Preliminary Analysis of Spectra

Preliminary Analysis of Spectra

With full orbital coverage of KU Cyg, one can conduct a preliminary visual analysis of the spectra. As originally noted by Popper (1964), double-lobed H$\alpha$ emission lines are observed at all orbital phases. Figure 3.1 displays a typical profile of this emission line, which indicates the existence of an accretion disk or ring around the primary, as originally suggested by Joy (1942). The violet (V) and red (R) emission lobes are clearly evident in Fig. 3.1.

Figure 3.1: Typical double H$\alpha$ emission observed in KU Cygni. The rest wavelength, $\lambda_0$, of H$\alpha$ is labeled. The V and R emission lobes are clearly evident.

The rest wavelength of H$\alpha$ is indicated, thus revealing the Doppler shift of each emission lobe. For the specified orbital phase in Fig. 3.1, the central H$\alpha$ absorption feature originates from the parts of the disk in the line of sight to the primary's photosphere.

Edward C. Olson (1999) measured the peak wavelengths of the V and R emission lobes in these spectra and kindly provided their corresponding Heliocentric radial velocities for this investigation. The V emission lobes contain information on gaseous regions that approach the observer; therefore, the radial velocity measurements are negative in value. The R lobe radial velocities are positive in value. These velocities were corrected for the systemic (center of mass) velocity of the system, where $\gamma=-13.1$ km/sec. In order to directly compare the radial velocities of each lobe, as a function of orbital phase, the quantities $V_V$ and $V_R$ as defined as follows:

$$V_V = \gamma - V,$$ (3.1)

$$V_R = R - \gamma,$$ (3.2)

where V and R are the radial velocity measurements of the V and R lobes, respectively. Note that the definition of $V_V$ allows for direct comparision to $V_R$. Considering $V_V$ and $V_R$ as departure velocities of each lobe from the center of mass, their values are plotted in Figure 3.2, as a function of orbital phase. For each spectroscopic observation obtained outside of primary (stellar) eclipse, the value of $V_V$ and $V_R$ are listed in the last two columns of Table 3.1. Notice that the departure velocity of the V lobe around phase 0.50 is much greater than the R lobe at this phase. This discrepancy can be attributed to the motion of the mass-transfer stream, which is located in the approaching limb of the disk near phase 0.50. Consequently, half an orbital phase later, near phase 0.0, the mass transfer stream recedes from the observer. Thus, the departure velocity of the R lobe is greater than the departure velocity of the V lobe near this phase.

Figure 3.2: Departure velocities of the V and R emission lobes. These velocities are relative to the center of mass.

Figure 3.3 (A-L) reveals the changes in profile and the variations in the strength of the emission lines around primary eclipse.

Figure 3.3: Variations of emission lobes near primary eclipse. Primary eclipse totality ranges from $0.961\leq\phi\leq0.039$, while disk eclipse effects are apparent from $0.91\leq\phi\leq0.09$.

Prior to primary (stellar) eclipse, the secondary star eclipses the disk surrounding the primary star. The spectra obtained prior to primary eclipse reveal a decrease in the strength of the V emission lobe. The V lobe decreases in intensity as the secondary star eclipses the emitting regions of the disk in motion towards the observer. In Figs. 3.3 (A-F), notice that the R emission lobes are stronger than the V lobes during these ingress phases. After primary (stellar) eclipse egress, the secondary star eclipses the other edge of the accretion disk that is receding from the observer. Therefore, the R lobe decreases in intensity while the V lobe is now largely unocculted. Thus, in Fig. 3.3 (H-L), the strengths of the lobes reverse, so that the V lobe is the stronger of the two.

During primary eclipse totality, as illustrated in Fig. 3.3 (F-I), the approaching and receding outer parts of the disk are both visible to varying degrees, suggesting that the disk radius is somewhat larger than the secondary star. The emission lobes appear much stronger during these phases, but this is an illusion caused by the normalization of the continuum to that of the less luminous secondary. Notice the abundance of weak stellar absorption features at these phases. Strong central absorptions are also noted at phases just outside primary eclipse, as shown in Fig. 3.3 (C-E, J), which is mostly caused by absorptions within the disk, being projected onto the primary (gainer). The cooler secondary (loser) also contributes its own H$\alpha$ absorption feature, further strengthening this spectral feature.

Figure 3.4: Variations of emission lobes near secondary eclipse.

Figure 3.4 (A-I) displays the changing spectra of KU Cygni about secondary eclipse. During these orbital phases, the disk and primary star will eclipse the secondary star. Prior to first contact of stellar eclipse, the accretion disk will occult the secondary star, which produces another H$\alpha$ absorption component. The absorption feature originates along a line of sight through the receding limb of the disk to the photosphere of the secondary star. This absorption column to the photosphere of the secondary can diminish the overall strength of the R emission lobe. This effect is somewhat apparent in Fig. 3.4 (B-D). The opposite effect can occur after mid-secondary eclipse, as shown in Fig. 3.4 (F-I). Here the absorption line originates increasingly through a line of sight through the approaching limb of the disk and reducing the V emission lobe. Increased absorption within the disk tends to produce a larger central absorption near mid-secondary eclipse, which adds to the central absorption arising from the disk material in front of the primary star.

Figure 3.5 (A-F) displays spectra near the quadrature phases of 0.25 and 0.50.

Figure 3.5: Variations of emission lobes near quadrature. Near first quadrature ($\phi=0.25$), notice that the R lobe is slightly stronger than the V lobe. Near second quadrature ($\phi=0.75$), the V lobe is stronger.

During quadrature, the two components of KU Cygni are in the sky plane, and no eclipse effects (stellar or disk) should be observed. Near phase 0.25, the R lobe is slightly stronger than the V lobe. Alternately, near phase 0.75, the V lobe is slightly stronger than the R lobe. The difference again suggests an asymmetry in the emitting regions of the disk. The difference in V and R lobe intensity cannot be attributed to the superpositioning of H$\alpha$ absorption from the secondary star. At phase 0.25, the secondary component is receding from the observer, thus redshifting any H$\alpha$ absorption line originating in its photosphere. If the emitting regions around the primary star were symmetrical, then the extra absorption from the secondary star would decrease the overall intensity of the R lobe during phase 0.25. This is not the case, as demonstrated with Fig. 3.5, where the R emission lobe is slightly stronger around phase 0.25.

Olson (1988) described the light curve of KU Cygni existing in both high and low brightness states, which could be attributed to variable mass-transfer rates. The spectroscopic observations of KU Cyg spanned four years through multiple orbital cycles. Figures 3.6 and 3.7 display spectra from different epochs at nearly the same orbital phases well outside of primary (stellar) eclipse. Comparison between epochs show small variations in the strength of the emission lobes. Figures 3.6B and 3.7C display the most striking differences in emission-line strength. Thus, the disk is not only asymmetrical, but variable with time.

Figure 3.6: Differences in emission line strength during different epochs.

Figure 3.7: Differences in emission line strength.

The radial extent of the accretion disk can be calculated by estimating the phases when the V and R lobes are eclipsed by the secondary star prior to and after primary (stellar) eclipse (Albright & Richards 1996). Prior to primary eclipse ingress, the secondary star will eclipse the approaching side of the disk, which is also named the leading side of the disk. The overall intensity of the V lobe will decrease because emitting regions on the approaching side of the disk are eclipsed. Similarly, after primary eclipse egress, the receding edge of the disk, also named the trailing side of the disk, will be occulted, which decreases the overall intensity of the R lobe. Near primary eclipse, the mass-transfer stream is located in the trailing side of the disk.

The ingress and egress phases of outermost disk occultations by the secondary star occur near phases 0.91 and 0.09, respectively. These phases were estimated by noting a decrease in the intensity of the V or R lobes before and after primary (stellar) eclipse, respectively. Figure 3.8 displays the ratio, V/R, of the emission intensities versus orbital phase.

Figure 3.8: Relative ratio of emission lobe intensity versus orbital phase. The two horizontal lines demarcate primary stellar eclipse phases. After primary eclipse near phase 0.09, notice that the relative intensity between V and R decrease to near unity, indicating the end of disk occultation by the secondary star.

The phases of primary stellar eclipse are marked by vertical lines. In this figure, the ratio of V/R decreases substantially after primary eclipse as the trailing side of the disk comes out of eclipse. Near phase 0.09 (egress), when the disk is no longer occulted, the intensity ratio of V/R decreases to approximately unity. The egress phase of disk eclipse is more apparent in Fig. 3.8 than for the ingress phase. Notice that prior to primary (stellar) eclipse, there is no clear beginning to the disk eclipse, as would be demonstrated by near equal intensity of the lobes. The phases after second quadrature ($\phi=-0.25$) leading up to primary eclipse are complicated by variations in the mass-transfer stream.

Assuming that the ingress and egress phases of the disk eclipse are correctly estimated, one would expect to observe enhanced H$\alpha$ absorption at phases that are incremented 0.50 from ingress and egress phases. Between phases 0.41 and 0.59, the strength of the H$\alpha$ absorption line should increase in strength because a line of sight passes through the disk to the photosphere of the secondary star. Referring to Fig. 3.4, the H$\alpha$ absorption does increase in strength from phase 0.41, through secondary (stellar) eclipse, and end near phase 0.59. Therefore, the estimated ingress and egress phases of disk eclipse are well estimated.

The radius of the accretion disk, $r_{disk}$, around the primary (gainer), in fractional units of orbital separation, can be calculated as follows:

$$\left[r_s+(r_p+r_{disk})\right]^2 = \sin^2\phi + \cos^2\phi \cos^2 i,$$ (3.3)

where $r_p$ and $r_s$ are the fractional radii of the primary and secondary stars, respectively, $\phi$ is the observed phase at the beginning of the eclipse, and i is the orbital inclination. The above equation assumes that the two stellar components are spherical in shape and in circular orbit around the center of mass. In solving for $r_{disk}$ in Eqn. 3.3, values of $r_s=0.211$, $r_p=0.0434$, $A=78.1$ $R_{\odot }$, i=86.5$^o$ (Olson et al. 1995), and $\phi=0.09$ are assumed, which determine a circular, disk radius of $r_{disk}\approx0.284$, or $R_{disk}\approx22$ $R_{\odot }$. (Note that the critical Roche lobe of the primary star is located 45 $R_{\odot }$ from its center).