Formation of Be stars via wind accretion: Case study on Black hole + Be star binaries

TL;DR

This work introduces wind Roche Lobe Overflow (WRLOF) as a formation channel for BHBe binaries, leveraging MESA binary evolution with WRLOF wind accretion and rapid population synthesis. The authors show WRLOF can efficiently spin up Be stars in wide, eccentric binaries and predict a Milky Way BHBe population of about 1.8–3.2×10^3 systems, dominated by very long-period orbits ($P_{ m orb} \gtrsim 10^3$ days, peak near $10^4$ days). The study contrasts WRLOF with the classical Roche-lobe overflow channel, finding WRLOF yields an order of magnitude more BHBe systems and allows Be stars with lower masses. Observationally, these wide, eccentric BHBe binaries are challenging to detect via X-ray emission but are promising targets for Gaia-like astrometric and interferometric surveys, offering a path to test wind-accretion physics in massive binaries. Uncertainties in wind prescriptions and BH natal kicks remain, particularly affecting the BH mass distribution and the exact Be-star population, but the WRLOF scenario provides a testable framework for understanding Be-star spin-up in binary contexts.

Abstract

Be stars are rapidly rotating main-sequence (MS) stars that play a crucial role in understanding stellar evolution and binary interactions. In this letter, we propose a new formation scenario for black hole (BH) + Be star binaries (hereafter BHBe binaries), where the Be star is produced through the Wind Roche Lobe Overflow (WRLOF) mechanism. Our analysis is based on numerical simulations of the WRLOF process in massive binaries, building upon recent theoretical work. We demonstrate that the WRLOF model can efficiently form BHBe binaries under reasonable assumptions on stellar wind velocities. Using rapid binary population synthesis, we estimate the population of such systems in the Milky Way, predicting approximately $\sim$ {1800-3200} currently existing BHBe binaries originating from the WRLOF channel. These systems are characterized by high eccentricities and exceptionally wide orbits, with typical orbital periods exceeding 1000 days and a peak distribution around $\sim$10000 days. Due to their long orbital separations, these BHBe binaries are promising targets for future detection via astrometric {and interferometric} observations.

Figures (7)

• Figure 1: The terminal wind speeds for stars in the fiducial model ($f_{\rm w} = 1$). The initial star masses are from 20 to $150\,M_\odot$ with a step of $5\,M_\odot$ from bottom to the top. The stellar winds according to the effective temperature of the star are divided into three regions: hot wind $T_{\rm eff}>30000\,\rm K$, warm wind ($6000<T_{\rm eff}<30000\,\rm K$) and cool wind ($T_{\rm eff}<6000\,\rm K$). The color bar indicates the specific values of terminal wind speeds, with the displayed range limited to velocities below $300 \,\rm km/s$. The dashed line is the so-called Humphreys-Davidson limit Humphreys1979.
• Figure 2: Two evolutionary examples for the formation of BHBe binaries in the WRLOF model. The initial binary parameters are $M_{\rm 1}=30\,M_\odot,\;M_{\rm 2}=5\,M_\odot,\;P_{\rm orb}=2977.6\,\rm d$ for the left column, and $M_{\rm 1}=80\,M_\odot,\;M_{\rm 2}=10\,M_\odot,\;P_{\rm orb}=277\,\rm d$ for the right column. The black solid lines and red dashed lines in the first row represent the wind mass-loss rates of the primary stars and wind accretion rates of the secondary stars, respectively. The second row shows the ratio between primary radius and primary RL radius. The black solid lines and red dashed lines in the third row correspond the speed ratio $\eta_{\rm wind}$ and the wind accretion efficiencies, and in the last row are for $\omega_{\rm 2}/\omega_{\rm crit,2}$ and accumulated masses of secondary stars, respectively. The colored regions represent the same features as those in Figure \ref{['fig:1']}.
• Figure 3: The parameter spaces for BHBe binaries in the WRLOF model. The grey shaded regions represent our fiducial model of $f_{\rm w} = 1$. Other cases with higher $f_{\rm w}$ of $1.5,2$ and $3$ are shown in blue dotted, red dash-dotted and green dashed contours, respectively. The primary stars below the lower boundaries would fill their RLs. For binaries above the upper boundaries, the accretion efficiencies are too low to form the Be stars due to the small RL filling factors.
• Figure 4: The density distributions of binary parameters for BHBe binaries from WRLOF model. The total number of BHBe binaries in the Galaxy at current epoch is $3225$. Note the color bar is shown in logarithm scale.
• Figure 5: Left panel: The parameter space for $M_{\rm 2}=10\,M_\odot$. The red and grey hatched regions correspond to the models with enhanced LBV winds and the fiducial case, respectively. Right panel: Comparison of several typical evolutionary tracks, where the red dashed lines and black solid lines represent the models with enhanced LBV winds and the fiducial case, respectively. The thick lines mark the wind accretion phase, defined as the period when the stellar radius lies between $0.4R_{\rm max}$ and $R_{\rm max}$, where $R_{\rm max}$ is the maximum evolutionary radius.