Apsidal motion and physical parameters in the eclipsing system V490 Sct

We report long-termed UBVRIRcIc photometry of the highly eccentric 12.04 day detached eclipsing binary V490 Sct (V =13.1, B9.5+A0, e = 0.40), which we use to determine its relative and absolute parameters. The absolute masses, radii, and temperatures are Ma = 2.33+/-0.1 Msun, Ra = 1.91+/-0.04 Rsun, and Ta = 9960+/-60 K for the primary and Mb = 2.24+/-0.1 Msun, Rb = 1.86+/-0.04 Rsun, and Tb = 9700+/-80 K for the secondary. The system displays a slow periastron advance that is dominated by general relativity (GR). Our measurement, dw/dt = 0.86 deg/century, is 32% less then the expected rate, dw/dt = 1.24 deg/century, which has an 83% contribution from GR. A comparison with current stellar evolution models shows a good match to the measured properties at an age of about 130 mln. years and Solar abundance. The photometrical parallax of the system pi = 0.77 +/- 0.02 mas, matches quite well the GAIA DR2 value, pi = 0.76 +/- 0.04 mas.


INTRODUCTION
V490 Sct was found to be variable by Dr H. van Gent who has investigated the variability of the stars in a region of 100 square degrees in the constellation of Sagittarius around the central star BD−18 • 5206. Most of the plates (382 pieces) were obtained by him with the help of the Franklin-Adams camera (D=25cm) of the Union Observatory. 8 more plates were received by P. Th. Oosterhoff with the Mount Wilson 10-inch refractor. J. Uiterdijk has investigated all new variables on these plates. He found that the star with serial number 42 in his list was the eclipsing variable. He derived its true period and due to displacement of the secondary minimum estimated its eccentricity as 0.4, Uitterdijk [1]. He noted that the data obtained need confirmation so he published individual observations in minima for further use. These relatively inaccurate photographical estimates obtained by the Neiland-Blazko method have played a role in our study of the apsidal motion due to the fact that they are 80 years away from the epoch of our observations. The star was firstly designated as V1049 Sgr but when GCVS research group realized that it is situated in Scutum constellation 8' west from the Sagittarius border it was renamed to V490 Sct Samus' et al. [2]. Based on Uiterdijk's data, the star was included in the lists of promising for internal structure and relativistic effect investigation objects such as Gimenez and Crawford [3] (named as V1049 Sgr), Kim et al. [4] (named as V490 Sct) and several other catalogues. No further researches followed the work of Uiterdijk although from the very beginning it was clear that due to the significant eccentricity and favorable orientation of the orbital ellipse, the star is a very promising object for the internal structure studying and general relativity (GR) testing.

OBSERVATIONS AND DATA REDUCTION
We included the star in our program of eclipsing eccentrical systems study, Volkov and Volkova [5]. The observations started as far as in 1989 year at Tien-Shan high altitude observatory of SAI. That time we failed to detect minima. We continued occasional observations of the star according the Uiterdijk's ephemeris, but things did not get off the ground until we began systematic observations of the star in 2004 in Crimean observatory of SAI and in Simeiz observatory of INASAN regardless the predictions of the ephemeris. In 2005 we finally found one of the minima and a meaningful accumulation of the observational data has begun. It turned out that the initial ephemeris gave an error of 10 hours for modern epoch. Also we found that the less deep minimum was assumed to be primary by Uiterdijk's ephemeris. Further we give the true formulae for minima timings prediction where the deeper minimum is designated as primary or Min I. Our further analysis showed that a less massive component with a lower temperature is eclipsed at this minimum. This situation is caused by the current orientation of the orbital ellipse, when at a deeper minimum the stars are closer to each other and the eclipsed area of the less brighter star is larger than eclipsed area of the more brighter star in shallower minimum. More massive and brighter component is designated "A" and it is eclipsed in secondary minimum or Min II. Less massive component with less temperature named "B" is eclipsed in primary minimum.
The star was observed at the following observatories (telescope, type of CCD array and photometric system): During minima searching we used every opportunity to obtain observations of the star, and this explains the wide range of tools and observatories used. Most of the observations were made with the 60-cm telescope and VersArray 512UV CCD during 18 nights in the same instrumental system. Comparison stars (TYC 5718-588-1=st1 and 2MASS 18584008-1352174=st2, with V = 12.56 and 12.26, respectively, their colour indices are close to variable) within 3 arcmin in the same field of view as the variable star were used to determine differential magnitudes. Normally the variable star differential magnitudes were referenced to the magnitude of the combined light of both comparison stars (variable minus comparisons) in each image. Sometimes, when observing with a CCD of small linear dimensions and a long-focus telescope, such as 1-m reflector and VersArray 512UV, only TYC 5718-588-1 was used as a comparison star, as it is only 1.3 arcmin from the variable. All the observations were corrected for the instrumental systems differences. The magnitudes were corrected also for nightly variations in the photometric zero point as we have done previously in similar studies (see, e.g.,Volkov et al. [6]). These corrections found in the course of Light Curve (LC) solutions reached ±0.01 mag of the mean.
A total of 4754 measurements in all photometrical bands were obtained over 54 nights between 2004 and 2021. All the original data can be found in a suitable computer form on-line.
We present 24 individual minima timings for V490 Sct, of which all, without exception, were observed or recalculated (two photographic timings) in this study and have never been published elsewhere.

LIGHT CURVE ANALYSIS, COLOUR INDICES, ABSOLUTE DIMENSIONS
We have derived the magnitudes of the variable and nearby stars relatively to equatorial standards 109 1082,  110 340, Moffett and Barnes [7] with 60-cm cassegrain and VersArray1340x1300 CCD in Nauchny and to nearby standard star from SAI catalogue HD171130 Kornilov et al. [8] with 48-cm reflector and W BV R photometer with photomultiplier EMI 9863 at Tien-Shan observatory. The averaged data of all estimates and their errors are presented in Table I. The temperatures of the components can be found as the colour indices of the light loss in minima. The corresponding calculations were performed for the most numerous and accurate BV R observations, see 2. The result is presented in Fig. 1 which demonstrates that a star with a little bit less colour indices (what means with higher temperature) is eclipsed in secondary minimum. Other possibility to get colour indices is to calculate them from relative luminosities, see Table II Table 11 in Straižys [9]. The reddening line crosses the fifth class of luminosity normal sequence in two points -firstly close to A7 spectral class, the father one near B9.5 -A0. Both positions correspond to a different temperatures and masses of the stars. It is necessary to make a right choice between them. Fig. 2 shows that the straight line connecting the position of the components in diagram is parallel to the line of normal colour indices precisely in the B9.5 -A0 area not in A7, where it just perpendicular to it. In other words, only B9.5 -A0 position provides the same interstellar extinction for both components of the eclipsing system. So for subsequent analysis, we used the hypothesis of significant interstellar absorption, which corresponds to the spectral types of B9.5 -A0 for the components. The colour indices calculated this way, 1, were applied to determine the temperatures with the help of Flower [10]  calibrations.
"A"component : (1) Let us compare the obtained value of interstellar reddening with surveys. At the GAIA DR2 distance of 1.3 kpc, the Pan-STARRS 1 3D reddening map Green et al. [11] indicates a reddening of E(B − V ) = 0.27 +0.03/-0.01 mag which is much less than obtained value of E(B − V ) = 0.626. Note that the effect has been already encountered in the study of young eclipsing stars with elliptical orbits such as GG Ori Volkov and Khaliullin [12], V944 Cep Volkov et al. [13], V2544 Cyg Volkov et al. [14], V839 Cep Volkov et al. [15] and V1103 Cas (unpublished). These colour indices correspond to T A = 9960 K and T B = 9560 K according to Flower [10] calibration. In the subsequent analysis the temperature of component "B" had to be increased by 140K. We used most accurate B − V temperature calibration, other measured indices do not contradict the obtained values of temperatures. The LCs of the binary show no proximity effects. Therefore, we used a model of two spherical stars with linear limb-darkening law moving on an elliptic orbit. We simulated the LCs using our program based on the algorithm described in Khaliullina and Khaliullin [17]. The limb-darkening coefficients were fixed according to Wade and Rucinski [18] for the temperatures and gravitational acceleration of the components. The final solution is given in Table II and  Table III.
Assuming a normal distribution for the residuals we    to the ratio of the radii of the components k = r B /r A for values of k between 0.7 and 1.3, see Figure 5. Popper [19] recommend to make a true choice by examination of systematic effects of residuals from various solutions in minima. When we used this recommendation for our observations at the minima, we did not find any systematics, see Figure 6. We point three factors which can explain the failure of the method in the case. 1. V490 Sct has inclination of the orbit near 88 deg, which implies partial eclipses in which the dependence of the LC on the ratio of the radii is not as pronounced as for DI Her, which Popper used for such analysis. 2. Popper, see Fig. 5 in Popper [19], does not consider the photometric zero point in his analysis of DI Her, the underestimation of which can also lead to systematic differences in the residuals. 3. Error in darkening coefficient of the eclipsed component also can produce the same systematic deviations near conjunction. So, in order to determine the correct value of k, we should use additional information. It's natural to assume that the distances to both components of the system should be the same. From our multicolour observations we directly get the temperatures of the components. Then fixing k in considered range we get a set of solutions from which we estimate the distances to each component. The plot in Figure 7 for most precise V -band observations and temperatures T A = 9960 K and T B = 9700 K demonstrates much more pronounced than in Figure 5 minimum at k = 0.9744. Assuming this value we obtain the final geometrical parameters shown in Table II. The flux ratio in V light, J B /J A = 0.9516, corresponds (Popper [20], Table 1) to a difference in B − V of 0.013 mag or 200K in temperature. Close enough to adopted value of 260K.
We estimated the absolute parameters such as semimajor axe, radii and masses by the non-direct method described in details in Khaliullin [21] and Volkov et al. [22].
Let us estimate the precision of the method. The obtained parameters are close to the parameters of other three eccentric systems derived by a similar method from our own U BV observations which we have calibrated by temperature according to Flower [10]. They are V541 Cyg, Volkov and Volkova [23], GG Ori, Volkov and Khaliullin [12] and AS Cam, Khaliullin and Kozyreva [24]. But these systems have well established masses derived from spectral observations, correspondingly: Torres et al. [25], Torres et al. [26], Pavlovski et al. [27]. We solved our LCs of these three systems and obtained their absolute parameters the same way as we did for V490 Sct, see Table IV. We found that the indirect estimations for  9. log L vs log T diagram. All designations are the same as in Fig. 8.

APSIDAL MOTION
We've got precise minima timings from our data by fitting the synthetic LCs to observations obtained during single overnight run by means of the same program as we used for LCs solution. All the geometrical parameters were fixed according to their values from Table II except of the specific epoch. In the case of simultaneous observations in several filters, the minima timings were weighted and mean values were calculated. The minima timings are listed in Table V. Note that no other data exist at the moment for the star. The same way we obtained mean timings for photographic observations assuming B band for them. Their formal weight calculated as 1/ 2 (given in the second column of Table V) appeared to be only 10 −2 of CCD observations weight, but they have sense, as they are 70 years away from the epoch of our observations. Solving the data from Table V by the least squares method separately for the primary and secondary minima we get the following ephemeris: HJD Min I = 2455073.39094(2) + 12.04395915(9) × E, HJD Min II = 2455069.39288(16) + 12.0439480(7) × E.
(3) The plots which illustrate the residuals given in the 5th column of Table V   ference between the periods (3) is evidence of the rotation of the line of apsides. The rate of apsidal motion from the periods difference may be found according to formula (6) from Khaliullin and Khaliullina [30]: ω obs = 0.0086 • (7) yr −1 , U = 41900(3400) years. Errors in eccentricity and periastron longitude, see Table II, are small and have a little effect on the resulting error of the measured value. The error in the received value is ten percent and is caused mainly by errors of the periods. We estimate the predicted rate of periastron advance from classical terms (tidal and rotational distortions) to beω class = 0.00219 • (5) yr −1 , where we have adopted internal structure constants for the two stars of logk 2A = -2.352 and logk 2B = -2.355 from the models by Claret [31] for 130 mln. years age and assuming that the components are synchronized in periastron. The GR contribution (e.g., Levi-Civita [32]; Gimenez [33]) is calculated to beω rel = 0.0103 • (2) yr −1 which is 4.8 times larger than the classical effect. The total expected apsidal motion is thenω theor = 0.0125 • (2) yr −1 . Our measurement is 32% less. We can say with confidence that the observed apsidal rotation is slower than it follows from synchronism conditions. Deceleration is not as pronounced as in the case of DI Her and AS Cam systems, but is quite noticeable. The reason for the apparent discrepancy could be the inclination of axial axes of the system components to the orbital plane, proposed in the work Shakura [34].

CONCLUSIONS
We obtained reliable parameters for the Algol-type binary V490 Sct: colour indices, interstellar reddening, masses, inclination, effective temperatures of the compo-