New HST Data and Modeling Reveal a Massive Planetesimal Collision

Home , Fomalhaut, Fomalhaut b

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Fomalhaut of image of planets the properties around the that swarms and satellite 100 star per- that to the has found of 20 phenomenon life Ref. the the that for assuming sisted from constraints the doi:10.1073/pnas.1912506117/-/DCSupplemental. at online information supporting contains article This 1 cec nttt SSI.Ormdln oe iky,cnb onoddfrom downloaded be Telescope can Space DiskDyn, the code, by modeling Mikulski maintained the Our website from (STScI). https://github.com/merope82/DiskDyn (MAST) downloaded Institute be Telescopes can Science Space data for observational raw Archive The deposition: Data the under Published Submission.y Direct PNAS a is article This paper.y interest.y the competing wrote no G.H.R. declare and authors A.G. The and A.G. data; research; analyzed performed A.G. 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ASTRONOMY Archival Data Mikulski Archive for Space Telescopes (MAST) website. We Fomalhaut b has been observed only in scattered light and only downloaded corrected ( drz.fits) files, which rectify the non- with HST. The stable optical system of HST and the lack of square pixels of the HRC detector and also correct the field atmospheric disturbance enable high-contrast imaging at visible distortions. In our reductions, we rejected observations with wavelengths with the aid of coronagraphs. Fomalhaut b was dis- issues such as poor centering on the coronagraph and also com- covered in images taken with the Advanced Camera for Surveys bined measurements in the same filter taken sufficiently closely (ACS) coronagraph in 2004 and 2006 (1). The failure of the high- in time that the relative motion of Fomalhaut b is insignificant resolution channel (HRC) (which included the coronagraph) of (GO9862 and GO11818). ACS in 2007 led to the Space Telescope Imaging Spectrograph Over an orbit, the Hubble Space Telescope undergoes ther- (STIS) becoming the single coronagraphic instrument onboard mal expansions (a.k.a. “breathing”), which vary the PSF. Addi- HST; thereafter the monitoring of Fomalhaut b continued with tionally, the ACS coronagraph transmits a small fraction of STIS. Images of Fomalhaut b taken with STIS in 2010 and in the occulted flux; the transmitted PSF depends on the total 2012 have been published by ref. 13. count received. Therefore, the ACS observations were target- The coronagraphs in these instruments differ in design and PSF paired based on exposure length and interorbit sequence. performance. The ACS Lyot coronagraph was located in the PSF subtraction residuals can become substantial if target obser- aberrated beam of the telescope. This limited the performance vations are not registered to ≤0.1 px with their PSFs. We of the coronagraph at smaller (≤300) inner working angles. How- determined the shifts between each image and its chosen PSF ever, it was able to observe using a suite of optical filters. The by observing the subtraction residuals by eye. Using the software STIS coronagraph is located in the corrected beam; however, IDP3, we registered the images well within 0.1 px by minimizing 00 it is unfiltered and therefore detects photons from 0.4 to 1 µm. the radial streak pattern over a radius of 10 from the occul- While this yields high sensitivity, it also limits the fidelity of the ter. We also registered the shifts between the target images in a chromatically dependent point spread function (PSF) of the tele- similar manner. We found an average offset in x and y pixel coor- scope, which must be observed close in time to the target star dinates of ∆x = −0.32 ± 0.21 and ∆y = 0.35 ± 0.422, which is because of temporal drifts in the image shape. close to the nominal quarter pixel value given in the Instrument Since 1999, 11 HST coronagraphic programs observed Foma- Handbook for pointing precision. The fluxes of the PSFs were lhaut, either with ACS or with STIS. Of these, only 7 were true scaled for each pairing by determining the background levels at high-contrast imaging, multiorbit, and multirotation-angle pro- the edges of the fields. grams as described in Table 1; the remaining 4 programs took To pinpoint the location of Fomalhaut, which then defines the only a single or a few images. Here, we describe the previously derotation center of the images, we determined the rotational unpublished 2013 and 2014 observations of Fomalhaut b and symmetry origin of each image. To do so, we rotated each image ◦ provide a coherent and independent rereduction and analysis of by 180 and subtracted it from its original version. Subtraction all of the useful HST data. residuals within the occulting spot became apparent at ∼ ±1-px offsets. We use this value, along with the rotational angles of Rereduction of Archival ACS Data. Three of the 11 HST corona- individual images and the full-width at half-maximum (FWHM) graphic programs used ACS (PI: Paul G. Kalas) and provided the of the target PSFs, to estimate astrometric errors. Following PSF discovery images of Fomalhaut b (1). We first give a brief descrip- subtraction, subtraction masking, and derotation, the individual tion of the observations and the observing techniques employed target images were combined. within these observations. We then describe our rereduction of these data, carried out so all of the available photometry is (Re)Reduction of Archival and Additional STIS Data. Four programs treated identically. using STIS employed a multiroll/multiorbit observation tech- Each ACS program observed Fomalhaut and Vega at multi- nique (PI: P. Kalas for all of them), which is necessary to achieve ple roll angles, the latter star to define the PSF. While Vega and high-contrast imaging. The results from the first two programs Fomalhaut are not exact color matches, the response of the sys- have been published (13); here we publish the results of the last tem through color filters to each source was approximately the two. As STIS is unfiltered for coronagraphic imaging, precise same. Various length exposures were taken of each source to color matching of the PSF source is critical. Since well-matched enable imaging of the inner and outer regions without saturation PSF calibrators may not be available nearby, it is common to and to high signal-to-noise ratios. employ the angular differential imaging (ADI) technique, where The publicly available data for these observations were a star becomes its own PSF calibrator by combining images of obtained from the Space Telescope Science Institute (STScI) it taken at different roll angles. This approach works well for

Table 1. Multiroll HST coronagraphic observations of the Fomalhaut system

Program ID Date Instrument Filters Apertures NImages NRotations PSF GO9862* 2004-05|08 ACS F814W CORON1.8 5 2 Vega GO10390* 2004-10 ACS F606W, F814W CORON1.8 32 3 Vega GO10598* 2006-07 ACS F435W, F606W, F814W CORON1.8, CORON3.0 53 4 Vega GO11818* 2010-06|09 STIS N/A WEDGEB2.5† 19 7‡ ADI GO12576* 2012-05 STIS N/A WEDGEB2.5 48 12‡ ADI GO13037 2013 STIS N/A WEDGEB2.5 48 12‡ ADI GO13726 2014 STIS N/A WEDGEB2.5† 24 8 Vega and ADI

Programs marked with “ADI” were planned to use angular differential imaging and therefore did not observe a PSF source. 05|08, May|August; 10, October; 07, July; 06|09, June|September; 05, May. *Previously published data. †Observations were also taken at additional apertures (BAR10 for GO11818 and BAR5 for GO13726), but were not included due to low S/N at the position of Fomalhaut b. ‡The majority of rotations were separated by only a few degrees (≤25◦).

2 of 11 | www.pnas.org/cgi/doi/10.1073/pnas.1912506117 Gasp´ ar´ and Rieke Downloaded by guest on September 25, 2021 Downloaded by guest on September 25, 2021 rlytesm o h opeeosrigporm This program. observing gen- complete remain the patterns STIS radial for the more the same As is and the ACS, PSF px. of coronagraphic erally define 0.1 that its to within than transparent, us stable coordinates not subtraction allowed pixel are eye radial occulters both by of in minimization tracking shifts their The as and within methods images program. patterns all same among the observation offsets used the the We measure an on to value. data well based ACS mask- full the mask, the saturation for of own generous 75% and its at mask ing generate occulter to STIS used underlying was download ( to images images opted the distortion-corrected we the For Therefore, analyze (22). necessary. and maps is distortion precision available b align- ment on subpixel Fomalhaut STIS however, based of measurements, for px, astrometric location distortion high-quality 0.5 the most geometric near at of offset of is largest level the detection The minimal; data. the is ACS for the adequate for photon still not are and The data contrast b. ADI. are the Fomalhaut for observations shorter so subtraction slightly PSF STIS limited, PSF a the better suppress for but a integrated to time, establishing (GO13726) helps as observations which 2014 angles well 12), 2012 roll as of in additional residuals total obtained using a were (GO13037) position (for 2013 occulting and same (GO12576) the at images oino h ore o h 04iae eso h w oain rdce ytetoidpnettaetr t.Tebih pt“er h predicted the “near” spot bright The G fits. trajectory independent b. two Fomalhaut the with second by associated predicted per considered locations counts two be 0.1 the to to show far [0 we too filter image, is per 2014 locations the level For same source. 3σ the the to with of scaled b, motion are Fomalhaut images of individual positions The current each). of descriptions for text (cts·s (see 2 observations is individual the which show rectangle, white the within image 1. Fig. 2.5 the Fomalhaut using observed 2010 program in GO11818 The of bars. occulting that two as such systems, disk narrow-belt Fomalhaut. inclined or edge-on asp ´ h euto fteSI aafloe iia tp othose to steps similar followed data STIS the of reduction The h TScrngahcnit ftoocligwde and wedges occulting two of consists coronagraph STIS The radRieke and ar ´ −1 2010, 2012,2013,2014 STIS combined 2006/ACS/F814W 2004-06/ACS/F814W o h 66 n 45 C le n o TSad0t .5cts·s 0.05 to 0 and STIS for and filter ACS F435W and F606W the for ) eincmie mg falmliolSI bevtos(00 02 03 n 04 fteFmlatsse.Fmlatbi iil nthe in visible is b Fomalhaut system. Fomalhaut the of 2014) and 2013, 2012, (2010, observations STIS multiroll all of image combined Median (Top) 00 wd oiino h B eg.Deeper wedge. “B” the on position -wide 2010/STIS 2004-10/ACS/F814W srmti ro ai,wietesalrca oo ice hwtepeiu oiin,t ihih h spatial the highlight to positions, previous the show circles color cyan smaller the while radii, error astrometric 00 × 1 00 nsz n ihihsteae hw ntepsaesapiae eo.Tepsaesapimages postage-stamp The below. images postage-stamp the in shown area the highlights and size in x.t) ahof Each sx2.fits). 2012/STIS 2004-10/ACS/F606W −1 TSiae,i smr ifiutt ipiti nteohr.For others. the 2012 in and it pinpoint 2010 to the is difficult and source more is ACS the it F606W While images, the images. STIS 2014 in forward and identifiable on 2013 clearly based was the and for in images 2012 (13) projections and coordinates 2010, published 2006, the 2004, from the started ACS the images in STIS b and Fomalhaut of location astrometric the Determining b Fomalhaut of Photometry and Astrometry epochs. all and at image b STIS Fomalhaut combined of snapshots signal-to-noise detailed high a including ysis, were images individual sub- the PSF following derotation, combined. images, and ACS masking, the the for tractions, mas) image tracking As (6 px coordinates. by 0.12 for both of (determined error in star small star remarkably subtraction a estate, the central has spikes) PSF of diffraction the real with location of the imaging registering residuals, locating image the PSF precise Following the reduces derotation. allows of and also wings processing it dur- the masking spikes image only additional diffraction necessitates and ing this the images While therefore, suppressed. the OTA; are in telescope the prominent of optical are edges HST the the from to also changes but technique, thermal ADI (OTA). images the assembly the exposure etc., follows in each second, method folds This for first, orbits. variations all PSFs all combining interorbit of construct median small to ID, notice sequence decided coor- however, therefore same the did, and to data We all dinates. of registering high-precision enables o h 84 C le] h re ice ihcosshglgttethen the highlight crosses with circles green The filter]. 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ASTRONOMY Table 2. Astrometry of the Fomalhaut b object values are generally in agreement with the previously published Date Instrument ∆R.A. (00) ∆δ (00) values for the ACS data, except for the single observation in the F435W ﬁlter. For STIS, our photometry agrees with that 2004/06 ACS (F814W) −8.542 ± 0.021 9.144 ± 0.021 of ref. 13; however, it is fainter than that of ref. 17 by a fac- 2004/10 ACS (F606W) −8.580 ± 0.011 9.198 ± 0.011 tor of 2. Such discrepancies have been noted in the literature 2004/10 ACS (F814W) −8.642 ± 0.017 9.194 ± 0.018 for this source and are likely an outcome of differences in data 2006/07 ACS (F435W) −8.614 ± 0.020 9.363 ± 0.020 reduction and photometry methods. Nevertheless, the general 2006/07 ACS (F606W) −8.683 ± 0.021 9.341 ± 0.021 conclusions of our paper are not affected by these discrepan- 2006/07 ACS (F814W) −8.590 ± 0.025 9.364 ± 0.026 cies because we have applied identical procedures to all of the 2010/09 STIS −8.850 ± 0.016 9.824 ± 0.016 images. 2012/05 STIS −8.915 ± 0.019 10.024 ± 0.020 The object fades in each individual band over time; however, 2013/05 STIS −9.018 ± 0.027 10.173 ± 0.025 there is a color shift between the various ACS ﬁlters and an 2014/09 (Bound model) −9.029* 10.273* 2014/09 (Cloud model) −9.093* 10.360*

*Projected location of the source (no detection). 06, June; 10, October; 07, 10.4 July; 09, September; 05, May. ACS F435W ACS F606W ACS F814W STIS the F435W and F814W images, we searched for peaks near the Bound orbit F606W positions, while for the 2013 STIS image forward pro- Cloud Trajectory jections from the previous epochs aided in locating the source. We calculated the locations using the centroiding algorithm in 10.2 the Image Reduction and Analysis Facility (IRAF) software, DAOPHOT.APPHOT, initiated on the brightest pixel within a 2-px radius of the predicted locations. The object is visibly expanding in size in the STIS dataset and therefore its astrometric position has an increasingly larger error. The object was not detected in the 2014 dataset at either model trajectory location. All peaks visible in the 2014 dataset are spatially far enough from 10.0 any realistic trajectory projection that they can be dismissed. The astrometric positions are summarized in Table 2 and plotted in Fig. 2. The astrometric errors are calculated as the root sum squares of the derotational errors and the PSF FWHM astrometric errors. The derotational errors in right ascension and declination were calculated for each individual observation, based on the 9.8 derotation angles within each observation set and the precision of image centering, weighted by the exposure time of each individual image. We calculated the derotational errors with a Monte

Carlo code. The centroiding astrometric errors were calculated Delta Dec (’’) based on the standard formula of 1 FWHM σ = , [1] 9.6 centroid 2.355 SNR where SNR gives the peak pixel signal to background pixel noise ratio. Centroiding FWHMs were provided by IRAF for both right ascension and declination. We performed aperture photometry of Fomalhaut b in all of the final reduced images. The photometry was performed with a 9.4 2.1-px radius aperture. The background was measured in 2.1-px radius apertures randomly placed at the same stellocentric distance as the target source (avoiding areas where the disk is prominent). The photometry error was determined as the SD of these background measurements. This is the same method that ref. 13 used to estimate the background and photometry errors. We applied aperture corrections of factors of 3.03, 9.2 2.56, 2.27, and 1.45 for the ACS (F814W, F606W, F435W) and STIS observations, respectively, based on TinyTim theoretical PSFs (23), which include broadening due to the Lyot stops. Planetesimal collision We summarize our photometry compared to previously published values in Table 3. The instrumental flux values 8.6 8.8 9.0 (counts·s−1) were converted to various physical flux units using Delta R.A. (’’) synphot, assuming the incident light that is scattered has a spec- Fig. 2. Astrometry of Fomalhaut b (see text for details). The circles show tral distribution identical to that of the host star (A3V) and using the projected location of the object in 2014 for both the bound orbit and conversion factors appropriate for the instrument setup and cloud models. The purple line and dots give the best-fitting bound orbit and observation date. The pivot wavelength of the instrument/filter locations for each observation, while the cyan line and dots give the same setup was used to calculate the Jansky (Jy) units. Our photometry for the dust cloud model.

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Fig. -1

log10(F) (F x Jy ) evolution dynamical the modeled we scenario, this test To -7.2 -6.8 -6.6 -6.4 -6.2 -7 -6 2004 h htmtyo oahu talosre pcsadwave- and epochs observed all at b Fomalhaut of photometry The ± ± ± .8mg() 24.92 (1); mag 0.08 .9mg() 24.97 (1); mag 0.09 .3mg()24.91 (1) mag 0.13 0.49 25.22 2006 ± .4cts·s 0.14 ± .8(6;3.6 (16); 0.18 0.50 2008 −1 ± ± ± ± 1) 6.1 (13); .1cts·s 0.11 .0mg(6;3.6 (16); mag 0.20 .0mg(6;6.3 (16); mag 0.10 .9mg(6;4.3 (16); mag 0.09 F N/A N/A N/A N/A N/A prev 2010 Date ± h fstbtenteASand ACS the between offset The . 0.9 ACS F814W ACS F606W ACS F435W ± −1 2.1 NSLts Articles Latest PNAS ×10 (13) STIS 2012 ×10 −7 −7 ± y(17) Jy ± ± 0.7 1.0 0.6 y(17) Jy 2014 ×10 (Model: ) (Model: ) (Model: ) (Model: ) ×10 ×10 −7 −7 −7 | y(17) Jy y(17) Jy y(17) Jy f11 of 5 2016 We

ASTRONOMY Fig. 6 shows the MCMC analysis of the initial location of the planetesimal collision and launch velocity of the observed dust particles, determined in the plane of the Fomalhaut system. The only constraint on the initial condition was that the collision had to occur within 150 au of Fomalhaut. As Fig. 6 shows, two families of solutions were found, one with a sharp probability peak at x = 91 au and one with a broader distribution (80 ≤ x ≤ 90 au). The best fit (with a reduced χ2 = 2.38—compared with 3.18 for the best bound orbit fit) was for a collision occur- ring at x = 91.24 au, y = −47.62 au, and z = −13.47 au, with an initial launch velocity of 1.59 au·y−1, twice the Keplerian orbital velocity for a circular orbit at the location of the collision. However, solutions with velocities between 0.59 and 22.13 au·y−1 (at different launch positions) produce fits with reduced χ2 lower than the best bound orbit fit. The best-fitting trajectories were from the first family of solutions, typically having larger velocities (from 1.08 au·y−1), while the best fits from the second family of solutions yielded fits with reduced χ2 similar to that of the bound orbit with velocities up to 0.8 au·y−1 (i.e., sub-Keplerian velocities, assuming circular orbits). Trajec- tories originating from elliptical bound orbits were found in both families. An additional constraint on the model is the speed at which the cloud expands. While the original launch velocity (combined with radiative forces for the dust particles) will determine the average central line of the trajectory, the collisional fragments will also Fig. 4. Posterior probability distributions over the free orbital parame- diverge radially from the central line (trajectory of the COM) ters of Fomalhaut b, assuming a stable bound orbit, using MCMC analysis due to the explosive nature of the event that produced them. In (6,000 chains, 5,000 steps, burn-in limit at 2,000 steps). The diagonal pan- Fig. 7, we show the observed evolution of the radius of the dust els show 1D projections (marginalized over all other parameters) of the probability density, while the off-diagonals show 2D projections of the cloud. The observed size depends on the instrumental PSF, the correlations between parameters. The mean and the 1σ levels of the pixel scale, the reduction algorithm, and observatory guiding arti- 1D projections are shown, while the global reduced χ2 = 3.18 minimum facts. We estimate and correct for these in our analysis in Fig. 8. of the distribution is at a = 385.5 au, e = 0.7604, ι = 9.90◦, w = 118.00◦, In 10 y the cloud has expanded considerably, to the point where Ω = 139.59◦. In SI Appendix, Fig. S1, we show the chains of our MCMC it is larger than the HST PSF (i.e., partially resolved). analysis. These measurements can be used to place limits on the collisional velocity that produced the cloud. Laboratory measurements have shown that the speeds of daughter particles in the effects of gravitational, radiative, and magnetic forces on collisions, relative to a stationary COM, are roughly identical to dust particles, as well as calculate the gravitational effects of a the relative impact velocities (26). Due to similar orbital paths large number of massive bodies. Additionally, DiskDyn provides between colliding bodies, the average collisional velocities in .fits images of the scattered light and thermal emission from the dust particles and complete SEDs. Due to the numerically inten- sive calculations, DiskDyn runs on graphical processing units (GPUs). While DiskDyn is a versatile modeling code, it does not provide fitting tools. Therefore, we first fitted the trajectory of the dust cloud in a similar fashion to that for the bound orbit solution (with MCMC) to obtain the input values for DiskDyn; however, for this fit, we did not constrain the trajectory to be bound. Instead, the launch location and velocity of the cloud were defined by its Cartesian coordinates and velocities (yielding an extra free parameter relative to the bound orbit solution). The trajectories of small dust grains are characterized by β, the ratio of radiation force to gravitational force on the particles. In Fig. 5, we show the total (thermal and scattered) flux as a function of particle size (weighted by the dust number density) at an observational wavelength of 0.6 µm, which corresponds to the wavelength observed with ACS in the F606W filter and with STIS. Fig. 5 also shows the β values, as a function of particle radius. The particle radius range most prominently observed with HST is between 0.07 and 0.7 µm, with flux peaks from dust with radii of 0.11 and 0.23 µm. These sizes have β values Fig. 5. The relative emission flux (thermal and scattered) at an observa- of 10.2 and 7.17, respectively. Therefore, for initial trajectory tional wavelength of 0.6 µm (approximating the F606W ACS filter and the fitting we assumed β = 10 for all particles. However, our final peak of the spectral response of the unfiltered STIS detector) as a function of particle size, assuming the modeled underlying power-law size distri- DiskDyn dust cloud model calculates realistic dust optical prop- bution. We also plot the value of β as a function of particle size on the erties [since we are concerned only with scattered light approx- secondary axis for the dust particles we modeled around an A0 spectral-type imated by Mie theory, we used astronomical silicates only (25)] star. The particles contributing most of the flux have a weighted average and dynamics. of β = 7.2.

6 of 11 | www.pnas.org/cgi/doi/10.1073/pnas.1912506117 Gasp´ ar´ and Rieke Downloaded by guest on September 25, 2021 Downloaded by guest on September 25, 2021 G n 03.Tesailyetne aueo h orei the in source the 2012, of (2010, nature observed extended is spatially it The visibly where is 2013). images cloud and STIS dust a the the still However, in in is observations. extended close first cloud happened the likely the to collision i.e., time the approx- values; therefore widths and theoretical source have the point images to ACS 2004 equal The of imately negligible). drift is result- per-orbit it possibly a i.e., to star, measured guide corresponds We single drifts. which a tracking using respectively. in done ing detectors, typically STIS Fomalhaut its is observing and of when and difficult ACS 85.5% is HST and the drift. which guiding 88.5% Additionally, stops, for guiding to pupil value also diameter the aperture nominal and to HST coronagraphs due the the broadens restrict PSF of instrumental stop The Lyot the to and tnaddvaino h prxmtn asin( (σ Gaussian approximating PSF wavelength-dependent the HST the of subtract deviation we standard value, radial measured collision source. is the this cloud during for the acquired velocities and of random expansion forces the The by radiative dominated orbits. unbound to onto experi- due deflected will velocity. acceleration be HST) launch radial by in additional (observed variations ence undergo particles small and smallest orbits the the bound to However, unde- in due and well. remain shear larger as will Keplerian orbit the they bound for so a dominant bodies, onto tected be project will velocity likely forces launch the then inherited Gravitational as will The expected, cloud disk. is the a fraction in of happen this relative not in direction did random variation collision a Some in COM. collision, the the veloc- an to Keplerian of acquire typical location a the likely of at 10% will ity to particles 5 around high-speed daughter velocity unlikely a the additional on is so originally It was orbit, (27). bodies velocity unbound colliding orbital the of the either of that 7.5% around are disks in shown are chains The global The au·y steps). (in is velocities 2,000 distribution and at the limit of burn-in minimum steps, reduced MCMC 5,000 using chains, orbit, model (6,000 cloud analysis unconstrained an assuming b, Fomalhaut of 6. Fig. asp ´ nFg ,w lutaeteepnino h lu.Fo each From cloud. the of expansion the illustrate we 8, Fig. In radRieke and ar ´ σ F814W otro rbblt itiuin vrtefe ria parameters orbital free the over distributions probability Posterior 0 = STIS 00 . .Teevle nld S raeigdue broadening PSF include values These 035). −1 0 = r endi h ln fteFmlatsystem. Fomalhaut the of plane the in defined are ) i.S2 . Fig. Appendix, SI 00 . 0 033, 00 . 0015 σ F435W e xoue(.%o pixel, a of (2.9% exposure per χ 2 0 = = 8 h oriae i au) (in coordinates The 2.38. 00 . 019, σ F606W σ 0 = fthe of ) 0 00 00 . . 026, 015, ee ih ue rp h peia xaso ftecloud the of expansion spherical scat- the individual drop; their fluxes Fomalhaut, light from tered farther Cloud. move Dust Modeled particles the of Brightness and Morphology global a as well as radial. the clear, increasingly of is is our trajectory dissipation that of its spatial trajectory on results The propagates 7. The it Fig. as system. in cloud the shown of also are angle dust taking modeling the viewing Fomalhaut, our calculations, astrosili- between and scattering angles for grains, scattering Mie constants the performed account optical into We with (33). steps, cates size spaced mically 0.1 of radii from = (L parameters cen- physical the For Fomalhaut’s steps. assumed time 15. we 0.01-y using star, GPU, tral Black Titan GTX observations. was the mass to dust calculations total efficient our The are scaling included). that from sizes are calculated all light as optical long scattering as at irrelevant, 0.1 is was size size largest particle dis- (the in minimum and The comets (30–32). off asteroids sublimating rupted dust of distribution size the dust (29). for zodiacal asteroids (α of in similar con- breakup but drag) shallower collisional is Slightly PR recent it by the in influenced and formed not (28), bands slope disks the debris make of (to of of value typical the slope be with distribution to sistent found size is a value with with was models tracers the particles of ticle cloud, au·y dust handful the 0.15 A the of variable. and of velocities a deter- brightness expansion as in radial kept surface dust the importance in the of and SD of decrease uncertainty evolution larger the its dynamical mining to the Due model cloud. to DiskDyn used trajectory date. their plot we to 2, Fig. due (assuming In ejected forces. be radiative will of influence before, the discussed as particles, dust smaller t ilrsl nabudobtof orbit bound 12. veloc- a and in This position result observations. launch will This ity 2004.03 first expansion. of the time the by collisional predicted the to 0.91, with prior agreement good d in is 39 result happened that event −0.232 values: The = following z either. the con- value these has this had to conforms than straints bodies also higher that much configuration colliding launch be best-fitting the cannot cloud 2) time the 2004, in of to in close up happened observations velocities event first collisional on the expan- constraints The to following observed 1) the The places collision: therefore, respectively. the cloud, velocity, the of orbital sion the of 0.5 5% to equal 1.0 bodies to colliding of the 0.08 of expansion velocity 0.050 orbital the of an to slope fitting, sponds a Following follows considered. cloud The be the b. to do artifacts need Fomalhaut level images not pixel-scale of STIS therefore, the epochs; that in respective sampled their than well at is smaller source b only times Fomalhaut background extended of a two deviation visi- of than standard A core more fitted data. the a raw possibly had the peak, galaxy, in elongated the features slightly investigated background we bly images, point-like of STIS nature of the extended in size 10%. the source within b of geomet- is Fomalhaut confirmation the the average independent take They radial third our we 13. a with if ref. As agreement dimensions; by the axis noted mean, already major ric also and was minor images give 2012 and 2010 h iky utcodmdlwseovdo GeForce a on evolved was model cloud dust DiskDyn The we velocity launch and location initial best-fitting this With 6L 36 6 −9.82 ◦ o h agrudtce rget ftecliin The collision. the of fragments undetected larger the for

au·y , 1 = R au, β ± −1 ,wt oiin akda ahobservation each at marked positions with 10), = .6au· 0.16 −1 x=0.719 = vx iligareduced a yielding , . R 8 . au·y ∼1.2 o1m eegnrtdi 9 logarith- 290 in generated were mm 1 to µm eeepoe.W generated We explored. were

, y 2M 1.92 = M −1 α suigacliinlvlct 0to 10 velocity collisional a assuming , au·y = −1 −3.50 n )teﬁa anhvelocity launch ﬁnal the 3) and , −1 − ∼ 334.4 = a , 91.23 = x ± y=0.783 = vy

on o particles for found 3 χ , .1 au·y 0.016 to pc 7. = d 2 NSLts Articles Latest PNAS 2 = −3. au, .48 lpswr found were slopes 3) au, and 0.695, = e au·y n collisional a and σ −1 α 0 .Ds particles Dust ). v = y 00 . = 10 hc corre- which , 042 ewe 0.05 between −1 This −3.65 6 −55.97 stedust the As and , utpar- dust >100 ± | 0 f11 of 7 00 . z= vz 008, µm µm ι au, ± ± =

ASTRONOMY Observations Models Obs. radial profiles

1.0 0.1 )

 = 0.023’’ -1 0.05 0.5 0

offset (’’) 2004 Jun ACS/F814W 2004 Jun ACS/F814W 0.0 -0.05 Flux (cts s

1.0 0.15 )

 = 0.043’’ -1 0.1 0.5 0.05

offset (’’) 0 2004 Oct ACS/F606W 2004 Oct ACS/F606W 0.0 -0.05 Flux (cts s

1.0 0.1 )

 = 0.029’’ -1 0.05 0.5 0

offset (’’) 2004 Oct ACS/F814W 2004 Oct ACS/F814W -0.05 0.0 -0.1 Flux (cts s

1.0 0.15 )

 = 0.030’’ -1 0.1 0.5 0.05

offset (’’) 2006 ACS/F435W 2006 ACS/F435W 0 0.0 -0.05 Flux (cts s

1.0 0.1 )

 = 0.051’’ -1 0.05 0.5 0 offset (’’) 2006 ACS/F606W 2006 ACS/F606W 0.0 -0.05 Flux (cts s

1.0 0.04 )

 = 0.036’’ -1 0.02 0.5 0 offset (’’) 2006 ACS/F814W 2006 ACS/F814W 0.0 -0.02 Flux (cts s

1.0 0.08 )

 = 0.077’’ -1 0.04 0.5 0

offset (’’) 2010 STIS 2010 STIS 0.0 -0.04 Flux (cts s

1.0 0.08 )

 = 0.073’’ -1 0.04 0.5 0

offset (’’) 2012 STIS 2012 STIS -0.04 0.0 Flux (cts s

1.0 0.06 )

 = 0.093’’ 0.04-1 0.02 0.5 0

offset (’’) 2013 STIS 2013 STIS -0.02 0.0 -0.04 Flux (cts s

1.0 )

 = 0.994’’ 0.04-1 0.02 0.5 0

offset (’’) 2014 STIS 2014 STIS -0.02 0.0 -0.04 Flux (cts s 0.0 0.5 1.0 1.5 0.0 0.5 1.0 1.5 0.0 0.1 0.2 0.3 offset (’’) offset (’’) R (’’)

Fig. 7. Comparison of the evolution of the spatial scale, location, and surface brightness of the dust cloud as observed and modeled. The scaling of the images is the same as in Fig. 1 for both models (Center column) and observations (Left column). Right column also shows the fitted radial profiles of the observations. The radial profiles are corrected for instrumental effects in Fig. 8.

results in its overall surface brightness dropping as well. To simu- The model predictions varied as a function of σv, the SD of the late the observations, we convolved the model images with their additional velocities of the daughter particles. The best fit was at −1 appropriate ACS and STIS PSFs. The model images shown in σv = 0.13 ± 0.01 au·y , which is 12% of the launch velocity and Fig. 7 take into account the convolution and pixel sizes. We mea- within 3 SD of the expansion slope fit. The results of the pho- sured the fluxes in the model images using the same aperture tometry of the model images, assuming this best-fitting σv value, radius and aperture corrections as we did for the data and then are shown in Fig. 3. The correspondence between the modeled finally scaled the model to the observations. observations and the actual photometry is excellent. The PSF

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Fig. G 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 of area surface scattering a equals This g· 3.5 of sity asp ´ Spatial scale (au) −8 22 ein ftefitn.Tedt necp ftefi adteestimated the (and fit the of intercept date The fitting. the of regions -0.1 radRieke and ar 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 ´ cm 0 M h pta vlto fteosre utcodadtebest-fitting the and cloud dust observed the of evolution spatial The Earth 2   a rdcdi h oahu ytm hs dust These system. Fomalhaut the in produced was ) cloud =0.05 auyr 2004 −1 cm nertn pt mi ais[suigaden- a [assuming radius in mm 1 to up integrating , π hc sjs lgtyhge hntecrua Kep- circular the than higher slightly just is which , r 2 −3 ufc rao cteig h xc oa dust total exact The scattering. of area surface -1 prpit o h ieycmoiin(25)]. composition likely the for appropriate 2006 y −1 2008 ± Date (year) 1 au·y 0.016 ttelcto ftecollision the of location the at 2010 4.8 −1 sarsl facatas- a of result a As hc is which , × 10 σ v 22 2012 0 = cm .%o the of ∼6.2% . 13 −2 ∼1.65 assum- , au·y 2014 Our −1 × × , ltl etoigbt ois rol rsv.Orppr(28) paper Our (com- erosive. catastrophic only either or bodies) be both will Depending destroying collision velocity. pletely the relative factors, their of those and values on (masses), The sizes calculated. their ing, be to factor and scaling the allowing over- the (X minus distribution, produced bodies, fragment continuous colliding fragment two largest the all of fragment masses second-largest the the equals is and it overall) (i.e., distribution continuous variable The the produced that and event collisional distribution, the in partaking object larger where is distribution collision the single in a in produced fragments mass of dust of total distribution The a collisional in planetesimals. probabilities considering collisional by mutual answer and the outcomes illustrate We system? for haut results similar yields masses largest the cases. total both to determine up smallest to impact. the survive fragments from Loosely will that distributions and 36). 39) the (37) (38, (35, sizes Integrating inefficiently size similar to energy in up impact m boulders these have convey 50 of piles to nature rubble 10 with the bound to (34) on up efficiently extending fragment strongly fragments can depend objects not Consolidated do bodies. size and mass the May. of 05, are September; 09, Positions July; flux. 07, cloud October; modeled 10, June; total 06, the COM. yield not may therefore (F814W) ACS 2012/05 (F606W) ACS 2010/09 (F435W) ACS 2006/07 (F814W) ACS 2006/07 (F606W) ACS 2006/07 (F814W) ACS 2004/10 2004/10 2004/06 h ai ftetre n h matr suigacliinlvlct of velocity collisional a assuming shown. impactor, the and m·s target 236 the of radii the 9. Fig. Instrument Date Fomalhaut the of brightness and object position b Modeled 4. Table 2014/09 2013/05 Impactor radius (km) 100 150 200 250 o rqetywudmjrcliin cu nteFomal- the in occur collisions major would frequently How and observations the as way same the measured were given fluxes The 50 0 Y 100 −1 µ h muto utpoue pt ai f1m safnto of function a as mm 1 of radii to up produced dust of amount The r endb h esl tegho h oiscollid- bodies the of strength tensile the by defined are oan rdcn . o2tmsteosre utms are mass dust observed the times 2 to 0.5 producing Domains . stems ftesalrobject, smaller the of mass the is v =236ms M 200 fr A Y (µ, sissaigfco.Terdsrbtdms also mass redistributed The factor. scaling its is M -1 STIS STIS STIS STIS ie h aso h ags rgeti the in fragment largest the of mass the gives 300 M γ fr (µ, stems-itiuinsoe(α slope mass-distribution the is = ) M 400 Z 0 Target radius(km) = ) Y ( µ,M µ 500 .3 .2 3.907e-7 9.822 4.684e-7 5.605e-7 9.356 −8.836 3.925e-7 9.187 9.153 −8.648 −8.593 −8.583 ..( ∆R.A. .9 0301.574e-7 1.885e-7 10.360 10.174 −9.093 −9.000 .3 0002.562e-7 10.040 −8.936 + ) M A(µ, ,wihi o ato the of part not is which ), 600 − 00 ) X M NSLts Articles Latest PNAS (µ, )m 700 M M −γ ∆δ stems fthe of mass the is ), +1 ( 800 00 dm (Jy) F ) , 3 = 900 3.208e-7 4.811e-7 3.896e-7 | γ f11 of 9 − 1.0 1.5 2.0 2.5 3.0 [3] [2] 2). -8 X Mdust (x 10 MEarth)

ASTRONOMY discusses these collisional outcomes in more detail. For tensile pared with the near-infrared rate of true exoplanet detections strength, we assume the curve of ref. 40, traditionally used in (e.g., ref. 42). debris disk cascade calculations. For the collisional speed, the Dynamical instability from planetary migration can stir plan- expansion of the dust cloud provides a good estimate, as it will etesimal populations and increase their collision rates. It is the be roughly equal to the relative velocity of colliding bodies. The most likely explanation for events like Fomalhaut b and was also size of the cloud yields a collisional speed of 0.05 au·y−1, while invoked by ref. 19. Such dynamical activity has been modeled the photometric modeling results in 0.13 au·y−1. These corre- in detail to explain the influence of planetary migration on the −1 spond to 236 and 616 m·s , respectively. In Fig. 9, we show the evolution of the solar system (43–45), leading to elevated plan- dust mass (up to radii of 1 mm) produced in collisions between etesimal collision rates as reflected, for example, in the heavy −1 various target–impactor sizes at a collisional speed of 236 m·s , bombardment indicated by the impact rate on the Moon (e.g., in the domain where the produced dust mass is half to twice refs. 46–49). as much as is observed in the dust cloud. The smallest target capable of producing so much dust is 109 km in radius (when Summary hit by a similar-size impactor); however, in erosive collisions, a The planetary nature of Fomalhaut b has been a mystery ever 56-km body impacting an 893-km object can also generate this since its detection over a decade ago. In this paper, we present amount of dust. At the faster impact velocity, the catastrophic previously unpublished measurements of this object and also outcome remains approximately the same, while the erosive limit rereduce all archival data to present a coherent analysis that drops the impactor radius to 47 km. The escape velocity from the −1 shows its behavior over a decade. largest fragment in the catastrophic collision is ∼137 m·s , sug- We find that the source has grown in extent since its discov- gesting a high impact velocity. However, the uncertainty in the ery. We use updated astrometry and orbital solutions, finding its expansion velocity is large and a larger impact velocity would not motion is consistent with radial (escaping) motion. To explain change our results. these observations, we model Fomalhaut b as an expanding dust The rate of collisions between planetesimals that could pro- cloud, containing copious amounts of dust produced in a mas- duce the required amount of dust depends on their number sive planetesimal collision. Our model produces a light curve, density and interaction velocity. Since Fomalhaut b is located angular extent, and orbital motion consistent with the obser- near the inner edge of the Fomalhaut debris belt, we assume the vations spanning a decade. While Fomalhaut b is not likely density of parent bodies at the collisional location to be simi- to be a directly imaged exoplanet, it is probably an extraor- lar to that in the belt. We calculate the belt mass and density dinary supercatastrophic planetesimal collision observed in an from its spectral energy distribution and thermal surface bright- exoplanetary system! Production of this amount of dust through ness, yielding a total of 26.15 MEarth, assuming a largest body planetesimal collisions in dynamically quiescent systems should in the distribution has a diameter of 2,000 km and that the −3 be very rare. The rate of such events would be increased substan- belt material has a bulk density of 3.5 g·cm . The timescale tially if hypothetical planets around Fomalhaut are undergoing for collisional events producing the required amount of dust orbital migration, resulting in a dynamically active population of can be estimated by integrating the differential rate of col- planetesimals. lisions in the projectile and target mass space highlighted in Fig. 9. We integrate the domain that produces dust half of to Data Availability. The raw observational data can be downloaded double the amount observed, yielding timescales of ∼0.59 and −1 −1 from the MAST website maintained by the STScI. Our mod- ∼0.15 My for the 236 m·s and 616 m·s collisional velocities, eling code, DiskDyn, can be downloaded from https://github. respectively. com/merope82/DiskDyn. Fomalhaut b was above the detection level for only a decade, making it unlikely to have arisen in a dynamically cold quiescent ACKNOWLEDGMENTS. We are grateful for the hardware donation from planetary system given the timescales just derived. Even if the Nvidia. We thank Paul Kalas for planning and obtaining the observa- dust production is more efficient than we have assumed, i.e., the tions described here and our referees for providing helpful comments throughout the multiround review process. We also sincerely appreciate slope of the size-frequency distribution is steeper than −3.65, the postacceptance in-depth review of an independent HST/STIS expert. the rarity of this object is shown by the lack of similar sources This work has been supported by NASA Exoplanets Research Program Grant among HST images of exoplanets and debris disks (41) com- 80NSSC20K0268 and NASA Grant 80NSSC18K0555.

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