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In this work, we study in detail the collision formation scenario of black holes (BHs) which lie in the pair-instability (PI) mass gap. We study the collision scenario of two massive stars by means of a smoothed-particle hydrodynamics (SPH) simulation and the post-collision evolution with detailed stellar evolutionary codes. We find that the stellar collision scenario is a suitable formation channel to populate the BHs' PI mass gap. [ABSTRACT FROM AUTHOR]

The detection of the binary black hole merger GW190521, with primary black hole mass |$85^{+21}_{-14} {\rm M}_{\odot }$|⁠ , proved the existence of black holes in the theoretically predicted pair-instability gap (⁠|$\sim 60-120 \, {\rm M}_{\odot }$|⁠) of their mass spectrum. Some recent studies suggest that such massive black holes could be produced by the collision of an evolved star with a carbon–oxygen core and a main sequence star. Such a post-coalescence star could end its life avoiding the pair-instability regime and with a direct collapse of its very massive envelope. It is still not clear, however, how the collision shapes the structure of the newly produced star and how much mass is actually lost in the impact. We investigated this issue by means of hydrodynamical simulations with the smoothed particle hydrodynamics code StarSmasher , finding that a head-on collision can remove up to 12 per cent of the initial mass of the colliding stars. This is a non-negligible percentage of the initial mass and could affect the further evolution of the stellar remnant, particularly in terms of the final mass of a possibly forming black hole. We also found that the main sequence star can plunge down to the outer boundary of the core of the primary, changing the inner chemical composition of the remnant. The collision expels the outer layers of the primary, leaving a remnant with an helium-enriched envelope (reaching He fractions of about 0.4 at the surface). These more complex abundance profiles can be directly used in stellar evolution simulations of the collision product. [ABSTRACT FROM AUTHOR]

We analyse how drag forces modify the orbits of objects moving through extended gaseous distributions. We consider how hydrodynamic (surface area) drag forces and dynamical friction (gravitational) drag forces drive the evolution of orbital eccentricity. While hydrodynamic drag forces cause eccentric orbits to become more circular, dynamical friction drag can cause orbits to become more eccentric. We develop a semi-analytic model that accurately predicts these changes by comparing the total work and torque applied to the orbit at periapse and apoapse. We use a toy model of a radial power-law density profile, ρ  ∝  r −γ , to determine that there is a critical γ  = 3 power index, which separates the eccentricity evolution in dynamical friction: orbits become more eccentric for γ < 3 and circularize for γ > 3. We apply these findings to the infall of a Jupiter-like planet into the envelope of its host star. The hydrostatic envelopes of stars are defined by steep density gradients near the limb and shallower gradients in the interior. Under the influence of gaseous dynamical friction, an infalling object's orbit will first decrease in eccentricity and then increase. The critical separation that delineates these regimes is predicted by the local density slope and is linearly dependent on polytropic index. More broadly, our findings indicate that binary systems may routinely emerge from common envelope phases with non-zero eccentricities that were excited by the dynamical friction forces that drove their orbital tightening. [ABSTRACT FROM AUTHOR]

Atmospheric escape from close-in exoplanets is thought to be crucial in shaping observed planetary populations. Recently, significant progress has been made in observing this process in action through excess absorption in-transit spectra and narrowband light curves. We model the escape of initially homogeneous planetary winds interacting with a stellar wind. The ram pressure balance of the two winds governs this interaction. When the impingement of the stellar wind on the planetary outflow is mild or moderate, the planetary outflow expands nearly spherically through its sonic surface before forming a shocked boundary layer. When the confinement is strong, the planetary outflow is redirected into a cometary tail before it expands to its sonic radius. The resultant transmission spectra at the He 1083 nm line are accurately represented by a 1D spherical wind solution in cases of mild to moderate stellar wind interaction. In cases of strong stellar wind interaction, the degree of absorption is enhanced and the cometary tail leads to an extended egress from transit. The crucial features of the wind–wind interaction are, therefore, encapsulated in the light curve of He 1083 nm equivalent width as a function of time. The possibility of extended He 1083 nm absorption well beyond the optical transit carries important implications for planning out-of-transit observations that serve as a baseline for in-transit data. [ABSTRACT FROM AUTHOR]

Tidal dissipation due to turbulent viscosity in the convective regions of giant stars plays an important role in shaping the orbits of pre-common-envelope systems. Such systems are possible sources of transients and close compact binary systems that will eventually merge and produce detectable gravitational wave signals. Most previous studies of the onset of common envelope episodes have focused on circular orbits and synchronously rotating donor stars under the assumption that tidal dissipation can quickly spin-up the primary and circularize the orbit before the binary reaches Roche lobe overflow (RLO). We test this assumption by coupling numerical models of the post-main-sequence stellar evolution of massive stars with the model for tidal dissipation in convective envelopes developed in Vick & Lai – a tidal model that is accurate even for highly eccentric orbits with small pericentre distances. We find that, in many cases, tidal dissipation does not circularize the orbit before RLO. For a |$10\, {\rm M}_{\odot }$| (⁠|$15\, {\rm M}_{\odot }$|⁠) primary star interacting with a |$1.4\, {\rm M}_{\odot }$| companion, systems with pericentre distances within 3 au (6 au) when the primary leaves the main sequence will retain the initial orbital eccentricity when the primary grows to the Roche radius. Even in systems that tidally circularize before RLO, the donor star may be rotating subsynchronously at the onset of mass transfer. Our results demonstrate that some possible precursors to double neutron star systems are likely eccentric at the Roche radius. The effects of pre-common-envelope eccentricity on the resulting compact binary merit further study. [ABSTRACT FROM AUTHOR]

In this work, we study in detail the collision formation scenario of black holes (BHs) which lie in the pair-instability (PI) mass gap. We study the collision scenario of two massive stars by means of a smoothed-particle hydrodynamics (SPH) simulation and the post-collision evolution with detailed stellar evolutionary codes. We find that the stellar collision scenario is a suitable formation channel to populate the BHs' PI mass gap. [ABSTRACT FROM AUTHOR]

In Early Modern English, verbal negation was commonly expressed by the addition of not directly after a lexical verb, a construction which subsequently underwent a pronounced decline in frequency as part of broader changes in verbal syntax. Even after the rise of the auxiliary do, however, constructions with the same surface form as the earlier pattern have continued to be used as a stylistically marked alternative. Data from the Hansard Corpus are presented here to show an increase in the frequency of these constructions since the mid twentieth century. The syntactic environments in which contemporary postverbal negation occurs are compared to the patterns existing in Early Modern English, and evaluated in the light of trends within constituent negation. The interpretation proposed is that a lexical split has occurred to produce two separate lexemes of the form not, with different syntactic properties. Postverbal negation would thus occur in Present-day English when speakers choose to make use of the new lexeme. [ABSTRACT FROM AUTHOR]

Common envelope evolution, the key orbital tightening phase of the traditional formation channel for close binaries, is a multistage process that presents many challenges to the establishment of a fully descriptive, predictive theoretical framework. In an approach complementary to global 3D hydrodynamical modeling, we explore the range of applicability for a simplified drag formalism that incorporates the results of local hydrodynamic "wind tunnel" simulations into a semi-analytical framework in the treatment of the common envelope dynamical inspiral phase using a library of realistic giant branch stellar models across the low, intermediate, and high-mass regimes. In terms of a small number of key dimensionless parameters, we characterize a wide range of common envelope events, revealing the broad range of applicability of the drag formalism as well its self-similar nature across mass regimes and ages. Limitations arising from global binary properties and local structural quantities are discussed together with the opportunity for a general prescriptive application for this formalism. [ABSTRACT FROM AUTHOR]

We present three-dimensional local hydrodynamic simulations of flows around objects embedded within stellar envelopes using a "wind tunnel" formalism. Our simulations model the common envelope dynamical inspiral phase in binary star systems in terms of dimensionless flow characteristics. We present suites of simulations that study the effects of varying the binary mass ratio, stellar structure, equation of state, relative Mach number of the object's motion through the gas, and density gradients across the gravitational focusing scale. For each model, we measure coefficients of accretion and drag experienced by the embedded object. These coefficients regulate the coupled evolution of the object's masses and orbital tightening during the dynamical inspiral phase of the common envelope. We extrapolate our simulation results to accreting black holes with masses comparable to that of the population of LIGO black holes. We demonstrate that the mass and spin accrued by these black holes per unit orbital tightening are directly related to the ratio of accretion to drag coefficients. We thus infer that the mass and dimensionless spin of initially nonrotating black holes change by of order 1% and 0.05, respectively, in a typical example scenario. Our prediction that the masses and spins of black holes remain largely unmodified by a common envelope phase aids in the interpretation of the properties of the growing observed population of merging binary black holes. Even if these black holes passed through a common envelope phase during their assembly, features of mass and spin imparted by previous evolutionary epochs should be preserved. [ABSTRACT FROM AUTHOR]

A principled model of mood selection in Old English (OE) has long proved elusive. We analyse the distribution of the indicative and subjunctive in the OE Bede in light of the Latin original, the syntactic construction, and a semantic model of modality which classifies clauses according to whether the situation is represented as holding in the actual world or in a possible world. The choice of mood in the Latin and OE Bede differs enough to rule out slavish imitation. In certain clauses, such as result and purpose clauses, the construction type, modality, and grammatical mood all match; however, in other clauses, such as concessives, the OE subjunctive is systematically used whether the situation is represented as actual or possible. Where the grammatical mood of OE forms is ambiguous, modal verbs are often seemingly used as a substitute for the subjunctive. Our results show that while the choice of mood in the OE Bede largely correlates with the syntactic construction, the subjunctive is close to being semantically redundant. This growing redundancy may have been one of the factors in the diminishing role of inflectional mood in the later history of English. [ABSTRACT FROM AUTHOR]

Binary systems undergoing unstable Roche Lobe overflow spill gas into their circumbinary environment as their orbits decay toward coalescence. In this paper, we use a suite of hydrodynamic models of coalescing binaries involving an extended donor and a more compact accretor. We focus on the period of unstable Roche Lobe overflow that ends as the accretor plunges within the envelope of the donor at the onset of a common envelope phase. During this stage, mass is removed from the donor and flung into the circumbinary environment. Across a wide range of binary mass ratios, we find that the mass expelled as the separation decreases from the Roche limit to the donor's original radius is of the order of 25% of the accretor's mass. We study the kinematics of this ejecta and its dependencies on binary properties and find that it assembles into a toroidal circumbinary distribution. These circumbinary tori have approximately constant specific angular momenta due to momentum transport by spiral shocks launched from the orbiting binary. We show that an analytic model with these torus properties captures many of the main features of the azimuthally averaged profiles of our hydrodynamic simulations. Our results, in particular the simple relationship between accretor mass and expelled mass and its spatial distribution, may be useful for interpreting stellar coalescence transients like luminous red novae and initializing hydrodynamic simulations of the subsequent common envelope phase. [ABSTRACT FROM AUTHOR]

We study the process of runaway, unstable Roche lobe overflow in coalescing binary systems and its dependence on the properties of the binary involved. We create three-dimensional hydrodynamic models of binary coalescences and follow them through a phase of increasing Roche lobe overflow until the accretor is engulfed by the donor at the onset of a common-envelope phase. In these models, we vary binary properties of mass ratio, donor structure and spin, and equation of state through the gas adiabatic index. We compare the numerical results to semianalytic models of binary orbit evolution based on mass and angular momentum exchange between two point masses. Using our hydrodynamic simulations, we measure the key parameters: the donor mass-loss rate and the angular momentum exchanged per unit mass loss from the donor. Using these calibrations, the semianalytic model closely reproduces the escalating mass loss and runaway orbital decay observed in the hydrodynamic models. The semianalytic model accurately reproduces the major differences in orbit evolution that arise with varying mass ratio and donor structure. We encapsulate the semianalytic model in a publicly released Python package, RLOF. We apply this model to the observed period decay and subsequent merger of the binary V1309 Sco and find that it can simultaneously reproduce the observed orbital decay and time of outburst. We further demonstrate that there is a relationship between the period derivative and second derivative that can be a useful metric for evaluating candidate merging binaries. [ABSTRACT FROM AUTHOR]

Abstarct: In Kawahara et al. (2018) and Masuda et al. (2019), we reported the discovery of four self-lensing binaries consisting of F/G-type stars and (most likely) white dwarfs whose masses range from 0.2 to 0.6 solar masses. Here we present their updated system parameters based on new radial velocity data from the Tillinghast Reflector Echelle Spectrograph at the Fred Lawrence Whipple Observatory, and the Gaia parallaxes and spectroscopic parameters of the primary stars. We also briefly discuss the astrophysical implications of these findings. [ABSTRACT FROM AUTHOR]

The level of mass segregation in the core of globular clusters has been previously proposed as a potential indicator of the dynamical constituents of the system, such as presence of a significant population of stellar-mass black holes (BHs), or even a central intermediate-mass black hole (IMBH). However, its measurement is limited to clusters with high-quality Hubble Space Telescope data. Thanks to a set of state-of-the-art direct N -body simulations with up to 200k particles inclusive of stellar evolution, primordial binaries, and varying BH/neutron stars, we highlight for the first time the existence of a clear and tight linear relation between the degree of mass segregation and the cluster structural concentration index. The latter is defined as the ratio of the radii containing 5 per cent and 50 per cent of the integrated light (R 5/ R 50), making it robustly measurable without the need to individually resolve low-mass stars. Our simulations indicate that given R 5/ R 50, the mass segregation Δ m (defined as the difference in main-sequence median mass between centre and half-light radius) is expressed as Δ m /M⊙ = −1.166 R 5/ R 50 + 0.3246, with a root-mean-square error of 0.0148. In addition, we can explain its physical origin and the values of the fitted parameters through basic analytical modelling. Such correlation is remarkably robust against a variety of initial conditions (including presence of primordial binaries and IMBHs) and cluster ages, with a slight dependence in best-fitting parameters on the prescriptions used to measure the quantities involved. Therefore, this study highlights the potential to develop a new observational tool to gain insight on the dynamical status of globular clusters and on its dark remnants. [ABSTRACT FROM AUTHOR]

The prevalence of binary stars at close separations implies that many of these systems will interact or merge during the binary's lifetime. This paper presents hydrodynamic simulations of the scenario of binary coalescence through unstable mass transfer, which drives the pair to closer separations. When the donor star does not rotate synchronously with respect to the orbit, dynamical tidal waves are excited in its envelope. We show that resonance crossings with high azimuthal order (m ∼ 3 to 6) fundamental modes induce a visible "polygram" distortion to the star. As the binary orbit tightens, the system sweeps through resonance with modes of decreasing azimuthal order, which are selectively excited. We compare our hydrodynamic simulations to predictions from linear theory of resonant-mode excitation. The linear theory provides an estimate of mode amplitudes to within a factor of two, even as the oscillations become quite nonlinear as the stars coalesce. We estimate that a wave with 10% radial amplitude generates approximately 1% photometric variability; this may be detectable if such a binary coalescence is caught in action by future photometric all-sky surveys. [ABSTRACT FROM AUTHOR]

Despite recent observational efforts, unequivocal signs for the presence of intermediate-mass black holes (IMBHs) in globular clusters (GCs) have not been found yet. Especially when the presence of IMBHs is constrained through dynamical modelling of stellar kinematics, it is fundamental to account for the displacement that the IMBH might have with respect to the GC centre. In this paper, we analyse the IMBH wandering around the stellar density centre using a set of realistic direct N-body simulations of star cluster evolution. Guided by the simulation results, we develop a basic yet accurate model that can be used to estimate the average IMBH radial displacement (rbh) in terms of structural quantities as the core radius (rc ), mass (Mc ), and velocity dispersion (σc), in addition to the average stellar mass (mc) and the IMBH mass (Mbh). The model can be expressed by the equation rbh /rc = A(mc/Mbh)α[σ2 c rc/(GMc)]β, in which the free parameters A, α, and β are calculated through comparison with the numerical results on the IMBH displacement. The model is then applied to Galactic GCs, finding that for an IMBH mass equal to 0.1 per cent of the GC mass, the typical expected displacement of a putative IMBH is around 1 arcsec for most Galactic GCs, but IMBHs can wander to larger angular distances in some objects, including a prediction of a 2.5 arcsec displacement for NGC 5139 (ω Cen), and >10 arcsec for NGC5053, NGC6366, and ARP2. [ABSTRACT FROM AUTHOR]

Abstract: In Old English, passive‐type constructions involving a copula and a passive participle could be used to express both events and states. Two different types of copula are found in these constructions: weorðan, meaning ‘become’, and wesan and beon, meaning ‘be’. There has been some dispute as to how the meaning of these copulas relates to the meaning of the construction as a whole, in both its eventive and its stative uses, and whether any of these constructions was grammaticalized in the sense that its meaning was non‐compositional. We propose a semantic model that represents these constructions compositionally and test it against a selected corpus of Old English texts in order to address two questions: whether the data provide evidence of non‐compositional meaning that would suggest grammaticalization, and whether other factors are also responsible for the choice of copula. Our analysis suggests that the attested Old English passives are fully compatible with a compositional analysis; we also discuss additional semantic factors that may be responsible for the lower frequency of passives with weorðan. [ABSTRACT FROM AUTHOR]

A lack of consensus has existed regarding the interaction of English modals with categories such as tense, and individual modal forms can vary in the extent to which they make assertions regarding temporal reference. The present work attempts to provide a compositional semantic account of English modals by proposing that these forms may be inflected both for tense and for mood. The crosslinguistic status of inflectional moods such as the subjunctive is examined; it is argued that an inflectional subjunctive exists in Modern English with semantic properties similar to those of comparable forms in older Indo- European languages, and the extent to which linguistic cues would permit learners of English to acquire such a category is discussed. Data on English modals are reviewed in light of the analysis proposed here to determine its compatibility with observed usage. It is suggested that the analysis proposed here has certain advantages over models in which the observed semantic range of English modals is presented in terms of an unprincipled heterogeneity. [ABSTRACT FROM AUTHOR]

In Old English, the present/past dichotomy of the Germanic verbal system was supplemented by the development of periphrastic forms such as the perfect and pluperfect. However, the inflected past tense continued to be used beside these newer forms to express similar temporal content. The research presented here aims to provide accurate quantitative data on the distribution within Old English texts both of the periphrastic forms and of semantically comparable preterites. Upon analysis, these data reveal a substantial degree of synchronic variation among Old English texts in their use of these grammatical categories, with no observable diachronic trends. The evidence does not suggest that this variation is grammatically motivated; it is hypothesised that the preterite and the periphrastic forms differed in their perceived stylistic value, although the exact details of such a difference may no longer be recoverable. [ABSTRACT FROM AUTHOR]

Stars may be tidally disrupted if, in a single orbit, they are scattered too close to a supermassive black hole (SMBH). Tidal disruption events are thought to power luminous but short-lived accretion episodes that can light up otherwise quiescent SMBHs in transient flares. Here we explore a more gradual process of tidal stripping where stars approach the tidal disruption radius by stellar evolution while in an eccentric orbit. After the onset of mass transfer, these stars episodically transfer mass to the SMBH every pericenter passage, giving rise to low-level flares that repeat on the orbital timescale. Giant stars, in particular, will exhibit a runaway response to mass loss and “spoon-feed” material to the black hole for tens to hundreds of orbital periods. In contrast to full tidal disruption events, the duty cycle of this feeding mode is of order unity for black holes Mbh ≳ 107M☼. This mode of quasi-steady SMBH feeding is competitive with indirect SMBH feeding through stellar winds, and spoon-fed giant stars may play a role in determining the quiescent luminosity of local SMBHs. [ABSTRACT FROM AUTHOR]

MacLeod-Morgan (1979) found a significant relationship between hypnotizability and EEG hemispheric specificity. Hemispheric specificity is defined as the extent to which the alpha ratio between hemispheres changes during lateralized task performance. The present study was designed to replicate and extend this finding. EEG was recorded bilaterally from 44 subjects during performance of two right- and two left-hemisphere discontinuous tasks from MacLeod-Morgan (1979), and four new comparable continuous tasks, As predicted, significant differences were found in hemispheric specificity between low and high hypnotizables especially during the continuous tasks. [ABSTRACT FROM AUTHOR]

White dwarfs (WDs) can be tidally disrupted only by massive black holes (MBHs) with masses less than ∼105M☼. These tidal interactions feed material to the MBH well above its Eddington limit, with the potential to launch a relativistic jet. The corresponding beamed emission is a promising indication of an otherwise quiescent MBH of relatively low mass. We show that the mass transfer history, and thus the light curve, is quite different when the disruptive orbit is parabolic, eccentric, or circular. The mass lost each orbit exponentiates in the eccentric-orbit case, leading to the destruction of the WD after several tens of orbits. We examine the stellar dynamics of clusters surrounding MBHs to show that single-passage WD disruptions are substantially more common than repeating encounters. The 1049 erg s–1 peak luminosity of these events makes them visible to cosmological distances. They may be detectible at rates of as many as tens per year by instruments like Swift. In fact, WD-disruption transients significantly outshine their main-sequence star counterparts and are the tidal interaction most likely to be detected arising from MBHs with masses less than 105M☼. The detection or nondetection of such WD-disruption transients by Swift is, therefore, a powerful tool to constrain the lower end of the MBH mass function. The emerging ultralong gamma-ray burst class of events all have peak luminosities and durations reminiscent of WD disruptions, offering a hint that WD-disruption transients may already be present in existing data sets. [ABSTRACT FROM AUTHOR]

The inspiral and merger of eccentric binaries leads to gravitational waveforms distinct from those generated by circularly merging binaries. Dynamical environments can assemble binaries with high eccentricity and peak frequencies within the LIGO band. In this paper, we study binary-single stellar scatterings occurring in dense stellar systems as a source of eccentrically inspiraling binaries. Many interactions between compact binaries and single objects are characterized by chaotic resonances in which the binary-single system undergoes many exchanges before reaching a final state. During these chaotic resonances, a pair of objects has a non-negligible probability of experiencing a very close passage. Significant orbital energy and angular momentum are carried away from the system by gravitational wave (GW) radiation in these close passages, and in some cases this implies an inspiral time shorter than the orbital period of the bound third body. We derive the cross section for such dynamical inspiral outcomes through analytical arguments and through numerical scattering experiments including GW losses. We show that the cross section for dynamical inspirals grows with increasing target binary semi-major axis a and that for equal-mass binaries it scales as a2/7. Thus, we expect wide target binaries to predominantly contribute to the production of these relativistic outcomes. We estimate that eccentric inspirals account for approximately 1% of dynamically assembled non-eccentric merging binaries. While these events are rare, we show that binary-single scatterings are a more effective formation channel than single-single captures for the production of eccentrically inspiraling binaries, even given modest binary fractions. [ABSTRACT FROM AUTHOR]

The article offers information on the longest tails of gas observed escaping a planet by a team of astronomers using the Habitable-zone Planet Finder Spectrograph (HPF) on Hobby-Eberly Telescope (HET). It mentions that Jupiter HAT-P-32 b was observed using high-resolution spectroscopy which measured helium equivalent widths (EWs) for all HPF spectra of HAT-P-32 A+ b and that three-dimensional (3D) hydrodynamic simulations of the system provided physical insight into the geometry of the outflow.

Sun-like stars are thought to be regularly disrupted by supermassive black holes (SMBHs) within galactic nuclei. Yet, as stars evolve off the main sequence their vulnerability to tidal disruption increases drastically as they develop a bifurcated structure consisting of a dense core and a tenuous envelope. Here we present the first hydrodynamic simulations of the tidal disruption of giant stars and show that the core has a substantial influence on the star's ability to survive the encounter. Stars with more massive cores retain large fractions of their envelope mass, even in deep encounters. Accretion flares resulting from the disruption of giant stars should last for tens to hundreds of years. Their characteristic signature in transient searches would not be the t–5/3 decay typically associated with tidal disruption events, but a correlated rise over many orders of magnitude in brightness on timescales of months to years. We calculate the relative disruption rates of stars of varying evolutionary stages in typical galactic centers, then use our results to produce Monte Carlo realizations of the expected flaring event populations. We find that the demographics of tidal disruption flares are strongly dependent on both stellar and black hole mass, especially near the limiting SMBH mass scale of ∼108M☼. At this black hole mass, we predict a sharp transition in the SMBH flaring diet beyond which all observable disruptions arise from evolved stars, accompanied by a dramatic cutoff in the overall tidal disruption flaring rate. Black holes less massive than this limiting mass scale will show observable flares from both main-sequence and evolved stars, with giants contributing up to 10% of the event rate. The relative fractions of stars disrupted at different evolutionary states can constrain the properties and distributions of stars in galactic nuclei other than our own. [ABSTRACT FROM AUTHOR]

Capturing planets in the act of losing their atmospheres provides rare opportunities to probe their evolution history. This analysis has been enabled by observations of the helium triplet at 10,833 angstrom, but past studies have focused on the narrow time window right around the planet's optical transit. We monitored the hot Jupiter HAT-P-32 b using high-resolution spectroscopy from the Hobby-Eberly Telescope covering the planet's full orbit. We detected helium escaping HAT-P-32 b at a 14σ significance,with extended leading and trailing tails spanning a projected length over 53 times the planet's radius. These tails are among the largest known structures associated with an exoplanet. We interpret our observations using three-dimensional hydrodynamic simulations, which predict Roche Lobe overflow with extended tails along the planet's orbital path.