Title : Large Impacts around a Solar Analog Star in the Era of Terrestrial Planet Formation

The final assembly of terrestrial planets occurs via massive collisions, which can launch copious clouds of dust that are warmed by the star and glow in the infrared. We report the real-time detection of a debris-producing impact in the terrestrial planet zone around a 35-million year-old solar analog star. We observed a substantial brightening of the debris disk at 3-5 μm, followed by a decay over a year, with quasi-periodic modulations of the disk flux. The behavior is consistent with the occurrence of a violent impact that produced vapor out of which a thick cloud of silicate spherules condensed that were ground into dust by collisions. These results demonstrate how the time domain can become a new dimension for the study of terrestrial planet formation. One Sentence Summary: We observe production and time evolution of dust clouds around a solar analog star, resulting from a violent collision of large bodies in the era of terrestrial planet formation. Main Text: Circumstellar disks are where planetary systems form and evolve. Gas rich and optically thick protoplanetary disks are born together with young stars but dissipate within a few million years (Myr), setting the timescale for gas giant planet formation (1). Dusty, optically thin debris disks then emerge, sustained by fragmentation of colliding planetesimals (2). They are warmed by their stars and light up in the infrared, allowing them to be detected over the entire lifetimes of main sequence stars. Consequently, debris disks are ideal tools to search for phases occurring in other planetary systems that are analogous to major events in the evolution of the solar system, such as the formation of terrestrial planets. Dynamical simulations and meteoritics indicate that the end stage of terrestrial planet formation, from ~30 to ~100 Myr (e.g., 3, 4), is marked by frequent large impacts, up to the scale of the one leading to the formation of the Moon (5-7). Such events can produce a huge amount of dust, which may dramatically increase the infrared emission from the debris disk (e.g., 8). ID8 (2MASS J08090250-4858172) is a young solar analog star with spectral type G6V and solar metallicity in the 35-Myr-old open cluster NGC 2547 (9). It emits strongly in the infrared, with a fractional disk luminosity of Ldisk/L*=3.2×10 (10). The mid-infrared spectrum of ID8 (observed in 2007) shows strong crystalline silicate features from 8 to 30 μm, indicative of very fine dust particles (Fig. 1); models for the observed spectral energy distribution (SED) require sub-μmsized amorphous silicate dust as well (cf. 10). Particles are blown out by radiation pressure and lost to the system if the ratio of radiation to gravitational forces is larger than 0.5. For ID8, the critical radius (11) below which non-porous silicate grains are lost is ~0.5 μm. The tiniest particles in the disk are smaller than this limit, suggesting ongoing dust replenishment in the system. The disk emission was recently found to vary on a yearly timescale (8). Collisional cascades among planetesimals sustain most debris disks. However variations this rapid cannot be supported by this means because the cascade timescales for significant variations in dust production are at least a few hundred orbits (8). To explore the origin of the variations, we have used the Infrared Array Camera (IRAC, 12) onboard the Spitzer Space Telescope to monitor the ID8 system. The observations extended from May 25, 2012 to August 23, 2013, providing a total time baseline of 454 days with a 157-day gap between visibility windows. At the same time, intensive optical monitoring of ID8 was obtained from the ground in the V and Cousins I (IC hereafter) bands where we found that the output of the star is stable within ~1.5% RMS (supplementary online text). Because the stellar contribution is effectively constant in time, we fitted its spectrum and removed it from the total (star + disk) infrared fluxes to obtain the light curves of the debris disk, as shown in Fig. 2. This revealed an average disk color of [3.6]-[4.5]=1.00, corresponding to a blackbody temperature of 730 K, consistent with the temperatures found in previous analyses of the infrared spectroscopy (10). We calculated the expected color trend of the entire ID8 system for possible causes of the disk variations and compared with our data. The result is not conclusive within the errors, but suggests that a combination of changing dust temperature and dust emitting area, or in area alone rather than purely in temperature, may be responsible for the disk variations (supplementary online text). In the following analysis, we focus on the 4.5 μm data where we have observations from both years and the disk is measured at a higher signal-to-noise ratio. The data at 3.6 μm show consistent behavior, although at lower signal-to-noise. In 2012, the disk flux density stayed near 2.2 milli-Jansky (mJy) despite ~10% variations. However, at the start of 2013 it had brightened to above 3.0 mJy, indicating a significant increase of the amount of dust, probably from a new impact before 2013. This elevated level then decayed throughout 2013. An exponential fit suggests a decay timescale of ~370 days at both wavelengths. This is too fast to be reconciled with decades-long collisional cascades (8), and is too slow for the direct radiative blowout of tiny particles, which should take <30 days at the orbit derived below for the disk. To better understand the impact, we estimate the disk mass based on a fit to the entire midinfrared spectrum, which is dominated by small grains. Since the new debris in the disk has not reached equilibrium in a full collisional cascade, we could not make the conventional assumption of a power law size distribution. For emitting grains of 0.5 μm in radius we found a disk mass of 1.1×10 kg, which is a lower limit since it ignores larger particles. An independent estimate assuming a power law grain size distribution up to 1 mm obtains an identical mass estimate (10). This mass, if the grains were compacted into a solid body, is equivalent to a ~180-km diameter asteroid (of density 3700 kg m). Given the estimated mass and particle size, the ID8 disk may be optically thick, in which significant mass could be obscured and unseen. Considering the decay in 2013, and assuming it applies to the full spectrum, we estimated the mass loss rate to be at least 10 kg s. The spectrum was obtained in 2007; however, the Spitzer and WISE photometric points (Fig. 1) imply that the mid-infrared spectrum had a similar shape at least from January 2004 through November 2010. That is, it appears that the small grains, with a net volume of a ~180-km diameter asteroid, were lost from the system and would have to be replenished on a decadal (or shorter) timescale to maintain the mid-infrared spectrum. Though arising from different physical processes, the mass loss rate is 5-7 orders of magnitude greater than the dust mass loss rates of comets Hale-Bopp (13) and Halley (14), among the dustiest comets known in the solar system, and is 3 orders of magnitude greater than that of the evaporating planet KIC 12557548b (15). The variability of the infrared emission of ID8 is much too fast to arise in a conventional debris disk sustained by a collisional cascade (8). We hypothesize that the impact responsible for the increased disk emission in 2013 involved two large bodies and was sufficiently violent to yield a silica-rich vapor plume. Glassy silicate spherules will condense from the vapor with diverse forms (e.g., 16), consistent with the presence of amorphous silicates in the SED model (10). In this case, there may have been temporal spectral features after the new impact, but would have been missed because we do not have new mid-infrared spectrum in 2013. The condensation process has been modeled in (17), which shows that the typical spherule size depends sensitively on the circumstances of the impact, particularly its velocity, but ranges from about 10 μm to 1 mm. The condensates are produced quickly over several hours. Initially, the cloud of spherules will not radiate efficiently in the mid-infrared because the total surface area of all the spherules is small. However, they will break each other down through collisions, which generate the observed μm-sized or smaller particles as daughter products. The infrared output will rise as the mass is distributed into many small grains, making the consequences of the initial impact visible as an increase in the infrared emission. Because the size distribution of condensate spherules is strongly peaked around the average (17), we treat them as being equal in size. Then, a rough estimate of the timescale for destroying them (and hence for the decay of the debris cloud) can be obtained by attributing all the disk mass to them immediately after the impact and assuming that they are removed by breakdown in a collisional cascade with eventual ejection, when their daughter particles are sub-μm in size, by radiation pressure. We found that different models for the destruction rate of such spherules give consistent timescales (18, 19). To order of magnitude, the range of decay timescales as a function of spherule size from 10 to 1000 μm is 100 days to 10 years. The observed decay time of the ID8 disk corresponds to a spherule size of ~100 μm, which corresponds to an impact velocity of 1518 km s (for a 100-1000 km diameter body impacting on an even larger one, 17). Thus, the oneyear exponential decay timescale is a natural result for a system where seed grains have condensed from a vapor cloud and are destroying themselves through collisions. An analysis with some similarities to ours for the bright debris disk of HD 172555 (20) found that dust created in a hypervelocity impact will have a size slope of ~-4, in agreement with the fits of (10) to the infrared spectrum of ID8. After the exponential decay is removed from the data (“detrending”), the light curves at both wavelengths appear to be quasi-periodic. The regular recovery of the disk flux and lack of extraordinary stellar activity essentially eliminate coronal mass ejection (21) as a possible driver for the disk variability. We employed the SigSpec algorithm (22) to search for complex patterns in the detrended, post-impact 2013 light curve. The analysis identified two significant frequencies with comparable amplitudes, whose periods are P1=25.4±1.1 days and P2=34.0±1.5 days (Fig. 3(A)) and are sufficient to reproduce qualitatively most of the observed light curve features (Fig. 3(B)). The quoted uncertainties (23) do not account for systematic effects due to the detrending, and thus are lower limits to the real errors. Other peaks with longer periods in the periodogram are aliases, or possibly reflect long-term deviation from the exponential decay. These artifacts make it difficult to determine if there are weak real signals near those frequencies. We now describe the most plausible interpretation of this light curve that we have found. The two identified periods have a peak-to-peak amplitude of ~6×10 in fractional luminosity, which provides a critical constraint for models of the ID8 disk. In terms of sky coverage at the disk distance inferred from the infrared SED, such an amplitude requires disappearance and reappearance every ~30 days of the equivalent of an opaque, stellar facing “dust panel” of radius ~110 Jupiter radii. One possibility is that the disk flux periodicity arises from recurring geometry that changes the amount of dust that we can see. At the time of the impact, fragments get a range of kick velocities when escaping into interplanetary space. This will cause Keplerian shear of the cloud (24), leading to an expanding debris concentration along the original orbit (supplementary online text). If the ID8 planetary system is roughly edge-on, the longest dimension of the concentration will be parallel to our line of sight at the greatest elongations, and orthogonal to the line of sight near conjunctions to the star. This would cause the optical depth of the debris to vary within an orbital period, in a range on the order of 1-10 according to the estimated disk mass and particle sizes. Our numerical simulations of such dust concentrations on moderately eccentric orbits are able to produce periodic light curves with strong overtones. P2 and P1 should have a 3:2 ratio if they are the first and second order overtones of a fundamental, which is consistent with the measurements within the expected larger errors (<2σ or better). In this case, the genuine period should be 70.8±5.2 days (lower limit errors), a value where it may have been submerged in the periodogram artifacts. This period corresponds to a semi-major axis of ~0.33 AU, which is consistent with the temperature and distance suggested by the spectral models (10). Despite the peculiarities of ID8, it is not a unique system. 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