Trailed Spectrogram of KU Cygni

Trailed Spectrogram of KU Cygni

The H$\alpha$ emission-line profiles in these spectra display the combined flux of emission regions at various radial velocities within the accretion disk around the primary star. If emission is observed at the rest wavelength of H$\alpha$, then the observed radial velocity of the source is zero, indicating zero net velocity in the line of sight to the observer. Recall that the accretion regions orbit around the primary star, which in turn orbits around the center of mass of the system. These two motions contribute to the observed radial velocity of each spectral feature.

A trailed spectrogram can be created for KU Cygni to distinguish any pattern in the spectral features for this system. A trailed spectrogram stacks spectra according to orbital phase, thus creating a 2-dimensional image of the spectra with orbital phase taking the appearance of the spatial (vertical) position. Figure 3.9 displays a trailed spectrogram of KU Cygni. (Note that the lighter grayscale regions in the trailed spectrogram represent the relative flux variations of the H$\alpha$ emission lobes).

Figure 3.9: Trailed spectrogram of H$\alpha$ emission lines for KU Cygni. (NOTE: The lighter shaded regions represent the sinusoidal flux variation of the H$\alpha$ emission lobes).

The flux of each H$\alpha$ emission lobe traces a sinusoidal shape in this trailed spectrogram, called the S-wave. The double S-wave of the emission lines in KU Cyg are very broad when compared to S-waves observed in cataclysmic variable (CV) systems. In CV systems, narrow S-waves correspond to emission from the ``hot spot'' where the mass stream impacts the edge of an accretion disk (Kaitchuck, Honeycutt & Schlegel 1985). In the Algol-type binary, KU Cygni, the double S-wave corresponds to the approaching and receding disk emission regions around the primary star. Any parcel of gas, that emits radiation, is described by its velocity component ($V_x$,$V_y$) in the rotating frame of the system. In this reference frame, the observed radial velocity of that emission source, in a steady flow around the primary, is related to its velocity components, $V_x$, $V_y$, and orbital phase, $\phi$, by the following equation:

$$V_{rad}(\phi) = -V_x cos(2\pi\phi) + V_y sin(2\pi\phi)$$ (3.4)

The velocity components of gas parcels in the disk correspond to radial velocity positions in the trailed spectrogram at a given orbital phase. Table 3.2 lists the orbital phases and image numbers used to create the trailed spectrogram. The spectrogram displays spectra at orbital phase intervals of 0.033, while the resolution of the spectrograph configuration sets the wavelength dispersion of 0.4 Å/pixel. (Note that uniform phase coverage was not obtained during spectroscopic observations of KU Cyg. Therefore, the spectrum that was observed nearest a specified orbital phase bin was chosen to create the spectrogram).

Spectra Used in Creation of Trailed Spectrogram

Table 3.2:

Orbital	Observed	Cycle	Image
Phase Bin	Orbital Phase	Number	Number
0.000	0.008	379	6242
0.033	0.033	379	6282
0.066	0.066	379	6376
0.100	0.108	400	10264
0.133	0.137	379	6472
0.166	0.166	379	6528
0.200	0.197	399	10076
0.233	0.225	399	10096
0.266	0.275	399	10156
0.300	0.290	359	1061
0.333	0.396	361	2139
0.366	0.398	368	3327
0.400	0.412	369	3642
0.433	0.427	379	6661
0.466	0.463	369	3714
0.500	0.501	368	3418
0.533	0.541	369	3876
0.566	0.541	369	3876
0.600	0.676	400	10292
0.633	0.676	400	10292
0.666	0.676	400	10292
0.700	0.702	400	10312
0.733	0.730	400	10336
0.766	0.753	400	10368
0.800	0.805	400	10428
0.833	0.831	400	10448
0.866	0.857	400	10496
0.900	0.905	378	6005
0.933	0.936	378	6075
0.966	0.962	378	6141