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Lynne A. Hillenbrand

Publications and source records attributed to Lynne A. Hillenbrand.

At least 91 records · Page 5Linked to original sources

PTF 14jg: The Remarkable Outburst and Post-Burst Evolution of a Previously Anonymous Galactic Star

We report the outbursting source PTF 14jg, which prior to the onset of its late 2013 eruption, was a faint, unstudied, and virtually uncatalogued star. The salient features of the PTF 14jg outburst are: (i) projected location near the W4 HII region and radial velocity consistent with physical association; (ii) a lightcurve that underwent a $\sim$6-7 mag optical (R-band) through mid-infrared (L-band) brightening on a few month time scale, that peaked and then faded by $\sim$3 mag, but plateaued still $>$3.5 mag above quiescence by $\sim$8 months post-peak, lasting to at least five years after eruption; (iii) strong outflow signatures, with velocities reaching -530 km/s; (iv) a low gravity and broad ($\sim$100-150 km/s FWHM) optical absorption line spectrum that systematically changes its spectral type with wavelength; (v) lithium; and (vi) ultraviolet and infrared excess. We tentatively identify the outburst as exhibiting characteristics of a young star FU Ori event. However, the burst would be unusually hot, with an absorption spectrum exhibiting high-excitation ($\sim$11,000-15,000 K) lines in the optical, and no evidence of CO in the near-infrared, in addition to exhibiting an unusual lightcurve. We thus also consider alternative scenarios including various forms of novae, nuclear burning instabilities, massive star events, and mergers -- finding them all inferior to the atypically hot FU Ori star classification. The source eventually may be interpreted as a new category of young star outburst with larger amplitude and shorter rise time than most FU Ori-like events. Continued monitoring of the lightcurve and spectral evolution will reveal its true nature.

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ATLAS Probe: Breakthrough Science of Galaxy Evolution, Cosmology, Milky Way, and the Solar System

ATLAS (Astrophysics Telescope for Large Area Spectroscopy) Probe is a concept for a NASA probe-class space mission. It is the follow-up space mission to WFIRST, boosting its scientific return by obtaining deep IR slit spectroscopy for 70% of all galaxies imaged by a 2000 sq deg WFIRST High Latitude Survey at z>0.5. ATLAS will measure accurate and precise redshifts for 200M galaxies out to z < 7, and deliver spectra that enable a wide range of diagnostic studies of the physical properties of galaxies over most of cosmic history. ATLAS Probe science spans four broad categories: (1) Revolutionizing galaxy evolution studies by tracing the relation between galaxies and dark matter from galaxy groups to cosmic voids and filaments, from the epoch of reionization through the peak era of galaxy assembly; (2) Opening a new window into the dark Universe by weighing the dark matter filaments using 3D weak lensing with spectroscopic redshifts, and obtaining definitive measurements of dark energy and modification of General Relativity using galaxy clustering; (3) Probing the Milky Way's dust-enshrouded regions, reaching the far side of our Galaxy; and (4) Exploring the formation history of the outer Solar System by characterizing Kuiper Belt Objects. ATLAS Probe is a 1.5m telescope with a field of view of 0.4 sq deg, and uses Digital Micro-mirror Devices (DMDs) as slit selectors. It has a spectroscopic resolution of R = 1000 over 1-4 microns, and a spectroscopic multiplex factor >5,000. ATLAS is designed to fit within the NASA probe-class space mission cost envelope; it has a single instrument, a telescope aperture that allows for a lighter launch vehicle, and mature technology. ATLAS Probe will lead to transformative science over the entire range of astrophysics: from galaxy evolution to the dark Universe, from Solar System objects to the dusty regions of the Milky Way.

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Age Determination in Upper Scorpius with Eclipsing Binaries

The Upper Scorpius OB association is the nearest region of recent massive star formation and thus an important benchmark for investigations concerning stellar evolution and planet formation timescales. We present nine EBs in Upper Scorpius, three of which are newly reported here and all of which were discovered from K2 photometry. Joint fitting of the eclipse photometry and radial velocities from newly acquired Keck-I/HIRES spectra yields precise masses and radii for those systems that are spectroscopically double-lined. The binary orbital periods in our sample range from 0.6-100 days, with total masses ranging from 0.2-8 $M_\odot$. At least 33% of the EBs reside in hierarchical multiples, including two triples and one quadruple. We use these EBs to develop an empirical mass-radius relation for pre-main-sequence stars, and to evaluate the predictions of widely-used stellar evolutionary models. We report evidence for an age of 5-7 Myr which is self-consistent in the mass range of 0.3-5 $M_\odot$ and based on the fundamentally-determined masses and radii of eclipsing binaries (EBs). Evolutionary models including the effects of magnetic fields imply an age of 9-10 Myr. Our results are consistent with previous studies that indicate many models systematically underestimate the masses of low-mass stars by 20-60% based on H-R diagram analyses. We also consider the dynamical states of several binaries and compare with expectations from tidal dissipation theories. Finally, we identify RIK 72 b as a long-period transiting brown dwarf ($M = 59.2 \pm 6.8\ M_\mathrm{Jup}$, $R = 3.10 \pm 0.31\ R_\mathrm{Jup}$, $P \approx 97.8$ days) and an ideal benchmark for brown dwarf cooling models at 5-10 Myr.

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Gaia 17bpi: An FU Ori Type Outburst

We report on the source Gaia 17bpi and identify it as a new, ongoing FU Ori type outburst, associated with a young stellar object. The optical lightcurve from Gaia exhibited a 3.5 mag rise with the source appearing to plateau in mid/late 2018. Mid-infrared observations from NEOWISE also show a $>$3 mag rise that occurred in two stages, with the second one coincident with the optical brightening, and the first one preceding the optical brightening by $\sim$1.5 years. We model the outburst as having started between October and December of 2014. This wavelength-dependent aspect of young star accretion-driven outbursts has never been documented before. Both the mid-infrared and the optical colors of the object become bluer as the outburst proceeds. Optical spectroscopic characteristics in the outburst phase include: a GK-type absorption spectrum, strong wind/outflow in e.g. Mgb, NaD, H$α$, KI, OI, and CaII profiles, and detection of LiI 6707 Å. The infrared spectrum in the outburst phase is similar to that of an M-type spectrum, notably exhibiting prominent $H_2O$ and $^{12}$CO (2-0) bandhead absorption in the K-band, and likely HeI wind in the Y-band. The new FU Ori source Gaia 17bpi is associated with a little-studied dark cloud in the galactic plane, located at a distance of 1.27 kpc.

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Kinematics in Young Star Clusters and Associations with Gaia DR2

The Gaia mission has opened a new window into the internal kinematics of young star clusters at the sub-km/s level, with implications for our understanding of how star clusters form and evolve. We use a sample of 28 clusters and associations with ages from 1-5 Myr, where lists of members are available from previous X-ray, optical, and infrared studies. Proper motions from Gaia DR2 reveals that at least 75% of these systems are expanding; however, rotation is only detected in one system. Typical expansion velocities are on the order of ~0.5 km/s, and, in several systems, there is a positive radial gradient in expansion velocity. Systems that are still embedded in molecular clouds are less likely to be expanding than those that are partially or fully revealed. One-dimensional velocity dispersions, which range from 1 to 3 km/s, imply that most of the stellar systems in our sample are supervirial and that some are unbound. In star-forming regions that contain multiple clusters or subclusters, we find no evidence that these groups are coalescing, implying that hierarchical cluster assembly, if it occurs, must happen rapidly during the embedded stage.

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Discovery of a Transiting Adolescent Sub-Neptune Exoplanet with K2

The role of stellar age in the measured properties and occurrence rates of exoplanets is not well understood. This is in part due to a paucity of known young planets and the uncertainties in age-dating for most exoplanet host stars. Exoplanets with well-constrained ages, particularly those which are young, are useful as benchmarks for studies aiming to constrain the evolutionary timescales relevant for planets. Such timescales may concern orbital migration, gravitational contraction, or atmospheric photo-evaporation, among other mechanisms. Here we report the discovery of an adolescent transiting sub-Neptune from K2 photometry of the low-mass star K2-284. From multiple age indicators we estimate the age of the star to be 120 Myr, with a 68% confidence interval of 100-760 Myr. The size of K2-284 b ($R_P$ = 2.8 $\pm$ 0.1 $R_\oplus$) combined with its youth make it an intriguing case study for photo-evaporation models, which predict enhanced atmospheric mass loss during early evolutionary stages.

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The many-faceted light curves of young disk-bearing stars in Upper Sco and $ρ$ Oph observed by $K2$ Campaign 2

The $K2$ Mission has photometrically monitored thousands of stars at high precision and cadence in a series of $\sim$80-day campaigns focused on sections of the ecliptic plane. During its second campaign, $K2$ targeted over 1000 young stellar objects (YSOs) in the $\sim$1-3 Myr $ρ$ Ophiuchus and 5-10 Myr Upper Scorpius regions. From this set, we have carefully vetted photometry from {\em WISE} and {\em Spitzer} to identify those YSOs with infrared excess indicative of primordial circumstellar disks. We present here the resulting comprehensive sample of 288 young disk-bearing stars from B through M spectral types and analysis of their associated $K2$ light curves. Using statistics of periodicity and symmetry, we categorize each light curves into eight different variability classes, notably including "dippers" (fading events), "bursters" (brightening events), stochastic, and quasi-periodic types. Nearly all (96\%) of disk-bearing YSOs are identified as variable at 30-minute cadence with the sub-1\% precision of {\em K2}. Combining our variability classifications with (circum)stellar properties, we find that the bursters, stochastic sources, and the largest amplitude quasi-periodic stars have larger infrared colors, and hence stronger circumstellar disks. They also tend to have larger H$α$ equivalent widths, indicative of higher accretion rates. The dippers, on the other hand, cluster toward moderate infrared colors and low H$α$. Using resolved disk observations, we further find that the latter favor high inclinations, apart from a few notable exceptions with close to face-on disks. These observations support the idea that YSO time domain properties are dependent on several factors including accretion rate and view angle.

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Three small planets transiting the bright young field star K2-233

We report the detection of three small transiting planets around the young K3 dwarf K2-233 (2MASS J15215519-2013539) from observations during Campaign 15 of the K2 mission. The star is relatively nearby ($d$ = 69 pc) and bright ($V$ = 10.7 mag, $K_s$ = 8.4 mag), making the planetary system an attractive target for radial velocity follow-up and atmospheric characterization with the James Webb Space Telescope. The inner two planets are hot super-Earths ($R_b$ = 1.40 $\pm$ 0.06 R$_\oplus$, $R_c$ = 1.34 $\pm$ 0.08 R$_\oplus$), while the outer planet is a warm sub-Neptune ($R_d$ = 2.6 $\pm$ 0.1 R$_\oplus$). We estimate the stellar age to be 360$^{+490}_{-140}$ Myr based on rotation, activity, and kinematic indicators. The K2-233 system is particularly interesting given recent evidence for inflated radii in planets around similarly-aged stars, a trend potentially related to photo-evaporation, core-cooling, or both mechanisms.

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Robo-AO Discovery and Basic Characterization of Wide Multiple Star Systems in the Pleiades, Praesepe, and NGC 2264 Clusters

We identify and roughly characterize 66 candidate binary star systems in the Pleiades, Praesepe, and NGC 2264 star clusters based on robotic adaptive optics imaging data obtained using Robo-AO at the Palomar 60" telescope. Only $\sim$10% of our imaged pairs were previously known. We detect companions at red optical wavelengths having physical separations ranging from a few tens to a few thousand AU. A 3-sigma contrast curve generated for each final image provides upper limits to the brightness ratios for any undetected putative companions. The observations are sensitive to companions with maximum contrast $\sim$6$^m$ at larger separations. At smaller separations, the mean (best) raw contrast at 2 arcsec is 3.8$^m$ (6$^m$), at 1 arcsec is 3.0$^m$ (4.5$^m$), and at 0.5 arcsec is 1.9$^m$ (3$^m$). PSF subtraction can recover close to the full contrast in to the closer separations. For detected candidate binary pairs, we report separations, position angles, and relative magnitudes. Theoretical isochrones appropriate to the Pleiades and Praesepe clusters are then used to determine the corresponding binary mass ratios, which range from 0.2-0.9 in $q=m_2/m_1$. For our sample of roughly solar-mass (FGK type) stars in NGC 2264 and sub-solar-mass (K and early M-type) primaries in the Pleiades and Praesepe, the overall binary frequency is measured at $\sim$15.5% $\pm$ 2%. However, this value should be considered a lower limit to the true binary fraction within the specified separation and mass ratio ranges in these clusters, given that complex and uncertain corrections for sensitivity and completeness have not been applied.

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How do stars gain their mass? A JCMT/SCUBA-2 Transient Survey of Protostars in Nearby Star Forming Regions

Most protostars have luminosities that are fainter than expected from steady accretion over the protostellar lifetime. The solution to this problem may lie in episodic mass accretion -- prolonged periods of very low accretion punctuated by short bursts of rapid accretion. However, the timescale and amplitude for variability at the protostellar phase is almost entirely unconstrained. In "A JCMT/SCUBA-2 Transient Survey of Protostars in Nearby Star Forming Regions", we are monitoring monthly with SCUBA-2 the sub-mm emission in eight fields within nearby (<500 pc) star forming regions to measure the accretion variability of protostars. The total survey area of ~1.6 sq.deg. includes ~105 peaks with peaks brighter than 0.5 Jy/beam (43 associated with embedded protostars or disks) and 237 peaks of 0.125-0.5 Jy/beam (50 with embedded protostars or disks). Each field has enough bright peaks for flux calibration relative to other peaks in the same field, which improves upon the nominal flux calibration uncertainties of sub-mm observations to reach a precision of ~2-3% rms, and also provides quantified confidence in any measured variability. The timescales and amplitudes of any sub-mm variation will then be converted into variations in accretion rate and subsequently used to infer the physical causes of the variability. This survey is the first dedicated survey for sub-mm variability and complements other transient surveys at optical and near-IR wavelengths, which are not sensitive to accretion variability of deeply embedded protostars.

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New low-mass eclipsing binary systems in Praesepe discovered by K2

We present the discovery of four low-mass ($M<0.6$ $M_\odot$) eclipsing binary (EB) systems in the sub-Gyr old Praesepe open cluster using Kepler/K2 time-series photometry and Keck/HIRES spectroscopy. We present a new Gaussian process eclipsing binary model, GP-EBOP, as well as a method of simultaneously determining effective temperatures and distances for EBs. Three of the reported systems (AD 3814, AD 2615 and AD 1508) are detached and double-lined, and precise solutions are presented for the first two. We determine masses and radii to 1-3% precision for AD 3814 and to 5-6% for AD 2615. Together with effective temperatures determined to $\sim$50 K precision, we test the PARSEC v1.2 and BHAC15 stellar evolution models. Our EB parameters are more consistent with the PARSEC models, primarily because the BHAC15 temperature scale is hotter than our data over the mid M-dwarf mass range probed. Both ADs 3814 and 2615, which have orbital periods of 6.0 and 11.6 days, are circularized but not synchronized. This suggests that either synchronization proceeds more slowly in fully convective stars than the theory of equilibrium tides predicts or magnetic braking is currently playing a more important role than tidal forces in the spin evolution of these binaries. The fourth system (AD 3116) comprises a brown dwarf transiting a mid M-dwarf, which is the first such system discovered in a sub-Gyr open cluster. Finally, these new discoveries increase the number of characterized EBs in sub-Gyr open clusters by 20% (40%) below $M<1.5$ $M_{\odot}$ ($M<0.6$ $M_{\odot}$).

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A Low-Mass Exoplanet Candidate Detected By ${\it K2}$ Transiting the Praesepe M Dwarf JS 183

We report the discovery of a repeating photometric signal from a low-mass member of the Praesepe open cluster that we interpret as a Neptune-sized transiting planet. The star is JS 183 (HSHJ 163, EPIC 211916756) with $T_{\rm eff} = 3325\pm100$ K, $M_{*} = 0.44\pm0.04$ $M_{\odot}$, $R_{*} = 0.44\pm0.03$ $R_{\odot}$, and $\log{g_*} = 4.82\pm0.06$. The planet has an orbital period of 10.134588 days and a radius of $R_{P}= 0.32\pm0.02$ $R_J$. Since the star is faint at $V=16.5$ and $J=13.3$, we are unable to obtain a measured radial-velocity orbit, but we can constrain the companion mass to below about 1.7 $M_J$, and thus well below the planetary boundary. JS 183b (since designated as K2-95b) is the second transiting planet found with ${\it K2}$ that resides in a several hundred Myr open cluster; both planets orbit mid-M dwarf stars and are approximately Neptune-sized. With a well-determined stellar density from the planetary transit, and with an independently known metallicity from its cluster membership, JS 183 provides a particularly valuable test of stellar models at the fully convective boundary. We find that JS 183 is the lowest-density transit host known at the fully convective boundary, and that its very low density is consistent with current models of stars just above the fully convective boundary but in tension with the models just below the fully convective boundary.

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The Greater Taurus-Auriga Ecosystem I: There Is A Distributed Older Population

The Taurus-Auriga association and its associated molecular cloud are a benchmark population for studies of star and planet formation. The census of Taurus-Auriga has been assembled over seven decades and has inherited the biases, incompleteness, and systematic uncertainties of the input studies. The notably unusual shape of the inferred IMF and the existence of several isolated disk-bearing stars suggest that additional (likely disk-free) members might remain to be discovered. We therefore have begun a global reassessment of the membership of Taurus-Auriga that exploits new data and better definitions of youth and kinematic membership. As a first step, we reconsider the membership of all disk-free candidate members from the literature with spectral type $\ge$F0, $3^h50^m<α<5^h40^m$, and $14^{\circ}<δ<34^{\circ}$. We combine data from the literature with Keck/HIRES and UH88/SNIFS spectra to test the membership of these candidates using HR diagram positions, proper motions, RVs, H$α$, lithium, and surface gravity. We find 218 confirmed or likely Taurus members, 160 confirmed or likely interlopers, and only 18 that still lack sufficient evidence to draw firm conclusions. A significant fraction of these stars (81/218=37%) are not included in the most recent canonical member lists. Intriguingly, there are few additional members in the immediate vicinity of the molecular clouds, preserving the IMFs that have been deemed anomalous in past work. Many of the likely Taurus members are distributed broadly across the search area. When combined with known disk hosts, our updated census reveals two regimes: a high-density population with a high disk fraction (indicative of youth) that broadly traces the molecular clouds, and a low-density population with low disk fraction (hence likely older) that most likely represents previous generations of star formation.

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A continuum of accretion burst behavior in young stars observed by K2

We present 29 likely members of the young $ρ$ Oph or Upper Sco regions of recent star formation that exhibit "accretion burst" type light curves in $K2$ time series photometry. The bursters were identified by visual examination of their ~80 day light curves, though all satisfy the $M < -0.25$ flux asymmetry criterion for burst behavior defined by Cody et al. (2014). The burst sources represent $\approx$9% of cluster members with strong infrared excess indicative of circumstellar material. Higher amplitude burster behavior is correlated with larger inner disk infrared excesses, as inferred from $WISE$ $W1-W2$ color. The burst sources are also outliers in their large H$α$ emission equivalent widths. No distinction between bursters and non-bursters is seen in stellar properties such as multiplicity or spectral type. The frequency of bursters is similar between the younger, more compact $ρ$ Oph region, and the older, more dispersed Upper Sco region. The bursts exhibit a range of shapes, amplitudes (~10-700%), durations (~1-10 days), repeat time scales (~3-80 days), and duty cycles (~10-100%). Our results provide important input to models of magnetospheric accretion, in particular by elucidating the properties of accretion-related variability in the low state between major longer duration events such as EX Lup and FU Ori type accretion outbursts. We demonstrate the broad continuum of accretion burst behavior in young stars -- extending the phenomenon to lower amplitudes and shorter timescales than traditionally considered in the theory of pre-main sequence accretion history.

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A Transient Transit Signature Associated with the Young Star RIK-210

We find transient, transit-like dimming events within the K2 time series photometry of the young star RIK-210 in the Upper Scorpius OB association. These dimming events are variable in depth, duration, and morphology. High spatial resolution imaging revealed the star is single, and radial velocity monitoring indicated that the dimming events can not be due to an eclipsing stellar or brown dwarf companion. Archival and follow-up photometry suggest the dimming events are transient in nature. The variable morphology of the dimming events suggests they are not due to a single, spherical body. The ingress of each dimming event is always shallower than egress, as one would expect for an orbiting body with a leading tail. The dimming events are periodic and synchronous with the stellar rotation. However, we argue it is unlikely the dimming events could be attributed to anything on the stellar surface based on the observed depths and durations. Variable obscuration by a protoplanetary disk is unlikely on the basis that the star is not actively accreting and lacks the infrared excess associated with an inner disk. Rather, we explore the possibilities that the dimming events are due to magnetospheric clouds, a transiting protoplanet surrounded by circumplanetary dust and debris, eccentric orbiting bodies undergoing periodic tidal disruption, or an extended field of dust or debris near the corotation radius.

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K2 Discovers a Busy Bee: An Unusual Transiting Neptune Found in the Beehive Cluster

Open clusters have been the focus of several exoplanet surveys but only a few planets have so far been discovered. The \emph{Kepler} spacecraft revealed an abundance of small planets around small, cool stars, therefore, such cluster members are prime targets for exoplanet transit searches. Kepler's new mission, K2, is targeting several open clusters and star-forming regions around the ecliptic to search for transiting planets around their low-mass constituents. Here, we report the discovery of the first transiting planet in the intermediate-age (800 Myr) Beehive cluster (Praesepe). K2-95 is a faint ($\mathrm{Kp = 15.5\,mag}$) $\mathrm{M3.0\pm0.5}$ dwarf from K2's Campaign 5 with an effective temperature of $\mathrm{3471 \pm 124\,K}$, approximately solar metallicity and a radius of $\mathrm{0.402 \pm 0.050 \,R_\odot}$. We detected a transiting planet with a radius of $\mathrm{3.47^{+0.78}_{-0.53} \, R_\oplus}$ and an orbital period of 10.134 days. We combined photometry, medium/high-resolution spectroscopy, adaptive optics/speckle imaging and archival survey images to rule out any false positive detection scenarios, validate the planet, and further characterize the system. The planet's radius is very unusual as M-dwarf field stars rarely have Neptune-sized transiting planets. The comparatively large radius of K2-95b is consistent with the other recently discovered cluster planets K2-25b (Hyades) and K2-33b (Upper Scorpius), indicating systematic differences in their evolutionary states or formation. These discoveries from K2 provide a snapshot of planet formation and evolution in cluster environments and thus make excellent laboratories to test differences between field-star and cluster planet populations.

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The Eruption of the Candidate Young Star ASASSN-15qi

Outbursts on young stars are usually interpreted as accretion bursts caused by instabilities in the disk or the star-disk connection. However, some protostellar outbursts may not fit into this framework. In this paper, we analyze optical and near-infrared spectra and photometry to characterize the 2015 outburst of the probable young star ASASSN-15qi. The $\sim 3.5$ mag brightening in the $V$ band was sudden, with an unresolved rise time of less than one day. The outburst decayed exponentially by 1 mag for 6 days and then gradually back to the pre-outburst level after 200 days. The outburst is dominated by emission from $\sim10,000$ K gas. An explosive release of energy accelerated matter from the star in all directions, seen in a spectacular cool, spherical wind with a maximum velocity of 1000 km/s. The wind and hot gas both disappeared as the outburst faded and the source returned to its quiescent F-star spectrum. Nebulosity near the star brightened with a delay of 10-20 days. Fluorescent excitation of H$_2$ is detected in emission from vibrational levels as high as $v=11$, also with a possible time delay in flux increase. The mid-infrared spectral energy distribution does not indicate the presence of warm dust emission, although the optical photospheric absorption and CO overtone emission could be related to a gaseous disk. Archival photometry reveals a prior outburst in 1976. Although we speculate about possible causes for this outburst, none of the explanations are compelling.

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A Neptune-sized transiting planet closely orbiting a 5-10-million-year-old star

Theories of the formation and early evolution of planetary systems postulate that planets are born in circumstellar disks, and undergo radial migration during and after dissipation of the dust and gas disk from which they formed. The precise ages of meteorites indicate that planetesimals - the building blocks of planets - are produced within the first million years of a star's life. A prominent question is: how early can one find fully formed planets like those frequently detected on short orbital periods around mature stars? Some theories suggest the in situ formation of planets close to their host stars is unlikely and the existence of such planets is evidence for large scale migration. Other theories posit that planet assembly at small orbital separations may be common. Here we report on a newly-born, transiting planet orbiting its star every 5.4 days. The planet is 50 per cent larger than Neptune, and its mass is less than 3.6 times Jupiter (at 99.7 per cent confidence), with a true mass likely to be within a factor of several of Neptune's. The 5-10 million year old star has a tenuous dust disk extending outwards from about 2 times the Earth-Sun separation, in addition to the large planet located at less than one-twentieth the Earth-Sun separation.

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