Table 3.
Summary of models and parameters.
| Category and | Symbol | Models | |||||||
|---|---|---|---|---|---|---|---|---|---|
| parameter | S | SVR | SVT | SV3 | SO | SOVR | SOVT | SOV3 | |
| Spectroscopy (S) | |||||||||
| Orbital period | Pf | * | * | * | * | * | * | * | * |
| Orbital eccentricity | ef | * | * | * | * | * | * | * | * |
| RV semi-amplitude | K1 | * | * | * | * | * | * | * | * |
| Argument of periastron | ωf | * | * | * | * | * | * | * | * |
| Mass of star (a) | m1,f | * | * | * | * | * | * | * | * |
| Resolved Orbit (O) | |||||||||
| Orbital inclination | if | * | * | * | * | ||||
| Longitude of the | Ωf | * | * | * | * | ||||
| Ascending node | |||||||||
| Velocities (V) | |||||||||
| Radial velocity (b) | Δvr = vr,f − vr,i | * | * | * | * | ||||
| Transverse velocities (b) | Δvα = vα, f − vα, i | * | * | * | * | ||||
| Δvδ = vδ, f − vδ, i | * | * | * | * | |||||
Notes. The parameters that are constrained for inert BHBs depend on the available observations. We only consider binaries that are detected with spectroscopy so all model names include an “S”. For those that have an astrometrically resolved orbit, we append an additional “O” to the model name. If the host association where the binary was born can be identified, it is possible that velocity constraints can be extracted. If only radial velocity measurements exist for both the system and host, the model has an appended “VR”. If only transverse velocity measurements exist for both the system and host, the model has an appended “VT”. If both exist, the model has “V3” appended.
A spectroscopic SB1 can only constrain the mass function f(m1,f). Additional stellar spectral modeling is required to get an estimate of m1,f, typically either through an estimate of log(g) or stellar track fitting.
The constraint Δvr depends on the observed radial velocity vr,f and the inferred initial velocity vr,i, which is assumed to be consistent with the birth environment radial velocity dispersion Vr, env. The transverse velocity constraints Δvα and Δvδ are treated similarly, except that they are derived from the parallax and proper motion, while the radial velocities are measured spectroscopically.
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