4 Radial velocity variations

 

 

Table 3: Heliocentric radial velocities (km s^-1) of V784 Cas (MJD = Hel. JD-2 400 000).

MJD	$v_{\rm rad}$	MJD	$v_{\rm rad}$	MJD	$v_{\rm rad}$	MJD	$v_{\rm rad}$	MJD	$v_{\rm rad}$
51480.6788	-6.69	51480.8135	-6.15	52191.7601	-3.38	52200.7600	-7.05	52200.8462	-8.45
51480.6878	-7.92	51480.8192	-5.40	52191.7730	-7.78	52200.7648	-8.22	52200.8499	-8.86
51480.6922	-7.35	51480.8236	-7.45	52191.8006	-10.85	52200.7685	-6.64	52200.8536	-11.27
51480.6966	-11.31	51480.8280	-8.64	52191.8063	-9.38	52200.7722	-5.25	52200.8573	-10.41
51480.7010	-11.88	51480.8324	-6.56	52191.8124	-5.72	52200.7784	-4.96	52200.8611	-9.06
51480.7074	-10.93	51480.8368	-6.05	52191.8188	-6.02	52200.7822	-3.61	52200.8648	-7.36
51480.7118	-10.06	51480.8433	-7.49	52191.8261	-3.51	52200.7864	-2.90	52200.8800	-2.52
51480.7162	-8.20	51480.8477	-4.56	52191.8326	-1.84	52200.7903	-2.78	52200.8838	0.35
51480.7206	-8.70	51480.8521	-4.20	52191.8395	-1.95	52200.7960	-1.31	52200.8875	-0.16
51480.7250	-7.86	51480.8565	-1.88	52200.7150	-0.58	52200.7998	-2.79	52200.8912	1.69
51480.7313	-6.34	51480.8609	-1.79	52200.7187	-2.37	52200.8035	-1.24	52200.8949	1.65
51480.7357	-6.09	51480.8667	-2.64	52200.7225	0.60	52200.8081	-1.39	52200.8987	2.71
51480.7401	-5.42	51480.8711	-1.91	52200.7262	-4.11	52200.8118	-1.17	52200.9040	1.58
51480.7445	-5.96	51480.8755	-2.30	52200.7302	-4.89	52200.8155	0.54	52200.9077	-0.69
51480.7489	-5.53	51480.8799	-2.82	52200.7339	-7.64	52200.8217	1.57	52200.9114	0.56
51480.7730	-7.70	51480.8843	-6.00	52200.7389	-6.76	52200.8254	-1.26	52200.9152	-0.41
51480.7949	-6.51	52191.7410	-3.66	52200.7413	-8.93	52200.8291	0.19	52200.9189	-0.41
51480.8002	-5.07	52191.7463	-3.09	52200.7465	-7.10	52200.8329	-1.22	52200.9226	-3.73
51480.8046	-5.14	52191.7510	-3.26	52200.7526	-8.66	52200.8366	-3.93
51480.8091	-5.65	52191.7556	-3.20	52200.7563	-6.86	52200.8403	-5.69

Radial velocity variation of V784 Cas was determined by measuring Doppler-shifts of the H$\alpha$ line. This is not an ideal choice because the line forming region of the H$\alpha$line extends to a much wider region than the photosphere, e.g. it may have strong chromospheric component in the line core (Lèbre & De Medeiros 1997 and references therein). However, the observed spectral region does not contain other strong lines, the detected metallic lines are too weak for radial velocity determination. And, as it will be shown below, they are substantially asymmetric suggesting the presence of non-radial oscillation.

Since the H$\alpha$ line is symmetric due to its saturation, the radial velocities were determined by fitting a parabola to the lowest points of the line profile. The barycentric corrections were calculated with the IRAF task rvcorr. The observed velocities are presented in Table 3. Their estimated accuracy is about $\pm$1 km s^-1, which is based on our earlier experiences when using the same equipment for studying other bright variables observed at similar S/N ratios (Kiss et al. 1999a,b). As an independent check, we have also determined line bisector velocities at various levels (see Kiss & Vinkó 2000 for an application of this technique in Cepheid variables). The mean difference of the resulting data is $\approx$0.5 km s^-1with a standard deviation of 1.0 km s^-1 (even the most deviant points did not differ more than 2 km s^-1 from the line-core velocities).

Figure 7: Comparison of the radial velocity curves (dots) with the extrapolated light curve fits (solid line). Note the reversed scale of the magnitude axes.

The light and radial velocity variations have been compared using the light curve fit consisting of four frequencies. The comparison is shown in Fig. 7. It is intended to illustrate the overall characteristics of the correlation between the light and radial velocity variations and the ability of the four-frequency fit to predict light variation both as interpolation (JD 2 451 480) and extrapolation (JD 2 452 191 and 2 452 200). We have estimated the value of $2K/\Delta V$ by taking the full amplitudes of the radial velocity curves and the calculated light curves. The result is 130 $\pm$ 30 km s^-1 mag^-1, being somewhat larger then the mean value of 93 km s^-1 mag^-1 found by Breger (1979). This ratio depends on the non-adiabatic behaviour of the modes and it is different depending on n and l values. That is why we do not find exact fit with the photometric solution. A much longer spectroscopic data series is required to draw firm conclusions on the non-radial nature of oscillation.

By a close visual inspection of the individual spectra, we found the metallic lines to show significant and highly variable asymmetries (see Fig. 8). The most straightforward explanation is the line profile distorsion caused by non-radial pulsation. Line profile variations among the multiply periodic $\delta$ Scuti stars are found frequently and their analysis is a common method of mode identification (see, e.g., Schrijvers et al. 1997; Telting & Schrijvers 1997 for theory and Mantegazza et al. 2000 for a recent application). Unfortunately, neither the resolution, nor the relatively high noise level allow us to use such spectroscopic methods, but the brightness of V784 Cas makes the star a good target object for further spectroscopic investigations.

As can be seen in Fig. 8, the spectral lines of V784 Cas are significantly broader than those of HD 187691 (for which SIMBAD lists $v\sin i=3$ km s^-1). Following the work of Solano & Fernley (1997), we have estimated the rotational velocity of the star from the blend-free line Fe I 6677.997 Å. The resulting $v\sin i=55\pm10$ km s^-1 is in agreement with the published value 66 $\pm$ 10 km s^-1 of De Medeiros & Mayor (1999). The most important point is that rapid rotation affecting the photometric parameters (Pérez Hernández et al. 1999) can be excluded.

Finally, we have to discuss the possible binarity, which may also produce asymmetric line profiles when the partially resolved components are of similar brightness. In our case the radial velocity measurements in the literature show quite high scatter that may be associated with long-term orbital motion in an unresolved binary system. We have searched the SIMBAD database for published radial velocities and found the following data: i) Evans (1967) lists $v_{\rm rad}=+15$ km s^-1; ii) the catalog of Fehrenbach et al. (1996) gives $v_{\rm rad}=+20$ km s^-1; iii) the latter value has been adapted in Duflot et al. (1995); iv) the first high-precision data were published by De Medeiros & Mayor (1999) giving $v_{\rm rad}=-6.09$ km s^-1 (and it was used in Lèbre & De Medeiros 1997). Our mean value is $\langle v_{\rm rad} \rangle =-6.3$ km s^-1 supporting the latest available data, which were taken in the early 90's. Although we do not know the uncertainty of the early data, the $\approx$25 km s^-1 difference found seems to be too high to just ignore it. Therefore, subsequent spectroscopy is highly desirable, either the mode identification, or the possible binarity is concerned. We note, that in light of the results presented in the next section, we favour the non-radial pulsation and associate the large velocity difference to the effects of metallic line profile distorsions. Furthermore, the lack of any variable asymmetry in the H$\alpha$ profile makes unlikely the presence of a secondary of similar brightness as the primary one producing strong metallic lines and having practically no contribution to the H$\alpha$ line. We did not find any change in the systematic velocity between 1999 and 2001, that is why we consider non-radial pulsation to be more likely cause of these asymmetries instead of a peculiar companion.