6. Kinematic model of the expanding envelope
6.1. Winds from the hot component
During the outburst of nova a mass shell is ejected as a consequence of a thermonuclear runaway on the white dwarf. After the ejection of the shell the mass loss continues in the form of the wind. Several mechanisms provide the energy for the wind. The most important one is the radiation pressure caused by the hot white dwarf.
The wind can be detected spectroscopically as the broad absorption in P Cygni profiles of UV and optical spectral lines. The line profiles of the Mg II lines in early UV spectra (Fig. 2 of the paper of Shore et al. (1993)) indicate the presence of a wind consisting of spherical and polar components. Very broad absorption centered at about 2400 km s-1 is caused by the spherical wind (A). The polar wind (B) forms the small absorption at about 4000 km s-1. As it is possible to see from Table 6 and Fig. 13, the RV of the wind absorptions seen in the UV region corresponds to the RV of double absorptions in the Orion spectrum seen in the visual region after day 48 (Chochol et al. 1993). The Orion absorptions are caused by the spherical and polar winds.
Table 6. Radial velocities of the spherical (A) and polar (B) wind absorptions
6.2. Outer envelope
The visual spectra of Nova V 1974 Cyg taken soon after maximum light showed the lines of superposed P -Cygni type profiles. Two violet-shifted absorption components with a central emission were visible (Chochol et al. 1993). Each can be considered to be produced in a different region of the outer envelope approaching the observer. Regions not approaching the observer contributed to the emission part of the profile. The increasing wavelength shift of double absorptions with time suggests that the outer expanding envelope was accelerated by the wind. Radial velocities of double absorptions are given in Table 7 and in Fig. 13. As we will show later, in the case of an expanding inner envelope both the approaching and receding RV sets were available, so the data could be used also for the determination of the gamma velocity of the system (see the footnote under the Table 8). Our data represent the radial velocities of the approaching parts of the outer envelope only, so a correction for gamma velocity was necessary. As it is possible to see from Table 6 and Table 7 the ratio of absorptions caused by the components of the wind is the same as in the case of the components of the outer envelope. We can conclude that shaping of the outer envelope was caused by the components of the wind, so it is natural that the outer envelope consisted of the spherical (A) and polar (B) components, too.
Table 7. Radial velocities of double absorptions in P Cyg profiles caused by the spherical (A) and polar (B) component of the outer envelope
Table 8. Radial velocities of the peaks of nebular emission lines
The optical spectra taken in early days after outburst (diffuse enhanced spectrum) reflected the expansion of the outer envelope detected as the radio envelope later on. The first two radio images, where the radio envelope was well developed were taken by Eyres et al. (1996) at 6cm by MERLIN on days 154 and 172. The envelope was elliptical indicating a roughly North-South elongation. The angular extent of emission in mas for given brightness temperature in two perpendicular elongations was as follows: day 154: 7500 K (200,160), 10000 K (180,140), 15000 K (150,110), 20000 K (110,80), 30000 K (50,50), day 172: 7500 K (260,190), 10000 K (240,170), 15000 K (210,150), 20000K (190,130), 30000K (160,90), 45000K (100,70). The mean ratio of the major to minor axis (i.e. the ratio of the angular extent of projected polar components to the diameter of the sphere) is = 1.37 0.05. This ratio is the same as the ratio of the major to minor axis of the maximum dimensions of the nova envelope on day 172, which allows to calculate the daily rates of expansion in semi-major and semi-minor axis as 0.7558 mas and 0.5523 mas, respectively. Using the ratio of this rates, which is equal to the ratio of tangential velocities and using the ratio of radial velocities of the same components from Table 7, we calculate the inclination angle of the polar outflow with respect to the observer from relation (12) as i = 39 2 1 5.
6.3. Inner main envelope - crude model of expansion
It is well known that the principal spectrum, which appears at visual maximum, reflects the expansion velocity of the main envelope of the nova visible later on as emission lines of nebular spectrum (McLaughlin, 1960; Gallagher and Anderson, 1976). The expansion velocity of the main envelope of Nova V 1974 Cyg, as derived by Andrillat and Houziaux (1993) from principal spectrum, was 800 km s-1. In Fig. 14 we present expansion velocities of the main envelope of the nova measured by us from emission lines taken in nebular stage using the optical spectra (Chochol et al., 1993), the IUE spectra (this paper) and the HST GHRS spectra published by Shore et al. (1993). We measured the full width at half maximum of the emission lines, which is a suitable measure of twice the expansion velocity of the shell (Cohen and Rosenthal, 1983). As it is clearly seen from Fig. 14 the upper limit of expansion velocity of Nova V 1974 Cyg is 1100 km s-1, which is in large disagreement with the value v = 1500 km s-1 used by Paresce (1994) for the distance determination. By inspecting Fig. 15, which shows the dependence of the true expansion velocity on t3 time for many well-observed novae, one may easily infer that Paresce's value is out of the range observed in almost all novae. The data for Fig. 15 were extracted from Slavin et al. (1995). The empirical v - t3 relation, which we have found from the nebular spectra of 13 novae:
is close to the empirical relation found by McLaughlin (1960) from the principal spectra of well observed novae:
The small difference between (10) and (11) can be easily understood as a result of non-uniform motion of the envelope caused by the different physical processes. The main important conclusion found from this crude approach is that any expanding component of the main envelope must have a true velocity in the interval between 800 and 1100 km s-1. These values are lower and upper limit of the expansion of the inner envelope, which through measured angular radius give the important restrictions on the distance of the nova. If we suppose uniform expansion with angular rate of 0.293 mas/day and velocities mentioned above, the range of possible distances of Nova V 1974 Cyg is between 1577 and 2168 pc.
6.4. Inner main envelope - detailed model of expansion
As we have shown in chapters 3 and 4, the basic components of the main inner envelope are an equatorial ring and two polar blobs. Radial velocities of emission peaks in the nebular stage of Nova V 1974 Cyg which correspond to the expanding equatorial ring and polar blobs are given in Table 8. Mean radial velocities calculated from receding and approaching components are depicted in Fig. 16.
We can use these data for the calculation of the inclination angle. The basic problem is that the HST data for determination of the expansion rates of the ring and blobs were taken between days 689 and 818, while suitable RV data were obtained between days 79 and 218. Moreover, the ring advances and the inclination angle of the ring changes. If we suppose that the blobs are perpendicular to the ring plane we can use the formulae (4) - (6) valid for axially symmetric case. The ratio of / is equal to ratio of expansion rates for the blobs and the ring given in Fig. 7. The mean ratio of radial velocities of ring and blobs is given in Table 8. The calculated inclination angle of ring and blobs is i = 35 1. This value is in small disagreement both with the mean value of inclination angle of the ring during days 79 and 218 i' = 30 9 1 1 found from Fig. 9 and with the inclination angle of the polar outflow i = 39 2 found from the outer envelope. If the inclination angles of the ring i' and the polar axis i differ, we have to use the relation (9) valid for the non-axially symmetric case. If we suppose that i' = 30 9 then i = 38 2 1 1 in good agreement with the value of i found from the outer envelope.
6.5. True expansion velocities and history of the expanding shell
The knowledge of the inclination angle i is pivotal for the
determination of the true expansion velocities of various parts of
both envelopes and the wind at any time after outburst. The unweighted
mean of both determinations found from the outer and inner envelope
True expansion velocities of the polar wind and polar outflow of the outer envelope calculated using this value are shown in Fig. 17. True velocities of the spherical wind and the spherical outer envelope are equal to radial velocities of these structures. Terminal velocities of the polar and spherical components of the wind are higher for about 600 km s-1 and 1500 km s-1, respectively. A spherical wind increased the velocity from 2200 km s-1 on day 5 to about 3000 km s-1 on day 50. A polar wind increased the velocity from 5000 km s-1 to 6000 km s-1 in the same time. The spherical component of the outer low-mass envelope started expansion with an initial velocity of 800 km s-1 and through an acceleration by the hot stellar wind reached a velocity of 1700 km s-1 on day 45. The polar component of the outer envelope increased the expansion velocity from 1700 km s-1 to 3650 km s-1 in the same time.
The inner envelope is more complicated than the outer one. It consists of a dense equatorial ring immersed in the spherical lower density envelope, and polar blobs. The polar axis of the blobs is not perpendicular to the equatorial ring plane. Moreover, there are indications that the polar axis and equatorial ring plane change the position in space with time.
True expansion velocities of the ring and blobs of the inner envelope are shown in Fig. 18. For the calculation of the true velocities of the ring at any time after the outburst we had to incorporate the observed increase of i'. The true expansion velocity of the ring was calculated for every value of RV using the relation (7) and the corresponding value of i' given by relation in Fig. 9. The decrease of with time after day 318 suggests either a true decrease due to interaction with surrounding circumstellar matter and/or an apparent decrease caused by the change of the inclination angle of the blob with time. As it is possible to see from Fig. 10, the blob is double. The first one expands in the initial direction, the second one is located in the centre of the magnetic fountain. Duplicity of the blob is visible also as a double emission peak, formed by the components of the blob in line profile of [Fe VII] in Fig. 9 of the work of Austin et al. (1996) on day 479.9. Unfortunately we have no data for evaluation of the time dependence of the change of the inclination of the blob. We just know that the mean value of i between day 80 and 218 is 38 7 and that i = 51 0 on day 818, but the error of this value is very uncertain. Due to the lack of data we did not incorporate a possible change of the inclination angle of the blob into the calculation of the true expansion velocities, but we used i = 38 7 for all data.
The inner part of the expanding envelope was ejected with an initial velocity of about 800 km s-1 (expansion found from principal spectrum) and accelerated by the stellar wind to 900 km s-1 (ring) and 1100 km s-1 (blob) around day 200 (Fig. 18). The reasons, why the true velocities of the ring and blob decreased about 200 km s-1 and 100 km s-1 after day 318 are discussed in Chapter 7.
The data in Fig. 17 and Fig. 18 can be used to calculate the accelerations of the expanding envelopes, caused by the wind. The maximum accelerations in the first days of expansion calculated for the polar and spherical outflow of the outer envelope are 1.4 m s-2 and 0.47 m s-2, respectively. The maximum accelerations of the blobs and ring of the inner envelope are 0.012 m s-2 and 4.5 10 , respectively. Due to the fact that the driving force for acceleration of both envelopes is the same (hot wind), it is clear that the mass of the inner envelope is considerably larger than that of the fast outer envelope. However, the quantitative analysis is highly model-dependent and is beyond the scope of the present paper. The acceleration of the inner envelope of Nova V 1974 Cyg is in agreement with accelerations as found in novae of different speed classes (HR Del, FH Ser, LV Vul) - see Grygar (1981).
6.6. Distance of the nova determined from our kinematic model
Radii of the edges of expanding structures calculated by integrating of parabolic fits through their true velocities are shown in Fig. 19. These data together with expansion rates found from radio and HST images for outer and inner envelope were used for calculation of the distance of the nova.
Table 9. Expansion rates and corresponding distances of the outer envelope (day 172) and the inner envelope (day 480) of Nova V 1974 Cyg.
Bjorkman et al. (1994) showed that the initial mass ejection in Nova V 1974 Cyg was asymmetric and that the degree of asymmetry decreased and then increased in an approximately orthogonal plane during the nebular stage. This result was confirmed by Hjellming (1995), who found from the early radio observations of Nova V 1974 Cyg an outer shell that was expanding in a direction perpendicular to the major axis of the shell observed by HST. Only at later stages the inner shell appeared with the same orientation as the HST image. Explanation of this puzzle is a by-product of our calculation presented above. On day 172 the projection of the edge of the polar outflow of the outer envelope onto the plane perpendicular to the line of sight was still larger than the radius of the sphere. On day 480 the projection of the blob of the inner envelope onto this plane was smaller than the edge of the ring. The larger difference in outflow velocities for components of the outer envelope in comparison with the inner one as well as the inclination of the polar ejecta with respect to the observer can easily explain why the initial mass ejection was asymmetric in one direction, while later on we have observed an expansion in approximately perpendicular direction.
© European Southern Observatory (ESO) 1997
Online publication: July 3, 1998