a reasonably smooth distribution of azimuth angles from near 0 ~ to near 90 ~ with a statistical preferenc e for values under 30 ~ (angles are measured relative to the long axis of the prominence). Both Leroy's results and earlier results give some indication that the field strength, B, increases slowly with height and is larger in polar prominences than in quiescent prominences in active region latitudes. More recent investigations by Leroy et al. (1983) of 120 quiescent prominences of the polar crown type show evidence for a solar cycle effect on the average field strength, which increases from 6 G near sunspot minimum to 12 G near sunspot maximum.
VECTOR MAGNETIC FIELDS IN PROMINENCES, III 5
In the present paper, we determine vector magnetic fields for 13 quiescent promi- nences, including those at both polar and active latitudes. The analysis uses the Hanle effect and yields the full vector field. No assumptions are made concerning the field strength or direction.
2. Observations
The data reported in this paper are complete Stokes profiles for the D 3 mutiplet of He observed in thirteen prominences. Two of the prominences, which occurred in April 1979, were observed with the High Altitude Observatory Stokes I polarimeter (Baur et al., 1980). The remaining eleven were observed in August, September, and October of 1980 with the HAO Stokes II polarimeter (Baur et al., 1981). A single observation of a prominence consists of complete wavelength profiles of all four Stokes parameters for the resolved components of the D 3 multiplet at one spatially resolved feature within the prominence. Through the use of two linear detector arrays to measure the polari- zation signals simultaneously at different wavelengths, the Stokes II instrument com- pletes the profile measurements in about 10%, or less, of the time required by the Stokes I instrument, for a given signal-to-noise ratio. This makes it possible to obtain measurements at many more points in a given prominence with the Stokes II instrument.
Typical observing times per prominence point are 1.5 to 2 min with the Stokes II instrument. The aperture area on the prominence is selected at either 10" • 3.8" or 10" • 6.8" at the discretion of the observer. The narrower dimension is the width of the spectrograph entrance slit which is aligned E-W in geocentric coordinates. The 10" axis of the aperture is therefore aligned N-S in geocentric coordinates. The Reticon detectors have 128 pixels with spectral resolution at D 3 of 22 mA per pixel providing a wavelength coverage of 2.8 ,~.
In a study of eight prominences observed in April 1978 and October 1980, the ratio of intensities for the two resolved multiplet components of D 3 averaged over individual prominences varied from 6.1 : 1 to 7.6 : 1. Similarly averaged Doppler widths varied from 140 to 190 mA. Average Doppler widths in the two resolved multiplet components are closely equal. The theoretical intensity ratio for optically thin radiation and no magnetic field is 8 : 1, and the thermal Doppler width at 6000 K is 98 mA. Since the chromosphere observed at the limb at eclipse is optically thin in D 3 (Athay and Menzel, 1956), it is highly likely that prominences are optically thin also. Thus, it is unlikely that either the intensity ratios within the multiplet or the line widths are influenced by optical thickness of the prominences. Further evidence for low optical thickness of prominences in D 3 is given by the close equality of the average widths for the two resolved components of the multiplet and by the relative faintness of prominences in D 3. If the optical thickness approached unity, for example, prominences would be expected to be much brighter than is observed.
Table I gives dates, position angles, prominence characteristics, aperture sizes, and numbers of vector magnetic field determinations for each of the thirteen prominences studied in the paper. The different prominences are identified with letters B through N
6 R. GRANT ATHAY ET AL.
according to the chronological order in which they were first observed. All of the prominences are associated with disk filaments and most are relatively quiescent. One prominence, G, was observed during eruption, and a second, B, showed considerable activity during the period of observation. Five of the prominences were observed on two or more consecutive days.
Position angles of the prominences are measured from solar north with positive angles to the east. Two other angles of critical importance to the analysis are the angle Z giving the angular distance from the point observed in the prominence to the plane containing the solar limb and the aspect angle giving the orientation of the long axis of the prominence relative to the line-of-sight. The first is important for determining the true height of the observed point above the solar surface, and the second is important for relating the azimuth angle of the vector magnetic field to the axis of the prominence itself. The Z and aspect angles vary with location in the prominence and are given subsequently in Table II.
The number of field determinations given in Table I includes only the cases that give reasonably well defined solutions for the vector field. In some cases where the data appear to be good, the vector field analysis gives either several disparate solutions of approximately equal apparent validity or gives a preferred solution with excessively high field strength and anomalous field angles. Since the analysis is based on the Hanle effect, which results in decreased polarization for larger field strengths, solutions with large field strengths are suspect. In principle, the Hanle effect as applied here, should give reliable results up to field strenghts of the order of 100 G. However, we find empirically that the results begin to look spurious for field strengths greater than about 40 G, and we reject most such solutions. A few exceptions are made where relatively strong fields have directions that are consistent with nearby data points. In the majority of cases favoring high field strengths, however, both the field strength and direction are markedly at variance with surrounding data points. The failure to successfully measure fields in excess of about 40 G could be due, in part, to other depolarizing processes, such as collisional excitation of the D 3 multiplet. It is probable, also, that fields of this strength are rare in the types of prominences studied in this paper.
For several of the prominences included in Table I a sizeable fraction of the data points gave unacceptable solutions, and in a prominence observed on 23 October, 1980 none of the data points gave acceptable results. Thus, some of the cases shown in Table I that have only a few data points are indicative of difficulties in satisfactorily determining the vector field.
It appears from an inspection of the data for cases giving unacceptable results that most of the difficulties occur when the height of the observed point is less than 15" from the limb or in prominences whose aspect angle (the angle between the long axis of the prominence and the line-of-sight) is small. The observations of the former class are probably confused by scattered light from the disk, and those of the latter class are probably confused by the long integration length for the observed radiation. However, in a few cases, where the prominences are favorably oriented the analyses fail to give acceptable fits to the Stokes profiles. Whether these are due to complex field structure
VECTOR MAGNETIC FIELDS IN PROMINENCES, 111 7
TABLE I
Summary of prominences observed
Designation Dates Average Slit width a No. of Filament pos. ang. results charac-
teristics
B 24-27 April, 1979 212 3.8 11 long, high, active
C 25 and 27 April, 1979 27 3.8 2 patehy, low
D 15 and 16 August, 1980 115 3.8 86 long, very high
E 17 September, 1980 262 6.8 1 patchy, low
F 17 and 19 September, 1980 355 6.8 25 polar crown~
patchy
G 19 and 20 September, 1980 45 6.8 26 long, high, eruptive
H 20 September, 1981 310 6.8 11 isolated patch
I 18 October, 1980 115 6.8 9 long, low
J 18 October, 1980 234 6.8 1 low mound
K 18 October, 1980 308 6.8 1 low mound
L 22 October, 1980 115 6.8 11 long, low
M 22 October, 1980 245 6.8 3 isolated cloud and low mound
N 30 October, 1980 70 6.8 6 low with extended arches
a E - W dimens ions of observ ing aperture in arc see. The N - S d imens ion is 10" in all cases .
in the prominences, to poor observing conditions or to instrumental causes is not known.
Prominences D, G, and N in Table I are of unusual interest. Figure 1 shows an He image of prominence D observed on 16 August together with a drawing showing the location of the data points. The numbering of the data points is discussed in Section 3.
8 R. G R A N T A T H A Y ET AL.
PROM D
12e 14 o8 ol3 0 �9 IlO&l �9 . ~ f V 1~ ' '4 "8 -13 ~ I O0 . 8 "15&4
- i � 9 3/b 014
PROM D 1 6 / 8 ,
Fig. l. An Hcr image of prominence D on 16 August and sketches of the prominence outline on 15 and 16 August. The numbered points indicate sequences of observational runs, and the dots, open circles, squares and triangles represent different observing sequences. The sketches and locations of observing
points are made from slitjaw images made at the times of observations.
VECTOR MAGNETIC FIELDS IN PROMINENCES, III 9
Both the large number of data points and the uniformity of the vector magnetic field make this an exceptional case.
Prominence G is shown in Figure 2 at three different epochs. The first set of observations was mde on 19 September during a quiescent phase. The second extensive set of observations was made on 20 September just prior to an eruptive phase. A third single observation made when the eruption was well underway gives a seemingly reliable field determination. A further unusual feature of this prominence is its association with two distinct filament channels. The southern end of the prominence joins with a NE-SW filament channel crossing the limb near position angle 52 ~ whereas the northern end joins with an E-W filament channel crossing the limb near position angle 40~ Evidently the prominence lies in a highly curved juncture of the two filament channels much as if the prominence were cradlet along the bottom of a V shaped channel.
Such a pattern is confirmed by both He disk images and full disk magnetograms made on several successive days following the eruption on 20 September. The magnetic region between the two filament channels is predominantly unipolar, and it is logical to join the two filament channels into a single magnetic neutral line with a blunted-V shape at
p~O~ G
PROM G 7 ~ ~ 20/9, OP
PROM G 20/9
Fig. 2. An He image of prominence G on 20 September and sketches of the prominence outline on 19 September and 20 September. The He image was made approximately four hours before the eruption and the two sketches on 20 September were made approximately two hours before and 12 rain after eruption.
Only one data point was obtained after eruption.
10 R. GRANT ATHAY ET AL.
its eastern extremity. In the He disk images following the eruption, there is no sign of a filament crossing the base of the V until after 24 September. Beginning on 25 Septem- ber and continuing on subsequent days, there is again evidence of a filament forming across the base of the V connecting the two extended legs of the filament channel. The association of the prominence with a bridge between two diverging legs of a magnetic neutral line is crucial to the interpretation of the magnetic field orientation in this prominence, as discussed in Section 3. Also, such an association accounts for the otherwise puzzling observation that the northern and southern extremities of the prominence cross the solar limb at about the same time even though neither of the associated filament channels has a N-S orientation. As a final case in point, the study of coronal transient events clearly associated with disk filament eruptions in Hc~ by Trottet and MacQueen (1980) shows a strong preference for the underlying filaments to have a N - S orientation. Their results imply that eruptive prominences, in general, have a preferred N - S orientation, which is consistent with the proposed orientation for the eruptive prominence of 20 September in our data set.
Prominence N, shown in Figure 3, is of unusual interest in that it shows bright curved arches extending from the main body of the prominence back to the chromosphere.
PROM N :.30/10
Fig. 3. An Hc~ slitjaw image and sketch of prominence N made on 30 October. The arches extending from the main body of the prominence provide an independent estimate of the magnetic field direction.
VECTOR MAGNETIC FIELDS IN PROMINENCES, III 11
Since the arches are long relative to their height, it is reasonable to assume that they are oriented more-or-less in the plane of the sky. Also, at the points where the arches branch from the main body of the prominence they parallel the solar limb. Thus, assuming that the arches follow magnetic lines of force, we have an indication that the field direction is close to 90 ~ from the line-of-sight and tangent to the solar limb. This provides a valuable consistency check for the vector field results from the polarization
data.
3. Vector Field Analysis
The theory of polarization in the D 3 multiplet arising from the Hanle effect and the detailed analysis of the Stokes profiles to determine the vector magnetic field is outlined in papers by Bommier and Sahal-Brechot (1978), Bommier (1980), Bommier etal .
(1981), and Landi Degl'Innocenti (1982). In summary, the analysis seeks a best fit between four observed quantities (amplitude and direction of linear polarization in the two resolved components of D3) and three magnetic field parameters (amplitude and two direction angles). In terms of the Stokes profiles, the four polarization parameters appear as the amplitudes of the Q and U profiles for the two components. Two additional parameters entering the analysis are the height, h, of the observed point above the solar surface and the angle, Z, giving the angular distance from the observed point to the solar limb. The height is necessary in the determination of the anisotropy of the radiation incident on the prominence, and X is necessary both for determining h and the geometry of scattering, which effects the observed polarization.
In performing the analysis, we assume that X and h are known from observations. In reality, of course, they are both uncertain. The uncertainty in Z is sometimes difficult to estimate, but is rarely better than about 5 ~ For most of the data, the absolute value of )~ is less than 10 ~ and the errors in h resulting from errors in X are estimated to be 5" to 10". In the extreme case, Z is as large as - 18 ~ and the error in h resulting from an error of + 5 o in Z is 30", which is a serious error. Errors in Z and h are ignored in the analysis.
Rather than repeat here the details of the diagnostic methods described by Bommier (1980), Bommier et aL (1981), and Landi Degl'Innocenti (1982), we give descriptive synopses. The magnetic field is defined by three quantities: B, 0, and q~. B is the field strength, and 0 is the polar angle measured from the vector B to the local solar radius. In the Landi method, q~ is the azimuth angle of the vector B from the line-of-sight measured in the plane perpendicular to the local radius, as shown in Figure 4. In the Bommier et al. method, however, the azimuth angle, t, is the angle between the field projection on the solar surface and the local latitude circle. We adopt the Landi convention for this analysis. Note that the planes in which 0 and q5 are measured are not fixed with respect to the line-of-sight - they vary with )~.
Using the observed values ofh and )~ at a given point in a prominence and the Landi method, we assume a value for one of the three parameters B, 0, and qS. We then construct a map of the 'distance parameter' d, as a function of the remaining two variables. The distance parameter is defined as the rms of the residuals between the four
12 R. GRANT ATHAY ET AL.
Fig. 4.
~ ~ Projected
An illustration of the angles 0 and q5 defining the magnetic field direction with respect to the local solar radius vector.
observed Stokes parameters and their predicted values for the assumed set for Z, h, B, 0, and q~. For example, if we choose a value for B together with Z and h, each pair of values for 0 and q~ define the polarization parameters, and these parameters, when compared to the observed ones, define d. Thus, the 0, ~p plane defines a contour plot of d. For a different assumed value of B, we obtain a new (and different) contour plot of d. For each observed point in the prominence, therefore, we compute a family of contour plots for d(O, 4, B). We then seach this family of contour plots for the minimum value of d. In principle, the procedure is straightforward even though it requires sub- stantial amounts of computing time.
In the Bommier etal. (1981) method, the two multiplet components are treated separately. Each component is used to determine B and t for fixed values of 0in intervals of 5 ~ Since there are two data points for each multiplet, B and t are uniquely determined for each selected value of 0. The final choice of 0 is made by minimizing the quantity
[ IB~(O) - Bm(O)l ]2 f(O) = , (1)
IBM(O) + ~ ,~ (0 ) ] ~
where BM(O ) and B,,(O) are the field vectors for the major and minor line components, respectively. For the results presented in this paper, the t angle used in the Bommier et aL method is converted to q~ to be consistent with the Landi method. "
Since the two methods of analysis contain the same physics and differ only in the numerical method for finding the preferred solution, they give very close results in almost all cases where both methods are used.
Unfortunately, there are other complicating factors. In determining the magnetic field
VECTOR MAGNETIC FIELDS IN PROMINENCES, IlI 13
vector using the Hanle effect, there is an inescapable two-fold ambiguity. A given magnetic field vector and its symmetric image obtained by a 180 ~ rotation around the line-of-sight axis produce exactly the same polarization signature. For )~ = 0, this symmetry is manifest in d(O, (o) contour plots (also in f (O)) as an exact symmetry between 0, 4) and n - 0, - 4). Thus, there are two identical minima at dl(01, 4)0 and dl(n - Ol, 4)1). Because the degeneracy arises from the physics of the scattering process, it is not possible to choose between the two on the basis of the polarimeter data.
When Z ~ 0, the scattering that produces the linear polarization in D 3 is observed in a plane that is not at right angles to the solar radius vector and the symmetry relations between 0, 4) and n - 0, -4) are approached but not quite fulfilled. The inherent ambiguity is still present, however. Since X is nearly always small and uncertain, we treat all solutions as being ambiguous with respect to 0, 4) and n - 0, - 4).
In some cases the ambiguity between 4) and - 4), can be interpreted as an ambiguity as to whether the vector field direction crosses the prominence in the same sense as the photospheric field crosses the magnetic neutral line underlying the prominence or whether the two fields have opposite sense. Such a choice is possible when the absolute values of both 4) and n - 4) are greater than the absolute value of the aspect angle of the prominence. If either 4) or rc - 4) fail to meet this criterion, both 4) and - 4) correspond to field directions crossing the prominence in the same sense.
Two further types of ambiguity arise from noise in the data and from fine structure in the major component of D3. Both effects produce valleys in the d(O, 4)) contour plots which then tend to have two or more minima of comparable value. Thus, one may find
several minima dl(Bl , O1, 4)0, dz(B2, 02, 4)2), d3(B3, 03, 4)3), etc., with nearly equal values.
In most cases, the choice of solutions clealy favors a single pair dl(B1, 01, 4)0 and its equivalent dl(B1, ~z - Ol, - 4)0. In other cases, where multiple solutions appear to be equally acceptable, the solutions are often close enough together to give one effective result. There are cases, however, where either there are no values of d~(B~, O1, 4)1) sufficiently small to be acceptable, or there are so many acceptable values with widely divergent combinations of B, 0, and 4)that no sensible choice can be made. Data points that fall within these latter two categories are discarded.
For the data reported in this paper, we use both methods of analysis described in the preceding paragraphs. The Bommier et al. method has been used on all prominences. The Landi method has been used on prominences D, E, F, G, and H. In the cases of prominences F, G, and H, the Landi method gives more definitive results than does the Bommier et al. method. The only distinguishing property of these prominences is that they have weaker than average magnetic field strengths.
Table II lists all of the vector field results in chronological order of the observations. Values of B, 0, and 4) in parenthesis are obtained using the Bommier et al. analysis, and those not in parenthesis are obtained using the Landi analysis. The observation number gives the observing order preceding the decimal followed by the operation number and the letter designation for the prominence. Operation numbers that are missing or have values less then 20 were made before noon, local time. Those that exceed 20 were made
14 R. GRANT ATHAY ET AL.
TABLE II
Tabulat ion of prominence parameters and vector magnetic field results listed chronologically
Date and location Obs. no. ~ h B 0 ~P ~*, ~s
24Apri l , 1979 3 B 10 33 (18) (50) (96) 146, - 4 6 P A 2 1 4 4 B 10 47 (11) (55) (123) 173, - 7 3 AA - 50 5 B 10 71 (12) (90) (165) - 145, - 115
PA221 8 B 0 20 (14) (50) (149) - 161, - 9 9
AA - 50
25Apri l , 1979 3 B 0 17 (11) (115) (141) - 159, - 81 PA 212 AA - 60
P A 2 7 10 C 0 15 (9) (95) (159) - 3 6 , 6
A A 1 5
26 April, 1979 3 B ' 10 32 (8) (85) (142) 142, - 142 PA208 4 B ' 5 42 (6) (95) (137) 137, - 137 A A 0 5 B ' 0 85 (15) (95) (127) 127, - 127
PA215 2 1 B 0 53 (13) (105) (130) - 155, - 5 5 AA - 7 5 22 B 0 114 (20) (90) (123) - 162, - 4 8
27Apri l , 1979 3 B ' 0 15 (10) (95) (117) 132, - 102
i 1.10 N 0 10 (7) (85) (70) 2.10 N 0 23 (4) (80) (72) 4.10 N 0 33 (29) (95) (65) 5.10 N 0 28 (46) (90) (124) 6.10 N 0 20 (21) (75) (136)
11.10 N 0 10 (32) (95) (51)
after noon. The observation points shown in Figures 1, 2, and 3 are numbered sequen- tially in the order in which they were made. Different operation numbers are indicated in Figure 3 by different types of points (dots, open circles, etc.). The two methods of analysis were not always used on the same sets of points within a prominence. Thus, the absence of a result from one or the other method is not necessarily an indication that the method failed.
Position angles and aspect angles are given under the dates using the same convention for aspect angles as for r The Z angle is given in degrees with negative angles behind the limb. Heights are given in arc seconds as true heights. B is in gauss.
Because of the symmetry properties for 0 and r all values of r are given between 0 ~ and 180 ~ . The column labelled ~b*, ~ gives the two possible values of the azimuth angle of the field relative to the long axis of the prominence. The first entry, ~p*, corresponds to the tabulated r and the second entry, r corresponds to - r Positive values of qS* or ~ represent fields crossing the prominence in the same sense as the underlying photospheric fields, which is from positive to negative polarity. Negative values repre- sent prominence fields in the opposite sense to those in the photosphere. In cases where the values of r determined by the two methods of analysis differ by 30 ~ or less, we average the two values. Otherwise, we choose the single value closest to the average for the prominence.
VECTOR MAGNETIC FIELDS IN PROMINENCES, III 19
The circularly polarized V Stokes profiles are normally within the noise level of the HAO instrument for the D 3 multiplet. In a few cases, however, good V profiles are obtained and can be used to check the results obtained from the analysis of linear polarization (Landi Degl'Innocenti, 1982). Eleven cases in which the V profiles confirm the solutions from the linear polarization analysis are indicated by asterisks preceding the observation number in Table II. Five cases where there is disagreement, are indicated by zeros preceding the observation number. In three of these five cases, the V profiles prefer solutions with field strengths near 50 G and 0 and q~ angles that are discordant with those elsewhere in the prominence. For the remaining two, the vector fields from the linear polarization give V profiles that look much like the observed ones but of opposite sign. All five of the discordant profiles are dominated by the Zeeman splitting term (Landi Degl'Innocenti, 1982).
In the following, we discuss the results for each prominence separately. Prominence B. A careful inspection of this prominence, shown in Figure 5, including
its extensions on the disk and the associated filament channel prior to west limb passage, indicate that the prominence was highly curved. The southern most extension of the prominence, labelled as B' in Table II, has an apparent aspect angle near 0 ~ whereas the northern half of the prominence has an aspect angle ranging from - 50 ~ on 24 April to - 75 ~ on 26 April.
Results for the B' segment show consistent values for the vector field with average values of B -- 10 G, 0 = 92 ~ ~ = 135 ~ and ~ = - 135 ~ . In segment B, however, there is less consistency. Four of the seven points show consistent field orientations in 0 and qS* whereas the remaining three are discordant. For the four consistent points the
Fig. 5. An He image of prominence B on 25 April.
20 R . G R A N T A T H A Y E T A L .
average values are B = 14 G, 0 = 100 ~ and ~p* = - 155 ~ . Values of ~p* for these same
four points are all negative, also, but scatter from - 48 ~ to - 115 ~ On this basis, the
preferred result is for a negative field orientation with ~b* = - 155 ~ for segment B and
(p* = - 135 ~ for segment B ' . Two other prominences, I and L, show a similar pattern.
Two reasonably good height sequences were observed in prominence B. These are
plotted in Figure 6 as fluctuations from the values at the lowest heights. The results are
inconclusive, but they suggest that any systematic vertical gradients in B, 0, or ~b that
might be present are not uniform throughout.
zx~
A0
. . . . . . . . . . . j ..... j ,
I / I
Prom. B .~ s
J J
/ / ' / I Z~0,A~=IO
/ \
\ \ \ \
- f f i
I o 50 IOO
HEIGHT (are sec)
Fig. 6. Fluctuations in B, 0, and q~ for two height sequences in prominence B. The fluctuations are measured relative to the values at the lowest heights. Similar plots for prominences D and G are shown in Figures 8
and 10.
During the time of observation, prominence B was moderately active and changed considerably in outline. The activity may account for some of the observed scatter in
0 and 4. Prominence C. This is a high latitude prominence with a small aspect angle and a
limited vertical extent. The associated disk filament consists mostly o f isolated clumps
rather than a continuous filament. The vector field is consistent on both o f the dates this prominence was observed even
though the dates are separated by two days. Average values are B = 12 G, 0 = 92 ~ 4)* = - 35~ and ~s* = 5 ~ For the choice of either ~b* or q~*, the field orientation is close
V E C T O R M A G N E T I C F I E L D S I N P R O M I N E N C E S , II1 21
to the long axis of the prominence. The northern halves of prominences G and B shows similar results.
The results for prominence C should be accepted with some caution. As noted, the observations are made close to the limb and at low aspect angle. Both of these conditions lead to difficulty in determining the field. Close to the limb the polarization is influenced by strong scattering from disk light, and at low aspect angles the path length through the prominence is presumably large.
Prominence D. This very large quiescent prominence, shown in Figure 1, is the most extensively observed of all the prominences in this study. During the two days of observation on 15 and 16 August and on the following day, the prominence remained stable and, except for rotation effects, showed little change in outline. At approximately 11 : 58 UT on 18 August the prominence erupted reaching an observed height of 0.58 R o (NOAA reports for SMM). The coronagraph polarimeter on the SMM satellite observed a large, bright coronal transient associated with the eruption (Wagner, private communication). On 20 August, after the filament channel had rotated onto the disk,
/ ' ~ _ , 0 ( - ) i ~ (+) , " \
/ ~ t / " ~ d �9 / z . \ \ \ / *
I ~ I I \\ J / \\ � 9 \t
t / ~ /\ / \ / ( \�9 �9 X X t l I I "~ \ \ l / / u * . : I% / I I * I / ~ \ z ~ / i � 9 1 4 9 1 4 9 � 9 1 4 9 I
/ '~ ^ \ ~ (-) / <it> (+) , ' \ . , , / t " r o m / t~S \ ~ - - ' i - ~ / x \
/ x / / \ � 9 14- x \ x / ~ / / \ \ \ / \
I ~/ . I * \ ~ ~ " - - - ~ /i \ .,A/ \ I I x x / ;" ~ 7 \ \ I I ~
I I 7 ~ l / \ , I I \ . / ' ~ \ ",
I F I .Z X I i / ~" �9 I t I I i I ~ \ i t i l I
I " I" (~ " 1% . 1 1 - 9 0 i - - ~ / ,- �9 9 0 I I I X t / Z ~' ," ~ / * * I I I I i l t \ / \ ~ / �9 \ � 9 ~ 1 �9 I , ~ , \ . " -' I ~1o ~ / "/ t �9 I
x \ / / ' ) ' , , \ \ \ \ / \ \ / 3 0 I ~ i I ~" \ ~z. v I " i
\ \ 1 \ / /
, ; z i8o .-"~
/ e~o~. 6N ', ~ ()_- / x / / ' ~
I x x t / / / \
I / "7~ i I \ \
I I I I ~ ~ \ - 9 0 ~ - - q r .;
I 1 t \ / x ~ /
I\ \ \ \ / / / \ \ I I \ \ < \l
~ y / \ \ \ /
\ / x \ \ /
I 4*(§ ? ' \ ", \ / \
I / ". \ / / \ / ", ~ \
p ~ \ I I I
, . / �9 1 9 0 1 x" I [
'>1o" - . / , I - \ 7 " ~ r II 11
\ \ / 3 0 /"/~ \ . - ~ >/
_ 4 0 / / / \ \ / / 1
\ \ 2 0
180
Fig. 7. Polar diagrams for prominences D, G, and I. Magnetic field strength (gauss) is plotted as the radial coordinate. Positive azimuth is plotted in the right hemisphere and negative azimuth in the left hemisphere. The azimuth angle is defined with respect to the plane of the prominence. A positive angle means that the magnetic field has the same sence as the underlying photospheric field. The two encircled points for
prominence G s represent the observation made after the prominence erupted.
ZX88 8
22 1~. G R A N T A T H A Y E T A L .
the filament had reformed in an approximately straight channel with an average aspect angle near 30 ~ . This is consistent with the appearance of the prominence at the limb and suggests a relatively simple planar geometry.
Values of B range from 10 to 45 G, with an average of 20 G. Values of 0 stay remarkably close to 90 ~ with an average of 88 ~ Nearly 80~o of the cases give 0between 80 ~ and 100 ~ The 4r* and q~*, which are plotted in Figure 7, cluster into two rather well defined groups with averages of qS* = 86 ~ and ~ = - 146 ~ It is very tempting, in this case, to choose the positive value, which places the field essentially at right angles to the prominence and in the same sense as the photospheric field. Similar options are available for the southern half of prominence G and prominences E and M.
Of the six V profiles tested for prominence D, three confirm the solutions from the linear polarization. Of the three that fail, two are of marginal signal-to-noise quality. In these cases, the solutions preferred by the V profiles correspond with the second or third best solutions from the Q and U profiles with preferred fields near 50 G. The third failure, at point 13.22D, has good signal-to-noise quality and indicates a solution near 50 G, 0 -- 36 ~ and q~ = 160 ~ which agrees with the results from the Q and U profiles using the Landi analysis. However, both of these results disagree with the results from the Bommier et al. analysis. It is significant that this observing point, labeled as 13 with a solid square in Figure 1, is very near the limb, which characteristically leads to difficulty in fitting the observed profiles. Thus, it appears wisest to consider this data point as being questionable.
I I
Prom, D
I I 50 100
HEIGHT (arc sec)
I I
AO
I I 50 IOO
HEIGHT (arc sec)
f I 50 I00
HEIGHT {arc sec)
Fig. 8. Fluctuations in B, 0, and ~p for nine height sequences in prominence D. The fluctuations are measured relative to the values at the lowest heights. Note the absence of any systematic trends and the
large fluctuations in qb as compared to the fluctuations in 0.
The stability and height of prominence D provided an excellent opportunity to study height gradients in the vector field. Figure 8 shows plots of AB/B, AO, and Aq~ for nine height sequences in prominence D. In each case, the reference values for B, 0, and q~ are the values at the lowest height in the sequence. It is immediately evident from the plots that there are no systematic average gradients of significance. One of the height
VECTOR MAGNETIC FIELDS IN PROMINENCES, II1 23
sequences shows an increase in AB/B of + 1 from 30" to 100". Aside from this one case, the average value of B at 100" is just the same as the average value at the bases of the
height sequences. The polar angle 0 is surprisingly steady with only one excursion in Figure 8 as large
as 10 ~ On the other hand, the azimuth angle, ~b, has a much larger variance with several excursions in excess of 20 ~ This same tendency for fluctuations in ~ to exceed considerably the fluctuations in 0 is present throughout the data for the entire promi- nence set. The increased variance in ~b could be due, in part at least, to curvature in the plane of the prominence. Otherwise, the fluctuations in B, 0, and ~ are probably indicative of the uncertainties in their determination.
Prominence E. Although there is only one observation in this prominence, the results giving B ~ 23 G, 0 ~ 92 ~ 4" = 89~ and ~ = - 179 ~ are entirely consistent with results from prominence D. Also, the V profile confirms this solution, which adds considerable confidence.
Prominence F. This prominence, in similarity with prominences C and N, is distin- guished by its relatively low height, its small aspect angle, and low magnetic field strengths. It is part of a polar crown filament of patchy character. The observations are made at the western extremity of the filament as it crosses the limb. Since the aspect angle is low, the line-of-sight through the prominence very likely encounters a number of regions with different polarization properties. Thus, the observed polarization is much more likely to be compromised by averaging than in cases where the aspect angles are reasonably large.
Average values for the vector field in prominence F are B = 6 G, 0 = 96 ~ qS* = 49 ~ and q~* = - 29 ~ The field strength is the lowest for any of the prominences observed. The 0 angle shows more spread than usual. However, ~ and 4" are reasonably well defined. In the two observations on 17 September for which good V profiles were obtained, the V profiles yield B = 10 G, 0 = 70 ~ qS* = 88 ~ and qS* = - 68 ~ These values are consistent with the linear polarization results for the same data points, but they differ substantially from the average values from 19 September. This suggests that the field orientation may have changed between the two dates.
Prominence G. The association of prominence G, shown in Figure 2, with a highly curved region of a magnetic neutral line was discussed in Section 2. Polar diagrams for
" ~ " ~ " LOS
Fig. 9. A cartoon of the adopted outline of prominence G as seen from above. The arrows show She average azimuthal direction of the magnetic field in the two sides of the prominence. Solid arrows have the positive
sense relative to photospheric fields and dashed arrows have the negative sense.
24 R. GRANT ATHAY ET AL.
the northern and southern branches of this prominence are shown in Figure 7. Average field parameters are B = 10 G, 0 = 100 ~ ~b* -- 21, and ~ = - 41 ~ for the northern branch and B = 20 G, 0 = 88 ~ 4r* = - 26 ~ and q~ = 106 ~ for the southern branch.
Figure 9 illustrates schematically the outline of prominence G together with the possible choices for the azimuth of the field. The solid arrows are positive azimuth and the dashed arrows are negative azimuth. Note that the choice of positive azimuth places the field nearly at right angles to the southern half of the prominence and nearly along the northern half of the prominence. On the other hand, the choice of negative azimuth maintains essentially the same field direction with respect to the two branches of the prominence.
Three good V profiles obtained on 20 September in the northern branch confirm the results from the linear polarization. Of four good V profiles obtained on 19 September in the southern branch, two confirm the linear polarization results and two fail to confirm. The two that fail to confirm have the correct shape but the wrong sign.
It is of interest that the highly curved photospheric neutral line and the overlying prominence may not be accompanied by the same rotation in the field direction in the prominence, as evidenced by the difference of about 85 ~ in the positive values of azimuth for the two halves of the prominence. We will comment further on this point in Section 4. It is of interest, also, that there is little apparent change in 0 and q~ in the southern half of the prominence between 19 September and after the eruption is well underway on 20 September.
Observations in the northern half of the prominence on 20 September ended at 16 : 16 UT. The one observation in the southern half after the prominences erupted was started at 18:40 UT. The drawing shown in Figure 2, made from filtergrams of the observed region, shows the top of the prominence at approximately 170" beyond the limb, which is about 100" above the pre-eruption height. Assuming an eruptive velocity of 100 km s- 1, we find the approximate time of eruption as 18:28 UT, which is some two hours after the observations in the northern half of the prominence ended. In view of this possible two hour delay, it seems likely that any major readjustment of the magnetic field associated with the eruption would have occurred after the termination of the observations in the northern half of the prominence. Also, the observation after the eruption was well underway is entirely consistent with observations in the same area made prior to eruption. It seems most logical, therefore, to associate the rotation in q~ between the northern and southern halves of the prominence with the changing orien- tation of the prominence rather than with a transition from quiescent to eruptive phase.
Figure 10 shows plots ofAB/B, AO, and Ac~ for four height sequences observed on 19 and 20 September. The top curve is for 20 September and the lower three are for 19 September. Again, there is little evidence for any systematic gradients of significance. The fluctuations that are present are more likely indicative of uncertainties in the vector field determinations than in real changes in the vector magnetic field.
Observations with the coronagraph polarimeter on SMM in the sector where prominence G erupted were not started until 21 : 35 UT, some three hours after the eruption. No remaining activity was observed.
VECTOR MAGNETIC FIELDS IN PROMINENCES, III 25
Fig. 10.
AO I I
Prom, G
~AO=IO /
I I 25 50 75
[ I
aS
25 50
HEIGHT (Qrc sec)
Fluctuations in B, 0, and q~ for four height sequences in prominence G.
Prominence H. This isolated patch of prominence material was observed on the disk
prior to west limb passage as a very short and rather dark filament of relatively stable appearance. In spite of its short length, it is possible to identify an aspect angle of 40 o.
Average vector field parameter for prominence H are B = 7 G, 0 = 93 ~ qr* = 64, and ~b* = - 144. With the exception of one point (2.9), the values of 0 and q~ are quite consistent throughout the prominence.
Prominence I. This long, low prominence observed at the east limb showed only weak polarization. Half of the eighteen points where observations were made could not be fitted well enough to give definitive results. The remaining half, given in Table II and
plotted in Figure 7, show an average field strength of 27 G, which is indicative of the
weak polarization. The polar angles, as in most filaments of this type, cluster near 90 ~ , with an average of 82 o. However, the q~ angle clusters into two distinct groups, one near
~b = 105 ~ and a second near ~b = 40 ~ For the former case, the choices relative to the axis of the prominence are 4" = 35~ and ~b* = - 175 ~ and, for the latter case, the choices are 4" = - 30 ~ and ~s = - 110 ~ Since three of the four choices give field directions close to the axis of the prominence, this appears to be the best choice.
Prominences J and K. These are two small mounds with undefined aspect angles. Both show polar angles near 90 o and azimuth angles near 70 ~ The field strengths of 25 G for prominence J and 13 G for prominence K are consistent with values observed in other prominences.
Prominence L. This is another long prominence of moderate height and reasonably well defined aspect angle. The field strengths average 7 G, which ranks among the lower group for prominences of this type. As in all of the well defined cases, the polar angles cluster near 90 ~ with an average of 91~ However, the azimuth angles, are somewhat scattered. Most of the scatter results from points 12.2, 14.2, and 16.2. If these points
26 R. GRANT ATHAY ET AL.
are omitted, the remaining eight points give an average q~ = 39 ~ This yields 4 ' = - 31 ~ and ~ = - 109 ~ There seems little doubt, therefore, that the azimuth angle is negative with respect to the axis of the prominence.
Prominence M. Point 1.4M in this prominence is a small isolated cloud of material disconnected from the rest of the prominence. The field strength of 5 G and the polar angle of 85 ~ seem reasonable for a small detached cloud. The ~p angle is rotated some 80 ~ with respect to the values at points 2.4M and 3.4M. However, these points were observed approximately 6 ~ in solar latitude north of point 1.4M. Points 2.4M and 3.4M are extensions of a patchy disk filament. Filaments of this type do not commonly show detached clouds of the type observed. Thus, it may well be that point 1.4M is not directly associated with the main prominence.
Points 2.4M and 3.4M have field strengths of 18 and 27 G, polar angles near 95 ~ and azimuth angles near 45 ~ The average values of ~p* = - 176 and ~ = 96 ~ again leave a choice between a field nearly parallel to the prominence axis or nearly at right angles to it.
Prominence N. This low latitude prominence has a small but uncertain aspect angle. The neutral line over which it formed meanders markedly. However, as shown in Figure 3 and as discussed in Section 2, the long arch structure extending from the prominence gives some suggestion of the field direction independently of the polari- zation data. The arches extending from the main body of the prominence appear to have a large aspect angle.
Points 1.10N and 2.108 are located near the junctures between the two brightest arches and the main prominence body. Both of these cases show field strenghts near 6 G, polar angles near 85 ~ and azimuth angles near 75 ~ These results suggest that the field lies along the arches consistently with the inferred directions of the arches discussed in Section 2.
For the remaining four seemingly good points in this prominence, the values for B and ~b are quite scattered. These points are well within the main body of the prominence where the aspect angle is small. This suggests that the only results to be taken seriously are for points 1.10N and 2.10N; which is not surprising in view of the difficulties sometimes experienced with prominences with low aspect angles.
4. Conclusions
A summary of the most acceptable results for twelve prominences is given in Table III. The averages quoted here represent all of the data points and do not necessarily agree with some of the selective averages quoted in the text. It is clear from the averages that the polar angle is consistently near 90 ~ Since the HAO Stokes polarimeters are the first instruments capable of measuring the polar angle, this is an important and unique result.
Of the 24 azimuth angles given in Table III, 13 are negative, 10 are positive, and one is + 180 ~ Considering both positive and negative values, we find 9 cases where the field is within 30 ~ of the prominence axis, 9 cases where it is between 30 ~ and 60 ~ and
VECTOR MAGNETIC FIELDS IN PROMINENCES~ III 27
T A B L E III
S u m m a r y o f vec to r m a g n e t i c field p a r a m e t e r s
P r o m i n e n c e PA B 0 ~* ~
B ~ 212 14 79 - 169 - 7 4
B s 208 10 93 135 - 135
C 27 12 93 - 35 5
D 115 20 88 86 - 146
E 262 23 90 90 • 180
F 355 6 96 49 - 29
G u 45 10 100 21 - 41
G s 50 20 88 - 26 106
H 310 7 93 - 144 64
I 115 27 82 7 - 147
J 234 25 90 -
K 308 13 110 -
L 115 7 91 - 14 - 126
M 250 23 98 - 176 96
6 cases where it is greater than 60 ~ For the cases greater than 60 ~ 5 are positive and one is negative. However, for cases between 30 ~ and 60 ~ only two are positive and 7 are negative, and, for cases less than 30 ~ 5 are negative, and one is neutral. Because of the ambiguity between & and q~*, it is possible in every case except two to choose positive field azimuth and in every case except one to choose negative field azimuth. This makes it difficult to attempt any generalization about azimuth angles. If the 11 cases where the field can be chosen as negative are each chosen in that sense, all 11 can be chosen to lie within 45 ~ of the prominence axis, and only two values can be chosen above 45 ~ On the other hand, if the 10 cases where positive azimuth can be chosen are each chosen in that sense, 7 lie above 45 ~ and only three lie below 45 ~ On this basis, it appears that if the fields are predominantly in the negative sense they are more likely to lie within 45 ~ of the prominence axis, whereas if they are predominantly in the positive sense they are more likely to lie beyond 45 ~ from the prominence axis.
The two cases, B~v and L, where only negative choices are allowed indicates that prominence fields sometimes do have the negative sense. Also, the two cases, G u and /, where the choice of either q~* or ~ gives field angles within 41 ~ of the axis of the prominence indicate that such cases are not uncommon. On the other hand, the possibility of choosing four cases, D, E, Gs, and M, for which the field direction is positive and greater than 70 ~ from the prominence axis is suggestive that this is a common mode. The large number of consistent data points for prominence D giving 4r* near 90 ~ makes it very tempting to adopt this as the true field orientation.
The absence of cases in which both ~p* and qS~* are close to + 90 ~ is not an argument against azimuth angles with such values. Such a result is possible observationally only in the case of prominences with low aspect angle for which we have few good examples.
The results in Table III disagree somewhat with some earlier results on prominence
28 R. G R A N T A T H A Y ET AL.
vector magnetic fields. Leroy (1977, 1978) has reported results from 82 quiescent prominence in which he finds an average field strength of 6.5 G and a notable tendency for more prominences with azimuth angles with respect to the prominence axis less than 30 ~ than with azimuth angles greater than 60 ~ .
In a recent study of 120 polar crown prominences, Leroy et al. (1983) find a cyclic effect in the field strength with the average B increasing from 6 G near sunspot minimum to 12 G near sunspot maximum. They again find a marked preference for azimuth angles in the range 15 ~ to 30 ~ Leroy's data are similar to ours in that they are based on polarization in D 3 and are interpreted in terms of the Hanle effect. They differ from ours in that they use only net polarization averaged over the multiplet whereas our data utilize the Stokes profiles for the two resolved components of D3. Since Leroy's data provide only two observational parameters (amplitude and direction of linear polarization), it is necessary in the analysis to assume one of the angular values for the vector field. Leroy assumes a polar angle of 90 ~ which, in view of our results, is not a serious limitation. Nevertheless, it should be kept in mind that our analysis is the first extended analysis of data from which it is possible to derive all three components of the vector magnetic field.
From a study of 70 quiescent prominences in which the fine-of-sight component of field strength was measured with a magnetograph using the Zeeman effect, Tandberg- Hanssen and Anzer (1970) concluded that the component of the field along the long axis of the prominence was statistically stronger than the field component normal to the prominence plane. They deduced from the relative strengths of the two components that the average value of 4" is near 15 ~ Similar results were recently published by Kim et al.
(1982). In our data, we find no evidence for such a trend. In addition to average field strengths increasing from 6 G near sunspot minimum to
12 G near sunspot maximum found by Leroy et al. (1983), there are a number of earlier measurements of the strength of the line-of-sight component B IJ from Zeeman splitting. Average values ofB pl quoted by different observers are 5 G (Rust, 1966), 6.6 G (Harvey, 1969), 7.3 G (Tandberg-Hanssen, 1970), and 11.7 G (Kim et aL, 1982). The results by Kim et al. (1982) and Leroy et aL (1983) for the same time period as our observations give average field strengths near 12 G, which compares favorably with the average value of 15 G for the present study.
We have checked our solutions to see if we have for some reason selected solutions that systematically favor higher field strengths. The result is negative. Of 83 field deter- minations in prominence D, 53 of our selected solutions give the minimum field strength. For these cases, any other reasonable choice would increase B. In 30 cases, there are possible choices with values of B lower than the one selected. If we take the lowest possible value of B among the range of acceptable solutions for these 30 cases, the average B for the 83 observations is reduced from 19 G to 15 G.
It appears from the results in Table III that average field strengths in quiescent prominences vary by at least a factor of four. As noted, there appears to be no significant trend in our data for a correlation between field strength and height. There does, however, seem to be a trend with position angle. Of the 6 prominences in our study
VECTOR MAGNETIC FIELDS IN PROMINENCES~ Il i 29
within 35 ~ of the solar equator, 4 have field strengths of 20 G, or higher, and an average of 18.5 G. On the other hand, of the three prominences within 35 ~ of the solar poles, 2 have field strengths of 10 G, or less, and an average of 10 G. Since the number of cases is small, this result is only suggestive of a possible trend.
Recently, a new source of data has yielded information on the orientation of the magnetic field at transition region heights relative to the photospheric neutral line. The line-of-sight direction of fluid flow observed in CIV with the Solar Maximum Mission satellite shows a close correlation with photospheric neutral lines (Athay et al., 1982). The persistence of sharply defined reversals in the line-of-sight velocity across neutral lines observed at low aspect angles strongly suggests that the field azimuth is sometimes at a small angle to the neutral line. In addition, individual loops observed on the disk in CIV, often cross neutral lines at a small angle (Athay et al., 1983). Many cases of flow at large angles to the neutral line and individual loops crossing the neutral lines nearly at right angles are also observed in CIV. Thus, the observed tendency for ~* to range over all angles in prominences is fully consistent with the CIV results.
The internal consistency of the results in Table II leave little doubt that, when circumstances were favorable, we successfully determined both 0 and 4) to an accuracy of the order of 5 ~ in 0 and 10 ~ in q~. In all except the simplest case of a perfectly planar prominence sheet, q~ undoubtedly varies with location in the prominence. This intrinsic fluctuation in ~ makes it more difficult to determine reliable average values, particularly at low aspect angles.
The internal consistency in our data decreases markedly for observations made within about 15" of the limb and for some prominences observed at low aspect angles. Neither case is surprising. The increased scattering of disk light near the limb reduces the accuracy of the polarimetric data, and at low aspect angles the increased path length through the prominence produces the equivalent of poor spatial resolution.
The problem at low aspect angles occurs commonly in attempts to study polar crown prominences. These are often relatively low, patchy filaments encircling the heliographic pole. Thus, at limb passage they are very often at low aspect angle. In future studies of magnetic fields in polar prominences care should be taken to select examples with aspect angles that are reasonably large.
In summary, we appear to have established a strong, perhaps universal, preference for prominence magnetic fields to lie in or near the horizontal plane. On the other hand, we find considerable evidence for a variety of azimuth angles relative to the prominence axis. Some cases are strongly suggestive of azimuth angles near 90 ~ , whereas others clearly favor small angles. Similarly, some prominences seem clearly to have field directions in the opposite sense to the underlying photospheric field whereas others appear to favor fields whose sense is the same as that in the photosphere. These diverse results for the azimuth angle are consistent with the results of Leroy (1977, 1978) and Leroy et al. (1983).
Our inability to remove the ambiguity in the azimuth angles for individual prominences is frustrating, but it is an inherent property of such measurements. It can be removed only by recourse to other independent observations of the field direction.
30 R. GRANT ATHAY ET AL.
Acknowledgements
The authors are indebted to T. Baur, D. Elmore, and D. Mohr for their efforts in carrying out the observational program and to S. Jackson and D. Mohr for their assistance with the data reduction and analysis.
References
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for publication. Rust, D.: 1966, Thesis, Univ. of Colorado, Boulder, Colo., U.S.A. Tandberg-Hanssen, E.: 1970, Solar Phys. 15, 359. Tandberg-Hanssen, E. and Anzer, U.: 1970, Solar Phys. 15, 158. Trotter, G. and MacQueen, R. M.: 1980, Solar Phys. 68, 177.
