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Two new long-period giant planets from the McDonald Observatory planet search and two stars with long-period radial velocity signals related to stellar activity cycles

We report the detection of two new long-period giant planets orbiting the stars HD 95872 and HD 162004 (ψ{sup 1} Dra B) by the McDonald Observatory planet search. The planet HD 95872b has a minimum mass of 4.6 M{sub Jup} and an orbital semimajor axis of 5.2 AU. The giant planet ψ{sup 1} Dra Bb has a minimum mass of 1.5 M{sub Jup} and an orbital semimajor axis of 4.4 AU. Both of these planets qualify as Jupiter analogs. These results are based on over one and a half decades of precise radial velocity (RV) measurements collected by our program using the McDonald Observatory Tull Coude spectrograph at the 2.7 m Harlan J. Smith Telescope. In the case of ψ{sup 1} Dra B we also detect a long-term nonlinear trend in our data that indicates the presence of an additional giant planet, similar to the Jupiter–Saturn pair. The primary of the binary star system, ψ{sup 1} Dra A, exhibits a very large amplitude RV variation due to another stellar companion. We detect this additional member using speckle imaging. We also report two cases—HD 10086 and HD 102870 (β Virginis)—of significant RV variation consistent with the presence of a planet, but that are probably caused by stellar activity, rather than reflexive Keplerian motion. These two cases stress the importance of monitoring the magnetic activity level of a target star, as long-term activity cycles can mimic the presence of a Jupiter-analog planet.

79 ASTRONOMY AND ASTROPHYSICS↗

Hydrogen-like atom in a superstrong magnetic field: Photon emission and relativistic energy level shift

Following our previous work, additional arguments are presented that in superstrong magnetic fields B ≫ (Zα){sup 2}B{sub 0}, B{sub 0} = m{sup 2}c{sup 3}/eħ ≈ 4.41 × 10{sup 13} G, the Dirac equation and the Schrödinger equation for an electron in the nucleus field following from it become spatially one-dimensional with the only z coordinate along the magnetic field, “Dirac” spinors become two-component, while the 2 × 2 matrices operate in the {0; 3} subspace. Based on the obtained solution of the Dirac equation and the known solution of the “onedimensional” Schrödinger equation by ordinary QED methods extrapolated to the {0; 3} subspace, the probability of photon emission by a “one-dimensional” hydrogen-like atom is calculated, which, for example, for the Lyman-alpha line differs almost twice from the probability in the “three-dimensional” case. Similarly, despite the coincidence of nonrelativistic energy levels, the calculated relativistic corrections of the order of (Zα){sup 4} substantially differ from corrections in the absence of a magnetic field. A conclusion is made that, by analyzing the hydrogen emission spectrum and emission spectra at all, we can judge in principle about the presence or absence of superstrong magnetic fields in the vicinity of magnetars (neutron stars and probably brown dwarfs). Possible prospects of applying the proposed method for calculations of multielectron atoms are pointed out and the possibility of a more reliable determination of the presence of superstrong magnetic fields in magnetars by this method is considered.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Relativistic Disk Reflection in the Neutron Star X-Ray BinaryXTE J1709-267 with NuSTAR

We perform the first reflection study of the soft X-ray transient and Type 1 burst source XTE J1709-267 using NuSTAR observations during its 2016 June outburst. There was an increase in flux near the end of the observations, which corresponds to an increase from ∼0.04 L {sub Edd} to ∼0.06 L {sub Edd} assuming a distance of 8.5 kpc. We have separately examined spectra from the low- and high-flux intervals, which are soft and show evidence of a broad Fe K line. Fits to these intervals with relativistic disk reflection models have revealed an inner-disk radius of 13.8{sub −1.8}{sup +3.0} R{sub g} (where R{sub g}=GM/c{sup 2}) for the low-flux spectrum and 23.4{sub −5.4}{sup +15.6} R{sub g} for the high-flux spectrum at the 90% confidence level. The disk is likely truncated by a boundary layer surrounding the neutron star (NS) or the magnetosphere. Based on the measured luminosity and the accretion efficiency for a disk around an NS, we estimate that the theoretically expected size for the boundary layer would be ∼0.9--1.1 R{sub g} from the NS’s surface, which can be increased by spin or viscosity effects. Another plausible scenario is that the disk could be truncated by the magnetosphere. We place a conservative upper limit on the strength of the magnetic field at the poles (assuming a{sub ∗}=0 and M{sub NS}=1.4M{sub ⊙}) of B⩽0.75−3.70×10{sup 9} G, though X-ray pulsations have not been detected from this source.

79 ASTRONOMY AND ASTROPHYSICS↗

Fantastic Striations and Where to Find Them: The Origin of Magnetically Aligned Striations in Interstellar Clouds

Thin, magnetically aligned striations of relatively moderate contrast with the background are commonly observed in both atomic and molecular clouds. They are also prominent in MHD simulations with turbulent converging shocks. The simulated striations develop within a dense, stagnated sheet in the midplane of the post-shock region where magnetically induced converging flows collide. We show analytically that the secondary flows are an inevitable consequence of the jump conditions of oblique MHD shocks. They produce the stagnated, sheet-like sub-layer through a secondary shock when, roughly speaking, the Alfvénic speed in the primary converging flows is supersonic, a condition that is relatively easy to satisfy in interstellar clouds. The dense sub-layer is naturally threaded by a strong magnetic field that lies close to the plane of the sub-layer. The substantial magnetic field makes the sheet highly anisotropic, which is the key to the striation formation. Specifically, perturbations of the primary inflow that vary spatially perpendicular to the magnetic field can easily roll up the sheet around the field lines without bending them, creating corrugations that appear as magnetically aligned striations in column density maps. On the other hand, perturbations that vary spatially along the field lines curve the sub-layer and alter its orientation relative to the magnetic field locally, seeding special locations that become slanted overdense filaments and prestellar cores through enhanced mass accumulation along field lines. In our scenario, the dense sub-layer, which is unique to magnetized oblique shocks, is the birthplace for both magnetically aligned diffuse striations and massive star-forming structures.

79 ASTRONOMY AND ASTROPHYSICS↗

ELECTRODYNAMICS OF AXISYMMETRIC PULSAR MAGNETOSPHERE WITH ELECTRON-POSITRON DISCHARGE: A NUMERICAL EXPERIMENT

We present the first self-consistent global simulations of pulsar magnetospheres with operating e {sup ±} discharge. We focus on the simple configuration of an aligned or anti-aligned rotator. The star is spun up from a zero (vacuum) state to a high angular velocity, and we follow the coupled evolution of its external electromagnetic field and plasma particles using the ''particle-in-cell'' method. A plasma magnetosphere begins to form through the extraction of particles from the star; these particles are accelerated by the rotation-induced electric field, producing curvature radiation and igniting e {sup ±} discharge. We follow the system evolution for several revolution periods, longer than required to reach a quasi-steady state. Our numerical experiment puts to test previous ideas for the plasma flow and gaps in the pulsar magnetosphere. We first consider rotators capable of producing pairs out to the light cylinder through photon-photon collisions. We find that their magnetospheres are similar to the previously obtained force-free solutions with a Y-shaped current sheet. The magnetosphere continually ejects e {sup ±} pairs and ions. Pair creation is sustained by a strong electric field along the current sheet. We observe powerful curvature and synchrotron emission from the current sheet, consistent with Fermi observations of gamma-ray pulsars. We then study pulsars that can only create pairs in the strong-field region near the neutron star, well inside the light cylinder. We find that both aligned and anti-aligned rotators relax to the ''dead'' state with suppressed pair creation and electric currents, regardless of the discharge voltage.

79 ASTRONOMY AND ASTROPHYSICS↗

A Comparison between Physics-based and Polytropic MHD Models for Stellar Coronae and Stellar Winds of Solar Analogs

The development of the Zeeman–Doppler Imaging (ZDI) technique has provided synoptic observations of surface magnetic fields of low-mass stars. This led the stellar astrophysics community to adopt modeling techniques that have been used in solar physics using solar magnetograms. However, many of these techniques have been neglected by the solar community due to their failure to reproduce solar observations. Nevertheless, some of these techniques are still used to simulate the coronae and winds of solar analogs. Here we present a comparative study between two MHD models for the solar corona and solar wind. The first type of model is a polytropic wind model, and the second is the physics-based AWSOM model. We show that while the AWSOM model consistently reproduces many solar observations, the polytropic model fails to reproduce many of them, and in the cases where it does, its solutions are unphysical. Our recommendation is that polytropic models, which are used to estimate mass-loss rates and other parameters of solar analogs, must first be calibrated with solar observations. Alternatively, these models can be calibrated with models that capture more detailed physics of the solar corona (such as the AWSOM model) and that can reproduce solar observations in a consistent manner. Without such a calibration, the results of the polytropic models cannot be validated, but they can be wrongly used by others.

79 ASTRONOMY AND ASTROPHYSICS↗

Limits on surface gravities of Kepler planet-candidate host stars from non-detection of solar-like oscillations

We present a novel method for estimating lower-limit surface gravities (log g) of Kepler targets whose data do not allow the detection of solar-like oscillations. The method is tested using an ensemble of solar-type stars observed in the context of the Kepler Asteroseismic Science Consortium. We then proceed to estimate lower-limit log g for a cohort of Kepler solar-type planet-candidate host stars with no detected oscillations. Limits on fundamental stellar properties, as provided by this work, are likely to be useful in the characterization of the corresponding candidate planetary systems. Furthermore, an important byproduct of the current work is the confirmation that amplitudes of solar-like oscillations are suppressed in stars with increased levels of surface magnetic activity.

79 ASTRONOMY AND ASTROPHYSICS↗

Final Technical Report for DOE DE-FG02-05ER54831 "Laboratory Studies of Dynamos."

Laboratory Studies of Dynamos: Executive Summary. The self-generation of magnetic fields by astrophysical bodies like planets, stars, accretion disks, galaxies, and even galaxy clusters arises due to a mechanism referred to as a homogeneous dynamo. It is quite simple to demonstrate the generation of a magnetic fi eld from a rotating copper disk coupled with a coil of wire, a device known as the homopolar dynamo. The device works like a magnetic fi eld ampli er with a feedback circuit: the differential rotation of a metal disk past an infinitesimally small seed magnetic field induces currents in the disk which, when coupled to a coil winding, can amplify the field until it becomes strong enough to slow the rotation of the disk. What is remarkable is that the same type of circuit may be achieved in a flowing conducting fluid such as a liquid metal in the case of planetary dynamos or a plasma in the case of astrophysical dynamos. The complexity of describing planetary and stellar dynamos despite their ubiquity and the plethora of observational data from the Earth and the Sun motivates the demonstration of a laboratory homogenous dynamo. To create a homogenous dynamo, one first needs a su fficiently large, fast flow of a highly conducting fluid that the velocity shear in the fluid can bend magnetic field lines. With a high Rm-flow, the magnetic fi eld can be ampli ed by the stretching action provided by di fferential rotation. The other critical ingredient is a flow geometry that provides feedback so that the ampli ed eld reinforces the initial in nitesimal seed field - a mechanism that recreates the feedback provided by the coil of wire in the homopolar dynamo. In the Madison Dynamo Experiment, this combination of magnetic ampli cation and feedback is feasible in the simple geometry of two counter-rotating helical vortices in a 1 meter-diameter spherical vessel lled with liquid sodium. For an optimal helical pitch of the flow the threshold for exciting a dynamo is predicted from laminar flow modeling to be at peak flow speeds of 5 m/s. Liquid metals tend to have viscosities similar to that of water yielding inviscid flows. Whereas the timescale for the dynamo instability is on the resistive dissipation time, the timescale for hydrodynamic instability of the shear layer is quite short meaning that the shear layer required to generate the magnetic eld is broken up by Kelvin-Helmholtz instabilities. The eddies generated by large-scale flow drive instabilities at progressively smaller scale giving rise to a cascade of turbulent eddies driven at the largest scale of the experiment. The major contribution of the Madison Dynamo Experiment has been quantifying the role this turbulence plays in the generation of magnetic elds. Overall, the Madison Dynamo Experiment has now operated for about 1 decade and carried out experiments related to magnetic fi eld generation by turbulent flows of liquid metal. The principle thrust of research and indeed the main scienti fic outcomes are related to how turbulent flows create and transport magnetic fi elds.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

POPULATIONS OF YOUNG STELLAR OBJECTS IN NEARBY MOLECULAR CLOUDS

We develop a new method for identifying young stellar objects (YSOs) from star-forming regions using the photometry data from Spitzer's c2d Legacy Project. The aim is to obtain YSO lists as complete as possible for studying statistical properties such as the star formation rate (SFR) and lifetimes of YSOs in different evolutionary stages. The largest obstacle in identifying YSOs comes from background galaxies with similar spectral energy distributions to YSOs. Traditionally, selected color-color and color-magnitude criteria are used to separate YSOs and galaxies. However, since there is no obvious boundary between YSOs and galaxies in color-color diagrams and color-magnitude diagrams (CMDs), those criteria may exclude faint YSOs near the boundary. In this paper, we separate the YSOs and galaxies in a multi-dimensional (multi-D) magnitude space, which is equivalent to using all variations of CMDs simultaneously. Comparing sources from molecular clouds to Spitzer's SWIRE data, which have a negligible amount of YSOs, we can naturally identify YSO candidates (YSOc) located outside of the galaxy-populated regions in the multi-D space. In the five c2d surveyed clouds, we select 322 new YSOc and miss/exclude 33 YSOc compared to Evans et al., and this results in 1313 YSOc in total. As a result, SFR increases 28% correspondingly, but the lifetimes of YSOs in different evolutionary stages remain unchanged. Compared to theories by Krumholz and McKee, our derived SFR suggests that star formation at a large scale is dominated by supersonic turbulence rather than magnetic fields. Furthermore, we identify seven new very low luminosity objects.

79 ASTRONOMY AND ASTROPHYSICS↗

ON THE TIDAL ORIGIN OF HOT JUPITER STELLAR OBLIQUITY TRENDS

It is debated whether the two hot Jupiter populations—those on orbits misaligned from their host star's spin axis and those well-aligned—result from two migration channels or from two tidal realignment regimes. Here I demonstrate that equilibrium tides raised by a planet on its star can account for three observed spin-orbit alignment trends: the aligned orbits of hot Jupiters orbiting cool stars, the planetary mass cut-off for retrograde planets, and the stratification by planet mass of cool host stars' rotation frequencies. The first trend can be caused by strong versus weak magnetic braking (the Kraft break), rather than realignment of the star's convective envelope versus the entire star. The second trend can result from a small effective stellar moment of inertia participating in the tidal realignment in hot stars, enabling massive retrograde planets to partially realign to become prograde. The third trend is attributable to higher-mass planets more effectively counteracting braking to spin up their stars. Both hot and cool stars require a small effective stellar moment of inertia participating in the tidal realignment, e.g., an outer layer weakly coupled to the interior. I demonstrate via Monte Carlo that this model can match the observed trends and distributions of sky-projected misalignments and stellar rotation frequencies. I discuss implications for inferring hot Jupiter migration mechanisms from obliquities, emphasizing that even hot stars do not constitute a pristine sample.

79 ASTRONOMY AND ASTROPHYSICS↗

HATS-18B: AN EXTREME SHORT-PERIOD MASSIVE TRANSITING PLANET SPINNING UP ITS STAR

We report the discovery by the HATSouth network of HATS-18b: a 1.980±0.077 M{sub J}, 1.337{sub −0.049}{sup +0.102} R{sub J} planet in a 0.8378 day orbit, around a solar analog star (mass 1.037±0.047 M{sub ⊙} and radius 1.020{sub −0.031}{sup +0.057} R{sub ⊙}) with V=14.067±0.040 mag. The high planet mass, combined with its short orbital period, implies strong tidal coupling between the planetary orbit and the star. In fact, given its inferred age, HATS-18 shows evidence of significant tidal spin up, which together with WASP-19 (a very similar system) allows us to constrain the tidal quality factor for Sun-like stars to be in the range of 6.5≲log{sub 10}(Q{sup ∗}/k{sub 2})≲7 even after allowing for extremely pessimistic model uncertainties. In addition, the HATS-18 system is among the best systems (and often the best system) for testing a multitude of star–planet interactions, be they gravitational, magnetic, or radiative, as well as planet formation and migration theories.

79 ASTRONOMY AND ASTROPHYSICS↗

GIANT X-RAY BUMP IN GRB 121027A: EVIDENCE FOR FALL-BACK DISK ACCRETION

A particularly interesting discovery in observations of GRB 121027A is that of a giant X-ray bump detected by the Swift/X-Ray Telescope. The X-ray afterglow re-brightens sharply at {approx}10{sup 3} s after the trigger by more than two orders of magnitude in less than 200 s. This X-ray bump lasts for more than 10{sup 4} s. It is quite different from typical X-ray flares. In this Letter we propose a fall-back accretion model to interpret this X-ray bump within the context of the collapse of a massive star for a long-duration gamma-ray burst. The required fall-back radius of {approx}3.5 Multiplication-Sign 10{sup 10} cm and mass of {approx}0.9-2.6 M{sub Sun} imply that a significant part of the helium envelope should survive through the mass loss during the last stage of the massive progenitor of GRB 121027A.

79 ASTRONOMY AND ASTROPHYSICS↗

GLOBAL SIMULATIONS OF MAGNETOROTATIONAL INSTABILITY IN THE COLLAPSED CORE OF A MASSIVE STAR

We performed the first global numerical simulations of magnetorotational instability from a sub-magnetar-class seed magnetic field in core-collapse supernovae. As a result of axisymmetric ideal MHD simulations, we found that the magnetic field is greatly amplified to magnetar-class strength. In the saturation phase, a substantial part of the core is dominated by turbulence, and the magnetic field possesses dominant large-scale components, comparable to the size of a proto-neutron star. A pattern of coherent channel flows, which generally appears during the exponential growth phase in previous local simulations, is not observed in our global simulations. While the approximate convergence in the exponential growth rate is attained by increasing spatial resolution, that of the saturation magnetic field is not achieved due to still large numerical diffusion. Although the effect of the magnetic field on the dynamics is found to be mild, a simulation with a high enough resolution might result in a larger impact.

79 ASTRONOMY AND ASTROPHYSICS↗

NuSTAR DISCOVERY OF A CYCLOTRON LINE IN KS 1947+300

We present a spectral analysis of three simultaneous Nuclear Spectroscopy Telescope Array and Swift/XRT observations of the transient Be-neutron star binary KS 1947+300 taken during its outburst in 2013/2014. These broadband observations were supported by Swift/XRT monitoring snapshots every three days, which we use to study the evolution of the spectrum over the outburst. We find strong changes of the power-law photon index, which shows a weak trend of softening with increasing X-ray flux. The neutron star shows very strong pulsations with a period of P ≈ 18.8 s. The 0.8-79 keV broadband spectrum can be described by a power law with an exponential cutoff and a blackbody component at low energies. During the second observation we detect a cyclotron resonant scattering feature at 12.5 keV, which is absent in the phase-averaged spectra of observations 1 and 3. Pulse phase-resolved spectroscopy reveals that the strength of the feature changes strongly with pulse phase and is most prominent during the broad minimum of the pulse profile. At the same phases the line also becomes visible in the first and third observation at the same energy. This discovery implies that KS 1947+300 has a magnetic field strength of B ≈ 1.1 × 10{sup 12}(1 + z) G, which is at the lower end of known cyclotron line sources.

79 ASTRONOMY AND ASTROPHYSICS↗

RADIAL TRANSPORT OF LARGE-SCALE MAGNETIC FIELDS IN ACCRETION DISKS. II. RELAXATION TO STEADY STATES

We study the time evolution of a large-scale magnetic flux threading an accretion disk. The induction equation of the mean poloidal field is solved under the standard viscous disk model. Magnetic flux evolution is controlled by two timescales: one is the timescale of the inward advection of the magnetic flux, τ{sub adv}. This is induced by the dragging of the flux by the accreting gas. The other is the outward diffusion timescale of the magnetic flux τ{sub dif}. We consider diffusion due to the Ohmic resistivity. These timescales can be significantly different from the disk viscous timescale τ{sub disk}. The behaviors of the magnetic flux evolution are quite different depending on the magnitude relationship of the timescales τ{sub adv}, τ{sub dif}, and τ{sub disk}. The most interesting phenomena occur when τ{sub adv} << τ{sub dif}, τ{sub disk}. In such a case, the magnetic flux distribution approaches a quasi-steady profile much faster than the viscous evolution of the gas disk, and the magnetic flux has also been tightly bundled to the inner part of the disk. In the inner part, although the poloidal magnetic field becomes much stronger than the interstellar magnetic field, the field strength is limited to the maximum value that is analytically given by our previous work. We also find a condition for the initial large magnetic flux, which is a fossil of the magnetic field dragging during the early phase of star formation that survives for a duration in which significant gas disk evolution proceeds.

79 ASTRONOMY AND ASTROPHYSICS↗

The Mysterious Dimmings of the T Tauri Star V1334 Tau

We present the discovery of two extended ∼0.12 mag dimming events of the weak-lined T Tauri star V1334. The start of the first event was missed but came to an end in late 2003, and the second began in 2009 February, and continues as of 2016 November. Since the egress of the current event has not yet been observed, it suggests a period of >13 years if this event is periodic. Spectroscopic observations suggest the presence of a small inner disk, although the spectral energy distribution shows no infrared excess. We explore the possibility that the dimming events are caused by an orbiting body (e.g., a disk warp or dust trap), enhanced disk winds, hydrodynamical fluctuations of the inner disk, or a significant increase in the magnetic field flux at the surface of the star. We also find a ∼0.32 day periodic photometric signal that persists throughout the 2009 dimming which appears to not be due to ellipsoidal variations from a close stellar companion. High-precision photometric observations of V1334 Tau during K2 campaign 13, combined with simultaneous photometric and spectroscopic observations from the ground, will provide crucial information about the photometric variability and its origin.

79 ASTRONOMY AND ASTROPHYSICS↗

UNVEILING A NETWORK OF PARALLEL FILAMENTS IN THE INFRARED DARK CLOUD G14.225-0.506

We present the results of combined NH{sub 3} (1,1) and (2,2) line emission observed with the Very Large Array and the Effelsberg 100 m telescope of the infrared dark cloud G14.225-0.506. The NH{sub 3} emission reveals a network of filaments constituting two hub-filament systems. Hubs are associated with gas of rotational temperature T{sub rot} {approx} 15 K, non-thermal velocity dispersion {sigma}{sub NT} {approx} 1 km s{sup -1}, and exhibit signs of star formation, while filaments appear to be more quiescent (T{sub rot} {approx} 11 K and {sigma}{sub NT} {approx} 0.6 km s{sup -1}). Filaments are parallel in projection and distributed mainly along two directions, at P.A. {approx} 10 Degree-Sign and 60 Degree-Sign , and appear to be coherent in velocity. The averaged projected separation between adjacent filaments is between 0.5 pc and 1 pc, and the mean width of filaments is 0.12 pc. Cores within filaments are separated by {approx}0.33 {+-} 0.09 pc, which is consistent with the predicted fragmentation of an isothermal gas cylinder due to the {sup s}ausage{sup -}type instability. The network of parallel filaments observed in G14.225-0.506 is consistent with the gravitational instability of a thin gas layer threaded by magnetic fields. Overall, our data suggest that magnetic fields might play an important role in the alignment of filaments, and polarization measurements in the entire cloud would lend further support to this scenario.

79 ASTRONOMY AND ASTROPHYSICS↗

Spin and magnetism of white dwarfs

The magnetism and rotation of white dwarf (WD) stars are investigated in relation to a hydromagnetic dynamo operating in the progenitor during shell burning phases. The downward pumping of angular momentum in the convective envelope, in combination with the absorption of a planet or tidal spin-up from a binary companion, can trigger strong dynamo action near the core–envelope boundary. Several arguments point to the outer core as the source for a magnetic field in the WD remnant: the outer third of a ∼0.55 M{sub ⊙} WD is processed during the shell burning phase(s) of the progenitor; the escape of magnetic helicity through the envelope mediates the growth of (compensating) helicity in the core, as is needed to maintain a stable magnetic field in the remnant; and the intense radiation flux at the core boundary facilitates magnetic buoyancy within a relatively thick tachocline layer. The helicity flux into the growing core is driven by a dynamical imbalance with a latitude-dependent rotational stress. The magnetic field deposited in an isolated massive WD is concentrated in an outer shell of mass ≲0.1 M{sub ⊙} and can reach ∼10 MG. A buried toroidal field experiences moderate ohmic decay above an age ∼0.3 Gyr, which may lead to growth or decay of the external magnetic field. The final WD spin period is related to a critical spin rate below which magnetic activity shuts off and core and envelope decouple; it generally sits in the range of hours to days. WD periods ranging up to a year are possible if the envelope re-expands following a late thermal pulse.

79 ASTRONOMY AND ASTROPHYSICS↗