New HST Data and Modeling Reveal a Massive Planetesimal Collision Around Fomalhaut

Home , Fomalhaut, Fomalhaut b, Paul Kalas

New HST data and modeling reveal a massive planetesimal collision around Fomalhaut

Andras´ Gasp´ ar´ a,1 and George H. Riekea

aSteward Observatory, The University of Arizona, Tucson, AZ 85719

Edited by Neta A. Bahcall, Princeton University, Princeton, NJ, and approved January 15, 2020 (received for review July 19, 2019)

The apparent detection of an exoplanet orbiting Fomalhaut the constraints from assuming that the phenomenon has per- was announced in 2008. However, subsequent observations of sisted for the life of the star and that the image is point-like. Fomalhaut b raised questions about its status: Unlike other exo- Ref. 20 found that satellite swarms around planets of mass 10 planets, it is bright in the optical and nondetected in the infrared, to 100 MEarth that have evolved for 100 to 400 My could match and its orbit appears to cross the debris ring around the star the properties of Fomalhaut b. Ref. 17 suggested that the object without the expected gravitational perturbations. We revisit pre- could consist of dust created in the collision of two modest-sized viously published data and analyze additional Hubble Space (50 km) planetesimals similar to members of the Kuiper Belt. Telescope (HST) data, finding that the source is likely on a radial Ref. 18 analyzed three possible origins for the required dust trajectory and has faded and become extended. Dynamical and cloud: 1) a giant planetesimal impact, 2) material captured from collisional modeling of a recently produced dust cloud yields the prominent debris disk of the star, or 3) dust generated in results consistent with the observations. Fomalhaut b appears a collisional cascade from a massive cloud of satellites around to be a directly imaged catastrophic collision between two large a recently formed planet. The first possibility was judged to be planetesimals in an extrasolar planetary system. Similar events unlikely to reproduce the observations (21). The other two pos- should be very rare in quiescent planetary systems of the age sibilities are constrained significantly by the assumption that the of Fomalhaut, suggesting that we are possibly witnessing the dust system should persist in a state similar to its present one effects of gravitational stirring due to the orbital evolution of for the main sequence lifetime of the star, i.e., ∼400 My. Ref. hypothetical planet(s) around the star. 19 suggested a possible solution to the lifetime issues by attribut- ing the source to a transient dust cloud produced by a collision extrasolar planets | circumstellar disks | directly imaged planets between planetesimals interior to the main debris belt around the star. We report that Fomalhaut b has grown in extent and faded he simultaneous announcements of images of massive plan- since its discovery in Hubble Space Telescope (HST) images Tets around Fomalhaut (1) and HR 8799 (2) were a bench- from 2004, with motion consistent with an escaping trajectory. mark in our exploration of exoplanets. The HR 8799 system This behavior is consistent with expectations for a dust cloud pro- has indeed become the prototype for complex systems of very duced in a planetesimal collision and dispersing dynamically. As massive planets and has been the subject of many studies of the cloud disperses, its surface brightness has dropped, making it such objects (e.g., refs. 3–7). However, Fomalhaut b has been less prominent in the most recent images. enigmatic. An issue with the massive planet hypothesis for Fomalhaut b was the nondetection with the Infrared Array Camera (IRAC) Significance onboard the Spitzer Space Telescope (8), which placed an upper limit of 3 Jupiter masses (MJup) on its mass assuming an age Although originally thought to be a massive exoplanet, the for Fomalhaut of 200 My. A similar limit was derived from the faintness of Fomalhaut b in the infrared and its failure to per- lack of apparent perturbations in the Fomalhaut debris ring; this turb Fomalhaut’s debris ring indicate a low mass. We use all work favored a significantly smaller mass, e.g., 0.5 MJup (9). An available data to reveal that it has faded in brightness and upward revision of the system age to 440 ± 40 My (10) relaxed grown in extent, with motion consistent with an escaping the limit from the infrared data, but a much deeper limit was orbit. This behavior confirms suggestions that the source is obtained with Spitzer IRAC that pushed the mass limit lower. In a dispersing cloud of dust, produced by a massive collision fact, this limit appeared to be incompatible with a massive planet between two planetesimals. The visible signature appears to accounting for the visible brightness of the object (11, 12). With be very fine dust escaping under the influence of radiation determination of an orbit for Fomalhaut b, it became apparent pressure. Such events should be rare in quiescent plane- that the object would cross the ring at least in projection (13). tary systems at the age of Fomalhaut, suggesting increased The implications on the ring structure placed a tentative limit on dynamical activity within the system possibly due to orbital the mass of Fomalhaut b as low as an Earth mass (14). migration of hypothetical planets. Given that the bright optical signature of Fomalhaut b seems

not to be light scattered from a giant planet, a number of alter- Author contributions: A.G. and G.H.R. designed research; A.G. performed research; A.G. native hypotheses have been proposed, e.g., light scattered by contributed analytic tools; A.G. analyzed data; and A.G. and G.H.R. wrote the paper.y a circumplanetary ring system (1) or by a dust cloud associated The authors declare no competing interest.y with a relatively low-mass planet (e.g., refs. 11, 15, and 16). A ten- This article is a PNAS Direct Submission.y tative ﬁnding that the image of Fomalhaut b might be extended Published under the PNAS license.y was interpreted to support the dust cloud hypothesis (17); how- Data deposition: The raw observational data can be downloaded from the Mikulski ever, it was suggested that this effect instead might be due to Archive for Space Telescopes (MAST) website maintained by the Space Telescope speckle and other noise sources (13, 18). Nonetheless, a dust Science Institute (STScI). Our modeling code, DiskDyn, can be downloaded from cloud appears to be the most plausible hypothesis. https://github.com/merope82/DiskDyn.y A number of papers have addressed the origin of this hypo- 1 To whom correspondence may be addressed. Email: [email protected] thetical dust cloud (15, 17–19). Ref. 15 suggested that collisions This article contains supporting information online at https://www.pnas.org/lookup/suppl/ among a swarm of satellites around a planet could be respon- doi:10.1073/pnas.1912506117/-/DCSupplemental.y sible and showed that certain models of this process lie within First published April 20, 2020.

9712–9722 | PNAS | May 5, 2020 | vol. 117 | no. 18 www.pnas.org/cgi/doi/10.1073/pnas.1912506117 Downloaded by guest on September 26, 2021 Downloaded by guest on September 26, 2021 O09*20-0ACS 2004-10 GO10390* O09*20-7ASF3W 66,F1WCRN.,CRN. 53 CORON3.0 CORON1.8, F814W F606W, F435W, ACS STIS 2010-06|09 2006-07 GO11818* GO10598* O27*21-5STIS 2013 2012-05 GO13037 GO12576* O32 2014 GO13726 G ‡ b. Fomalhaut of † data. May. published 05, *Previously June|September; 06|09, July; 07, October; ACS Instrument 2004-05|08 Date GO9862* system Fomalhaut the of ID observations Program coronagraphic HST Multiroll 1. 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ASTRONOMY edge-on or inclined narrow-belt disk systems, such as that of enables high-precision registering of all data to the same coor- Fomalhaut. dinates. We did, however, notice small interorbit variations The STIS coronagraph consists of two occulting wedges and and therefore decided to construct PSFs for each exposure two occulting bars. The GO11818 program observed Fomalhaut sequence ID, median combining all first, second, etc., images in 2010 using the 2.500-wide position on the “B” wedge. Deeper of all orbits. This method follows the ADI technique, but also images at the same occulting position were obtained in 2012 folds in the thermal changes to the HST optical telescope (GO12576) and 2013 (GO13037) using additional roll angles assembly (OTA). (for a total of 12), which helps to suppress PSF subtraction The Lyot stop for the STIS coronagraph blocks only light residuals as well as establishing a better PSF for ADI. The from the edges of the OTA; therefore, the diffraction spikes 2014 observations (GO13726) integrated for a slightly shorter are prominent in the images and only the wings of the PSF time, but the STIS observations are contrast and not photon are suppressed. While this necessitates additional masking dur- limited, so the data are still adequate for the detection of ing image processing and reduces the imaging real estate, Fomalhaut b. it also allows precise locating of the central star for image The reduction of the STIS data followed similar steps to those derotation. Following image registering with PSF subtraction for the ACS data. The level of geometric distortion for STIS residuals, the location of the star (determined by tracking the is minimal; the largest offset near the location of Fomalhaut b diffraction spikes) has a remarkably small error of 0.12 px (6 mas) is at most 0.5 px, based on available distortion maps (22). For in both coordinates. As for the ACS images, following PSF sub- high-quality astrometric measurements, however, subpixel align- tractions, masking, and derotation, the individual images were ment precision is necessary. Therefore, we opted to download combined. and analyze the distortion-corrected images ( sx2.fits). Each of In Fig. 1, we show the results of our image reductions and anal- the images was used to generate its own mask, based on the ysis, including a high signal-to-noise combined STIS image and underlying STIS occulter mask and generous saturation mask- detailed snapshots of Fomalhaut b at all epochs. ing at 75% of the full well value. We used the same methods as for the ACS data to measure the offsets among all images within Astrometry and Photometry of Fomalhaut b an observation program. The tracking of radial subtraction Determining the astrometric location of Fomalhaut b in the ACS patterns and their minimization by eye allowed us to define and STIS images started from the published coordinates (13) in shifts in both pixel coordinates within 0.1 px. As the STIS the 2004, 2006, 2010, and 2012 images and was based on forward occulters are not transparent, its coronagraphic PSF is more projections for the 2013 and 2014 images. While the source is stable than that of ACS, and the radial patterns remain gen- clearly identifiable in the F606W ACS and the 2010 and 2012 erally the same for the complete observing program. This STIS images, it is more difficult to pinpoint it in the others. For

STIS combined 2010, 2012, 2013, 2014

2004-06/ACS/F814W 2004-10/ACS/F814W 2004-10/ACS/F606W 2006/ACS/F435W 2006/ACS/F606W

2006/ACS/F814W 2010/STIS 2012/STIS 2013/STIS 2014/STIS

Fig. 1. (Top) Median combined image of all multiroll STIS observations (2010, 2012, 2013, and 2014) of the Fomalhaut system. Fomalhaut b is visible in the image within the white rectangle, which is 200 × 100 in size and highlights the area shown in the postage-stamp images below. The postage-stamp images show the individual observations (see text for descriptions of each). The individual images are scaled to the same level per filter [0 to 0.1 counts per second (cts·s−1) for the F606W and F435W ACS filter and for STIS and 0 to 0.05 cts·s−1 for the F814W ACS filter]. The green circles with crosses highlight the then current positions of Fomalhaut b, with 3σ astrometric error radii, while the smaller cyan color circles show the previous positions, to highlight the spatial motion of the source. For the 2014 image, we show the two locations predicted by the two independent trajectory fits. The bright spot “near” the predicted locations is too far to be considered associated with Fomalhaut b.

9714 | www.pnas.org/cgi/doi/10.1073/pnas.1912506117 Gasp´ ar´ and Rieke Downloaded by guest on September 26, 2021 Downloaded by guest on September 26, 2021 G photometry Our units. and (Jy) instrument/filter Jansky the the setup calculate of to used instrument wavelength was setup pivot the The for date. using observation and appropriate (A3V) values star factors spec- host a the flux conversion of has that scattered to instrumental is identical that distribution tral light The incident the 3. assuming synphot, Table in (counts·s values stops. published Lyot the to theoretical due broadening TinyTim and include F435W) on which F606W, 3.03, (23), based photome- (F814W, PSFs of respectively, ACS and factors the observations, background of for STIS 1.45 corrections the and aperture estimate 2.27, applied method 2.56, to We same is used errors. the try disk SD 13 is the the This ref. as measurements. where that determined background areas was these (avoiding error of source photometry dis- The target stellocentric prominent). the same the as at 2.1-px tance placed in randomly measured was apertures a background radius with The performed aperture. was radius photometry 2.1-px The images. reduced both final the for IRAF by declination. provided and ascension were noise right pixel FWHMs background to Centroiding signal pixel ratio. peak the gives SNR where of calculated formula were standard errors the on astrometric based centroiding indi- The Monte a each code. with of errors Carlo derotational time the exposure calculated We the precision image. by the vidual the weighted and on centering, set based image observation of observation, astrometric each within individual FWHM angles each derotation PSF for declination the calculated and ascension were right and in errors errors derotational The errors. derotational the of in plotted and 2 Table 2. in Fig. summarized The dismissed. are be positions can from astrometric they enough that far projection spatially trajectory location. are realistic dataset trajectory any 2014 model the not in either was visible at object peaks dataset All visibly The 2014 error. is the larger in astromet- object increasingly its detected an therefore The and has locations. dataset position STIS ric predicted the in the within size in of pixel expanding software, radius brightest (IRAF) 2-px the Facility a on Analysis in initiated and algorithm DAOPHOT.APPHOT, centroiding Reduction source. the the Image using locating pro- the locations in forward the aided image calculated epochs STIS We previous the 2013 the near the from peaks for jections for while searched we positions, images, F606W F814W and F435W the 07, October; 10, June; 06, detection). (no source model) the (Cloud of STIS location *Projected model) (Bound STIS 2014/09 STIS 2014/09 2013/05 (F814W) ACS 2012/05 (F606W) ACS 2010/09 (F435W) ACS 2006/07 (F814W) ACS 2006/07 (F606W) ACS 2006/07 (F814W) ACS Instrument 2004/10 2004/10 2004/06 object b Fomalhaut Date the of Astrometry 2. Table asp uy 9 etme;0,May. 05, September; 09, July; ´ esmaieorpooer oprdt previously to compared photometry our summarize We of all in b Fomalhaut of photometry aperture performed We squares sum root the as calculated are errors astrometric The radRieke and ar ´ −1 eecnetdt aiu hsclflxuisusing units flux physical various to converted were ) σ centroid = 2.355 −9.018 −8.915 −8.850 −8.590 −8.683 −8.614 −8.642 −8.580 −8.542 1 ∆ −9.093* −9.029* ..( R.A. FWHM SNR ± ± ± ± ± ± ± ± ± .2 9.144 0.021 .2 10.173 10.024 9.824 0.027 9.364 0.019 9.341 0.016 9.363 0.025 9.194 0.021 9.198 0.020 0.017 0.011 00 ) , 10.360* 10.273* ∆δ ± ± ± ± ± ± ± ± ± ( 00 ) 0.025 0.020 0.016 0.026 0.021 0.020 0.018 0.011 0.021 [1] hr saclrsitbtentevrosASfitr n an and filters ACS various the between shift color a is the there of all discrepan- to these procedures by identical applied affected images. have not we are because general fac- data paper cies in the a our literature differences Nevertheless, by of of the methods. 17 outcome conclusions in photometry ref. an noted likely and of been are reduction that and have than source that discrepancies this fainter with Such for in is agrees 2. observation it photometry of however, single tor our 13; the STIS, ref. for For of except filter. data, F435W ACS published the previously the the for with agreement values in generally are values oain o ahosrain hl h ynln n osgv h same the give dots and model. line cloud cyan and dust the orbit and the while orbit for bound bound observation, the best-fitting each the both give for for dots locations and 2014 line in purple The object models. the cloud of location projected the i.2. Fig. Delta Dec (’’) h betfdsi ahidvda adoe ie however, time; over band individual each in fades object The 10.0 10.2 10.4 9.2 9.4 9.6 9.8 srmtyo oahu setx o eal) h ice show circles The details). for text (see b Fomalhaut of Astrometry Cloud Trajectory Bound orbit STIS ACS F814W ACS F606W ACS F435W 8.6 Planetesimal collision PNAS | a ,2020 5, May Delta R.A.(’’) 8.8 | o.117 vol. | o 18 no. 9.0 | 9715

ASTRONOMY Table 3. Photometry of the Fomalhaut b object −1 Date Filter F (cts·s ) F (Jy) mVega mAB Fprev 2004/06 F814W 0.65 ± 0.16 3.83e-7 24.51 24.94 N/A 2004/10 F606W 1.70 ± 0.22 5.23e-7 24.51 24.61 24.43 ± 0.08 mag (1); 24.92 ± 0.10 mag (16); 6.3 ± 1.0 ×10−7 Jy (17) 2004/10 F814W 0.72 ± 0.23 4.23e-7 24.40 24.83 N/A 2006/07 F435W 1.28 ± 0.26 8.90e-7 24.11 24.03 25.22 ± 0.18 (16); 3.6 ± 0.9 ×10−7 Jy (17) 2006/07 F606W 1.52 ± 0.15 4.71e-7 24.63 24.72 25.13 ± 0.09 mag (1); 24.97 ± 0.09 mag (16); 4.3 ± 0.6 ×10−7 Jy (17) 2006/07 F814W 0.56 ± 0.08 3.24e-7 24.69 25.12 24.55 ± 0.13 mag (1) 24.91 ± 0.20 mag (16); 3.6 ± 0.7 ×10−7 Jy (17) 2010/09 Clear 0.77 ± 0.10 3.58e-7 24.77 25.02 0.49 ± 0.14 cts·s−1 (13); 6.1 ± 2.1 ×10−7 Jy (17) 2012/05 Clear 0.58 ± 0.10 2.71e-7 25.07 25.32 0.50 ± 0.11 cts·s−1 (13) 2013/05 Clear 0.47 ± 0.08 2.17e-7 25.32 25.56 N/A 2014/09* Clear 0.32 ± 0.14 1.48e-7 25.73 25.97 N/A 2014/09† Clear 0.23 ± 0.14 1.07e-7 26.09 26.33 N/A

06, June; 10, October; 07, July; 09, September; 05, May. *Flux at the predicted location of the source using the bound orbit trajectory. †Flux at the predicted location of the source using the unbound cloud model trajectory.

offset between the ACS and STIS data in general. The color Fomalhaut b as a Dynamically Dissipating Collisional Dust Cloud. We shift is a natural consequence of the dust cloud being slightly now consider an alternative model tracing the evolution of the bluer than the central star. The offset between the ACS and system through the following steps: 1) Two large (≥100 km in STIS data is most likely an artifact, brought on by the com- radius) asteroids collide catastrophically; 2) the collision frag- bination of changes in two variables: 1) The source becomes ment sizes follow a power-law distribution down to the sub- extended over time and 2) the STIS photometry aperture is micrometer level; 3) the fragments inherit random velocities, physically larger than the ACS one, due to the larger projected resulting in the expansion of the dust cloud relative to the cen- pixel sizes of the detector (Fig. 3 legend). The precision align- ter of mass (COM) of the colliding asteroids; and 4) the final ment of the STIS data and lack of any higher signal points near trajectories depend on fragment size: larger ones unaffected by the predicted location of the source (even with a wide margin radiative forces will undergo Keplerian shear, while the smaller of astrometric error) give high confidence to our nondetection ones will converge onto radial trajectories and leave the system. in 2014. The surface area of the dust cloud observed in scattered light is dominated by the submicrometer particles that are leaving Interpretations of the Observations the system. The apparent motion of the observed image should We draw three basic conclusions about Fomalhaut b from the reflect such motion. observations: 1) It is probably moving out of the system, 2) it To test this scenario, we modeled the dynamical evolution has become increasingly extended, and 3) it has faded below our of such a hypothetical system using our code DiskDyn. Devel- detection limits. We support these conclusions first by comparing oped to model the dynamical evolution of debris disks and dust bound and unbound fits to the observed motion of the object. We clumps, DiskDyn is a complex numerical code able to include then analyze its evolution in size and brightness using a model providing a self-consistent explanation of all three unique aspects of its behavior. ACS F435W (Model: ) -6 Bound Orbit of Fomalhaut b. If the underlying object for Fomal- ACS F606W (Model: ) ACS F814W (Model: ) haut b is planetary, it should be following a stable bound orbit. STIS (Model: ) To fit the best solution for such an orbit and its joined Bayesian -6.2

errors, we used a Markov chain Monte Carlo (MCMC) ﬁtting ) routine (24). Orbital solutions were projected forward to each -1 -6.4 epoch from the orbital point closest to the ﬁrst observation location. We assumed uniform priors on the orbital elements -6.6 (F) (F x Jy

(semimajor axis a, eccentricity e, inclination ι, argument of 10

periapsis w, right ascension of the ascending node Ω) and deter- log -6.8 mined their statistics using 5,000 steps following a burn-in limit of 2,000 steps for 6,000 test chains. These orbital elements are defined in the plane of the Fomalhaut disk (assuming a system -7 position angle of 336◦ and inclination of 66◦). In Fig. 4, we show the results. -7.2 2004 2006 2008 2010 2012 2014 2016 In Fig. 2, we also plot (with purple color) the best orbital solu- Date tion (at the reduced χ2 minimum, given in the Fig. 4 legend), assuming this stable bound orbit. Although the observations lie Fig. 3. The photometry of Fomalhaut b at all observed epochs and wave- near the track of the “best” orbit, the positions along that track lengths. The error bars shown are at 1σ. The offset between the ACS and do not agree with the observations within errors. This issue is STIS data is most likely an artifact, due to the larger STIS pixel sizes, the prominent for 2013, the point to the upper right, where the spatial expansion of the dust cloud, and the method of photometry that observed position is significantly ahead of the bound orbit predic- was necessary. The expansion of the dust cloud over time, convolved with the HST PSF, results in the central peak brightening. This artifact is further tion (purple dot, Fig. 2), consistent with the object experiencing enhanced by the larger STIS pixel size. As we had to use larger physi- nongravitational acceleration directed away from the star. A cal apertures for the STIS data than for the ACS data (same number of planetary body would also not explain the fading and extent pixels), the object seems to brighten artificially. Identical photometry of the of the image. Therefore, additional models of the motion and cloud model ACS and STIS data, shown with open circles, exhibits similar behavior of the source are necessary. behavior.

9716 | www.pnas.org/cgi/doi/10.1073/pnas.1912506117 Gasp´ ar´ and Rieke Downloaded by guest on September 26, 2021 Downloaded by guest on September 26, 2021 G (25)] only silicates astronomical approx- used light dynamics. we and scattered theory, with Mie only by concerned imated prop- are optical we dust [since realistic trajectory erties calculates initial model cloud for dust DiskDyn Therefore, assumed respectively. we 7.17, fitting 0.23 and and 0.7 10.2 0.11 and of of 0.07 radii with between dust observed is prominently most HST and range filter with radius particle F606W the The the shows radius. also in cle 5 ACS Fig. a with STIS. as observed with 0.6 density) wavelength flux of number the scattered) wavelength dust to and the observational (thermal by an particles. (weighted total at size the the particle on show of force we function gravitational 5, to Fig. by force In characterized radiation are of grains solution). dust ratio orbit small bound of the (yield- cloud to trajectories velocities relative the The be parameter and of free coordinates to extra velocity Cartesian an trajectory DiskDyn; ing its and the for by location constrain defined values launch not were the did input solu- we Instead, the orbit fit, bound. bound obtain this the to for for the however, that MCMC) of to (with fashion trajectory similar the tion a fitted in first cloud we dust Therefore, tools. fitting vide units processing graphical on runs (GPUs). inten- DiskDyn numerically the the calculations, to from Due sive emission SEDs. thermal complete and and light particles a dust scattered of the effects provides of DiskDyn images gravitational on Additionally, .fits the bodies. forces massive calculate of magnetic as number and large well as radiative, particles, gravitational, dust of effects the analysis. reduced at 1σ = global Ω is the the distribution the while the and of shown, of mean projections are the The 2D projections of 1D show parameters. parameters) off-diagonals other between pan- all the correlations diagonal over while The (marginalized density, steps). analysis projections 2,000 probability MCMC at 1D using limit show orbit, burn-in bound els steps, stable 5,000 a chains, assuming (6,000 b, Fomalhaut of ters 4. Fig. asp ´ hl iky savraiemdln oe tde o pro- not does it code, modeling versatile a is DiskDyn While 139.59 radRieke and ar ´ otro rbblt itiuin vrtefe ria parame- orbital free the over distributions probability Posterior ◦ In . eso h hiso u MCMC our of chains the show we , S1 Fig. Appendix , SI β a 10 = = au, 385.5 o l atce.Hwvr u final our However, particles. all for β .Teeszshave sizes These µm. e aus safnto fparti- of function a as values, = 0.7604, ,wt u ek from peaks flux with µm, ,wihcorresponds which µm, ι = 9.90 χ 2 = ◦ 8minimum 3.18 , eeso the of levels w = β 118.00 values β the , ◦ , ewe oldn ois h vrg olsoa eoiisin velocities collisional paths average orbital the similar to bodies, Due colliding to (26). identical between velocities in roughly impact particles are relative COM, daughter stationary the of mea- a speeds to Laboratory the relative cloud. collisions, that shown the have produced surements that velocity resolved). collisional partially where (i.e., point PSF the HST to the 8. considerably, than Fig. expanded larger in has is analysis it cloud our the in y these 10 for In correct and the estimate arti- We PSF, guiding dust observatory facts. instrumental the and algorithm, the of reduction on radius the scale, depends the pixel of size In evolution them. observed observed produced The COM) that the cloud. event show the the we of of 7, (trajectory nature Fig. explosive also line the will central to fragments the due collisional from the radially trajectory, diverge the average the of determine line will particles) central dust the for with (combined forces velocity radiative launch original the While expands. cloud au· both 0.8 in to found were up orbits families. bound velocities Trajec- elliptical with orbits). from originating circular orbit tories reduced assuming bound velocities, with the sub-Keplerian fits of (i.e., yielded that having to solutions typically lar of solutions, family of au second family 1.08 first (from velocities the larger from were tories colli- the 22.13 of χ and location 0.59 the between velocities at au·y with orbit solutions au· circular However, a 1.59 sion. for of velocity velocity orbital launch initial an ih31 o h etbudobtfi)wsfracliinoccur- collision a for was fit) orbit bound at best ring the for 3.18 with w aiiso ouin eefud n ihasapprobabil- shows, sharp 6 x a Fig. with at As one colli- peak found, Fomalhaut. the ity were of that solutions au of was 150 families within condition two occur initial to the had on sion system. observed Fomalhaut constraint the the only of of plane The the velocity in launch determined particles, and dust collision planetesimal the tr h atce otiuigms fteflxhv egtdaverage weighted a have flux the of most spectral-type of contributing A0 an particles around modeled distri- The we star. of particles size dust value the power-law for the underlying axis secondary function plot modeled a also as the We detector) assuming bution. 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Fig. 2 ≤ β hs esrmnscnb sdt lc iiso the on limits place to used be can measurements These the which at speed the is model the on constraint additional An i.6sosteMM nlsso h nta oainof location initial the of analysis MCMC the shows 6 Fig. oe hntebs on ri t h etfitn trajec- best-fitting The fit. orbit bound best the than lower .Tebs t(ihareduced a (with fit best The au). 90 = −1 7.2. h eaieeiso u temladsatrd ta observa- an at scattered) and (thermal flux emission relative The a ifrn anhpstos rdc t ihreduced with fits produce positions) launch different (at 4au, 91.24 = x 1au 91 = x PNAS apoiaigteF0WASfitradthe and filter ACS F606W the (approximating µm n n ihabodrdsrbto (80 distribution broader a with one and = y and au, −47.62 | a ,2020 5, May ·y β −1 safnto fpril ieo the on size particle of function a as ,wietebs t rmthe from fits best the while ), y −1 | wc h Keplerian the twice , o.117 vol. χ = z 2 2 = with au, −13.47 .38—compared | o 18 no. χ 2 | simi- y 9717 −1 ≤

ASTRONOMY 2010 and 2012 images was also already noted by ref. 13. They give minor and major axis dimensions; if we take the geometric mean, the agreement with our radial average is within 10%. As a third independent confirmation of the extended nature of the Fomalhaut b source in the STIS images, we investigated the size of point-like background features in the raw data. A visibly slightly elongated peak, possibly the core of a background galaxy, had a fitted standard deviation of only 000. 042 ± 000. 008, more than two times smaller than that of Fomalhaut b. The extended Fomalhaut b source is well sampled in the STIS images at their respective epochs; therefore, pixel-scale level artifacts do not need to be considered. Following fitting, the expansion of the cloud follows a slope of 0.050 ± 0.016 au·y−1, which corresponds to an orbital velocity of the colliding bodies equal to 0.5 ± 0.08 to 1.0 ± 0.16 au·y−1, assuming a collisional velocity 10 to 5% of the orbital velocity, respectively. The observed expansion of the cloud, therefore, places the following constraints on the collision: 1) The collisional event happened close in time to the first observations in 2004, 2) the colliding bodies had velocities up to ∼1.2 au·y−1, and 3) the final launch velocity of the cloud cannot be much higher than this value either. The best-fitting launch configuration that also conforms to these constraints has the following values: x = 91.23 au, y = −55.97 au, z = −9.82 au, vx = 0.719 au·y−1, vy = 0.783 au·y−1, and vz = −0.232 au·y−1, yielding a reduced χ2 = 2.48 and a collisional event that happened 39 d prior to the first observations. This Fig. 6. Posterior probability distributions over the free orbital parameters result is in good agreement with the collisional time of 2004.03 ± of Fomalhaut b, assuming an unconstrained cloud model orbit, using MCMC 0.91, predicted by the expansion. This launch position and veloc- analysis (6,000 chains, 5,000 steps, burn-in limit at 2,000 steps). The global 2 ity will result in a bound orbit of a = 334.4 au, e = 0.695, and ι = reduced minimum of the distribution is χ = 2.38. The coordinates (in au) 12.6◦ for the larger undetected fragments of the collision. The and velocities (in au·y−1) are defined in the plane of the Fomalhaut system. The chains are shown in SI Appendix, Fig. S2. smaller dust particles, as discussed before, will be ejected due to the influence of radiative forces. In Fig. 2, we plot their trajectory (assuming β = 10), with positions marked at each observation disks are around 7.5% of the orbital velocity (27). It is unlikely date. that either of the colliding bodies was originally on a high-speed With this best-fitting initial location and launch velocity we unbound orbit, so the daughter particles will likely acquire an used DiskDyn to model the dynamical evolution of the dust additional velocity around 5 to 10% of a typical Keplerian veloc- cloud. Due to its larger uncertainty and importance in deter- ity at the location of the collision, in a random direction relative mining the decrease in surface brightness of the cloud, the to the COM. Some variation in this fraction is expected, as the SD of the radial expansion velocities of the dust particles was collision did not happen in a disk. The inherited launch velocity kept as a variable. A handful of models with σv between 0.05 of the cloud will then likely project onto a bound orbit as well. and 0.15 au·y−1 were explored. We generated 106 dust par- Gravitational forces will be dominant for the larger and unde- ticle tracers with a size distribution slope of α = −3.65. This tected bodies, so they will remain in bound orbits and undergo value is found to be typical of debris disks (28), and it is con- Keplerian shear due to the small variations in launch velocity. sistent with the value of α = −3.50 found for particles >100 µm However, the smallest particles (observed by HST) will experi- (to make the slope not influenced by PR drag) in zodiacal dust ence additional radial acceleration due to radiative forces and bands formed in the recent collisional breakup of asteroids (29). be deflected onto unbound orbits. The expansion of the cloud is Slightly shallower but similar (α ∼ −3 to −3.3) slopes were found dominated by the random velocities acquired during the collision for the size distribution of dust sublimating off comets and in dis- for this source. rupted asteroids (30–32). The minimum particle size was 0.1 µm In Fig. 8, we illustrate the expansion of the cloud. From each (the largest size is irrelevant, as long as all sizes that are efficient measured radial value, we subtract the wavelength-dependent at scattering optical light are included). The total dust mass was standard deviation of the approximating Gaussian (σ) of the calculated from scaling our calculations to the observations. 00 00 00 HST PSF (σSTIS = 0. 033, σF435W = 0. 019, σF606W = 0. 026, The DiskDyn dust cloud model was evolved on a GeForce 00 and σF814W = 0. 035). These values include PSF broadening due GTX Titan Black GPU, using 0.01-y time steps. For the cen- to the Lyot stop of the coronagraphs and also guiding drift. tral star, we assumed Fomalhaut’s physical parameters (L= The instrumental PSF broadens due to the pupil stops, which 15.36 L , R = 1.8 R , M = 1.92 M , d = 7.7 pc). Dust particles restrict the HST aperture diameter to 88.5% and 85.5% of its from radii of 0.1 µm to 1 mm were generated in 290 logarith- nominal value for the ACS and STIS detectors, respectively. mically spaced size steps, with optical constants for astrosili- Additionally, guiding HST is difficult when observing Fomalhaut cates (33). We performed Mie scattering calculations, taking and is typically done using a single guide star, possibly result- into account the scattering angles between Fomalhaut, the dust ing in tracking drifts. We measured a per-orbit drift of 000. 015, grains, and our viewing angle of the system. The results of our which corresponds to 000. 0015 per exposure (2.9% of a pixel, modeling are also shown in Fig. 7. The spatial dissipation of the i.e., it is negligible). The 2004 ACS images have widths approx- cloud as it propagates on its trajectory is clear, as well as a global imately equal to the theoretical values; i.e., the cloud is still a trajectory that is increasingly radial. point source and therefore the collision likely happened close in time to the first observations. However, the dust cloud is visibly Morphology and Brightness of the Modeled Dust Cloud. As the dust extended in the STIS images where it is observed (2010, 2012, particles move farther from Fomalhaut, their individual scat- and 2013). The spatially extended nature of the source in the tered light fluxes drop; the spherical expansion of the cloud

9718 | www.pnas.org/cgi/doi/10.1073/pnas.1912506117 Gasp´ ar´ and Rieke Downloaded by guest on September 26, 2021 Downloaded by guest on September 26, 2021 G then and aperture data observations. the same the to for the model did the using we scaled images as finally corrections model aperture the and mea- in We radius in sizes. fluxes shown pixel and the images convolution the sured model account The into take PSFs. their 7 Fig. STIS with images and model ACS the appropriate convolved simu- we To well. observations, as the dropping late brightness surface overall its in results 8. Fig. in effects instrumental for corrected are profiles radial The observations. mgsi h aea nFg o ohmdl (Center models both for 1 Fig. in as same the is images 7. Fig. asp ´ radRieke and ar ´ oprsno h vlto ftesailsae oain n ufc rgteso h utcoda bevdadmdld h cln fthe of scaling The modeled. and observed as cloud dust the of brightness surface and location, scale, spatial the of evolution the of Comparison

offset (’’) offset (’’) offset (’’) offset (’’) offset (’’) offset (’’) offset (’’) offset (’’) offset (’’) offset (’’) 0.0 0.5 1.0 0.0 0.5 1.0 0.0 0.5 1.0 0.0 0.5 1.0 0.0 0.5 1.0 0.0 0.5 1.0 0.0 0.5 1.0 0.0 0.5 1.0 0.0 0.5 1.0 0.0 0.5 1.0 0.0 2014 STIS 2013 STIS 2012 STIS 2010 STIS 2006 ACS/F814W 2006 ACS/F606W 2006 ACS/F435W 2004 OctACS/F814W 2004 OctACS/F606W 2004 JunACS/F814W 0.5 bevtosMdl Obs.radialprofiles Models Observations offset (’’) 1.0 1.5 oun n bevtos(Left observations and column) 0.0 2014 STIS 2013 STIS 2012 STIS 2010 STIS 2006 ACS/F814W 2006 ACS/F606W 2006 ACS/F435W 2004 OctACS/F814W 2004 OctACS/F606W 2004 JunACS/F814W 0.5 offset (’’) 1.0 bevtosadteata htmtyi xeln.TePSF The excellent. is modeled photometry the actual between pho- correspondence the the The and of 3. observations Fig. results in best-fitting The this shown fit. assuming are slope images, model expansion the the of tometry of SD 3 within diinlvlcte fteduhe atce.Tebs twsat was fit best The particles. σ daughter the of velocities additional v h oe rdcin aida ucinof function a as varied predictions model The 1.5 0 = .13 column). 0.0 ± 0. 01 Right 0.1 au·y R (’’) ounas hw h te ailpolso the of profiles radial fitted the shows also column PNAS −1           0.2 hc s1%o h anhvlct and velocity launch the of 12% is which , =0.043’’ =0.023’’ =0.994’’ =0.093’’ =0.073’’ =0.077’’ =0.036’’ =0.051’’ =0.030’’ =0.029’’ | a ,2020 5, May 0.3 0.1 0.15 -0.05 0.05 0.1 -0.04 -0.02 0.02 0.04 -0.04 -0.02 0.02 0.04 0.06 -0.04 0.04 0.08 -0.04 0.04 0.08 -0.02 0.02 0.04 -0.05 0.05 0.1 -0.05 0.05 0.1 0.15 -0.1 -0.05 0.05 0.1 -0.05 0.05 0 0 0 0 0 0 0 0 0 0

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ASTRONOMY Downloaded by guest on September 26, 2021 9720 required The dust bodies. of massive amount more much this of Producing collisions also surface. we requires why scattering is which the slope, distribution provide size the on depends mass simple a ing of radially variation fragments a the with disperses trajectory, COM event the explosive from The au. au·y 107 0.89 at of velocity solution a lerian with asteroids, two au·y the 1.09 of of con- trajectory fragments COM The the radius. of on in distribution tinue kilometers continuous of (∼4.8 tens a to of particles up observa- end fragments, dust small of of the set represent density first particles surface the to high prior a 10 time 2004, short of in a order tions the radius, on in asteroids km massive 100 two between collision Dynamics. trophic Cloud Dust Modeled of Summary results model. photometry unlikely. best-fitting and astrometry is our the of cloud summarize dust we in 4, the Table measurements of In HST detection 2014 of future the lack years, on the Based subsequent possible. and not model, is our the aperture observations, capture larger to a optimized with photometry flux increasing full image, pho- the with subtrac- in using source PSF artifacts the a of tion Given on brightness. result surface source a decreasing overall point and is extent a The 2013 for artifact. to suitable observational 2004 tometry an from images, is decrease model This STIS apparent the observed. in peak as higher a just in dissipation resulted the cloud, with the combined of rebinning, pixel and convolutions earlier slightly only expansion, the fits. on and astrometric based the 2-, by 2004.03 1-, predicted the at than show is areas time) blue collision shaded The multiplying system. and widths the 3σ profile to observed wavelength-dependent distance the the the from observed by subtracting PSFs HST the by the converted scales of We Gaussian spatial location. to collisional profiles the radial 0.05 at of velocity increase Keplerian size a with slope 8. 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E. 10. mn S mgso xpaesaddbi ik 4)com- (41) sources disks similar debris of and lack the exoplanets by of shown images is than HST object steeper among this is of distribution the rarity i.e., size-frequency the the assumed, the if have we Even of than derived. slope efficient more just is timescales quiescent production cold the dust dynamically given a in system arisen planetary have to unlikely it making to of half m·s respectively. of 236 in dust the timescales produces for highlighted yielding col- My that ∼0.15 observed, space of domain amount mass the rate the target integrate double differential and We the dust 9. projectile Fig. of integrating the the amount by in that required lisions estimated g·cm and the 3.5 km be producing of 2,000 can events density of bulk collisional diameter a for a has material has density belt distribution and 26.15 mass the of belt bright- total in the surface a simi- thermal calculate yielding and be We distribution ness, to energy belt. spectral location the its collisional in from the that the at to assume bodies we lar located number belt, parent is debris their of Fomalhaut b the on density of Fomalhaut edge depends Since inner the dust velocity. near interaction of and amount density required the duce not would the velocity in results. impact larger our uncertainty a change the and large However, is velocity. velocity expansion impact high a is the collision gesting from catastrophic velocity the escape in The fragment km. largest 47 catastrophic to the radius limit impactor erosive velocity, the the drops impact while this same, faster the generate approximately the also remains outcome At can (when a dust. object collisions, radius of 893-km erosive in target amount an in km smallest impacting however, 109 body The impactor); twice is 56-km cloud. similar-size to dust a dust half much by the is so hit in producing mass observed of dust is capable produced as the much where between as m·s domain collisions 236 of in the speed produced collisional in mm) a 1 at sizes of target–impactor radii various to (up mass m·s au·y dust 616 au·y and 0.13 236 0.05 in to of results spond speed modeling collisional The a photometric bodies. will yields colliding the it cloud of as the velocity estimate, of relative good the size the a to in equal provides speed, used roughly cloud collisional be traditionally dust the the 40, For of ref. calculations. expansion of cascade tensile curve disk For the debris detail. assume more we in strength, outcomes collisional these discusses G .E hag .Kt,P aa,J .Gaa,M lmi,Fmlatsdbi ikand disk debris Fomalhaut’s Clampin, M. Graham, R. J. Kalas, P. Kite, E. Chiang, E. 9. Marengo M. 8. Zurlo A. 7. Marley S. chem- M. 6. and Clouds Marois, C. Currie Konopacky, T. M. 5. Q. a Macintosh, of Images B. Barman, T. Barman, Macintosh, B. S. T. Konopacky, 4. M. Q. Zuckerman, B. Marois, C. 3. Marois C. 2. Kalas P. 1. asp ´ oahu a bv h eeto ee o nyadecade, a only for level detection the above was b Fomalhaut pro- could that planetesimals between collisions of rate The interpretation. morphology. disk from b (2009). Fomalhaut 734–749 of 693, mass the Constraining planet: Eridani. epsilon and Fomalhaut system. exoplanetary 8799 HR the (2016). of astrometry and J. Astrophys. formation. and (2011). masses, 128 properties, 729, atmospheric for Implications 8799: HR8799b. planet extrasolar of atmosphere (2011). the in istry 8799. HR orbiting planet fourth (2008). 1348–1352 322, (2008). 1345–1348 322, radRieke and ar ´ pia mgso neooa lnt2 ih-er rmearth. from light-years 25 planet exosolar an of images Optical al., et is ih fteVTpae ne PEE I.Nwspectrophotometry New III. SPHERE. finder planet VLT the of light First al. , et obndsbr/L/M 1-5 subaru/VLT/MMT combined A al., et ietiaigo utpepaesobtn h trH 8799. HR star the orbiting planets multiple of imaging Direct al., et nrrdnndtcino oahu :Ipiain o h planet the for Implications b: Fomalhaut of non-detection Infrared al., et 3 (2012). 135 754, pte/nrrdarycmr iist lntr opnosof companions planetary to limits camera array Spitzer/infrared al., et ass ai,adcodpoete fteH 79planets. 8799 HR the of properties cloud and radii, Masses, al., et srpy.J. Astrophys. 1 (2012). 116 747, −1 −1 srpy.J. Astrophys. Nature epciey nFg ,w hwthe show we 9, Fig. In respectively. , n 1 m·s 616 and M 0018 (2010). 1080–1083 468, Earth 6715 (2009). 1647–1657 700, suigalretbody largest a assuming , td fpaesobtn HR orbiting planets of study µm −1 srpy.J. Astrophys. srn Astrophys. Astron. olsoa velocities, collisional srpy.J. Astrophys. −3 3 m· ∼137 −1 h timescale The . hs corre- These . 2 (2012). L20 754, .9and ∼0.59 srpy.J. Astrophys. srpy.J. Astrophys. −1 s 65–82 733, −1 while , A57 587, −3.65, Science Science sug- , −1 , 5 .M end,M .Wat olsoa vlto firglrstlieswarms: satellite irregular Currie of T. evolution 16. Collisional Wyatt, C. M. Kennedy, M. G. 15. Beust of imaging H. coronagraphic 14. STIS Clampin, M. Fitzgerald, P. M. Graham, R. J. Kalas, P. 13. Janson M. 12. 0 .J eyn .C rme,Cliinlcsaecluain o reua satellite b. irregular Fomalhaut for for orbit eccentric calculations an of Frequent cascade Consequences Tamayo, cloud: Collisional D. dust Bromley, 21. a C. as B. b Kenyon, Fomalhaut J. S. Gladman, B. 20. aspects Testing Greenstreet, dust: S. of cloud Lawler, a M. as S. b Fomalhaut 19. Bromley, Independent C. B. b: Currie, T. Fomalhaut Kenyon, J. Macintosh, S. B. 18. Zuckerman, B. Marois, C. Galicher, R. 17. h otcetnei-et eiwo nidpnetHTSI expert. Grant Program HST/STIS 80NSSC18K0555. Research Grant Exoplanets independent comments NASA NASA appreciate and an by observa- 80NSSC20K0268 helpful supported sincerely of been the providing has also review work We obtaining This for in-depth process. and referees postacceptance review planning the our multiround for and the Kalas throughout here Paul described tions thank We Nvidia. ACKNOWLEDGMENTS. from mod- downloaded Our STScI. be the can com/merope82/DiskDyn. by DiskDyn, maintained code, website eling MAST the from Availability. 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Soc. solar around dust dust Detectable outer the on effects (2014). dynamical the b. Fomalhaut of orbit the and (2013). structure belt Main Fomalhaut: and Fomalhaut, Soc. b. Fomalhaut in swarms disk. Fomalhaut the within collisions theory. formation planet of data. archive public telescope space Hubble (2013). the of analysis (2012). 1725 (2011). 2137–2153 412, 5738 (2014). 3577–3586 438, ietiaigcnrainadcaatrzto fadust- a of characterization and confirmation imaging Direct al., et nidpnetdtriaino oahu ’ ri and orbit b’s Fomalhaut of determination independent An al., et ihcnrs mgn ihsizr eposrain fVega, of observations Deep spitzer: with imaging High-contrast al., et Eridani. h a bevtoa aacnb downloaded be can data observational raw The eaegaeu o h adaednto from donation hardware the for grateful are We srpy.J. Astrophys. PNAS srn Astrophys. Astron. srpy.J. Astrophys. | a ,2020 5, May srpy.J. Astrophys. 0(2015). 60 811, 0(2014). 70 786, 10(2015). A120 574, 2 (2015). 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