#### Title

Predicting Transit Timing Variations and Masses of Unseen Planets

#### Poster Number

17C

#### Format

Poster Presentation

#### Faculty Mentor Name

Daniel Jontof-Hutter

#### Faculty Mentor Department

Department of Physics

#### Abstract/Artist Statement

The Kepler mission revealed the existence of thousands of exoplanets beyond our solar system, but many unseen neighbors of these known exoplanets remain undiscovered. One way to detect these neighbors is through analyzing precisely measured mid-transit times. When a planet transits in front of its star, these transits should occur at equally spaced time intervals if it is alone in the system. However, if its transits happen slightly earlier or later than expected given its average orbital period, and if this pattern of earliness and lateness occurs with a regular period over many orbits, this cycle of transit timing variations (TTVs) could be caused by the gravitational pull of an unseen additional planet in the system.

Using data gathered from the Kepler Mission on the planet KOI-315.01, we used a Monte Carlo Markov Chain method to create many model sine curves and see which one most closely modeled that planet’s TTVs. Each model accounted for the orbital period, time of the first transit, angular frequency, amplitude of the TTV signal, and initial phase of the signal. By extrapolating these transit times, we can obtain accurate predictions of when future transits will occur for later observations.

For any planets with periodic TTVs, it is not initially clear whether the unseen perturber is the outer or inner planet relative to the known exoplanet. However, by characterizing the posterior distributions of the TTV parameters, we can place constraints on the mass of the unseen perturber and its location by assuming that the planets are in near-resonance with each other. Then we solve for the masses associated with each near-resonance possibility. These results can be compared with ground-based radial velocity spectroscopy measurements, which, alongside our TTV constraints, can further constrain the nature of hidden planets in this exoplanetary system.

#### Location

Information Commons, William Knox Holt Memorial Library and Learning Center

#### Start Date

29-4-2023 10:00 AM

#### End Date

29-4-2023 1:00 PM

Predicting Transit Timing Variations and Masses of Unseen Planets

Information Commons, William Knox Holt Memorial Library and Learning Center

The Kepler mission revealed the existence of thousands of exoplanets beyond our solar system, but many unseen neighbors of these known exoplanets remain undiscovered. One way to detect these neighbors is through analyzing precisely measured mid-transit times. When a planet transits in front of its star, these transits should occur at equally spaced time intervals if it is alone in the system. However, if its transits happen slightly earlier or later than expected given its average orbital period, and if this pattern of earliness and lateness occurs with a regular period over many orbits, this cycle of transit timing variations (TTVs) could be caused by the gravitational pull of an unseen additional planet in the system.

Using data gathered from the Kepler Mission on the planet KOI-315.01, we used a Monte Carlo Markov Chain method to create many model sine curves and see which one most closely modeled that planet’s TTVs. Each model accounted for the orbital period, time of the first transit, angular frequency, amplitude of the TTV signal, and initial phase of the signal. By extrapolating these transit times, we can obtain accurate predictions of when future transits will occur for later observations.

For any planets with periodic TTVs, it is not initially clear whether the unseen perturber is the outer or inner planet relative to the known exoplanet. However, by characterizing the posterior distributions of the TTV parameters, we can place constraints on the mass of the unseen perturber and its location by assuming that the planets are in near-resonance with each other. Then we solve for the masses associated with each near-resonance possibility. These results can be compared with ground-based radial velocity spectroscopy measurements, which, alongside our TTV constraints, can further constrain the nature of hidden planets in this exoplanetary system.