arXiv subjects

Zachary Langford

Publications and source records attributed to Zachary Langford.

7 recordsLinked to original sources

arXiv2026

Self-consistent dynamical modelling of the Milky Way bar with orbital frequency analysis

We present an update to the frequency analysis method for measuring the properties of a galactic bar. The method involves computing the fundamental frequencies of orbits in rotating, N-body-derived potential models, classifying the stars as members of bar supporting orbits, and finding the extent of the apo-centre distribution. In this work, we apply an updated classification criterion designed to isolate the so-called "Warm" inner Lindblad resonance (ILR) orbits. These orbits have been shown to contain the looped x1 orbits, which dominate the "shoulder regions" of the bar and largely contribute to the radial extent. We apply this method to existing Gaia, APOGEE, and OGLE data of more than 200,000 stars to constrain the properties of the Milky Way bar. We find that multiple bar lengths and pattern speeds are consistent with the data to within 5 percent.

astro-ph.GA↗

arXiv2025

Order-by-order Modeling of Exoplanet Radial Velocity Data

Precise radial velocity (RV) measurements are a crucial tool for exoplanet discovery and characterization. Today, the majority of these measurements are derived from Echelle spectra in the optical wavelength region using cross-correlation techniques. Although for certain stars these approaches can produce RVs with sub-1 m~s$^{-1}$ measurement errors, for many others, we are now in a regime where instrumental precision is fundamentally below the intrinsic RV variations of the star that result from astrophysical processes that can be correlated in both time and wavelength. We explore new methods for measuring exoplanet orbital parameters that take advantage of the fact that RV data sets are fundamentally multi-wavelength. By analyzing NEID extremely precise radial velocity (EPRV) data of three known exoplanet systems, we show that fitting a single Keplerian model to multi-wavelength RVs can produce a factor of 1.5 -- 6.8 better $M_p \sin i$ uncertainties compared to fitting RVs that are derived from a weighted average across wavelength.

astro-ph.EP↗

arXiv2025

A differentiable N-body code for transit timing and dynamical modelling -- II. Photodynamics

Exoplanet transits contain substantial information about the architecture of a system. By fitting transit light curves we can extract dynamical parameters and place constraints on the properties of the planets and their host star. Having a well-defined probabilistic model plays a crucial role in making robust measurements of these parameters, and the ability to differentiate the model provides access to more robust inference tools. Gradient-based inference methods can allow for more rapid and accurate sampling of high-dimensional parameter spaces. We present a fully differentiable photodynamical model for multiplanet transit light curves that display transit timing variations. We model time-integrated exposures, compute the dynamics of a system over the full length of observations, and provide analytic expressions for derivatives of the flux with respect to the dynamical and photometric model parameters. The model has been implemented in the Julia language and is available open-source on GitHub. We demonstrate with a simulated data set that Bayesian inference with the NUTS HMC algorithm, which uses the model gradient, can outperform the affine invariant (e.g. emcee) MCMC algorithm in CPU time per effective sample, and we find that the relative sampling efficiency improves with the number of model parameters.

astro-ph.EP↗

arXiv2023

The DECam Ecliptic Exploration Project (DEEP) III: Survey characterization and simulation methods

We present a detailed study of the observational biases of the DECam Ecliptic Exploration Project's (DEEP) B1 data release and survey simulation software that enables direct statistical comparisons between models and our data. We inject a synthetic population of objects into the images, and then subsequently recover them in the same processing as our real detections. This enables us to characterize the survey's completeness as a function of apparent magnitudes and on-sky rates of motion. We study the statistically optimal functional form for the magnitude, and develop a methodology that can estimate the magnitude and rate efficiencies for all survey's pointing groups simultaneously. We have determined that our peak completeness is on average 80\% in each pointing group, and our magnitude drops to $25\%$ of this value at $m_{25} = 26.22$. We describe the freely available survey simulation software and its methodology. We conclude by using it to infer that our effective search area for objects at 40 au is $14.8°^2$, and that our lack of dynamically cold distant objects means that there at most $8\times 10^3$ objects with $60 < a < 80$ au and absolute magnitudes $H \leq 8$.

astro-ph.EP↗

arXiv2023

The DECam Ecliptic Exploration Project (DEEP) VI: first multi-year observations of trans-Neptunian objects

We present the first set of trans-Neptunian objects (TNOs) observed on multiple nights in data taken from the DECam Ecliptic Exploration Project (DEEP). Of these 110 TNOs, 105 do not coincide with previously known TNOs and appear to be new discoveries. Each individual detection for our objects resulted from a digital tracking search at TNO rates of motion, using two to four hour exposure sets, and the detections were subsequently linked across multiple observing seasons. This procedure allows us to find objects with magnitudes $m_{VR} \approx 26$. The object discovery processing also included a comprehensive population of objects injected into the images, with a recovery and linking rate of at least $94\%$. The final orbits were obtained using a specialized orbit fitting procedure that accounts for the positional errors derived from the digital tracking procedure. Our results include robust orbits and magnitudes for classical TNOs with absolute magnitudes $H \sim 10$, as well as a dynamically detached object found at 76 au (semi-major axis $a\approx 77 \, \mathrm{au}$). We find a disagreement between our population of classical TNOs and the CFEPS-L7 three component model for the Kuiper belt.

astro-ph.EP↗

arXiv2021

A differentiable N-body code for transit timing and dynamical modeling. I. Algorithm and derivatives

When fitting N-body models to astronomical data - including transit times, radial velocity, and astrometric positions at observed times - the derivatives of the model outputs with respect to the initial conditions can help with model optimization and posterior sampling. Here we describe a general-purpose symplectic integrator for arbitrary orbital architectures, including those with close encounters, which we have recast to maintain numerical stability and precision for small step sizes. We compute the derivatives of the N-body coordinates and velocities as a function of time with respect to the initial conditions and masses by propagating the Jacobian along with the N-body integration. For the first time we obtain the derivatives of the transit times with respect to the initial conditions and masses using the chain rule, which is quicker and more accurate than using finite differences or automatic differentiation. We implement this algorithm in an open source package, NbodyGradient.jl, written in the Julia language, which has been used in the optimization and error analysis of transit-timing variations in the TRAPPIST-1 system. We present tests of the accuracy and precision of the code, and show that it compares favorably in speed to other integrators which are written in C.

astro-ph.EP↗

arXiv2021

Refining the transit timing and photometric analysis of TRAPPIST-1: Masses, radii, densities, dynamics, and ephemerides

We have collected transit times for the TRAPPIST-1 system with the Spitzer Space Telescope over four years. We add to these ground-based, HST and K2 transit time measurements, and revisit an N-body dynamical analysis of the seven-planet system using our complete set of times from which we refine the mass ratios of the planets to the star. We next carry out a photodynamical analysis of the Spitzer light curves to derive the density of the host star and the planet densities. We find that all seven planets' densities may be described with a single rocky mass-radius relation which is depleted in iron relative to Earth, with Fe 21 wt% versus 32 wt% for Earth, and otherwise Earth-like in composition. Alternatively, the planets may have an Earth-like composition, but enhanced in light elements, such as a surface water layer or a core-free structure with oxidized iron in the mantle. We measure planet masses to a precision of 3-5%, equivalent to a radial-velocity (RV) precision of 2.5 cm/sec, or two orders of magnitude more precise than current RV capabilities. We find the eccentricities of the planets are very small; the orbits are extremely coplanar; and the system is stable on 10 Myr timescales. We find evidence of infrequent timing outliers which we cannot explain with an eighth planet; we instead account for the outliers using a robust likelihood function. We forecast JWST timing observations, and speculate on possible implications of the planet densities for the formation, migration and evolution of the planet system.

astro-ph.EP↗