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At least 235 records · Page 13

The Long-term Light Curves of X-ray Binaries Contain Simultaneous Periodic and Random Components

LMC X-3 and Cyg X-2 show large amplitude X-ray fluctuations that have been attributed to a warped accretion disk. Cyg X-3 displays high amplitude, apparently non-periodic oscillations. We reanalyze these systems using RXTE ASM data and time-frequency decomposition techniques. We find that the long-term variations in Cyg X-2 can be completely characterized by excursions whose durations are integer multiples of the orbital period, including one essentially identical to the reported "period" of 78 days. Cyg X-3 can be characterized in terms of integer multiples of a 71-day fundamental period unrelated to the 4.8 day orbital period, but suggestively close to the approximately equal to greater than 60 day reported precession period of the relativistic jet inferred from recent radio observations. The long-term excursions of LMC X-3 are related to each other by rational fractions, suggesting the characteristic time scale is 10.594 days, shorter than any observed excursion to date. We explore the phase space evolution of the light curves using a natural embedding and find that all three systems possess two rotation centers that organize the phase space trajectories, one of low luminosity and the other of high luminosity. The implications of this repeatable behavior on generic models of accretion disk dynamics and mass transfer variability are explored.

White, Nicholas E.↗

MULTI-OBJECTIVE REINFORCEMENT LEARNING FOR LOW-THRUST TRANSFER DESIGN BETWEEN LIBRATION POINT ORBITS

Multi-Reward Proximal Policy Optimization (MRPPO) is a multi-objective reinforcement learning algorithm used to construct low-thrust transfers between periodic orbits in multi-body systems. Previous implementations of MRPPO have relied on a predefined reference transfer to successfully train each policy. In this paper, an algorithmic modification labeled the ‘moving reference’, is introduced to autonomously construct these reference trajectories during training. With this modification, MRPPO is used to recover various low-thrust transfers between two periodic orbits in the Earth-Moon circular restricted three-body problem to solve a multi-objective optimization problem. These results are then compared with the solutions recovered via a gradient descent optimization scheme to validate the performance of MRPPO with the moving reference modification.

Christopher J. Sullivan↗

MULTI-OBJECTIVE REINFORCEMENT LEARNING FOR LOW-THRUST TRANSFER DESIGN BETWEEN LIBRATION POINT ORBITS

Multi-Reward Proximal Policy Optimization (MRPPO) is a multi-objective reinforcement learning algorithm used to construct low-thrust transfers between periodic orbits in multi-body systems. Previous implementations of MRPPO have relied on a predefined reference transfer to successfully train each policy. In this paper, an algorithmic modification labeled the ‘moving reference’, is introduced to autonomously construct these reference trajectories during training. With this modification, MRPPO is used to recover various low-thrust transfers between two periodic orbits in the Earth-Moon circular restricted three-body problem to solve a multi-objective optimization problem. These results are then compared with the solutions recovered via a gradient descent optimization scheme to validate the performance of MRPPO with the moving reference modification

Christopher John Sullivan↗

Superorbital Periodic Modulation in Wind-Accretion High-Mass X-Ray Binaries from Swift Burst Alert Telescope Observations

We report the discovery using data from the Swift-Burst Alert Telescope (BAT) of superorbital modulation in the wind-accretion supergiant high-mass X-ray binaries 4U 1909+07 (= X 1908+075), IGR J16418−4532, and IGR J16479−4514. Together with already known superorbital periodicities in 2S 0114+650 and IGR J16493−4348, the systems exhibit a monotonic relationship between superorbital and orbital periods. These systems include both supergiant fast X-ray transients and classical supergiant systems, and have a range of inclination angles. This suggests an underlying physical mechanism which is connected to the orbital period. In addition to these sources with clear detections of superorbital periods, IGR J16393−4643 (= AX J16390.4−4642) is identified as a system that may have superorbital modulation due to the coincidence of low-amplitude peaks in power spectra derived from BAT, Rossi X-Ray Timing Explorer Proportional Counter Array, and International Gamma-Ray Astrophysics Laboratory light curves. 1E 1145.1−6141 may also be worthy of further attention due to the amount of low-frequency modulation of its light curve. However, we find that the presence of superorbital modulation is not a universal feature of wind-accretion supergiant X-ray binaries.

superorbital↗

A disk about PSR 1957+20?

Although the PSR 1957+20 binary system displays a large orbital period derivative, radio observations of the ablated wind from the companion reveal a low free electron density. If the orbital period derivative provides a true indication of the mass loss rate, then the ablated material must be overwhelmingly neutral or largely confined to a narrow region about the orbital plane. However, the companion's high orbital velocity, the observed turbulence in the eclipsing wind, and the energy density of the pulsar's spin-down radiation conspire to make a neutral evaporate unlikely. Radio, optical and infrared observations are shown to suggest that the companion to PSR 1957+20 is bloated, perhaps approaching the size of its Roche lobe. The wind off the companion is most probably a low velocity flow which does not travel far from the orbital plane.

Fruchter, A. S.↗

The Shape of Long Outbursts in U Gem Type Dwarf Novae from AAVSO Data

We search the American Association of Variable Star Observers (AAVSO) archives of the two best studied dwarf novae in an attempt to find light curves for long out bursts that are extremely well-characterized. The systems are U Gem and S8 Cyg. Our goal is to search for embedded precursors such as those that have been found recently in the high fidelity Kepler data for superoutbursts of some members of the 8U UMa subclass of dwarf novae. For the vast majority of AAV80 data, the combination of low data cadence and large errors associated with individual measurements precludes one from making any strong statement about the shape of the long outbursts. However, for a small number of outbursts, extensive long term monitoring with digital photometry yields high fidelity light curves. We report the finding of embedded precursors in two of three candidate long outbursts. This reinforces van Paradijs' finding that long outbursts in dwarf novae above the period gap and superoutbursts in systems below the period gap constitute a unified class. The thermal-tidal instability to account for superoutbursts in the SU UMa stars predicts embedded precursors only for short orbital period dwarf novae, therefore the presence of embedded precursors in long orbital period systems - U Gem and SS Cyg - argues for a more general mechanism to explain long outbursts.

Cannizzo, John K.↗

Unexpected Short-period Variability in Dwarf Carbon Stars from the Zwicky Transient Facility

Dwarf carbon (dC) stars, main-sequence stars showing carbon molecular bands, are enriched by mass transfer from a previous asymptotic-giant-branch (AGB) companion, which has since evolved to a white dwarf. While previous studies have found radial-velocity variations for large samples of dCs, there are still relatively few dC orbital periods in the literature and no dC eclipsing binaries have yet been found. Here, we analyze photometric light curves from DR5 of the Zwicky Transient Facility for a sample of 944 dC stars. From these light curves, we identify 34 periodically variable dC stars. Remarkably, of the periodic dCs, 82% have periods less than two days. We also provide spectroscopic follow-up for four of these periodic systems, measuring radial velocity variations in three of them. Short-period dCs are almost certainly post-common-envelope binary systems, because the periodicity is most likely related to the orbital period, with tidally locked rotation and photometric modulation on the dC either from spots or from ellipsoidal variations. We discuss evolutionary scenarios that these binaries may have taken to accrete sufficient C-rich material while avoiding truncation of the thermally pulsing AGB phase needed to provide such material in the first place. We compare these dCs to common-envelope models to show that dC stars probably cannot accrete enough C-rich material during the common-envelope phase, suggesting another mechanism like wind-Roche lobe overflow is necessary. The periodic dCs in this paper represent a prime sample for spectroscopic follow-up and for comparison to future models of wind-Roche lobe overflow mass transfer.

79 ASTRONOMY AND ASTROPHYSICS↗

The inter-outburst behavior of cataclysmic variables

Existing International Ultraviolet Explorer (IUE) and American Association of Variable Star Observers (AAVSO) archive data was used to accomplish a large scale study of what happens to the ultraviolet flux of accretion disk systems during the quiescent intervals between outbursts and how it relates to the preceding outburst characteristics of amplitude and width. The data sample involved multiple IUE observations for 16 dwarf novae and 8 novae along with existing optical coverage. Results indicate that most systems show correlated ultraviolet (UV) flux behavior with interoutburst phase, with 60 percent of the dwarf novae and 50 percent of the novae having decreasing flux trends while 33 percent of the dwarf novae and 38 percent of the novae show rising UV flux during the quiescent interval. All of the dwarf novae with decreasing UV fluxes at 1475A have orbital periods longer than 4.4 hours, while all (except BV Cen) with flat or rising fluxes at 1475A have orbital periods less than two hours. There are not widespread correlations of the UV fluxes with the amplitude of the preceding outburst and no correlations with the width of the outburst. From a small sample (7) that have relatively large quiescent V magnitude changes between the IUE observations, most show a strong correlation between the UV and optical continuum. Interpretation of the results is complicated by not being able to determine how much the white dwarf contributes to the ultraviolet flux. However, it is now evident that noticeable changes are occurring in the hot zones in accreting systems long after the outburst, and not only for systems that are dominated by the white dwarf. Whether these differences are due to different outburst mechanisms or to changes on white dwarfs which provide varying contributions to the UV flux remains to be determined.

Szkody, Paula↗

Two Intermediate-mass Transiting Brown Dwarfs from the TESS Mission

We report the discovery of two intermediate-mass transiting brown dwarfs (BDs), TOI-569b and TOI-1406b, from NASA’s Transiting Exoplanet Survey Satellite mission. TOI-569b has an orbital period of P = 6.55604 ± 0.00016 days, a mass of M {sub b} = 64.1 ± 1.9 M{sub J}, and a radius of R {sub b} = 0.75 ± 0.02 R{sub J}. Its host star, TOI-569, has a mass of M {sub ⋆} = 1.21 ± 0.05 M{sub ⊙}, a radius of R {sub ⋆} = 1.47 ± 0.03 R{sub ⊙}, [Fe/H]=+0.29±0.09 dex, and an effective temperature of T {sub eff} = 5768 ± 110 K. TOI-1406b has an orbital period of P = 10.57415 ± 0.00063 days, a mass of M {sub b} = 46.0 ± 2.7 M{sub J}, and a radius of R {sub b} = 0.86 ± 0.03 R{sub J}. The host star for this BD has a mass of M {sub ⋆} = 1.18 ± 0.09 M{sub ⊙}, a radius of R {sub ⋆} = 1.35 ± 0.03 R{sub ⊙}, [Fe/H]=−0.08±0.09 dex, and an effective temperature of T {sub eff} = 6290 ± 100 K. Both BDs are in circular orbits around their host stars and are older than 3 Gyr based on stellar isochrone models of the stars. TOI-569 is one of two slightly evolved stars known to host a transiting BD (the other being KOI-415). TOI-1406b is one of three known transiting BDs to occupy the mass range of 40–50 M{sub J} and one of two to have a circular orbit at a period near 10 days (with the first being KOI-205b). Both BDs have reliable ages from stellar isochrones, in addition to their well-constrained masses and radii, making them particularly valuable as tests for substellar isochrones in the BD mass–radius diagram.

79 ASTRONOMY AND ASTROPHYSICS↗

Mission Design for Global Mapping Orbits at Primitive Bodies

Global mapping campaigns are part of most primitive body exploration missions. However, designing a mapping orbit without station keeping maneuvers is challenging due to the highly perturbed environment near small bodies. In this paper, we present a new design methodology to support mapping campaigns using 'quasi-terminator' orbits, a class of quasi-periodic orbits that exist in the vicinity of the well-known terminator orbits. The inherent stability of quasi-terminator trajectories and their wide variety of viewing geometries make them a very compelling option for mapping campaigns. A high-fidelity test case solution is also presented to prove the existence of these mapping orbits in full ephemeris.

quasi-periodic orbits↗

Comments on SEE: Comparative Advantages and and Experimental Consequences

The Satellite Energy Exchange experiment measures the periodic, near-miss encounters between a sheppard satellite and a small test body (satellite) in approximately the same orbit about a primary. Several important experimental requirements have been chosen to enhance capabilities: (a) The satellite be flown in a sun-synchronous orbit at an altitude of about 1350 Km, (b) Passive temperature system stabilized by spacecraft axial rotation with sunshade baffles at the end of the spacecraft, (c) Test bodies with different material composition be available for experiments, (d) The containment spacecraft fly about the sheppard mass in a zero-g environment whereas the test bodies, experience average zero-g environment over an orbital period, (e) Primary attitude and station-keeping uses magnetic field alignment plus micro-Newton thrusters such as Field Emission Electric Propulsion, and (f) Very low power (nW) laser tracking systems minimize impulse delivered to test bodies. With the above conditions, SEE has the capabilities: (1) Long duration (several years life-time) flight experiment (2) Long-term, active (with historical time record), self-calibration of satellite mass distribution (capsule geodesy) over lifetime of the spacecraft. (3) Novel passive thermal stabilization systems designed to attain cryogenic temperatures around 78K. (4) Novel spacecraft stabilization systems. (5) Ability to measure G to 1 part in 10(exp 6-7) depending on ultimate duration of experiment. (6) Ability to place limits on both temporal and spacial variations on G. (7) Ability to set experimental limits on the Post Newtonian parameters (PPN) alpha(2) and zeta(2). (8) Ability to measure (or place limits on) the non Einsteinian eccentricity of the Earth-Sun system (and the parameter alpha(1)) for long duration flight. (9) Ability to measure Delta((dot)-G)/G to 1 part in 10(exp 12-13). The MiniSTEP, competes in a limited way with Project SEE. It is designed to improve the measurement of the equivalence principle by seven orders of magnitude using active, low temperature (1.8 K) cooling for SQUID based, differential superconducting circuits. The experiment consists of a small cylinder concentrically located within a larger cylinder at its null gravitational point. The satellite is operated in zero-g mode using four differential accelerometers consisting to two test bodies of different material composition. The SQUIDS are needed to measure test body motion to precisions of 10(exp -18) over a four orbit period. The entire satellite moves in a very precise zero-g mode since the accelerometers are rigidly attached to the satellite. This limits the experiment to an approximately six month due to limitations on helium storage used in cryogenic cooling and thrust control to maintain the zero-g operation.

Smalley, Larry L.↗

The interoutburst behavior of cataclysmic variables

Existing IUE and AAVSO archive data were used to accomplish a large scale study of what happens to the UV flux of accretion disk systems during the quiescent intervals between outbursts, and how it relates to the preceding outburst characteristics of amplitude and width. The data sample involved multiple IUE observations for 16 dwarf novae and 8 novae along with existing optical coverage. Results indicate that most systems show correlated UV flux behavior with interoutburst phase, with 60 percent of the dwarf novae and 50 percent of the novae having decreasing flux trends while 33 percent of the dwarf novae and 38 percent of the novae show rising UV flux during the quiescent interval. All of the dwarf novae with decreasing UV fluxes at 1475 A have orbital periods longer than 4.4 hours, while all (except BV Cen) with flat or rising fluxes at 1475 A have orbital periods less than two hours. From a small sample (7) that have relatively large quiescent V magnitude changes between the IUE observations, most show a strong correlation between the UV and optical continuum. Interpretation of the results is complicated by not being able to determine how much the white dwarf contributes to the ultraviolet flux. However, it is now evident that noticeable changes are occurring in the hot zones in accreting systems long after the outburst, and not only for systems that are dominated by the white dwarf.

Szkody, Paula↗

A Real-time View of Orbital Evolution in HM Cancri

HM Cancri is a double-degenerate binary with the shortest orbital period presently known. The 5.36 minute period is seen as a large amplitude, soft X-ray modulation, likely resulting from a hot-spot produced by direct impact accretion. With such a7short orbital period it is expected to have a gravitational wave luminosity comparable8to or larger than that in the X-ray, and its orbital frequency is known to be increasing9at a rate consistent with the expected loss of angular momentum due to gravitational radiation. We use recent Neutron Star Interior Composition Explorer(NICER) observations to extend its long-term X-ray timing baseline to almost 20 yr. Phase coherent timing of these new data combined with existing Chandra data demonstrates conclusively that the rate of orbital frequency increase is slowing, and we measure a non-zero f0=8.95 ± 1.4 x 1027 Hz s2, to our knowledge the first such measurement of its kind for any compact astrophysical binary. With the simultaneous high precision measurement of f0= 3.557 ± 0.005 x 1016 Hz s1, we estimate that the system17will reach its maximum orbital frequency of fmax 3.1172091 mHz in 1,260 ± 200 yr, indicating that the system is close to its epoch of maximum orbital frequency. Assuming mass transfer is conservative, the measurement of f<0 implies that the20accretion rate from the donor is growing, with 5.4 x 1010<M2<4.0 x 1010 M⊙yr2. Further quantitative comparisons with theoretical models should enable more precise inferences regarding its current evolutionary state.

White dwarfs↗

Activity-driven structure variations as a cause of period changes in RS Canis Venaticorum-like systems

Magnetic activity cycles of a convective star in a close binary system may lead to orbit period changes through tidal spin-orbit coupling. An increase in the mean magnetic field throughout the convection zone provides an additional pressure support and increases the star's moment of inertia. In order for the system to conserve angular momentum instantaneously, the convective star must reduce its rotation rate. When this happens, the system is no longer synchronous; in particular, the equilibrium tide now suffers a phase lag. A tidal torque must act, transferring angular momentum from the star's rotation to the orbit, lengthening the period. When the field decays, these events reverse and the period shortens. Observed period changes in RS CVn-like systems are of the order delta p/p = 10 to the -6th, implying variations in the mean field strength at the base of the convection zone of approximately 1000 G over time scales of 10-30 yr. It is predicted that the strength of magnetic activity indicators will track orbital period changes in a given system: the period will be largest during the active portion of the magnetic cycle and smallest during the quiescent part.

Van Buren, D.↗

TRMM On-Orbit Performance Re-Accessed After Control Change

The Tropical Rainfall Measuring Mission (TRMM) spacecraft, a joint mission between the U.S. and Japan, launched onboard an HI1 rocket on November 27,1997 and transitioned in August, 2001 from an average operating altitude of 350 kilometers to 402.5 kilometers. Due to problems using the Earth Sensor Assembly (ESA) at the higher altitude, TRMM switched to a backup attitude control mode. Prior to the orbit boost TRMM controlled pitch and roll to the local vertical using ESA measurements while using gyro data to propagate yaw attitude between yaw updates from the Sun sensors. After the orbit boost, a Kalman filter used 3-axis gyro data with Sun sensor and magnetometers to estimate onboard attitude. While originally intended to meet a degraded attitude accuracy of 0.7 degrees, the new control mode met the original 0.2 degree attitude accuracy requirement after improving onboard ephemeris prediction and adjusting the magnetometer calibration onboard. Independent roll attitude checks using a science instrument, the Precipitation Radar (PR) which was built in Japan, provided a novel insight into the pointing performance. The PR data helped identify the pointing errors after the orbit boost, track the performance improvements, and show subtle effects from ephemeris errors and gyro bias errors. It also helped identify average bias trends throughout the mission. Roll errors tracked by the PR from sample orbits pre-boost and post-boost are shown in Figure 1. Prior to the orbit boost the largest attitude errors were due to occasional interference in the ESA. These errors were sometime larger than 0.2 degrees in pitch and roll, but usually less, as estimated from a comprehensive review of the attitude excursions using gyro data. Sudden jumps in the onboard roll show up as spikes in the reported attitude since the control responds within tens of seconds to null the pointing error. The PR estimated roll tracks well with an estimate of the roll history propagated using gyro data. After the orbit boost, the attitude errors shown by the PR roll have a smooth sine-wave type signal because of the way that attitude errors propagate with the use of gyro data. Yaw errors couple at orbit period to roll with '/4 orbit lag. By tracking the amplitude, phase, and bias of the sinusoidal PR roll error signal, it was shown that the average pitch rotation axis tends to be offset from orbit normal in a direction perpendicular to the Sun direction, as shown in Figure 2 for a 200 day period following the orbit boost. This is a result of the higher accuracy and stability of the Sun sensor measurements relative to the magnetometer measurements used in the Kalman filter. In November, 2001 a magnetometer calibration adjustment was uploaded which improved the pointing performance, keeping the roll and yaw amplitudes within about 0.1 degrees. After the boost, onboard ephemeris errors had a direct effect on the pitch pointing, being used to compute the Earth pointing reference frame. Improvements after the orbit boost have kept the the onboard ephemeris errors generally below 20 kilometers. Ephemeris errors have secondary effects on roll and yaw, especially during high beta angle when pitch effects can couple into roll and yaw. This is illustrated in figure 3. The onboard roll bias trends as measured by PR data show correlations with the Kalman filter's gyro bias error. This particularly shows up after yaw turns (every 2 to 4 weeks) as shown in Figure 3, when a slight roll bias is observed while the onboard computed gyro biases settle to new values. As for longer term trends, the PR data shows that the roll bias was influenced by Earth horizon radiance effects prior to the boost, changing values at yaw turns, and indicated a long term drift as shown in Figure 4. After the boost, the bias variations were smaller and showed some possible correlation with solar beta angle, probably due to sun sensor misalignment effects.

Bilanow, Steve↗

TRMM On-Orbit Performance Reassessed After Control Change

The Tropical Rainfall Measuring Mission (TRMM) spacecraft, a joint mission between the U.S. and Japan, launched onboard an H-I1 rocket on November 27, 1997, and transitioned in August, 2001, from an average operating altitude of 350 kilometers to 402.5 kilometers. Due to problems using the Earth Sensor Assembly (ESA) at the higher altitude, TRMM switched to a backup attitude control mode. Prior to the orbit boost TRMM controlled pitch and roll to the local vertical using ESA measurements while using gyro data to propagate yaw attitude between yaw updates from the Sun sensors. After the orbit boost, a Kalman filter used 3-axis gyro data with Sun sensor and magnetometers to estimate onboard attitude. While originally intended to meet a degraded attitude accuracy of 0.7 degrees, the new control mode met the original 0.2 degree attitude accuracy requirement after improving onboard ephemeris prediction and adjusting the magnetometer calibration onboard. Independent roll attitude checks using a science instrument, the Precipitation Radar (PR) which was built in Japan, provided a novel insight into the pointing performance. The PR data helped identify the pointing errors after the orbit boost, track the performance improvements, and show subtle effects from ephemeris errors and gyro bias errors. It also helped identify average bias trends throughout the mission. Roll errors tracked by the PR from sample orbits pre-boost and post-boost are shown in Figure 1. Prior to the orbit boost, the largest attitude errors were due to occasional interference in the ESA. These errors were sometime larger than 0.2 degrees in pitch and roll, but usually less, as estimated from a comprehensive review of the attitude excursions using gyro data. Sudden jumps in the onboard roll show up as spikes in the reported attitude since the control responds within tens of seconds to null the pointing error. The PR estimated roll tracks well with an estimate of the roll history propagated using gyro data. After the orbit boost, the attitude errors shown by the PR roll have a smooth sine-wave type signal because of the way that attitude errors propagate with the use of gyro data. Yaw errors couple at orbit period to roll with 1/4 orbit lag. By tracking the amplitude, phase, and bias of the sinusoidal PR roll error signal, it was shown that the average pitch rotation axis tends to be offset from orbit normal in a direction perpendicular to the Sun direction, as shown in Figure 2 for a 200 day period following the orbit boost. This is a result of the higher accuracy and stability of the Sun sensor measurements relative to the magnetometer measurements used in the Kalman filter. In November, 2001 a magnetometer calibration adjustment was uploaded which improved the pointing performance, keeping the roll and yaw amplitudes within about 0.1 degrees.

Bilanow, Stephen↗

Associating Long-term Gamma-ray Variability with the Superorbital Period of LS I + 61 Deg. 303

Gamma-ray binaries are stellar systems for which the spectral energy distribution (discounting the thermal stellar emission) peaks at high energies. Detected from radio to TeV gamma rays, the gamma-ray binary LS I + 61◦303 is highly variable across all frequencies. One aspect of this system's variability is the modulation of its emission with the timescale set by the approx. 26.4960 day orbital period. Here we show that, during the time of our observations, the gamma-ray emission of LS I + 61 deg. 303 also presents a sinusoidal variability consistent with the previously known superorbital period of 1667 days. This modulation is more prominently seen at orbital phases around apastron, whereas it does not introduce a visible change close to periastron. It is also found in the appearance and disappearance of variability at the orbital period in the power spectrum of the data. This behavior could be explained by a quasi-cyclical evolution of the equatorial outflow of the Be companion star, whose features influence the conditions for generating gamma rays. These findings open the possibility to use gamma-ray observations to study the outflows of massive stars in eccentric binary systems.

Be↗

Topological analysis of chaotic orbits: Revisiting Hyperion

There is emerging interest in the possibility of chaotic evolution in astrophysical systems. To mention just one example, recent well-sampled ground-based observations of the Saturian satellite Hyperion strongly suggest that it is exhibiting chaotic behavior. We present a general technique, the method of close returns, for the analysis of data from astronomical objects believed to be exhibiting chaotic motion. The method is based on the extraction of pieces of the evolution that exhibit nearly periodic behavior-episodes during which the object stays near in phase space to some unstable periodic orbit. Such orbits generally act as skeletal features, tracing the topological organization of the manifold on which the chaotic dynamics takes place. This method does not require data sets as lengthy as other nonlinear analysis techniques do and is therefore well suited to many astronomical observing programs. Well sampled data covering between twenty and forty characteristic periods of the system have been found to be sufficient for the application of this technique. Additional strengths of this method are its robustness in the presence of noise and the ability for a user to clearly distinguish between periodic, random, and chaotic behavior by inspection of the resulting two-dimensional image. As an example of its power, we analyze close returns in a numerically generated data set, based on a model for Hyperion extensively studied in the literature, corresponding to nightly observations of the satellite. We show that with a small data set, embedded unstable periodic orbits can be extracted and that these orbits can be responsible for nearly periodic behavior lasting a substantial fraction of the observing run.

Boyd, Patricia T.↗