The GQ Lup system is comprised of three objects: The host star of this system is GQ Lup A with a sub-stellar companion, GQ Lup B. Another object is present in the GQ Lup system, which is subsequently named GQ Lup C or 2MASS J15491331-3539118. The GQ Lup system hosts a pair of stars, GQ Lup A and C, at large distances from one another. GQ Lup A and C likely formed through core fragmentation as described in Alcal à et al. (2020). The subject of interest in this system is GQ Lup B as many of its characteristics such as its mass, period, distance from its host star, and orbit have only been estimated and not yet confirmed. GQ Lup B is estimated to have a mass of ˜10-40 M_Jup at a distance of ˜100 AU with likely a low-eccentricity and possibly high inclination orbit (Wu et al. 2017). With such a large semi-major axis, the orbital period of GQ Lup is estimated to be ˜1000 years using Kepler's Third Law approximation: p²yr =a³AU . All of these characteristics of GQ Lup B are approximations signifying that there is still much to be confirmed. Currently, it is not known whether GQ Lup B is a large-mass exoplanet or a brown dwarf due to only having an estimate of its mass. With GQ Lup B's large orbital period, it is not realistically feasible to observe in its entirety.

The small portion of GQ Lup B's large orbit was observed consisting of less than 20 years of observation. This data was partly captured by the instrument GRAVITY, which is part of the Very Large Telescope Interferometer (VLTI). This instrument performed optical interferometry to directly image GQ Lup B. The data captured revealed that GQ Lup B is still actively accreting material onto its surface as evident in its low-density debris disk (Stolker et al. 2021). From this data, the orbit of the GQ Lup B can be modeled by Bayesian statistics and the package Orbitize! (Blunt et al. 2020). This package can create a best-fit orbit model that uses the highest likelihood of orbital parameters. These orbital parameters include eccentricity (e), Semi-major axis (a), Argument of Periastron (ω), Longitude of Ascending Node (Ω), Epoch of Periastron Passage (τ), and orbital inclination (i). Once a best-fit orbit is created, a high-accuracy recreation of GQ Lup B's orbit is made and can be analyzed. The analysis consists of comparing our results of the orbit fit to previously created orbit fits of other data sets from other orbit observations. The purpose of the analysis is to observe whether there are any similarities in our orbit fits or data to find any errors or new findings within our models. The best-fit orbit model will confirm the assumed orbital parameters and categorize the type of object GQ Lup B, either as an exoplanet or brown dwarf. The findings of the analysis of the orbit models will then add to the dynamic formation history of the GQ Lup system.

GRAVITY Used to Directly Image GQ Lup B

GRAVITY is an instrument on the Very Large Telescope Interferometer (VLTI) located at the ESO's European Southern Observatory (GRAVITY Collaboration et al. 2019). GRAVITY is an instrument capable of performing interferometric astrometry, which typically consists of multiple antennae in an array of differing distances from each other. These differing distances are referred to as baselines. The antennae effectively act as one large mirror similar to a reflective optical telescope. Also, similar to a reflective telescope, the resolution of the interferometer is dictated by the baseline between each antenna. GRAVITY can directly observe an exoplanet such as it did with HR 8799e (GRAVITY Collaboration et al. 2019) and recently with the GQ Lup system. GRAVITY was used to gather astrometry for the Right Ascension offset, Declination offset, the correlation between the two parameters as well as the separation and position angle of GQ Lup B.

Orbitize! Creates Posterior of Orbital Parameters

Orbitize! is a Python-based package used to create the orbit fits as seen in Figure 1 (Blunt et al. 2020). The version of orbitize! used to create the orbit fit models utilized Markov Chain Monte Carlo (MCMC). The purpose of using MCMC with orbitize! is to explore all of the parameter space to find the orbital parameters that would best fit our orbit model. orbitize! creates an array of the best-fit orbit parameters from a sampler consisting of semi-major axis, inclination, eccentricity, position angle and others that did have an effect on the orbit model . Using the data acquired from GRAVITY of a small section GQ Lup B's orbit it can iterate multiple simulated orbits created to find the best-fit orbit.

The data collected of GQ Lup B's orbit both from the recent GRAVITY observations and archival data from Stolker et al. (2021), Wu et al. (2017), and Ginski et al. (2014) were compiled within the orbit model in Figure 1. As previously mentioned, the posteriors of the orbital parameters created by orbitize! are used to create a model of GQ Lup B's orbit. The 100 best-fit orbits are as the orbital cone (grey lines) in Figure 1's separation and position angle plots. Both the GRAVITY and archival data align with the orbital cone of the orbit model. All data sets aligned with the orbital cone signify that the data are consistent with our orbit models of GQ Lup B. The next task was to compare the distribution of GQ Lup B's orbit parameter posteriors to GQ Lup A's inclination and position angle.

The inclination of both GQ Lup A's debris disk and rotation are displayed in the inclination distribution plots in Figure 2 as green and red dashed lines, respectively. There is not a strong correlation between the inclination of GQ Lup A's rotation axis, i_A=27°. The weak correlation between the rotation axis and GQ Lup B's orbit signifies that they are not coplanar. The inclination of the GQ Lup A's disk, i_Adisk=60.5° has a stronger correlation with GQ Lup B's inclination. The position angle distribution contrast what is seen in the inclination distribution for the coplanarity between GQ Lup A's disk and GQ Lup B's orbit. The position angle of the disk, Ω_A=346°, has a small correlation with the position angle. This small correlation shows that there is no correlation between GQ Lup B's orbit and GQ Lup A's disk. Finally, using GQ Lup B and A's inclination and position angle, the coplanarity between these two objects can be found.