Nucleus of Active Asteroid 358P/Pan-STARRS (P/2012 T1) J

A&A 616, A54 (2018) Astronomy https://doi.org/10.1051/0004-6361/201832761 & © ESO 2018 Astrophysics

Nucleus of active asteroid 358P/Pan-STARRS (P/2012 T1) J. Agarwal1 and M. Mommert2,3

1 Max Planck Institute for Solar System Research, Justus-von-Liebig-Weg 3, 37077 Göttingen, Germany e-mail: [email protected] 2 Lowell Observatory, 1400 W Mars Hill Rd, Flagstaff, AZ 86001, USA 3 Department of Physics and Astronomy, Northern Arizona University, PO Box 6010, Flagstaff, AZ 86011, USA

Received 2 February 2018 / Accepted 17 May 2018

ABSTRACT

Context. The dust emission from active asteroids is likely driven by collisions, fast rotation, sublimation of embedded ice, and combinations of these. Characterising these processes leads to a better understanding of their respective inﬂuence on the evolution of the asteroid population. Aims. We study the role of fast rotation in the active asteroid 358P (P 2012/T1). Methods. We obtained two nights of deep imaging of 358P with SOAR/Goodman and VLT/FORS2. We derived the rotational light curve from time-resolved photometry and searched for large fragments and debris >8 mm in a stacked, ultra-deep image. Results. The nucleus has an absolute magnitude of mR = 19.68, corresponding to a diameter of 530 m for standard assumptions on the albedo and phase function of a C-type asteroid. We do not detect fragments or debris that would require fast rotation to reduce surface gravity to facilitate their escape. The 10-h light curve does not show an unambiguous periodicity. Key words. minor planets – asteroids: individual: 358P

1. Introduction lifting of dust against gravity by a weak gas flow (Jewitt et al. 2014; Agarwal et al. 2016). Active asteroids have orbits typical of asteroids (with a Tisserand The active asteroid 358P (formerly designated P/2012 T1) parameter relative to Jupiter >3; Kresák 1972), but temporarily was discovered in October 2012 by the Pan-STARRS1 survey display dust activity similar to comets (Hsieh & Jewitt 2006; (Chambers et al. 2016) owing to its bright cometary appearance Jewitt 2012; Jewitt et al. 2015b). While cometary activity is (Wainscoat et al. 2012). 358P had passed perihelion at 2.41 AU generally thought to be driven by the sublimation of embedded on 10 September 2012, about one month before its discovery. The volatiles (Whipple 1950), the situation is likely more diverse brightness of its dust coma first increased and then decreased in asteroids. Main belt asteroids have spent most of the time over the following months, consistent with sublimation-driven since their formation between the orbits of Mars and Jupiter, activity (Hsieh et al. 2013). Numerical simulations reconstruct- where solar heating prevents the persistence of near-surface ing the production rate, size distribution, and ejection velocity ice over solar-system age timescales. But water ice can exist in of dust from the appearance of the dust tail indicate that the the interiors of main belt asteroids if protected by a mantle of activity must have been ongoing for 3–5 months, starting at dust and debris (Schorghofer 2008; Prialnik & Rosenberg 2009; or one month before perihelion (Moreno et al. 2013). Spec- Capria et al. 2012). troscopic searches for water vapour yielded an upper limit of 25 1 Currently, five main belt asteroids are known to have ejected 7.63 10 molecules s− (O’Rourke et al. 2013; Snodgrass et al. dust for extended periods of weeks to months during con- 2017),× which is still consistent with weak sublimation of water secutive perihelion passages (Hsieh et al. 2004, 2015, 2011; ice lifting the observed amount of dust. Hsieh & Sheppard 2015; Jewitt et al. 2015a; Agarwal et al. We have observed 358P in July and August 2017, at true 2017). This combination of protracted and recurrent activity anomaly angles of 291◦ and 296◦, prior to its return to perihelion is interpreted as a strong indication that the dust was lifted in April 2018. The purpose of our observations was to (1) char- by gas-drag from sublimating ice (Hsieh et al. 2004). This acterise the size, rotation and shape of the bare nucleus, which subgroup of active asteroids is therefore also called the had been hidden in dust during all previous observations, and (2) main belt comets (MBCs; Hsieh & Jewitt 2006). In some to search for a debris trail and larger fragments along the orbit of of the other active asteroids, the dust ejection has been an 358P. The goal was to investigate whether fast rotation might instantaneous process, such as an impact (Ishiguro et al. be supporting ice sublimation in lifting the dust from 358P. We 2011a,b; Kim et al. 2017) or possibly break-up by fast rotation describe the observations and data analysis in Sect.2. The results (Jewitt et al. 2013a; Hirabayashi & Scheeres 2014; Hirabayashi are presented in Sect.3 and discussed in Sect.4. et al. 2014; Drahus et al. 2015). These same processes are also considered as the most likely triggers of sublimation- driven activity in MBCs by excavating ice from the interior 2. Observations and data processing (e.g. Haghighipour et al. 2016, 2018). Why sublimation is trig- 2.1. SOAR/Goodman gered in some objects and not in others may depend on the abundance and depth of ice, the magnitude of the excavat- We observed 358P using the Goodman imaging spectrograph ing process, or both. Conversely, fast rotation can support the (Clemens et al. 2004) mounted on the Southern Astrophysical

Article published by EDP Sciences A54, page 1 of7 A&A 616, A54 (2018) J. Agarwal and M. Mommert: Nucleus of active asteroid 358P

Research (SOAR) Telescope located on Cerro Pachón, Chile. 23.0 19.0 23.2 Observations took place between 27 July 2017 UT 22:11 and 23.3 28 July 2017 UT 10:08; the observing geometry is described in 23.5 19.5 Table1. We used Goodman in imaging mode with 2 2 binning 23.4 × (0.300pixel scale) and tracked the telescope at the rate of the tar- 24.0 20.0 23.5 get. We used integration times of 120 s (first 20 frames) and 150 s; background stars were trailed by l = 300 and l = 400, respec- 23.6 tively. The goal of the observations was the recovery of the target 24.5 20.5 23.7 (3σ positional uncertainty of the orbit at the time of observations: 30), the measurement of its rotational period using the 25.0 21.0 23.8 Absolute magnitude broadband∼ VR filter (centred at 610 nm with full width at half Apparent magnitude 23.9 maximum – FWHM – of 200 nm), and the measurement of 25.5 21.5 24.0 its optical colours using Sloan g, r, and i filters to put con- Apparent magnitude in Cousins R-band straints on its taxonomic classification. Our observations were 26.0 22.0 24.1 compromised by highly variable transparency conditions and 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 cloud coverage, allowing for useful observations over only about Hours relative to 28 July 2017 UT 00:00 Seeing FWHM [pixels] 2 h out of 9 h. Furthermore, the target turned out to be signifi- 23.1 cantly fainter than the brightness predicted by the JPL Horizons Fig. 2. Measured magnitude from VLT data as a function of the seeing system (Giorgini et al. 1996). We were able to recover the tar- 23.2 19.4 FWHM, which is proportional to the aperture radius. The two quantities show a weak degree of statistical dependence (R=0.17). Open symbols get (Mommert et al. 2017) and extract a partial light curve from 23.3 19.5 indicate data points obtained after UT 8:00 (see Fig. 1.) our VR observations. The g, r, and i filter observations were excluded from further analysis because of their marginal S/N. 23.4 19.6 The image data were corrected using bias and dome flat-field 23.5 19.7 images taken on the same night. Astrometry and instrumental aperture photometry were derived from the VR images taken 23.6 19.8 400 during the clear portion of the night using the PHOTOME- 23.7 19.9 TRYPIPELINE (PP; Mommert 2017). The PP provides auto- Absolute magnitude 23.8 20.0 mated astrometric and photometric analysis for imaging data and 300 has been specifically designed for moving target observations. 23.9 20.1 We photometrically calibrated our observations against Cousins Apparent magnitude in Cousins R-band R-band transformed from Pan-STARRS DR1 r magnitudes 24.0 20.2 -1 0 1 2 3 4 5 6 7 8 9 10 200 (Tonry et al. 2012; Flewelling et al. 2016), using no less than five Hours relative to 18 August 2017 UT 00:00 Fourier Order n background stars with solar-like colours (0.24 g r 0.64 and Spectral Power n = 1 ≤ − ≤ 0.09 r i 0.31 in Sloan gri) in order to minimise system- Fig. 1. Light curve of 358P on 28 July 2017 observed with 100 n = 2 − ≤ − ≤ Fig. 1. Light curve of 358P on 28 July 2017 observed with atic effects caused by the use of the VR filter while calibrating SOAR/GoodmanSOAR/Goodman (top (top panel panel)) and and on on 18 18 August August 2017 2017 observed observed with with n = 3 against R. Because of the highly variable seeing conditions, we VLT/FORS2VLT/FORS2 (bottom (bottom panel panel).). The The flux was was measured measured in in apertures apertures of of ra- n = 4 n = 5 adopted variable apertures for both 358P and the background radiusdius 1.3 1.3DD,, and and for for the the VLT VLT data dataset corrected set corrected by an o byffset an of offset -0.09 mag of 0 to account for the loss of flux due to the small aperture. This correction stars; the full width at half maximum (FWHMbg) of the back- –0.09 mag to account for the loss of flux due to the small aperture. This 0 2 4 6 8 10 was not applied for the SOAR data set because the FWHM was mea- ground stars varies between 0.500and 1.500over the transparent correction was not applied for the SOAR data set because the FWHM Lightcurve Period (hr) wassured measured as average as average over the over moderately the moderately trailed stars. trailed The stars. loss ofThe flux loss due of to part of the night. We used aperture radii of r = 1.3 FWHMbg the small aperture was therefore less than in the FORS data. The correc- for 358P, and of r = l/2 + 1.3 FWHM for stars.× In order flux due to the small aperture was therefore less than in the FORS data. Fig. 3. Spectral power distributions for the light curve period (which × bg Thetion correction would have would been have small been compared small compared to the large to the scatter large and scatter error and bars corresponds to half the rotation period for a shape-induced double to mitigate effects caused by the different aperture sizes, we errorof the bars data. of the Open data. symbols Open symbols in the bottom in the panelbottom indicate panel indicate data obtained data peaked light curve) of 358P using a statistical approach. For any period applied empirical magnitude offsets to the target photometry in obtainedafter UT after 8:00 UT for 8:00 comparison for comparison with Fig. with 2. The Fig. scale2. The on scale the right-hand on the in the range, the distributions provide the spectral power as derived with such a way as to keep the flux level of five bright stars con- right-handside vertical side axes vertical indicates axes indicates the derived the absolute derived magnitudeabsolute magnitude according a Lomb-Scargle algorithm; the coloured lines denote different Fourier stant; these corrections are significantly smaller than the typical accordingto Eq. 1 andto Eq. for (1G)= and0.15. for TheG = shaded 0.15. The areas shaded in both areas panels in both indicate panels the orders. We are unable to identify a clear periodicity in the period range photometric uncertainties of the target. The measured photome- indicaterange of the absolute range of magnitudes absolute magnitudes covered by covered the VLT by data. the VLT data. that was probed. try from our SOAR observations, which is subject to significant noise, is plotted in the top panel of Fig.1. The weighted aver- Table 1. Journal of our observations of 358P. age brightness of the target from this partial light curve is complexity of the rotational light curve (Fourier order n), we re- tometric uncertatinties, or that the object’s rotational period is mR = 23.84 0.11. peat this analysis for a range of Fourier orders (1 n 5). significantly longer than 10 hr. We discuss this result in detail in ± Tel. Start date [UT] Rh ∆ ≤α≤ ν The resulting spectral power distributions are shown in Fig. Section 4. 2.2. VLT/FORS2 3.SOAR Relative 27-07-2017 power maxima 22:11 independent 2.741 1.773 of the 8.0 Fourier◦ 290.8 order◦ n VLT 17-08-2017 23:37 2.695 1.707 5.9 295.7 appear at approximately 2 hr and 4 hr. For n >◦1, additional◦ 3.2. Radial profile and dust coma We also observed 358P for 10 h beginning on 17 August 2018 power maxima appear in between, all of which have compa- UT 23:37, using the FOcal Reducer and low dispersion Notes.rableThe strength. quantities Therh 4and hr∆ periodicity,refer to the heliocentric which would and indicate geocentric an To search for dust near the nucleus in the FORS2 images, we Spectrograph 2 (FORS2; Appenzeller et al. 1998) mounted on distances8 hr rotation in AU, periodα is the for phase a double-peaked angle, and ν the light true anomaly.curve, agrees with compared radial flux profiles of 358P with those of field stars. the Unit 1 telescope (UT1) of the European Southern Observa- the light curve behaviour observed during the first 8 hr of our Since stars were trailed in the exposures targeting 358P, we used tory’s (ESO) Very Large Telescope (VLT) on Cerro Paranal in VLTThe/FORS2 images observations were bias-subtracted (filled symbols and flatfieldedin Figs.1 and using 2). Data the two calibration exposures of standard star fields obtained at side- Chile. We obtained 77 images with an exposure time of 400 s Esorexfrom the pipeline, last two version hours (open3.11.1 symbols (Freudling in Figs.1 et al. and2013 2)). were We rial tracking at the beginning and end of the night, respectively, in the R_SPECIAL+76 filter (central wavelength 655 nm, band- derivedobtained the under temporal deteriorated variation seeing of the conditions seeing from and profiles may be of 22less to measure the stellar radial profiles. We averaged the normalised width 165.0 nm) in 2 2 binning mode, corresponding to a linear fieldreliable. stars From not saturating Fig. 3 we the are CCD unable detector. to derive Stars an wereunambiguous trailed profiles of 14 and 26 non-saturated field stars, respectively. For × pixel scale of 0.2500. The sky conditions were clear, possibly pho- byrotationall = 13.67 period pixels for because 358P. Potential the telescope explanations was tracking are that the the comparison, we selected exposures of 358P obtained under sim- tometric. The geometry and distance at the time of observation non-siderialobject is rather motion spherical of 358P, or observed and the from trails a were polar inclined perspective, by ilar seeing conditions (as indicated by the FITS header keyword are listed in Table1. 29leading◦ relative to a to light the curve image amplitudex-axis. We that fitted is smaller brightness than profilesour pho- FWHMLINOBS). The keyword FWHMLINOBS seems to have

A54, page 2 of7 Article number, page 3 of 7 J. Agarwal and M. Mommert: Nucleus of active asteroid 358P

23.0 19.0 23.2

23.3 23.5 19.5 23.4

24.0 20.0 23.5

23.6 24.5 20.5 23.7

25.0 21.0 23.8 Absolute magnitude Apparent magnitude 23.9 25.5 21.5 24.0 Apparent magnitude in Cousins R-band

26.0 22.0 24.1 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 Hours relative to 28 July 2017 UT 00:00 Seeing FWHM [pixels]

23.1 Fig. 2. Measured magnitude from VLT data as a function of the seeing 23.2 19.4 FWHM, which is proportional to the aperture radius. The two quantities show a weak degree of statistical dependence (R=0.17). Open symbols 23.3 19.5 indicate data points obtained after UT 8:00 (see Fig. 1.) 19.6 J. Agarwal and M. Mommert: Nucleus23.4 of active asteroid 358P J. Agarwal & M. Mommert: Nucleus of active asteroid 358P 23.5 19.7 23.0 19.0 23.2 23.6 19.8 400 23.3 19.9 23.5 19.5 23.7 23.4 Absolute magnitude 23.8 20.0 300 24.0 20.0 23.5 23.9 20.1 Apparent magnitude in Cousins R-band 23.6 24.0 20.2 24.5 20.5 200 23.7 -1 0 1 2 3 4 5 6 7 8 9 10 Hours relative to 18 August 2017 UT 00:00 Fourier Order n 25.0 21.0 23.8 Spectral Power n = 1 Absolute magnitude Fig.Apparent magnitude 1. Light curve of 358P on 28 July 2017 observed with 100 n = 2 SOAR23.9/Goodman (top panel) and on 18 August 2017 observed with n = 3 25.5 21.5 n = 4 VLT24.0/FORS2 (bottom panel). The flux was measured in apertures of ra- Apparent magnitude in Cousins R-band n = 5 dius 1.3D, and for the VLT data set corrected by an offset of -0.09 mag 0 26.0 22.0 to account24.1 for the loss of flux due to the small aperture. This correction 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 0 2 4 6 8 10 was not applied for the SOAR data set because the FWHM was mea- Lightcurve Period (hr) Hours relative to 28 July 2017 UT 00:00 sured as average over the moderatelySeeing FWHM trailed [pixels] stars. The loss of flux due to 23.1 the small aperture was therefore less than in the FORS data. The correc- Fig. 3.SpectralSpectral power power distributions distributions for for the the light light curve curve period period (which (which Fig. 2.MeasuredMeasured magnitude magnitude from from VLT VLT data data as as a a function function of of the the seeing seeing Fig. 3. Fig.tion 2. would have been small compared to the large scatter and error bars correspondscorresponds to to half half the the rotation rotation period period for for a shape-induced a shape-induced double- double 19.4 FWHM,FWHM, which which is is proportional proportional to to the the aperture aperture radius. radius. The The two two quantities quantities 23.2 of the data. Open symbols in the bottom panel indicate data obtained peakedpeaked light light curve) curve) of of 358P 358P using using a statistical a statistical approach. approach. For For any any period period showshow a a weak weak degree degree of of statistical statistical dependence dependence (R (R==00.17)..17). Open Open symbols symbols 19.5 after UT 8:00 for comparison with Fig. 2. The scale on the right-hand inin the the range, range, the the distributions distributions provide provide the the spectral spectral power power as as derived derived with with 23.3 indicateindicate data data points points obtained obtained after after UT UT 8:00 8:00 (see (see Fig. Fig.1.) 1.) side vertical axes indicates the derived absolute magnitude according a Lomb–Scarglea Lomb-Scargle algorithm; algorithm; the the coloured coloured lines lines denote denote different different Fourier Fourier 23.4 19.6 to Eq. 1 and for G=0.15. The shaded areas in both panels indicate the orders.orders. We We are are unable unable to to identify identify a clear a clear periodicity periodicity in in the the period period range range range of absolute magnitudes covered by the VLT data. thatthat was was probed. probed. 23.5 19.7 measured parallel to the y-axis with a Gaussian function, and used its FWHM, D, as a proxy of that of the seeing disc. The 23.6 19.8 quantitycomplexity400 D varied of the between rotational 3 and light 6 pixelscurve (Fourier (0.7500 and order 1.5n00),) over we re- intometric a Gaussian uncertatinties, way, according or that to the object’s derived uncertainties. rotational period We is 23.7 19.9 the course of the night. apply the Lomb–Scargle algorithm to this randomised data set

Absolute magnitude peat this analysis for a range of Fourier orders (1 n 5). significantly longer than 10 hr. We discuss this result in detail in The data analysis procedure used for the VLT≤ data≤ is very and derive the power-frequency distribution for potential light 23.8 20.0 The resulting spectral power distributions are shown in Fig. Section 4. similar300 to that used for our SOAR observations. Using PP, we curve periods between 1 and 10 h (the duration of the obser- 3. Relative power maxima independent of the Fourier order n 23.9 20.1 performed aperture photometry on background stars using an vations). By repeating this method for 1000 randomised data Apparent magnitude in Cousins R-band > apertureappear radius at approximately of r = l/2 + 2 1.3 hrD andand 4 derivedhr. For n the1, magnitude additional sets3.2. and Radial summing profile up and the dust individual coma power-frequency distribu- 24.0 20.2 power maxima appear in between, all of which have compa- zeropoint200 for each frame calibrated against Pan-STARRS DR1 tions, we obtain a distribution that accounts for the significant -1 0 1 2 3 4 5 6 7 8 9 10 rable strength. The 4 hr periodicity, which would indicate an To search for dust near the nucleus in the FORS2 images, we Hours relative to 18 August 2017 UT 00:00 r photometry transformed to Cousins R, requiringFourier Or ade minimumr n photometric uncertainties in the data. Because of the unknown of8 threeSpectral Power hr rotation non-saturated period for background a double-peaked stars with light solar-like curve,n = 1 agrees colours. with complexitycompared of radial the fluxrotational profiles light of 358P curve with (Fourier those order of fieldn), stars. we Fig. 1. Light curve of 358P on 28 July 2017 observed with Targetthe100 light aperture curve photometry behaviour was observed obtained during using the a firstvariablen = 2 8 hr aper- of our repeatSince this stars analysis were trailed for a range in the of exposures Fourier orders targeting (1 358P,n 5 we). used / n = 3 SOAR/Goodman (top panel) and on 18 August 2017 observed with tureVLT withFORS2 radius observationsr = 1.3D (Fig. (filled1, bottom). symbols We in applied Figs.1 empiricaland 2). Data twoThe calibration resulting exposures spectral of power standard distributions star fields obtainedare≤ shown≤ at side- in n = 4 VLT/FORS2 (bottom panel). The flux was measured in apertures of ra- magnitudefrom the offsets last two to hours the target (open photometry symbols in in Figs.1 such a and way 2) as were to Fig.rial3. tracking Relative at power the beginning maxima independent and end of the of the night, Fourier respectively, order D ff n = 5 dius 1.3 , and for the VLT data set corrected by an o set of -0.09 mag keepobtained the0 flux under level deteriorated of ten bright seeing stars constant; conditions these and corrections may be less n toappear measure at the approximately stellar radial 2 profiles. and 4 We h. averaged For n >1, the additional normalised to account for the loss of flux due to the small aperture. This correction arereliable. significantly0 From smaller Fig.2 3 we than4 are the unable typical6 to photometric derive8 an unambiguous uncertain-10 powerprofiles maxima of 14 andappear 26 non-saturatedin between, all field of stars, which respectively. have compa- For was not applied for the SOAR data set because the FWHM was mea- rotational period for 358P.Lightcurve Potential Period (hr) explanations are that the comparison, we selected exposures of 358P obtained under sim- sured as average over the moderately trailed stars. The loss of flux due to ties of the target. To account for the systematic loss of flux due rable strength. The 4 h periodicity, which would indicate an toobject the small is rather aperture, spherical we corrected or observed the measured from a polar magnitudes perspective, by 8ilar h rotation seeing period conditions for a (as double-peaked indicated bylight the FITS curve, header agrees keyword with the small aperture was therefore less than in the FORS data. The correc- Fig.leading 3. Spectral to a light power curve distributions amplitude for thatthe light is smaller curve period than our (which pho- FWHMLINOBS). The keyword FWHMLINOBS seems to have tion would have been small compared to the large scatter and error bars subtractingcorresponds 0.09 to half (Sect. the 3.2 rotation). The period weighted for a average shape-induced brightness double of the light curve behaviour observed during the first 8 h of our of the data. Open symbols in the bottom panel indicate data obtained thepeaked target light derived curve)of from 358P all using VLT astatistical data points approach. shown For in any Fig. period1 is VLT/FORS2 observations (filled symbolsArticle in Figs. number,1 and2 page). Data 3 of 7 after UT 8:00 for comparison with Fig. 2. The scale on the right-hand minR the= 23 range,.46 the0 distributions.01. provide the spectral power as derived with from the last 2 h (open symbols in Figs.1 and2) were obtained side vertical axes indicates the derived absolute magnitude according a Lomb-ScargleFigure2 ±shows algorithm; the measured the coloured apparent lines magnitude denote different as a func-Fourier under deteriorated seeing conditions and may be less reliable. to Eq. 1 and for G=0.15. The shaded areas in both panels indicate the tionorders. of the We measured are unable FWHMto identify of a the clear seeing, periodicity which in is the proportional period range From Fig.3 we are unable to derive an unambiguous rotational range of absolute magnitudes covered by the VLT data. tothat the was employed probed. aperture radius. The Pearson correlation coef- period for 358P. Potential explanations are that the object is ficient between the corresponding flux and the FWHM is R = rather spherical or observed from a polar perspective, leading 0.17, indicating a weak correlation between the measured flux to a light curve amplitude that is smaller than our photometric complexity of the rotational light curve (Fourier order n), we re- andtometric employed uncertatinties, aperture size. or that the object’s rotational period is uncertatinties, or that the object’s rotational period is signif- peat this analysis for a range of Fourier orders (1 n 5). significantly longer than 10 hr. We discuss this result in detail in ≤ ≤ icantly longer than 10 h. We discuss this result in detail in The resulting spectral power distributions are shown in Fig. Section 4. Sect.4. 3. Relative power maxima independent of the Fourier order n 3. Results appear at approximately 2 hr and 4 hr. For n >1, additional 3.1.3.2. Light Radial curve profile and dust coma 3.2. Radial profile and dust coma power maxima appear in between, all of which have comparable strength. The 4 hr periodicity, which would indicate an ToTo assess search the for rotational dust near properties the nucleus of in 358P, the FORS2 we concentrate images, on we To search for dust near the nucleus in the FORS2 images, we 8 hr rotation period for a double-peaked light curve, agrees with thecompared VLT data, radial which flux have profiles a longer of 358P time coverage with those than of the field SOAR stars. compared radial flux profiles of 358P with those of field stars. the light curve behaviour observed during the first 8 hr of our dataSince and stars smaller were photometric trailed in the uncertainties. exposures targeting Using an 358P, implemen- we used Since stars were trailed in the exposures targeting 358P, we used VLT/FORS2 observations (filled symbols in Figs.1 and 2). Data tationtwo calibration of the Lomb–Scargle exposures of standard periodogram star fields provided obtained by astropy at side- two calibration exposures of standard star fields obtained at side- from the last two hours (open symbols in Figs.1 and 2) were (rialAstropy tracking Collaboration at the beginning et al. and2013 end), we of investigate the night, respectively, periodicity rial tracking at the beginning and end of the night, respectively, obtained under deteriorated seeing conditions and may be less into the measure brightness the stellar variations radial plotted profiles. in We Fig. averaged1 (bottom). the normalised Since the to measure the stellar radial profiles. We averaged the normalised reliable. From Fig. 3 we are unable to derive an unambiguous amplitudeprofiles of of 14 the and variation 26 non-saturated is of the order field of stars, a few respectively. 0.1 mag, which For profiles of 14 and 26 non-saturated field stars, respectively. rotational period for 358P. Potential explanations are that the iscomparison, only slightly we higher selected than exposures the typical of 358P photometric obtained uncertainty, under sim- For comparison, we selected exposures of 358P obtained under object is rather spherical or observed from a polar perspective, weilar take seeing a statistical conditions approach. (as indicated We account by the FITS for the header photometric keyword similar seeing conditions (as indicated by the FITS header key- leading to a light curve amplitude that is smaller than our pho- uncertainties,FWHMLINOBS). by varying The keyword the measured FWHMLINOBS brightness in seems each to frame have word FWHMLINOBS). The keyword FWHMLINOBS seems to

Article number, page 3 of 7 A54, page 3 of7 A&A 616, A54 (2018)

1.2 Since the stated uncertainties of the mean correspond to 1σ, the two measurements are marginally consistent. 1.0 We base our following estimate of the nucleus size on the value HR = 19.68 0.01 measured from the VLT data and assuming a C-type± phase function. For a geometric albedo of 0.8 pV = 0.06 (we approximate pR with pV , which is reason- ably close for low albedos) typical for C-type asteroids 0.6 (Nugent et al. 2016), the absolute magnitude corresponds to an equivalent-sphere radius of 0.4 1/2 (M HR)/5 Enclosed normalised flux r = p− 10 − 1 AU (2) n V × 0.2 358P at FWHM=3.4pix 358P at FWHM=5.4pix Stellar mean at FWHM=3.4pix (e.g. Harris & Lagerros 2002). For a solar magnitude of Stellar mean at FWHM=5.4pix M = 27.15 in Cousins R-band (Binney & Merrifield 1998), 0.0 − 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 we obtain rn = 263 m. The main source of uncertainty is the Aperture radius [FWHM ] unknown albedo of 358P. The C-type albedos given in Nugent et al.(2016) vary within a factor of 3, which leads to a radius Fig. 4. Normalised radial profiles of 358P and field stars in the FORS2 uncertainty of a factor 1.7. The unknown phase function, by data, measured for two different values of the seeing FWHM, D. The contrast, induces only a small uncertainty due to the low green lines indicate the aperture radius in which the light curve (Fig.1) phase angle at the time of observation. The radius derived for was measured and the corresponding flux level of 92%. The x-axis is G = 0.25 would only be 3% smaller than for G = 0.15. The in units of the FWHM at observation, i.e. a unit interval corresponds to 3.4 pixels for the blue dots and 5.4 pixels for the red dots. radius uncertainty introduced by the photometric uncertainty is also 3%. The escape speed from the surface of a non-rotating 3 body of sub-km size and assuming a density of ρ = 1500 kg m− 1 have generic values for the first 21 frames of the data, which we (Hanuš et al. 2017) is vesc = 0.2 m s− . The density reported by consider unreliable. For the remaining 56 frames, the values of Hanuš et al.(2017) was measured for C-type asteroids >100 km FWHMLINOBS and our measured D are well correlated with a in diameter. We use this value for the much smaller 358P owing Pearson correlation coefficient of 0.88. The frames we used for to the lack of measurements for a C-type object of this size. comparison to the standard star fields are from this second part An asteroid with known density and comparable in size to 3 of the data set. We used a single 358P exposure (frame 40) for 358P is the S-type (25143) Itokawa. Its density ρ = 1900 kg m− comparison with the first standard star field, and six exposures (Fujiwara et al. 2006) is near the lower end of the interval 3 (frames 70 + 73–77) for the second star field that we averaged in of (2000–4000) kg m− observed for S-types by Hanuš et al. the co-moving frame. Figure4 shows the resulting radial profiles. (2017), which is a result of Itokawa’s high macroporosity and For both values of the seeing parameter D, the profiles of 358P rubble-pile nature (Fujiwara et al. 2006). and the stars are similar, and they are also similar for different seeing conditions if expressed in units of D. The radial profile of 3.4. Upper limits for trail brightness and fragment size 358P is consistent with that of a point source. It does not show evidence of broadening by dust. Figure4 shows that the percent- We searched for a faint dust trail in a deep composite image age of flux enclosed in a given multiple of D is independent of of all 77 FORS2 exposures. To obtain the composite, we first the value of D. At a radius of 1.3D, the aperture encloses 92% scaled each background-subtracted exposure, i, with a factor 0.4∆Mi of the total flux, requiring a magnitude correction of ∆M = –0.09 fi = 10 to compensate for the variable atmospheric extinc- (cf. Fig.1). tion, where ∆Mi is the offset of the averaged instrumental magnitude of a set of field stars from an (arbitrary) reference 3.3. Nucleus size magnitude. Subsequently, we averaged all frames in the side- rial reference frame rejecting the faintest and the three brightest We constrain the size of the nucleus from the VLT/FORS2 obser- values at each position, and subtracted the resulting stellar com- vations only, since they cover a longer fraction of the target’s posite from each exposure. Finally, we averaged all frames in the light curve and we assume these observations provide a better co-moving frame of 358P with the same rejection rule. Figures5 approximation of its mean brightness than the SOAR/Goodman and6 show the resulting deep image of 358P. To derive an upper observations. The absolute magnitude, HR (corresponding to limit for the surface brightness of the debris trail, we assume rh = ∆ = 1 AU and α = 0) is given by that an extended linear object having S/N = 1 per pixel is eas- ily detectable to the human eye (Agarwal et al. 2010), and that HR = mR 5 log10(R∆) + 2.5 log10(Φ(α)), (1) the trail surface brightness must therefore be smaller than the − local standard deviation of the background flux, σ = 20 ADU, where Φ(α) is the phase function describing the ratio of the in the composite image (Fig.5). This corresponds to an upper 2 scattered light at phase angle α to that at α = 0◦. We used limit on the surface brightness of 28.4 mag arcsec− in Cousins the HG approximation of Φ(α) with G = 0.15 corresponding R, which is three magnitudes fainter than the surface brightness to C-type asteroids (Bowell et al. 1989). The measured appar- of the debris trails of the active asteroids P/2010 A2 (Jewitt et al. ent magnitude of mR = 23.46 0.01 (Sect. 2.2) corresponds 2013b) and 331P (Drahus et al. 2015). to an absolute magnitude of H ±= 19.68 0.01. Assuming an We proceed to infer an upper limit on the size of individ- R ± S-type phase function with G = 0.25 would result in HR = 19.74 ual large fragments assuming that point sources with S/N > 3 0.01 instead. The absolute magnitude derived from the aver- would be detectable. Following Makovoz & Marleau(2005), we ± age brightness in the SOAR/Goodman data (mR = 23.84 0.11) use S/N = f /(σ √πr), where f is the total flux from the point is H = 19.84 0.11 (G = 0.15) or H = 19.91 0.11 (G =± 0.25). source and r is the radius of the aperture. For r = 4 pixels, we R ± R ± A54, page 4 of7 J. Agarwal and M. Mommert: Nucleus of active asteroid 358P

J.J. Agarwal Agarwal and & M. M. Mommert: Mommert: Nucleus Nucleus of of active active asteroid asteroid 358P 358P J. Agarwal and M. Mommert: Nucleus of active asteroid 358P

Fig. 5. 358P in a composite of 77 FORS2 exposures, averaged in the co-moving frame of the asteroid. The brightness scale is inverted and linear, and the arrows indicate the anti-solar direction and the projected negative orbital velocity vector. No indication of a debris trail (which should be parallel to the negative velocity vector) is visible.

Fig. 5. 358P in a composite of 77 FORS2 exposures, averaged in the co-moving frame of the asteroid. The brightness scale is inverted and linear, Fig. 5. 358P in a composite of 77 FORS2 exposures, averaged in the co-moving frame of the asteroid. The brightness scale is inverted and linear, andand the arrows indicate the anti-solar direction and the projected negative orbitalhatched velocity blue vector. area in No Fig. indication 7 shows of a possible debris trail backward (which should ejection be paralleland the arrowsto the negative indicate velocity the anti-solar vector) direction is visible. and the projected negative orbital velocity vector. No indication of a debris trail (which should be parallel to the the negative velocity vector) vector) is is visible. visible. speeds as a function of particle size.

hatched blue area inPossible Fig. 7 showsterminal velocity possible from backward active patch ejection hatched blue area in Fig. 7 shows possible backward ejection speeds as a function ofAllowable particle backward size. velocity to stay in FOV speeds as a function of particle size. Moreno et al. (2013) 100

Possible terminal velocity from active patch PossibleAllowable terminal backward velocity velocity from to activestay in patch FOV Allowable backward velocityMoreno to etstay al. in(2013) FOV 100 10 Moreno et al. (2013) 100

10 1 10

Fig. 6. Zoom-in on Fig. 5. The brightness scale is inverted and logarith- Terminal velocity [m/s] mic, and the size of the image is 3500 2100. × 0.11 1

Terminal velocity [m/s] 0.0001 0.001 0.01 0.1

Fig. 6. Zoom-in on Fig. 5. The brightness scale is inverted and logarith- Terminal velocity [m/s] Fig.find 6. thatZoom-inf > on425 Fig. ADU 5. The is brightnessrequired, scalecorresponding is inverted andto a logarith- limiting Particle radius [m] Fig.mic, and6. Zoom-in the size of on the Fig. image5. The is 35 brightness00 2100. scale is inverted and logarithmic,mic,apparent and the magnitude and size the of the size image of of 27.8 the is image 35 in00 Cousins× is21 350000. R-band.2100. At the position 0.1 of 358P during our VLT/FORS2× observations,× this corresponds Fig.Fig. 7.0.1 7.PossiblePossible terminal terminal velocities velocities as as a a function function of of particle particle size. size. The The blueblue hatched hatched 0.0001 area area shows shows velocities 0.001 velocities towards towards the the0.01 negative negative orbital orbital direc-0.1 direc- findto an that absolutef > 425 magnitude ADU is required, of 24.0 (Eq. corresponding 1) or a diameter to a limiting of 72 m 0.0001 0.001 0.01 0.1 find that f > 425425ADU ADU is is required, required, corresponding corresponding to to a limiting tiontion that that would would enable enable a a particle particleParticle of of givenradius given [m] size size to to remain remain in in the the FOV FOV apparent(Eq. 2). magnitude of 27.8 in Cousins R-band. At the position Particle radius [m] apparent magnitude of 27.8 in in Cousins CousinsR R-band.-band. At At the the position ofof FORS2 FORS2 in in August August 2017. 2017. The The red red area area indicates indicates velocities velocities consistent consistent of 358P during our VLT/FORS2 observations, this corresponds Fig.with 7. thePossible observed terminal upper velocities limit of the as gasa function production of particle rate according size. The to of 358P during during our our VLT/FORS2 VLT/FORS2 observations, observations, this this corresponds corresponds Fig.with 7. thePossible observed terminal upper limitvelocities of the as gas a function production of particle rate according size. The to to an absolute magnitude of 24.0 (Eq. 1) or a diameter of 72 m blueEq.Eq. (A5) hatched A5 in in Jewitt area shows et al.(2014 (2014) velocities) and and for towards for the the parameters parameters the negative described described orbital in direc- in the the toto3.5. an an absolute absoluteProduction magnitude magnitude of cm-sized of of 24.0 24.0 debris (Eq. (Eq. (1 1))) or or a a diameter of 72 m m tionblue that hatched would area enable shows a velocities particle of towards given size the tonegative remain orbital in the direc- FOV (Eq.(Eq. ( 2).2)). tiontext.text. that The The would overlap overlap enable region region a corresponds corresponds particle of givento to combinations combinations size to remain of of size size in and the and back- FOV back- (Eq.Whether 2). a particle ejected in 2012 remains in the FOV of our ofwardward FORS2 ejection ejection in August velocity velocity 2017. for for particles particles The red that areathat could could indicates be be expected expected velocities in in our consistent our image. image. withof FORS2 the observed in August upper 2017. limit The of red the area gas indicates production velocities rate according consistent to 2017 observation depends on its velocity component, ve, parallel withTheThe solidthe solid observed line line represents represents upper limit the the velocity-sizeof velocity-size the gas production relationship relationship rate from accordingfrom Moreno Moreno to Eq. A5 in Jewitt et al. (2014) and for the parameters described in the3 3 3.5.to the Production Production orbital motion of of cm-sized cm-sized of 358P debris debris upon decoupling from its gravi- Eq.etet al. al.A5(2013 (2013) in) Jewitt given given et in al. inEq. (2014) Eq. (6) 6 assuming andassuming for the a a bulk parameters bulk density density described of of 1500 1500 kgin kg m the m−− 3.5. Production of cm-sized debris text. The overlap11 region corresponds to combinations of size and back- andandvv0== 25 m s−− .. Whethertationala influence particle (Müller ejected inet al.2012 2001), remains and inon the the FOV ratio of solarour wardtext. The0 ejection overlap velocity region for corresponds particles that to could combinations be expected of size in our and image. back- Whether a particle ejected in 2012 remains in the FOV4 of our ward ejection velocity for particles that could be expected in our image. Whetherradiation a pressure particle to ejected local solar in 2012 gravity, remainsβ = 5 in.77 the10 FOV− Qpr of/( ourρa), The solid line represents the velocity-size relationship from Moreno 2017 observation observation depends depends on on its its velocity component,× vee,, parallel parallel 2017where observationa and ρ are depends the radius on its and velocity bulk density component, of thev particlee, parallel and The solidIn the line following, represents we the derive velocity-size the maximum relationship particle from speed Moreno con-3 toto the the orbital orbital motion motion of of 358P 358P upon upon decoupling decoupling from from its its gravi- gravi- et al. (2013) given in Eq. 6 assuming a bulk density of 1500 kg m−3 ethatchedsistent al. (2013) with blue given1 thearea measured in in Eq. Fig. 67 assuming shows upper limit possible a bulk of density the backward water of 1500 production ejection kg m− tothe the dimensionless orbital motion parameter of 358PQ uponpr characterises decoupling the from optical its gravi- prop- and v0=25 m s−1. tationaltational influence influence ( (MüllerMüller et al. 2001 2001),), and and on on the the ratio ratio of of solar solar andspeedsv0=25 as m a sfunction− . 25 of particle size.1 tationalerties of influence the material (Müller (Burns et al. et 2001), al. 1979). and onWe the numerically ratio44 of solar sim- rate Qmax=7.63 10 molecules s− (O’Rourke et al. 2013), as- radiation pressure to local solar gravity, ββ==5..77 10− Qpr/(ρa), × radiation pressure to local solar gravity, β = 5.77 10−4 pr/(ρ ), sumingIn the that following, the activity we derive was confined the maximum to a patch particle on speedthe surface. con- whereradiationulateda theand pressure motionρρ are to theof local test radius solar particles and gravity, bulk ejected density5 during77×× of10 the the− Q 2012 particlepr ( per-a), In the following, we derive the maximum particle speed con- where a and ρ are the radius and bulk density of× the particle and sistentTheIn temperature the with following, the measured of wea sublimating derive upper the limit maximum surface of the containing water particle production speed water con- ice rate at andwhereihelion thea dimensionlessand passageare that the radius have parameter a and wide bulkQ range densitycharacterises of values of the forparticle theβ opticaland andve, sistent with the25 measured upper1 limit of the water production the dimensionless parameter Qpr characterisespr the optical prop- sistentQmax = with 7.63 the10 measuredmolecules upper s− ( limitO’Rourke of the et water al. 2013 production), assum- theand dimensionless calculated their parameter positionsQ relativepr characterises to 358P the at the optical time prop- of our ratetheQ heliocentric=7.63× 10 distance25 moleculesrh is given s 1 from(O’Rourke the equilibrium et al. 2013), of solar as- propertieserties of the of material the material (Burns (Burns et al. et 1979). al. 1979 We). numerically We numerically sim- rateing thatQmax the=7.63 activity1025 wasmolecules confined s− to1 (O’Rourke a patch on the et al. surface. 2013), The as- ertiesFORS2 of theobservation material in (Burns August et2017. al. 1979). Only We particles numerically that have sim- sumingirradiationmax that with the× activity cooling was by radiation confined− and to a sublimation, patch on the surface. simulatedulated the the motion motion of test of test particles particles ejected ejected during during the 2012 the 2012 per- sumingtemperature that theof a× activity sublimating was confined surface containing to a patch water on the ice surface. at the ulated the motion of test particles ejected during the 2012 per- The temperature of a sublimating surface containing water ice at perihelionihelion passage passage that that have have a awide wide range range of of values values for forββ and vee,, heliocentric distance rh is given from the equilibrium of solar 1 5 β v The temperatureL of a sublimating4 surfaceI containing water ice at ihelionβ < (7. passage9 sm− vb that+ 3. have9) 10 a wide− range of values for and (3)e, the heliocentric distance r is given from the equilibrium of solar and calculated their positions relative to 358P 358P at at the the time of our irradiationQ withH2O + coolingσT = byh(1 radiationAB) andcos sublimation,θ, (4) and calculated their positions× relative to 358P at the time of our the heliocentric distance rh is given from2 the equilibrium of solar irradiationNAmH2O with cooling by radiation− r and sublimation, FORS2 observation in August 2017. 2017. Only Only particles particles that that have have irradiation with cooling by radiationh and sublimation, FORS2would stillobservation be in the in FOV August of our 2017. observations, Only particles where thatvb have= ve is L 4 I 1 5 − βpositive < (7.9 sm towards−1vb + 3 the.9) direction10− 5 opposite to the orbital motion(3) of whereL QandH2O A+BσareT4 the= (1 emissivityAB)I andcos θ, Bond albedo of the(4) sur- β < (7.9 sm−1vb + 3.9) 10−5 (3) L σ I 2 θ, β < . − + . × − NAmH2O QH2O + T 4 = (1 − AB) r cos (4) 358P.(7 9 Particles sm vb ejected3 9) × to10 this direction stay closer to the nucleus(3) face, σ andQH ON+A theσT Stefan-Boltzmann= (1 AB) 2h cos andθ, Avogadro constants,(4)L × NAmH2O 2 − rh2 wouldthan particles still be in ejected the FOV to the of ourforward observations, direction whereat the samevb = relativeve is N=Am51000H2O J/mol the latent heat− ofr waterh ice, mH O the molecular would still be in the FOV of our observations, where vb = −ve is 2 positivewouldspeed still because towards be in thebackward FOV direction of ejection our opposite observations, decreases to the whereorbital the orbitalv motionb = − energyve ofis wheremass of and water,AB andare theθ the emissivity angle between and Bond the surface albedo ofnormal the sur- and positive towards the direction opposite to the orbital motion− of where and AB are the emissivity and Bond albedo of the sur- 358P.positiveand period Particles towards ofejected the the particle, direction to this counteracting direction opposite stay to radiation the closer orbital to pressure. the motion nucleus The of whereface,solarσ direction.andandNAAB theare The Stefan–Boltzmann the value emissivityQH O is and the and Bondsublimation Avogadro albedo rate of constants, the of water sur- 358P. Particles ejected to this direction stay closer to the nucleus face, σ and NA the1 Stefan-Boltzmann2 and Avogadro constants, L than358P. particles Particles ejected ejected to to the this forward direction direction stay closer at the to same the nucleusrelative face,L = 51σ 000and JN molthe− Stefan-Boltzmannthe latent heat of water and Avogadro ice, m constants,the molec-L than particles ejected to the forward direction at the same relative = 51000 J/molA the latent heat of water ice, m Hthe2O molecular speedthan particles because ejected backward to the ejection forward decreases direction at the the orbital same relative energy =ular51000 mass J/ ofmol water, the latent and θ heatthe angle of water between ice,Articlem theH number,2O surfacethe molecular page normal 5 of 7 speed because backward ejection decreases the orbital energy mass of water, and θ the angle between the surfaceH2O normal and andspeed period because of the backward particle, ejection counteracting decreases radiation the orbital pressure. energy The massand solar of water, direction. and θ Thethe anglevalue betweenQH2O is the surfacesublimation normal rate and of and period of the particle, counteracting radiation pressure. The solar direction. The value QH2O is the sublimation rate of water and period of the particle, counteracting radiation pressure. The solar direction. The value QH2O is the sublimation rate of water A54, page 5 of7 Article number, page 5 of 7 Article number, page 5 of 7 A&A 616, A54 (2018)

1 2 water ice in vacuum in kg s− m− given by have been small, while we cannot constrain the production rates of particles with a < 8 mm. The model described by Moreno r m et al.(2013) implies a mass of 15 106 kg of particles in the Q = p (T) H2O , (5) ∼ × H2O subl 1–10 cm size range, which corresponds to Afρm 0.3 cm; this 2πkBT value is consistent with our upper limit, but represents∼ 75% of where the sublimation pressure is given by psubl(T) = the total produced mass. This shows that despite their low sur- A exp( B/T) with A = 3.56 1012 Pa and B = 6141 K (Fanale & face brightness, such particles could have carried a significant Salvail− 1984). × percentage of the ejected dust mass. Assuming extreme values of = 1, AB = 0 and normal inci- dence (θ = 0), we obtain an upper limit for the temperature 4. Summary and discussion Tmax = 191 K at the perihelion distance of 358P (rh = We observed the active asteroid 358P at true anomaly angles of 2.41 AU), and a sublimation rate of QH2O/mH2O = 1.74 21 1 2 × 10 molecules s− m− . Assuming that the activity was confined 290.8◦ and 295.7◦ and obtain the following key results: to a circular patch on the surface, and that this patch was not – The peak-to-peak amplitude of the rotational light curve in illuminated and inactive for 50% of each diurnal cycle, the obser- August 2017 was likely 0.2 mag, but might be smaller than ∼ vational upper limit Qmax translates to a maximum patch radius that. of 170 m, or 10% of the surface. – The 10 h VLT/FORS2 light curve observation does not From a patch of this size, assuming a bulk density of show an obvious periodicity but might marginally indicate 1500 kg m 3 for both dust and nucleus and a unit gas drag a rotation period of 8 h. − ∼ coefficient, the maximum escaping grain size would be 5 cm – The radial profile of 358P in August 2017 was consis- (Eq. (A6) in Jewitt et al. 2014; cf. Fig.7). The maximum liftable tent with that of a point source, showing no evidence of grain radius scales about linearly with the patch radius. Assum- broadening by dust. 3 ing instead a comet-like density of 500 kg m for both dust and – We derive an average absolute magnitude HR = 19.68 0.01 − ± nucleus would increase the maximum liftable grain radius to assuming a C-type phase function, and HR = 19.74 0.01 for ± 35 cm. an S-type phase function. ∼ The size and velocity ranges compatible with both the – Assuming a geometric albedo of 0.06, this corresponds to a gas production and dynamical constraint (overlapping red and cross section equivalent sphere of 530 m diameter that has hatched areas in Fig.7) are consistent with the velocity-size an uncertainty of a factor 1.7 owing to the unknown albedo. 3 relation used by Moreno et al.(2013), that is – For a density of 1500 kg m− , the surface escape velocity is 1 0.2 m s− . 0.5 v = v0 β , (6) – Our observation was sensitive to individual fragments >70 m in diameter, which we did not detect. 1 where v0 = 25 m s− . Figure7 indicates that our observations are – We did not detect a debris trail along the projected orbit, sensitive to particles in the size range 8 mm < a < 5 cm. and derive an upper limit to its surface brightness in Cousins 2 Adopting Eq. (6) and assuming isotropic ejection, we derive R-band of 28.4 mag arcsec− , three magnitudes fainter than an upper limit on the production rate of such particles from our for active asteroids with known debris trails. detection limit of the trail surface brightness. We found that the – Our observation is sensitive to dust particles in the size 2017 position of particles depends only weakly on the actual range 8 mm–5 cm, for which we derive an upper limit of emission time within an interval of a few months around peri- 52 106 kg produced during the 2012 perihelion passage. helion, and therefore studied only the motion of grains ejected – The× contribution of such particles to the coma brightness in at perihelion. We calculated the image position as a function of 2012 must have been <10%, while they may still have carried size and the corresponding surface brightness for a given total a significant percentage of the ejected mass. dust production using the computer code described in Agarwal Our primary goal was to study the rotation state of 358P and et al.(2010). its possible inter-relation with the activity. We approached this For differential size distribution exponents α > 4.5, the sur- question both directly by measuring the rotational light curve, face brightness has a maximum near the eastern end− of the trail, and indirectly through the size and velocities of the ejected dust. while for α < 4.5, it increases towards the west. For α = –3.5, The latter approach did not yield any indication that fast the maximum− surface brightness would be at distances between rotation would be needed to explain the ejection of refractory 7000 and 10000. Particles with a > 8 mm would be located >2000 material. We do not detect large fragments or debris >8 mm, and west of the nucleus. the derived upper limits are consistent with acceleration by gas Assuming α = –3.5 and the same phase function and albedo drag only. 2 as for 358P, our detection limit of 28.4 mag arcsec− corresponds The direct measurement of the rotational light curve was lim- to an upper limit of 52 106 kg of particles having 8 mm < ited by the unexpected faintness of 358P and the likely small a < 5 cm ejected over the× whole 2012 period of activity. The amplitude of the light curve. Our attempt at deriving the rotation total R-band magnitude of particles in the 2017 FORS2 FOV period of the target was inconclusive. While a rotation period of would have been > Mmin = 21.7, and their velocities would have 8 h seems compatible with some of our data, it is incompatible 1 ∼ been of the order 20 cm s− (Fig.7). They would have remained with other parts obtained at unfavourable seeing. Our ability to within an aperture of 3 for 6 months in 2012 (1 1000 km). derive a conclusive rotational period might be hampered by the 00 00 ∼ We derive an upper limit of (Afρ)FOV = 1 cm (A’Hearn et al. fact that the actual light curve amplitude of the target is smaller 1995) contributed by particles acceptable in the 2017 FOV to the than the variability that we measured. This possible explanation Afρobs 12 cm measured within an aperture of 500 (Hsieh et al. is underlined by the fact that our photometric uncertainties are 2013). ∼ of the same order of magnitude. A different possible explana- Our observations imply that the contribution of particles tion for our failing to derive the rotational period might be that with a > 8 mm to the coma brightness observed in 2012 must the rotation is insufficiently sampled. The period might be much

A54, page 6 of7 J. Agarwal & M. Mommert: Nucleus of active asteroid 358P longer than the 10 h interval for which we observed 358P, or it Capria, M. T., Marchi, S., de Sanctis, M. C., Coradini, A., & Ammannito, E. might be small compared to our cadence ( 10 min). The latter 2012, A&A, 537, A71 seems unlikely because it would imply that∼ 358P rotates faster Chambers, K. C., Magnier, E. A., Metcalfe, N., et al. 2016, ArXiv e-prints [arXiv:1612.05560] than the critical 2.2 h period applicable for rubble piles, although Clemens, J. C., Crain, J. A., & Anderson, R. 2004, Proc. SPIE, 5492, 331 its size indicates a high probability that 358P is a rubble pile Drahus, M., Waniak, W., Tendulkar, S., et al. 2015, ApJ, 802, L8 (Warner et al. 2009). Fanale, F. P., & Salvail, J. R. 1984, Icarus, 60, 476 We find some indication of a discrepancy between the aver- Flewelling, H. A., Magnier, E. A., Chambers, K. C., et al. 2016, ArXiv e-prints [arXiv:1612.05243] age absolute brightness of 358P during our SOAR/Goodman and Freudling, W., Romaniello, M., Bramich, D. M., et al. 2013, A&A, 559, A96 VLT/FORS2 observations (Sect.2). A significant variability in Fujiwara, A., Kawaguchi, J., Yeomans, D. K., et al. 2006, Science, 312, 1330 brightness is also seen in additional photometry obtained with Giorgini, J. D., Yeomans, D. K., Chamberlin, A. B., et al. 1996, Bull. Am. Astron. Gemini South (Mommert et al. 2017), where the corresponding Soc., 28, 1158 absolute magnitudes fluctuate of the order of 1 mag over the Haghighipour, N., Maindl, T. I., Schäfer, C., Speith, R., & Dvorak, R. 2016, ApJ, 830, 22 course of several weeks. This might support the idea that the Haghighipour, N., Maindl, T. I., Schaefer, C. M., & Wandel, O. J. 2018, ApJ, light curve period is longer than the duration of our observation 855, 60 (10 h) or that 358P deviates from a simple periodicity owing to Hanuš, J., Viikinkoski, M., Marchis, F., et al. 2017, A&A, 601, A114 presently unknown reasons. Possible factors adding complexity Harris, A. W., & Lagerros, J. S. V. 2002, Asteroids in the Thermal Infrared, eds. W. F. Bottke, Jr., A. Cellino, P. Paolicchi, & R. P. Binzel, 205 to the light curve could be the existence of a binary partner, or Hirabayashi, M., & Scheeres, D. J. 2014, ApJ, 780, 160 non-principal axis rotation (“tumbling”). We conclude that we Hirabayashi, M., Scheeres, D. J., Sánchez, D. P., & Gabriel, T. 2014, ApJ, 789, cannot rule out a rotation faster than 10 h if the light curve ampli- L12 tude (peak-to-peak) is less than 0.2 mag, nor a slow rotation Hsieh, H. H., & Jewitt, D. 2006, Science, 312, 561 with a period longer than 10 h. ∼ Hsieh, H. H., & Sheppard, S. S. 2015, MNRAS, 454, L81 Hsieh, H. H., Jewitt, D. C., & Fernández Y. R. 2004, AJ, 127, 2997 Hsieh, H. H., Meech, K. J., & Pittichová, J. 2011, ApJ, 736, L18 Acknowledgements. J.A. was supported in part by the European Research Council Hsieh, H. H., Kaluna, H. M., Novakovic,´ B., et al. 2013, ApJ, 771, L1 (ERC) Starting Grant No. 757390. M.M. was supported in part by NASA grant Hsieh, H. H., Hainaut, O., Novakovic,´ B., et al. 2015, ApJ, 800, L16 No. NNX17AG88G from the Near Earth Object Observations programme. This Ishiguro, M., Hanayama, H., Hasegawa, S., et al. 2011a, ApJ, 740, L11 work is based in part on observations obtained at the Southern Astrophysical Ishiguro, M., Hanayama, H., Hasegawa, S., et al. 2011b, ApJ, 741, L24 Research (SOAR) telescope, which is a joint project of the Ministério da Ciência, Jewitt, D. 2012, AJ, 143, 66 Tecnologia, Inovaçãos e Comunicaçãoes (MCTIC) do Brasil, the U.S. National Jewitt, D., Agarwal, J., Weaver, H., Mutchler, M., & Larson, S. 2013a, ApJ, 778, Optical Astronomy Observatory (NOAO), the University of North Carolina at L21 Chapel Hill (UNC), and Michigan State University (MSU). The results presented Jewitt, D., Ishiguro, M., & Agarwal, J. 2013b, ApJ, 764, L5 in this work are based in part on observations made with ESO Telescopes at the Jewitt, D., Ishiguro, M., Weaver, H., et al. 2014, AJ, 147, 117 La Silla Paranal Observatory under programme ID 099.C-0530(A). 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