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A radial velocity and photometric study of the eclipsing binary RT Andromedae
@ Pergamon Press Ltd Printed in Great Britain 0275-1962/92~10.00+.00
Chin. Akron. Astrophys.( 1992)16/2,162-172 A tram&&ion of Acta ~trophys.Si~.(l992~12/~~2~-33
A radial velocity and photometric study of the eclipsing binary RT Andromedae* WANG Xiu-mei
LU Wen-xian
Shanghai Observatory, Chinese Academy of Science, Shanghai 200030
Radial velocity observations of the eclipsingbinary RT Andromedae made in 1984-1985 are presented. Based on a point source model, the following set of spectroscopic elements is obtained: V& = -1.0 km/s, VOZ= +5.0 km/s, fr’r = 131.4 km/s, Ks = 168.4 km/s, TO = HJD 2,445,977.0997. The mass ratio q is found to be 0.780. A joint solution for the velocity and light curves was made using the WilsonDevinney code. The absolute dimensions are found to be: A = 3.80&, Rx = 1.14&, tiz = 1.05%, Mr = 1.05&&, Mz = O.SlM,. The luminosities and absolute magnitudes are L1 = 1.78L0, L2 = 0.54Lo, MV, = 4.m14, My; = 5,m65. A distance of 50 pc is estimated. RT And is a detached system consisting of two main sequence stars both of which show a slight departure from the ZAMS. Abstract
Key words: Stars-eclipsing
binaries-masses
and radii
1. INTRODUCTION RT And (BD +52"3383a, a!= 23h8m.9(1950),6 = 52*45’(1950)) is a short-period, Algol-type eclipsing binary. As far as we know, there is only one published spectroscopic solution- the one by Payne-Gaposchkin based on photographic radial velocities [Il. This author obtained 25 velocity points for the main star which gave a rather good solution, but for the companion star, she only had 5 points near quadrature. Apparently, these observational points and the orbital element Ks based on them are quite unreliable. ‘Original
version received 1990 July 2; revised version received November
26
RT And
163
With the aim of determining the radial velocity of the companion star for a new determination of the spectroscopic orbit, one of us (LU Wen-xian) made new radial velocity observations. The application of modern observing technique and reduction method has led to success. Under the premise that the point source model can yield a reliable spectroscopic mass-ratio, and by means of the Wilson-Devinny method based on Roche equipotential surface model, we made a new solution of the spectroscopic and photometric data, determined the absolute parameters of the system and gained more knowledge about its structure and evolution. 2. RADIAL
VELOCITY
SOLUTION
BASED
During the period September
OBSERVATION. ON
POINT-SOURCE
SPECTROSCOPIC MODEL
1984 -July 1985, LU Wen-xian used the Cassegrain image tube spectrograph and Reticon detector on the 1.8 m telescope of the Dominion Astrophysical Observatory and obtained 105 spectrograms at a dispersion of 15 A/mm, using an iron-argon source as comparison. Because RT And is quite bright, a high time resolution was possible. Near quadrature, an integration time of 5 minutes was enough to give high signal-to-noise ratio spectra, corresponding to a phase resolution of 0.006. Even around the main eclipse, an integration of some 12 minutes would be sufficient. 95 observing points were obtained for the main star, and 71 for the companion star. 10 other frames were taken too close to the eclipses to be useful for radial velocity measurement. Table 1 lists the radial velocity data. The times shown in Table 1 are the midexposure times and are expressed in Heliocentric Julian Days. The phase is reckoned from To, the time of principal photometric minimum. O-C is the observed radial velocity minus the calculated value from the spectroscopic solution. During the observing period of RT And, the radial velocity standards HD 222368, HD 187691, HD 184467, HD 154417 and HD 144579 were also observed. The determination of radial velocity was made through cross correlation function, a technique widely used at present. The software used was VCROSS written by HillI’ and the spectral range selected was 4000 A-4280 RV ltm a-‘1 A. In the application of the cross correlation technique, the reference star was HD Fig. 1 Two examples of the cross- 154417 (GOV). Fig. 1 shows two cross corcorrelation function profiles of RT And relation profiles near phases 0.25 and 0.75.
164
WANG Xiu-mei and LU Wen-xian
The existence of the profle of the companion star is obvious in the figure. The main star here is much brighter than the companion star; our photometric solution below shows that the magnitude difference in the B band is as much as lm.79. For systems like this, visual inspection of the spectrum plate will not reveal the spectral lines of the companion star, whereas this difficulty is easily overcome by the cross correlation technique. In our solution for the spectroscopic orbit, we took 84 velocity points for the main star and 57 for the companion star. Some points around the eclipses were not used because they suffered from confusion between the two stars. For the companion star, the velocities resulting from correlation profiles far from quadratures were given half weight in the solution. The orbital period was taken from the photometric data, P= 0.62892965 d13]. For consistency between the spectroscopic and photometric phases, the phase of maximum radial velocity of the main star was taken to be 0.75. The solution was made for a circular orbit, e z 0. We had tried an elliptical orbit but did not get any significant eccentricity. Since RT And has a variable period, the To of the spectroscopic solution was not fixed at the photometric value, rather, it was taken as an element to be determined. The value of TO so obtained was in almost perfect agreement with that in the epoch formula of Ref. [3] as regards phase. The velocity of the centre of mass of the system found separately from the two stars was vo, = -1.0 km/s and V& = t5.0 km/s. Here, then, is another instance where the two components give discrepant centre of mass velocities; this is an unsolved problem, a discussion of which is given in Ref. [4). Table 2 lists the elements of the spectroscopic orbit of RT And based on the point source model, together with some derived quantities. All the errors in Table 2 and subsequent tables are median errors, unless otherwise specified. Fig. 2 graphs the velocity curves, all the velocities of the companion having been corrected by -6.0 km/s, to bring them in line with the main star.
3. ROCHE MODEL
SOLUTION OF THE LIGHT AND VELOCITY CURVES
Multiple set photometric solutions of RT And have been published in the literature, e.g., Refs. [5] and [6], but whether they resulted from the classical method or the WD method, they were all based on the incorrect spectroscopic mass ratio q = 0.65 given in Ref. [I]. Here, we shall not be solving for all the available light curves; we shall select the most recent set, combine it with the radial velocity measurements obtained here and derive a set of unified parameters and absolute dimensions for RT And.
RT And
Table 1
165
Radial Velocity Observations of RT And -
r
Primary Velocity O-C (km/eec)
H.J.D 2,400,000+
Phase
Secondary VelocityO-C (km/set)
45962.7594 45962.7652 45962.7707 45962.7761 45962.7812 45962.7865 45962.7922 45962.7979 45962.8036 45962.8088
0.1989 0.2081 0.2169 0.2254 0.2336 0.2420 0.2511 0.2601 0.2692 0.2775
-124.9 -126.7 -128.6 - 128.5 -129.2 - 128.5 -131.1 -138.7 -135.0 -129.2
+o.a +1.1 +0.9 +2.3 +2.5 +3.7 +1.3 -6.6 -3.6 +1.2
45962.8143 45962.8199 45962.8325 45962.8373 45962.8479 45962.8527 45962.8584 45962.8641 45962.8697 45962.8750
0.2862 0.2951 0.3151 0.3228 0.3396 0.3473 0.3563 0.3654 0.3743 0.3827
- 123.9 -125.2 - 133.5 -119.3 -111.2 -105.2 - 103.8 -99.6 -92.9 -91.0
45962.8798 45962.8861 45962.8915 45962.8971 45962.9027 45962.9079 45962.9i27 45962.9175 45962.9224* 45962.9274*
0.3903 0.4003 0.4089 0.4179 0.4268 0.4350 0.4427 0.4503 0.4572 0.4649
-96.8 -74.3 -74.4 -68.1 -58.2 -54.2 -38.9 -32.8 -28.5 -27.5
45962.9322* 45962.9375* 45962.9436* 45962.9509e 45962.9581t 45962.96SOe 45962.9718 45962.9779 45962.9843 45962.9906
0.4726 0.4810 0.4907 0.5023 0.5138 O.S247 0.5366 0.5463 0.5565 0.5665
-23.6 -19.0 -9.6 +4.5 +a.8 +18.6 +26.8 +31.a +41.9 +49.5
-2.2 -4.9 -2.8 -2.9
45962.9966 45963.0028 45963.0093 45963.0153 45693.0220 45693.0282 45693.0343 45693.0394 45970.7272 45970.7361
0.5761 0.5859 0.5963 0.6058 0.6165 0.6263 0.6360 0.6441 0.8678 0.8819
+56.3 +59.9 +70-a +79.5 +88.1 +96.1 +94.6 +99.7 +95.a +85.2
-3.2 -6.7 -2.9 -0.6 +1.3 +3.4 -3.5 -2.7 -0.3 -2.6
- 107.3*
45970.7432 45970.7490 45970.7551 45970.7611 45970.7672 45970.7730 45970.7788 45970.7847* 45972.7218* 45972.7273*
0.0932 0.9024 0.9121 0.9217 0.9313 0.9406 0.9498 0.9591 0.0391 0.0479
+79.6 +82.5 +67.9 +61.5 +58.0 -j-48.2 +47.0 +47.2 -48.9 -53.8
-1.1 +7.9 -0.0 -0.4 +4.1 +1.3 +7.2
-91.3# -73.4* -79.4* -lll.O* -104.7*
+162.3 t-154.9 +170.5 + 170.3 +172.1 +167.2 +166.0 +172.3 +163.4 +162.3
-2.5 -12.7 +0.7 -1.1 -0.4 -6.0 -7.4 -0.8 -8.8 -8.6
+5.2 +1.9 -11.7 -0.4 +0.9 +3.4 +0.3 -0.3 +1.4 -1.7
+165.3 +155.5 +151.7 +153.2 +144.7 +144.8 /123.8 l-131.1 +130.8# -f-129.7*
-3.8 -11.2 -11.8 -2.9 -2.7 +1.9 -13.4 +0.1 +6.2 +11.5
-11.9 +3.6 -2.3 -2.3 +1.1 -1.1 +a.4 +a.5
+104.5* +132.3* +94.3* +96.9* +91.0* +67.9*
-79.9*
- 100.2* - 110.7# -114.1# -114.4 - 128.9 - 134.4 -124.4 -116.9#
-11.9 -6.6 +0.6 -6.9 -7.0 -5.1 -8.2 +a.4
166
WANG Xiu-mei and LU Wen-xian Table 1 (contd.) Secondary Velocity O-C (km/secI
Primary Velocity O-C (km/ccc)
H.J.D 2,400,000+
PhlSC
45972.7323 45972.7383 45972.7434 45972.7482 4S972.7530 45972.7S80 45972.7637 45972.7688 45972.7741 45972.7798
o.oss9 0.0614 0.0731 0.0811 0.0888 0.0975 O.lOS8 0.1139 0.1223 0.1314
-S3.2 -S8.1 -60.9 -61.9 -69.6 -80.9 -82.0 -86.6 -91.0 -97.9
-7.0 -4.6 -1.4 -0.8 +0.9 -4.4 +o.o +0.6 +1.3 -0.4
+126.1# + 126.2# +130.1* +lS4.2
+17.2 +10.7 +8.0 -f 25.4
45976.8761 41976.8819 45976.8862 45976.8913 45976.8965 45976.9027 45976.9088 45976.9135 45976.9238 45976.9304
0.6452 0.6537 0.6606 0.6687 0.6770 0.6868 0.696s 0.7040 0.7204 0.7309
+101.6 +107.8 + 109.2 +llS.6 +116.0 + 122.3 + 126.4 +126.0 +132.8 + 125.3
- 1.3 +0.7 -1.0 +2.0 -0.8 +2.1 +3.4 +1.1 i-4.7 -4.1
- 128.5 - 13s.o - 136.6 -140.9 - 149.9 - 147.0 - 154.2 - 148.4 - 147.0 -171.2
-0.4 -1.6 +0.8 +0.9 -4.0 +3.2 -0.3 +7.9 +13.4 -9.1
41976.9363 4S976.9446 45976.9549 46028.7451 46028.iS30 46035.6729 46035.6824 46035.6954 46035.7064 46266.9014
0.7402 0.7534 0.7698 0.1163 0.1289 0.131s 0.1467 0.1673 0.1848 0.7853
+ 127.5 f133.0 +133.2 -92.3 -99.1 -97.1 - 109.3 - 107.9 - 125.7 + 122.9
-2.6 +2.6 +3.8 -3.6 -3.0 -0.0 -3.7 +6.7 -4.2 -4.3
- 168.0 - 162.4 - 162.0 +123.9# + 138.7# +138.7 +1ss.3 +166.8 +169.5 - 159.8
-s.o +0.9 +o.o +6.5 +11.7 +9.9 +16.2 +15.6 +10.0 -0.6
46266.9080 46266.9150 46266.9229 46266.9302 46266.9372
0.7958 0.8070 0.8195 0.8311 0.8422
+121.1 +120.3 + 122.5 +118*6 + 103.9
-4.4 -1.8 +3.8 +4.9 -5.2
- lS6.0 -141.2 -146.0 -144.6 -155.6
+0.8 +11.s +1.6 -2.7 - 19.5
*
Obtained
l
Lower
Table 2
from weights
conjunction
and
were
because
given
Spectroscopic
not
used
for
they were
the
Standard
solution from
of the
guirc
-1.o+/-0.4
V&m/s)
+s.o+/-1.2
Mkmls)
131.4+/-0.5
Mkmls) 7’,(2,445,900+)
168.4+/-1.4
cr,sini(lO’km)
1.136+/-0.004
77.0997+/-0.0004
a,sini(lO‘km)
1.456+/-0.012
m,sin’i(Mo)
0.989+/-0.018
m,sin’i(&)
0.771+/-0.009
cl(m,/m,)
0.780+/-0.007
s.d,*(km/s)
+/-3.3
~.d,*(km/s)
+/-a.4
deviation
point
blended
SOUTCC
c.c.f.
model.
profiles.
Elements of RT And from the Point Source Model
Y&m/s)
*
orbital
measured
+70.6*
uf observation
of unit
weight.
RT And
167
We took the photometric normal points of Mancuso et aZ.[fland, to save computer time, further grouped those in the phase intervals 0.1-0.4 and 0.6-0.9 to result in 60 grouped points in each of the three colours, UBV, giving each a weight equal to the number of normal points used.
Fig. 2 Radial velocity curves of R!TAnd As judged from the spectrum we obtained at phase 0.5, the main star of RT And has a spectral type of F8V, 50 we take its surface effective temperature to be 6250 Klsl. For some other model parameters such as the limb darkening coefficient X, the albedo A and the gravity darkening coefficient g, usual values were taken. The mass ratio.was taken in the first instance to be qlp (=0.780). Model 2 of the WD code, i.e., the detached model, was then used to find the separate photometric solution. The parameters to be adjusted were the inclination i, the effective temperature of the companion star 2’2, the surface potentials of the two stars 521 and Q, and the luminosity of the main star I&. These were adjusted until a preliminary convergence was achieved. The mass ratio was then set to be freely adjustable, until final convergence. The value of the photometric mass ratio so obtained is q = 0.7796 f 0.0024. We then started on the velocity solution, using the photometric results for the relevant geometrical and physical parameters and got the new spectroscopic mass ratio, !l = 0.7615 f 0.0065. The weighted mean of the two results, q = 0.7773 f 0.0023 was then taken as the mass ratio in the combined photometric and velocity solution. The results of the combined solution are given in Table 3 and the light curves from the combined solution are shown in Fig. 3. For clarity we have moved the blue light curve down by Om.35. Before using the Roche model to solve the velocity curves,
WANG
168
Xiu-mei and LU Wen-xian
we had, in accordance with the difference between IGiland V& given by the point source model, applied a correction of -6.0 km/s to the velocities of the companion star listed in Table 1. The theoretical curves obtained are shown in Fig. 2. In the course of deriving the photometric solution, we found the light curves of Ref. [7] were not symmetrical, namely, the intensity at phase 0.25 was less than that at 0.75. Usually, for RS CVn stars like RT And, such asymmetry is caused by darkened regions on the surface of the components produced by spot groups. Milan0 et al., when using the WD method, did not allow for this effect. Mancuso et al.f’l found that the spectrum of RT And at phase 0.06 showed H and K core emissions; we also found such weak emission lines, this shows that the there is quite strong chromospheric activity in the atmospheres of the component stars. But neither Table 3 prraueters
Rocbe Model Solutions of RT And photo.sol.
joint
sol.
velocity
sol.
-
me)
3.796+/-0.017
-0.0004+/-0.0010
00
-
Vr(Ws)
-1.4+/-0.s
a1.29+/-0.17
i(deg.)
-0.0006+/-0.0010
81.20+/-0.16
3.807+/-0.018
_-0.0007+/-0.0008 _-1.s+/-0.s 81.20
El =zx
0.32r
0.32-e
0.32;
A,=A
o.so*
o.so+
o.so*
0.61*
0.61+
x,v
0.71*
0.718
X,B
0.74*
0.74*
0.79t
WJ
o.as*
O.BS+
0.91*
X,U
0.82*
0.82.
XGJ
0.958
0.95
0,
4.1SB9+/-0.0321
4.1905+/-0.032s
4.1905
0,
4.0096+/-0.0151
3.9947+/-0.0147
3.9947
I
x,v
3.3778**
Qi* T,(k)
62SOe
62SOe
T,(k)
4827+/-9
4a26+/-9
q(mJm,)
0.7796+/-0.0024
0.7773+/-0.0023
L/CL,
f&Y
0.8029+/-0.0018
o.aooo+/-0.0019
L,/(b
+&)B
o.a410+/-0.0013
o.a3aa+/-0.0015
wu-,
+wJ
o.aa37+/-0.0009
0.8824+/-0.0009
'c(Pole)
0.2922+/-0.0027
0.2904+/-0.0015
r,(point)
0.3133+/-0.0037
0.3107+/-0.0022
r,(side)
O-2990+/-0.0030
0.2970+/-0.0018
r,(back)
0.3077+/-0.0034
0.3054+/-0.0019
‘*(Pole)
0.2656+/-0.0013
0.2665+/-0.0024
r,(poiot)
0.2874+/-0.0018
0.2887+/-0.003s
r,(ride)
O.ZllS+/-0.001s
0.2725+/-0.0029
r,(bact)
0.2814+/-0.0018
0.2826+/-0.0034
l
Values
assumed.
**Theoretical
value.
625Oe 4826 0.7615+/-0.0065
RT And
Fig. 3
Light curves of RT And
ourselves can determine which component these emission lines originate in. Now, near quadrature, the luminosity of the companion star accounts for only 20% in the V band and for even less in the B and U bands. Hence, if the spots are on the companion star, then the spots must be enormous-almost unreasonably large. So we put a small spot on the main star and re-draw its light curves, in the manner of Ref. [G]. We only tried three sets of spot parameters, longitude cr = llO”, radius r = 15“, spot/photosphere temperature ratio f = 0.9 and latitude 4 = 90°, 70°,400. The results showed the smallest residuals for # = 70°, which we adopted in our solution. 4. BASIC Table 4 lists the basic parameters
PARAMETERS
of this system jointly
deduced
from the photomet-
ric and spectroscopic solutions. A is the separation between the components in units of solar radius. We estimated the luminosities L and the bolometric magnitudes Mm from the surface effective temperatures, taking the Sun’s temperature to be 5780 K and its bolometric magnitude to be 4m. 75. The absolute visual magnitude of the main star is &Iv, = Mw - BC, its spectral type being F8V, BC = -0.02[‘“1, hence Mv, = 4m.14. The photometric solution shows the companion star to be fainter than the main star by lm.51 in the visual band, hence we get Mvz = 5”‘.65. The combined absolute visual magnitude is then n/iv = 3m.90. With an apparent magnitude of mv = 8m.55[111, and a latitude of -7O (hence Av = lm.2, on using R = 3
WANG Xiu-mei and LU Wen-xian
170
and the reddening-latitude relation of Ref. [12]), we then estimate the distance of RT And to be N 50 pc. The photometric parallax for RT And listed in Ref. [12] is A = 0.010 f 0.002 arcsec, which corresponds to a distance d N 100 pc.
Table 4
Beeic prrmaeterr
of RT And
parameter
R(rep..
1.04s+/-0.013
0.812+/-0.009
1.142+/-0.009
1.053+/-0.020
6250
4626
1.78
0.54
4.12
5.42
4.14
5.65
R@)
3.796+-J-0.017
i
81.20+-J-0.16
9(mh)
0,7773+J-0.0024 50
d(PC)
5. CONCLUSIONS
AND
DISCUSSION
Using modern observing techniques and methods of data reduction, we have correctly determined the radial velocity of the companion star of RT And and ascertained its spectroscopic solution. Our results confirm that the #i value of Ref. [l] was good enough, while the I<2 value should be replaced by the new determination. The new point source model spectroscopic solution shows that the orbital eccentricity of RT And is zero and is not 0.089 as given in Ref. [l]. There is also a large difference between the determinations of the centre of mass velocity in the two papers. In the course of our observations of RT And we also observed some radial velocity standards and we found these to be in basic agreement with the lAU system[131. Apparently, there seems to be a systematic difference between the two. The observing accuracy in Ref. fl] is comparatively low and this may be one of the factors for the difference. In this paper we managed to obtain a reliable value for the mass ratio, which provides a basis for the further study of the structure and evolution of this binary system. Using the new mass ratio and allowing for the existence of spots, we used the WD method to solve the photoelectric observations of Mancuso et al. and determined the geometrical and physical quantities of the system. The absolute quantities including the radii and masses of the component stars have an accuracy of determination of l-2%, so the results can be regarded as reliable and improved.
l?l
RT And
#
Fig. 4
The Roche configuration of KI’ Aud
Our combined solution shows that RT And is a pair of detached, main sequence stars, in agreement with the conclusion of Ref. 141. The Roche configuration of the two components is shown in Fig. 4. In the lg(M/&) lg(R/&) diagram, we can see that the two components depart slightly from This the zero age main sequence. is also the case on the lg(M/Mo) lg(L/L~) diagram. Both components, then, shows some signs of evolution.
The spectrum we got at phase 0.5 confirms that the spectral type of the main star is F8V. As the combined solution shows, at this phase, the contribution of the companion to the total luminosity is less than 7%, so we can approximately regard the observed spectrum at the time to be that of the main star. As the primary eclipse is partial eclipse, we cannot determine the spectral type of the companion star. But we can do so indirectly from its position on the HR diagram. According to the statistical relation181 between the MK type, T, and L, with Te = 4826 K, the spectral type of the companion could be either K2V or KOIV, corresponding Since we found lg(L/& = -0.268, to lg(Lf&) = -0.417 or 0.890), respectively. it appears that the spectral type is K2V. This is 2 subtypes away from the KOV published by Dumitrescul’51. In the combined solution, in order to reproduce the asymmetry in Mancuso et al.‘s light curve, we used a very crude spot model and only applied only to the surface of the main star through inference. As to what the actual situation is, we have to await more refined spectral analysis or even other techniques. Our theoretical curve does not fit the observations at the secondary eclipse very well and further work is called for. In this paper we did not consider changes in the period, and from the many available light curves we only selected one and did not make a comprehensive study.
Thus,
the present
investigation
remains
a fairly superficial
one.
Acknowledgement All the calculation in this paper was carried out on the Micro VAX II Computer of the Shanghai Observatory. We thank Mr LIANG Hai-qi and others for help with the graphics. LU Wen-xian thanks the DA0 for the telescope time during his visit.
WANG
172
Xiu-mei and LU Wen-xian
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Chin. Akron. Astrophys.( 1992)16/2,162-172 A tram&&ion of Acta ~trophys.Si~.(l992~12/~~2~-33
A radial velocity and photometric study of the eclipsing binary RT Andromedae* WANG Xiu-mei
LU Wen-xian
Shanghai Observatory, Chinese Academy of Science, Shanghai 200030
Radial velocity observations of the eclipsingbinary RT Andromedae made in 1984-1985 are presented. Based on a point source model, the following set of spectroscopic elements is obtained: V& = -1.0 km/s, VOZ= +5.0 km/s, fr’r = 131.4 km/s, Ks = 168.4 km/s, TO = HJD 2,445,977.0997. The mass ratio q is found to be 0.780. A joint solution for the velocity and light curves was made using the WilsonDevinney code. The absolute dimensions are found to be: A = 3.80&, Rx = 1.14&, tiz = 1.05%, Mr = 1.05&&, Mz = O.SlM,. The luminosities and absolute magnitudes are L1 = 1.78L0, L2 = 0.54Lo, MV, = 4.m14, My; = 5,m65. A distance of 50 pc is estimated. RT And is a detached system consisting of two main sequence stars both of which show a slight departure from the ZAMS. Abstract
Key words: Stars-eclipsing
binaries-masses
and radii
1. INTRODUCTION RT And (BD +52"3383a, a!= 23h8m.9(1950),6 = 52*45’(1950)) is a short-period, Algol-type eclipsing binary. As far as we know, there is only one published spectroscopic solution- the one by Payne-Gaposchkin based on photographic radial velocities [Il. This author obtained 25 velocity points for the main star which gave a rather good solution, but for the companion star, she only had 5 points near quadrature. Apparently, these observational points and the orbital element Ks based on them are quite unreliable. ‘Original
version received 1990 July 2; revised version received November
26
RT And
163
With the aim of determining the radial velocity of the companion star for a new determination of the spectroscopic orbit, one of us (LU Wen-xian) made new radial velocity observations. The application of modern observing technique and reduction method has led to success. Under the premise that the point source model can yield a reliable spectroscopic mass-ratio, and by means of the Wilson-Devinny method based on Roche equipotential surface model, we made a new solution of the spectroscopic and photometric data, determined the absolute parameters of the system and gained more knowledge about its structure and evolution. 2. RADIAL
VELOCITY
SOLUTION
BASED
During the period September
OBSERVATION. ON
POINT-SOURCE
SPECTROSCOPIC MODEL
1984 -July 1985, LU Wen-xian used the Cassegrain image tube spectrograph and Reticon detector on the 1.8 m telescope of the Dominion Astrophysical Observatory and obtained 105 spectrograms at a dispersion of 15 A/mm, using an iron-argon source as comparison. Because RT And is quite bright, a high time resolution was possible. Near quadrature, an integration time of 5 minutes was enough to give high signal-to-noise ratio spectra, corresponding to a phase resolution of 0.006. Even around the main eclipse, an integration of some 12 minutes would be sufficient. 95 observing points were obtained for the main star, and 71 for the companion star. 10 other frames were taken too close to the eclipses to be useful for radial velocity measurement. Table 1 lists the radial velocity data. The times shown in Table 1 are the midexposure times and are expressed in Heliocentric Julian Days. The phase is reckoned from To, the time of principal photometric minimum. O-C is the observed radial velocity minus the calculated value from the spectroscopic solution. During the observing period of RT And, the radial velocity standards HD 222368, HD 187691, HD 184467, HD 154417 and HD 144579 were also observed. The determination of radial velocity was made through cross correlation function, a technique widely used at present. The software used was VCROSS written by HillI’ and the spectral range selected was 4000 A-4280 RV ltm a-‘1 A. In the application of the cross correlation technique, the reference star was HD Fig. 1 Two examples of the cross- 154417 (GOV). Fig. 1 shows two cross corcorrelation function profiles of RT And relation profiles near phases 0.25 and 0.75.
164
WANG Xiu-mei and LU Wen-xian
The existence of the profle of the companion star is obvious in the figure. The main star here is much brighter than the companion star; our photometric solution below shows that the magnitude difference in the B band is as much as lm.79. For systems like this, visual inspection of the spectrum plate will not reveal the spectral lines of the companion star, whereas this difficulty is easily overcome by the cross correlation technique. In our solution for the spectroscopic orbit, we took 84 velocity points for the main star and 57 for the companion star. Some points around the eclipses were not used because they suffered from confusion between the two stars. For the companion star, the velocities resulting from correlation profiles far from quadratures were given half weight in the solution. The orbital period was taken from the photometric data, P= 0.62892965 d13]. For consistency between the spectroscopic and photometric phases, the phase of maximum radial velocity of the main star was taken to be 0.75. The solution was made for a circular orbit, e z 0. We had tried an elliptical orbit but did not get any significant eccentricity. Since RT And has a variable period, the To of the spectroscopic solution was not fixed at the photometric value, rather, it was taken as an element to be determined. The value of TO so obtained was in almost perfect agreement with that in the epoch formula of Ref. [3] as regards phase. The velocity of the centre of mass of the system found separately from the two stars was vo, = -1.0 km/s and V& = t5.0 km/s. Here, then, is another instance where the two components give discrepant centre of mass velocities; this is an unsolved problem, a discussion of which is given in Ref. [4). Table 2 lists the elements of the spectroscopic orbit of RT And based on the point source model, together with some derived quantities. All the errors in Table 2 and subsequent tables are median errors, unless otherwise specified. Fig. 2 graphs the velocity curves, all the velocities of the companion having been corrected by -6.0 km/s, to bring them in line with the main star.
3. ROCHE MODEL
SOLUTION OF THE LIGHT AND VELOCITY CURVES
Multiple set photometric solutions of RT And have been published in the literature, e.g., Refs. [5] and [6], but whether they resulted from the classical method or the WD method, they were all based on the incorrect spectroscopic mass ratio q = 0.65 given in Ref. [I]. Here, we shall not be solving for all the available light curves; we shall select the most recent set, combine it with the radial velocity measurements obtained here and derive a set of unified parameters and absolute dimensions for RT And.
RT And
Table 1
165
Radial Velocity Observations of RT And -
r
Primary Velocity O-C (km/eec)
H.J.D 2,400,000+
Phase
Secondary VelocityO-C (km/set)
45962.7594 45962.7652 45962.7707 45962.7761 45962.7812 45962.7865 45962.7922 45962.7979 45962.8036 45962.8088
0.1989 0.2081 0.2169 0.2254 0.2336 0.2420 0.2511 0.2601 0.2692 0.2775
-124.9 -126.7 -128.6 - 128.5 -129.2 - 128.5 -131.1 -138.7 -135.0 -129.2
+o.a +1.1 +0.9 +2.3 +2.5 +3.7 +1.3 -6.6 -3.6 +1.2
45962.8143 45962.8199 45962.8325 45962.8373 45962.8479 45962.8527 45962.8584 45962.8641 45962.8697 45962.8750
0.2862 0.2951 0.3151 0.3228 0.3396 0.3473 0.3563 0.3654 0.3743 0.3827
- 123.9 -125.2 - 133.5 -119.3 -111.2 -105.2 - 103.8 -99.6 -92.9 -91.0
45962.8798 45962.8861 45962.8915 45962.8971 45962.9027 45962.9079 45962.9i27 45962.9175 45962.9224* 45962.9274*
0.3903 0.4003 0.4089 0.4179 0.4268 0.4350 0.4427 0.4503 0.4572 0.4649
-96.8 -74.3 -74.4 -68.1 -58.2 -54.2 -38.9 -32.8 -28.5 -27.5
45962.9322* 45962.9375* 45962.9436* 45962.9509e 45962.9581t 45962.96SOe 45962.9718 45962.9779 45962.9843 45962.9906
0.4726 0.4810 0.4907 0.5023 0.5138 O.S247 0.5366 0.5463 0.5565 0.5665
-23.6 -19.0 -9.6 +4.5 +a.8 +18.6 +26.8 +31.a +41.9 +49.5
-2.2 -4.9 -2.8 -2.9
45962.9966 45963.0028 45963.0093 45963.0153 45693.0220 45693.0282 45693.0343 45693.0394 45970.7272 45970.7361
0.5761 0.5859 0.5963 0.6058 0.6165 0.6263 0.6360 0.6441 0.8678 0.8819
+56.3 +59.9 +70-a +79.5 +88.1 +96.1 +94.6 +99.7 +95.a +85.2
-3.2 -6.7 -2.9 -0.6 +1.3 +3.4 -3.5 -2.7 -0.3 -2.6
- 107.3*
45970.7432 45970.7490 45970.7551 45970.7611 45970.7672 45970.7730 45970.7788 45970.7847* 45972.7218* 45972.7273*
0.0932 0.9024 0.9121 0.9217 0.9313 0.9406 0.9498 0.9591 0.0391 0.0479
+79.6 +82.5 +67.9 +61.5 +58.0 -j-48.2 +47.0 +47.2 -48.9 -53.8
-1.1 +7.9 -0.0 -0.4 +4.1 +1.3 +7.2
-91.3# -73.4* -79.4* -lll.O* -104.7*
+162.3 t-154.9 +170.5 + 170.3 +172.1 +167.2 +166.0 +172.3 +163.4 +162.3
-2.5 -12.7 +0.7 -1.1 -0.4 -6.0 -7.4 -0.8 -8.8 -8.6
+5.2 +1.9 -11.7 -0.4 +0.9 +3.4 +0.3 -0.3 +1.4 -1.7
+165.3 +155.5 +151.7 +153.2 +144.7 +144.8 /123.8 l-131.1 +130.8# -f-129.7*
-3.8 -11.2 -11.8 -2.9 -2.7 +1.9 -13.4 +0.1 +6.2 +11.5
-11.9 +3.6 -2.3 -2.3 +1.1 -1.1 +a.4 +a.5
+104.5* +132.3* +94.3* +96.9* +91.0* +67.9*
-79.9*
- 100.2* - 110.7# -114.1# -114.4 - 128.9 - 134.4 -124.4 -116.9#
-11.9 -6.6 +0.6 -6.9 -7.0 -5.1 -8.2 +a.4
166
WANG Xiu-mei and LU Wen-xian Table 1 (contd.) Secondary Velocity O-C (km/secI
Primary Velocity O-C (km/ccc)
H.J.D 2,400,000+
PhlSC
45972.7323 45972.7383 45972.7434 45972.7482 4S972.7530 45972.7S80 45972.7637 45972.7688 45972.7741 45972.7798
o.oss9 0.0614 0.0731 0.0811 0.0888 0.0975 O.lOS8 0.1139 0.1223 0.1314
-S3.2 -S8.1 -60.9 -61.9 -69.6 -80.9 -82.0 -86.6 -91.0 -97.9
-7.0 -4.6 -1.4 -0.8 +0.9 -4.4 +o.o +0.6 +1.3 -0.4
+126.1# + 126.2# +130.1* +lS4.2
+17.2 +10.7 +8.0 -f 25.4
45976.8761 41976.8819 45976.8862 45976.8913 45976.8965 45976.9027 45976.9088 45976.9135 45976.9238 45976.9304
0.6452 0.6537 0.6606 0.6687 0.6770 0.6868 0.696s 0.7040 0.7204 0.7309
+101.6 +107.8 + 109.2 +llS.6 +116.0 + 122.3 + 126.4 +126.0 +132.8 + 125.3
- 1.3 +0.7 -1.0 +2.0 -0.8 +2.1 +3.4 +1.1 i-4.7 -4.1
- 128.5 - 13s.o - 136.6 -140.9 - 149.9 - 147.0 - 154.2 - 148.4 - 147.0 -171.2
-0.4 -1.6 +0.8 +0.9 -4.0 +3.2 -0.3 +7.9 +13.4 -9.1
41976.9363 4S976.9446 45976.9549 46028.7451 46028.iS30 46035.6729 46035.6824 46035.6954 46035.7064 46266.9014
0.7402 0.7534 0.7698 0.1163 0.1289 0.131s 0.1467 0.1673 0.1848 0.7853
+ 127.5 f133.0 +133.2 -92.3 -99.1 -97.1 - 109.3 - 107.9 - 125.7 + 122.9
-2.6 +2.6 +3.8 -3.6 -3.0 -0.0 -3.7 +6.7 -4.2 -4.3
- 168.0 - 162.4 - 162.0 +123.9# + 138.7# +138.7 +1ss.3 +166.8 +169.5 - 159.8
-s.o +0.9 +o.o +6.5 +11.7 +9.9 +16.2 +15.6 +10.0 -0.6
46266.9080 46266.9150 46266.9229 46266.9302 46266.9372
0.7958 0.8070 0.8195 0.8311 0.8422
+121.1 +120.3 + 122.5 +118*6 + 103.9
-4.4 -1.8 +3.8 +4.9 -5.2
- lS6.0 -141.2 -146.0 -144.6 -155.6
+0.8 +11.s +1.6 -2.7 - 19.5
*
Obtained
l
Lower
Table 2
from weights
conjunction
and
were
because
given
Spectroscopic
not
used
for
they were
the
Standard
solution from
of the
guirc
-1.o+/-0.4
V&m/s)
+s.o+/-1.2
Mkmls)
131.4+/-0.5
Mkmls) 7’,(2,445,900+)
168.4+/-1.4
cr,sini(lO’km)
1.136+/-0.004
77.0997+/-0.0004
a,sini(lO‘km)
1.456+/-0.012
m,sin’i(Mo)
0.989+/-0.018
m,sin’i(&)
0.771+/-0.009
cl(m,/m,)
0.780+/-0.007
s.d,*(km/s)
+/-3.3
~.d,*(km/s)
+/-a.4
deviation
point
blended
SOUTCC
c.c.f.
model.
profiles.
Elements of RT And from the Point Source Model
Y&m/s)
*
orbital
measured
+70.6*
uf observation
of unit
weight.
RT And
167
We took the photometric normal points of Mancuso et aZ.[fland, to save computer time, further grouped those in the phase intervals 0.1-0.4 and 0.6-0.9 to result in 60 grouped points in each of the three colours, UBV, giving each a weight equal to the number of normal points used.
Fig. 2 Radial velocity curves of R!TAnd As judged from the spectrum we obtained at phase 0.5, the main star of RT And has a spectral type of F8V, 50 we take its surface effective temperature to be 6250 Klsl. For some other model parameters such as the limb darkening coefficient X, the albedo A and the gravity darkening coefficient g, usual values were taken. The mass ratio.was taken in the first instance to be qlp (=0.780). Model 2 of the WD code, i.e., the detached model, was then used to find the separate photometric solution. The parameters to be adjusted were the inclination i, the effective temperature of the companion star 2’2, the surface potentials of the two stars 521 and Q, and the luminosity of the main star I&. These were adjusted until a preliminary convergence was achieved. The mass ratio was then set to be freely adjustable, until final convergence. The value of the photometric mass ratio so obtained is q = 0.7796 f 0.0024. We then started on the velocity solution, using the photometric results for the relevant geometrical and physical parameters and got the new spectroscopic mass ratio, !l = 0.7615 f 0.0065. The weighted mean of the two results, q = 0.7773 f 0.0023 was then taken as the mass ratio in the combined photometric and velocity solution. The results of the combined solution are given in Table 3 and the light curves from the combined solution are shown in Fig. 3. For clarity we have moved the blue light curve down by Om.35. Before using the Roche model to solve the velocity curves,
WANG
168
Xiu-mei and LU Wen-xian
we had, in accordance with the difference between IGiland V& given by the point source model, applied a correction of -6.0 km/s to the velocities of the companion star listed in Table 1. The theoretical curves obtained are shown in Fig. 2. In the course of deriving the photometric solution, we found the light curves of Ref. [7] were not symmetrical, namely, the intensity at phase 0.25 was less than that at 0.75. Usually, for RS CVn stars like RT And, such asymmetry is caused by darkened regions on the surface of the components produced by spot groups. Milan0 et al., when using the WD method, did not allow for this effect. Mancuso et al.f’l found that the spectrum of RT And at phase 0.06 showed H and K core emissions; we also found such weak emission lines, this shows that the there is quite strong chromospheric activity in the atmospheres of the component stars. But neither Table 3 prraueters
Rocbe Model Solutions of RT And photo.sol.
joint
sol.
velocity
sol.
-
me)
3.796+/-0.017
-0.0004+/-0.0010
00
-
Vr(Ws)
-1.4+/-0.s
a1.29+/-0.17
i(deg.)
-0.0006+/-0.0010
81.20+/-0.16
3.807+/-0.018
_-0.0007+/-0.0008 _-1.s+/-0.s 81.20
El =zx
0.32r
0.32-e
0.32;
A,=A
o.so*
o.so+
o.so*
0.61*
0.61+
x,v
0.71*
0.718
X,B
0.74*
0.74*
0.79t
WJ
o.as*
O.BS+
0.91*
X,U
0.82*
0.82.
XGJ
0.958
0.95
0,
4.1SB9+/-0.0321
4.1905+/-0.032s
4.1905
0,
4.0096+/-0.0151
3.9947+/-0.0147
3.9947
I
x,v
3.3778**
Qi* T,(k)
62SOe
62SOe
T,(k)
4827+/-9
4a26+/-9
q(mJm,)
0.7796+/-0.0024
0.7773+/-0.0023
L/CL,
f&Y
0.8029+/-0.0018
o.aooo+/-0.0019
L,/(b
+&)B
o.a410+/-0.0013
o.a3aa+/-0.0015
wu-,
+wJ
o.aa37+/-0.0009
0.8824+/-0.0009
'c(Pole)
0.2922+/-0.0027
0.2904+/-0.0015
r,(point)
0.3133+/-0.0037
0.3107+/-0.0022
r,(side)
O-2990+/-0.0030
0.2970+/-0.0018
r,(back)
0.3077+/-0.0034
0.3054+/-0.0019
‘*(Pole)
0.2656+/-0.0013
0.2665+/-0.0024
r,(poiot)
0.2874+/-0.0018
0.2887+/-0.003s
r,(ride)
O.ZllS+/-0.001s
0.2725+/-0.0029
r,(bact)
0.2814+/-0.0018
0.2826+/-0.0034
l
Values
assumed.
**Theoretical
value.
625Oe 4826 0.7615+/-0.0065
RT And
Fig. 3
Light curves of RT And
ourselves can determine which component these emission lines originate in. Now, near quadrature, the luminosity of the companion star accounts for only 20% in the V band and for even less in the B and U bands. Hence, if the spots are on the companion star, then the spots must be enormous-almost unreasonably large. So we put a small spot on the main star and re-draw its light curves, in the manner of Ref. [G]. We only tried three sets of spot parameters, longitude cr = llO”, radius r = 15“, spot/photosphere temperature ratio f = 0.9 and latitude 4 = 90°, 70°,400. The results showed the smallest residuals for # = 70°, which we adopted in our solution. 4. BASIC Table 4 lists the basic parameters
PARAMETERS
of this system jointly
deduced
from the photomet-
ric and spectroscopic solutions. A is the separation between the components in units of solar radius. We estimated the luminosities L and the bolometric magnitudes Mm from the surface effective temperatures, taking the Sun’s temperature to be 5780 K and its bolometric magnitude to be 4m. 75. The absolute visual magnitude of the main star is &Iv, = Mw - BC, its spectral type being F8V, BC = -0.02[‘“1, hence Mv, = 4m.14. The photometric solution shows the companion star to be fainter than the main star by lm.51 in the visual band, hence we get Mvz = 5”‘.65. The combined absolute visual magnitude is then n/iv = 3m.90. With an apparent magnitude of mv = 8m.55[111, and a latitude of -7O (hence Av = lm.2, on using R = 3
WANG Xiu-mei and LU Wen-xian
170
and the reddening-latitude relation of Ref. [12]), we then estimate the distance of RT And to be N 50 pc. The photometric parallax for RT And listed in Ref. [12] is A = 0.010 f 0.002 arcsec, which corresponds to a distance d N 100 pc.
Table 4
Beeic prrmaeterr
of RT And
parameter
R(rep..
1.04s+/-0.013
0.812+/-0.009
1.142+/-0.009
1.053+/-0.020
6250
4626
1.78
0.54
4.12
5.42
4.14
5.65
R@)
3.796+-J-0.017
i
81.20+-J-0.16
9(mh)
0,7773+J-0.0024 50
d(PC)
5. CONCLUSIONS
AND
DISCUSSION
Using modern observing techniques and methods of data reduction, we have correctly determined the radial velocity of the companion star of RT And and ascertained its spectroscopic solution. Our results confirm that the #i value of Ref. [l] was good enough, while the I<2 value should be replaced by the new determination. The new point source model spectroscopic solution shows that the orbital eccentricity of RT And is zero and is not 0.089 as given in Ref. [l]. There is also a large difference between the determinations of the centre of mass velocity in the two papers. In the course of our observations of RT And we also observed some radial velocity standards and we found these to be in basic agreement with the lAU system[131. Apparently, there seems to be a systematic difference between the two. The observing accuracy in Ref. fl] is comparatively low and this may be one of the factors for the difference. In this paper we managed to obtain a reliable value for the mass ratio, which provides a basis for the further study of the structure and evolution of this binary system. Using the new mass ratio and allowing for the existence of spots, we used the WD method to solve the photoelectric observations of Mancuso et al. and determined the geometrical and physical quantities of the system. The absolute quantities including the radii and masses of the component stars have an accuracy of determination of l-2%, so the results can be regarded as reliable and improved.
l?l
RT And
#
Fig. 4
The Roche configuration of KI’ Aud
Our combined solution shows that RT And is a pair of detached, main sequence stars, in agreement with the conclusion of Ref. 141. The Roche configuration of the two components is shown in Fig. 4. In the lg(M/&) lg(R/&) diagram, we can see that the two components depart slightly from This the zero age main sequence. is also the case on the lg(M/Mo) lg(L/L~) diagram. Both components, then, shows some signs of evolution.
The spectrum we got at phase 0.5 confirms that the spectral type of the main star is F8V. As the combined solution shows, at this phase, the contribution of the companion to the total luminosity is less than 7%, so we can approximately regard the observed spectrum at the time to be that of the main star. As the primary eclipse is partial eclipse, we cannot determine the spectral type of the companion star. But we can do so indirectly from its position on the HR diagram. According to the statistical relation181 between the MK type, T, and L, with Te = 4826 K, the spectral type of the companion could be either K2V or KOIV, corresponding Since we found lg(L/& = -0.268, to lg(Lf&) = -0.417 or 0.890), respectively. it appears that the spectral type is K2V. This is 2 subtypes away from the KOV published by Dumitrescul’51. In the combined solution, in order to reproduce the asymmetry in Mancuso et al.‘s light curve, we used a very crude spot model and only applied only to the surface of the main star through inference. As to what the actual situation is, we have to await more refined spectral analysis or even other techniques. Our theoretical curve does not fit the observations at the secondary eclipse very well and further work is called for. In this paper we did not consider changes in the period, and from the many available light curves we only selected one and did not make a comprehensive study.
Thus,
the present
investigation
remains
a fairly superficial
one.
Acknowledgement All the calculation in this paper was carried out on the Micro VAX II Computer of the Shanghai Observatory. We thank Mr LIANG Hai-qi and others for help with the graphics. LU Wen-xian thanks the DA0 for the telescope time during his visit.
WANG
172
Xiu-mei and LU Wen-xian
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