Absolute parameters of the newly-identified contact binary star IS Canis Major

This paper presents the results of the first high-resolution spectroscopic observations of the Southern W UMa type system IS CMa. Spectroscopic observations of the system were made at Mt. John University Observatory using a HERCULES fibre-fed échelle spectrograph in September 2007. The first radial velocities of the component stars of the system were determined by using the spectral disentangling technique. The resulting orbital elements of IS CMa are: $a_1\sin i=0.0041\pm 0.0001$ AU, $a_2\sin i=0.0135\pm 0.0001$ AU, $M_1{\sin }^{3}i=1.48\pm 0.01{\mathrm{M}}_{\odot }$, and $M_2{\sin }^{3}i=0.44\pm 0.01{\mathrm{M}}_{\odot }$. The components were found to be in synchronous rotation taking into account the disentangled ${\mathrm{H}}_{\delta }$ line profiles of both components of the system. The Hipparcos light curve was solved by means of the Wilson–Devinney method supplemented with a Monte Carlo type algorithm. The radial velocity curve solutions including the proximity effects give the mass ratio of the system as 0.297 ± 0.001. The combination of the Hipparcos light and radial velocity curve solutions give the following absolute parameters of the components: $M_1=1.68\pm 0.04{\mathrm{M}}_{\odot }\text{,}{\mathrm{M}}_2=0.50\pm 0.02{\mathrm{M}}_{\odot }\text{,}{R}_1=2.00\pm 0.02{\mathrm{R}}_{\odot }\text{,}{R}_2=1.18\pm 0.03R_{\odot }\text{,}{L}_1=7.65\pm 0.60$ ${\mathrm{L}}_{\odot }$ and $L_2=1.99\pm 0.80{\mathrm{L}}_{\odot }$. The distance to IS CMa was calculated as $87\pm 5$ pc using the distance modulus with corrections for interstellar extinction. The position of the components of IS CMa in the HR diagram are also discussed: the system seems to have an age of 1.6 Gyr.     

An application of the tensor virial theorem to hole + vortex + bulge systems

The tensor virial theorem for subsystems is formulated for three-component systems and further effort is devoted to a special case where the inner subsystems and the central region of the outer one are homogeneous, the last surrounded by an isothermal homeoid. The virial equations are explicitly written under the additional restrictions: (i) similar and similarly placed inner subsystems, and (ii) spherical outer subsystem. An application is made to hole + vortex + bulge systems, in the limit of flattened inner subsystems, which implies three virial equations in three unknowns. Using the Faber-Jackson relation, $R_{\text{e}}\propto {\sigma }_0^2$, the standard $M_{\text{H}}$-${\sigma }_0$ form $(M_{\text{H}}\propto {\sigma }_0^4)$ is deduced from qualitative considerations. The projected bulge velocity dispersion to projected vortex velocity ratio, $\eta =({\sigma }_{\text{B}}{)}_{33}/\{[(v_{\text{V}}{)}_{\mathit{qq}}{]}^2+[({\sigma }_{\text{V}}{)}_{\mathit{qq}}{]}^2{\}}^{1/2}$, as a function of the fractional radius, $y_{\text{BV}}=R_{\text{B}}/R_{\text{V}}$, and the fractional masses, $m_{\text{BH}}=M_{\text{B}}/M_{\text{H}}$ and $m_{\text{BV}}=M_{\text{B}}/M_{\text{V}}$, is studied in the range of interest, $0?m_{\text{VH}}=M_{\text{V}}/M_{\text{H}}?5$ [Escala, A., 2006. ApJ, 648, L13] and $229?m_{\text{BH}}?795$ [Marconi, A., Hunt, L.H., 2003. ApJ 589, L21], consistent with observations. The related curves appear to be similar to Maxwell velocity distributions, which implies a fixed value of $\eta$ below the maximum corresponds to two different configurations: a compact bulge on the left of the maximum, and an extended bulge on the right. All curves lie very close one to the other on the left of the maximum, and parallel one to the other on the right. On the other hand, fixed $m_{\text{BH}}$ or $m_{\text{BV}}$, and $y_{\text{BV}}$, are found to imply more massive bulges passing from bottom to top along a vertical line on the $(\mathsf{O}{y}_{\text{BV}}\eta )$ plane, and vice versa. The model is applied to NGC 4374 and NGC 4486, taking the fractional mass,$m_{\text{BH}}$, and the fractional radius, $y_{\text{BV}}$, as unknowns, and the bulge mass is inferred from the knowledge of the hole mass, and compared with results from different methods. In presence of a massive vortex $(m_{\text{VH}}=5)$, the hole mass has to be reduced by a factor 2–3 with respect to the case of a massless vortex, to get the fit. Finally, the assumptions of homogeneous inner bulge and isotropic stress tensor are discussed.