Constraints on Neutrino Natal Kicks from Black-Hole Binary VFTS 243

The recently reported observation of VFTS 243 is the first example of a massive black-hole binary system with negligible binary interaction following black-hole formation. The black-hole mass ($\approx 10M_{\odot }$) and near-circular orbit ($e\approx 0.02$) of VFTS 243 suggest that the progenitor star experienced complete collapse, with energy-momentum being lost predominantly through neutrinos. VFTS 243 enables us to constrain the natal kick and neutrino-emission asymmetry during black-hole formation. At 68% confidence level, the natal kick velocity (mass decrement) is $\lesssim 10\mathrm{km}/\mathrm{s}$ ($\lesssim 1.0M_{\odot }$), with a full probability distribution that peaks when $\approx 0.3M_{\odot }$ were ejected, presumably in neutrinos, and the black hole experienced a natal kick of $4\mathrm{km}/\mathrm{s}$. The neutrino-emission asymmetry is $\lesssim 4\%$, with best fit values of $\sim 0–0.2\%$. Such a small neutrino natal kick accompanying black-hole formation is in agreement with theoretical predictions.

Figure 1

Constraints on the natal kick from VFTS 243. This figure shows the probability distribution of matching the current orbital period, eccentricity, and systemic velocity of VFTS 243, given a certain mass loss ($dM$) and natal-kick magnitude ($v_{\mathrm{kick}}$) following BH formation. In the heat map, darker (lighter) regions indicate a higher (lower) probability for a certain $dM\text{−}{v}_{\mathrm{kick}}$ pair to reproduce the orbital configuration of VFTS 243. The blue shaded region, delimited by the solid blue vertical lines, shows the estimates for neutrino mass-loss decrements from stellar models of BH progenitors [66]. The side panels display the marginalized probability distribution functions (PDF, gray histograms) and cumulative distribution functions (CDF, red curves). With $\mathrm{CDF}(dM=1.0M_{\odot })=\mathrm{CDF}(v_{\mathrm{kick}}=10\mathrm{km}/\mathrm{s})=0.68$, we conclude that solutions with low mass loss and small natal kicks are preferred. The marginalized distributions peak at around $dM=0.3M_{\odot }$ and $v_{\mathrm{kick}}=4\mathrm{km}/\mathrm{s}$, which is consistent with a solution where the mass decrement comes exclusively from neutrino emission.

Figure 2

Observed sample of field black-hole (BH) binaries with massive companions. For each binary, we show the BH mass ($M_{\mathrm{BH}}$) on the abscissa, the stellar companion mass ($M_{*}$) on the ordinate, and the eccentricity ($e$) through the color bar. We use circles to indicate high-mass x-ray binaries (HMXBs) and triangles for inert BH binaries (Inert BHB). The symbol of VFTS 243 is slightly larger for clarity.