The periastron regression of 2M1510 AB, the jet precession of M87* and Telisto/Planet Nine: three different scenarios for a possible common cause

TL;DR

The paper develops a general analytic framework to compute secular perturbations on a bound two-body system caused by a distant pointlike third body at Newtonian quadrupole order, averaged over the inner orbit. Using osculating Keplerian elements and Lagrange planetary equations, it derives closed-form expressions for the averaged rates of change of all six orbital elements, encapsulated through the disturbing function and geometry. The authors apply these results to three astrophysical scenarios—perpendicular circumbinary planets around 2M1510 AB, the jet precession of M87*, and Telisto/Planet Nine—producing exclusion plots that constrain the perturber’s mass, orbit, and eccentricity. They conclude that an IMBH near M87* is unlikely to explain the jet precession, that the 2M1510 AB case allows only restricted combinations of a massive circumbinary planet, and that Tl/P9 remains viable only up to roughly five Earth masses with a distant, aphelion-oriented orbit, while highlighting the importance of incorporating distant perturber effects in ephemeris modeling for robust inference.

Abstract

The long-term rates of change of all the Keplerian orbital elements of a two-body system acted upon by a remote massive pointlike object are analytically worked out, to the Newtonian quadrupolar level, without any restriction either on the orbital eccentricity and inclination of the disturbed pair or the position of the distant perturber. The latter is considered fixed during the average over one orbital revolution of the inner binary by means of which its orbital perturbations are calculated. The results are presented in a compact form that facilitates a straightforward application, for example, to the cases of the eclipsing binary 2M1510 AB made of two brown dwarfs, the supermassive black hole-or megapyknon-M87$^\ast$ and our solar system, although they are not limited to such interesting astronomical scenarios alone. The aforementioned systems may all have in common the presence of a distant point mass perturbing in some ways their inner dynamics. That is, respectively, a circumbinary exoplanet whose orbital plane should be perpendicular to that of its host inner binary, an intermediate mass black hole potentially causing the observed jet precession, and a still unseen planet, known as Telisto or Planet Nine, which may, perhaps, have been recently spotted in archival images although in a quite different orbit with respect to that originally expected. For each of the considered cases, exclusion plots in their parameter spaces are provided.

Figures (5)

• Figure 1: Allowed regions in the $\left\{M^{'},\,P^{'}\right\}$ plane for the mass $M^{'}$, in unit of Jovian masses $M_{\jupiter}$, and the orbital period $P^{'}$, in days, of the circumbinary exoplanet 2M1510 (AB)b orbiting the diioessa 2M1510 AB perpendicularly to the orbital plane of the latter for different values of the planetary eccentricity $e^{'}$. The observational constraint of Equation (\ref{['proc']}) was applied to the doubly averaged periastron precession of Equation (\ref{['dodt3']}) assumed as a function of the two independent variables $M^{'}$ and $P^{'}$ parameterized by $e^{'}$.
• Figure 2: Allowed domains in the 3D parameter space spanned by $u:=\log_{10}\left(M^{'}/M_\odot\right)$, $v:=r^{'}-r_\mathrm{t}$, in units of $R_\mathrm{g}$, $w:=\varphi$, in degrees, according to the condition of Equation (\ref{['condiz']}). The value $r_0=14.1\,R_\mathrm{g}$ is assumed for the effective disk radius.
• Figure 3: Plot of $f^{'}$, in $^\circ$, as a function of $\alpha^{'},\,\delta^{'}$. They are allowed to vary within their intervals displayed in Table \ref{['Tab:1']} from which the maximum likelihood values of $I^{'},\,{\mathit{\Omega}}^{'},\,\varpi^{'}$ are retrieved as well.
• Figure 4: A collection of joint constraints from the perihelion precessions of Mars and Saturn on the Tl/P9 allowed regions in the $\left\{a^{'},\,q^{'},\,f^{'}\right\}$ parameter space obtained for given sets of maximum/minimum values of $M^{'},\,I^{'},\,{\mathit{\Omega}}^{'},\,\varpi^{'}$, retrieved from Table \ref{['Tab:1']}, that are compatible with the ranges for $f^{'}$ inferred from the permitted intervals of $\alpha^{'},\,\delta^{'}$ provided by 2021AJ....162..219B and shown in Figure \ref{['Fig:f']}.
• Figure 5: Another collection of joint constraints from the perihelion precessions of Mars and Saturn on the Tl/P9 allowed regions in the $\left\{a^{'},\,q^{'},\,f^{'}\right\}$ parameter space obtained for given sets of maximum/minimum values of $M^{'},\,I^{'},\,{\mathit{\Omega}}^{'},\,\varpi^{'}$, retrieved from Table \ref{['Tab:1']}, that are compatible with the ranges for $f^{'}$ inferred from the permitted intervals of $\alpha^{'},\,\delta^{'}$ provided by 2021AJ....162..219B and shown in Figure \ref{['Fig:f']}.