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Proper motions of 64 RR Lyrae variable stars
C h i n e s e Astronomy
3 (1979) 296-307
Pergamon P r e s s . P r i n t e d i n G r e a t B r i t a i n
0146-6364/79/0901-0296-$07.50/0
Acta Astr. Sinica 1.~9 (1978) 192-203
PROPER MOTIONS OF 64 RR LYRAE VARIABLE STARS
Wan Lai
He Miao-fu
Zhu Guo-liang
Shanghai Observatory, Academia Sinica Li
Zhong-yuan
University of ScienceandTechnologyofChina ABSTRACT The r e l a t i v e p r o p e r m o t i o n s o f 64 RR Lyrae v a r i a b l e s a r e d e t e r m i n e d u s i n g T u r n e r ' s method. The f i r s t - e p o c h p o s i t i o n s a r e t a k e n from t h e C a r t e du C i e l A s t r o g r a p h i c C a t a l o g u e , w h i l e t h e s e c o n d - e p o c h p o s i t i o n s a r e measured p o s i t i o n s from p l a t e s t a k e n w i t h t h e 40-cm r e f r a c t o r ( f = 6 . 9 m) o f t h e Z6-S~ S e c t i o n , Shanghai O b s e r v a t o r y , i n 1962-65. The a v e r a g e i n t e r v a l b e t w e e n t h e two epochs i s about 60 y e a r s . The mean e r r o r in the proper motion i s ± 0,005"/y. The a b s o l u t e p r o p e r m o t i o n s o f t h e s e v a r i a b l e s a r e found a f t e r c o r r e c t i n g f o r t h e p a r a l l a c t i c m o t i o n s and t h e g a l a c t i c d i f f e r e n t i a l rotation. The r e s u l t s a r e g i v e n i n 5 TABLES.
INTRODUCTION RR Lyrae v a r i a b l e s t a r s a r e m o s t l y A - t y p e (a few a r e F - t y p e ) g i a n t s h a v i n g r e l a t i v e l y l u m i n o s i t i e s and m a s s e s , t h e i r
light
large
shows v e r y r e g u l a r c h a n g e s , t h e p e r i o d s a r e s h o r t ,
between 0.0S t o 1.2 d a y s , t h e l i g h t a m p l i t u d e s do n o t e x c e e d 1 o r 2 m a g n i t u d e s , and f o r them " p e r i o d - l u m i n o s i t y " and ' ~ e r i o d - a m p l i t u d e " r e l a t i o n s distributed
obviously exist.
o v e r t h e sky, and up t o now more t h a n 4400 o f them have been d i s c o v e r e d [1]; t h e y
b e l o n g t o t h e e x t r e m e P o p u l a t i o n I I , and form a s l i g h t l y and a h i g h - v e l o c i t y structure
They a r e w i d e l y
group [2].
flattened
s u b s y s t e m o£ t h e Galaxy,
Because o f t h e i m p o r t a n t r o l e t h e y p l a y i n t h e s t u d y o f t h e
and e v o l u t i o n o f t h e Galaxy, much a t t e n t i o n
has b e e n p a i d i n t h e l a s t
few d e c a d e s t o
t h e q u e s t i o n o f d e t e r m i n i n g t h e i r p r o p e r m o t i o n s a c c u r a t e l y and i n l a r g e numbers. respect,
many r e s u l t s
In t h i s
have b e e n p u b l i s h e d by t h e L e i d e n , Greenwich, L i c k , S t e r n b e r g and
McCormack O b s e r v a t o r i e s [ 5 - 7 ] .
Between 200 and 500 RR Lyrae v a r i a b l e s have now had t h e i r
p r o p e r m o t i o n s d e r m i n e d ; t h e aim has been t o d e t e r m i n e e v e r more a c c u r a t e l y t h e i r mean absolute magnitude.
I t i s w i t h t h e same aim t h a t we began our work o f d e t e r m i n i n g t h e p r o p e r
m o t i o n s o f t h e RR Lyrae s t a r s .
Our f i r s t
s e t o f p r o p e r m o t i o n s and s p a c e m o t i o n s f o r 30 RR
Lyrae s t a r s was p u b l i s h e d i n Vol. 26 o£ our Annals [ 8 ] .
Here we c o n t i n u e w i t h t h e p u b l i c a t i o n
o£ t h e p r o p e r m o t i o n s o f 64 more such o b j e c t s . 1. METHOD OF DETERMINING RELATIVE PROPER MOTION By means o f two p h o t o g r a p h i c p l a t e s of the variables relative our p l a t e s
for the first
t a k e n some t i m e a p a r t , we d e t e r m i n e t h e p r o p e r m o t i o n s
t o t h e same r e f e r e n c e s t a r s .
We use t h e p l a t e s o£ C a r t e du C i e l as
epoch, w h i l e as our s e c o n d - e p o c h p l a t e s ,
we u s e t h e p l a t e s
our t w i n a s t r o g r a p h ( a p e r t u r e 40 cm, f o c a l l e n g t h 6.5 m) i n t h e p e r i o d 1962-196S.
taken with The
Proper Motions of RR Lyrae Stars
interval
297
e e t w e e n t h e e p o c h s i s a b o u t 60 y e a r s on t h e a v e r a g e .
The r e d u c t i o n i s made by a p p l y i n g T u r n e r ' s f o r m u l a e t o t h e measured s t a n d a r d c o o r d i n a t e s o f the variable
s t a r and t h e r e f e r e n c e s t a r s .
Its principle
d e s c r i b e d as f o l l o w s :
is briefly
Let t h e v a r i a b l e have measured c o o r d i n a t e s x01, Y01 and x02, E02 r e s p e c t i v e l y on t h e f i r s t and second epoch p l a t e s , ~1'
Y i l and x i 2 , Y£2"
and l e t t h e c o r r e s p o n d i n g c o o r d i n a t e s f o r t h e i - t h
A l s o , l e t t h e p r o p e r m o t i o n s o f t h e v a r i a b l e and t h e i - t h
s t a r i n t h e measured c o o r d i n a t e s y s t e m o f t h e f i r s t ~ y i ' and l e t At be t h e i n t e r v a l reference stars,
r e f e r e n c e s t a r be
epoch be r e s p e c t i v e l y
between t h e two e x p o s u r e s .
reference
~xO" ~ 0 and
ux'f."
Then, f o r t h e v a r i a b l e and t h e
we have [9]
~=o A¢ :
(ax.
( ~ a - - Xo,) -I-
p , ozxt = (yo, -
y.)
U , i A t ---- (xl2 - - x . )
~.,zx~ :
(y,, -
-1- b y . -I- c ) . ~
(axe, + ~y~ + / ) ;
+
(1)
J
+ ( a x t , + byta + ¢ ) : !
(1 ' )
i
y.) + (a=,, + .y~, + / ) ,
where aj b, oj ds e, f a r e c a l l e d t h e c o n n e c t i n g c o n s t a n t s o f t h e two p l a t e s ,
and i n ( 1 ' ) ,
the
the suffix i runs over all reference stars. To s i m p l i f y t h e r e d u c t i o n t h a t f o l l o w s , we t r a n s f o r m t h e s e f o r m u l a e as f o l l o w s : we form t h e d i f f e r e n c e b e t w e e n (1) and ( 1 ' ) and w r i t e
a'--~-- a , . b ' ~ - - b , c" =
d'=' - - d , e ' = - - e ,
- - tZ~oAt, [ ' =
,l
Xi : xn - - Xo:, Yt ffiffiYi2 - - Yo:; X~ :
(2)
I
- - PyoAt,
xil - - xot, Y~ : yn - - Yol
(3)
and so obtain
Xt--X~a'Xj+b'Yi+c'+F~iAt"
} (4)
Yt--Y~=d'Xl+e'Yt+J'+pyiAt. t h e n we s e t
Axi = X , -
X~,
Ay, = Ya-
(s)
Y~.
( t h e s e a r e t h e d i f f e r e n c e s b e t w e e n t h e measured c o o r d i n a t e s o f a r e f e r e n c e s t a r and t h e v a r i a b l e s t a r on t h e two p l a t e s )
and f i n a l l y
get
Axifffia'Xi+~Yi+c'+p~iAt~ Ay~==d,Xt+e,yt+f
}
+pyiAt.
(6)
The measured c o o r d i n a t e s o f t h e v a r i a b l e and t h e r e f e r e n c e s t a r s
on t h e f i r s t - e p o c h p l a t e s
were s i m p l y looked up i n t h e p u b l i s h e d C a r t e du C i e l C a t a l o g u e s , w h i l e t h e i r
c o o r d i n a t e s on t h e
s e c o n d - e p o c h p l a t e s were measured w i t h our Z e i s s c o o r d i n a t e m e a s u r i n g machine.
The
measuring details
From (3) and
have been g i v e n b e f o r e i n [8] and w i l l n o t be r e p e a t e d h e r e .
( 5 ) , we t h u s g e t AxiJ &Vi; a f t e r
inserting
t h e s e i n (6) and r e g a r d i n g a l l t h e r e f e r e n c e s t a r s
t o have z e r o p r o p e r m o t i o n s , we can s o l v e t h e e q s . and c ' ,
f'
by l e a s t
squares.
By s u b s t i t u t i n g
these
(6) so formed f o r t h e c o n s t a n t s a, b, d j e back i n ( 6 ) , we t h e n g e t t h e r e s i d u a l s
vx£" vvi" which, i f t o o l a r g e , would mean t h e p r o p e r motion o f t h a t p a r t i c u l a r not neglegible.
We took 0P050 as t h e u p p e r l i m i t ,
p r o p e r m o t i o n s g r e a t e r t h a n t h i s v a l u e and t h e n s o l v e d a g a i n by l e a s t constants.
r e f e r e n c e was
and d i s c a r d e d a l l r e f e r e n c e s t a r s w i t h
A c c o r d i n g t o ( 2 ) , t h e p r o p e r motion o f t h e v a r i a b l e
squares for the
in the right
a s c e n s i o n and
.298
P r o p e r M o t i o n s o f RR Lyrae S t a r s
declination
directions
a r e t h e n g i v e n by ~. c o s ~
~z° = -- ~'/Z~t~
=
~8 = ~y. ---- - - l / ~ . The r e s u l t s
w i l l be i n u n i t s
of
mm/y,
J
C7)
t o c o n v e r t t o a r c s e c / y we m u l t i p l y by t h e f a c t o r
k
g i v e n i n t h e C a r t e du C i e l C a t a l o g u e s . In an effort to secure the most accurate and reliable results, we made our reductions, as far as possible, using two plates of each epoch, which were compared severally in pairs and then taking the mean of the values obtained.
This was done for 26 variable stars.
However,
for the other 38 variables, either because the relevant Cart du Ciel Catalogue does not contain its position or because there was difficulty in selecting suitable references, or because our observatory happens to lack the particular catalogue, we were unable to secure two first-epoch positions, and we had to be content with the comparison of the two second-epoch plates with the same first-epoch plate, or of even only one pair of plates in all. The laborious reduction was carried out with the assistance of the comrades of the Shanghai Computing Technique Research Institute.
2. ERROR ANALYSIS OF PROPER MOTION DETERMINATION Here we were mainly concerned with the errors arising from the measuring devices and not personal errors, which can be regarded as random factors. i. Errors in the Zeiss Measurin~ Machine.
Previous studies of the errors in this
apparatus have shown that the error in a single coordinate measurement arising from structural and other causes is less than 1 micron ( % OP03).
In other words, the error produced this way
in the proper motion will be less than 0?000S/y, which is much less than the errors due to personal factors and poor image quality, and can therefore be neglected. 2. Error due to the Non-Coincidence of Optical Centres on Plates of the Two Epochs. Let the difference in the optical centre position between the two plates be X, Y along the coordinate axes of the second epoch.
Then, the focal length of the astrographic telescopes used in
making the Carte du Ciel being f' (=3440 ~ ) ,
Axl. = X ( 2 z , , -
the formulae giving the errors so arising are
Xo,)* "b Y ( 2 x i , -
xs)(2y,,-
Yo,) ..n
1"
Ay~ = X ( 2 x , , -
y~) + V ( 2 y , , -
should first
~ ,
reference
before carrying out the proper motion reduction.
However, a n a l y s e s show t h a t are three reasons
positional between reference
shifts
in the position
Nevertheless,
arising
involved all
3) The s h i f t s
hence the net effect
from t h i s
cause are also very small.
have small f i e l d s
of the optical
so c a u s e d w i l l be f u r t h e r
t h e two e p o c h s . stars,
be added t o t h e m e a s u r e d c o o r d i n a t e s x~8, Y~2 o f t h e
the errors
: l) the telescopes
to f i n d any d i f f e r e n c e
(8)
y..)' mm
The c o r r e c t i o n s stars
ayi2
x~)(2y,,-
) '
and i t
is extremely rare
c e n t r e t h a t e x c e e d s 0?80. 2) The s m a l l
reduced after
d i v i d i n g by t h e number o f y e a r s
so c a u s e d a r e a b o u t t h e same f o r t h e v a r i a b l e on t h e r e l a t i v e
proper motion is very small.
f o r t h e s a k e o f a c c u r a c y , we a p p l i e d t h e above c o r r e c t i o n s
r e d u c t i o n whenever the change in the p o s i t i o n
There
of the optical
before the
c e n t r e e x c e e d e d 0?75.
and t h e
P r o p e r Motions o f RR Lyrae S t a r s
As r e g a r d s o t h e r e r r o r s such as c a u s e d by e m u l s i o n s h i f t generally held that their
effects
299
o r annual p a r a l l a x * ,
it
is
on t h e p r e s e n t work a r e s m a l l and t h e y can be n e g l e c t e d .
3. E s t i m a t i n g t h e Accuracy o f t h e P r o p e r Motion Measurement. Let n be t h e number o f reference stars used. ~yl.
In a c t u a l f a c t ,
A f t e r s o l v i n g n p a i r s o f E q s . ( 6 ) , we have t h e n p a i r s o f r e s i d u a l s
~z~j
t h e s e include not only the proper motions of the r e f e r e n c e s t a r s but also
the measuring errors.
Obviously, the latter
a r e r e p r e s e n t e d by t h e d i f f e r e n c e i n r e s i d u a l s o f
t h e same r e f e r e n c e s t a r o b t a i n e d from two p a i r s o f p l a t e s ,
6Vx/, ~ y l .
T h e r e f o r e , t h e mean
e r r o r i n t h e p r o p e r m o t i o n measurement o f a g i v e n v a r i a b l e s t a r i s g i v e n [ 1 0 ]
~0.7979
I
~[(~..,)'+(~.,,)']
(9)
~=I
2n O b v i o u s l y , t h i s can o n l y be done where t h e two p a i r s o f p l a t e s have t h e same s e t o f r e f e r e n c e stars. We
can
a l s o g i v e an e r r o r e s t i m a t e f o r a l l
t h e p r o p e r motion s t a r s .
F i r s t we u s e t h e
formula
] ~ [(~-,,"~,-~-,.:"D ~+
a,
(~,,.",,-
~,,.",D']
0.7979
2 n . A---~ t o e s t i m a t e an a v e r a g e e r r o r f o r each v a r i a b l e formula,
~z41" ~yil
and
~x{2" ~yi2
are respectively
o b t a i n e d from t h e two p a i r s o f p l a t e s , pairs.
A-{is the average
of all
(10)
s t a r and t h e n t a k e t h e mean o f t h e s e . the residuals
of the i-th
and A t l , At 2 a r e t h e same t i m e i n t e r v a l s
In t h i s
reference star i n t h e two
At, which we took t o be 60 y e a r s f o r s i m p l i c i t y .
As in [8], our e s t i m a t e came t o ~ - ~ " _+ 0~'005. For a g i v e n v a r i a b l e ,
(ll)
i t s mean e r r o r i n p r o p e r motion can now be s i m p l y e s t i m a t e d t o be at ~t"
(12)
3. CONVERSION FROM RELATIVE TO ABSOLUTE PROPER MOTIONS To the relative proper motions obtained above, we must add the mean proper motions of the reference stars to arrive at the absolute proper motions. Since the peculiar motions of the reference stars averaging, their
a v e r a g e p r o p e r motion i s e s s e n t i a l l y
motion i n s p a c e ( t h e p a r a l l a c t i c The c o r r e c t i o n s
l a r g e l y c a n c e l one a n o t h e r out d u r i n g t h e sum o f t h o s e caused by t h e S u n ' s
m o t i o n s ) and by t h e d i f f e r e n t i a l
rotation
o f t h e Galaxy.
f o r t h e a b s o l u t e c o n v e r s i o n can be c a l c u l a t e d a c c o r d i n g t o t h e f o l l o w i n g
f o r m u l a e [ii]:
/,(~,) = v'(h--]-~p)+ Q',
(13)
4.74 * As t h e s e v a r i a b l e s a r e a l l d i s t a n t o b j e c t s , t h e i r annual p a r a l l a x e s a r e n e g l i g i b l e compared to t h e i r proper motions. I f t h e p l a t e s o f t h e two epochs were t a k e n a t t h e same time o f t h e y e a r t h e n t h i s e f f e c t would be s m a l l e r s t i l l .
300
P r o p e r M o t i o n s o f RR LyTae S t a r s
Here Y® = 20 k m / s i s t h e s o l a r
m o t i o n , ~ i s t h e mean a n n u a l p a r a l l a x
w h i c h c a n be f o u n d f r o m t h e s t a t i s t i c a l pj p t j
and Qj Qr a r e c o n s t a n t s
reference tables
stars
b e t w e e n mean p a r a l l a x
d e p e n d i n g on t h e c o o r d i n a t e s
and on t h e p a r a m e t e r o f g a l a c t i c
rotation,
stars,
and mean m a g n i t u d e .
of the solar
apex, those of the
and t h e y c a n b e l o o k e d u p i n
from Ill].
4. The t h r e e
following
tables
a b o v e and some r e l e v a n t I n TABLE l , its
relation
of the reference
g i v e t h e p r o p e r m o t i o n s o f 64 RR L y r a e v a r i a b l e s
the serial
n u m b e r , Column 2 t h e name o f t h e v a r i a b l e ,
magnitude,
Column 6 s h o w s t h e p a r t i c u l a r number o f t h e v a r i a b l e
two e p o c h s i n y e a r s ,
determined as
data.
Column 1 g i v e s t h e s e r i a l
median apparent photographic
declination;
RESULTS OF DETERMINATION
Columns 4 and 5, catalogues
in the catalogue,
its
right
ascension
o f t h e C a r t e du C i e l u s e d ,
Colunm 8 t h e t i m e i n t e r v a l
and Column 9 t h e n u m b e r o f r e f e r e n c e
Column 3
and Colunm 7,
between the
stars.
Table No.
variable
C a r t e du C i e l C a t .
NCdC
~t
n
~ec ')
~1900.0
~ltOe.O +23 ° 53~2
Par. Ph.
lb08m+23 °
103
69.9~.
9
34.8 34.0
8 8
1
RUPsc
10.~2
O1h 09m 00'
2
XXAnd
11.0
Ol
11 46
+38
25.4
Hyd.Ph.
lh10m+38° lhlSm-l-39 °
901 093
3
SVScl
11.5
01 40 27
--30
34.2
Cord. Ph.
lh39m--30 ° lh43m_31 o
827
50.0
8
90
49.0
8
4
SSFor
9.5
02 03 20
--27
20.4
Cord. Ph.
2h04m--27°
655
53.9
10
5
RVAri
12.3
02 09 37
+17
36.5
Par. Ph.
2h08m'l'18 °
163
67.8
10
6
RZCet
11.5
02 23 37
--08
48.5
S. F. Ph.
2h24m--7 °
75
71.9
9
7
XAri
06
+10
03.9
Toa. Ph. Bord. Ph.
3hO4m+10° 3h00m+ll °
40 139
42.9 51.9
10 9
8
ARPer
10.7
04 10 01
+47
09.1
Cat. Ph.
4h05a'l'47°
4hlOm+48 °
82 109
60.7 60.8
8 7
9
BCEri
10.2
04 42 25
--14
48.2
Ta~ Ph.
4h44m--15°
44
59.8
10
I0
RXEri
8.9
04 45
13
--15
54.8
Tac. Ph.
4h44m--15°
97
59.8
7
I1
RRGem
11.6
07
15 I1
+31
04.2
Oxf. Ph..
7h16m-l-31°
19153
60.6
10
12
SZGem
11.7
07 47 55
+19
32.0
Par. Ph.
7h48m-t-19°
84
69.5
I0
13
SSCn¢
12.0
08 O0 29
+23
32.2
Par. Ph.
7h56m-l-23°
243
70.0
9
14
XXPup
11.6
08 03 55
--16
14.8
Tac. Ph. Hyd. Ph.
8h00m--16e 8h04m--17°
1052 23779
60.0 49.0
10 10
9.4
03
03
Proper
Motions
Table
of
RR L y r a e
Stars
301
1 (contd.) Cat.
Ncac
xxt
H e h . Ph.
9u00=+44 * 8h55m+450
14 75
70.9 70.9
8 10
11.8
Tac. Ph.
9h04=--16 ° 9h08=_15 o
180 59
57.9 63.0
9 9
--08
54.4
S . F . Ph.
9h12=--8 ° 9h12= 8 o
21 21
70.7 70.9
6 6
I0
+29
29.2
Oxf. Ph.
9h13=+29 ° 9h09=+30 °
27191 22953
62.0 60.8
8 8
48
18
+02
31.7
Alg. Ph.
9h48=+3 * 9h52=+2 o
202 5
53.9 55.0
9 7
10
00
05
+39
50.7
Hels. Ph.
10h00=+40 °
43
70.9
8
11.4
I0
19
48
+29
17.6
Oxf. Ph.
10h16=+29 ° 29482 10h21=+30 * 25244
58.1 62.7
10 10
SZLeo
11.9
10
56
24
+08
42.2
Tou. Ph.
llh00=+9 °
66
65.9
8
23
TVLeo
10.6
11
06
18
--05
20.9
S . F . Ph.
llh08m--5° llh08m 5 o
43 43
54.9 54.9
10 10
24
STLeo
11.6
11
33
23
+11
07.0
Bord. Ph. Tou. Ph.
111'32m+11 ° 11h32=+11 °
54 63
53.0 54.9
9 7
25
XCrt
11.0
11
43
51
--09
53.4
Tac. Ph.
11h44 = - 1 0 ° 11h44 = - 10 °
102 102
58.9 59.0
10 10
26
UUVir
10.2
12
03
28
+00
04.2
Alg. Ph.
12h00=0 ° 12h04=+1 o
66 87
67.0 55.0
7 7
27
UVVir
12.1
12
16
I0
+00
55.4
Alg. Ph.
12h16=0 ° 12h20m+l o
29 82
72.1 54.9
7 9
28
SVHya
10.6
12
25
16
--25
29.7
Cord. Ph.
12h24m--26 °
21
53.0
10
29
SCom
11.3
12
27
48
+27
34.9
Oxf. Ph.
12h28=+27 ° 29529 12h27=+28 ° 34910
66.0 63.1
8 8
30
UCom
12.0
12
35
08
+28
02.9
Oxf. Ph.
J 2h36m+27 ° 29755 12h36m+28 ° 35371
65.1 62.9
9 8
31
ASVir
11.7
12
47
34
--09
42.4
Tac. Ph.
121148=--10 °
75
57.7
7
32
RYCom
11.8
13
00
16
+23
48.9
Par. Ph.
13h00=+23 °
37
68.0
8
33
RXCVn
12.6
13
44
29
+41
53.0
Hels. Ph.
13h40m+42 ° 13h40m+42 o
61 61
67.9 67.9
8 8
34
BBVir
11.0
13
46
40
+06
55.0
Tou. Ph.
13h48m+7 °
58
56.8
9
35
UYBoo
11.3
13
53
54
+13
26.2
Bord. Ph.
13h56=+13 ° 13h52.+14 o
16 114
56.0 57.0
10 10
36
SZBoo
11.6
14
37
52
+28
37.9
Oxf. Ph.
35966
57.9
dh,oo.o
a,too.,
No.
variable
~ p t ~'
15
TTLyn
1091
08 h 56 = 28 s
+ 4 4 ° 58"8
16
XXHya
11.2
09
05
08
--15
17
SZHya
11.3
09
08
58
18
RWCne
11.6
09
13
19
TSex
10.5
09
20
XLMI
11.4
21
VLMi
22
Carte
du Ciel
14h37m+29 °
I
/
10
Proper Motion of RR Lyrae Stars
302
Table
1 (contd.)
~1~0.0
~1~00.0
lO.mO
14 h 53 m 47 s
- - 0 0 ° 32~9
Alg. Ph.
APSer
10.6
12
09
10
+10
21.7
39
TVLib
11.6
15
13
00
--08
40
VYSer
10.1
15
25
59
41
ANSer
11.1
15
48
42
DYHer
10.6
16
43
V,,Sco
11.8
44
STOph
45
No.
var£able
~Pc
37
EHLIb
38
Ncdc
~,t
n
14h52m--1 ° 14h56m0 o
47 177
63.0: 72.9
13 13
Bord. Ph.
15h08~+11 °
180
51.9
9
05.8
S. F. Ph.
15h12m--8°
169
67.8
9
+02
01.5
Alg. Ph.
15h24m+3 °
150
54.0
8
51
+13
16.1
Bord. Ph.
15h48m+13 °
48
57.1
7
26
37
+12
13.3
Bord. Ph.
16h24m+12° 16h28m+13 °
75 73
56.8 59.0
10 9
17
28
29
--34
19.5
Perth. Ph.
17h28m--35° 17h28m--35 °
863 863
50.9 50.9
12 12
11.9
17
28
50
--01
00.7
Alg. Ph.
17h32m--1 ° 17h32m io
93 93
71.8 72.1
10 10
ATHer
10.5
17
33
14
+45
01.3
Hels. Ph.
17h35~+45 °
72
69.9
8
46
CEHer
12.0
17
37
23
+15
07.6
Bord. Ph.
17h40m+15c 17h36='t'16 c
19 361
61.0 67.0
8 8
47
Vs67Oph
11.8
17
53
22
+01
06.8
Alg. Ph.
17h56m+l° 17h52a+2°
255 310
54.8 55.0
8 8
48
EZLyr
11.5
18
44
08
+35
52.8
U d e - P a r . P h . 18h40m+35 c H y d . Ph. 18h45m+36 °
412 568
18.9 29.9
8 9
49
BNVul
11.6
19
23
44
+24
08.7
Par. Ph. Oxf. Ph.
555 60954
72.0 59.6
12 12
50
V44oSgr
9.8
19
26
19
--24
03.8
C o r d . Ph.
19h28m--24c 19h24m--25 c
380 529
53.9 52.0
10 8
51
gZCyg
9.6
19
30
26
+56
10.3
Vat. Ph.
1 9 h 3 6 = + 5 6 © 56919 19h30m+57 ~ 51641
56.2 55.9
9 9
52
CWCge
11.4
19
55
31
+18
54.3
Par. ph.
19h52m+18 ~ 19h56m+19 ~
66.0 59.2
13 10
53
XXCyg
12.0
20
01
18
+58
40.3
Vat. Ph.
50306
59.0
10
54
EGDel
12.8
20
48
59
+16
07.3
Bord. Ph.
20h48®+16¢ 20h48m+16 °
145 145
65.9 66.0
9 12
55
UYCyg
11.2
20
52
17
+30
02.6
Oxf. Ph.
20h51m+30 © 62429 20h51~+30~ 62429
62.9 63.0
8 8
56
DMCyg
11.0
21
17
00
+31
46.0
Oxf. Ph. 21h13m+31 ° 64001 PosUiam Ph. 21h17m+32 c 203
59.9 68.9
7 8
57
CGPeg
11.2
21
36
46
+24
19.4
Oxf. Ph. Par. Ph.
74407 199
59.0 71.0
10 12
58
DELac
t0.75B I)
22
05
54
+40
25.7
Hels. Ph.
41 299
66.9 67.0
8 7
Carte
du Ciel
Cat.
19h20~+24 ° 19h24m+25 °
20h06~+59 °
21h40m+25 * 21h36m+24 ° 22h10m+40 ~ 22b05m+41 o
610" 443
Proper
Motion
of
Table No°
variable
59
WPeR
ll.m8
60
DHPeR
61
RR L y r a e
Ncdc
At
n
22h08m+18 °
343
58.0
10
T o u . Ph.
22h12m+7 ° 22h12~+7o
115 115
57.7 57.7
8
19.9
Vat. Ph.
22630m+64 °
25401
49.7
9
--24
45.9
Cord. Ph.
23h16m--25 ° 23h16~_25 ¢
400 400
51.8 52.0
9 9
37
--08
42.1
S. F. Ph.
23h44m--8° 23h44~--8 °
63 63
52.8 54.2
9 9
40
--25
30.1
Cord. Ph.
23h56 m - 25 c 23h56m_ 25 c
319 319
52.1 53.9
10 9
Carte d u Ciel Cat
~1900.0
22 h 08 m 17'
+ 1 7 ° 57~4
Par. Ph.
9.7
22
10
25
+06
19.3
RZCep
9.5
22
35
44
+64
62
DNAqr
10.2
23
13
57
63
BSAqr
9.0
23
43
64
RUScl
10.2
23
57
2)
The m values listed are taken from Pg B-magnitudes i n t h e UBV- p h o t o m e t r i c
Table No.
variable
b
303
1 (contd.)
~IPO0.O
1)
Stars
~
8
[1]. system.
2
(h/p)
p,
Q
Q'
1
RUPsc
--38 °
12~4
0Y0131
+0.81
--0.57
--0Y0024
--0~I0016
2
XXAnd
--23
12.1
0.0111
+0.81
--0.57
-0.0029
--0.0012
3
SVScl
--77
12.3
0.0155
+0.77
--0.26
+0.0010
+0.0006
4
SSFor
--72
10.6
0.0259
+0.73
-0.26
+0.0011
+0.0006
5
RVAri
--40
13.7
0.0091
+0.72
--0.63
--0.0009
--0.0014
6
I~ZCet
--59
12.9
0.0128
+0.69
-0.44
+0.0005
--0.0003
7
XAri
--39
11.7
0.0164
+0.60
-0.61
+O.0O04
--0.0010
8
ARPer
--I
11.7
0.0093
+0.39
-0.90
0.0000
9
BCEri
--33
13.0
0.0101
+0.28
-0.29
+0.0010
+0.0019
I0
RXEri
--32
12.7
0.0109
+0.27
-0.27
+0.OOLO
+0.0020
11
RRGem
+21
12.2
OJO104
--0.27
-0.86
--0.0002
--0.0010
• 12
SZGem
+24
11.5
0.0136
--0.39
--0.75
--0.0010
--0.0004
13
SSCnc
+28
11.2
0.0159
--0.43
--0.77
--0.0010
-0.0005
14
XXPup
+10
12.7
0.0073
--0.44
--0.29
--0.0029
+0.0036
15
TTLyn
+43
11.8 12.9
0.0165 0.0118
--0.60
--0.80
0.0000
--0.0009
16
XXHya
+22
13.0
0.0083
-0.63
-0.34
--0.0039
+0.0035
17
SZHya
+27
12.2
0.0116
-0.63
--0.41
--0.0036
+0.0029
18
RWCne
+45
12.6
0.0133
-0.64
--0.73
--0.0011
--0.0005
19
TSex
+42
11.6
0.0177
-0.71
--0.53
--0.0037
+0.0018
--0.0002
20
XLMi
+55
12.1
0.0161
-0.74
--0.0007
VLMi
+59
12.5
0.0145
-0.77
--0.67 --0.62
-0.0004
21
--0.0012
--0.0001
22
SZLeo
+59
12.5
0.0146
--0.82
--0.54
--0.0027
+0.0014
23
TVLeo
+50
12.3
0.0150
--0.83
--0.0036
+0.0023
24
STLeo
+67
11.6
0.0191
--0.85
--0.49 --0.52
--0.0022
+0.0012
25
KCrt
+50
13.1
0.0118
--0.85
--0.50
--0.0034
+0.0022
26
UUVir
+61
12.0
0.0168
--0.86
--0.51
--0.0025
+0.0018
304
P r o p e r M o t i o n s o f RR L y r a e S t a r s
Table 2 (contd. No.
variable
27 28
UVVir SVHya
29
p,
~
O/p)
+62 ° +36
1195 11.5
0~197 0.0167
-0.85
--0.51 --0.50
--0~0022 --0.0034
+0~'0017
-0.85
SCom
+87
12.6
0.0143
-0.85
-0.40
--0.0002
+0.0000
30
UCom
+89
12.3 12.8
0.0156 0.0134
-0.84
--0.39
--0.0001
-0.0001
31 32 33
ASVir RYCom RXCVn
-0.83 -0.76 -0.76 -0.75 -0.66
--0.38
--0.40 --0.20
--0.0022 0.0000 +0.0015 --0.0001 +0.0003 +0.0013
+0.0018 +0.0001 -0.0016 +0.0007 +0.0004 --0.0012
37
EHLib
+47
0.0119 0.0165 0.0109 0.0159 0.0226 0.0121 0.0146 0.0187
--0.53
BBVir UYBoo SZBoo
13.1 12.1 13.5 12.2 11.0 13.1 12.3 11.5
-0.84
34 35 36
+52 +84 +71 +63 +67 +64
-0.62
--0.51
+0.0006
+0.0006
12.5
0.0142
--0.58
+38 +43
13.0 12.0
0.0108 0.0154
--0.57 --0.53
--0.40 --/0.59
+0.0010
39 40 41
APSer TVLib VYSer ANSer
+51
--0.0003 +0.0008 +0.0001
42 43 44 45 46
DYHer V4.,Sco STOph ATHer CEHer
+44 +35 -- 2 +15
12.3 12.4 12.8 12.4
0.0143 0.0125 0.0067 0.0088
47
Vs,7Oph
+31 +21 +12
12.3 11.6 12.3
0.0144 0.0122 0.0086
--0.46 --0.34 --0.12 --0.11 --0.10 --0.08 --0.03
--0.89 -0.52 +0.23 --0.28 --0.49
+0.0006 +0.0009 +0.0013 +0.001I +0.0006 +0.0005 +0.0001 +0.0003 +0.o001
48
EZLyr
+15
+0.08
--0.0014
--0.0052
BNVul
+2
+0.30
--0.15
--0.0022
--0.0043
50
V44oSgr
--21
+0.31
--0.79
--0.0004
+0.0007
51
XZCyg
+~6
+0.32
+0.37
--0.0027
--0.0057
+0.41
--0.24
--0.0028
-0.0039
+14
0.0067 0.0085 0.0058 0.0078 0.0113 0.0136 0.0084 0.0096 0.0080 0.0083
+0.16
49
13.3 12.5 13.3 12.3 11.9 11.3 12.6 11.7 12.3 12.5
+0.43
+0.38
--0.0034
--19 - - 10
12.3 12.3
0.009 ! 0.0082
+ 0.57 +0.59
--0.32
--0.0037
--0.0055 --0.0035
-o.i3
-0.0042
--0.0046
13 --22 - - 13
12.5 11.4 11.7
0.0082 0.0135 0.0104
+0.65 +0.69 + 0.75
-0.15 --0.26
-0.0045
--0.0044
--0.0045
--0.0039
--31 --40
12.8 11.7
0.0105 0.0166
+o.75
--0.35
+ 5 --70 --67
12.4 12.0 12.9
0.0077 0.0168 0.0128
+0.76 +0.79 +0.83 +0.85
--0.47 +0.06 --0.54 --0.51
-0.0050 --0.0045 --0.0040 --0.0048 --0.0013 --0.0023
--0.0038 --0.0033 --0.0025 --0.0024 --0.0003 --0.0013
--80
12.0
0.0168
+0.86
--0.46
--0.0008
-0.0004
38
52
CWCge
53 54 55
XXCyg EGDel UYCyB DMCyg CGPeg DELac VVPeg DHPeg RZCep DNAqr BSAqr RUScl
56 57 58 59 60 61 62 63 64
b
--
7
--
--0.14 --0.46
--0.49
--0.35 --0.34
--0.14
0'
+0.0021
--0.0010 --0.0013 +0.0011 --0.0007 --0.0052 --0.0026 --0.0011
P r o p e r M o t i o n s o f RR L y r a e S t a r s
305
Table 3 No.
variable
~,cos~ (rel.)
a#.
~a (rcl.)
a~a
A/Z,C~$
~,Pa
/.~cos8 (abs.)
Pa (abs.)
1
RUPse
+0/'100
+0/r004
--0[t030
+0It004
+0/t008
--0/~009
+0[q08
-0['039
2
XXAnd
+0.056
9
--0.022
9
+0.006
--0.007
+0.062
--0.029
3
SVSd
--0.013
6
--0.039
6
+0.013
--0.003
0.000
--0.042
4
SSFor
+0.026
6
--0.063
6
+0.020
--0.006
+0.046
--0.069
5
RVAri
--
0.004
4
+0.007
4
+0.006
--0.007
+0.002
0.000
6
RZCet
+0.014
4
+0.009
4
+0.009
--0.006
+0.023
+0.003
7
XAri
+0.064
6
--0.074
6
+0.010
--0.011
+0.074
--0.085
8
ARPer
--0.002
5
+0.026
5
+0.004
--0.008
+0.002
+0.018
9
BCEri
+0.008
5
+0.010
5
+0.004
--0.001
+0.012
+0.009
10
RXEri
--0.030
5
+0.017
5
+0.004
0.000
--0.026
+0.017
11
RRGem
--0.003
5
+0.015
5
--0.003
--0.010
--0.006
+0.005
12
SgGem
--0.013
4
--0.024
4
--0.006
--0.011
--0.019
--0.035
13
SSCnc
+0.013
4
+0.005
4
--0.008
--0.013
+0.005
--0.008
14
XXPup
--0.022
5
--0.006
5
--0.006
+0.002
--0.028
-0.004
15
TTLyn
--0.081
4
--0.038
4
--0.008
--0.012
--0.089
--0.050
16
XXHya
+0.017
5
-0.035
5
--0.009
+0.001
+0.008
--0.034
17
SZHya
+0.034
4
--0.042
4
--0.011
--0.002
+0.023
--0.044
18
RWCnc
+0.018
5
--0.027
5
--0.010
--0.010
+0.008
--0.037
19
TSex
--0.009
5
--0.016
5
--0.017
--0.008
--0.026
--0.024
20
XLMi
+0.021
4
--0.008
4
--0.012
--0.011
+0.009
--0.019
21
VLMi
+0.023
5
--0.019
5
--0.012
--0.009
+0.011
--0.028
22
SZLeo
--0.001
4
--0.005
4
--0.015
--0.006
--0.016
--0.011
--0.016
--0.005
+0.005
+0.024
23
TVLeo
+0.021
5
+0.029
5
24
STLeo
+0.002
5
--0.046
5
--0.018
--0.009
--0.016
--0.055
25
XCrt
+0.006
5
--0.038
5
--0.013
--0.004
--0.007
--0.042
26
UUVir
--0.008
5
--0.002
5
--0.017
--0.007
--0.025
--0.009
27
UVVir
--0.001
4
-0.023
4
--0.019
--0.008
--0.020
--0.031
28
SVHya
+0.008
6
0.000
6
--0.018
--0.006
--0.010
--0.006
29
SCorn t)
+0.002
5
+0.023
5
--0.012
--0.033
--0.010
--0.010
30
UCom
--0.042
5
-0.009
5
--0.012
--0.006
--0.054
--0.015
31
ASVir
+0.032
5
--0.033
5
--0.012
--0.004
+0.020
--0.037
32
RYCom
+0.014
4
+0.023
4
--0.014
--0.006
0.000
+0.017
33
P,XCVn
+0.044
4
--0.024
4
--0.007
--0.003
+0.037
--0.027
34
BBVir
--0.031
5
+0.003
5
--0.012
--0.007
--0.043
--0.004
306
P r o p e r Motions o f RR Lyrae S t a r s
Table 3 (contd.) No. 35
variable
UYBoo
/ZoCOS6 (rel.) +0"008
~e (rel.)
o~, +0"005
--0"037
A~.cos8
O~, +0"005
Apa
/~cos/~ Cabs.)
Pe Cabs.)
--0"017
--0"009
--0"009
--0"046
--0.007
--0.004
--0.015
+0.012 --0.018
36
SZBoo
--0.008
5
+0.016
5
37
EHLib
--0.006
4
--0.010
4
--0.009
--0.008
--0.015
38
Al~3er
--0.041
6
--0.023
6
--0.007
--0.006
--0.048
--0.029
+0.013
4
--0.006
--0.006
--0.002
+0.007
+0.006
5
--0.007
--0.007
-0.018
--0.001
--0.005
--0.006
- - 0 . 0 1 1 --0.011
--0.006
--0.001
39
TVLib
+0.004
4
40
VYSer
--0.011
5
41
ANSer
--0.006
5
--0.005
5
42
DYHer
+ 0.002
5
+0.018
5
--0.003
43
V,a,Sco
--0.014
6
--0.012
6
0.000
--0.005
--0.014
-0.017
+0.008
4
0.000
--0.005
-0.008
+0.003
+0.012
44
STOph
-- 0.008
4
45
ATHer
+0.007
4
+0.066
4
--0.001
--0.002
+0.006
+0.064
46
CEHer
+0.002
5
--0.008
5
--0.001
--0.006
+0.001
-0.014
47
Vs6,Oph
--0.006
5
+0.016
5
0.000
-0.005
--0.006
+0.011
48
EZLyr
--0.006
12
--0.007
12
0.000
-0.004
--0.006
-0.011
-0.030
5
0.000
--0.006
-0.051
- 0.036
--0.041
6
+0.004
--0.009
-0.002
-0.050
0.000
--0.003
+0.084
-0.031
+0.001
--0.006
+0.010
-0.016
49
BNVul
--0.051
5
50
V~4oSgr
-- 0. 006
6
51
XgCyg
+0.084
5
--0.028
5
52
CWCge
+ O.009
5
--0.010
5
53
XXCyB
--0.005
5
+0.026
5
--0.005
4
-0.004
54
EGDel
--0.010
4
55
UYCyg
--0.012
5
--0.002
-0.005
+0.024
+0.002
--0.007
-0.008
--0.012
5
+0.001
--0.006
-0.011
--0.010
+0.001
--0.006
-0.004
--0.003
+0.006
--0.008
-O.Oll
-0.012
56
DMCyg
-0.005
5
+0.003
5
57
CGPeg
--0.017
5
--0.004
5
58
DELa¢
0.000
--0.005
4
+0.004
4
+0.003
--0.005
-0.002
--0.001
+0.012
5
+0.003
--0.007
+0.010
+0.005
59
VVPeg
+0.007
5
60
DHPeg
+0.002
5
+0.008
5
+0.009
--0.010
+0.011
--0.002
+0.203
6
+0.001
--0.002
+0.091
+0.201
--0.007
6
+0.012
--0.009
+0.046
--0.016
+0.008
--0.008
+0.040
--0.026
+0.013
--0.008
+0.059
-0.022
61
RZCep
+0.090
6
62
DNAqr
+0.037
6
63
BSAqr
+0.032
6
--0.018
6
64
RUSd
+0.046
6
--0.014
6
i) Here we used the corrections
for conversions
into absolute motions
given in [I0]
P r o p e r Motions o f RR Lyrae S t a r s
307
In TABLE 2, Columns 1 and 2 are again the serial number and name of the variable, Column 3 gives its galactic latitude, Column 4 the mean photographic magnitude of the reference stars, and Columns 5, 6, 7, 8 and 9 give respectively the values of ~/~, P, P', Q and Q'. In TABLE 3, the first two columns are the same as before, Columns 3 and 4 give the star's relative
proper motion in right ascension and its mean error, Columns S and 6, the same in
declination, Columns 7 and 8 give the absolute conversion corrections in right ascension and declination, and the last two columns give the star's absolute proper motion in right ascension and declination.
REFERENCES
[i]
Kukarkin, V.V., et al., Obshchii Katalog Peremennykh Zvezdj Srd Edition I (1969), I I (19709, I I I {1971).
[2] [3] [4] [5] [6] [7] [8]
Bok, B.J. and Bok, P.F., "The Milky Way" p. 121, {1974). Van Herk G., B.A.N., 18 (1965), 71. Clube, S.V.M. et al, Roy. Ob8. Bull., No. 136 (1968), No. 161 (1971). Klemola, A.R., Lick Obs. Bull., No. 613. (1971). Karimova,D.K., et a l . , Peremennye Zvezdy ]9 (1974) 401-402. Hemenway,M.K., A.J. 80 {1975), 194-198. Wan Lai, He Miao-fu, Li Zhong-yuan, Zhu Guo-liang, T ~ e n NY~rnk~n
[9]
6 {1966) 18-41. "Tianmenxu8 Jiaocheng" (Course on Astronomy) compiled by the Department of
[i0] [ii]
Astronomy, Nanking University, Volume Two, (1961) p.217. Pavlovskaya, E.D., Perem. Zv. 9 (1953) 233-255. Parenago, P.P., Ast~on. Zh. 22 {1945) 129-149.
{Astronomical
Annals), Zo-se Section, Shanghai Observatory, Academia Sinica,
3 (1979) 296-307
Pergamon P r e s s . P r i n t e d i n G r e a t B r i t a i n
0146-6364/79/0901-0296-$07.50/0
Acta Astr. Sinica 1.~9 (1978) 192-203
PROPER MOTIONS OF 64 RR LYRAE VARIABLE STARS
Wan Lai
He Miao-fu
Zhu Guo-liang
Shanghai Observatory, Academia Sinica Li
Zhong-yuan
University of ScienceandTechnologyofChina ABSTRACT The r e l a t i v e p r o p e r m o t i o n s o f 64 RR Lyrae v a r i a b l e s a r e d e t e r m i n e d u s i n g T u r n e r ' s method. The f i r s t - e p o c h p o s i t i o n s a r e t a k e n from t h e C a r t e du C i e l A s t r o g r a p h i c C a t a l o g u e , w h i l e t h e s e c o n d - e p o c h p o s i t i o n s a r e measured p o s i t i o n s from p l a t e s t a k e n w i t h t h e 40-cm r e f r a c t o r ( f = 6 . 9 m) o f t h e Z6-S~ S e c t i o n , Shanghai O b s e r v a t o r y , i n 1962-65. The a v e r a g e i n t e r v a l b e t w e e n t h e two epochs i s about 60 y e a r s . The mean e r r o r in the proper motion i s ± 0,005"/y. The a b s o l u t e p r o p e r m o t i o n s o f t h e s e v a r i a b l e s a r e found a f t e r c o r r e c t i n g f o r t h e p a r a l l a c t i c m o t i o n s and t h e g a l a c t i c d i f f e r e n t i a l rotation. The r e s u l t s a r e g i v e n i n 5 TABLES.
INTRODUCTION RR Lyrae v a r i a b l e s t a r s a r e m o s t l y A - t y p e (a few a r e F - t y p e ) g i a n t s h a v i n g r e l a t i v e l y l u m i n o s i t i e s and m a s s e s , t h e i r
light
large
shows v e r y r e g u l a r c h a n g e s , t h e p e r i o d s a r e s h o r t ,
between 0.0S t o 1.2 d a y s , t h e l i g h t a m p l i t u d e s do n o t e x c e e d 1 o r 2 m a g n i t u d e s , and f o r them " p e r i o d - l u m i n o s i t y " and ' ~ e r i o d - a m p l i t u d e " r e l a t i o n s distributed
obviously exist.
o v e r t h e sky, and up t o now more t h a n 4400 o f them have been d i s c o v e r e d [1]; t h e y
b e l o n g t o t h e e x t r e m e P o p u l a t i o n I I , and form a s l i g h t l y and a h i g h - v e l o c i t y structure
They a r e w i d e l y
group [2].
flattened
s u b s y s t e m o£ t h e Galaxy,
Because o f t h e i m p o r t a n t r o l e t h e y p l a y i n t h e s t u d y o f t h e
and e v o l u t i o n o f t h e Galaxy, much a t t e n t i o n
has b e e n p a i d i n t h e l a s t
few d e c a d e s t o
t h e q u e s t i o n o f d e t e r m i n i n g t h e i r p r o p e r m o t i o n s a c c u r a t e l y and i n l a r g e numbers. respect,
many r e s u l t s
In t h i s
have b e e n p u b l i s h e d by t h e L e i d e n , Greenwich, L i c k , S t e r n b e r g and
McCormack O b s e r v a t o r i e s [ 5 - 7 ] .
Between 200 and 500 RR Lyrae v a r i a b l e s have now had t h e i r
p r o p e r m o t i o n s d e r m i n e d ; t h e aim has been t o d e t e r m i n e e v e r more a c c u r a t e l y t h e i r mean absolute magnitude.
I t i s w i t h t h e same aim t h a t we began our work o f d e t e r m i n i n g t h e p r o p e r
m o t i o n s o f t h e RR Lyrae s t a r s .
Our f i r s t
s e t o f p r o p e r m o t i o n s and s p a c e m o t i o n s f o r 30 RR
Lyrae s t a r s was p u b l i s h e d i n Vol. 26 o£ our Annals [ 8 ] .
Here we c o n t i n u e w i t h t h e p u b l i c a t i o n
o£ t h e p r o p e r m o t i o n s o f 64 more such o b j e c t s . 1. METHOD OF DETERMINING RELATIVE PROPER MOTION By means o f two p h o t o g r a p h i c p l a t e s of the variables relative our p l a t e s
for the first
t a k e n some t i m e a p a r t , we d e t e r m i n e t h e p r o p e r m o t i o n s
t o t h e same r e f e r e n c e s t a r s .
We use t h e p l a t e s o£ C a r t e du C i e l as
epoch, w h i l e as our s e c o n d - e p o c h p l a t e s ,
we u s e t h e p l a t e s
our t w i n a s t r o g r a p h ( a p e r t u r e 40 cm, f o c a l l e n g t h 6.5 m) i n t h e p e r i o d 1962-196S.
taken with The
Proper Motions of RR Lyrae Stars
interval
297
e e t w e e n t h e e p o c h s i s a b o u t 60 y e a r s on t h e a v e r a g e .
The r e d u c t i o n i s made by a p p l y i n g T u r n e r ' s f o r m u l a e t o t h e measured s t a n d a r d c o o r d i n a t e s o f the variable
s t a r and t h e r e f e r e n c e s t a r s .
Its principle
d e s c r i b e d as f o l l o w s :
is briefly
Let t h e v a r i a b l e have measured c o o r d i n a t e s x01, Y01 and x02, E02 r e s p e c t i v e l y on t h e f i r s t and second epoch p l a t e s , ~1'
Y i l and x i 2 , Y£2"
and l e t t h e c o r r e s p o n d i n g c o o r d i n a t e s f o r t h e i - t h
A l s o , l e t t h e p r o p e r m o t i o n s o f t h e v a r i a b l e and t h e i - t h
s t a r i n t h e measured c o o r d i n a t e s y s t e m o f t h e f i r s t ~ y i ' and l e t At be t h e i n t e r v a l reference stars,
r e f e r e n c e s t a r be
epoch be r e s p e c t i v e l y
between t h e two e x p o s u r e s .
reference
~xO" ~ 0 and
ux'f."
Then, f o r t h e v a r i a b l e and t h e
we have [9]
~=o A¢ :
(ax.
( ~ a - - Xo,) -I-
p , ozxt = (yo, -
y.)
U , i A t ---- (xl2 - - x . )
~.,zx~ :
(y,, -
-1- b y . -I- c ) . ~
(axe, + ~y~ + / ) ;
+
(1)
J
+ ( a x t , + byta + ¢ ) : !
(1 ' )
i
y.) + (a=,, + .y~, + / ) ,
where aj b, oj ds e, f a r e c a l l e d t h e c o n n e c t i n g c o n s t a n t s o f t h e two p l a t e s ,
and i n ( 1 ' ) ,
the
the suffix i runs over all reference stars. To s i m p l i f y t h e r e d u c t i o n t h a t f o l l o w s , we t r a n s f o r m t h e s e f o r m u l a e as f o l l o w s : we form t h e d i f f e r e n c e b e t w e e n (1) and ( 1 ' ) and w r i t e
a'--~-- a , . b ' ~ - - b , c" =
d'=' - - d , e ' = - - e ,
- - tZ~oAt, [ ' =
,l
Xi : xn - - Xo:, Yt ffiffiYi2 - - Yo:; X~ :
(2)
I
- - PyoAt,
xil - - xot, Y~ : yn - - Yol
(3)
and so obtain
Xt--X~a'Xj+b'Yi+c'+F~iAt"
} (4)
Yt--Y~=d'Xl+e'Yt+J'+pyiAt. t h e n we s e t
Axi = X , -
X~,
Ay, = Ya-
(s)
Y~.
( t h e s e a r e t h e d i f f e r e n c e s b e t w e e n t h e measured c o o r d i n a t e s o f a r e f e r e n c e s t a r and t h e v a r i a b l e s t a r on t h e two p l a t e s )
and f i n a l l y
get
Axifffia'Xi+~Yi+c'+p~iAt~ Ay~==d,Xt+e,yt+f
}
+pyiAt.
(6)
The measured c o o r d i n a t e s o f t h e v a r i a b l e and t h e r e f e r e n c e s t a r s
on t h e f i r s t - e p o c h p l a t e s
were s i m p l y looked up i n t h e p u b l i s h e d C a r t e du C i e l C a t a l o g u e s , w h i l e t h e i r
c o o r d i n a t e s on t h e
s e c o n d - e p o c h p l a t e s were measured w i t h our Z e i s s c o o r d i n a t e m e a s u r i n g machine.
The
measuring details
From (3) and
have been g i v e n b e f o r e i n [8] and w i l l n o t be r e p e a t e d h e r e .
( 5 ) , we t h u s g e t AxiJ &Vi; a f t e r
inserting
t h e s e i n (6) and r e g a r d i n g a l l t h e r e f e r e n c e s t a r s
t o have z e r o p r o p e r m o t i o n s , we can s o l v e t h e e q s . and c ' ,
f'
by l e a s t
squares.
By s u b s t i t u t i n g
these
(6) so formed f o r t h e c o n s t a n t s a, b, d j e back i n ( 6 ) , we t h e n g e t t h e r e s i d u a l s
vx£" vvi" which, i f t o o l a r g e , would mean t h e p r o p e r motion o f t h a t p a r t i c u l a r not neglegible.
We took 0P050 as t h e u p p e r l i m i t ,
p r o p e r m o t i o n s g r e a t e r t h a n t h i s v a l u e and t h e n s o l v e d a g a i n by l e a s t constants.
r e f e r e n c e was
and d i s c a r d e d a l l r e f e r e n c e s t a r s w i t h
A c c o r d i n g t o ( 2 ) , t h e p r o p e r motion o f t h e v a r i a b l e
squares for the
in the right
a s c e n s i o n and
.298
P r o p e r M o t i o n s o f RR Lyrae S t a r s
declination
directions
a r e t h e n g i v e n by ~. c o s ~
~z° = -- ~'/Z~t~
=
~8 = ~y. ---- - - l / ~ . The r e s u l t s
w i l l be i n u n i t s
of
mm/y,
J
C7)
t o c o n v e r t t o a r c s e c / y we m u l t i p l y by t h e f a c t o r
k
g i v e n i n t h e C a r t e du C i e l C a t a l o g u e s . In an effort to secure the most accurate and reliable results, we made our reductions, as far as possible, using two plates of each epoch, which were compared severally in pairs and then taking the mean of the values obtained.
This was done for 26 variable stars.
However,
for the other 38 variables, either because the relevant Cart du Ciel Catalogue does not contain its position or because there was difficulty in selecting suitable references, or because our observatory happens to lack the particular catalogue, we were unable to secure two first-epoch positions, and we had to be content with the comparison of the two second-epoch plates with the same first-epoch plate, or of even only one pair of plates in all. The laborious reduction was carried out with the assistance of the comrades of the Shanghai Computing Technique Research Institute.
2. ERROR ANALYSIS OF PROPER MOTION DETERMINATION Here we were mainly concerned with the errors arising from the measuring devices and not personal errors, which can be regarded as random factors. i. Errors in the Zeiss Measurin~ Machine.
Previous studies of the errors in this
apparatus have shown that the error in a single coordinate measurement arising from structural and other causes is less than 1 micron ( % OP03).
In other words, the error produced this way
in the proper motion will be less than 0?000S/y, which is much less than the errors due to personal factors and poor image quality, and can therefore be neglected. 2. Error due to the Non-Coincidence of Optical Centres on Plates of the Two Epochs. Let the difference in the optical centre position between the two plates be X, Y along the coordinate axes of the second epoch.
Then, the focal length of the astrographic telescopes used in
making the Carte du Ciel being f' (=3440 ~ ) ,
Axl. = X ( 2 z , , -
the formulae giving the errors so arising are
Xo,)* "b Y ( 2 x i , -
xs)(2y,,-
Yo,) ..n
1"
Ay~ = X ( 2 x , , -
y~) + V ( 2 y , , -
should first
~ ,
reference
before carrying out the proper motion reduction.
However, a n a l y s e s show t h a t are three reasons
positional between reference
shifts
in the position
Nevertheless,
arising
involved all
3) The s h i f t s
hence the net effect
from t h i s
cause are also very small.
have small f i e l d s
of the optical
so c a u s e d w i l l be f u r t h e r
t h e two e p o c h s . stars,
be added t o t h e m e a s u r e d c o o r d i n a t e s x~8, Y~2 o f t h e
the errors
: l) the telescopes
to f i n d any d i f f e r e n c e
(8)
y..)' mm
The c o r r e c t i o n s stars
ayi2
x~)(2y,,-
) '
and i t
is extremely rare
c e n t r e t h a t e x c e e d s 0?80. 2) The s m a l l
reduced after
d i v i d i n g by t h e number o f y e a r s
so c a u s e d a r e a b o u t t h e same f o r t h e v a r i a b l e on t h e r e l a t i v e
proper motion is very small.
f o r t h e s a k e o f a c c u r a c y , we a p p l i e d t h e above c o r r e c t i o n s
r e d u c t i o n whenever the change in the p o s i t i o n
There
of the optical
before the
c e n t r e e x c e e d e d 0?75.
and t h e
P r o p e r Motions o f RR Lyrae S t a r s
As r e g a r d s o t h e r e r r o r s such as c a u s e d by e m u l s i o n s h i f t generally held that their
effects
299
o r annual p a r a l l a x * ,
it
is
on t h e p r e s e n t work a r e s m a l l and t h e y can be n e g l e c t e d .
3. E s t i m a t i n g t h e Accuracy o f t h e P r o p e r Motion Measurement. Let n be t h e number o f reference stars used. ~yl.
In a c t u a l f a c t ,
A f t e r s o l v i n g n p a i r s o f E q s . ( 6 ) , we have t h e n p a i r s o f r e s i d u a l s
~z~j
t h e s e include not only the proper motions of the r e f e r e n c e s t a r s but also
the measuring errors.
Obviously, the latter
a r e r e p r e s e n t e d by t h e d i f f e r e n c e i n r e s i d u a l s o f
t h e same r e f e r e n c e s t a r o b t a i n e d from two p a i r s o f p l a t e s ,
6Vx/, ~ y l .
T h e r e f o r e , t h e mean
e r r o r i n t h e p r o p e r m o t i o n measurement o f a g i v e n v a r i a b l e s t a r i s g i v e n [ 1 0 ]
~0.7979
I
~[(~..,)'+(~.,,)']
(9)
~=I
2n O b v i o u s l y , t h i s can o n l y be done where t h e two p a i r s o f p l a t e s have t h e same s e t o f r e f e r e n c e stars. We
can
a l s o g i v e an e r r o r e s t i m a t e f o r a l l
t h e p r o p e r motion s t a r s .
F i r s t we u s e t h e
formula
] ~ [(~-,,"~,-~-,.:"D ~+
a,
(~,,.",,-
~,,.",D']
0.7979
2 n . A---~ t o e s t i m a t e an a v e r a g e e r r o r f o r each v a r i a b l e formula,
~z41" ~yil
and
~x{2" ~yi2
are respectively
o b t a i n e d from t h e two p a i r s o f p l a t e s , pairs.
A-{is the average
of all
(10)
s t a r and t h e n t a k e t h e mean o f t h e s e . the residuals
of the i-th
and A t l , At 2 a r e t h e same t i m e i n t e r v a l s
In t h i s
reference star i n t h e two
At, which we took t o be 60 y e a r s f o r s i m p l i c i t y .
As in [8], our e s t i m a t e came t o ~ - ~ " _+ 0~'005. For a g i v e n v a r i a b l e ,
(ll)
i t s mean e r r o r i n p r o p e r motion can now be s i m p l y e s t i m a t e d t o be at ~t"
(12)
3. CONVERSION FROM RELATIVE TO ABSOLUTE PROPER MOTIONS To the relative proper motions obtained above, we must add the mean proper motions of the reference stars to arrive at the absolute proper motions. Since the peculiar motions of the reference stars averaging, their
a v e r a g e p r o p e r motion i s e s s e n t i a l l y
motion i n s p a c e ( t h e p a r a l l a c t i c The c o r r e c t i o n s
l a r g e l y c a n c e l one a n o t h e r out d u r i n g t h e sum o f t h o s e caused by t h e S u n ' s
m o t i o n s ) and by t h e d i f f e r e n t i a l
rotation
o f t h e Galaxy.
f o r t h e a b s o l u t e c o n v e r s i o n can be c a l c u l a t e d a c c o r d i n g t o t h e f o l l o w i n g
f o r m u l a e [ii]:
/,(~,) = v'(h--]-~p)+ Q',
(13)
4.74 * As t h e s e v a r i a b l e s a r e a l l d i s t a n t o b j e c t s , t h e i r annual p a r a l l a x e s a r e n e g l i g i b l e compared to t h e i r proper motions. I f t h e p l a t e s o f t h e two epochs were t a k e n a t t h e same time o f t h e y e a r t h e n t h i s e f f e c t would be s m a l l e r s t i l l .
300
P r o p e r M o t i o n s o f RR LyTae S t a r s
Here Y® = 20 k m / s i s t h e s o l a r
m o t i o n , ~ i s t h e mean a n n u a l p a r a l l a x
w h i c h c a n be f o u n d f r o m t h e s t a t i s t i c a l pj p t j
and Qj Qr a r e c o n s t a n t s
reference tables
stars
b e t w e e n mean p a r a l l a x
d e p e n d i n g on t h e c o o r d i n a t e s
and on t h e p a r a m e t e r o f g a l a c t i c
rotation,
stars,
and mean m a g n i t u d e .
of the solar
apex, those of the
and t h e y c a n b e l o o k e d u p i n
from Ill].
4. The t h r e e
following
tables
a b o v e and some r e l e v a n t I n TABLE l , its
relation
of the reference
g i v e t h e p r o p e r m o t i o n s o f 64 RR L y r a e v a r i a b l e s
the serial
n u m b e r , Column 2 t h e name o f t h e v a r i a b l e ,
magnitude,
Column 6 s h o w s t h e p a r t i c u l a r number o f t h e v a r i a b l e
two e p o c h s i n y e a r s ,
determined as
data.
Column 1 g i v e s t h e s e r i a l
median apparent photographic
declination;
RESULTS OF DETERMINATION
Columns 4 and 5, catalogues
in the catalogue,
its
right
ascension
o f t h e C a r t e du C i e l u s e d ,
Colunm 8 t h e t i m e i n t e r v a l
and Column 9 t h e n u m b e r o f r e f e r e n c e
Column 3
and Colunm 7,
between the
stars.
Table No.
variable
C a r t e du C i e l C a t .
NCdC
~t
n
~ec ')
~1900.0
~ltOe.O +23 ° 53~2
Par. Ph.
lb08m+23 °
103
69.9~.
9
34.8 34.0
8 8
1
RUPsc
10.~2
O1h 09m 00'
2
XXAnd
11.0
Ol
11 46
+38
25.4
Hyd.Ph.
lh10m+38° lhlSm-l-39 °
901 093
3
SVScl
11.5
01 40 27
--30
34.2
Cord. Ph.
lh39m--30 ° lh43m_31 o
827
50.0
8
90
49.0
8
4
SSFor
9.5
02 03 20
--27
20.4
Cord. Ph.
2h04m--27°
655
53.9
10
5
RVAri
12.3
02 09 37
+17
36.5
Par. Ph.
2h08m'l'18 °
163
67.8
10
6
RZCet
11.5
02 23 37
--08
48.5
S. F. Ph.
2h24m--7 °
75
71.9
9
7
XAri
06
+10
03.9
Toa. Ph. Bord. Ph.
3hO4m+10° 3h00m+ll °
40 139
42.9 51.9
10 9
8
ARPer
10.7
04 10 01
+47
09.1
Cat. Ph.
4h05a'l'47°
4hlOm+48 °
82 109
60.7 60.8
8 7
9
BCEri
10.2
04 42 25
--14
48.2
Ta~ Ph.
4h44m--15°
44
59.8
10
I0
RXEri
8.9
04 45
13
--15
54.8
Tac. Ph.
4h44m--15°
97
59.8
7
I1
RRGem
11.6
07
15 I1
+31
04.2
Oxf. Ph..
7h16m-l-31°
19153
60.6
10
12
SZGem
11.7
07 47 55
+19
32.0
Par. Ph.
7h48m-t-19°
84
69.5
I0
13
SSCn¢
12.0
08 O0 29
+23
32.2
Par. Ph.
7h56m-l-23°
243
70.0
9
14
XXPup
11.6
08 03 55
--16
14.8
Tac. Ph. Hyd. Ph.
8h00m--16e 8h04m--17°
1052 23779
60.0 49.0
10 10
9.4
03
03
Proper
Motions
Table
of
RR L y r a e
Stars
301
1 (contd.) Cat.
Ncac
xxt
H e h . Ph.
9u00=+44 * 8h55m+450
14 75
70.9 70.9
8 10
11.8
Tac. Ph.
9h04=--16 ° 9h08=_15 o
180 59
57.9 63.0
9 9
--08
54.4
S . F . Ph.
9h12=--8 ° 9h12= 8 o
21 21
70.7 70.9
6 6
I0
+29
29.2
Oxf. Ph.
9h13=+29 ° 9h09=+30 °
27191 22953
62.0 60.8
8 8
48
18
+02
31.7
Alg. Ph.
9h48=+3 * 9h52=+2 o
202 5
53.9 55.0
9 7
10
00
05
+39
50.7
Hels. Ph.
10h00=+40 °
43
70.9
8
11.4
I0
19
48
+29
17.6
Oxf. Ph.
10h16=+29 ° 29482 10h21=+30 * 25244
58.1 62.7
10 10
SZLeo
11.9
10
56
24
+08
42.2
Tou. Ph.
llh00=+9 °
66
65.9
8
23
TVLeo
10.6
11
06
18
--05
20.9
S . F . Ph.
llh08m--5° llh08m 5 o
43 43
54.9 54.9
10 10
24
STLeo
11.6
11
33
23
+11
07.0
Bord. Ph. Tou. Ph.
111'32m+11 ° 11h32=+11 °
54 63
53.0 54.9
9 7
25
XCrt
11.0
11
43
51
--09
53.4
Tac. Ph.
11h44 = - 1 0 ° 11h44 = - 10 °
102 102
58.9 59.0
10 10
26
UUVir
10.2
12
03
28
+00
04.2
Alg. Ph.
12h00=0 ° 12h04=+1 o
66 87
67.0 55.0
7 7
27
UVVir
12.1
12
16
I0
+00
55.4
Alg. Ph.
12h16=0 ° 12h20m+l o
29 82
72.1 54.9
7 9
28
SVHya
10.6
12
25
16
--25
29.7
Cord. Ph.
12h24m--26 °
21
53.0
10
29
SCom
11.3
12
27
48
+27
34.9
Oxf. Ph.
12h28=+27 ° 29529 12h27=+28 ° 34910
66.0 63.1
8 8
30
UCom
12.0
12
35
08
+28
02.9
Oxf. Ph.
J 2h36m+27 ° 29755 12h36m+28 ° 35371
65.1 62.9
9 8
31
ASVir
11.7
12
47
34
--09
42.4
Tac. Ph.
121148=--10 °
75
57.7
7
32
RYCom
11.8
13
00
16
+23
48.9
Par. Ph.
13h00=+23 °
37
68.0
8
33
RXCVn
12.6
13
44
29
+41
53.0
Hels. Ph.
13h40m+42 ° 13h40m+42 o
61 61
67.9 67.9
8 8
34
BBVir
11.0
13
46
40
+06
55.0
Tou. Ph.
13h48m+7 °
58
56.8
9
35
UYBoo
11.3
13
53
54
+13
26.2
Bord. Ph.
13h56=+13 ° 13h52.+14 o
16 114
56.0 57.0
10 10
36
SZBoo
11.6
14
37
52
+28
37.9
Oxf. Ph.
35966
57.9
dh,oo.o
a,too.,
No.
variable
~ p t ~'
15
TTLyn
1091
08 h 56 = 28 s
+ 4 4 ° 58"8
16
XXHya
11.2
09
05
08
--15
17
SZHya
11.3
09
08
58
18
RWCne
11.6
09
13
19
TSex
10.5
09
20
XLMI
11.4
21
VLMi
22
Carte
du Ciel
14h37m+29 °
I
/
10
Proper Motion of RR Lyrae Stars
302
Table
1 (contd.)
~1~0.0
~1~00.0
lO.mO
14 h 53 m 47 s
- - 0 0 ° 32~9
Alg. Ph.
APSer
10.6
12
09
10
+10
21.7
39
TVLib
11.6
15
13
00
--08
40
VYSer
10.1
15
25
59
41
ANSer
11.1
15
48
42
DYHer
10.6
16
43
V,,Sco
11.8
44
STOph
45
No.
var£able
~Pc
37
EHLIb
38
Ncdc
~,t
n
14h52m--1 ° 14h56m0 o
47 177
63.0: 72.9
13 13
Bord. Ph.
15h08~+11 °
180
51.9
9
05.8
S. F. Ph.
15h12m--8°
169
67.8
9
+02
01.5
Alg. Ph.
15h24m+3 °
150
54.0
8
51
+13
16.1
Bord. Ph.
15h48m+13 °
48
57.1
7
26
37
+12
13.3
Bord. Ph.
16h24m+12° 16h28m+13 °
75 73
56.8 59.0
10 9
17
28
29
--34
19.5
Perth. Ph.
17h28m--35° 17h28m--35 °
863 863
50.9 50.9
12 12
11.9
17
28
50
--01
00.7
Alg. Ph.
17h32m--1 ° 17h32m io
93 93
71.8 72.1
10 10
ATHer
10.5
17
33
14
+45
01.3
Hels. Ph.
17h35~+45 °
72
69.9
8
46
CEHer
12.0
17
37
23
+15
07.6
Bord. Ph.
17h40m+15c 17h36='t'16 c
19 361
61.0 67.0
8 8
47
Vs67Oph
11.8
17
53
22
+01
06.8
Alg. Ph.
17h56m+l° 17h52a+2°
255 310
54.8 55.0
8 8
48
EZLyr
11.5
18
44
08
+35
52.8
U d e - P a r . P h . 18h40m+35 c H y d . Ph. 18h45m+36 °
412 568
18.9 29.9
8 9
49
BNVul
11.6
19
23
44
+24
08.7
Par. Ph. Oxf. Ph.
555 60954
72.0 59.6
12 12
50
V44oSgr
9.8
19
26
19
--24
03.8
C o r d . Ph.
19h28m--24c 19h24m--25 c
380 529
53.9 52.0
10 8
51
gZCyg
9.6
19
30
26
+56
10.3
Vat. Ph.
1 9 h 3 6 = + 5 6 © 56919 19h30m+57 ~ 51641
56.2 55.9
9 9
52
CWCge
11.4
19
55
31
+18
54.3
Par. ph.
19h52m+18 ~ 19h56m+19 ~
66.0 59.2
13 10
53
XXCyg
12.0
20
01
18
+58
40.3
Vat. Ph.
50306
59.0
10
54
EGDel
12.8
20
48
59
+16
07.3
Bord. Ph.
20h48®+16¢ 20h48m+16 °
145 145
65.9 66.0
9 12
55
UYCyg
11.2
20
52
17
+30
02.6
Oxf. Ph.
20h51m+30 © 62429 20h51~+30~ 62429
62.9 63.0
8 8
56
DMCyg
11.0
21
17
00
+31
46.0
Oxf. Ph. 21h13m+31 ° 64001 PosUiam Ph. 21h17m+32 c 203
59.9 68.9
7 8
57
CGPeg
11.2
21
36
46
+24
19.4
Oxf. Ph. Par. Ph.
74407 199
59.0 71.0
10 12
58
DELac
t0.75B I)
22
05
54
+40
25.7
Hels. Ph.
41 299
66.9 67.0
8 7
Carte
du Ciel
Cat.
19h20~+24 ° 19h24m+25 °
20h06~+59 °
21h40m+25 * 21h36m+24 ° 22h10m+40 ~ 22b05m+41 o
610" 443
Proper
Motion
of
Table No°
variable
59
WPeR
ll.m8
60
DHPeR
61
RR L y r a e
Ncdc
At
n
22h08m+18 °
343
58.0
10
T o u . Ph.
22h12m+7 ° 22h12~+7o
115 115
57.7 57.7
8
19.9
Vat. Ph.
22630m+64 °
25401
49.7
9
--24
45.9
Cord. Ph.
23h16m--25 ° 23h16~_25 ¢
400 400
51.8 52.0
9 9
37
--08
42.1
S. F. Ph.
23h44m--8° 23h44~--8 °
63 63
52.8 54.2
9 9
40
--25
30.1
Cord. Ph.
23h56 m - 25 c 23h56m_ 25 c
319 319
52.1 53.9
10 9
Carte d u Ciel Cat
~1900.0
22 h 08 m 17'
+ 1 7 ° 57~4
Par. Ph.
9.7
22
10
25
+06
19.3
RZCep
9.5
22
35
44
+64
62
DNAqr
10.2
23
13
57
63
BSAqr
9.0
23
43
64
RUScl
10.2
23
57
2)
The m values listed are taken from Pg B-magnitudes i n t h e UBV- p h o t o m e t r i c
Table No.
variable
b
303
1 (contd.)
~IPO0.O
1)
Stars
~
8
[1]. system.
2
(h/p)
p,
Q
Q'
1
RUPsc
--38 °
12~4
0Y0131
+0.81
--0.57
--0Y0024
--0~I0016
2
XXAnd
--23
12.1
0.0111
+0.81
--0.57
-0.0029
--0.0012
3
SVScl
--77
12.3
0.0155
+0.77
--0.26
+0.0010
+0.0006
4
SSFor
--72
10.6
0.0259
+0.73
-0.26
+0.0011
+0.0006
5
RVAri
--40
13.7
0.0091
+0.72
--0.63
--0.0009
--0.0014
6
I~ZCet
--59
12.9
0.0128
+0.69
-0.44
+0.0005
--0.0003
7
XAri
--39
11.7
0.0164
+0.60
-0.61
+O.0O04
--0.0010
8
ARPer
--I
11.7
0.0093
+0.39
-0.90
0.0000
9
BCEri
--33
13.0
0.0101
+0.28
-0.29
+0.0010
+0.0019
I0
RXEri
--32
12.7
0.0109
+0.27
-0.27
+0.OOLO
+0.0020
11
RRGem
+21
12.2
OJO104
--0.27
-0.86
--0.0002
--0.0010
• 12
SZGem
+24
11.5
0.0136
--0.39
--0.75
--0.0010
--0.0004
13
SSCnc
+28
11.2
0.0159
--0.43
--0.77
--0.0010
-0.0005
14
XXPup
+10
12.7
0.0073
--0.44
--0.29
--0.0029
+0.0036
15
TTLyn
+43
11.8 12.9
0.0165 0.0118
--0.60
--0.80
0.0000
--0.0009
16
XXHya
+22
13.0
0.0083
-0.63
-0.34
--0.0039
+0.0035
17
SZHya
+27
12.2
0.0116
-0.63
--0.41
--0.0036
+0.0029
18
RWCne
+45
12.6
0.0133
-0.64
--0.73
--0.0011
--0.0005
19
TSex
+42
11.6
0.0177
-0.71
--0.53
--0.0037
+0.0018
--0.0002
20
XLMi
+55
12.1
0.0161
-0.74
--0.0007
VLMi
+59
12.5
0.0145
-0.77
--0.67 --0.62
-0.0004
21
--0.0012
--0.0001
22
SZLeo
+59
12.5
0.0146
--0.82
--0.54
--0.0027
+0.0014
23
TVLeo
+50
12.3
0.0150
--0.83
--0.0036
+0.0023
24
STLeo
+67
11.6
0.0191
--0.85
--0.49 --0.52
--0.0022
+0.0012
25
KCrt
+50
13.1
0.0118
--0.85
--0.50
--0.0034
+0.0022
26
UUVir
+61
12.0
0.0168
--0.86
--0.51
--0.0025
+0.0018
304
P r o p e r M o t i o n s o f RR L y r a e S t a r s
Table 2 (contd. No.
variable
27 28
UVVir SVHya
29
p,
~
O/p)
+62 ° +36
1195 11.5
0~197 0.0167
-0.85
--0.51 --0.50
--0~0022 --0.0034
+0~'0017
-0.85
SCom
+87
12.6
0.0143
-0.85
-0.40
--0.0002
+0.0000
30
UCom
+89
12.3 12.8
0.0156 0.0134
-0.84
--0.39
--0.0001
-0.0001
31 32 33
ASVir RYCom RXCVn
-0.83 -0.76 -0.76 -0.75 -0.66
--0.38
--0.40 --0.20
--0.0022 0.0000 +0.0015 --0.0001 +0.0003 +0.0013
+0.0018 +0.0001 -0.0016 +0.0007 +0.0004 --0.0012
37
EHLib
+47
0.0119 0.0165 0.0109 0.0159 0.0226 0.0121 0.0146 0.0187
--0.53
BBVir UYBoo SZBoo
13.1 12.1 13.5 12.2 11.0 13.1 12.3 11.5
-0.84
34 35 36
+52 +84 +71 +63 +67 +64
-0.62
--0.51
+0.0006
+0.0006
12.5
0.0142
--0.58
+38 +43
13.0 12.0
0.0108 0.0154
--0.57 --0.53
--0.40 --/0.59
+0.0010
39 40 41
APSer TVLib VYSer ANSer
+51
--0.0003 +0.0008 +0.0001
42 43 44 45 46
DYHer V4.,Sco STOph ATHer CEHer
+44 +35 -- 2 +15
12.3 12.4 12.8 12.4
0.0143 0.0125 0.0067 0.0088
47
Vs,7Oph
+31 +21 +12
12.3 11.6 12.3
0.0144 0.0122 0.0086
--0.46 --0.34 --0.12 --0.11 --0.10 --0.08 --0.03
--0.89 -0.52 +0.23 --0.28 --0.49
+0.0006 +0.0009 +0.0013 +0.001I +0.0006 +0.0005 +0.0001 +0.0003 +0.o001
48
EZLyr
+15
+0.08
--0.0014
--0.0052
BNVul
+2
+0.30
--0.15
--0.0022
--0.0043
50
V44oSgr
--21
+0.31
--0.79
--0.0004
+0.0007
51
XZCyg
+~6
+0.32
+0.37
--0.0027
--0.0057
+0.41
--0.24
--0.0028
-0.0039
+14
0.0067 0.0085 0.0058 0.0078 0.0113 0.0136 0.0084 0.0096 0.0080 0.0083
+0.16
49
13.3 12.5 13.3 12.3 11.9 11.3 12.6 11.7 12.3 12.5
+0.43
+0.38
--0.0034
--19 - - 10
12.3 12.3
0.009 ! 0.0082
+ 0.57 +0.59
--0.32
--0.0037
--0.0055 --0.0035
-o.i3
-0.0042
--0.0046
13 --22 - - 13
12.5 11.4 11.7
0.0082 0.0135 0.0104
+0.65 +0.69 + 0.75
-0.15 --0.26
-0.0045
--0.0044
--0.0045
--0.0039
--31 --40
12.8 11.7
0.0105 0.0166
+o.75
--0.35
+ 5 --70 --67
12.4 12.0 12.9
0.0077 0.0168 0.0128
+0.76 +0.79 +0.83 +0.85
--0.47 +0.06 --0.54 --0.51
-0.0050 --0.0045 --0.0040 --0.0048 --0.0013 --0.0023
--0.0038 --0.0033 --0.0025 --0.0024 --0.0003 --0.0013
--80
12.0
0.0168
+0.86
--0.46
--0.0008
-0.0004
38
52
CWCge
53 54 55
XXCyg EGDel UYCyB DMCyg CGPeg DELac VVPeg DHPeg RZCep DNAqr BSAqr RUScl
56 57 58 59 60 61 62 63 64
b
--
7
--
--0.14 --0.46
--0.49
--0.35 --0.34
--0.14
0'
+0.0021
--0.0010 --0.0013 +0.0011 --0.0007 --0.0052 --0.0026 --0.0011
P r o p e r M o t i o n s o f RR L y r a e S t a r s
305
Table 3 No.
variable
~,cos~ (rel.)
a#.
~a (rcl.)
a~a
A/Z,C~$
~,Pa
/.~cos8 (abs.)
Pa (abs.)
1
RUPse
+0/'100
+0/r004
--0[t030
+0It004
+0/t008
--0/~009
+0[q08
-0['039
2
XXAnd
+0.056
9
--0.022
9
+0.006
--0.007
+0.062
--0.029
3
SVSd
--0.013
6
--0.039
6
+0.013
--0.003
0.000
--0.042
4
SSFor
+0.026
6
--0.063
6
+0.020
--0.006
+0.046
--0.069
5
RVAri
--
0.004
4
+0.007
4
+0.006
--0.007
+0.002
0.000
6
RZCet
+0.014
4
+0.009
4
+0.009
--0.006
+0.023
+0.003
7
XAri
+0.064
6
--0.074
6
+0.010
--0.011
+0.074
--0.085
8
ARPer
--0.002
5
+0.026
5
+0.004
--0.008
+0.002
+0.018
9
BCEri
+0.008
5
+0.010
5
+0.004
--0.001
+0.012
+0.009
10
RXEri
--0.030
5
+0.017
5
+0.004
0.000
--0.026
+0.017
11
RRGem
--0.003
5
+0.015
5
--0.003
--0.010
--0.006
+0.005
12
SgGem
--0.013
4
--0.024
4
--0.006
--0.011
--0.019
--0.035
13
SSCnc
+0.013
4
+0.005
4
--0.008
--0.013
+0.005
--0.008
14
XXPup
--0.022
5
--0.006
5
--0.006
+0.002
--0.028
-0.004
15
TTLyn
--0.081
4
--0.038
4
--0.008
--0.012
--0.089
--0.050
16
XXHya
+0.017
5
-0.035
5
--0.009
+0.001
+0.008
--0.034
17
SZHya
+0.034
4
--0.042
4
--0.011
--0.002
+0.023
--0.044
18
RWCnc
+0.018
5
--0.027
5
--0.010
--0.010
+0.008
--0.037
19
TSex
--0.009
5
--0.016
5
--0.017
--0.008
--0.026
--0.024
20
XLMi
+0.021
4
--0.008
4
--0.012
--0.011
+0.009
--0.019
21
VLMi
+0.023
5
--0.019
5
--0.012
--0.009
+0.011
--0.028
22
SZLeo
--0.001
4
--0.005
4
--0.015
--0.006
--0.016
--0.011
--0.016
--0.005
+0.005
+0.024
23
TVLeo
+0.021
5
+0.029
5
24
STLeo
+0.002
5
--0.046
5
--0.018
--0.009
--0.016
--0.055
25
XCrt
+0.006
5
--0.038
5
--0.013
--0.004
--0.007
--0.042
26
UUVir
--0.008
5
--0.002
5
--0.017
--0.007
--0.025
--0.009
27
UVVir
--0.001
4
-0.023
4
--0.019
--0.008
--0.020
--0.031
28
SVHya
+0.008
6
0.000
6
--0.018
--0.006
--0.010
--0.006
29
SCorn t)
+0.002
5
+0.023
5
--0.012
--0.033
--0.010
--0.010
30
UCom
--0.042
5
-0.009
5
--0.012
--0.006
--0.054
--0.015
31
ASVir
+0.032
5
--0.033
5
--0.012
--0.004
+0.020
--0.037
32
RYCom
+0.014
4
+0.023
4
--0.014
--0.006
0.000
+0.017
33
P,XCVn
+0.044
4
--0.024
4
--0.007
--0.003
+0.037
--0.027
34
BBVir
--0.031
5
+0.003
5
--0.012
--0.007
--0.043
--0.004
306
P r o p e r Motions o f RR Lyrae S t a r s
Table 3 (contd.) No. 35
variable
UYBoo
/ZoCOS6 (rel.) +0"008
~e (rel.)
o~, +0"005
--0"037
A~.cos8
O~, +0"005
Apa
/~cos/~ Cabs.)
Pe Cabs.)
--0"017
--0"009
--0"009
--0"046
--0.007
--0.004
--0.015
+0.012 --0.018
36
SZBoo
--0.008
5
+0.016
5
37
EHLib
--0.006
4
--0.010
4
--0.009
--0.008
--0.015
38
Al~3er
--0.041
6
--0.023
6
--0.007
--0.006
--0.048
--0.029
+0.013
4
--0.006
--0.006
--0.002
+0.007
+0.006
5
--0.007
--0.007
-0.018
--0.001
--0.005
--0.006
- - 0 . 0 1 1 --0.011
--0.006
--0.001
39
TVLib
+0.004
4
40
VYSer
--0.011
5
41
ANSer
--0.006
5
--0.005
5
42
DYHer
+ 0.002
5
+0.018
5
--0.003
43
V,a,Sco
--0.014
6
--0.012
6
0.000
--0.005
--0.014
-0.017
+0.008
4
0.000
--0.005
-0.008
+0.003
+0.012
44
STOph
-- 0.008
4
45
ATHer
+0.007
4
+0.066
4
--0.001
--0.002
+0.006
+0.064
46
CEHer
+0.002
5
--0.008
5
--0.001
--0.006
+0.001
-0.014
47
Vs6,Oph
--0.006
5
+0.016
5
0.000
-0.005
--0.006
+0.011
48
EZLyr
--0.006
12
--0.007
12
0.000
-0.004
--0.006
-0.011
-0.030
5
0.000
--0.006
-0.051
- 0.036
--0.041
6
+0.004
--0.009
-0.002
-0.050
0.000
--0.003
+0.084
-0.031
+0.001
--0.006
+0.010
-0.016
49
BNVul
--0.051
5
50
V~4oSgr
-- 0. 006
6
51
XgCyg
+0.084
5
--0.028
5
52
CWCge
+ O.009
5
--0.010
5
53
XXCyB
--0.005
5
+0.026
5
--0.005
4
-0.004
54
EGDel
--0.010
4
55
UYCyg
--0.012
5
--0.002
-0.005
+0.024
+0.002
--0.007
-0.008
--0.012
5
+0.001
--0.006
-0.011
--0.010
+0.001
--0.006
-0.004
--0.003
+0.006
--0.008
-O.Oll
-0.012
56
DMCyg
-0.005
5
+0.003
5
57
CGPeg
--0.017
5
--0.004
5
58
DELa¢
0.000
--0.005
4
+0.004
4
+0.003
--0.005
-0.002
--0.001
+0.012
5
+0.003
--0.007
+0.010
+0.005
59
VVPeg
+0.007
5
60
DHPeg
+0.002
5
+0.008
5
+0.009
--0.010
+0.011
--0.002
+0.203
6
+0.001
--0.002
+0.091
+0.201
--0.007
6
+0.012
--0.009
+0.046
--0.016
+0.008
--0.008
+0.040
--0.026
+0.013
--0.008
+0.059
-0.022
61
RZCep
+0.090
6
62
DNAqr
+0.037
6
63
BSAqr
+0.032
6
--0.018
6
64
RUSd
+0.046
6
--0.014
6
i) Here we used the corrections
for conversions
into absolute motions
given in [I0]
P r o p e r Motions o f RR Lyrae S t a r s
307
In TABLE 2, Columns 1 and 2 are again the serial number and name of the variable, Column 3 gives its galactic latitude, Column 4 the mean photographic magnitude of the reference stars, and Columns 5, 6, 7, 8 and 9 give respectively the values of ~/~, P, P', Q and Q'. In TABLE 3, the first two columns are the same as before, Columns 3 and 4 give the star's relative
proper motion in right ascension and its mean error, Columns S and 6, the same in
declination, Columns 7 and 8 give the absolute conversion corrections in right ascension and declination, and the last two columns give the star's absolute proper motion in right ascension and declination.
REFERENCES
[i]
Kukarkin, V.V., et al., Obshchii Katalog Peremennykh Zvezdj Srd Edition I (1969), I I (19709, I I I {1971).
[2] [3] [4] [5] [6] [7] [8]
Bok, B.J. and Bok, P.F., "The Milky Way" p. 121, {1974). Van Herk G., B.A.N., 18 (1965), 71. Clube, S.V.M. et al, Roy. Ob8. Bull., No. 136 (1968), No. 161 (1971). Klemola, A.R., Lick Obs. Bull., No. 613. (1971). Karimova,D.K., et a l . , Peremennye Zvezdy ]9 (1974) 401-402. Hemenway,M.K., A.J. 80 {1975), 194-198. Wan Lai, He Miao-fu, Li Zhong-yuan, Zhu Guo-liang, T ~ e n NY~rnk~n
[9]
6 {1966) 18-41. "Tianmenxu8 Jiaocheng" (Course on Astronomy) compiled by the Department of
[i0] [ii]
Astronomy, Nanking University, Volume Two, (1961) p.217. Pavlovskaya, E.D., Perem. Zv. 9 (1953) 233-255. Parenago, P.P., Ast~on. Zh. 22 {1945) 129-149.
{Astronomical
Annals), Zo-se Section, Shanghai Observatory, Academia Sinica,