arXiv subjects

Timothy D Brandt

Publications and source records attributed to Timothy D Brandt.

4 recordsLinked to original sources

arXiv2026

Closed-Form Statistical Relations Between Projected Separation, Semimajor Axis, Companion Mass, and Host Acceleration

I derive the statistical relationship between a radial velocity or astrometric acceleration (a trend), a companion's mass, and the projected separation of the companion. These relationships, expressed as probability density functions, are analytic and independent of all Keplerian orbital elements so long as orbits are randomly oriented in space. I also derive a closed-form expression for the probability distribution of the ratio of the projected separation to the semimajor axis at fixed eccentricity. This expression can be numerically integrated over eccentricity for an arbitrary distribution of eccentricities. I verify my results with empirical comparisons to equivalent but more complex expressions in the literature based on the equations of Keplerian orbits. The closed-formed expressions derived here would be especially useful for any calculation that requires derivatives, e.g., Hamiltonian Monte Carlo. I also provide a Jupyter notebook including all figures and calculations.

astro-ph.SR↗

arXiv2026

Astrometric Radial Velocities from the Hipparcos-Gaia Catalog of Accelerations and Implications for Astrometric Acceleration Measurements

Astrometry from the Gaia satellite and from the long-term combination of Hipparcos and Gaia are now sensitive to sky-plane accelerations as low as $\approx$1 m/s/yr. This paper quantifies and explores an important caveat: apparent nonlinear motion due to a star's nonzero radial velocity can be indistinguishable from real astrometric acceleration. This nonlinear motion is parallel to the proper motion, so it can be both quantified and avoided by projecting apparent astrometric accelerations into components parallel and perpendicular to the proper motion. We illustrate this distinction for a sample of very nearby, fast-moving stars from the Hipparcos-Gaia Catalog of Accelerations (HGCA). We then generalize the effect of stellar radial velocity and projections of the astrometric acceleration to binary stars in which we observe the acceleration of both components. Finally, we demonstrate that the proper motion differences in the HGCA are statistically well-behaved even for the nearest and fastest-moving stars, at least in the component perpendicular to the proper motion. This distinction -- between astrometric acceleration parallel and perpendicular to proper motion -- could have important consequences for future missions reaching extreme astrometric sensitivities around nearby stars.

astro-ph.SR↗

arXiv2024

Significant mutual inclinations between the stellar spin and the orbits of both planets in the HAT-P-11 system

Planet-star obliquity and planet-planet ]mutual inclination encode a planetary system's dynamical history, but both of their values are hard to measure for misaligned systems with close-in companions. HAT-P-11 is a K4 star with two known planets: a close-in, misaligned super-Neptune with a $\approx$5-day orbit, and an outer super-Jupiter with a $\approx$10-year orbit. In this work we present a joint orbit fit of the HAT-P-11 system with astrometry and S-index corrected RV data. By combining our results with previous constraints on the orientation of the star and the inner planet, we find that all three angular momenta -- those of the star, planet b, and planet c -- are significantly misaligned. We confirm the status of planet c as a super-Jupiter, with $2.68\pm0.41\, \mathrm{M_{\rm Jup}}$ at a semimajor axis of $4.10\pm0.06\,$AU, and planet b's mass of $\mathrm{M_b\sin{i_b}}=0.074\pm0.004\, \mathrm{M_{\rm Jup}}$. We present the posterior probability distribution of obliquity between star A and planet c, and mutual inclination between planet b and planet c.

astro-ph.EP↗

arXiv2019

Performance and Early Science with the Subaru Coronagraphic Extreme Adaptive Optics Project

We describe the current performance of the Subaru Coronagraphic Extreme Adaptive Optics (SCExAO) instrument on the Subaru telescope on Maunakea, Hawaii and present early science results for SCExAO coupled with the CHARIS integral field spectrograph. SCExAO now delivers H band Strehl ratios up to $\sim$ 0.9 or better, extreme AO corrections for optically faint stars, and planet-to-star contrasts rivaling that of GPI and SPHERE. CHARIS yield high signal-to-noise detections and 1.1--2.4 $μm$ spectra of benchmark directly-imaged companions like HR 8799 cde and kappa And b that clarify their atmospheric properties. We also show how recently published as well as unpublished observations of LkCa 15 lead to a re-evaluation of its claimed protoplanets. Finally, we briefly describe plans for a SCExAO-focused direct imaging campaign to directly image and characterize young exoplanets, planet-forming disks, and (later) mature planets in reflected light.

astro-ph.IM↗