Probabilistic orbits and dynamical masses of emission-line binaries

Abstract

The observed orbits of emission-line stars may be affected by systematics owing to their broad emission lines being formed in complex and extended environments. This is problematic when orbital parameter probability distributions are estimated assuming radial-velocity data are solely comprised of Keplerian motion plus Gaussian white noise, leading to overconfident and inaccurate orbital solutions, with implications for the inferred dynamical masses and hence evolutionary models. We present a framework in which these systems can be meaningfully analysed. We synthesise benchmark datasets, each with a different and challenging noise formulation, for testing the performance of different algorithms. We make these datasets freely available with the aim of making model validation an easy and standardised practice in this field. Next, we develop an application of Gaussian processes to model the radial-velocity systematics of emission-line binaries, named marginalised $\mathcal {GP}$. We benchmark this algorithm, along with current standardised algorithms, on the synthetic datasets and find our marginalised $\mathcal {GP}$ algorithm performs significantly better than the standard algorithms for data contaminated by systematics. Finally, we apply the marginalised $\mathcal {GP}$ algorithm to four prototypical emission-line binaries: Eta Carinae, GG Carinae, WR 140, and WR 133. We find systematics to be present in several of these case studies; and consequently, the predicted orbital parameter distributions, and dynamical masses, are modified from those previously determined.

Changes in the Na D1 Absorption Components of η Carinae Provide Clues on the Location of the Dissipating Central Occulter

“…This material has resulted in a bipolar shell of ejecta surrounding the system from the Great Eruption in the 1840s and from the second Lesser Eruption in the 1890s, known as the Homunculus and the Little Homunculus, respectively. The binary is in a long-period 5.54 yr orbit (2022.7 ± 0.3 days; Damineli 1996;Damineli et al 1997;Teodoro et al 2016) that is highly eccentric (e = 0.9; e.g., Damineli et al 2000;Grant et al 2020;Grant & Blundell 2022). The primary star provides some ionization to the surrounding gas, such as causing Fe II emission lines, while the secondary star further ionizes the Homunculus and the Little Homunculus.…”

The orbital kinematics of eta Carinae over three periastra with a possible detection of the elusive secondary's motion

“…This effect causes differences from the true orbital motion for lower energy transitions, making it difficult to determine accurate orbits (Grant et al 2020). Grant & Blundell (2022) confirmed that their methods used for emission-line stars worked for the WR binaries WR 133 and WR 140 that have combined spectroscopic and interferometric orbits (Richardson et al 2021;Thomas et al 2021).…”

“…We use a phase convention in which the lowionization state observed by Gaviola (1953) in 1948 is deemed to be cycle 1, so that the low-ionization state starting in Feb. 2020 marks the start of cycle 14. We leave the kinematics analysis of the metal lines for a future analysis in order to confirm the results of Grant et al (2020) and Grant & Blundell (2022) here, with plans of using higher signal-to-noise spectra in a future analysis.…”

“…The CHIRON spectra are normalized through a comparison with a measured blaze function from the star HR 4468 (B9.5V), as was done in the analysis of Richardson et al (2016). Example spectra are shown in Figure . 1, with a comparison to a spectrum used by Grant et al (2020) and Grant & Blundell (2022).…”

“…The primary star in the Car system is a luminous blue variable star, with the largest measured value for a mass-loss rate for a massive star with = 8.5 × 10 −4 ⊙ yr −1 and a terminal wind speed of ∞ = 420 km s −1 (Davidson & Humphreys 1997;Groh et al 2012). Prior to the recent kinematic studies of Grant et al (2020) and Grant & Blundell (2022), the best constraints on the companion star parameters, while indirect, came from the X-ray variability analyses from RXTE, Swift, and NICER observations of the system (Corcoran et al 2001(Corcoran et al , 2017Espinoza-Galeas et al 2022). These analyses point to a secondary star with a mass-loss rate on the order of ∼ 10 −5 ⊙ yr −1 and a terminal velocity of ∞ ∼ 3000 km s −1 (Pittard & Corcoran 2002).…”