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Perturbations, TTVs & the (Un)reliability of Ephemerides of Kepler Planets

Fractional uncertainties quoted for orbital periods of the vast majority of planet candidates listed in recent Kepler catalogs are $<10^{-5}$, with values $\sim 10^{-6}$ (corresponding to 2 minutes per 4 years) being typical. These small uncertainties suggest ephemeris predictions for most Kepler planets are robust for decades to come. Tabulated periods list formal uncertainties in the mean times between midpoints of successive transits during the time interval in which transits were observed. However, transit timing variations (TTVs) produce errors in estimates of some planets’ orbital periods that need to be accounted for in certain dynamical investigations and ephemeris predictions. Periodic TTVs with timescales short compared to the interval of Kepler observations largely average out and do not produce significant errors in estimates of orbital periods. TTVs with timescales comparable to the interval of Kepler observations have been fit for dozens of Kepler planet candidates to estimate long-term average orbital periods (Holczer et al. 2016, ApJS 225, 9), and more detailed dynamical models have been used to estimate long-term average periods of a small number of well-studied planets. Most Kepler planets that show large TTVs are near mean-motion orbital resonances with other planets. The largest effect for planets moderately close to two-body resonances are due to rotation of the forced eccentricity vector by resonant perturbations; the timescale for this precession is typically short, so the variations tend to average out. Libration of planets locked in resonances typically occurs on timescales longer than the Kepler baseline, but few Kepler planets appear to be resonantly-locked. The more general but smaller (during the era of Kepler observations) effect is caused by secular precession of the planets' free eccentricities usually has a period much longer than the baseline of the Kepler observations, so it is not accounted for in estimates of mean periods or uncertainties. This precession causes a discrepancy between Kepler era mean orbital period and long-term mean orbital period can exist even for planets having TTVs that are too small to be observable during the epoch of Kepler observations.

Kepler↗
NASA NTRS2022

The Contribution of Planetary Period Oscillations Toward Circulation and Mass Loss in Saturn's Magnetosphere

Magnetic reconnection is a process during which magnetic energy is released as kinetic energy. It is considered a crucial driver of energy transport and mass loss within Saturn's magnetosphere. On longterm timescales, is thought to be predominantly driven by the rapid rotation of equatorially mass-loaded flux tubes (i.e., the Vasyliunas cycle), but there is some non-negligible driving from the solar wind as well (i.e., the Dungey cycle). In this study, we investigate an atmospheric driven phenomenon that modulates Saturn's magnetosphere every ∼10.6–10.8 hr, known as planetary period oscillations (PPOs), as an additional driver of magnetic reconnection at Saturn. Using an empirical model of PPO dynamics and Cassini magnetic field and plasma measurements, we find that PPO-driven magnetic reconnection is likely to occur in Saturn's magnetosphere, however, the occurrence of the phenomenon depends on temporally variable characteristics of the PPO systems and spatial asymmetries within Saturn's equatorial magnetosphere. Thus, it is not expected to be an on-going process. On year-long timescales, we find that PPOs are expected to be on par with the Dungey Cycle in driving circulation within Saturn's magnetosphere. However, on ∼1–2 weeks-long timescales, under specific conditions where PPO-driven reconnection is expected to be active, this phenomenon can become more significant than the Vasyliunas cycle, and thus dominate circulation within Saturn's magnetosphere. On year-long timescales, this process is estimated to remove upwards of ∼20% of the mass loaded into the magnetosphere by Enceladus.

O. Agiwal↗
NASA NTRS1989

The evolution of energetic particles and the emitted radiation in solar flares

The evolution of accelerated particle distributions in a magnetized plasma and the resulting radiation are calculated, and the results are applied to solar flares. To study the radiation on timescales of order the particle lifetimes, the evolution of the particle distribution is determined by the use of the Fokker-Planck equation including Coulomb collisions and magnetic mirroring. Analytic solution to the equations are obtained for limiting cases such as homogeneous injection in a homogeneous plasma, and for small pitch angle. These analytic solutions are then used to place constraints on flare parameters such as density, loop length, and the injection timescale for very short implusive solar flares. For general particle distributions in arbitrary magnetic field and background density, the equation is solved numerically. The relative timing of microwaves and X-rays during individual flares is investigated. A number of possible sources for excessive microwave flux are discussed including a flattening in the electron spectrum above hard X-ray energies, thermal synchrotron emission, and trapping of electron by converging magnetic fields. Over shorter timescales, the Fokker-Planck equation is solved numerically to calculate the temporal evolution of microwaves and X-rays from nonthermal thick target models. It is shown that magnetic trapping will not account for the observed correlation of microwaves of approximately 0.15 seconds behind X-rays in flares with rapid time variation, and thus higher energy electrons must be accelerated later than lower energy electrons.

Lu, Edward Tsang↗
NASA NTRS1990

Solar Response to Luminosity Variations

The connection between solar luminosity and magnetic fields is now well-established. Magnetic fields under the guise of sunspots and faculae enhance or suppress heat transfer through the solar surface, leading to changes in the total solar luminosity. This raises the question of the effect that such surface heat transfer perturbations have on the internal structure of the sun. The problem has been considered previously by Foukal and Spruit. Here, researchers generalize the calculation of Spruit, removing the assumption of a constant heat diffusivity coefficient by treating the full mixing length heat transfer expression. Further, they treat the surface conditions in a simpler manner, and show that the previous conclusions of Foukal and Spruit are unaffected by these modifications. The model shows that following the application of a step function emissivity change: a fraction 1 - D(sub 0) of the luminosity change relaxes away after approx. 50 days. This corresponds to the thermal diffusion time across the convection zone, adjusting to a value in correspondence with the surface change. In other words, the whole convection zone feels the perturbation on this timescale. The remaining fraction relaxes away on a timescale of 10 to the 5th power years, corresponding to the convective layer radiating away enough energy so that it can adjust to its new adiabat. These are the same results arrived at by Spruit and Foukal. For variations of sigma on timescales of 10 to 200 years, then, the only important relaxation is the 50 day one. If the amplitude of this relaxation is small, the luminosity follows the sigma variation.

Arendt, S.↗
NASA NTRS1992

Non-Hamiltonian perturbations of integrable systems and resonance trapping

This paper studies general, non-Hamiltonian perturbations of integrable systems with two degrees of freedom and derives conditions for temporary and permanent resonance trapping. The analysis involves a noncanonical transformation of variables near the resonant manifold and averaging with respect to the fast phase to investigate oscillatory behavior on the intermediate timescale. The resulting reduced system is Hamiltonian to leading order and permits, after averaging on the intermediate, or libration, timescale, a canonical transformation to action-angle variables in the oscillation zone. The final system so obtained reveals the possible existence of two- and three-dimensional invariant tori in the vicinity of the resonant manifold. An explicit divergence condition for general perturbations to be dissipative on the slow timescale follows from the analysis. An application of this approach to the problem of resonant trapping and escape is outlined for the restricted problem of three bodies subject to dissipative perturbations with a radial symmetry.

Ghil, M.↗
NASA NTRS1992

Long slit spectroscopy of NH2 in comets Halley, Wilson, and Nishikawa-Takamizawa-Tago

Long-slit spectra of comets Halley, Wilson and Nishikawa-Takamizawa-Tago were obtained with the 3.9 meter Anglo-Australian Telescope. Spectra of comets Halley and Wilson were obtained with the IPCS at a spectral resolution of 0.5 A and a spatial resolution of 10(exp 3) km. Spectra of comets Wilson and Nishikawa-Takamizawa-Tago were obtained with a CCD at a spectral resolution of 1.5 A and a spatial resolution of approximately 3 x 10(exp 3) km. Surface brightness profiles for NH2 were extracted from the long-slit spectra of each comet. The observed surface brightness profiles extend along the slit to approximately 6 x 10(exp 4) km from the nucleus in both sunward and tailward directions. By comparing surface distribution calculated from an appropriate coma model with observed surface brightness distributions, the photodissociation timescale of the parent molecule of NH2 can be inferred. The observed NH2 surface brightness profiles in all three comets compares well with a surface brightness profile calculated using the vectorial model, an NH3 photodissociation timescale of 7 x 10(exp 3) seconds, and an NH2 photodissociation timescale of 34,000 seconds.

Rettig, Terrence W.↗
NASA NTRS1991

UCSD High Energy X-ray Timing Experiment magnetic shield design and test results

Results are reported from an effort to define a passive magnetic field concept for the High Energy X-ray Timing Experiment (HEXTE), in the interest of reducing the detector-gain variations due to 0.5-1.0-sec timescale magnetic field variations. This will allow a sensitivity of the order of 1 percent of the HEXTE background. While aperture modulation and automatic gain control will minimize effects on timescales of tens of seconds and longer, passive magnetic shielding of the photomultiplier tubes will address 1-sec timescale variations due to aperture motions.

Rothschild, Richard E.↗
NASA NTRS1993

The effects of orbital and climatic variations on Martian surface heat flow

Large changes in the orbital elements of Mars on timescales of 10(exp 4) to 10(exp 6) years will cause widely varying climate, specifically surface temperatures, as a result of varying insolation. These surface temperature oscillations will produce subsurface thermal gradients which contribute to the total surface heat flux. We investigate the thermal behavior of the Martian regolith on orbital timescales and show that this climatological surface heat flux is spatially variable and contributes significantly to the total surface heat flux at many locations. We model the thermal behavior of the Martian regolith by calculating the mean annual surface temperatures for each epoch (spaced 1000 years apart to resolve orbital variations) for the past 200,000 years at a chosen location on the surface. These temperatures are used as a boundary condition for the deeper regolith and subsurface temperature oscillation are then computed. The surface climatological heat flux due to past climate changes can then be found from the temperature gradient between the surface and about 150 m depth (a fraction of the thermal skin depth on these timescales). This method provides a fairly accurate determination of the climatological heat flow component at a point; however, this method is computationally time consuming and cannot be applied to all points on the globe. To map the spatial variations in the surface heat flow we recognize that the subsurface temperature structure will be largely dominated by the most recent surface temperature oscillations. In fact, the climate component of the surface heat flow will be approximately proportional to the magnitude of the most recent surface temperature change. By calculating surface temperatures at all points globally for the present epoch and an appropriate past epoch, and combining these results with a series of more precise calculations described above, we estimate the global distribution of climatological surface heat flow.

Mellon, Michael T.↗
NASA NTRS1992

The application of artificial intelligence to astronomical scheduling problems

Efficient utilization of expensive space- and ground-based observatories is an important goal for the astronomical community; the cost of modern observing facilities is enormous, and the available observing time is much less than the demand from astronomers around the world. The complexity and variety of scheduling constraints and goals has led several groups to investigate how artificial intelligence (AI) techniques might help solve these kinds of problems. The earliest and most successful of these projects was started at Space Telescope Science Institute in 1987 and has led to the development of the Spike scheduling system to support the scheduling of Hubble Space Telescope (HST). The aim of Spike at STScI is to allocate observations to timescales of days to a week observing all scheduling constraints and maximizing preferences that help ensure that observations are made at optimal times. Spike has been in use operationally for HST since shortly after the observatory was launched in Apr. 1990. Although developed specifically for HST scheduling, Spike was carefully designed to provide a general framework for similar (activity-based) scheduling problems. In particular, the tasks to be scheduled are defined in the system in general terms, and no assumptions about the scheduling timescale are built in. The mechanisms for describing, combining, and propagating temporal and other constraints and preferences are quite general. The success of this approach has been demonstrated by the application of Spike to the scheduling of other satellite observatories: changes to the system are required only in the specific constraints that apply, and not in the framework itself. In particular, the Spike framework is sufficiently flexible to handle both long-term and short-term scheduling, on timescales of years down to minutes or less. This talk will discuss recent progress made in scheduling search techniques, the lessons learned from early HST operations, the application of Spike to other problem domains, and plans for the future evolution of the system.

Johnston, Mark D.↗
NASA NTRS1994

SMM observations of gamma-ray transients. 3: A search for a broadened, redshifted positron annihilation line from the direction of the Galactic center

We have searched for 1980-1988 Solar Maximum Mission gamma-ray spectrometer data for transient emission on timescales from hours to approximately 12 days of broad gamma-ray lines at energies approximately 400 keV, which were reported by the High Energy Astronomy Observatory (HEAO) 1 and SIGMA experiments from two sources lying toward the Galactic center. The lines have been interpreted as the product of the annihilation of positrons in pair plasmas surrounding the black hole candidate 1E 1740.7-2942 and the X-ray binary 1H 1822-371. Our results from a combined exposure of approximately 1.5 x 10(exp 7)s provide no convincing evidence for transient emission of this line on any timescale between approximately 9 hr and approximately 1 yr. Our 3 sigma upper limits on the line flux during approximately 12 day intervals are characteristically 4.8 x 10(exp -3) photon/sq cm/s, while for approximately 1 day intervals our 3 sigma upper limits are characteristically 4.9 x 10(exp -3) photon/sq cm/s. These results imply a duty cycle of less than 1.3% for the transient line measured from 1H 1822-371 during a approximately 3 week interval in 1977 by HEAO 1, and a duty cycle of less than or = 0.8% for the transient line detected in 1990 and 1992 from 1E 1740.7-2942 on approximately 1 day timescales by SIGMA.

Harris, Michael J.↗
NASA NTRS1994

Using FU Orionis outbursts to constrain self-regulated protostellar disk models

One-dimensional, convective, vertical structure models and one dimensional time-dependent, radial diffusion models are combined to create a self-consistent picture in which FU Orionis outbursts occur in young stellar objects (YSOs) as the result of a large-scale, self-regulated, thermal ionization instability in the surrounding protostellar accretion disk. Although active accretion disks have long been postulated to be ubiqitous among low-mass YSOs, few constraints have until now been imposed on physical conditions in these disks. By fitting the results of time-dependent disk models to observed timescales of FU Orionis events, we estimate the magnitude of the effective viscous stress in the inner disk (r approximately less than 1 AU) to be, in accordance with an ad hoc 'alpha' prescription, the product of the local sound speed, pressure scale height, and an efficiency factor alpha of 10(exp -4) where hydrogen is neutral and 10(exp 3) where hydrogen is ionized. We hypothesize that all YSOs receive infall onto their outer disks which is steady (or slowly declining with time) and that FU Orionis outbursts are self-regulated, disk outbursts which occur only in systems which transport matter inward at a rate sufficiently high to cause hydrogen to be ionized in the inner disk. We estimate a critical mass flux of dm(sub crit)/dt = 5 x 10(exp 7) solar mass/yr independent of the magnitude of alpha for systems with one solar mass, three solar radius central objects. Infall accretion rates in the range of dm(sub in)/dt = 1-10) x 10(exp -6) solar mass/yr produce observed FU Orionis timescales consistent with estimates of spherical molecular cloud core collapse rates. Modeled ionization fronts are typically initiated near the inner edge of the disk and propogate out to a distance of several tens of stellar radii. Beyond this region, the disk transports mass steadily inward at the supplied constant infall rate. Mass flowing through the innermost disk annulus is equal to dm(sub in)/dt only in a time-averaged sense and is regulated by the ionization of hydrogen in the inner disk such that long intervals (approximately 1000 yr) of low-mass flux: (1-30) x 10(exp -8) solar mass/yr are punctuated by short intervals (approximately 100 yr) of high-mass flux: (1-30) x 10(exp -5) solar mass/yr. Timescales and mass fluxes derived for quiescent and outburst stages are consistent with estimates from observations of T Tauri and FU Orionis systems, respectively.

Bell, K. R.↗
NASA NTRS1995

Chromospheric variations in main-sequence stars

The fluxes in passbands 0.1 nm wide and centered on the Ca II H and K emission cores have been monitored in 111 stars of spectral type F2-M2 on or near the main sequence in a continuation of an observing program started by O. C. Wilson. Most of the measurements began in 1966, with observations scheduled monthly until 1980, when observations were schedueld sevral times per week. The records, with a long-term precision of about 1.5%, display fluctuations that can be idntified with variations on timescales similar to the 11 yr cycle of solar activity as well as axial rotation, and the growth and decay of emitting regions. We present the records of chromospheric emission and general conclusions about variations in surface magnetic activity on timescales greater than 1 yr but less than a few decades. The results for stars of spectral type G0-K5 V indicate a pattern of change in rotation and chromospheric activity on an evolutionary timescale, in which (1) young stars exhibit high average levels of activity, rapid rotation rates, no Maunder minimum phase and rarely display a smooth, cyclic variation; (2) stars of intermediate age (approximately 1-2 Gyr for 1 solar mass) have moderate levels of activity and rotation rates, and occasional smooth cycles; and (3) stars as old as the Sun and older have slower rotation rates, lower activity levels and smooth cycles with occasional Maunder minimum-phases.

Baliunas, S. L.↗
NASA NTRS1995

Particle chaos and pitch angle scattering

Pitch angle scattering is a factor that helps determine the dawn-to-dusk current, controls particle energization, and it has also been used as a remote probe of the current sheet structure. Previous studies have interpreted their results under the exception that randomization will be greatest when the ratio of the two timescales of motion (gyration parallel to and perpendicular to the current sheet) is closet to one. Recently, the average expotential divergence rate (AEDR) has been calculated for particle motion in a hyperbolic current sheet (Chen, 1992). It is claimed that this AEDR measures the degree of chaos and therefore may be thought to measure the randomization. In contrast to previous expectations, the AEDR is not maximized when Kappa is approximately equal to 1 but instead increases with decreasing Kappa. Also contrary to previous expectations, the AEDR is dependent upon the parameter b(sub z). In response to the challenge to previous expectations that has been raised by this calculation of the AEDR, we have investigated the dependence of a measure of particle pitch angle scattering on both the parameters Kappa and b(sub z). We find that, as was previously expected, particle pitch angle scattering is maximized near Kappa = 1 provided that Kappa/b(sub z) greater than 1. In the opposite regime, Kappa/b(sub z) less than 1, we find that particle pitch angle scattering is still largest when the two timescales are equal, but the ratio of the timescales is proportional to b(sub z). In this second regime, particle pitch angle scattering is not due to randomization, but is instead due to a systematic pitch angle change. This result shows that particle pitch angle scattering need not be due to randomization and indicates how a measure of pitch angle scattering can exhibit a different behavior than a measure of chaos.

Burkhart, G. R.↗
NASA NTRS1996

Short-Term Chromospheric Variability in alpha Tauri (K5 III): Results from IUE Time Series Observations

We evaluate time series observations of chromospheric lines (Mg II, Mg I, and C II) for the K giant alpha Tau obtained using the IUE LWP camera at high dispersion. These observations cover a time span of about 2 weeks in 1994 February-March and were designed to resolve variations occurring within hours, days, and weeks. We consider the observational results in relation to theoretical acoustic heating models, motivated by the fact that alpha Tau may exhibit a basal (i.e., minimum) level of chromospheric activity. The data reveal flux variations between the extremes of 8% in Mg II h+k and 15% in each emission component. These variations occur on timescales as short as 8 hr but not on timescales longer than approx.3 days. For the h and k components, flux variations occurring on a timescale as short as 1.5 hr are also found. These changes are often not correlated (and are sometimes even anticorrelated), leading to remarkable differences in the h/k ratios. We argue that these results are consistent with the presence of strong acoustic shocks, which can lead to variable Mg II line emission when only a small number of strong shocks are propagating through the atmosphere. We deduce the electron density in the C II lambda 2325 line formation region to be log(base e) of N. approx. equals 9.0, in agreement with previous studies. Our data provide evidence that the Mg II basal flux limit for K giants might be a factor of 4 higher than suggested by Rutten et al.

Cuntz, Manfred↗
NASA NTRS1996

X-Ray Spectral Variability in NGC 7469

We present analyses of two Ginga observations and two observations from the ROSAT database of NGC 7469, focusing on the spectral variability observed on timescales of days and longer. During the 1988 Ginga observation, the hardness ratio (8-21 keV/3.4-5.7 keV) increased significantly as the total flux decreased by 30%. As the spectrum is well fit by the reflection model and since the spectra variability dominates the higher energy band, this could be explained by either a variation in the power law index or in the effective covering fraction of the reflecting material. This ambiguity is inherent in reflection modeling of Ginga spectra from moderate flux Seyfert 1 galaxies. Assuming that the power law index did not change, we find that the reflected flux is consistent with being constant, suggesting that much of the reflecting material may be located more than 3 light-days from the continuum source with the molecular torus being a plausible site. This scenario is also supported by the report of a narrow rather than broad iron K-alpha line in the ASCA data by Guainazzi et al. NGC 7469 was faint during the 1989 Ginga observation, but variability was observed with doubling timescale of 5 hr, and the spectrum was harder. A reflection component could not be constrained, and the change in the spectrum could be explained by an increase in neutral absorption. The brighter of two ROSAT spectra was significantly softer, and in both spectra there was evidence of spectral complexity, as has been previously reported by Turner, George, & Mushotzky and Brandt et al. The spectrum could be fit by a variety of two-component models, including a warm absorber model, an ionized disk model, and a thermal model with single-component blackbody spectrum, but joint fitting of the 1988 average Ginga spectrum and the nonsimultaneous ROSAT spectra favored thermal models, and other models required an anomalously high reflection ratio. This model is supported by the observation of a soft excess component and the lack of ionized absorption edges in the ASCA spectrum by Guainazzi et al. The long-term spectral variability could be explained by relative variability between the power-law and soft excess component normalizations, perhaps implying that hard X-ray reprocessing in thermal material does not dominate on long timescales.

Leighly, Karen↗
NASA NTRS1999

Linkages Between Multiscale Global Sea Surface Temperature Change and Precipitation Variabilities in the US

A growing number of evidence indicates that there are coherent patterns of variability in sea surface temperature (SST) anomaly not only at interannual timescales, but also at decadal-to-inter-decadal timescale and beyond. The multi-scale variabilities of SST anomaly have shown great impacts on climate. In this work, we analyze multiple timescales contained in the globally averaged SST anomaly with and their possible relationship with the summer and winter rainfall in the United States over the past four decades.

Lau, K. M.↗
NASA NTRS1997

Torque Reversal and Spin-Down of the Accretion-Powered Pulsar 4U 1626-67

Over 5 yr of hard X-ray (20-60 keV) monitoring of the 7.66 s accretion-powered pulsar 4U 1626-67 with the Compton Gamma Ray Observatory/BATSE large-area detectors has revealed that the neutron star is now steadily spinning down, in marked contrast to the steady spin-up and spin-down torques differ by only 15% with the neutron star spin changing on a timescale |v/v| approximately equals 5000 yr in both states. The current spin-down rate is itself decreasing on a timescale |v/v| approximately equals 26 yr. The long-term timing history shows small-amplitude variations on a 4000 day timescale, which are probably due to variations in the mass transfer rate. The pulsed 20-60 keV emission from 4U 1626-67 is well-fitted by a power-law spectrum with photon index gamma = 4.9 and a typical pulsed intensity of 1.5 x 10(exp -10) ergs cm (exp -2)s(exp -1). The low count rates with BATSE prohibited us from constraining the reported 42 minute binary orbit, but we can rule out long-period orbits in the range 2 days < or = P(orb) < or = 900 days. We compare the long-term torque behavior of 4U 1626-67 to other disk-fed accreting pulsars and discuss the implications of our results for the various theories of magnetic accretion torques. The abrupt change in the sign of the torque is difficult to reconcile with the extremely smooth spin-down now observed. The strength of the torque noise in 4U 1626-67, approximately 10(exp -22) Hz(exp 2)s(exp -2) Hz(exp -1), is the smallest ever measured for an accreting X-ray pulsar, and it is comparable to the timing noise seen in young radio pulsars. We close by pointing out that the core temperature and external torque (the two parameters potentially relevant to internal sources of timing noise) of an accreting neutron star are also comparable to those of young radio pulsars.

Chakrabarty, Deepto L.↗
NASA NTRS1998

Tidal Disruption of Strengthless Rubble Piles: A Dimensional Analysis

A relatively simple prescription for estimating the number of debris clumps (n) that form after a catastrophic tidal disruption event is presented. Following the breakup event, it is assumed that the individual debris particles follow keplerian orbits about the planet until the debris' gravitational contraction timescale (t(sub c)) becomes shorter than its orbital spreading timescale (t(sub s)). When the two timescales become comparable, self-gravity breaks up the debris train into n = L/D clumps, which is the debris length/diameter ratio at that instant. The clumps subsequently orbit the planet independent of each other. The predicted number of clumps n is in good agreement with more sophisticated N-body treatments of tidal breakup for parabolic encounters, and the dependence of n upon the progenitor's density as well as its orbit is also mapped out for hyperbolic encounters. These findings may be used to further constrain both the orbits and densities of the tidally disrupted bodies that struck Callisto and Ganymede. A cursory analysis shows that the Gomul and Gipul crater chains on Callisto, which have the greatest number of craters among the known chains, were formed by projectiles having comet-like densities estimated at rho(sub o) < 1 gm/cc.

Hahn, Joseph M.↗