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At least 109 records · Page 6

The K2 and TESS Synergy. I. Updated Ephemerides and Parameters for K2-114, K2-167, K2-237, and K2-261

Although the Transiting Exoplanet Survey Satellite (TESS) primary mission observed the northern and southern ecliptic hemispheres, generally avoiding the ecliptic, and the Kepler space telescope during the K2 mission could only observe near the ecliptic, many of the K2 fields extend far enough from the ecliptic plane that sections overlap with TESS fields. Using photometric observations from both K2 and TESS, combined with archival spectroscopic observations, we globally modeled four known planetary systems discovered by K2 that were observed in the first year of the primary TESS mission. Specifically, we provide updated ephemerides and system parameters for K2-114 b, K2-167 b, K2-237 b, and K2-261 b. These were some of the first K2 planets to be observed by TESS in the first year and include three Jovian sized planets and a sub-Neptune with orbital periods less than 12 days. In each case, the updated ephemeris significantly reduces the uncertainty in prediction of future times of transit, which is valuable for planning observations with the James Webb Space Telescope and other future facilities. The TESS extended mission is expected to observe about half of the K2 fields, providing the opportunity to perform this type of analysis on a larger number of systems.

79 ASTRONOMY AND ASTROPHYSICS↗

TOI-824 b: A New Planet on the Lower Edge of the Hot Neptune Desert

We report the detection of a transiting hot Neptune exoplanet orbiting TOI-824 (SCR J1448-5735), a nearby (d = 64 pc) K4V star, using data from the Transiting Exoplanet Survey Satellite. The newly discovered planet has a radius R {sub p} = 2.93 ± 0.20 R{sub ⊕} and an orbital period of 1.393 days. Radial velocity measurements using the Planet Finder Spectrograph and the High Accuracy Radial velocity Planet Searcher spectrograph confirm the existence of the planet, and we estimate its mass to be 18.47 ± 1.84 M{sub ⊕}. The planet’s mean density is ρ{sub p} = 4.03{sub −0.78}{sup +0.98} g cm{sup −3}, making it more than twice as dense as Neptune. TOI-824 b's high equilibrium temperature makes the planet likely to have a cloud-free atmosphere, and thus it is an excellent candidate for follow-up atmospheric studies. The detectability of TOI-824 b’s atmosphere from both ground and space is promising and could lead to the detailed characterization of the most irradiated small planet at the edge of the hot Neptune desert that has retained its atmosphere to date.

79 ASTRONOMY AND ASTROPHYSICS↗

TOI 540 b: A Planet Smaller than Earth Orbiting a Nearby Rapidly Rotating Low-mass Star

We present the discovery of TOI 540 b, a hot planet slightly smaller than Earth orbiting the low-mass star 2MASS J05051443-4756154. The planet has an orbital period of P = 1.239149 days (±170 ms) and a radius of r=0.903±0.052R{sub ⊕}, and is likely terrestrial based on the observed mass–radius distribution of small exoplanets at similar insolations. The star is 14.008 pc away and we estimate its mass and radius to be M=0.159±0.014 M{sub ⊙} and R=0.1895±0.0079R{sub ⊙}, respectively. The star is distinctive in its very short rotational period of P{sub rot}=17.4264±0.0094 hr and correspondingly small Rossby number of 0.007 as well as its high X-ray-to-bolometric luminosity ratio of L{sub X}/L{sub bol}=0.0028 based on a serendipitous XMM-Newton detection during a slew operation. This is consistent with the X-ray emission being observed at a maximum value of L{sub X}/L{sub bol}≃10{sup −3} as predicted for the most rapidly rotating M dwarfs. TOI 540 b may be an alluring target to study atmospheric erosion due to the strong stellar X-ray emission. It is also among the most accessible targets for transmission and emission spectroscopy and eclipse photometry with the James Webb Space Telescope, and may permit Doppler tomography with high-resolution spectroscopy during transit. This discovery is based on precise photometric data from the Transiting Exoplanet Survey Satellite and ground-based follow-up observations by the MEarth team.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

TESS Observations of the WASP-121 b Phase Curve

We study the red-optical photometry of the ultrahot Jupiter WASP-121 b as observed by the Transiting Exoplanet Survey Satellite (TESS) and model its atmosphere through a radiative transfer simulation. Given its short orbital period of ∼1.275 days, inflated state, and bright host star, WASP-121 b is exceptionally favorable for detailed atmospheric characterization. Toward this purpose, we use allesfitter to characterize its full red-optical phase curve, including the planetary phase modulation and secondary eclipse. We measure the day- and nightside brightness temperatures in the TESS passband as 3012{sub −42}{sup +40} and 2022{sub −602}{sup +254} K, respectively, and do not find a statistically significant phase shift between the brightest and substellar points. This is consistent with inefficient heat recirculation on the planet. We then perform an atmospheric retrieval analysis to infer the dayside atmospheric properties of WASP-121 b, such as its bulk composition, albedo, and heat recirculation. We confirm the temperature inversion in the atmosphere and suggest H{sup −}, TiO, and VO as potential causes of the inversion, absorbing heat at optical wavelengths at low pressures. Future Hubble Space Telescope and James Webb Space Telescope observations of WASP-121 b will benefit from its first full phase curve measured by TESS.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

A Near-infrared Chemical Inventory of the Atmosphere of 55 Cancri e

We present high-resolution near-infrared spectra taken during eight transits of 55 Cancri e, a nearby low-density super-Earth with a short orbital period (<18 hr). While this exoplanet’s bulk density indicates a possible atmosphere, one has not been detected definitively. Our analysis relies on the Doppler cross-correlation technique, which takes advantage of the high spectral resolution and broad wavelength coverage of our data, to search for the thousands of absorption features from hydrogen-, carbon-, and nitrogen-rich molecular species in the planetary atmosphere. Although we are unable to detect an atmosphere around 55 Cancri e, we do place strong constraints on the levels of HCN, NH{sub 3}, and C{sub 2}H{sub 2} that may be present. In particular, at a mean molecular weight of 5 amu, we can rule out the presence of HCN in the atmosphere down to a volume mixing ratio (VMR) of 0.02%, NH{sub 3} down to a VMR of 0.08%, and C{sub 2}H{sub 2} down to a VMR of 1.0%. If the mean molecular weight is relaxed to 2 amu, we can rule out the presence of HCN, NH{sub 3}, and C{sub 2}H{sub 2} down to VMRs of 0.001%, 0.0025%, and 0.08%, respectively. Our results reduce the parameter space of possible atmospheres consistent with the analysis of Hubble Space Telescope/WFC3 observations by Tsiaras et al. and indicate that if 55 Cancri e harbors an atmosphere, it must have a high mean molecular weight or clouds.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

NEMESIS: Exoplanet Transit Survey of Nearby M-dwarfs in TESS FFIs. I

In this work, we present an analysis of 33,054 M-dwarf stars, located within 100 parsecs, via the Transiting Exoplanet Survey Satellite (TESS) full-frame images (FFIs) of observed sectors 1–5. We present a new pipeline called NEMESIS, developed to extract detrended photometry, and to perform transit searches of single-sector data in TESS FFIs. As many M-dwarfs are faint, and are not observed with a two-minute cadence by TESS, FFI transit surveys can provide an empirical validation of how many planets are missed, using the 30-minute cadence data. In this work, we detect 183 threshold crossing events, and present 29 candidate planets for sectors 1–5, 24 of which are new detections. Our sample contains orbital periods ranging from 1.25 to 6.84 days, and planetary radii from 1.26 to 5.31 R {sub ⊕}. With the addition of our new planet candidate detections, along with detections previously observed in sectors 1–5, we calculate an integrated occurrence rate of 2.49 ± 1.58 planets per star, for the period range ∈ [1, 9] days, and planet radius range ∈ [0.5,11] R {sub ⊕}. We project an estimated yield of 122 ± 11 transit detections of nearby M-dwarfs. Of our new candidates, 23 have signal-to-noise ratios >7, transmission spectroscopy metrics >38, and emission spectroscopy metrics >10. We present all of our data products for our planet candidates via the Filtergraph data visualization service, located at https://filtergraph.com/NEMESIS.

47 OTHER INSTRUMENTATION↗

Systematics and Consequences of Comet Nucleus Outgassing Torques

Anisotropic outgassing from comets exerts a torque sufficient to rapidly change the angular momentum of the nucleus, potentially leading to rotational instability. Here, we use empirical measures of spin changes in a sample of comets to characterize the torques, and to compare them with expectations from a simple model. Both the data and the model show that the characteristic spin-up timescale, τ {sub s}, is a strong function of nucleus radius, r {sub n}. Empirically, we find that the timescale for comets (most with perihelion 1–2 au and eccentricity ∼0.5) varies as τ{sub s}∼100r{sub n}{sup 2}, where r {sub n} is expressed in kilometers, and τ {sub s} is in years. The fraction of the nucleus surface that is active varies as f{sub A}∼0.1r{sub n}{sup −2}. We find that the median value of the dimensionless moment arm of the torque is k {sub T} = 0.007 (i.e., ∼0.7% of the escaping momentum torques the nucleus), with weak (<3σ) evidence for a size dependence k{sub T}∼10{sup −3}r{sub n}{sup 2}. Sub-kilometer nuclei have spin-up timescales comparable to their orbital periods, confirming that outgassing torques are quickly capable of driving small nuclei toward rotational disruption. Torque-induced rotational instability likely accounts for the paucity of sub-kilometer short-period cometary nuclei, and for the pre-perihelion destruction of sungrazing comets. Torques from sustained outgassing on small active asteroids can rival YORP torques, even for very small (≲1 g s{sup −1}) mass-loss rates. Finally, we highlight the important role played by observational biases in the measured distributions of τ {sub s}, f {sub A}, and k {sub T}.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Stellar Activity Manifesting at a One-year Alias Explains Barnard b as a False Positive

Barnard’s star is among the most studied stars given its proximity to the Sun. It is often considered the radial velocity (RV) standard for fully convective stars due to its RV stability and equatorial decl. Recently, an Msin i=3.3M{sub ⊕} super-Earth planet candidate with a 233 day orbital period was announced by Ribas et al. New observations from the near-infrared Habitable-zone Planet Finder (HPF) Doppler spectrometer do not show this planetary signal. We ran a suite of experiments on both the original data and a combined original + HPF data set. These experiments include model comparisons, periodogram analyses, and sampling sensitivity, all of which show the signal at the proposed period of 233 days is transitory in nature. The power in the signal is largely contained within 211 RVs that were taken within a 1000 day span of observing. Our preferred model of the system is one that features stellar activity without a planet. We propose that the candidate planetary signal is an alias of the 145 day rotation period. This result highlights the challenge of analyzing long-term, quasi-periodic activity signals over multiyear and multi-instrument observing campaigns.

47 OTHER INSTRUMENTATION↗

TOI-1231 b: A Temperate, Neptune-sized Planet Transiting the Nearby M3 Dwarf NLTT 24399

We report the discovery of a transiting, temperate, Neptune-sized exoplanet orbiting the nearby (d = 27.5 pc), M3V star TOI-1231 (NLTT 24399, L 248-27, 2MASS J10265947-5228099). The planet was detected using photometric data from the Transiting Exoplanet Survey Satellite and followed up with observations from the Las Cumbres Observatory and the Antarctica Search for Transiting ExoPlanets program. Combining the photometric data sets, we find that the newly discovered planet has a radius of 3.65{sub −0.15}{sup +0.16} R{sub ⊕} and an orbital period of 24.246 days. Radial velocity measurements obtained with the Planet Finder Spectrograph on the Magellan Clay telescope confirm the existence of the planet and lead to a mass measurement of 15.5 ± 3.3 M {sub ⊕}. With an equilibrium temperature of just 330 K, TOI-1231 b is one of the coolest small planets accessible for atmospheric studies thus far, and its host star’s bright near-infrared brightness (J = 8.88, K {sub s} = 8.07) makes it an exciting target for the Hubble Space Telescope and the James Webb Space Telescope. Future atmospheric observations would enable the first comparative planetology efforts in the 250–350 K temperature regime via comparisons with K2-18 b. Furthermore, TOI-1231's high systemic radial velocity (70.5 km s{sup −1}) may allow for the detection of low-velocity hydrogen atoms escaping the planet by Doppler, shifting the H i Lyα stellar emission away from the geocoronal and interstellar medium absorption features.

47 OTHER INSTRUMENTATION↗

A Systematic Search for Outbursting AM CVn Systems with the Zwicky Transient Facility

AM CVn systems are a rare type of accreting binary that consists of a white dwarf and a helium-rich, degenerate donor star. Using the Zwicky Transient Facility (ZTF), we searched for new AM CVn systems by focusing on blue, outbursting stars. We first selected outbursting stars using the ZTF alerts. We cross matched the candidates with Gaia and Pan-STARRS catalogs. The initial selection of candidates based on the Gaia BP-RP contains 1751 unknown objects. We used the Pan-STARRS g-r and r-i color in combination with the Gaia color to identify 59 strong AM CVn candidates. We obtained identification spectra of 35 sources, of which 18 are high-priority candidates, and discovered nine new AM CVn systems and one magnetic CV that shows only He-ii lines. Using the outburst recurrence time, we estimate the orbital periods of the nine new AM CVn systems that are in the range of 29–50 minutes. We conclude that targeted follow up of blue, outbursting sources is an efficient method to find new AM CVn systems and we plan to follow up all candidates we identified to systematically study the population of outbursting AM CVn systems.

79 ASTRONOMY AND ASTROPHYSICS↗

A White Dwarf with Transiting Circumstellar Material Far outside the Roche Limit

We report the discovery of a white dwarf exhibiting deep, irregularly shaped transits, indicative of circumstellar planetary debris. Using Zwicky Transient Facility DR2 photometry of ZTF J013906.17+524536.89 and follow-up observations from the Las Cumbres Observatory, we identify multiple transit events that recur every ≈107.2 days, much longer than the 4.5–4.9 hr orbital periods observed in WD 1145+017, the only other white dwarf known with transiting planetary debris. The transits vary in both depth and duration, lasting 15–25 days and reaching 20%–45% dips in flux. Optical spectra reveal strong Balmer lines, identifying the white dwarf as a DA with ${T}_{\mathrm{eff}}=10,530\pm 140\,{\rm{K}}$ and $\mathrm{log}(g)=7.86\pm 0.06$. A Ca ii K absorption feature is present in all spectra both in and out of transit. Spectra obtained during one night at roughly 15% transit depth show increased Ca ii K absorption with a model atmospheric fit suggesting [Ca/H] = –4.6 ± 0.3, whereas spectra taken on three nights out of transit have [Ca/H] of –5.5, –5.3, and –4.9 with similar uncertainties. While the Ca ii K line strength varies by only 2σ, we consider a predominantly interstellar origin for Ca absorption unlikely. Here, we suggest a larger column density of circumstellar metallic gas along the line of site or increased accretion of material onto the white dwarf's surface are responsible for the Ca absorption, but further spectroscopic studies are required. In addition, high-speed time series photometry out of transit reveals variability with periods of 900 and 1030 s, consistent with ZZ Ceti pulsations.

79 ASTRONOMY AND ASTROPHYSICS↗

Exosphere Modeling of Proxima b: A Case Study of Photochemical Escape with a Venus-like Atmosphere

Exoplanets orbiting M dwarfs within habitable zones are exposed to stellar environments more extreme than that terrestrial planets experience in our solar system, which can significantly impact the atmospheres of the exoplanets and affect their habitability and sustainability. This study provides the first prediction of hot oxygen corona structure and the associated photochemical loss from a 1 bar CO 2 -dominated atmosphere of a Venus-like rocky exoplanet, where dissociative recombination of O 2 + ions is assumed to be the major source reaction for the escape of neutral O atoms and formation of the hot O corona (or exospheres) as on Mars and Venus. We employ a 3D Monte Carlo code to simulate the exosphere of Proxima Centauri b (PCb) based on the ionosphere simulated by a 3D magnetohydrodynamic model. Our simulation results show that variability of the stellar wind dynamic pressure over one orbital period of PCb does not affect the overall spatial structure of the hot O corona but contributes to the change in the global hot O escape rate that varies by an order of magnitude. The escape increases dramatically when the planet possesses its intrinsic magnetic fields as the ionosphere becomes more extended with the presence of a global magnetic field. Furthermore, the extended hot O corona may lead to a more extended H exosphere through collisions between thermal H and hot O, which exemplifies the importance of considering nonthermal populations in exospheres to interpret future observations.

79 ASTRONOMY AND ASTROPHYSICS↗

The SDSS-HET Survey of Kepler Eclipsing Binaries. A Sample of Four Benchmark Binaries

The purpose of this work is to extend a sample of accurately modeled, benchmark-grade eclipsing binaries (EBs) with accurately determined masses and radii. We select four "well-behaved" Kepler binaries, KIC 2306740, KIC 4076952, KIC 5193386 and KIC 5288543, each with at least eight double-lined spectra from the Apache Point Observatory Galactic Evolution Experiment instrument that is part of the Sloan Digital Sky Surveys III and IV, and from the Hobby–Eberly High Resolution Spectrograph. We obtain masses and radii with uncertainties of 2.5% or less for all four systems. Three of these systems have orbital periods longer than 9 days, and thus populate an undersampled region of the parameter space for extremely well-characterized detached EBs. We compare the derived masses and radii against MESA MIST isochrones to determine the ages of the systems. All systems were found to be coeval, showing that the results are consistent across MESA MIST and PHOEBE .

79 ASTRONOMY AND ASTROPHYSICS↗

Occurrence of Gravitational Collapse in the Accreting Neutron Stars of Binary-driven Hypernovae

The binary-driven hypernova (BdHN) model proposes long gamma-ray bursts (GRBs) originate in binaries composed of a carbon–oxygen (CO) star and a neutron star (NS) companion. The CO core collapse generates a newborn NS and a supernova that triggers the GRB by accreting onto the NSs, rapidly transferring mass and angular momentum to them. This article aims to determine the conditions under which a black hole (BH) forms from NS collapse induced by the accretion and the impact on the GRB's observational properties and taxonomy. We perform three-dimensional, smoothed particle hydrodynamics simulations of BdHNe using up-to-date NS nuclear equations of state, with and without hyperons, and calculate the structure evolution in full general relativity. We assess the binary parameters leading either NS in the binary to the critical mass for gravitational collapse into a BH and its occurrence time, t col . We include a nonzero angular momentum of the NSs and find that t col ranges from a few tens of seconds to hours for decreasing NS initial angular momentum values. BdHNe I are the most compact (about 5 minute orbital period), promptly form a BH, and release ≳10 52 erg of energy. They form NS–BH binaries with tens of kiloyears merger timescales by gravitational-wave emission. BdHNe II and III do not form BHs, and release ~10 50 –10 52 erg and ≲10 50 erg of energy, respectively. They form NS–NS binaries with a range of merger timescales larger than for NS–BH binaries. In some compact BdHNe II, either NS can become supramassive, i.e., above the critical mass of a nonrotating NS. Magnetic braking by a 10 13 G field can delay BH formation, leading to BH–BH or NS–BH with tens of kiloyears merger timescales.

79 ASTRONOMY AND ASTROPHYSICS↗

Characterization of Low-mass Companions to Kepler Objects of Interest Observed with APOGEE-N

We report the characterization of 28 low-mass (0.02 M ⊙ ≤ M 2 ≤ 0.25 M ⊙ ) companions to Kepler objects of interest (KOIs), eight of which were previously designated confirmed planets. These objects were detected as transiting companions to Sunlike stars (G and F dwarfs) by the Kepler mission and are confirmed as single-lined spectroscopic binaries in the current work using the northern multiplexed Apache Point Observatory Galactic Evolution Experiment near-infrared spectrograph (APOGEE-N) as part of the third and fourth Sloan Digital Sky Surveys. We have observed hundreds of KOIs using APOGEE-N and collected a total of 43,175 spectra with a median of 19 visits and a median baseline of ~1.9 yr per target. We jointly model the Kepler photometry and APOGEE-N radial velocities to derive fundamental parameters for this subset of 28 transiting companions. The radii for most of these low-mass companions are overinflated (by ~10%) when compared to theoretical models. Tidally locked M dwarfs on short-period orbits show the largest amount of inflation, but inflation is also evident for companions that are well separated from the host star. We demonstrate that APOGEE-N data provide reliable radial velocities when compared to precise high-resolution spectrographs that enable detailed characterization of individual systems and the inference of orbital elements for faint (H > 12) KOIs. The data from the entire APOGEE-KOI program are public and present an opportunity to characterize an extensive subset of the binary population observed by Kepler.

79 ASTRONOMY AND ASTROPHYSICS↗

Spacecraft Geometry Effects on Kinetic Impactor Missions

Abstract The DART (Double Asteroid Redirection Test) mission will impact a spacecraft on the secondary (Dimorphos) of the binary asteroid system Didymos in 2022 September, with the goal of altering the orbital period of Dimorphos about Didymos sufficiently to be observed from ground-based observations. Numerical impact modeling is a crucial component in understanding the outcome of the DART experiment, and while many have investigated the effects of target properties, such as material strength and porosity (which remain unknown), an often overlooked factor is the importance of accurately representing the spacecraft itself in such models. Most impact modeling to date has considered simple impactor geometries such as a solid uniform sphere, but in reality the spacecraft is a complex shape full of different components, open spaces, and thin walled structures. At a minimum, a simple solid representation underestimates the surface area of the impact: for a small body such as Dimorphos (approximately 160 m in diameter), the difference between a spacecraft spanning 20 m (including solar arrays) impacting and a sub-1 m idealized shape may be important. In this paper, we compare models impacting high-fidelity models of the spacecraft based on the CAD geometry with various simplified impactors, in order to assess the potential importance of this effect. We find that the difference between the simplest impactor geometries (such as a uniform sphere) and the real spacecraft is measurable, and has an interesting dependence on the material properties of the asteroid itself.

36 MATERIALS SCIENCE↗

Achievement of the Planetary Defense Investigations of the Double Asteroid Redirection Test (DART) Mission

NASA's Double Asteroid Redirection Test (DART) mission was the first to demonstrate asteroid deflection, and the mission's Level 1 requirements guided its planetary defense investigations. Here, we summarize DART's achievement of those requirements. On 2022 September 26, the DART spacecraft impacted Dimorphos, the secondary member of the Didymos near-Earth asteroid binary system, demonstrating an autonomously navigated kinetic impact into an asteroid with limited prior knowledge for planetary defense. Months of subsequent Earth-based observations showed that the binary orbital period was changed by –33.24 minutes, with two independent analysis methods each reporting a 1 σ uncertainty of 1.4 s. Dynamical models determined that the momentum enhancement factor, β , resulting from DART's kinetic impact test is between 2.4 and 4.9, depending on the mass of Dimorphos, which remains the largest source of uncertainty. Over five dozen telescopes across the globe and in space, along with the Light Italian CubeSat for Imaging of Asteroids, have contributed to DART's investigations. These combined investigations have addressed topics related to the ejecta, dynamics, impact event, and properties of both asteroids in the binary system. A year following DART's successful impact into Dimorphos, the mission has achieved its planetary defense requirements, although work to further understand DART's kinetic impact test and the Didymos system will continue. In particular, ESA's Hera mission is planned to perform extensive measurements in 2027 during its rendezvous with the Didymos–Dimorphos system, building on DART to advance our knowledge and continue the ongoing international collaboration for planetary defense.

79 ASTRONOMY AND ASTROPHYSICS↗

Measurement and feedback-driven adaptive dynamics in the classical and quantum kicked top

In classical dynamical systems, stochastic feedback can stabilize otherwise unstable periodic orbits, giving rise to distinct controlled and uncontrolled phases as the rate of control application is varied. In this work, we apply these control protocols in classical, semiclassical, and quantum regimes to the kicked top, a paradigmatic model of quantum chaos. The quantum kicked top, modeled as the dynamics of a spin-S object, naturally interpolates between these regimes with the spin size S acting as an effective Planck constant. We show that the dynamics of the kicked top in classical, semiclassical, and fully quantum limits can all be controlled using stochastic feedback protocols. Comparing the full quantum dynamics to a truncated Wigner approximation that captures quantum noise but neglects interference beyond the Ehrenfest time, we find that low-moment observables are largely accounted for semiclassically, while the remaining discrepancy in higher moments is consistent with contributions from interference and possibly nonlinearities in rare trajectories that explore the compact phase space. We also find rapid purification in the numerics studied for all rates of control considered, suggesting that control quenches the top's ability to encode a qubit of quantum information even in the uncontrolled phase.

Prasad, Mahaveer [Tata Inst.; Singapore U. Tech. D↗