arXiv subjects

Jeremy Goodman

Publications and source records attributed to Jeremy Goodman.

At least 37 records · Page 2Linked to original sources

arXiv2022

Observation of axisymmetric standard magnetorotational instability in the laboratory

We report the first direct evidence for the axisymmetric standard magnetorotational instability (SMRI) from a combined experimental and numerical study of a magnetized liquid-metal shear flow in a Taylor-Couette cell with independently rotating and electrically conducting end caps. When a uniform vertical magnetic field $B_i$ is applied along the rotation axis, the measured radial magnetic field $B_r$ on the inner cylinder increases linearly with a small magnetic Reynolds number $Rm$ due to the magnetization of the residue Ekman circulation. Onset of the axisymmetric SMRI is identified from the nonlinear increase of $B_r$ beyond a critical $Rm$ in both experiments and nonlinear numerical simulations. The axisymmetric SMRI exists only at sufficiently large $Rm$ and intermediate $B_i$, a feature consistent with theoretical predictions. Our simulations further show that the axisymmetric SMRI causes the velocity and magnetic fields to contribute an outward flux of axial angular momentum in the bulk region, just as it should in accretion disks.

astro-ph.IM↗

arXiv2022

Identification of a non-axisymmetric mode in laboratory experiments searching for standard magnetorotational instability

The standard magnetorotational instability (SMRI) is a promising mechanism for turbulence and rapid accretion in astrophysical disks. It is a magnetohydrodynamic (MHD) instability that destabilizes otherwise hydrodynamically stable disk flow. Due to its microscopic nature at astronomical distances and stringent requirements in laboratory experiments, SMRI has remained unconfirmed since its proposal, despite its astrophysical importance. Here we report a nonaxisymmetric MHD instability in a modified Taylor-Couette experiment. To search for SMRI, a uniform magnetic field is imposed along the rotation axis of a swirling liquid-metal flow. The instability initially grows exponentially, becoming prominent only for sufficient flow shear and moderate magnetic field. These conditions for instability are qualitatively consistent with SMRI, but at magnetic Reynolds numbers below the predictions of linear analyses with periodic axial boundaries. Three-dimensional numerical simulations, however, reproduce the observed instability, indicating that it grows linearly from the primary axisymmetric flow modified by the applied magnetic field.

physics.plasm-ph↗

arXiv2021

Tidally distorted barytropes and their Roche limits, with application to WASP-12b

The hot Jupiter WASP-12b has been found to be on a decaying 1.09-day orbit. The mean density of the planet inferred from transit and radial-velocity data is near its Roche limit; just how near depends on the planet's uncertain internal structure. There is also spectroscopic evidence of mass loss. We accurately calculate the Roche density on the assumption of a synchronously rotating $n=1$ polytrope, and find this to be only $15-20\%$ below the observational estimates for the mean density. We discuss the implied shape of the planet, its lifetime before complete disruption, and its current rate of mass loss based on our improved tidal model. The present mass-loss rate is at least as sensitive to the opacity and temperature profiles of the planet's atmosphere as to its internal structure, however.

astro-ph.EP↗

arXiv2021

Knowledge from Probability

We give a probabilistic analysis of inductive knowledge and belief and explore its predictions concerning knowledge about the future, about laws of nature, and about the values of inexactly measured quantities. The analysis combines a theory of knowledge and belief formulated in terms of relations of comparative normality with a probabilistic reduction of those relations. It predicts that only highly probable propositions are believed, and that many widely held principles of belief-revision fail.

cs.LO↗

arXiv2021

Kepler's Goat Herd: An Exact Solution to Kepler's Equation for Elliptical Orbits

A fundamental relation in celestial mechanics is Kepler's equation, linking an orbit's mean anomaly to its eccentric anomaly and eccentricity. Being transcendental, the equation cannot be directly solved for eccentric anomaly by conventional treatments; much work has been devoted to approximate methods. Here, we give an explicit integral solution, utilizing methods recently applied to the "geometric goat problem" and to the dynamics of spherical collapse. The solution is given as a ratio of contour integrals; these can be efficiently computed via numerical integration for arbitrary eccentricities. The method is found to be highly accurate in practice, with our C++ implementation outperforming conventional root-finding and series approaches by a factor greater than two.

physics.comp-ph↗

arXiv2021

Evolution of Retrograde Orbiters in an AGN Disk

AGN disks have been proposed as promising locations for the mergers of stellar mass black hole binaries (BBHs). Much recent work has been done on this merger channel, but the majority focuses on stellar mass black holes (BHs) orbiting in the prograde direction. Little work has been done to examine the impact of retrograde orbiters (ROs) on the formation and mergers of BBHs in AGN disks. Quantifying the retrograde contribution is important, since roughly half of all orbiters should initially be on retrograde orbits when the disk forms. We perform an analytic calculation of the evolution of ROs in an AGN disk. Because this evolution could cause the orbits of ROs to cross those of prograde BBHs, we derive the collision rate between a given RO and a given BBH orbiting in the prograde direction. In the examples given here, ROs in the inner region of the disk experience a rapid decrease in the semimajor axis of their orbits while also becoming highly eccentric in less than a million years. This rapid orbital evolution could lead to extreme mass ratio inspirals detectable by the Laser Interferometer Space Antenna. The collision rates of our example ROs with prograde BBHs in the migration trap depend strongly on the volume of the inner radiation-pressure-dominated region which depends on the mass of the supermassive black hole (SMBH). Rates are lowest for larger mass SMBHs, which dominate the AGN merger channel, suggesting that merger rates for this channel may not be significantly altered by ROs.

astro-ph.HE↗

arXiv2020

The role of FUV Pumping in exciting the [Oi] lines in Protostellar Disks and Winds

We use Cloudy to re-examine excitation of [Oi] 6300 A and [Oi] 5577 A in the X-ray driven photo-evaporative wind models of Owen and collaborators, and in more recent magnetothermal models by Wang et al. We find that, at the measured accretion luminosities, the FUV radiation would populate the upper levels of the oxygen atom which would eventually contribute to the [Oi] lines. FUV pumping competes with collisions as an excitation mechanism of the [Oi] lines, and they each originate from a distinct region in the protostellar disk environment depending on the specifics of the hydrodynamical model that the simulation was based on. Consequently, the line strengths and shapes of [Oi] 6300 A and[Oi] 5577 A would be affected by the inclusion of FUV pumping in the radiation transport simulations.

astro-ph.SR↗

arXiv2018

Global Simulations of Protoplanetary Disk Outflows with Coupled Non-ideal Magnetohydrodynamics and Consistent Thermochemistry

Magnetized winds may be important in dispersing protoplanetary disks and influencing planet formation. We carry out global full magnetohydrodynamic simulations in axisymmetry, coupled with ray-tracing radiative transfer, consistent thermochemistry, and non-ideal MHD diffusivities. Magnetized models lacking EUV photons ($hν>13.6\ \mathrm{eV}$) feature warm molecular outflows that have typical poloidal speeds $\gtrsim 4\ \mathrm{km\ s}^{-1}$. When the magnetization is sufficient to drive accretion rates $\sim 10^{-8}\ M_\odot\ \mathrm{yr}^{-1}$, the wind mass-loss rate is comparable. Such outflows are driven not centrifugally but by the pressure of toroidal magnetic fields produced by bending the poloidal field. Both the accretion and outflow rates increase with the poloidal field energy density, the former almost linearly. The mass-loss rate is also strongly affected by ionization due to UV and X-ray radiation near the wind base. Adding EUV irradiation to the system heats, ionizes, and accelerates the part of the outflow nearest the symmetry axis, but reduces the overall mass-loss rate by exerting pressure on the wind base. Most of our models are non-turbulent, but some with reduced dust abundance and therefore higher ionization fractions exhibit magnetorotational instabilities near the base of the wind.

astro-ph.EP↗

arXiv2018

Understanding WASP-12b

The orbital period of the hot Jupiter WASP-12b is apparently changing. We study whether this reflects orbital decay due to tidal dissipation in the star, or apsidal precession of a slightly eccentric orbit. In the latter case, a third body or other perturbation would be needed to sustain the eccentricity against tidal dissipation in the planet itself. We have analyzed several such perturbative scenarios, but none is satisfactory. Most likely therefore, the orbit really is decaying. If this is due to a dynamical tide, then WASP-12 should be a subgiant without a convective core as Weinberg et al. (2017) have suggested. We have modeled the star with the MESA code. While no model fits all of the observational constraints, including the luminosity implied by the GAIA DR2 distance, main-sequence models are less discrepant than subgiant ones.

astro-ph.EP↗

arXiv2018

Binary companions of evolved stars in APOGEE DR14: Orbital circularization

Short-period binary star systems dissipate orbital energy through tidal interactions that lead to tighter, more circular orbits. When at least one star in a binary has evolved off of the main sequence, orbital circularization occurs for longer-period (~100 day) systems. Past work by (Verbunt & Phinney 1995) has shown that the orbital parameters and the circularization periods of a small sample of binary stars with evolved-star members can be understood within the context of standard tidal circularization theory. Using a sample of binaries with subgiant, giant, and red clump star members that is nearly an order of magnitude larger, we reexamine predictions for tidal circularization of binary stars with evolved members. We confirm that systems predicted by equilibrium-tide theory to have circular orbits generally have negligible measured eccentricities. The circularization period is correlated with the surface gravity (i.e. size) of the evolved member, indicating that the circularization timescale must be shorter than the evolutionary timescale along the giant branch. A few exceptions to the conclusions above are mentioned in the discussion: Some of these exceptions are likely systems in which the spectrum of the secondary biases the radial velocity measurements, but four appear to be genuine, short-period, moderate-eccentricity systems.

astro-ph.SR↗

arXiv2018

The linear theory of tidally excited spiral density waves: application to CV and circumplanetary disks

We revisit linear tidal excitation of spiral density waves in the disks of cataclysmic variables (CVs), focusing on scalings with orbital Mach number in order to bridge the gap between numerical simulations and real systems. If an inner Lindblad resonance (ILR) lies within the disk, ingoing waves are robustly excited, and the angular-momentum flux they carry is independent of Mach number. But in most CVs, the ILR lies outside the disk. The wave flux and its scaling with Mach number are then very sensitive to conditions near the disk edge. If the temperature and sound speed vanish there, excitation tends to be exponentially suppressed. If the Mach number remains finite in the outer parts but the radial and vertical density scale lengths become comparable due to subkeplerian rotation, resonance can occur with acoustic-cutoff and stratification frequencies. These previously neglected resonances excite waves, but the Mach-number scaling remains very steep if the radial scale length decreases gradually. The scaling can be less strong - algebraic rather than exponential - if there are sharp changes in surface density at finite sound speed. Shocks excited by streamline-crossing or by the impact of the stream from the companion are unlikely to be important for the angular-momentum budget, at least in quiescence. Our results may also apply to circumplanetary disks, where Mach numbers are likely lower than in CVs.

astro-ph.SR↗

arXiv2016

Numerical simulations of the Princeton magneto-rotational instability experiment with conducting axial boundaries

We investigate numerically the Princeton magneto-rotational instability (MRI) experiment and the effect of conducting axial boundaries or endcaps. MRI is identified and found to reach a much higher saturation than for insulating endcaps. This is probably due to stronger driving of the base flow by the magnetically rather than viscously coupled boundaries. Although the computations are necessarily limited to lower Reynolds numbers ($\Re$) than their experimental counterparts, it appears that the saturation level becomes independent of $\Re$ when $\Re$ is sufficiently large, whereas it has been found previously to decrease roughly as $\Re^{-1/4}$ with insulating endcaps. The much higher saturation levels will allow for the first positive detection of MRI beyond its theoretical and numerical predictions.

physics.flu-dyn↗

arXiv2015

Magneto-thermal Disk Wind from Protoplanetary Disks

Global evolution and dispersal of protoplanetary disks (PPDs) is governed by disk angular momentum transport and mass-loss processes. Recent numerical studies suggest that angular momentum transport in the inner region of PPDs is largely driven by magnetized disk wind, yet the wind mass-loss rate remains unconstrained. On the other hand, disk mass loss has conventionally been attributed to photoevaporation, where external heating on the disk surface drives a thermal wind. We unify the two scenarios by developing a 1D model of magnetized disk winds with a simple treatment of thermodynamics as a proxy for external heating. The wind properties largely depend on 1) the magnetic field strength at the wind base, characterized by the poloidal Alfvén speed $v_{Ap}$, 2) the sound speed $c_s$ near the wind base, and 3) how rapidly poloidal field lines diverge (achieve $R^{-2}$ scaling). When $v_{Ap}\gg c_s$, corotation is enforced near the wind base, resulting in centrifugal acceleration. Otherwise, the wind is accelerated mainly by the pressure of the toroidal magnetic field. In both cases, the dominant role played by magnetic forces likely yields wind outflow rates that well exceed purely hydrodynamical mechanisms. For typical PPD accretion-rate and wind-launching conditions, we expect $v_{Ap}$ to be comparable to $c_s$ at the wind base. The resulting wind is heavily loaded, with total wind mass loss rate likely reaching a considerable fraction of wind-driven accretion rate. Implications for modeling global disk evolution and planet formation are also discussed.

astro-ph.EP↗

arXiv2015

On obliquely magnetized and differentially rotating stars

We investigate the interaction of differential rotation and a misaligned magnetic field. The incompressible magnetohydrodynamic equations are solved numerically for a free-decay problem. In the kinematic limit, differential rotation annihilates the non-axisymmetric field on a timescale proportional to the cube root of magnetic Reynolds number ($Rm$), as predicted by Rädler. Nonlinearly, the outcome depends upon the initial energy in the non-axisymmetric part of the field. Sufficiently weak fields approach axisymmetry as in the kinematic limit; some differential rotation survives across magnetic surfaces, at least on intermediate timescales. Stronger fields enforce uniform rotation and remain non-axisymmetric. The initial field strength that divides these two regimes does not follow the scaling $Rm^{-1/3}$ predicted by quasi-kinematic arguments, perhaps because our $Rm$ is never sufficiently large or because of reconnection. We discuss the possible relevance of these results to tidal synchronization and tidal heating of close binary stars, particularly double white dwarfs.

astro-ph.SR↗

arXiv2013

A method for the microlensed flux variance of QSOs

A fast and practical method is described for calculating the microlensed flux variance of an arbitrary source by uncorrelated stars. The required inputs are the mean convergence and shear due to the smoothed potential of the lensing galaxy, the stellar mass function, and the absolute square of the Fourier transform of the surface brightness in the source plane. The mathematical approach follows previous authors but has been generalized, streamlined, and implemented in publicly available code. Examples of its application are given for Dexter and Agol's inhomogeneous-disk models as well as the usual gaussian sources. Since the quantity calculated is a second moment of the magnification, it is only logarithmically sensitive to the sizes of very compact sources. However, for the inferred sizes of actual QSOs, it has some discriminatory power and may lend itself to simple statistical tests. At the very least, it should be useful for testing the convergence of microlensing simulations.

astro-ph.CO↗

arXiv2012

A New Way to Conserve Total Energy for Eulerian Hydrodynamic Simulations with Self-Gravity

We propose a new method to conserve the total energy to round-off error in grid-based codes for hydrodynamic simulations with self-gravity. A formula for the energy flux due to the work done by the the self-gravitational force is given, so the change in total energy can be written in conservative form. Numerical experiments with the code Athena show that the total energy is indeed conserved with our new algorithm and the new algorithm is second order accurate. We have performed a set of tests that show the numerical errors in the traditional, non-conservative algorithm can affect the dynamics of the system. The new algorithm only requires one extra solution of the Poisson equation, as compared to the traditional algorithm which includes self-gravity as a source term. If the Poisson solver takes a negligible fraction of the total simulation time, such as when FFTs are used, the new algorithm is almost as efficient as the original method. This new algorithm is useful in Eulerian hydrodynamic simulations with self-gravity, especially when results are sensitive to small energy errors, as for radiation pressure dominated flow.

astro-ph.IM↗

arXiv2012

Ruling Out Bosonic Repulsive Dark Matter in Thermal Equilibrium

Self-interacting dark matter (SIDM), especially bosonic, has been considered a promising candidate to replace cold dark matter (CDM) as it resolves some of the problems associated with CDM. Here, we rule out the possibility that dark matter is a repulsive boson in thermal equilibrium. We develop the model first proposed by Goodman (2000) and derive the equation of state at finite temperature. Isothermal spherical halo models indicate a Bose-Einstein condensed core surrounded by a non-degenerate envelope, with an abrupt density drop marking the boundary between the two phases. Comparing this feature with observed rotation curves constrains the interaction strength of our model's DM particle, and Bullet Cluster measurements constrain the scattering cross section. Both ultimately can be cast as constraints on the particle's mass. We find these two constraints cannot be satisfied simultaneously in any realistic halo model---and hence dark matter cannot be a repulsive boson in thermal equilibrium. It is still left open that DM may be a repulsive boson provided it is not in thermal equilibrium; this requires that the mass of the particle be significantly less than a millivolt.

astro-ph.CO↗

arXiv2012

Stability of quasi-Keplerian shear flow in a laboratory experiment

Context: Subcritical transition to turbulence has been proposed as a source of turbulent viscosity required for the associated angular momentum transport for fast accretion in Keplerian disks. Previously cited laboratory experiments in supporting this hypothesis were performed either in a different type of flow than Keplerian or without quantitative measurements of angular momentum transport and mean flow profile, and all of them appear to suffer from Ekman effects, secondary flows induced by nonoptimal axial boundary conditions. Such Ekman effects are expected to be absent from astronomical disks, which probably have stress-free vertical boundaries unless strongly magnetized. Aims: To quantify angular momentum transport due to subcritical hydrodynamic turbulence, if exists, in a quasi-Keplerian flow with minimized Ekman effects. Methods: We perform a local measurement of the azimuthal--radial component of the Reynolds stress tensor in a novel laboratory apparatus where Ekman effects are minimized by flexible control of axial boundary conditions. Results: We find significant Ekman effects on angular momentum transport due to nonoptimal axial boundary conditions in quasi-Keplerian flows. With the optimal control of Ekman effects, no statistically meaningful angular momentum transport is detected in such flows at Reynolds number up to two millions. Conclusions: Either a subcritical transition does not occur, or, if a subcritical transition does occur, the associated radial transport of angular momentum in optimized quasi-Keplerian laboratory flows is too small to directly support the hypothesis that subcritical hydrodynamic turbulence is responsible for accretion in astrophysical disks. Possible limitations in applying laboratory results to astrophysical disks due to experimental geometry are discussed.

astro-ph.IM↗