Astron. Astrophys. 345, 137-148 (1999)

8. Discussion and conclusion

8.1. Contact binary

The peculiar observational effects (complications) which have to be taken into account to make a detailed model of the system are as follows:

• The long-term period decrease of the orbital period;

• The secondary minimum in the U light occurring (9622) s later than in the B and V lights;

• The delay of the secondary minima = (5427) s;

• The larger variations of the LC around maximum I than around maximum II. The maximum I in the U light is about 0.01 mag brighter than the maximum II;

• The lowest scatter of observations is around maximum II;

• During the active stages the relative brightness of maxima varies. In some LCs the maximum I is suppressed, so the maximum II becomes brighter;

• Asymmetries of the LC increasing from the V to U light;

• The presence of the third light in the photometric solutions of the UBV LCs, which increases from the V to U light;

• An increase of EWs after the primary minimum and a decrease of EWs around phase 0.9;

• A variable activity of the system;

• A mid-eclipse brightening (or brightness variations) in the secondary minimum.

Most of these observational effects can be explained by the mass transfer from the more massive primary to the less massive secondary component and occasional outflow of matter from the system. Both processes can lead to the observed orbital period decrease. The delay of the secondary minimum (largest in U passband) can be explained by the presence of spot(s) on the surface of the contact binary.

The mass loss occurs through the outer Lagrangian point L₂. The density of the escaping gaseous stream, bent by the action of the Coriolis force, quickly decreases (Shu et al., 1979). The observer sees the approach of the most dense parts of the stream just after the primary minimum, which causes an additional decrease of the RV. The gaseous stream causes the equivalent widths of the lines to increase during its projection on the contact system in phases after the primary minimum. Emission from the same stream decreases the equivalent widths of the lines around the phase 0.9. During the large outflow from the system the maximum I is suppressed by absorption in the escaping gaseous stream, so the maximum II is brighter.

The variable activity can be explained in terms of changes of the fill-out factor. When the surface of AW UMa contact binary approaches the outer critical surface (deep LC), the outflow is violent. An uneven distribution of matter in the flow can account for pronounced variations of the LC most marked between the phases 0-0.5.

Streams of matter escaping from the secondary component were also suggested to explain the intrinsic polarization of AW UMa with its maximum around the orbital phase 0.25 (Oschepkov, 1974). This polarimetry was performed from March to May, 1972, close to the periastron passage of the suggested fourth body (the maximum of activity occurred in 1989-90 and P₄ = 17 years). Tidal effects of the fourth body on contact binary could cause an increase of the fill-out factor and outflow of matter from L₂ in 1972. On the other hand, Piirola (1975) did not find any polarization in the light of AW UMa in March and April, 1974.

The mass transfer from the more to less massive component accompanied by mass outflow from the L₂ point, explains the observed long-term orbital period decrease. It can be shown that both processes get more effective towards the smaller mass ratios.

In the case of conservative mass transfer, the relative period change is:

Observed orbital continuous period decrease of AW UMa can be fully explained by a mass transfer rate = 2.16 10^-8 M y^-1. If two sudden jumps occurred, the mass required to cause them was = 1.04 10^-6 M and = 1.03 10^-6 M, respectively.

If the mass is transferred from the primary to secondary component and afterward lost through L₂ then (Pribulla, 1998):

where is the distance of the L₂ from the mass center (in the units of the semi-major axis). It is possible to show, that for a wide range of mass ratios. To account for an observed period change, the system needs to loose 1.7 times less mass as in the case of the mass transfer (case a). In both formulae, the spin angular momentum of the components was neglected.

Our observations of AW UMa revealed the occasional presence of a mid-eclipse brightening or brightness variability in the secondary minimum. This effect is possibly caused by the matter flowing around the contact system between its surface and the outer critical surface.

The masses of the components of the contact binary (calculated from the mass function = 0.00074 M, inclination angle i = 78.3^o and the photometric mass ratio q = 0.08) are = (1.790.14) M and M₂ = (0.1430.011) M, so the system is located on the ZAMS. The mean radii of the components are = (1.870.05) R and = (0.660.02) R. The distance between the components is a = (3.050.07) R. The luminosities of the components computed by the W&D code (Sect. 4.2) are = (7.270.39) L and = (0.8320.045) L. The distance to the system calculated from our solution, BC = 0.07, E(B-V) = 0 (Mochnacki, 1981) and = 4.64 is d = (75.92.1) pc. This value is somewhat larger than d = (664) pc determined by Hipparcos. This discrepancy is probably caused by the presence of other components in the system, which affects the apparent brightness as well as the position of the contact binary on the celestial sphere (see Kovalevski, 1995). Another possible cause of the discrepancy could be the mass outflow from L₂, which increases the amplitude of the RV of the primary component. Agreement with the Hipparcos can be obtained for = 22.1 km s^-1. The corresponding masses of the components ( = 1.20 M, = 0.096 M) set the system on the TAMS. Further spectroscopic observations in a non-active stage are needed to solve this dilemma.

8.2. Multiplicity of the system

Observational facts relevant for the multiplicity of AW UMa are as follows:

• Changes of the orbital period in the diagram (the long-term continuous decrease of the orbital period removed) with a period of = 6250 days, explained by the light-time effect;

• Changes of the orbital period in the diagram (the broken-line ephemerides (1)-(3) removed) with a period of 403 days, or in the diagram (light-time effect with = 6250 days removed) with a period of 407 days;

• Systemic velocity variations with a period of 398 days.

The best explanation of the observed changes of the period, systemic velocity and activity involves a quadruple-star model of AW UMa.

The spectroscopic orbit of the mass center of the contact binary with the period = 398 days provides the mass function = 0.075 M, which can be used to calculate the mass of the third component as = (0.850.13) M, assuming that the orbits of the third component and contact binary are coplanar. The eccentricity of the third component orbit = 0.227 is rather small, so it is reasonable to assume that the third component evolved together with the contact binary from the same protostellar cloud. The ratio of periods =908 and the almost circular orbit make the triple system highly stable (Kiseleva et al., 1994). The existence of a systemic velocity shifts caused by the third body should be definitely proved by several homogeneous sets of new spectroscopic observations over a 398-day orbital period of the third body.

The possible fourth component revolves around the mass center of the system on a 6250-day-period orbit with eccentricity 0.63. The mass of this component depends on the inclination of its orbit. For inclinations smaller than 30^o, the close encounters of this component with the third one would cause the system to be unstable (the ratio of periods is = 15.7). For inclinations close to 90^o, the fourth component would be too far from the contact binary during the periastron passages to affect its activity. The most probable inclinations of the fourth component orbit are 60^o - 40^o. The corresponding range of its masses is 0.168 - 0.229 M. The orbit of the fourth component, determined from the light-time effect, shows that its last periastron passage occurred in December, 1989. The strongest variations of the LC were recorded in 1989 and 1990 (Derman et al., 1990). In the same time, the surface of the contact binary was close to the outer critical surface (Rucinski, 1992).

Fekel (1992) found in the sample of 3 dozen multiple systems that most of them have orbital periods in the range of 1-20 years. The orbital periods of the third and fourth component of AW UMa are within this range.

If the long period decrease in diagram is interpreted as two sudden period changes 6200 days apart, we have to find an internal mechanism connected with the contact system, which triggers the long-term periodicity of the activity. Nevertheless the quadruple-star model is more elegant than an alternative triple model with an internal activity mechanism.

© European Southern Observatory (ESO) 1999

Online publication: April 12, 1999
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