OPTICAL AND INFRARED OBSERVATIONS OF SU T a u V. T. D o r o s h e n k o , Yu. S . E f i m o v , A. E . V. Yu. T e r e b i z h , a n d V. I . S h e n a v r i n
Rozenbush
The results are given of narrow-band (with resolution 50 A a n d 100 A) a n d w i d e band (in the standard J o h n s o n UBVJK s y s t e m ) p h o t o m e t r y , and also polarization observations o f SU T a u i n 1 9 7 4 - 1 9 7 7 . The observed polarization o f SU T a u i s m m basically of interstellar origin. The e s t i m a t e AV ~ 1 . 3 - 2 . 0 for the interstellar absorption l e a d s t o t h e a b s o l u t e m a g n i t u d e MV m _ 3 m o f t h e s t a r , which is characteristic o f RCTB t y p e s t a r s . T h e c o n t i n u u m o f SU T a u n e a r t h e l i g h t maximum c o r r e s p o n d s to supergiants of spectral class not later t h a n G1. In the spectral region 1.25-2.2 ~ t h e r e i s an e x c e s s c o r r e s p o n d i n g to black body radiation of dust with temperature around 103~ Th e d e c r e a s e in the brightness can be attributed to the screening effect of a cloud of graphite particles m with radius ~ 0 . 0 6 ~m. A reduction of the brightness b y ~3 r e q u i r e s a surface density of the dust particles o f o r d e r 1 . 5 . 1 0 1 0 cm- 2 . Th e c h a n g e s i n t h e light o f t h e s t a r a r e a c c o m p a n i e d by c o m p l i c a t e d changes in the color. The greatest reddening is observed during the rising branch of the light curve, which is characteristic o f o t h e r RCrB t y p e s t a r s . Introduction T h e s t a r SU T a u b e l o n g s t o t h e c l a s s o f RCrB t y p e v a r i a b l e s . The comparatively few observations w h i c h h a v e b e e n made o f i t c o r r e s p o n d b a s i c a l l y to the maximal light epoch (see t h e r e v i e w s o f O r l o v [1] a n d F e a s t [2]). In the present p a p e r , we g i v e t h e r e s u l t s of photometric observations in the visible and n e a r i n f r a r e d regions and p o l a r i z a t i o n and spectroscopic observations made i n 1 9 7 4 - 1 9 7 7 a t t h e C r i m e a n S t a t i o n o f t h e P . K. S h t e r n b e r g State Astronomical Institute, the Crimean Astrophysical Observatory, and the Principal Astronomical Observatory o f t h e A c a d e m y o f S c i e n c e s o f t h e U k r a i n i a n SSR. Observations Photometric Observations. In the visible p a r t o f t h e s p e c t r u m t h e s e c o v e r t h e mi ni mum i n 1975 a n d t h e r i s e f r o m t h e minimum i n 1976. For the observations at the Crimean Station, we u s e d t h e 6 0 - c m r e f l e c t o r (Zeiss) with photometer in the photon-counting regime [3], and the 125-cm reflector witha two-channel spectometer also operating in the photon-counting regime, this making it possible to measure simultaneously t h e f l u x i n t h e UBV s y s t e m a n d scan the spectrum [4]. At t h e C r i m e a n O b s e r v a t o r y , measurements of the light, color, and polarization w e r e made w i t h t h e 2 6 0 - c m r e f l e c t o r with the polarimeter described i n [5] a n d the 50-cm meniscus telescope with television attachment [6]. Some e s t i m a t e s o f t h e UBV m a g n i t u d e s w e r e o b t a i n e d w i t h an e l e c t r o p h o t o m e t e r of the Principal Astronomical Observatory fitted to the 48-cm reflector (AZT-14) of the High-Altitude Station on Mount T e r s k o l [7]. The results of the photometric observations a r e g i v e n i n T a b l e 1 , i n w h i c h we h a v e s u c cessively: t h e d a t e s and mean J u l i a n days of the observations, the V magnitudes, the color i n d i c e s B -- V a n d U -- B, a n d t h e t e l e s c o p e used for the observations. The estimates obtained during one night with different instruments have been averaged. Th e rms e r r o r s of the meas u r e m e n t s a r e o v = CB = 0m02 a n d ~U = 0 ~ 0 6 . light
Figure 1 shows the light curve published i n t h e IAU C i r c u l a r s
meter
Polarization [5] a t t h e
o f SU T a u i n t h i s p e r i o d , visual estimates [8 , 9] b e i n g i n c l u d e d f o r c o m p l e t e n e s s .
Observations. T h e s e w e r e made w i t h a s i n g l e - c h a n n e l Cassegrain focus of the 260-cm reflector. The r e s u l t s
of
the
star's
photoelectricpolariof the observations
Crimean Station, P. K. Shternberg State Astronomical Institute; Crimean Astrophysical Observatory; Principal Astronomical Observatory, Academy of Sciences of the Ukrainian SSR. Translated from Astrofizika, Vol. 14, No. I, pp. 5-15, January-March, 1978. Original article submitted August I0, 1977.
0571-7132/78/1401-0001507.50 9 1978 Plenum Publishing Corporation
1
"1974 lX Xl
I
'111
1975 V VII
IX
xi
I
III
1976 V Vii
IX
XI
1977 HI V
~
I
~4
A
t
&
,l
i
?.'
t,'
15
!
9
.,
11
t
,,
t
.
I
,
I
1.2 ~' m 1.6 2.0 >
9
I
......
J
@
"
I
g
"
!
;, , ,
,
! i
9 I
, ,=~
I
" l
9
"" ~"
'I.
% 9
r
3 I . . . .
"3442300
I
I
'
-
0.4
0.82I'
!
400
500
"6(to
,
I,-
700
t
800
900
2_443000 100
200
300
JD Fig. I. V a r i a t i o n s in the light and c o l o r i n d i c e s of S U T a u in 1 9 7 4 - 1 9 7 7 ; the b l a c k t r i a n g l e s are the r e s u l t s of [8, 9] and t h e b l a c k c i r c l e s t h o s e of the p r e s e n t i n v e s t i g a t i o n .
TABLE
Date 19,11.74 25.11.74 02,12.74 15.12.74 I3.01.75 14.01.75 19.01.75 20.01.75 05.03.75 08.03.75 12.03.75 13.03.75 14.03.75 15.03.75 17,03.75 03,12.75 05.12.75 16,01.77 19.01.77 20.01.77 23,01.77 27,01.77 17.02.77 09.03.77 25,03.77 26,03.77 29.03.77
1
JD
t V I
2442371.53 [ 11.25 377.38 [II.28 384.46 II.07 3~7.40 10.86 426.29 11.67 427.22 I1.87 432.46 13.24 433.25 13.70 477.28 13.2 480.35 12.90 484.28 12.4 485.25 12.48 486.31 12.38 487.31 12.27 489.33 12.16 750.47 11.00 752.33 10.93 2443160.34 14.57 163.38 14.33 164.37 14.31 167.44 14.22 170.5 14.0: 192.50 11.90 212.38 11.73
228.35 t 10.78 229.36 / 10. 72 232.33 J[ 10.59
B'V
U--B
-~-1.52 1.54
1.47 1.26 1.44 1.44 l .53 1.52 1.83 1.8 1.86 1.85 1.78 1.74 1.38 1 34 1.80 1.68 1.68 1.65 1.8: 1.38 1.10 1.40 1.37 1.38
+0.64 0.78 0.76 0.77 0.63 0.69
1.18
[
Telescope 260-cm Zeiss
Z e i s s , AZT-14 AZT-14 50-cm, TV 260-cm 50-cm, TV Zeiss
1.34
1.40 1.18
0.82 0.91
AZT-14 Zeiss
1.11 1.03
1.0: 0.46 0.64 0.96 0.75 0.47
125-em 125-em, Zeiss Zeiss 125-em
Zeiss
TABLE 2
B
Date
Jn
19.11.74
2442371.53
16.12.74
398.42
08.03.75
480.35
08.11.75
725.52
P% l 1.66 162.0
V
O
"~
p%! o
]
po/.
2.00! 163.3 1.961 164.41 1.88 , 161.2 IT 1.4 0.07t+ I.O 2.041162.6 1.84 i 162.1] 1.97 159.4 :0.10[+ 1.4 -+0.1:1• 2.s]-+0.09 + 1 . 3 t.52] 158.8 - - [ 11.59 167.0 9O. 191+ 3.5 t I+o.21 --+- 3.8 1.871- 58.o 2.001 155.8t 1.~ i 152.0 :0.07[+ 1.1 -+o.osL 1.2~_,o.2~ If: 5. 3
_+o.o81_+1.11__o.1
il;iiii;
are g i v e n in T a b l e 2, w h i c h c o n t a i n s the d a t e s and J u l i a n days of the o b s e r v a t i o n s , the m e a n v a l u e of the_ d e g r e e of p o l a r i z a t i o n ~ and its rms error q~, the m e a n v a l u e of the p o l a r i z a tion a n g l e 8 of the p l a n e of the e l e c t r i c v e c t o r in the e q u a t o r i a l c o o r d i n a t e s y s t e m and its rms e r r o r ~ for the b a n d s B, V, O, and R w i t h e f f e c t i v e w a v e l e n g t h 4340, 5450, 6190, and 7440 A, r e s p e c t i v e l y . Spectrophotometric Observations. T h e s e w e r e m a d e by m e a n s of two i n s t r u m e n t s . a t the C a s s e g r a i n focus of the 1 2 5 - c m r e f l e c t o r ; a s p e c t r o m e t e r of the Sei--Namioka s y s t e m [i0] in the s p e c t r a l r e g i o n 3 3 0 0 - 7 8 0 0 A w i t h exit slit 6k = 50 A and w i t h the t w o - c h a n n e l s p e c t r o p h o t o m e t e r m e n t i o n e d a b o v e in the r e g i o n 3 5 0 0 - 7 5 0 0 ~ w i t h r e s o l u t i o n ~k = 100 ~. The s t a r s B Ari, BS 2199, and ~ Ari w e r e u s e d as s p e c t r o p h o t o m e t r i c standards. D a t a on the e n e r g y d i s t r i b u t i o n s in the s p e c t r a of t h e s e stars g i v e n in the c a t a l o g [ii] w e r e corr e c t e d w i t h a l l o w a n c e for the n e w c a l i b r a t i o n of a Lyr by H a y e s and L a t h a m [12]. In the e v a l u a t i o n of the o b s e r v a t i o n a l d a t a for 1975 a l l o w a n c e was m a d e for the m e a n annual atmospheric extinction; in 1977, the a t m o s p h e r i c e x t i n c t i o n was d e t e r m i n e d e a c h n i g h t from o b s e r v a t i o n s of a s t a n d a r d star at d i f f e r e n t z e n i t h d i s t a n c e s . Infrared Observations. T h e s e w e r e m a d e w i t h the 1 2 5 - c m r e f l e c t o r b y m e a n s of a photom e t e r w i t h a zinc s u l p h i d e r e s i s t a n c e in the s t a n d a r d J o h n s o n JK s y s t e m w i t h e f f e c t i v e w a v e l e n g t h s 1.25 ~m and 2.2 ~m. In T a b l e 3 we g i v e s u c c e s s i v e l y : the d a t e and J u l i a n day of the o b s e r v a t i o n s , the m a g n i t u d e s in J and K, and the l o g a r i t h m s of the e x t r a a t m o s p h e r i c f l u x e s in the s a m e s p e c t r a l r e g i o n s . D i s c u s s i o n of the R e s u l t s Photometry. As r e g a r d s p h o t o m e t r y , SU T a u is as a c t i v e as RCrB: it has light m i n i m a almost once a year. T h e a m p l i t u d e of the v a r i a t i o n s and the d u r a t i o n of the m i n i m a v a r y considerably. As a rule, the light d e c r e a s e s m o r e r a p i d l y than it increases. In J a n u a r y - - F e b r u a r y 1975, a n o t h e r d e c r e a s e in the l'ight of SU T a u began, a l t h o u g h at that time the star had not yet r e t u r n e d to the n o r m a l state (for which, a c c o r d i n g to F e r n i e et al [13], V = 9.77, B -- V = +1.08, U -- B = +0.43). The d e c r e a s e in the light b ~ 3 m from D e c e m b e r 15, 1974 to J a n u a r y 20, 1975 was a c c o m p a n i e d by an i n c r e a s e in B -- V by 0.3; at the same time, the c o l o r i n d e x U -- B did not c h a n g e w i t h i n the e r r o r s of the o b s e r v a t i o n s . The l a r g e s t v a l u e s of the c o l o r i n d i c e s (B -- V ~ 1.8, U -- B ~ 1.4, V -- J ~ 3.76) w e r e obs e r v e d in the m i d d l e of the r i s i n g b r a n c h of the light c u r v e in the m i d d l e of M a r c h 1975. T h e m i n i m u m of 1976 was d e e p e r and m o r e p r o l o n g e d
t h a n its p r e d e c e s s o r .
TABLE 3 Date
JD 2442000+
17.03.75 17.02.76
489.29 826.42 .44 827.37 848.34 873.27
18.02.76 10.03.76 04.04.76
J
?.eff=1.25 vm
K ?.eft =2.2 um
8.4
ig EA(erg..era-2.sec- i.A-I )
~.=1.25 vm --12.800
6.42~0.05 7.84-+0.09 8.07.-k0.09 8.19-t-0.06
8.20 +__0.15
k=2.2 ~m
6.43+__0.03 6.75~0.06 (6.26-[-0.07):
--12.968 --12.616 --12.708 --12.972 --12.760
--12.972 --13.000 --12.904:
It is i n t e r e s t -
in g to note that, a c c o r d i n g to the m e a s u r e m e n t s of Landolt [14], the color indices at the light m i n i m u m (JD 2443109, V = 16.89) had the values B -- V = +1.08 and U -- B = +0.30 chara c t e r i s t i c of the normal state. As in 1975, the largest c o l o r indices B -- V ~ 1.7 and U -- B ~ 1.1 were o b s e r v e d during the s u b s e q u e n t increase in the light of the star (January 20, 1977). S i m i l a r effects have b e e n o b s e r v e d in o t h e r stars of this type: RCrB [15] and RY Sgr [16]. Polarlmetry. The p o l a r i z a t i o n o b s e r v a t i o n s of SU Tau were m a d e in the p r e - m a x i m u m p h a s e (November 19, 1974, D e c e m b e r 16, 1974, and N o v e m b e r 8, 1975) and d u r i n g the e m e r g e n c e of the star from the deep m i n i m u m (March 8, 1975). As can be seen from Table 2, the p o l a r i z a t i o n in all spectral b a n d s was fairly large (p ~ 1.8%), while the changes in the p o s i t i o n angle 8 w e r e small. The degree of p o l a r i z a t i o n c h a n g e d only s l i g h t l y with the time and was almost i n d e p e n d e n t of the wavelength. A small change in the p o l a r i z a t i o n was o b s e r v e d on M a r c h 8, 1975, w h e n the star was leaving the minimum. The changes in the p o l a r i z a t i o n are c e r t a i n l y m u c h less than those o b s e r v e d d u r i n g the light m i n i m u m of RCrB in 1972. The p o l a r i z a t i o n p a r a m e t e r s of the c o m p a r i s o n star in the immediate p r o x i m i t y of SU Tau were close to those m e a s u r e d for SU Tau. This suggests that the m a j o r part of the o b s e r v e d p o l a r i z a t i o n of SU T a u is due to the i n t e r s t e l l a r medium. To test this assumption, we compared the p o l a r i z a t i o n p a r a m e t e r s of SU Tau and 17 d i s t a n t stars in its n e i g h b o r h o o d in a radius of about 4~ taken from the catalogs of H i l t n e r [17] and M a t h e w s o n and Ford [18]o It was found that the p o s i t i o n angles of the planes of p o l a r i z a t i o n of SU Tau and the n e i g h b o r ing stars w e r e n e a r l y equal. The w a v e l e n g t h d e p e n d e n c e of the degree of p o l a r i z a t i o n for the m a j o r i t y of the o b s e r v a t i o n dates was also little d i f f e r e n t from the d e p e n d e n c e for the i n t e r s t e l l a r m e d i u m (Fig. 2). Thus, the o b s e r v e d p o l a r i z a t i o n of SU Tau is b a s i c a l l y of i n t e r s t e l l a r origin. A c c o r d i n g to H i l t n e r [17], the ratio of the d e g r e e of p o l a r i z a t i o n e x p r e s s e d in magnitudes to the a b s o r p t i o n Au in the d i r e c t i o n of SU Tau is a p p r o x i m a t e l y 0.03, Assuming ~ 1.8% for SU Tau, we then find A V = i~3. C o n s t r u c t i n g thee in a c c o r d a n c e w i t h the data of [17, 18] the d e p e n d e n c e of AV and p on the true d i s t a n c e modulus for stars in the direction of SU Tau (Fig. 3), we o b t a i n the e s t i m a t e m -- M ~ 10-11, w h i c h for m V m a x ~ 9.5 and A V ~ i~5 leads to MV ~ --3 and a d i s t a n c e r z 2 . 5 % p c for the d i s t a n c e to the star~ Spectrophotometry. Our data on the e n e r g y d i s t r i b u t i o m in the c o n t i n u m u of SU Tau refer to three d i f f e r e n t p h o t o m e t r i c states of the star: I) the onset of the d e c r e a s e in the light (January 1975, V ~ 11.4, B -- V ~ +1.4, U -- B ~ +0.8), 2) the state near the m i n i m u m (.January 1977, V ~ 14.3, B -- V ~ +1.6, U -- B ~ +1.0), and 3) a state a p p r o a c h i n g the normal state after the star has left the m i n i m u m (February 1977, V ~ I1.9, B -- V ~ +I~ U -- B
15
\
1.0
0.5 1.0
I
12
I
~
J L R 1.5 0
~
L
~
V 2.0
~ ~~
B
2.5
I/A(~m) Fig. 2. D e g r e e of p o l a r i z a t i o n as f u n c t i o n of the w a v e l e n g t h , i, 2, 3, 4 are the m e a s u r e m e n t s of N o v e m b e r 19, 1974, D e c e m b e r i~, 1974, M a r c h 8, 1975, and N o v e m b e r 8, 1975; 5 and 6 are the c o r r e s p o n d i n g f u n c t i o n s for i n t e r s t e l lar p o l a r i z a t i o n and R a y l e i g h scattering, respectively.
5-
i.
I
I
I
I
I
--
4
;.,...-,
r~
o~O 3-
'~
...
p
2
9 i
I
I
I
|
I
I
I
!
I
I
"~
|
I
I
I
8
9
10
11
12
13
2--
,<
1-
m0-M F i g . 3. Degree of polarization and instellar absorption as functions of the true distance modulus for s t a r s i n t h e n e i g h b o r h o o d o f SU T a u .
-13.5
-44.0
, ~
-14.5
-150 ~ 3000
I
I
I
I
i
4000
5000
6000
7000
8000
Fig. 4. Energy distribution in the cont i n u u m o f SU T a u ; b, c, and d are the observed distributions o n J a n u a r y 10, 1 9 7 5 , F e b r u a r y 17, 1 9 7 7 , a n d J a n u a r y 19/" 20, 1977; a is the distribution b corrected for interstellar absorption.
I
I
i
A
&
B v
-,12.0 r
? -12~S ~0
"~ Gll 1,
~
I
!
~
~.o
~s
~-o
F i g . 5. Energy distribution t r u m o f SU T au a t t h e p e r i o d light.
+0.5).
The c o r r e s p o n d i n g
distributions
are
.
C...--
in the specof maximal
shown in Fig.
4o
The r e l a t i v e energy distributions o n t h e e n t r y t o t h e m i n i m u m a n d when t h e s t a r l e a v e s minimum a r e a l m o s t t h e same. The e n e r g y d i s t r i b u t i o n in the continuum near the light mi n i m u m i s a p p r e c i a b l y "redder" than the distributions i n t h e two o t h e r s t a t e s . Thus, one observes a recovery of the spectral and photometric characteristics of the normal state irrespective of the depth and duration o f t h e minimum. the
Using the estimate made a b o v e f o r t h e i n t e r s t e l l a r absorption (A V ~ 1 ~ 5 ) , we c o r r e c t e d the energy distribution o b s e r v e d o n J a n u a r y 1 0 , 1975 i n t h e c o n t i n u u m o f SU T a u f o r i n t e r stellar absorption (Fig. 4). The r e s u l t i n g energy distribution agrees well with the energy distributionin the continuum of supergiants of the spectral c l a s s G1 ( T e l f ~ 5 0 0 0 - 5 5 0 0 ~ ) . According to modern ideas, the decrease in the brightness o f RCrB t y p e s t a r s a n d t h e corresponding changes in the energy distribution i n t h e c o n t i n u u m a r e due t o t h e a b s o r p t i o n of light resulting from the formation of graphite particles above the photosphere~ The e f fective sizes of the particles can be estimated from spectroscopic observations made n e a r t h e l i g h t m i n i m a and maxima. The s p e c t r o s c o p i c characteristics o f RCrB a r e known t o v a r y d u r i n g d i f f e r e n t minima in much t h e s a m e w a y . Since the spectroscopic variations o f SU T a u h a v e b e e n i n a d e q u a t e l y studied, we s h a l l a s s u m e t h a t t h e o b s e r v a t i o n s o f J a n u a r y 1 9 , 1977 c o r r e s p o n d t o t h e t y p i c a l state of minimal light, and t h e o b s e r v a t i o n s o f J a n u a r y 1 0 , 1975 t o t h e t y p i c a l state near t h e maximum. The e n e r g y d i s t r i b u t i o n a t t h e minimum i s g i v e n by I m i n ( ~ ) = Imax(X) exp ( p ~ X ) , w h e r e TX = n - s - Q ~ a 2 i s t h e o p t i c a l thickness of the dust cloud, s is its geometrical thickness, n and a are, respectively, the concentration a n d mean r a d i u s o f t h e g r a p h i t e partic!es~ a nd QX i s t h e a t t e n u a t i o n efficiency factor. U s i n g t h e d a t a on t h e e n e r g y d i s t r i b u t i o n , we c a n show t h a t TA a s a f u n c t i o n o f ~ - 1 i s an a p p r o x i m a t e l y linear function w i t h s l o p e o~ about 0.67, which, according to the calculations of Patterson et al [20], corresponds to particles with diameters 0 . 0 1 ~m a n d 0 . 0 6 ~m. Here, the larger size of particle must probably be taken since otherwise the observed wavelength dependence of the degree of polarization would differ more from that for the interstellar polarization in the direction of the dependence characteristic for polarization in the case of Eayleigh scattering. It can on the other hand be assumed that the sizes of the particles of the interstellar d u s t c l o u d do n o t e x c e e d those of the p a r t i c l e s of i n t e r s t e l l a r dust. A s s u m i n g for the g r a p h i t e p a r t i c l e s < a ) ~ 0.065 ~m, (T~) = 3, T$ = 5000~ ( Q } ~ 1.5-2.0 [21], we find that the total n u m b e r of p a r t i c l e s in a column of unit cross s e c t i o n is N = 1.5-1010 cm-2. For RCrB, on the b a s i s of the o b s e r v a t i o n s of the m i n i m u m in 1974--1975, P a t t e r s o n et al [20] found the similar
value N ~ i0 I0 cm -2. Infrared Photometry. The e s t i m a t e s g i v e n f o r t h e l i g h t o f SU T a u i n t h e i n f r a r e d range are as yet the only ones made for this star. The o b s e r v a t i o n s o f 1976 r e f e r t o t h e p h a s e of normal light. According to the data of [9], mvi s ~ 10.2 at this period. Assuming that t h e c o l o r i n d i c e s B - - V and U -- B o f t h e s t a r a t t h e t i m e t h e i n f r a r e d observations were made a r e e q u a l t o t h e v a l u e s + 1 . 0 8 a n d + 0 . 4 3 t y p i c a l for the maximal light state, we c a n readily obtain the energy distribution i n t h e SU T a u s p e c t r u m i n t h e r e g i o n o f 0 . 4 - 2 . 2 ~m (Fig. 5). As c a n b e s e e n f r o m F i g . 5, t h e e n e r g y d i s t r i b u t i o n i n t h e s p e c t r u m o f SU T a u (.corrected for interstellar absorption) agrees satisfactorily in the wide spectral interval 0.4-1.25 pm w i t h t h e s p e c t r u m f o r a s t a r o f t h e s p e c t r a l class GII. At longer wavelengths, t h e SU T a u s p e c t r u m h a s a n e x c e s s o f r a d i a t i o n , due probably to the presence of the dust. According to Feast and Glass [19], such infrared e x c e s s e s a r e o b s e r v e d i n a l l s t a r s o f RCrB type. If the entire e x c e s s i n t h e SU T a u s p e c t r u m i s a s c r i b e d to the presence of dust in the atmosphere of the star, then the temperature o f t h e d u s t i s c l o s e t o 1 O00-1100~ Thus, a dust component is also present a t t h e t i m e s when t h e s t a r i s i n t h e n o r m a l s t a t e .
LITERATURE CITED 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. ii. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21.
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