arXiv subjects

Lawrence M. Widrow

Publications and source records attributed to Lawrence M. Widrow.

At least 19 recordsLinked to original sources

arXiv2026

Galactic magnetic fields seeded by ultralight dark photons

In this work, we show that ultralight dark photons, which couple to the Standard Model photon through kinetic mixing, can potentially source galactic scale magnetic fields. Although these magnetic fields would be too weak to detect at present in galaxies due to plasma screening effects, we show that dark photons can provide the seed magnetic field strength ($10^{-20}$ G) required for dynamo amplification in galaxies. Such dynamo-amplified magnetic fields are consistent with observations of $μ$G strength galactic magnetic fields.

hep-ph↗

arXiv2026

Mean Mass Density near the Sun from the Divergence Theorem and Pulsar Accelerations

We introduce a new, non-parametric method for estimating the mass enclosed within a sphere of arbitrary radius centered on the Sun. The method is based on the divergence theorem as applied to measurements of the line-of-sight accelerations of millisecond pulsars. We describe a procedure for inferring the mean mass density within a sphere of a given radius centered on the Sun and find results that are consistent with previous analyses. When combined with a model for the distribution of baryons, this provides the mean mass density of dark matter as a function of distance from the Sun, rather than a single value as is typically reported by kinematic studies. However, with the present pulsar data, the method cannot unambiguously measure a signal from the local distribution of dark matter at this time; such a measurement is expected to soon become possible as the amount of pulsar acceleration data grows and its precision improves. We derive an extension of the well-known shell theorem to a spherical-harmonics expansion of the density and potential, and use the result to obtain estimates for density asymmetries with respect to the Galactic midplane from the observed acceleration data. The predicted asymmetries do not follow the observed distribution of MW disk stars or gas; this can potentially be explained by a non-uniform distribution of dark matter in the Solar neighborhood.

astro-ph.GA↗

arXiv2025

Gaussian Process Methods for Very Large Astrometric Data Sets

We present a novel non-parametric method for inferring smooth models of the mean velocity field and velocity dispersion tensor of the Milky Way from astrometric data. Our approach is based on Stochastic Variational Gaussian Process Regression (SVGPR) and provides an attractive alternative to binning procedures. SVGPR is an approximation to standard GPR, the latter of which suffers severe computational scaling with N and assumes independently distributed Gaussian Noise. In the Galaxy however, velocity measurements exhibit scatter from both observational uncertainty and the intrinsic velocity dispersion of the distribution function. We exploit the factorization property of the objective function in SVGPR to simultaneously model both the mean velocity field and velocity dispersion tensor as separate Gaussian Processes. This achieves a computational complexity of O(M^3) versus GPR's O(N^3), where M << N is a subset of points chosen in a principled way to summarize the data. Applied to a sample of ~8 x 10^5 stars from the Gaia DR3 Radial Velocity Survey, we construct differentiable profiles of the mean velocity and velocity dispersion as functions of height above the Galactic midplane. We find asymmetric features in all three diagonal components of the velocity dispersion tensor, providing evidence that the vertical dynamics of the Milky Way are in a state of disequilibrium. Furthermore, our dispersion profiles exhibit correlated structures at several locations in |z|, which we interpret as signatures of the Gaia phase spiral. These results demonstrate that our method provides a promising direction for data-driven analyses of Galactic dynamics.

astro-ph.GA↗

arXiv2025

Empirical Modeling of Magnetic Braking in Millisecond Pulsars to Measure the Local Dark Matter Density and Effects of Orbiting Satellite Galaxies

We present a novel method that enables us to estimate the acceleration of individual millisecond pulsars (MSPs) using only their spin period and its time derivative. For our binary MSP sample, we show that one can obtain an empirical calibration of the magnetic braking term that relies only on observed quantities. We find that such a model for magnetic braking is only valid for MSPs with small surface magnetic field strengths ($<3\times10^8$ G) and large characteristic ages ($>$ 5 Gyr). With this method we are able to effectively double the number of pulsars with line-of-sight acceleration measurements, from 27 to 53 sources. This expanded dataset leads to an updated measurement of the total density in the midplane, which we find to be $ρ_0$ = 0.108 $\pm$ 0.008 \textit{stat}. $\pm$ 0.011 \textit{sys} M$_\odot$/pc$^3$, and the first $>3σ$ measurement of the local dark matter density from direct acceleration measurements, which we calculate to be $ρ_{0,\mathrm{DM}}$ = 0.0098 $\pm$ 0.0025 \textit{stat.} $\pm$ 0.0003 \textit{sys}. M$_\odot$/pc$^3$ (0.37 $\pm$ 0.10 GeV/cm$^3$). This updated value for $ρ_{0,\mathrm{DM}}$ is in good agreement with literature values derived from kinematic estimates. The pulsar accelerations are very asymmetric above and below the disk; we show that the shape and size of this asymmetry can be largely explained by the north-south asymmetry of disk star counts and the offset in the Milky Way disk and halo centers of mass due to the Large Magellanic Cloud.

astro-ph.HE↗

arXiv2024

Linear operator theory of phase mixing

We study solutions of the collisionless Boltzmann equation (CBE) in a functional Koopman representation. This facilitates the use of linear spectral techniques characteristic of the analysis of Schrodinger-type equations. For illustrative purposes, we consider the classical phase mixing of a non-interacting distribution function in a quartic potential. Solutions are determined perturbatively relative to a harmonic oscillator. We impose a form of coarse-graining by choosing a finite dimensional basis to represent the distribution function and time evolution operators, which sets a minimum length scale on phase space structure. We observe a relationship between the dimension of the representation and the multiplicity of the harmonic oscillator eigenvalues. System dynamics are understood in terms of degenerate subspaces of the linear operator spectra. Each subspace is associated with a mode of the harmonic oscillator, the first two being bending and breathing structures. The quartic potential splits the degenerate eigenvalues within each subspace. This facilitates the formation of spiral structure as deformations from the harmonic oscillator modes. We ultimately argue that this construction provides a promising avenue for study of self-interacting systems experiencing phase mixing, which is an outstanding problem in the context of the Gaia DR2 vertical phase space spirals.

astro-ph.GA↗

arXiv2024

Galactic Structure From Binary Pulsar Accelerations: Beyond Smooth Models

We measure the line-of-sight accelerations of 26 binary pulsars due to the Milky Way's gravitational potential, and produce a 3-dimensional map of the acceleration field of the Galaxy. Acceleration measurements directly give us the change in the line-of-sight velocity at present day, without requiring any assumptions inherent to kinematic modeling. We measure the Oort limit ($ρ_0=0.062\pm0.017$ \msun/pc$^3$) and the dark matter density in the midplane ($ρ_{0,\textrm{DM}}=-0.010\pm0.018$ \msun/pc$^3$); these values are similar to, but have smaller uncertainties than previous pulsar timing measurements of these quantities. Here, we provide for the first time, values for the Oort constants and the slope of the rotation curve from direct acceleration measurements. We find that $A=15.4\pm2.6$ km/s/kpc and $B=-13.1\pm2.6$ km/s/kpc (consistent with results from \textit{Gaia}), and the slope of the rotation curve near the Sun is $-2\pm5$ km/s/kpc. We show that the Galactic acceleration field is clearly asymmetric, but due to data limitations it is not yet clear which physical processes drive this asymmetry. We provide updated models of the Galactic potential that account for various sources of disequilibrium; these models are incompatible with commonly used kinematic potentials. This indicates that use of kinematically derived Galactic potentials in precision tests (e.g., in tests of general relativity with pulsar timing) may be subject to larger uncertainties than reported. The acceleration data indicates that the mass of the Galaxy within the Solar circle is $2.3 \times 10^{11}$ M$_\odot$, roughly twice as large as currently accepted models. Additionally, the residuals of the acceleration data compared to existing Galactic models have a dependence on radial position; this trend can be explained if the Sun has an additional acceleration away from the Galactic center.

astro-ph.GA↗

arXiv2023

The Formation of Bars and Warps in Rotating Halos

We investigate the effects of halo kinematics on the dynamics of stellar discs by simulating the evolution of isolated disc-halo systems from equilibrium initial conditions. Our main results come from four simulations where the initial disc is identical and the halo is either treated as a rigid potential or is live with isotropic orbits or orbits that preferentially rotate with or counter to the disc. We confirm previous results that bar formation is more vigorous in models with a live halo than a rigid one and is further enhanced when halo orbits preferentially rotate with the disc. We discuss two types of buckling events with different symmetries about the mid plane, one that occurs just as the bar is forming and the other well after the bar has been established. We also show that warps are most easily excited and maintained when the halo is counter-rotating with the disc, in agreement with theoretical predictions. Our most novel result is the discovery of a rotating halo instability, which causes the disc and halo cusp to spiral outward from the centre of mass of the system whether the halo rotates with the disc or counter to it and also occurs in a disc bulge halo system that does not form a bar. We provide a heuristic linear model that captures the essential dynamics of the instability.

astro-ph.GA↗

arXiv2023

Fuzzy Dark Matter Dynamics and the Quasiparticle Hypothesis

Dark matter may be composed of ultra-light bosons whose de Broglie wavelength in galaxies is of order 1 kpc. The standard model for this fuzzy dark matter (FDM) is a complex scalar field that obeys the Schrödinger-Poisson equations. The wavelike nature of FDM leads to fluctuations in the gravitational field that can pump energy into the stellar components of a galaxy. Heuristic arguments and theoretical analyses suggest that these fluctuations can be modelled by replacing FDM with a system of quasiparticles (QPs). We test this hypothesis by comparing self-consistent simulations of a Schrödinger field with those using a system of QPs in one spatial dimension. Simulations of pure FDM systems allow us to derive a phenomenological relation between the number of QPs that is required to model FDM with a given de Broglie wavelength. We also simulate systems of FDM and stars and find that the FDM pumps energy into the stars whether it is described by QPs or a Schrödinger field with the FDM adiabatically contracting and the stellar system adiabatically expanding. However, we find that QPs overestimate dynamical heating.

astro-ph.CO↗

arXiv2023

Swing Amplification and the Gaia Phase Spirals

We explore the interplay between in-plane and vertical dynamics in stellar discs within the framework of the shearing box approximation. Julian and Toomre used the shearing sheet to show that leading density waves are amplified as they swing into a trailing ones. We extend their formalism into the dimension perpendicular to the disc and obtain explicit solutions for the response of a disc to an impulsive, external excitation. An excitation that is is symmetric about the mid plane produces a density/breathing wave as well as two-armed phase spirals in the vertical phase space plane. On the other hand, an excitation that is antisymmetric about the mid plane leads to a bending wave and single-armed phase spirals. In either case, self-gravity plays a crucial role in driving the evolution of the disturbance and determining the amplitude and pitch angle of the ensuing spirals. We also show that when the disc is excited by a co-rotating cloud, it develops stationary phase spirals in the wake of the cloud. The results call into question simple kinematic arguments that have been used to determine the age of the phase spirals seen in the Gaia survey

astro-ph.GA↗

arXiv2022

Mapping Milky Way disk perturbations in stellar number density and vertical velocity using Gaia DR3

We have mapped the number density and mean vertical velocity of the Milky Way's stellar disk out to roughly two kiloparsecs from the Sun using Gaia Data Release 3 (DR3) and complementary photo-astrometric distance information from StarHorse. For the number counts, we carefully masked spatial regions that are compromised by open clusters, great distances, or dust extinction and used Gaussian processes to arrive at a smooth, non-parametric estimate for the underlying number density field. We find that the number density and velocity fields depart significantly from an axisymmetric and mirror-symmetric model. These departures, which include projections of the Gaia phase-space spiral, signal the presence of local disturbances in the disk. We identify two features that are present in both stellar number density and mean vertical velocity. One of these features appears to be associated with the Local Spiral Arm. It is most prominent at small heights and is largely symmetric across the mid-plane of the disk. The density and velocity field perturbations are phase-shifted by roughly a quarter wavelength, suggesting a breathing mode that is propagating in the direction of Galactic longitude $l\sim 270$ deg. The second feature is a gradient in the stellar number density and mean vertical velocity with respect to Galactocentric radius. This feature, which extends across the entire region of our analysis, may be associated with the extension of the Galactic warp into the Solar neighbourhood in combination with more localised bending waves.

astro-ph.GA↗

arXiv2022

Gaussian Process Model for the Local Stellar Velocity Field from Gaia Data Release 2

We model the local stellar velocity field using position and velocity measurements for 4M stars from the second data release of Gaia. We determine the components of the mean or bulk velocity in ~27k spatially-defined bins. Our assumption is that these quantities constitute a Gaussian process where the correlation between the bulk velocity at different locations is described by a simple covariance function or kernel. We use a sparse Gaussian process algorithm based on inducing points to construct a non-parametric, smooth, and differentiable model for the underlying velocity field. We estimate the Oort constants A, B, C, and K and find values in excellent agreement with previous results. Maps of the velocity field within 2 kpc of the Sun reveal complicated substructures, which provide clear evidence that the local disk is in a state of disequilibrium. We present the first 3D map of the divergence of the stellar velocity field and identify regions of the disk that may be undergoing compression and rarefaction.

astro-ph.GA↗

arXiv2022

Estimate of the Mass and Radial Profile of the Orphan-Chenab Stream's Dwarf Galaxy Progenitor Using MilkyWay@home

We fit the mass and radial profile of the Orphan-Chenab Stream's (OCS) dwarf galaxy progenitor by using turnoff stars in the Sloan Digital Sky Survey (SDSS) and the Dark Energy Camera (DEC) to constrain N-body simulations of the OCS progenitor falling into the Milky Way on the 1.5 PetaFLOPS MilkyWay@home distributed supercomputer. We infer the internal structure of the OCS's progenitor under the assumption that it was a spherically symmetric dwarf galaxy comprised of a stellar system embedded in an extended dark matter halo. We optimize the evolution time, the baryonic and dark matter scale radii, and the baryonic and dark matter masses of the progenitor using a differential evolution algorithm. The likelihood score for each set of parameters is determined by comparing the simulated tidal stream to the angular distribution of OCS stars observed in the sky. We fit the total mass of the OCS's progenitor to ($2.0\pm0.3$) $\times 10^7 M_\odot$ with a mass-to-light ratio of $γ=73.5\pm10.6$ and ($1.1\pm0.2$)$\times10^6M_{\odot}$ within 300 pc of its center. Within the progenitor's half-light radius, we estimate total a mass of ($4.0\pm1.0$)$\times10^5M_{\odot}$. We also fit the current sky position of the progenitor's remnant to be $(α,δ)=((166.0\pm0.9)^\circ,(-11.1\pm2.5)^\circ)$ and show that it is gravitationally unbound at the present time. The measured progenitor mass is on the low end of previous measurements, and if confirmed lowers the mass range of ultrafaint dwarf galaxies. Our optimization assumes a fixed Milky Way potential, OCS orbit, and radial profile for the progenitor, ignoring the impact of the Large Magellanic Cloud.

astro-ph.GA↗

arXiv2021

Inferring Time-Dependent Distribution Functions from Kinematic Snapshots

We propose a method for constructing the time-dependent phase space distribution function (DF) of a collisionless system from an isolated kinematic snapshot. In general, the problem of mapping a single snapshot to a time-dependent function is intractable. Here we assume a finite series representation of the DF, constructed from the spectrum of the system's Koopman operator. This reduces the original problem to one of mapping a kinematic snapshot to a discrete spectrum rather than to a time-dependent function. We implement this mapping with a convolutional neural network (CNN). The method is demonstrated on two example models: the quantum simple harmonic oscillator, and a self-gravitating isothermal plane. The latter system exhibits phase space spiral structure similar to that observed in Gaia Data Release 2.

astro-ph.GA↗

arXiv2021

The Stellar Distribution Function and Local Vertical Potential from Gaia DR2

We develop a novel method to simultaneously determine the vertical potential, force and stellar $z-v_z$ phase space distribution function (DF) in our local patch of the Galaxy. We assume that the Solar Neighborhood can be treated as a one-dimensional system in dynamical equilibrium and directly fit the number density in the $z-v_z$ plane to what we call the Rational Linear DF (RLDF) model. This model can be regarded as a continuous sum of isothermal DFs though it has only one more parameter than the isothermal model. We apply our method to a sample of giant stars from Gaia Data Release 2 and show that the RLDF provides an excellent fit to the data. The well-known phase space spiral emerges in the residual map of the $z-v_z$ plane. We use the best-fit potential to plot the residuals in terms of the frequency and angle of vertical oscillations and show that the spiral maps into a straight line. From its slope, we estimate that the phase spirals were generated by a perturbation $\sim540$ Myr years ago. We also determine the differential surface density as a function of vertical velocity dispersion, a.k.a. the vertical temperature distribution. The result is qualitatively similar to what was previously found for SDSS/SEGUE G dwarfs. Finally, we address parameter degeneracies and the validity of the 1D approximation. Particularly, the mid-plane density derived from a cold subsample, where the 1D approximation is more secure, is closer to literature values than that derived from the sample as a whole.

astro-ph.GA↗

arXiv2020

The Milky Way's Shell Structure Reveals the Time of a Radial Collision

We identify shell structures in the Milky Way for the first time. We find 2 shells in the Virgo Overdensity (VOD) region and 2 shells in the Hercules Aquila Cloud (HAC) region using Sloan Digital Sky Survey, Gaia, and LAMOST data. These shell stars are a subset of the substructure previously identified as the Virgo Radial Merger (VRM). Timing arguments for these shells indicate that their progenitor dwarf galaxy passed through the Galactic center 2.7 +/- 0.2 Gyr ago. Based on the time of collision, it is also possible that the VRM is related to the phenomenon that created phase-space spirals in the vertical motion of the disk and/or the Splash, and could have caused a burst of star formation in the inner disk. We analyze phase mixing in a collection of radial merger N-body simulations, and find that shell structure similar to that observed in Milky Way data disappears by 5 Gyr after collision with the Galactic center. The method used to calculate the merger time of the VRM was able to reliably recover the correct merger times for these simulations. Previous work supports the idea that the VRM and the Gaia Sausage/Gaia-Enceladus Merger are the same. However, the Gaia Sausage is widely believed to be 8--11 Gyr old. The disparate ages could be reconciled if the larger age is associated with an infall time when the progenitor crossed the virial radius; we do not constrain the time at which the progenitor became bound to the Milky Way. Alternatively, the Gaia Sausage could be younger than previously thought.

astro-ph.GA↗

arXiv2019

Eigenfunctions of Galactic Phase Space Spirals from Dynamic Mode Decomposition

We investigate the spatiotemporal structure of simulations of the homogeneous slab and isothermal plane models for the vertical motion in the Galactic disc. We use Dynamic Mode Decomposition (DMD) to compute eigenfunctions of the simulated distribution functions for both models, referred to as DMD modes. In the case of the homogeneous slab, we compare the DMD modes to the analytic normal modes of the system to evaluate the feasibility of DMD in collisionless self gravitating systems. This is followed by the isothermal plane model, where we focus on the effect of self gravity on phase mixing. We compute DMD modes of the system for varying relative dominance of mutual interaction and external potential, so as to study the corresponding variance in mode structure and lifetime. We find that there is a regime of relative dominance, at approximately $ 4:1 $ external potential to mutual interaction where the DMD modes are spirals in the $ (z,v_z) $ plane, and are nearly un-damped. This leads to the proposition that a system undergoing phase mixing in the presence of weak to moderate self gravity can have persisting spiral structure in the form of such modes. We then conclude with the conjecture that such a mechanism may be at work in the phase space spirals observed in Gaia Data Release 2, and that studying more complex simulations with DMD may aid in understanding both the timing and form of the perturbation that lead to the observed spirals.

astro-ph.GA↗

arXiv2018

Emergence of the Gaia Phase Space Spirals from Bending Waves

We discuss the physical mechanism by which pure vertical bending waves in a stellar disc evolve to form phase space spirals similar to those discovered by Antoja et al. ( arXiv:1804.10196) in Gaia Data Release 2. These spirals were found by projecting Solar Neighbourhood stars onto the $z-v_z$ plane. Faint spirals appear in the number density of stars projected onto the $z-v_z$ plane, which can be explained by a simple model for phase wrapping. More prominent spirals are seen when bins across the $z-v_z$ plane are coloured by median $v_R$ or $v_ϕ$. We use both toy model and fully self-consistent simulations to show that the spirals develop naturally from vertical bending oscillations of a stellar disc. The underlying physics follows from the observation that the vertical energy of a star (essentially, its "radius" in the $z-v_z$ plane) correlates with its angular momentum or, alternatively, guiding radius. Moreover, at fixed physical radius, the guiding radius determines the azimuthal velocity. Together, these properties imply the link between in-plane and vertical motion that lead directly to the Gaia spirals. We show that the cubic $R-z$ coupling term in the effective potential is crucial for understanding the morphology of the spirals. This suggests that phase space spirals might be a powerful probe of the Galactic potential. In addition, we argue that self-gravity is necessary to properly model the evolution of the bending waves and their attendant phase space spirals.

astro-ph.GA↗

arXiv2018

The large-scale structure of the halo of the Andromeda galaxy II. Hierarchical structure in the Pan-Andromeda Archaeological Survey

The Pan-Andromeda Archaeological Survey is a survey of $>400$ square degrees centered on the Andromeda (M31) and Triangulum (M33) galaxies that has provided the most extensive panorama of a $L_\star$ galaxy group to large projected galactocentric radii. Here, we collate and summarise the current status of our knowledge of the substructures in the stellar halo of M31, and discuss connections between these features. We estimate that the 13 most distinctive substructures were produced by at least 5 different accretion events, all in the last 3 or 4 Gyrs. We suggest that a few of the substructures furthest from M31 may be shells from a single accretion event. We calculate the luminosities of some prominent substructures for which previous estimates were not available, and we estimate the stellar mass budget of the outer halo of M31. We revisit the problem of quantifying the properties of a highly structured dataset; specifically, we use the OPTICS clustering algorithm to quantify the hierarchical structure of M31's stellar halo, and identify three new faint structures. M31's halo, in projection, appears to be dominated by two `mega-structures', that can be considered as the two most significant branches of a merger tree produced by breaking M31's stellar halo into smaller and smaller structures based on the stellar spatial clustering. We conclude that OPTICS is a powerful algorithm that could be used in any astronomical application involving the hierarchical clustering of points. The publication of this article coincides with the public release of all PAndAS data products.

astro-ph.GA↗