proper motions, absolute magnitudes and spatial distribution of zirconium stars
TRANSCRIPT
Astron. Nachr. 318 (1997) 6,369-386
Proper motions, absolute magnitudes and spatial distribution of Zirconium stars
S.M.CHANTURIYA, Abastumani, Georgia
Abastumani Astrophysical Observatory, Academy of Sciences of Georgia
Received 1993 August 24; revised 1993 November 24; accepted 1997 September 15
The computational algorithm to determine the the proper motions of Zirconium stars on the basis of catalogues "Carte du Ciel" and on the recent photographic observations carried out with the 70cm Abastumani meniscus telescope is presented. It allowed to determine the proper motions of 288 stars in the region around a Per with a rms error o f f 0,004 arcsec/yr. Applying the method proper motions of 74 Zirconium stars and 146 control stars have been obtained. The error of proper motions obtained for the North Zone (6 > -2') 109 AGKs control stars is f 0.006 arcsec/yr. On the basis of proper motions absolute magnitudes were separately calculated for the MCLPZS and LASZS. For the MCLPZS the average absolute visual magnitude at maximum, corresponding to the mean period of P = 350 days, equals -3m9. For the LASZS the mean absolute visual magnitude, corresponding to the apparent median ones equals -1m9. Low luminosity (Mv = -1m9) Zirconium stars escape rather far (at a distance of up to 2 kpc) to the South from the Galactic plane into the region 1 - 240 - 260°, where its assumed to be a connection with the Large Magellanic Cloud (LMC) begins to appear. Low luminosity Zirconium stars are weakly correlated with the position of the Galaxy spiral arms. The MCLPZS show a somewhat other distribution.
Key words: astrometry: proper motions - absolute magnitudes - spatial distribution - Zirconium stars
A A A subject classification: 111; 115; 155
1. Introduction
For more detailed study of red giants it is needed to have the space distribution parameters for which a precise scale distances should be determined. Unfortunately, the statistical parallaxes are almost the only way to determine the distance scale of Zirconium stars (ZS).
Here were investigated Mira Ceti long-period variable Zirconium stars (MCLPZS) and low-amplitude variables and stationary Zirconium stars (LASZS). All previous determinations of the absolute magnitudes of ZS are given in Table 1. As it is seen Feast, Gulver and Ianna, Takayanagi, Scalo and Mendoza obtained comparatively high luminosities for MCLPZS while luminosities obtained by Eggen, Wilson and Merrill, Osvalds, Risley and Ikaunieks are almost twice fainter. Stephenson's determination is quite different from others because he did not separate variable ZS from nonvariable ones.
a) systematic errors in proper motions b) different methods of absolute magnitude calculation c) difference in adopted Galactic and solar motion parameters d) large uncertainties of the interstellar absorption. For example, Osvalds and Risley (1961) used the value of Oort's constant A = +34 km/sec/kpc, and therefore they got Mv=-lm6 for MCLPZS. Feast adopted A = +15 km/sec/kpc for ZS and received MV = -3m4. Takayanagi (1960) has compiled proper motions and radial velocities from different catalogues. He adopted the interstellar absorption coefficient aov = 0.5 mag per kpc all over the sky, the Sun's velocity equals to 19.5 km/sec and Oort's constant A = +17.5 km/sec/kpc. We suppose the values of Vo=15.5 km/sec (Vyssotsky and Janssen 1951), aov = 1.6 mag per kpc (Sharov 1963), A = +15 km/sec/kpc are more appropriate. Using last ones and data collected by Takayanagi we would get Mv = -4m8 (instead of -3m4) from radial velocities for MCLPZS and from proper motions Mv = -3118 (instead of -3mO).
More recent investigations of ZS were given by Yorka and Wing (1979), Evans and Catchpole (1989), Feast (1989) , Catchpole and Feast( 1985) , and others. Yorka and Wing (1979) conclude that MCLPZS at maximum are brighter than non-Mira ZS, but are not as bright as Mv = -3.0. The surface distribution of all known ZS stars indicates that most of them belong to the older Population I .
219
We suppose that the differences caused by the following factors:
370 Astron. Nachr. 318 (1997) 6
On the basis of infrared photometry and spectroscopy of 72 ZS Evans and Catchpole (1989) conclude that these objects are of much higher mass than C-type stars.
The ages, masses and evolutionary stage of 260 peculiar red giants are discussed on the basis of kinematic and other data by Feast (1989). He indicates that the bulk of the S and C type stars are low mass objects of intermediate age. There is some indication from the kinematical data that the C stars as a group may be younger and more massive than the ZS and SC type stars.
An earlier review of this general topic ’Population studies of C, S type and other stars in the Galaxy and in the Magellanic Clouds’ was published by Catchpole and Feast (1985). Blanco et al. (1981) discovered a Zirconium star in the Small Magellanic Cloud with an absolute bolometric magnitude of -5ml. Evans (1983) inferred, that most of the non-Carbon stars in the Magellanic Clouds brighter than Mbol = -4T3 are ZS. Aaronson, Mould and Cook (1985) discovered the first S star in NGC 6822. Infrared photometry yields
Obviously there exists a large spread in the absolute magnitudes and other data. Therefore we intended to determine the absolute magnitudes of ZS on the basis of Carte du Ciel (epoch I) and 70cm meniscus plates (epoch 11). So we have more homogeneous and reliable data, and this is the main goal of our study.
= -5m15.
Table 1. Determination of the absolute magnitudes of ZS
authors n MPax MTed MEfX MFax date remarks
Wilson, Merrill Feast Takaianagi Osvalds, Risley Feast Feast Mendoza Mendoza Barnes Ikaunieks Eggen Eggen Culver, Ianna Feast scalo Stephenson Takaianagi Takaianagi Warner Warner Boesgaard Eggen Eggen Eggen
17 -1110 1 -1.0
18 -3.0 22 -1.6
-3.4
1 1
31 -0.5 -1.2
1 -1.2 1 -2.4 4 1 -3.4
+2.4 26 12 -0.7
1 -1.0 1 -0.8 1 -0.6 1 1 1
-Om6
-0.1 -0.5
-4114 -5114
-2.8 -3.2 -2.4 -3.1 -5.6 -3.4
1942 1953 1960 1961 1963 1963 1967 1967
1971 1972a 1972b 1975
1976 1978 1960 1960 1965 1965 1969 1972b 1972a 1972b
-5m9 1970
-5.4 1976
Mira Ceti 9 ,
1,
,t
9 3
,! 0
,?
I,
91
,, all zircon. stars non Mira Ceti Spectral class MS
( 9
It
$7
2. The method of determination of proper motions
The problem of application of Carte du Ciel catalogues as the first epoch in determination of proper motion may be realized in two ways. The first one is when the measured x, y coordinates in both epochs of a number of comparison stars with known proper motions are compared and as a result of reduction relative proper motions of obdects under study are obtained. In the second one the spherical coordinates of objects are independently determined on the plates of both epochs and by means of their comparison proper motions are calculated.
We applied the second method to determine the proper motions (Kiselev and Chanturiya 1977) which has been approved for 288 stars in the vicinity of Q Per. For the first epoch seven plates of Catania zone in the Carte du Ciel catalogues were used, while for the second one four plates, obtained on the 70cm meniscus telescope ( F = 2102 mm). The AGK3 catalogue was used as a reference one, because we had no most accurate PPM catalogue. Arrangement of plates is presented on Fig. 1, where the circle represents a sky area with the diameter 3O around a Per on the plates of epoch I1 suitable for astrometric work. The meniscus plates were measured on the semi-automatic measuring machine ”Ascorecord” and all possible precautions have been taken into account to increase thermostability. In addition, there were for markings on each of plates the measured coordinates of which shouldn’t to cross the bounds of a square measuring 2x2 microns.
S.M.Chanturiya: Zirconium stars
2668
371
18 78
7098
- +50'
- r49'
- +48'
2543
Fig. 1. Disposition of the plates of Carte du Ciel catalogue relative to the area around aPer with the centre (I = 3h 17m273, 6 = +48' 56'19'' (1900).
2.1. Reduction algorithm
The overlapping of plates is of primary importance to reduce the systematic errors in the measured coordinates on the edge of plates. Construction of such calculation scheme is promoted by the arrangement of plate centres in the Carte du Ciel catalogue (Fig. 1). Assuming the systematic errors in regional zones to be symmetric, spherical coordinates of a star must be averaged on the neighbouring plates with correctly selected weighting coefficients depending on location of reference stars by the following formulae:
where P k r and P k s are unknown weights on the plates n, and ns for stark . The error of a stellar position on plate IIr (Bronnikova and Kiselev 1973) is calculated from
Here U m k r is measuring error of s k , ~ 1 , error of a weight unit at the reduction of plate nr by Turner's method; { D k ; } are Schlezinger's "dependences" of n, reference stars relative to S k . We have got similar formula for plate II,; um is supposed to be knowna priori; other parameters in (2) are determined in the process of reduction. Having assumed a suitable error of the unit weight E O , the unknown weights P k r and P k a are calculated as
(3) p - 2 2 p - 2 2 k r - & o / & k r ; k s - & O / & k s .
A mean weighted position ( f Y k 1 6 k ) of the star s k will be the most probable one and improved as a result of compensation of errors in the zone of overlapping. The weight and error of the improved stellar position are calculated by the formulae:
P-- k ( r + s ) - P k r + p k s ; &k(r+s)= &O/d--. The coordinates of stars which satisfied the relations
(4)
1510, - c1~Icos6 5 2arcsec; 16, - 6,1 < Sarcsec,
are averaged by eqs. (1) and (3). The program provides the possibility of treating the Carte du Ciel catalogue for sky regions much larger than the zone around Q Per.
2.2. Results and discussion
The algorithm has been applied to determine the positions of 288 stars around CY Per at two epochs: 1900 and 1974. On te basis of 745 independently measured images, a list of positions of 288 stars around Q Per has been 27a Asuon. Nacbr. 318 (1997) 6
372 Astron. Nachr. 318 (1997) 6
compiled. The mean errors, calculated by eqs. (2),(3) and (4), are f 0 , 2 3 arcsec (2,5 plates) for the whole Carte du Ciel catalogue and f0,10 arcsec (4 plates) for second epoch. As a result two lists of tangential stellar coordinates were obtained, related to one centre A0 = 3h21"00.s0, DO = +49"7'0O'' in axes, oriented by the equator 1950.0. Having compared these coordinates and divided their differences by the difference of epochs (- 75 years), we obtained proper motions pt and pq whose errors were calculated by formula:
1
Here EI and €11 are mean errors of the positions of stars in epochs I and 11, calculated in the time of the reduction (errors by( and 17 were averaged). Results of these determinations of proper motions, as well as the details of astrometric reduction are given by Kiselev and Chanturiya (1977, Tables 1,2 and 6).
Having adopted values E ( ~ , ~ ) I = f 0 , 2 3 arcsec and E ( C , q ) r I = f 0 , 10 arcsec accuracy of proper motions of our list was estimated by the eq. ( 5 ) : E~ = fO, 0036 arcsec/yr. One can estimate accuracy of proper motions externally as well, having compared them to the data of these catalogues by a linear formula (Heckman et al. 1956, Artiukhina and Kalinina 1973):
where p and p' are proper motions of a star in two systems being compared. Having solved the system (6) by the least squares method, let us find the error of a unit of weight f f 1 , A p as a total effect of errors in the lists being compared:
2 2 2 u l , A p = + , (7)
This comparison has been carried out for 75 stars on the basis of the formula (6). The results are presented in Table 2.
Table 2. Results of comparison of proper motions (Abastumani, Bergedorf and Moscow; eq. (6))
A - B B - M M - A 5 rl t tl t q
0 . lo7. l"/mm +2f2 -10f2 -15f2 -9f2 +13f2 +19f2 p.107.1"/mm -7f2 +5f3 Of3 +5f3 +7f2 -1lf2 y . lo4. l"/nm -19f5 +73f5 +50f6 -9f6 -31f5 -67f6 U l A P f!'0043 f!'0043 f!'0052 f!'0052 f!'0043 f!'0052
Dimensions: a - [l"/mm],P - [l"/mm],o and y - 1". Designations: A - Abastumani, B - Bergedorf, M - Moscow.
As it is seen from the table the Abastumani system of proper motions noticeably differs from the systems (B) and (M) . In accidental relation all three lists are sufficiently accurate and slightly differ from each other, which is easily explained by the fact that the catalogue "Carte du Ciel" has served as their common source. Of course they cannot be considered as independent. Therefore random errors of proper motions, obtained in accordance with values 0 1 , ~ ~ from Table 2 and represented in Table 3, are not fully correct.
Table 3. Accidental errors of proper motions of different lists by Table 2
A B M
( f0!'0022 f0!'0037 f0!'0037 q f0!'0030 f0!'0030 f0!'0043
Due to the revealed difference of the systems of proper motions of the lists (A)l(B),(M)l they were compared with the catalogue AGK3, which served as a comparison one only in our case. Comparison results are given in Table 4, where proper motions in units 0.001 arcsec/yr.
S.M.Chanturiya: Zirconium stars
+0.020
0.000
-0.020
373
-
-
-
-. t -0.040
*0.*060 *0.030 0.000 -0030
Fig. 2. Vector diagram of proper motions of stars of our list around cyPer.
Table 4. Results of comparison of proper motions of different Lists and catalogue AGK3
A-AGK3 B-AGK3 M-AGK3 < ‘I E 11 E II
p - p +0!’0012 +0!’0015 +0!’0027 -0!’0065 -0!‘0015 -0!’0045 &A,, f0.0008 fO.OO1O fO.OO1O f0.0009 f0.0011 fO.OO1O n 46 46 46 46 44 44
As it is evident Abastumani list reliably preserves the AGK3 system. Systems of the lists (B) and (M) significantly differ from the latter. On the basis of proper motions obtained the apex of a cluster around a Per was determined. According to the vector diagram (Fig. 2) of proper motions (in units 0.001 arcsec/yr), the following values of the components of group motion of this cluster’s stars have been obtained :
p q = -0.012arcsec/yr . pc = +0.024arcsec/yr;
Besides having used proper motions of 44 stars of the cluster and Mitchell’s data (1960) availability of magnitude and colour equations was checked in the Abastumani list of proper moticjns. Only an insignificant (of the order of -0.005 arcsec/yr) magnitude equation for p was found within the range of 5 stellar ,magnitudes, while the colour equation is totally absent.
3.
Our list of ZS was mainly compiled from Stephenson’s catalogue (1976). About 80 % of 74 ZS from the Abastumani list were supplied with two or even three overlapping plates of Carte
du Ciel catalogues. Second epoch plates were taken with the Abastumani 70cm meniscus telescope on ORWO ZU-1 emulsion. Each of 145 plates covers about 20 square deg (18x18 cm). For every object two negatives with 5 exposures on each were obtained. Details of astrometric reduction are given by Chanturiya (1980a’ Table 1 and 2). The SAO catalogue was used in the Southern zone from -20’ to -lo and the AGK3 catalogue in the Northern zone 6 > -1’. The 146 common stars were selected from epochs I and 11- having the proper motion data in reference catalogues to control the obtained results. The position of an optical centre of the 70cm meniscus telescope was studied separately using Kiselev’s method (1960).
3.1. Results and their discussion
As a result of treatment of measurements of both epoch’s tangential coordinates have been obtained, oriented by equator 1950.0, and afterwards on their basis a list of proper motions of 74 ZS, given in the form of Table 5, was compiled.
Here numbers of objects according to Stephenson’s catalogue (1976), visual apparent stellar magnitudes from Eggen (1972)’ Stephenson (1976)’ Kukarkin et al. (1969)’ Blanco et al. (1968)’ spherical coordinates for equinox 1950.0, observational epochs, proper motions in units 0.001 arcsec/yr, their errors, calculated by formula (5), BD numbers and variability type are presented.
A list of proper motions of Zirconium stars
21 a*
374
Table 5. The list of proper motions of Zirconium stars
Astron. Nachr. 318 (1997) 6
1 2 3 4 5 6 7 8 9
10 11 12 1 3 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74
7 8
11 20 21 33 34 36 39
64 69 70 74 78 84 96 98
113 128 149 156 168 179 184 197 210 217 229 230 233 251 254 256 261 266 270 305 336 452 464
496 517 527 532 539 561 574 588 598
617 624 625 633 639 644 649 650 651 669 670 680 685 700 714 715 718 723 733 740
5 “8 6.9 8 4 6.6 9.7 8.6 9.6 7.4 9.2 8.8 9.1 9.3
10.0 10.0 9.9 4.7 8 .3 6.8 9.6
10.3 9.9
10.5 9.9 7.6 9.1 7.2 7.9 8.4
11.8 7.6 8.6
11.5 5.7 9.6 8.0 7.9 7.6 7.5 8.9 7.4 9.8 3 .O 4.6 6.7 9.6 8.7 9.1
12.1 6.6 7.6 9.2 9.1 7.7
11.6 9.7
10.1 3.3 9.5 9.8
10.5 10.0
9.8 8.8
11.0 8.0
10.1 10.0
7.5 9.7
11.7 8.5 6.6 9.4 7.6
Oh19”14!535 0 21 22.974 0 43 33.111 1 1 1 19.716 1 15 57.772 1 51 33.302 1 58 58.384 2 14 18.184 2 15 13.411 3 16 53.315 4 03 04.091 4 21 50.772 4 24 48.718 4 32 49.491 4 47 10.741 4 49 42 033 5 16 39.197 5 19 54.896 5 40 26.198 6 00 10.134 6 24 11.719 6 33 07.331 6 40 17.731 6 45 42.184 6 46 41.214 6 57 10.764 7 09 34 092 7 15 01.664 7 22 55.473 7 24 33.442 7 24 43.018 7 36 04.855 7 39 14.108 7 39 55.313 7 46 18.184 7 47 32.373 7 50 43.627 8 18 52.028 8 52 58.722
12 41 45.598 1 3 19 07.212 13 26 58.426 1 3 49 58.182 13 53 02.823 15 49 16.695 17 11 16.293 17 20 02.421 17 39 06.037 17 55 22.335 18 28 49.331 18 39 31.209 19 00 50.043 19 13 21.263 19 31 10.927 19 37 13.371 19 46 54.017 19 48 38.518 20 02 36.660 20 12 03.763 20 20 21.085 20 23 23.582 20 25 14.001 20 29 36.424 20 55 05.523 20 56 06.728 21 1 3 3 4 5 7 5 21 28 09.457 22 15 54.352 22 47 57.586 22 47 55.236 22 52 07.544 23 06 59.939 23 27 14.418 23 59 33.678
-20°20’06!’42 38 18 00.89 47 58 17.67 28 15 55.79 72 20 56.54 21 38 37.48 52 19 15.34 44 07 52.94 31 31 08.34 -1 14 46.68 24 35 52.74 -2 38 48.82 22 14 42.44 12 35 39.24 79 55 05.20 14 10 07.04
-22 15 48.40 -8 42 46.91 5 03 44.59
31 38 49.00 15 55 34.03 14 15 16.66 25 48 37.28
5 35 54.20 -20 22 04.90 55 24 06.33 68 53 25.71
1 11 17.65 -20 27 46.31 46 05 35.37
-11 3 7 07.98 -15 56 26.42 14 19 36.88
-10 45 39.59 23 51 38.47
-18 52 47.46 -11 29 39.28 17 26 42.20
6 20 35.50 61 22 00.14 44 14 55.10
-23 01 24.42 64 58 11.22
-18 00 15.91 4 8 37 57.63
5 51 56.57 23 51 52.91
6 45 07.34 45 21 21.20 36 12 47.41
6 46 10.07 12 10 40.87
-17 03 37.61 23 32 47.33 67 04 27.58 41 29 12.29 32 47 10.61 36 40 26.03 16 51 44.49 23 19 48.91 25 0 3 51.90 36 23 09.59 32 23 40.51 29 08 27.71 44 35 38.72 31 33 07.35 51 03 08.84
-21 09 06.96 17 37 42.17 59 23 41.05 16 40 30.51 8 24 21.88
28 59 07.60 -14 57 15.02
72.02 78.02 71.99 77.15 73.85 77.15 72.72 72.01 72.02 72.02 72.48 71.99 72.02 72.08 71.99 72.00 72.02 71.99 77.18 77.18 71.99 72.02 72.02 71.99 72.02 72.02 71.99 72.02 72.52 72.02 72.02 72.02 75.92 73.18 73.18 72.02 73.01 72.02 71.99 72.38 72.38 73.34 72.38 73.34 72.38 77.39 72.38 72.38 72.38 77.39 71.57 71.57 71.58 72.60 71.57 72.68 72.74 72.74 77.63 77.63 73.17 77.63 72.72 71.57 77.63 77.63 77.63 72.68 72.72 72.76 72.72 72.72 77.64 75.95
[‘‘/year1 4-062 -009 -009
t o 4 9 -004 -004 -006 -004
t o 3 2 +011 +013 +006 -007 -035
0 -007
+008 +050 -008
t o o 1 t o 0 2 -001
+007 +007 +001 -01 1
+010 -010 -012 -007
0 +002 -003
+007 +002 -018 -007 -005 -014 -017 -014 -053 -011 -035 -006 -009 -003
+005 t o 1 4 -025
t o 2 4 +002 t o 0 6 t o 0 3 -024
t o 0 2 -014 -006
+025 0
t o 1 2 t o 0 4 +001 -008 -014 -008
0 -003
+001 +009 -002
+010 0
+008
I” /year1 -001 -037
t o 0 4 -045
+002 0
t o 0 7 +005 t o 1 5 +001 -014
+008 4-015 t o 0 4 t o 1 5 -056
+011 0
-002 t o o 9 -008
t o 0 2 -015
t o l l -012 -008
+014 4-003 +019 -008 -009
t o 0 2 -020 -005 -002 -012 -009
+oo2 -006 -009
+006 $009 -002
$032 -020 -014
t o 0 4 -022 -033
t o o 1 -003 -013
4-005 +003 t o o 1 +008 -040 -008
4-004 -003 -010
4-01 1 -003 -003
COO3 0 0
t o 1 1 +005 -004 -011
+011 -005 -008
007 6 4 3 6 5 4 4 4 4 4 3 4 6 4 5 6 6 4 5 4 4 4 6 5 5 4 5 7 4 4 4 3 5 3 6 6 5 4 5 4 6 5 6 4 6 4 7 3 6 5 4 5 4 4 3 7 7 4 3 5 8 7 4 3 5 4 7 5 6 4 5 4 5
006 5 4 3 G 5 4 4 3 4 3 4 4 5 4 5 6 6 4 4 4 4 4 7 5 4 4 4 7 4 4 4 3 5 3 5 5 5 4 5 4 6 6 6 4 6 3 7 4 6 5 4 5 4 4 3 7 7 4 3 5 8 7 4 3 4 4 7 5 6 4 5 4 5
- zoo 80 +37 58
+47 194 +27 196
t 7 1 66 +21 255 t 5 1 471
+43 461a +31 392 X Cet
+24 620 -2 891
t 2 2 700 t 1 2 612 4-79 156 +14 777 -22 1070 -8 1099
t 5 1000 BB Aur
t 1 5 1200 t 1 4 1350 +25 1397
+5 1414 -20 1589 55 1154
+69 413 RR Mon BX C Ma +46 1271 -11 1941 -15 1953
+14 1729 -10 2171
+24 1778 -18 2040 -11 2141
+17 1825 t 6 2063
+61 1313 9-44 2267 R Hyd
t 4 8 2334 +5 3352
+23 3093 V ~ 1 2 Oph t 4 5 2627 +36 3157
+6 3898 t 1 2 3780 -17 5546
C E Vul
xy CYg t 3 2 3593 +36 3852 t 1 6 4199 +23 3992
+36 4076 t 3 2 3850 4-28 3944 +44 3649 +31 4391
X Aqr SX Peg
CV Cep $16 4833 +7 4981
t 2 8 4592 -15 6531
SRa M M
M
Var M
Var M
SRb
SRa
M
M SRb S R ,
Lb
Lb
SRb M
M
M Var M
SRb
SRb Lb
Lb Lb
Lb M
M M
SRb
S R .
SR. Lb
M M SR
M
On an average through the whole material according to (2),(3),(4) and ( 5 ) , random errors for the position of epochs I and I1 and proper motions have turned out to be:
E I = f0.26arcsec; €11 = f0.16arcsec; E,, = fO.O046arcsec/yr .
S.M.Chanturiya: Zirconium stars 375
n 1 20
Figs. 3 and 4. Plots of distribution of the Northern zone Zirconium stars by mean quadratic errors of determinations of proper motions.
The last estimate is somewhat formal, as a difference of epochs varies in a broad range from 38 to 85 years. A more real estimate of random errors can be obtained from the analysis of results, obtained by reference stars from the formula
where UA,, is a total effect of errors of proper motions of a reference catalogue peat and the studied list PAb, and
Applying the AGK3 catalogue in the Northern zone we get O A ~ = fO.OlOarcsec/yr. Having adopted upk to be equal f0.008 arcsec/yr for random errors of proper motions by AGK3, for the Northern zone stars the error up of proper motions of the Abastumani list, according to (8)’ turned out to equal k0.006 arcsec/yr. Similarly for 37 stars of SAO catalogue we shall get by the formula (9) OA,, = k0.018 arcsec/yr. Assuming in the formula (8) for truth the obtained value up = f0.006 arcsec/yr by AGK3, we obtain the value of a SAO catalogue proper motion error to f0.016 arcsec/yr, which apparently fully corresponds to the real value.
Systematic errors of the Abastumani list were also studied by control stars. As it turned out proper motions do not show any systematic differences from the AGK3 catalogue proper motions: Apc = -0.0005 arcsec/yr, 4% = +0.0011 arcsec/yr. Nevertheless in the Southern zone there exists a significant difference from catalogue SAO : Apt = +0.0054 arcsec/yr, Ap,, = $0.0017 arcsec/yr. The reason of such a difference wasn’t found and it was decided that in further discussion we would give weight 0.5 to the Southern zone proper motions of the Abastumani list.
In Figs. 3 and 4 distributions of rrns errors of the Northern zone (6 > -2’) proper motions are presented. Proper motions of more than 80% of stars have been determined with rms errors up 5 f0.005 arcsec/yr, their mean value being equal to 50.0045 arcsec/yr.
4. Determination of mean absolute magnitudes of Zirconium stars
Radial velocities were taken from Wilson’s catalogue (1953) and supplemented from Keenan-Take’s (1956) and Smak’s (1965) lists, Abt and Biggs’ catalogue (1972). Weights were given to radial velocities according to the criteria of Wilson’s catalogue.
Visual apparent stellar magnitudes were taken mainly from Eggen (1972b), Blanco et al. (1968), Stephenson (1976), Kukarkin et al. (1969). The accuracy of the last two estimates is doubtful, but we didn’t have any opportunity to carry out their revision.
Due to an accuracy of apparent stellar magnitudes of the Mira Ceti type long-period variables in brightness maximum is higher, their mean maximum values have been used. For the variables having low-amplitude median values of apparent stellar magnitudes were taken. Based. on the works of Takayanagi (1960) ~ Stephenson (1978) and our results on 16 ZS, the value +lm5 has been applied for an average normal colour index.
On the basis of Ikaunieks’ (1963)’ Takayanagi’s (1960) and having also taken into account the limited number of objects, LASZS were considered as one group. Full interstellar absorption was calculated for each star from Parenago’s formula (1940) with parameters taken from (Sharov 1963):
376 Astron. Nachr. 318 (1997) 6
Besides, the velocity of the Sun relative to the Local Standard of Rest (LSR) of 15.5 km/sec and the apex coordinates are A = 265.OOD = 20.O7 (Vyssotsky and Janssen 1951) are used.
4.1.
In order to determine a mean absolute magnitude of a group of stars first of all it is necessary to reconstruct a true picture of proper motions and radial velocities of distributions, which are usually distorted by random observational errors. A t the same time it is necessary to obtain peculiar motions, for which some kinematical model should be assumed, whose parameters depend on adopted distance scale. Our immediate task lies in verification of the distance scale by means of the observed proper motions and radial velocities and it is solved with the consecutive approximation method.
A complete calculation scheme was developed by Karimova, Kukarkin and Pavlovskaya (1972, 1976, 1976) which consist of two preliminary and basic stages:
A preliminary stage
Algorithm and a calculation scheme
1. We have got observed proper motions pa6. Let us release them from a parallactic motion. Corrections to proper motions are calculated by the formulae:
Apa = VQ sin X sin 4/4.74r; Ap6 = VQ sin cos +/4.74r, (11)
vp E v,' = v, + v, cos A, (12)
cos X = sin 6 sin D + cos 6 cos D cos(a - A )
where X is the angular distance of a star from apex, and II, the positional angle at a star between the large circles: celectial pole-star and apex-antiapex. While the observed radial velocities V, are released from parallactic effect by (12), and the values Va, A and D, as it was mentioned above, were taken according to Vyssotsky and Janssen. We get p",,a .
2. Then we transform them into Galactic components by the formulae:
pi' = pa cos cp + pa sin cp; p[ = -pb sin cp + p~ cos cp, (13)
where cp is the angle a t a star between the directions towards the Galactic and celestial poles and is calculated by the formula:
cot cp = 0.518cos6sec(a - 282.25') + sin6 tan(cr - 282.25').
We will get P;,~.
3. T h e observed proper motions pf,b and radial velocities Vp , corrected for the solar motion are used to determine parameters of the ZSR relative to the LSR. For this purpose kinematic model is adopted, which besides Galactic rotation, takes into account radial expansion and/or contraction of a system relative to the centre of the Galaxy, as well as a motion along Z coordinate. Parameters of ZSR were obtained by a mutual solutioii of the following system of equations by the least squares method:
4.74rpl
4.74rpb = -RoAwsinIsinb- Ro(R- Ro)w'sinIsinb+
= Ro Aw cos 1 + ( R - Ro)(Ro cos 1 - r cos b)w' - rw cos b + + A V ~ s i n l + 0.5w"(R- R ~ ) ~ ( R o c o s l - rcosb),
+AV~cos l s inb - rEOsinbcosb+0.5(R- &)2Row"sinlsinb,
Ro Aw sin 1 cos b + Ro(R - Ro)w' sin 1 cos b + &Or cos 2b + +0.5(R- R0)'Row''sinlcosb- hVRcos1coSb ,
V,' =
where w is the angular velocity of galactic rotation of the ZSR at a distance Ro = lOkpc of the Sun from the galactic centre, w, is the angular velocity of rotation of a LSR at a distance R = 10 kpc, taken to be equal to 25 km/sec/kpc, Aw = w - W O , E is the velocity of radial motion of the ZSR, AVR is the difference of velocities of radial motions of the ZSR and LSR a t a distance Ro, w' and w" represent derivatives of w of the orders I and 11. Using these parameters, we get for each star a correction for galactic rotation and other motions, which are subtracted from the observed proper motions and radial velocities. We get pf i and K!'g .
S. M. Chanturi ya: Zirconium stars 377
4 . We reduce peculiar pf’i to one and the same distance r g by the formula:
where Vpg and proper motions pf,;.
= (l/ro) and rg is the approximate individual distance. Thus, we have got peculiar radial velocities
5. To get the true distribution of obtained parameters we applied Eddington’s (1940) solution in the form (Trumpler and Weaver 1953):
Q ( Z ) = -Zf’(.)/f(.) (16)
f(x) is the observed distribution function, ~ ( 2 ) - a correction to the value I, and is the mean value of the square of rms of I. Assuming that a value, being corrected, is distributed by normal law, in case of proper motions the formula (16) will have the following form:
where u2 is a dispersion, p the distribution centre of p , and E~ its rms error
A basic stage
1. Let’s go back to the observed pa,a and transform them into p [ , b by formula (13).
2. We correct p l , b and vr for galactic rotation, radial expansion and contraction of a system relative to the centre of the Galaxy and motion along the 2 coordinate, using corrections obtained. We get pab and Vp.
3. We correct proper motions pfb and radial velocities Vp for the effect of random errors, using corrections, already calculated. We have p f i and Vp
4. We transfer pH,; into equatorial components by formulae (13). We obtain pCa
5. We reduce these proper motions to one and the same distance by formula (15).
6. We calculate v , r components of proper motions by the formulae:
where $J is a positional angle of a star between the directions towards the celestial pole and antiapex. It is likewise possible to calculate u’ - a peculiar part from u. Thus we have got the u, r, u’ components of proper motions with a parallactic motion of the Sun.
- - 7. Calculate nu, Il, and nut mean parallaxes and their probable errors by the formulae:
378 Astron. Nachr. 318 (1997) G
- n,i = 4.74UUl/U",,
where V: is a peculiar radial velocity of a star, and Vo the velocity of the Sun relative to the LSR and equals 15.5 km/sec. The weights P,,, P,, Put have been introduced due to the dissimilar accuracy of proper motions. From the calculated values nu, n,, nu!, we obtain their mean value no.
8. By values g ~ , allowed in approximation I, we calculate n for the studied objects, corrected for interstellar
- - -
absorption KO, by the known formula: - M I = KO 4- 5 4- 5/gn, (29)
9. We calculate correction to the previously adopted MI by the formula: - -
A M = 5.!gn/no, (30)
10. With this correction we are specifying a value for the studied objects and obtain a new value and then more accurate distances.
11, The obtained specified distances are likewise corrected for the effect of random errors by the same formula (16) and in accordance with Feast and Shuttleworth's method (1965). The required distribution function is constructed for distance moduli. Correction of distances is carried on by the formula:
(31) -be r, = re , where b = 0.460518.
Here the first stage of calculations is over. Afterwards the whole calculation scheme is repeated with new specified estimates of distances. This consecutive iterative process may be realized several times as the need arises. I n order to obtain values of distances of the MCLPZS a period-luminosity relation from Ferrari (1973) has been employed as the first approximation, while for a LASZS Takayanagi's value (1960), = - Om1 was used.
4.2. Results and discussion
Results of the first approximation, obtained for absolute magnitudes and mean statistical parallaxes after the application of the above described methods, are presented in Table 6, where in the lst , 2nd, 3rd, 5th, 6th, 8th and 9th columns correction values to the adopted absolute magnitudes are given according to the formulae (19,20,21,22,23,24,25) accordingly, and their rms errors as well. In the 4th, 7th and 10th columns corrections are given, corresponding to the mean weighted values of mean parallaxes, computed by the formulae (19,20,21), (19,22,23) and (19,24,25). On the first and fifth lines of Table 6 parallax values, and on the third and seventh lines corrections to the absolute magnitudes are presented. On the second, fourth, sixth and eighth lines corresponding rms errors are given.
Table 6. Mean parallaxes and absolute magnitudes of Zirconium stars ( I approach)
BY " BY BY u' Mean By 171 By Iu'I Mean By ar By a", Mean
0.002430 f.002869 -1.40 f1.30
0.002858 f.000947 -0.52 f0.75
0.001 833 f.001130 -2.01 f1.34
0.001072 f.000925 -2.64 f 1.88
0.001715 f ,001 123 -2.15 f 1.43
0 000808 f ,000733 -3.26 f 1.98
0.001991 f.000768 -1.83 f0.85
0.001434 f.000491 -2.01 f0.77
Non + low variable 0.002229 0.001967 f.000500 f.000441 -1.58 - 1.86 f0.50 f0.50
Mira Ceti 0.002048 0.001601 f.000544 f.000425 -1.24 - 1 .?? f0.61 f0.61
0.002117 f.000329 -1.70 f0.50
0.001892 f.000316 -1.41 f0.61
0.002215 f.000497 -1.60 *0.50
0.001928 f .000512
- 1.37 f0.61
0.002333 f.000523 -1.49 f0.50
0.001461 f .000388 -1.97 f0.61
0.002311 f.000358 -1.51 f0.50
0 001749 f.000294 -1.58 f0.61
S.M.Chanturiya: Zirconium stars 379
The results obtained after the second approximation are given in the Table 7, where all variants of calculation of mean statistical parallaxes and corrections to the adopted absolute magnitudes have been merged. The data arrangement in Table 7 is similar to that of Table 6. Nevertheless some explanations are necessary: In the 1st and 3rd (variant A) and 25th,27th (variant G) lines parallax and correction values are presented, corresponding to the assumption that ZS do not have a tendency towards galactic concentration (pl + p b + vr), i.e. parameters of systematic motions have been obtained by the mutual solution of the equation (14). For the random errors’ effect only radial velocities and proper motions ( E $ ~ , E : ) were corrected.
Variants B and H (the 5th, 7th, 29th and 31st lines) correspond to the assumption, that ZS have got a tendency to concentration towards Galactic plane (pi + Vr)] i.e. parameters of systematic motions were obtained by a joint solution of only the first and last equations (14), while for the random errors’ effect only radial velocities and proper motions ( E $ ~ , E : ) were corrected.
In variants C (9th and 11th lines) and K (33rd and 35th lines) parameters of systematic motions were obtained by a joint solution of equations (14), corresponding to the assumption that ZS do not possess galactic concentration (pi + pb + Vr)] while for the random errors’ effect radial velocities, as well as proper motions and distances ( E $ ~ , E:, E : ) were corrected.
Variants D (the 13th and 15th lines) and L (the 37th and 39th lines) correspond to the case when a concentration is allowed of objects in the Galaxy plane (pr + Vr) and for the random errors’ effect radial velocities, as well as proper motions and distances ( E $ ~ , ~f , E: ) were corrected.
At last variants E (the 17th and 19th lines) and F (the 21st and 23rd lines) as compared to variants C and D correspond to the case, when nothing was corrected for the effect of random errors.
Table 7. Mean parallaxes and absolute magnitudes of Zirconium stars (I1 approach)
B Y u BY 7 BY u‘ Mean BY IrI BY lu l l Mean By or By u,,, Mean
0.002613 f .001323
+0.35
f l . 1 1
0.002353
+0.13 f.OOll9l
f l . 1 1
0.002458 f.001159
+0.42
f l . 1 1
0.002187 f.001120
+0.17
f l . 1 2
0.002920 f.001478
+0.60 f l . 1 1
f .001270
f l . 1 1
0.002508
+0.26
0.001131 f .000383
-0.86
f0.76
0.001825 f .000618
+O.l8
f0.76
0.001029 f .000340
-0.85
f0.74
o .oo 1629 f.000537
+O.lS f0.74
0.002149 f ,001 397
-0.07
f l . 4 2
0.002191 f ,001 404
-0.03
f l . 4 0
0.002108 f.001362
+0.09
f l . 4 1
0.0021 51 f.001369
+0.14
f 1.39
0.003147 f.002061
+0.82 f 1.38
0.003513 f.002079
+0.87 f1.37
o.ooioa4 f.000918
-1.07
f1.96
0.001716 f.001083
+0.05
f 1.38
0.001117 f.001014
-0.54
f l . 8 6
0.001609 f.001071
+o. ia
f l . 4 6
0.001648 f.OOlll6
-0.65
f 1.60
0.001626 f .ooiaoLi
-0.67
f l . 6 1
0.001639 f.001184
-0.46
f1.57
0.001616 f .001169
-0.48
f 1 . 5 7
0.002364 f 001823
+0.14 f 1.68
0.002349 f.001764
f l . 6 4 +o. ia
0 .OO 1131 f.000168
-0.86
f1.68
0.0017oa f.001061
+0.03
f l . 3 7
0.001330 f.oolo2a
-0.29 f l . 6 9
0.001586 f.001054
+0.07
f1.47
0.002107 f.000753
- 0 . 1 1
f0 .79
o.002047 f.000728
-0.16
f0 .78
0.002048 f.ooo7as
+0.03
f0 .78
0.001975 f.000696
-0.05
f0.78
o.ooaaa9 f .001003
+0.53 f0.78
0.003624 f.000923
+0.36 f0 .77
0.001 117 f.000327
-0.88
f0 .67
0.001779 f.000479
+O.l3
f O . 8 2
0.001070 f.000307
-0.76
f0 .65
0.001613 f.000437
+0.13
fO.62
0.00269a
+o.42 f.000604
f 0 . 5 0
0.002707 f.000507
+0.43
fO.50
0.002623 f . 0 0 0 5 8 8
4.0.56
f O . 5 0
0.002637 f .000592
+ o m f0.50
o.ooa953 f.ooo66a
+0.62 f0.50
0.003000 f.000673
+0.65 f O . 5 0
0.001973
4-0.35
f0.61
0.002347 f.000623
+0.73
f0.61
*.ooosa4
o.ooa309
+0.91
f0.61
f .0006 13
o.ooa455 f.000651
+ 1.04
fO.61
Non + low variable o.ooa246
+o.oa f O . 5 0
0.002228 *.000500
+O.Ol
*o.so
f.000504
0.002197 f.000493
+O.l8
f0.50
o.ooa160 f.000486
4-0.15
fO.50
0.001955 f.000438
-0 .18 f O . 5 0
0.001761 f.000395
-0.50 f O . 5 0
0.002443 f.000371
+o.21
f0.50
0.0024 1 5 f ,000367
+O.l8
fO.50
0.002380 f.000362
+0.35
f O . 5 0
0.002340 f.000358
4.0.32
f 0 . 5 0
0.001298 f .000355
4-0.07 f O . 5 0
0.002107 f.000329
-0.11 f O . 5 0
Mira Ceti o.ooi9a6 0.001558 f.000511 f.000264
+0.30 -0.16
f0.61 f0.61
0.002371 0.002178 f.000629 f.000360
+0.75 +0.56
50 .61 f0.61
0.002419 0.001522 f.000642 f.000270
+l.Ol 0.00
f0.61 f0.61
0.002491 o.ooai1i f.000661 f.000351
+].Or +0.71
f0.61 f0.61
0.002365 f.000530
+0.14
f0 .50
0.002429 f.000545
+o.ao f O . 6 0
0.002333 f .000523
+0.31
f O . 5 0
0.002397 f.000538
+0.37
fO.50
0.002924 f.000656
+0.60 fO.50
0.003043
+0.68 f.ooo68a
f O . 5 0
0.00’2083 f.000548
+0.45
f0.61
0.002757 f.000732
+ l . O S
f O . 6 1
0.002350 f .000614
+O.SS
f0.61
o.ooa585 f .000686
+ l . l S
f0.61
0.002482 f.000557
+0.24
f0 .50
0.002415 f.000542
+o .m f0 .50
0.002438 f.000549
+0.41
f0.50
o . o o a ~ 6 9 f.000531
4-0.34
f O . 5 0
0.002518 f.000665
+0.27 f O . 5 0
0.002401 f.000539
4-0.17 f O . 5 0
0.001037 f.000514
+0.31
f0.61
o.ooa5~6
+0.91 f.000678
f0.61
0.002291 f.000608
+0.89
f0.61
0.001488 f.000660
4-1.07
f0.61
0.002436 f.000369
+0.20
f O . 5 0
0.002416 f.000366
+ O . l S
f O . 5 0
o.ooa389 f.000362
4-0.36
f0 .50
0.002363 f.000358
+0.34
f0.50
0.002709 f .0004 1 1
+0.43 f O . 5 0
0.000633 f.000401
+0.37 f0.50
0.001573
-0.14
f 0 . 6 1
0.002315 f.000387
+0.71
f0.61
0.001317
f.oooa68
f.oooass 0.00
f0.61
0.002135 f.000356
+0.74
fO.61
F
( P I + Vr)
As it is evident from Table 7 variants A,B,G and H do not significantly differ from correspondingly C, D, K and L. This probably should have been expected as ZS are not very distant stars, so corrections of distances for random errors cannot give noticeable results. 28 AS~TMI. Nachr. 318 (1997) 6
380
n L
Astron. Nachr. 318 (1997) 6
Figs. 5,6 and 7. Distribution of Zirconium stars along the Z coordinate (MCLPZS, LASZS)
As regards variants E and F as compared to variants C and D, accordingly, a luminosity decrease tendency is obvious. The effect of random errors statistically increases proper motions and accordingly grows mean Fsrallax of the observed stellar group.
The distribution of ZS (long-period variables, low-amplitude variables and stationary) along the 2 coordinate is presented in Fig. 5, 6 and 7, respectively.
As ZS do not have a significant galactic concentration (see Figs. 5, 6 and 7), parameters of systematic motions were finally obtained by the joint solution of eqs. (14) and correspond to variants C and K.
Thus, three series of corrections were obtained to each adopted absolute stellar magnitudes, presented in the 4th, 7th and 10th columns of the table and corresponding to variants C and K . Before giving preference to this or that series of results one must bear in mind that Eddington’s method, applied by us, correcting proper motions for random errors, decreases dispersion and thus makes results of the third series, obtained by the formulae (19), (24) and (25), less reliable. Similarly one may reason about results of the second series, obtained by the formulae (19), (22) and (23), which are really near by values to the results of the third series.
So the most reliable is the result of the first series, given in the 4th column of Table 7 and obtained by formulae (19), (20) and (21).
Correction to the zero point of an adopted Ferrari’s period-luminosity relation (1973) for 15 MCLPZS has turned out to be -2m77. The mean value of absolute stellar magnitude a t maximum, corresponding to the mean period P = 350d is -3m89 fOm7.
Proceeding from this, Ferrari’s formula for the Mira Ceti type Zirconium variables with a period 160d 5 p 5 500d will acquire the following form:
200 M V = -- - 3 m 09,
P - 100
when MV is the visual absolute magnitude at a brightness maximum. Simultaneously, a correction to the adopted value of Takayanagi’s luminosity value (1960) for the LASZS on
the one hand and mean absolute stellar magnitude, on the other hand, has turned out to equal for 21 stars -1% and ZV = 1m9 hOm8, accordingly.
Besides, the parameter values obtained as a result of solving eqs. (14) after the I and I1 approximation are given in Table 8.
Table 8. Meaning of parameters of equations (14)
Variant Aw W’ w” AV, wo € 0 Remarks
C +0.26 f0.67
+0.47 f0.94
K +0.51 f0.82
+0.38 f1.51
Non + low variable
-10.94 - t1.57 +44.97 f5.06 f6.76 f38.19
-4.08 -4.03 -3.66 +17.25 f3.50 f2.67 f9.09 523.10
Mira Ceti
-7.82 -1.60 -1.53 +73.22 f3.08 f2.85 f6.94 320.77
-2.26 -1.25 -2.13 $38.03 f2.45 f1.06 f12.70 f15.54
-25.67 I approach f22.32
-12.91 I1 approach f13.38
+ll.70 I approach f9.54
+6.31 I1 approach f7.40
S.M.Chanturiya: Zirconium stars 38 1
A question remains open on the objects which are not supplied by radial velocities, but supplied good proper motions. As the computation scheme works at the available of both proper motions and radial velocities, we were obliged to spread parameters, obtained only from the first two equations (14), on all 56 objects. Then carry out only part of calculations on the computer. Proper motion components v, r, v’ reduced to one distance, and a parallax by component v for variables with low-amplitude and stationary stars were obtained. Neglecting the last equation (14) is justified, as absence of radial velocities may only worsen the results. Further on by the formulae (22),(23) and (30) mean parallaxes n7 and and corrections to the adopted absolute magnitudes were calculated. It should be noted that the adopted value IV:l = 30.8 km/sec was obtained by stars, supplied by both radial velocities and proper motions. As a result the value of mean weighted mean parallax equal to 0.00154 f 0.00015, while correction value to the absolute stellar magnitude equal to +Om54 fOm21. In table 7 to this value corresponds +Om35.
Conclusion: the mean absolute magnitude at maximum for the MCLPZS, corresponding to the mean period of 350 days, equals -3m9 f0m7; for LASZS absolute stellar magnitude, corresponding to the median brightness value, is equals to -1*9 fOm8 (Chanturiya 1980b).
5. Space distribution of Zirconium stars
The mean absolute magnitudes of ZS estimated on the basis of proper motions of 74 objects, although their number in Stephenson’s catalogue (1976) reaches 740. To avoid selection effect in their space distribution it was necessary to increase the number of objects involved in the discussion as much as possible (Chanturiya 1982).
From Stephenson’s Catalogue of ZS (1976) and the General Catalogue of Variable Stars (Kukarkin et al. 1969) 430 objects were selected among 740, having reliable visual apparent stellar magnitudes determined, which corre- spond to the mean maximum and median brightness values for the MCLPZS and LASZS, respectively. Apparent stellar magnitudes, are given in the catalogues with an accuracy of 0.1 mag.
Total stellar absorption was individually calculated for each object from (10). Distances were calculated assuming the mean absolute visual magnitude of LASZS equals -1m9 fOm8, and is being set by the formula (32) for MCLPZS.
5.1.
The distributions of 430 ZS along the Z coordinate have been constructed for the MCLPZS (Fig. 5), LASZS (Fig. 6) and stars with constant brightness (Fig. 7) separately. In Table 9 (2nd, 3rd and 6th columns) t,he number of stars in parallel layers with different Z is presented.
The Z distribution of Zirconium stars
Table 9. Distribution of Zirconium stars
Zone Non Low Nontlow Mira All n % n %
IZI < loops 69 17 86 23.3 9 95 22.0 100< 1.1 < 200 81 19 100 27.2 3 103 23.9 200< 1.1 < 500 101 16 117 31.8 17 134 31.1 500< 1.1 < 1000 40 5 45 12.2 16 61 14.2
121 > looops 17 3 20 5.4 18 38 8.8
In the 4th and 5th coluims a total number and percentage of LASZS in the corresponding layers are presented.
On the basis of Table 9 and Figs. 5,6 and 7 the following conclusion can be drawn: a) ZS are not characterized by strong galactic concentration and are located rather symmetrically on both side
b) In the layer with 121 < 500 pc only a half of the total number of long-period variables and more than 4/5
c) In the layer with 121 < 100 pc there exist 1/4 of all considered variables with LASZS, while in the layer with
d) The second half of all investigated stars is located beyond the boundaries of a 400 pc thickness layer. According to the space distribution of ZS, they can be divided into two distinctive groups. The MCLPZS which
are uniformly spread out of Galactic plane belongs to the first one, while the low-amplitude and nonvariables
Similar data for all ZS are given in the 7th and 8th columns.
of the Galactic plane.
of LASZS are being found.
121 < 200 pc there are 1/2.
28’
382 Astron. Nachr. 318 (1997) 6
Fig. 8. A plot of the two-dimensional distribution of selected objects (mark - 0), "tracing" Galaxy arms, and Zirconium stars (mark - 0 ) with IZI < 200 pc.
characterized by the Galactic concentration to the second one. It was previously noted by Takayanagi (1960), Mc Cuskey (1970), Mavridis (1969) and Keenan (1954).
5.2.
Westerlund (1964) indicates on a possible connection of ZS with spiral arms. Mc Cuskey (1970), Mavridis (1969) and Schmidt-Kaler (1969) showed that ZS are objects of the spiral arms of the Galaxy. In order to verify this on the basis of our data only LASZS with 121 < 200 pc were put on the plot of the twc+dimensional distribution of 0-BO aggregates, HI1 areas, 0-B3 clusters, dark nebulae, Cepheids with MV < -5TO and Bpe -stars, of the Galaxy (Schmidt-Kaler 1976) (Fig. 8). All the area, occupied by Fig. 8, was divided by us on 6 sectors; the Sun's distance from the Galactic centre is assumed to be equal to 10 kpc. For each sector the distribution of ZS has been plotted depending on their distance from the Galactic centre (Fig. 9). A similar distribution was plotted for 0-BO aggregates, 0-B3 clusters, Cepheids and B,, stars (Fig. 10).
In Fig. 11 a plot of distribution of maxima in each sector depending on the distances from the Galaxy centre by Figs. 9 and 10 (the points correspond to ZS).
In Figs. 8 and 11 a weak correlation can be observed of the ZS having 121 < 200pc, with the objects "tracing" the Galactic spiral arms (accounting for the available errors in distances).
In Fig. 8 conventional boundaries are given among the inner (Carina-Sagittarius), Local and outer (Perseus) arms (dashed curve).
It was very interesting to consider the distribution of ZS (with the exception of MCLPZS) by Z-coordinate depending on galactic longitude in each "traced" arm separately. Such distribution was plotted by us for the inner (Fig. 12), Local (Fig. 13) and outer (Fig. 14) arms.
In the inner arm region ZS reveal a tendency to "diving" under the Galactic plane, which is especially noticeable in the directions 1 - 10' and 280'.
In the outer arm of Perseus ZS also reveal the tendency of'diving" under the Galactic plane, nevertheless, their limited number does not permit to maintain something more definite.
In the Local arm the ZS are located symmetrically relative to the Galaxy plane with the exception of the direction 1 - 240', where they abruptly dive under the plane up to 2 kpc and more.
For the ZS (except the MCLPZS) projected according to our data in the Local arm region (Fig. 8), a plot of distribution of objects by Z has been constructed (Fig. 15). On the abscissae axis rcosbcosfl were plotted (6 is an angle between a direction to the star and a plane lying in the direction 1 N 240' perpendicular to the Galaxy plane).
Comparative distribution of Zirconium stars in the Galactic plane
S.M.Chanturiya: Zirconium stars 383
ni
0 , 0 ; t , J , .
n 10 c
5 !L 0
7 5
n l o t
Figs. 9 and 10. Distribution of Zirconium stars and selected objects, "tracing" Galaxy arms, depending on the distance to the centre of the Galaxy.
I , O 1 O I O , @ , O , @ l Fig. 11. A plot of the distribution of Zirconium stars (points) and selected objects (crosses) by sectors in accordance with Fig. 8 depending on the distance to the Galactic centre.
384 Astron. Nachr. 318 (1997) G
Fig. le
ZrF .1 t hncr
Fig. 14
-2 F =lPc * l t LoceL
.2 i . .
Fip. 13
. . e
60' 90' 120' 150' 180' 210' 2k0' 270' 300' 330' 360' 30'
Figs. 12, 13 and 14. Distribution of the Zirconium stars along the 2 coordinate depending on the galactic longitude in the Galaxy arms, being "traced".
210'
Fig. 15. Distribution of Zirconium stars by the Z coordinate on the Local arm depending on the distance to the Sun.
S.M.Chanturiya: Zirconium stars 385
In other words Fig. 15 is a projection of ZS of the Local arm, to the plane, perpendicular to the Galaxy plane and lying in the direction 1 - 240’. It is observed that low luminosity ZS (LASZS) deviated rather far to the South from the Galaxy plane. On Fig. 15 vertical lines at the stars with large Z indicated to the value of errors in 2 (according to the error in luminosity equal to kOm8). Simultaneously, for some stars, lying, according to Sharov’s map (1963), on the boundary of several regions with different parameters of interstellar absorption, distances were calculated, corresponding to several variants of these parameters (positions of stars, corresponding to different variants have been connected in Fig. 15 by dashed lines).
As it is evident from Fig. 15 the tendency of ZS to deviate to the South from the Galaxy plane remains valid and in some favourable (in the sense of selection of interstellar absorption parameters) variant a stellar distribution region becomes more compact.
It is likewise interesting to recall that such a picture of distribution of O-B stars was obtained in Pannekoek’s work (1929), in which the direction 1 - 264’ in the Southern part of the Galaxy is the only place, where an excess of O-B stars is being observed rather far from the plane.
As it is shown in Mc Cuskey’s work (1935) there exists also an excess of stars in a band in the same direction 1 - 267O, but starting from the Large Magellanic Cloud (LMC).
Based on the results of these works, Vaucouleurs (1954) has summarized that between our Galaxy and LMC, in the region of galactic longitudes 260 - 270’ there exists an area filled with stars and interstellar matter, connecting our Galaxy with LMC.
Extension of high velocity hydrogen atoms to great distances from the Galaxy plane (exceeding 2 kpc! was found by Kepner (1970), Verschuur (1973) and Davis (1972) based on radio observations. Moreover, asymmetric distribution of hydrogen clouds at such distances is explained by some authors as a destruction of the outer arm during perigalactic passage of LMC 4, 5.108 years ago at a distance of 20 kpc from our Galaxy (Hunter and Toomre 1969; Avner and King, 1967; Elwert and Hablick, 1965).
In the light of these investigations it should be pointed out that ZS from our list with a relatively low luminosity (av = -1m8) deflect like some other objects of the Galaxy towards the South, to the place in the immediate neighbourhood with that region of the Galaxy, where its supposed connection with the LMC is beginning to show.
6. Conclusions
1. Study of proper motions of stars around Q Per shows that Carte du Ciel catalogue may be effectively applied
2. On the basis of proper motions of 74 ZS determined the mean absolute magnitudes were calculated for Mira
3. There is slightly noticeable correlation of space distribution of ZS with spiral structure of the Galaxy. 4. The space distributions of Mira Ceti type, low amplitude and constant stars are significantly different. The
Mira Ceti type stars have more or less uniform,space distribution while other one are mostly concentrated to the galactic plane.
for determination of proper motions with rms 0.004 arcsec/year.
Ceti type and low amplitude variables. They are equal to -3m9 f0.7 and -1m8 f0.8, respectively.
5. There is a tendency of ZS’ location below the galactic plane at longitudes 240O. Acknowledgements. I am deeply grateful to Prof. R.I. Kiladze and Drs. A.Sh. Khatisashvili, A.A. Kiselev,
Finally, I am deeply indebted and would like to thank the anonymous referee for critical reading and useful O.M. Kurtanidze, E.D. Pavlovskaya for their invaluable advice, support and discussions throughout the project.
comments, which significantly improved the manuscript.
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Address of the author:
S.M. Chanturiya Abastumani Astrophysical Observatory Mt. Kanobili 383762 Republic of Georgia