3 Analysis of the data

3.1 Radial velocity curve

The measurements of the lines of the short-period RS CVn systems are difficult for several reasons. First, the lines arising from each component are rotationally broadened and blended with the surrounding metal lines of itself and the companion star. Second, the profiles are distorted by the presence of emission features. The absorption H$_{\alpha }$ and FeI 6678 lines show double profiles outside the eclipses. Although the FeI 6678 line is significantly weaker than H$_{\alpha }$ its doubling is better pronounced.

Figure 1: An illustration of the fitting procedure.

Figure 2: Radial velocity curves of SV Cam.

Figure 3: H$_{\alpha }$ profiles of SV Cam from Nov. 30.

Figure 4: H$_{\alpha }$ profiles of SV Cam from Dec. 1.

In order to determine the radial velocity of the lines we tried both gaussian and 6th-order polynomial fits. It turned out that the obtained values agree to within 0.045 Å (2 kms^-1) (Fig. 1). The measured values of the radial velocities together with their error are given in Table 1 and shown in Fig. 2 where the values of the FeI line are phase shifted by 0.01 in order to avoid superposing of the errors bars. The radial velocities for the two lines were derived by fitting a sinusoid curve to the data (shown in Fig. 2) and the result of the least square fit is: $K_{\rm 1}=123.1\pm1.2$ kms^-1, $K_{\rm 2}=207.6\pm1.8$ kms^-1and $\gamma=8.1\pm1.9$ kms^-1. It should be noted that our $\gamma$ value may not reflect the genuine systemic velocity since we did not observe the standard stars.

Figure 5: H$_{\alpha }$ profiles of SV Cam from Dec. 1, continued.

Figure 6: H$_{\alpha }$ profiles of SV Cam from Dec. 1, continued.

Figure 7: H$_{\alpha }$ profiles of SV Cam from Dec. 2.

Figure 8: FeI 6678 profiles of SV Cam from Nov. 30.

Figure 9: FeI 6678 profiles of SV Cam from Dec. 1.

Figure 10: FeI 6678 profiles of SV Cam from Dec. 1, continued.

Figure 11: FeI 6678 profiles of SV Cam from Dec. 1, continued.

Figure 12: FeI 6678 profiles of SV Cam from Dec. 2.

 

 

Table 1: Radial velocities of the H$_{\alpha }$ and FeI 6678 lines in kms^-1.

Phase	RV1(H$_{\alpha }$)	$\Delta RV_{1}$(H $_{\alpha})$	RV2(H$_{\alpha }$)	$\Delta RV_{2}$(H $_{\alpha})$	RV1(FeI)	$\Delta RV_{1}$(FeI)	RV2(FeI)	$\Delta RV_{2}$(FeI)
0.105	-60.4	7.60			-69.6	24.78	121.3	11.70
0.130	-74.0	10.60			-73.0	19.13	134.0	15.20
0.153	-90.0	3.42			-96.6	23.04	164.0	28.00
0.177	-94.6	6.09			-105.6	20.86	191.0	28.00
0.200	-96.9	6.66			-114.5	20.86	195.0	25.80
0.225	-99.2	8.53			-116.8	26.95
0.250	-101.5	11.26	205.0	27.50	-119.0	28.69	218.0	50.40
0.270	-106.0	10.66			-123.5	23.04	195.4	21.06
0.295	-103.7	9.13	200.0	25.00	-105.6	19.13	183.0	18.66
0.320	-101.5	7.93	195.0	27.40	-105.6	30.43	173.0	33.60
0.590	81.4	10.93			62.9	26.52	-123.0	30.13
0.613	92.8	8.00			78.6	24.78	-132.5	26.66
0.637	104.2	6.06			96.5	11.73
0.660	111.1	5.80			110.0	22.60
0.668	118.0	4.93	-193.0	22.00	119.0	27.40
0.700	122.5	4.80	-199.7	17.80	128.0	28.20	-195.4	49.06
0.720	145.3	4.92			134.7	20.80
0.740	151.0	6.26			137.0	27.39	-213.9	49.06
0.766	145.3	6.27	-201.0	20.30	130.0	23.40	-213.0	41.86
0.790	140.3	6.26	-197.0	21.65	123.0	23.47	-204.0	45.33
0.814	137.0	5.93	-193.0	24.20	114.0	27.40	-198.0	30.93
0.840					105.0	29.13
0.860					96.5	21.30	-186.0	19.20

Our $K_{\rm 1}$ value is almost the same as that determined by Rainger et al. (1991) (122.3 kms^-1) and that of Hiltner (1953) (123 kms^-1) but it is slightly bigger than that of Hempelmann et al. (1997) (117 kms^-1) and that of Pojmanski (1998) (118.3 kms^-1). Our value of $K_{\rm 2}$ is close to the only value known so far, published by Pojmanski (211.5 kms^-1) and obtained from the analysis of near IR CaII spectral lines.

Assuming the photometrically determined value of $i=80{\hbox{$^\circ$ }}$ (Hilditch et al. 1979; Kjurkchieva et al. 2000a) and using our values for $K_{\rm 1}$ and $K_{\rm 2}$ the resulting values of the mass ratio and masses of the components are $q=0.593\pm0.011$, $M_{\rm 1}=1.47\pm0.06~M_{\odot}$and $M_{\rm 2}=0.87\pm0.06~M_{\odot}$.

On the basis of our radial velocity solution and photometrically obtained fractional radii $r_{\rm 1}=0.35$ and $r_{\rm 2}=0.24$ (Paper I), we determined the absolute star's radii $R_{\rm 1}=1.38\pm0.05~R_{\odot}$and $R_{\rm 2}=0.94\pm0.06~R_{\odot}$. It should be noted that the values of $r_{\rm 1}$ and $r_{\rm 2}$ determined by different authors lie in the ranges 0.32-0.4 and 0.19-0.25 (Budding $\&$ Zeilik 1987; Zeilik et al. 1988; Patkos $\&$ Hempelmann 1994; Djurasevic 1998; Heckert et al. 1998). The radii of the components of SV Cam corresponding to their masses calculated from the mass-radius relation for MS stars are $R_{\rm 1}=1.32~R_{\odot}$and $R_{\rm 2}=0.91~R_{\odot}$ for the primary and secondary, respectively. This means that the masses and the radii of the two components almost obey the mass-radius relation for MS stars in spite of their gravity distortions.

We determined the rotational broadenings of the two profiles of the investigated lines by measurements of the widths at the continuum level of the 6th order polynomial fit (Fig. 1). The mean values of the full width of the broadened profiles are almost the same for the H$_{\alpha }$ and FeI 6678 lines: $\Delta\lambda_{\rm 1}^{\rm rot}=5\pm 0.2$ Å for the primary profiles and $\Delta\lambda_{\rm 2}^{\rm rot}=4\pm 0.3$ Å for the secondary ones. The corresponding equatorial velocities to these rotational broadenings ( $2V_{\rm eq}\sin i=c\Delta\lambda_{\rm rot}/\lambda$) are $V_{\rm eq}^{\rm 1}=116 \pm 9$ kms^-1 and $V_{\rm eq}^{\rm 2}= 79\pm14$ kms^-1. For comparison, assuming synchroneous rotation of the components and the obtained stars' radii the calculated equatorial velocities of the stars ( $V_{\rm eq}=2\pi R/P_{\rm rot}$) are $V_{\rm eq}^{\rm 1}=117.7$ kms^-1 and $V_{\rm eq}^{\rm 2}= 80.7$ kms^-1. Hence, in spite of the fact that the spectral lines are distorted by different effects their widths agree with the expected rotational broadenings.

3.2 Phase behavior of the profiles

The normalized H$_{\alpha }$ and FeI 6678 profiles are shown in Figs. 3-12 together with the corresponding orbital phases. We established the following pecularities in the phase behavior of the H$_{\alpha }$ profile of the primary star:

(1) The profile has a central pseudo-emission bump in the middle of the primary eclipse. We attribute this distortion to the obscuration of the primary star by the cooler secondary that causes masking of a part of the primary's absorption line. The width of the central bump is 3.4 Å and corresponds precisely to the secondary star's radius (see the previous section).

(2) The profile is deeper around the second quadrature than around the first one. The shape of the H$_{\alpha }$ profile is symmetrical at the second quadrature and distorted at the first quadrature.

(3) Some emission feature at the end of the left wing of the profile appears at phase range 0.95-0.98 that repeats on two dates (Figs. 3 and 5). One can also note a similar, weaker emission feature almost half orbital cycle later (in the phase range 0.54-0.56) at the end of the right wing. This feature may be due to the emission from circumstellar matter, perhaps ejected from the component(s) whose contribution is most apparent in the spectra around the eclipses. The presence of circumstellar matter in SV Cam was suspected a long time ago on the basis of its optical light curves (Patkos 1982a,b) and the X-ray data (Hempelmann et al. 1997). Another reason for the emission feature can be the increased contribution of the trailing and leading part of the secondary star chromosphere in the corresponding phase ranges.

(4) The profile has a nearly flat core at phases 0.86, 0.105 and 0.79. The first two phases are almost symmetric relative to the primary eclipse. We found the same behavior in the H$_{\alpha }$ line of the primary star in the short-period RS CVn-type star RT And (Kjurkchieva et al. 2001).

(5) The profile is distorted and filled-in in the phase ranges 0.2-0.34 and 0.84-0.91. The distortions of the profile are variable and seem to be caused by features that moves through the stellar disk during the above phases (see Figs. 4 and 6). They could be attributed, at least partially, to the effects of cool spots. The phases 0.27 and 0.86 of the biggest distortions (flat cores) of the H$_{\alpha }$ profile almost coincide with phases of the maximum spot visibility determined by modeling of the SV Cam light curves (Paper I). It should be stressed out that the strong decrease of the profiles depths at the phase range 0.225-0.295 is difficult to explain only by spots with a reasonable size.

We established the following similarities in the phase behavior of the FeI 6678 and H$_{\alpha }$ profiles of the primary star: (i) the depth of the FeI 6678 line is also greater around the second quadrature than around the first one but the difference between them is smaller for FeI 6678; (ii) there is also an emission feature at the end of the left wing of the profile at the phases 0.95-0.98; (iii) in the middle of the primary eclipse, the FeI 6678 profile also has a central pseudo-emission bump with the same width (about 3.4 Å), but its relative height is somewhat less than in H$_{\alpha }$.

We found additional peculiarities of the FeI 6678 profile of the primary star:

(1) Apparent central emission features are visible at phases 0.25, 0.84 and 0.564. The first two of them almost coincide with the phases of maximum visibility of the two spots on the primary star reproducing the distortion light curve of SV Cam from 1997 (Paper I). We may calculate the angular size $\alpha^{\rm sp}$ of the spots from the equation (Kjurkchieva 1995):

$$\frac{\Delta \lambda^{\rm sp}_{\rm rot}} {\Delta\lambda^{\rm st}_{\rm rot}}=\sin \alpha^{\rm sp}$$ (2)

where $\Delta \lambda^{\rm sp}_{\rm rot}$ and $\Delta\lambda^{\rm st}_{\rm rot}$are the rotational broadenings of the spot spectral feature and the star profile, respectively. From our spectra we measured: $\Delta\lambda^{\rm sp}_{\rm rot}=1.6$ Å, $\Delta\lambda^{\rm st}_{\rm rot}=5$ Å and obtained $\alpha^{\rm sp}=18\hbox{$.\!\!^\circ$ }5$. This value is not far from the angular size of 20 ${\hbox{$^\circ$ }}$ of the spots determined from the modeling of the light curve of SV Cam (Paper I);

(2) A strong increase of the depth of the profile is seen at phase 0.98 that repeats on two dates.

Consequently, the phase behavior of the H$_{\alpha }$ and FeI 6678 profiles show the presence of two cool spots on the primary star of SV Cam. The Doppler image of SV Cam obtained by Hempelmann et al. (1997) also shows a distinct spot on the primary star whose location coincides with the spot found by modeling of the optical light curve.

Our observations out of the eclipses show a weak H$_{\alpha }$absorption profile from the secondary star that is deeper around the second quadrature than around the first one similarly to the behavior of the H$_{\alpha }$ line of the primary star. For comparison, the H$_{\alpha }$ profiles obtained by Hempelmann et al. (1997) revealed no features that could be attributed to the secondary star at the out-of-eclipse phases and they determined the contribution of the secondary star by an analysis of the single H$_{\alpha }$ profile during both eclipses. Our observations of the FeI 6678 line outside the eclipses show also an absorption line from the secondary star. This line is shallower at quadratures than in the phases around them.

The central intensities ( $R_{\rm c}=1-I_{\rm line}/I_{\rm cont}$) of the primary's and secondary's H$_{\alpha }$ profiles change during the orbital cycle in the ranges 0.2-0.38 and 0.02-0.07 while intensities for the FeI 6678 line vary in the ranges 0.015-0.04 and 0.005-0.01.

3.3 Emission from the stellar components

Because we have no observations of standard, non-active stars we cannot apply the widespread method of substraction of comparison spectrum from that of the active star (Strassmeier et al. 1990; Frasca $\&$ Catalano 1994; Pojmanski 1998; Frasca et al. 2000, etc.). However, in order to obtain some information about the emission from the stellar components of SV Cam we analyzed the profiles at the primary eclipse. The line profile in the middle of this eclipse (adopting $\sin i \simeq 1$) is described roughly by the expressions:

$$I(x)=2I_{\rm 1}\int_{R_{\rm 2}}^{R_{\rm 1}}\cos\theta_{\rm 1}... ...d}z +2I_{\rm 2}\int_{0}^{R_{\rm 2}}\cos\theta_{\rm 2}{\rm d}z$$ (3)

for $-R_{\rm 2}<x<R_{\rm 2}$ and

$$I(x)=2I_{\rm 1}\int_{0}^{R_{\rm 1}}\cos\theta_{\rm 1}$$ (4)

for $-R_{\rm 1}<x<-R_{\rm 2}$ and $R_{\rm 2}<x<R_{\rm 1}$ where

$$\cos\theta_{i}=\frac{\sqrt{R_{i}^{2}-x^{2}-z^{2}}}{R_{i}},$$ (5)

$$x=(1-\lambda/\lambda_{\rm0})cR_{i}/V_{\rm eq}^{i} ,$$ (6)

$I_{\rm 1}$ and $I_{\rm 2}$ are the surface intensities (they are positive for emission lines and negative for absorption lines) of the primary and secondary star at the wavelength of the line considered.

The expressions (3) and (4) describe the line profile with two-wave or W-like shape, i.e. a line profile with a central bump. The main parameters of this profile are:

(a) width of the bump $w_{\rm c}=2\lambda_{0}V_{\rm eq}^{2}/c$;

(b) width of the whole profile $w=2\lambda_{0}V_{\rm eq}^{1}/c$;

(c) depth of the center of the bump

$$d_{\rm b}(0)=\frac{\pi I_{2}R_{2}}{2}+ \frac{\pi I_{1}R_{1}}{2}- I_{1}R_{1}(k\omega+{\rm arccos}\, \omega)$$ (7)

where $k=R_{\rm 2}/R_{\rm 1}$ and $\omega=\sqrt{1-k^{2}}$;

(d) depths of the ends of the bump

$$d_{\rm b}(e)=I_{1}R_{1}\omega^{2}\pi/2 .$$ (8)

The depths of the centers of the primary's and secondary's profiles are respectively: 0pt

  

$$d_{\rm 1}(0)=2I_{\rm 1}R_{\rm 1}/\pi ;$$ (9)

$$d_{\rm 2}(0)=2I_{\rm 2}R_{\rm 2}/\pi .$$ (10)

From the above equations one can obtain the following simple relations: 0pt

  

$$\frac{d_{\rm b}(e)}{d_{\rm 1}(0)}=\omega^{2} ;$$ (11)

$$\frac{d_{\rm b}(0)}{d_{\rm 1}(0)}=1+\frac{d_{\rm 2}(0)}{d_{\rm 1}(0)} -\frac{2(\omega \sqrt{k}+{\rm arccos}\,\omega)}{\pi}\cdot$$ (12)

The variability of the lines of the primary star during the cycle rises a question at which phase one should measure the value of $d_{\rm 1}(0)$. Because the H$_{\alpha }$ line has most undistorted and symmetrical profile at the phase 0.67 we decided to measure its depth at this phase. In order to compare parameters of the two investigated lines we measured $d_{\rm 1}(0)$of the FeI 6678 line at the same phase, fitting its distorted profile with a gaussian curve. The measured values of the above parameters for the H$_{\alpha }$and FeI 6678 profiles are presented in Table 2.

 

 

Table 2: Measured parameters of the H$_{\alpha }$ and the FeI 6678 lines.

Line	$d_{\rm 1}$(0)	$d_{\rm 2}$(0)	$d_{\rm b}$(0)	$d_{\rm b}$(e)
H$_{\alpha }$	0.380	0.060	0.120	0.175
FeI 6678	0.085	0.012	0.034	0.048

For the H$_{\alpha }$ profile the measured and calculated values of $d_{\rm b}(0)/d_{\rm 1}(0)$ are respectively 0.316 and 0.38, i.e. the calculated value is about $20\%$ bigger than the observed one. The measured and calculated values of $d_{\rm b}$(e)/ $d_{\rm 1}(0)$ are respectively 0.46 and 0.55, i.e. the calculated value is also about $20\%$ bigger than the observed one. Consequently, the observed bump of the H$_{\alpha }$ profile in the middle of the primary eclipse is higher than one would expect. We attribute this to the H$_{\alpha }$ emission from the secondary star. For the FeI 6678 line, the measured and calculated values of $d_{\rm b}(0)/d_{\rm 1}$(0) are 0.4 and 0.36, respectively. Therefore, the calculated value for this parameter is smaller than the measured one. The measured and calculated values of $d_{\rm b}$(e)/$d_{\rm 1}$(0), 0.55 and 0.56, respectively agree very well. Thus the calculated profile of FeI 6678 in the middle of the primary eclipse is slightly above the observed one. In this way, our spectral observations show an enhanced emission of the secondary star of SV Cam in the H$_{\alpha }$ line but not in the FeI 6678 line. The result of our analysis supports the conclusion of Ozeren et al. (2001) about the H$_{\alpha }$ emission excess from the secondary star of SV Cam obtained by spectral substraction technique as well as the more general conclusion of Frasca $\&$ Catalano (1994) about the H$_{\alpha }$emission in late-type active binaries.