Understanding the impact of binary mass transfer in the accretor's measurable parameters

Abstract

Binaries and higher order systems can experience mass transfer events between their components. The angular momentum carried by the gained mass can change the observable parameters of the accretor and spin it up to critical rotation. In this work, we aim to explore the spin-up effect of direct accretion through a stream as a possible mechanism for an accretor to gain more than a tenth of its initial mass without acquiring enough momentum to reach critical rotation. We present a novel analytical model to characterize the effects of direct mass transfer on the accretor's measurable parameters as a function of the binary's semi-major axis and eccentricity and the donor's rotation velocity. This model takes a two-body approach to the problem, where a stream is decomposed as many discrete particles that do not interact with each other and are influenced by the accretor's gravitational potential only. Each parcel has an instant orbital solution derived from its initial conditions. The contribution each accreted parcel has to the total spin-up of the accretor is given by its tangential velocity at impact, through conservation of angular momentum. Direct mass transfer proves to be inefficient at spinning up the accretor and thus enables the star to gain a great fraction of its initial mass without reaching critical rotation. We also quantify the fraction of mass that directly impacts the accretor in contrast to the mass that is either lost from the system or creates a disk around a star. Our results show that systems are the most mass-conservative when the orbit is tighter or when the donor's spin is greater. In terms of eccentricity, the conservation of mass shows mixed results depending on the system's other initial properties. However, systems with higher eccentricity are consistently a hundred percent conservative within our parameter space.

Figures (33)

• Figure 1: Diagram of the system. The accreting star's position is fixed to the origin of the reference frame while the donor star, of mass $m_{\text{don}}$, orbits around it. A parcel of mass, located at a distance $r_{\text{L1}}$ from the accretor's center of mass, is let go with an initial velocity $\Vec{v}_i = \Vec{v}_{\text{orb}} + \Vec{v}_{\text{extra}}$.
• Figure 2: Inclination of a parcel's orbit (blue) with respect to the donor's orbit (in the same direction of the gray dashed $L1$ position). Angle $\theta$ in red represents the true anomaly of the starting point of a parcel with respect to the donor's orbit while $\theta_p$ in blue represents the true anomaly of the parcel's starting point with respect of the parcel's orbit.
• Figure 3: Resulting velocity $\Vec{v_i}$ for a parcel in the first half ($\theta < \pi$) and the second half of the donor's orbit ($\theta > \pi$). The accretor is represented as a pink circle to the right while two different positions of the donor are displayed to the top and bottom left of the figure in light blue. A parcel at the surface of the donor is drawn as a small blue circle. Top left: The angle between $\Vec{v}_{\text{orb}}$ and $\Vec{v}_{\text{extra}}$ is always greater than $\pi$. This produces an initial velocity $\Vec{v}_i$ that always points back towards the donor star ($\alpha_i > \alpha_{\text{orb}}$). Bottom left: The angle between $\Vec{v}_{\text{orb}}$ and $\Vec{v}_{\text{extra}}$ is always smaller than $\pi$. This produces an initial velocity $\Vec{v}_i$ that always points away from the donor star ($\alpha_i < \alpha_{\text{orb}}$).
• Figure 4: Impact angle $\alpha_{\text{imp}}$ as a function of the donor rotation rate $v_{\text{extra}}/v_{\text{per}}$ in our model. From left to right, the systems have semi-major axes of 1.30, 1.80 & 2.20 AU. From top to bottom, the systems have mass ratios of 0.50, 1.00 & 1.50. The data from our model is plotted as open black circles, while the best polynomial fit of order 6 is shown as a continuous green line. The coefficients for the fits can be found in the top half of table \ref{['tab:coefficients']}.
• Figure 5: Akin to figure \ref{['fig:model_fit']} but for the three-body simulations. The coefficients for the fits can be found in the bottom half of table \ref{['tab:coefficients']}.