Uninterrupted optical light curves of main-belt asteroids from the K2 Mission
R. Szabó, A. Pál, K. Sárneczky, Gy. M. Szabó, L. Molnár, L. L. Kiss, O. Hanyecz, E. Plachy, Cs. Kiss
aa r X i v : . [ a s t r o - ph . E P ] S e p Astronomy & Astrophysicsmanuscript no. k2_asteroids_v09 c (cid:13)
ESO 2016September 12, 2016
Uninterrupted optical light curves of main-belt asteroids from theK2 Mission
R. Szabó , A. Pál , , K. Sárneczky , , Gy. M. Szabó , , , L. Molnár , L. L. Kiss , , , O. Hanyecz , , E. Plachy , andCs. Kiss Konkoly Observatory, Research Centre for Astronomy and Earth Sciences, Hungarian Academy of Sciences, H-1121 Budapest,Konkoly Thege Miklós út 15-17, Hungarye-mail: [email protected] Eötvös Loránd Tudományegyetem, H-1117 Pázmány Péter sétány 1 / A, Budapest, Hungary Gothard-Lendület Research Team, H-9704 Szombathely, Szent Imre herceg út 112, Hungary ELTE Gothard Astrophysical Observatory, H-9704 Szombathely, Szent Imre herceg út 112, Hungary Sydney Institute for Astronomy, School of Physics A28, University of Sydney, NSW 2006, Australiareceived; accepted
ABSTRACT
Context.
Due to the failure of the second reaction wheel, a new mission was conceived for the otherwise healthy
Kepler spacetelescope. In the course of the K2 Mission, the telescope is staring at the plane of the Ecliptic, hence thousands of Solar Systembodies cross the K2 fields, usually causing extra noise in the highly accurate photometric data.
Aims.
In this paper we follow the someone’s noise is another one’s signal principle and investigate the possibility of deriving contin-uous asteroid light curves, that has been unprecedented to date. In general, we are interested in the photometric precision that the K2Mission can deliver on moving Solar System bodies. In particular, we investigate space photometric optical light curves of main-beltasteroids.
Methods.
We study the K2 superstamps covering the M35 and Neptune / Nereid fields observed in the long cadence (29.4-min sam-pling) mode. Asteroid light curves are generated by applying elongated apertures. We use the Lomb-Scargle method to find periodic-ities due to rotation.
Results.
We derived K2 light curves of 924 main-belt asteroids in the M35 field, and 96 in the path of Neptune and Nereid. Thelight curves are quasi-continuous and several days long. K2 observations are sensitive to longer rotational periods than usual ground-based surveys. Rotational periods are derived for 26 main-belt asteroids for the first time. The asteroid sample is dominated by faint( >
20 mag) objects. Due to the faintness of the asteroids and the high density of stars in the M35 field, only 4.0% of the asteroids withat least 12 data points show clear periodicities or trend signalling a long rotational period, as opposed to 15.9% in the less crowdedNeptune field. We found that the duty cycle of the observations had to reach ∼
60% in order to successfully recover rotational periods.
Key words.
Techniques: photometric – Minor planets, asteroids: general – Minor planets, asteroids: individual: (111), (2785), (2954),(3785), (9105), (17771), (29628), (37201), (57648)
1. Introduction
The
Kepler space telescope revolutionized time-domain astron-omy, and its unique capabilities were demonstrated by the detec-tion of short (Sanchis-Ojeda et al. 2014) and long period tran-siting exoplanets (Kipping et al. 2016), the application of stel-lar seismology (Chaplin et al. 2011), and the renewed interestin studying classical variable stars (Gilliland et al. 2010). In thelatter case e.g. a new dynamical phenomenon was discovered inRR Lyrae stars (Szabó et al. 2010), whose detection had beenpreviously hampered by the diurnal variations a ff ecting ground-based observations.In 1901 von Oppolzer first noticed the brightness variation ofan asteroid, (433) Eros (von Oppolzer 1901), and its first correctperiod was published in Bailey (1913) with several other minorplanets. During the more than hundred years since then the lightvariation of over 10000 main-belt asteroids were measured, butthe length of the continuous observations has been always lim-ited by the maximal duration of a winter night. The re-purposed Kepler mission (K2) (Howell et al. 2014) made it possible forthe first time to measure the brightness of a large number of main-belt asteroids quasi-continuously. In this paper we showthe results obtained from the photometry of close to 1000 main-belt asteroids, most of them followed continuously for up to 3–4days or longer, a small fraction of them up to 6 days in two largesuper-stamps of the K2 Mission.In a series of works we have been investigating the possi-bilities of high-precision space photometric observations of So-lar System objects with the rejuvenated
Kepler space telescope(Howell et al. 2014). In Szabó et al. (2015) the e ff ects of main-belt asteroid encounters on K2 photometry of stellar targets wereinvestigated. In Pál et al. (2015) we analyzed two faint Trans-Neptunian Objects, namely 2002 GV and 2007 JJ , measuringtheir rotation periods. These are among the faintest objects Ke-pler has measured so far. We also outlined the methodology todeal with these moving targets that
Kepler had not been designedfor. Special masks were allocated to these targets making theircontinuous observations possible. By complementing recent K2observations with archival
Herschel data, we analyzed the ther-mophysical parameters of 2007 OR in Pál et al. (2016). Article number, page 1 of 9 & Aproofs: manuscript no. k2_asteroids_v09
Fig. 1.
Mosaic of the M35 open cluster (as well as NGC 2158) as seen by K2. The area is covered by 154 sub-apertures amounting to 800 × ′ × ′ ). In this work we turn our attention to two special fields thatK2 has observed, both of which have been covered by mul-tiple sub-apertures, creating large enough fields to search forasteroids. In Campaign 0 a well-known, bright open cluster,M35 (NGC 2168) was observed with Kepler. It was coveredwith a mosaic of 154 50 ×
50 pixel small stamps amounting to800 ×
550 pixels (53 ′ × ′ on the sky), EPIC IDs ranging from2000000811 to 200000964. The observed field includes the opencluster NGC 2158 as well. By quickly investigating the imagesit was immediately obvious that hundreds of asteroids crossedthis field of view. We choose these observations because of thelarge, contiguous field and the large number of asteroids avail-able. Campaign 0 covers the period Mar 8 to May 30, 2014, itwas implemented as a full-length engineering test to prove thatK2 was a viable mission. The Kepler spacecraft was not in finepoint for the first 16 days of C0, causing large photometric scat-ter. Eventually, the
Kepler spacecraft went into safe mode thatlasted for about 24 days. After that stopping, high-quality, fine-point measurements began, which span 35 days. The data qualityimproved in the second half of the campaign. We used data fromonly this part of the campaign. Jupiter was crossing the field,but fell on the dead Module 3, and caused only increased back-ground flux.Campaign 3 started on 15 November, 2014, and ended on23 January, 2015. In this campaign Neptune and its satellite,Nereid was observed (GO IDs: 3057, 3060, 3115), their pathwas also tiled with 305 narrow strips of pixel masks (EPIC IDs 200004468–200004762). We refer to this field as Nereid fieldhenceforth. While Campaign 0, and especially the vicinity ofM35 contains a crowded field, this small stripe of the sky gavean opportunity to analyze light curves of asteroids usually free oftoo large number of stellar sources. However, due to the proxim-ity of Neptune we had to deal with other problems (high back-ground, saturation, etc). The change in bandwidth for pointingcontrol (from 50 to 20 seconds) for C3 resulted in an increasein SNR for short cadence by a factor of roughly 4–9, with thelarger improvement seen at the higher frequency end. Campaign3 had a nominal duration of 80 days, but an actual duration ofonly 69.2 days. The campaign ended earlier than expected be-cause the on-board storage filled up faster than anticipated dueto unusually poor data compression .A similar study about Jovian Trojan asteroids observed bythe K2 Mission will be published in a related paper (Szabó et al.,2016).
2. Data analysis
In Fig. 1 we show the result of stitching the small sub-fields cov-ering the open cluster M35, while Fig. 2 displays the path cov-ered by Nereid in the vicinity of Neptune. http: // keplerscience.arc.nasa.gov / k2-data-release-notes.htmlArticle number, page 2 of 9. Szabó et al.: Uninterrupted optical light curves of main-belt asteroids from the K2 Mission Fig. 2.
Mosaic covering the paths of Neptune and Nereid observed by the K2 Mission. The length of the mosaic is approximately 20 ′ . P ho t o m e t r i c e rr o r [ m ag ] Brightness [mag]
Pre-flight estimateCDPP noise levelEPIC 210282474
Fig. 3.
Photometric errors of the individual K2 asteroid measurementsin the M35 field, as a function of the apparent brightness of the as-teroids (light blue dots). The red line is the
Kepler pre-flight estimateof the photometric precision (Van Cleeve & Caldwell 2016) , the pur-ple line is the scaled Combined Di ff erential Photometric Precision data(Christiansen et al. 2013), the black line is the photometry of a faint RRLyrae star in Leo IV for comparison (Molnár et al. 2015), the dashedline is a linear interpolation between the last two. We used only long-cadence (29.4-min sampling) observations ofboth fields. For preparing the light curves and deriving photom-etry we used the FITSH package (Pál 2012). Some aspects ofobtaining precise photometry of moving targets with the
Kepler space telescope during the K2 Mission have already been dis-cussed by our group in Pál et al. (2015, 2016) and in Kiss et al.(2016). Here, due to the main belt asteroid targets we had to dealwith more elongated trails during the long cadence observationsas opposed to Trans-Neptunian objects in our earlier works. Themethod is based on a process that fits a circular aperture con-volved with the apparent track of the asteroid. The track is ap-proximated with a linear curve. The details of the methodology isgiven in Szabó et al. (in prep). In Fig. 3 we plot the photometricerror of each individual data point for every asteroids in the M35field as a function of brightness. The error contains the noisefrom the background and the shot noise. The background noiseis determined from a circular or elongated ring around the target,while the shot noise is computed from the known electron / ADU conversion rates. For the brightest targets we added a conserva-tive upper error limit (0.001 mag for the brightest objects, 0.002mag for slightly fainter observations, etc.), since the error com-putation gives an unrealistically low error limit due to neglectingsystematic errors (e.g. errors caused by passing through brightstellar objects). Our approach is an attempt to compensate forthis underestimation. We believe that this choice does not af-fect the information content of the figure and it a ff ects only anegligible portion of the targets. The precision reaches a fewmmag for the brightest objects, 0 m .
01 for a 18 th magnitude ob-ject and 0 m . th magnitude. We note thatthe error values do not contain systematic errors. The precisionwe achieved is better than the conservative pre-flight estimate of Kepler , but slightly worse than the precision derived from ac-tual photometry of stellar targets. For the latter comparison wescaled the Combined Di ff erential Photometric Precision (CDPP,Christiansen et al. 2013) values of the original Kepler missionto a single long cadence exposure. However, these data only ex-tended to 16 mag, so we also included the measurements of theextragalactic RR Lyrae EPIC 210282474, the only variable starin Leo IV that was not a ff ected by blending (Molnár et al. 2015).Finally, we added a linear interpolation between the two datasets. We searched for significant periodicities using the Lomb-Scargleperiodogram functions of the gatspy
Python package . Al-though Fourier-based methods were considered as well, as im-plemented in the Period04 program package (Lenz & Breger2005), we got very similar results in several test cases, there-fore we decided to stick to the Lomb-Scargle method. We notethat the errors of the individual photometric points are taken intoaccount by the used implementation of the Lomb-Scargle algo-rithm. Only those signals were considered that were significanton the 3 σ -level compared to the background local noise in theLomb-Scargle periodogram. We phase-folded the light curveswith the best period and its double value, then decided whichgives a better fit based on a visual inspection. In many cases Tabulated values: http: // keplergo.arc.nasa.gov / CalibrationSN.shtml https: // github.com / astroML / gatspy / Article number, page 3 of 9 & Aproofs: manuscript no. k2_asteroids_v09
Table 1.
Sample table of the observed asteroids in the K2 M35 superstamp. The whole table containing 867 objects with at least 12 photometricpoints is available electronically.
ID start end length > > Table 2.
Same as Table 1, but for the asteroids in the Nereid field observed during K2 Campaign 3. The full table containing 88 asteroids with atleast 12 data points is available electronically.
ID start end length m ag po w e r m ag po w e r m ag po w e r m ag po w e r m ag po w e r m ag po w e r Fig. 5.
Examples of periodic long cadence (29.4-min sampling) asteroid light curves in decreasing brightness order. Left panels: asteroids crossingM35 field, right panel: asteroids observed in the Neptune-Nereid path. In each case the left panel shows the K2 light curve with error bars foldedby the adopted (double) period, the right panel is the Lomb-Scargle plot. The error bars for bright asteroids are smaller than the size of the symbols.The sine plotted in red is fitted to the data to guide the eye. The adopted period and the ID of the asteroid is shown in the middle of the left andright panels, respectively. there were significant deviations in odd and even cycles. In thesecases the two-period folding was chosen. If the inspection wasinconclusive, or resulted in a dynamically untenable short period( i.e. less than 2 hours) then we chose the double-period solution.Following this method we did not retain any single-periodic so-lutions in accordance with other main-belt asteroid works. Wenote that the chosen 2-hour limit is plausible, since K2 did notobserve smaller asteroids in these fields. In order to demonstratethis let’s consider a close-by asteroid of the Hungaria family inthe classical Main Belt. If its brightness in opposition is 21 mag-nitude (it’s fainter than 22 magnitude in the K2 field), this cor-responds to H = M35 field : Out of 924 asteroids crossing the M35 field 867had more than 12 data points. We retained only these asteroidsto have a set of reasonably covered light curves. Although thisnumber might vary from light curve to light curve depending onthe distribution of data points, we found that this number gives agood coverage for the short-period asteroids and still gives someinformation for longer rotational periods. Among the 867 lightcurves 23 showed clear periodicities, i.e. above the 3 σ limit. Theperiods ranged from 3.89 h to 88.41 h, with a median of 9.83 h.The length of the covered paths ranged from 0.26 days to 6.05days with a median of 2.06 days. The median number of obser-vations per asteroid was 48. Nereid field:
Out of 96 light curves 88 had more than 12points in their K2 Campaign 3 light curves, of which 14 showed
Article number, page 4 of 9. Szabó et al.: Uninterrupted optical light curves of main-belt asteroids from the K2 Mission du t y cyc l e all M35 asteroidsshowing periodicities153045 25 50 75 Fig. 4.
Duty cycle vs. length of observations for asteroids in the M35K2 field. Blue dots are all the 924 asteroids crossing the superstamp,red ones are those that exhibit significant periodicity or trend. The his-tograms show the distribution of the observing length and the duty cy-cle. m ag
111 0 5 10 15frequency [c/d]0.000.050.100.150.200.250.300.350.400.45 po w e r Fig. 6.
Light curve (left panel) and Lomb-Scargle periodogram (rightpanel) of (111) Ate, the brightest member of our sample. The peri-odogram shows three peaks, the largest one corresponds to a period of20.63 ± periodicities above the 3 σ limit. The shortest detected period is3.71 hours, while the longest is 14.63 hours, the median being4.96 h. The length of observation varied from a few data points( ∼ i.e. less points had to be dropped. To put it quantita-tively, the median number of retained observations per asteroidwas 57. This is due to the less crowded nature of the field.To end this section we show the case of (111) Ate, an ex-ample where our period search did not result in unambiguousperiod value. In the left panel of Fig. 6 we show the light curve.The three minima clearly define two periods in our light curve.The periodogram (right panel of the same figure) shows threesignificant peaks, but we could not decide on the value basedon this accurate, but short light curve. The largest peak corre-sponds to 20.63 ± σ level), which isclearly o ff from the 22.072 ±
3. Results
In Table 1 we present the asteroids identified in the M35 super-stamp during the second half of Campaign 0. Only those objects
Table 3.
Photometry of main-belt asteroids observed in the M35 super-stamp by K2 during Campaign 0. The full table is available electroni-cally.
ID time USNO R R errBJD - 2,456,700 [mag] [mag]111 101.2871 13.130 0.001111 101.3076 13.127 0.001111 101.3280 13.166 0.001111 101.3484 13.202 0.001111 101.3689 13.162 0.001... ... ... ...are listed that showed at least 12 useful photometric data points.The table gives the identification, the start and end date of thetime interval during which the minor planet was passing throughthe superstamp. The number of useful long cadence observationsand the calculated duty cycle is also given. The duty cycle is 1.0if all the photometric points were retained, and 0 if all had to bediscarded. We also provide the median brightness transformedto the USNO R band (Pál et al. 2015). If reliable period and am-plitude were found, these values were added to the table(s). InTable 2. the same parameters are given for the main-belt aster-oids crossing the Nereid superstamp.As we discussed in detail in Szabó et al. (2015) no (or veryfew) new main-belt asteroid discoveries are expected in the K2campaign fields due to the available limiting magnitude. Indeed,among the 1020 identified asteroids in the two fields, we have notseen unknown objects. The procedure of prediction and identi-fication of the main-belt asteroids as seen from Kepler was de-scribed in detail in Szabó et al. (2015) and was followed here,as well.Fig. 4 shows the duty cycle (percentage of the number ofobserved 29,4-min cadences with respect to the maximally pos-sible during the length of observation), i.e. how many cadenceshave been lost due to technical problems originating mainly fromthe photometric pipeline (outliers, encountering too bright stars,stellar residuals, etc.), versus the length of observations in thecase of the M35 asteroids. Most of our objects were observedfor 1–4 days, and we were able to follow some of them for 5–6days. The vast majority of our targets were observed with a dutycycle between 20 and 80%, a handful of them above 80%. Onlyone asteroid was followed with 100% duty cycle, i.e. in this caseno long cadence observations had to be discarded.Objects that exhibited significant periodicities are shownwith red dots in Fig. 4. It is evident that the majority of the mi-nor planets showing periodicities were found among the onesobserved with high duty cycle. Namely, we found all the peri-odicities or long periods (seen as trends) only where the dutycycle was close to or above 60%. Similarly, we found that themore continuous the light curve in the Nereid field, the more thechance to detect variability at a statistically significant level.Twelve asteroids in the M35 field exhibited long-term trendsor incompletely covered half rotation periods. We identifiedthese with longer-period asteroids. One example was foundwith literature data, namely asteroid (3345), for which wefound a rotational period that is longer than 34 hours, andBenishek & Coley (2014) gives 187 hours.In Tables 3 and 4 we give the format and the content of thefiles that contain the K2 photometry for all the targets in theM35 and Nereid fields, respectively. The full tables are availableonline.
Article number, page 5 of 9 & Aproofs: manuscript no. k2_asteroids_v09
Table 4.
The same as Table 3, but for the main-belt asteroids in theNereid field in Campaign 3. The full table is made available electroni-cally.
ID time USNO R R errBJD - 2,456,900 [mag] [mag]2001QZ114 111.9575 19.935 0.0692001QZ114 111.9780 19.898 0.0512001QZ114 111.9984 19.983 0.0712001QZ114 112.0188 20.171 0.0852001QZ114 112.0393 20.189 0.079... ... ... ...
In the left panels of Fig. 5 we show a few selected main-beltasteroid light curves in the M35 field along with their Lomb-Scargle diagrams, demonstrating the high quality of K2 observa-tions. The right panels of the same figure show asteroids crossingour Nereid field. Both the light curves and the periodograms areof better quality in the latter field, which underpins our suspi-cions that more crowding precludes obtaining high-quality lightcurves for main-belt asteroids with Kepler. The fact that we re-covered light curves with clear periodicities, incomplete cyclesor long-term trends implying long rotational period for 35 out of867 asteroids (4.0%) in the M35 superstamp, and 14 out of 88objects (15.9%) in the Nereid field also underlines this finding.Tables 5-6 show rotational periods and amplitudes alongwith literature data where available. In the cases where onlytrends or partially covered cycles were found we could estab-lish only lower limits for the rotational period. The agreementbetween our rotational periods and literature values is excel-lent in each case despite the di ff erences in observational strate-gies (multiple nights with ground-based telescopes vs. quasi-continuous for a few nights in the K2 mission). One exception is(111) Ate, which we discussed earlier. For more than half of ourobjects in Tables 5-6 (26 /
47 combined) we publish unambiguousrotational parameters for the first time thanks to the continuouscoverage of Kepler. The observed amplitudes are also in satisfac-tory agreement with available literature values. The uncertaintyof the rotational period (also given in Tables 5-6) depends on anumber of factors, such as the brightness of the object, the lengthof observations, and the number of observational points in thelight curve.
Trimodal ( i.e. three maxima during one rotation) and com-plex light curves are still considered as peculiar asteroid lightcurve shapes, although they were investigated as early as inthe 1950s (Gehrels & Owings 1962). The first known examplesof complex light curve were detected among the brightest as-teroids e.g. (16) Psyche, (21) Lutetia, (37) Fides, (39) Laeti-tia, (43) Ariadne, (52) Europa, (532) Herculina (Zappalà et al.1983; Cellino, Zappalà, & Farinella 1989). It has also been rec-ognized that the same asteroids exhibit bimodal or even uni-modal light curves at varying phase and aspect angles, therefore,shading e ff ects, phase e ff ects and / or unusual rotational geom-etry were usually invoked to explain the complex light varia-tions ( e.g. Zappalà et al. (1983); Michalowski (1996)). More re-cently, Harris et al. (2014) derived the higher-order harmonicsdue to polygonal shapes, and concluded that rotating trianglesenhance the sixth harmonics, therefore leading to light curves R m agn i t ude Phase18.418.618.819.019.219.419.6 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1(29628) - P = 16.08 h R m agn i t ude Phase18.418.618.8 981.6 981.8 982 982.2 982.4 982.6(37201) R m agn i t ude JD-2456000
Fig. 7.
The light curve of asteroid (29628) with three di ff erent peaksobserved in the Nereid field. Upper panel: light curve folded with tripleperiods, lower panel: the same data folded by sixtuple period. The curveline is a sixth-order Fourier-fit. Bottom panel: the light curve of asteroid(37201). with six maxima and not exceeding 0.156 magnitude full ampli-tude of the sixth harmonics. They also presented two examples:(5404) Uemura and 2010 RC130, where the composite lightcurve of six maxima was far more convincing than with threemaxima. Moreover, they remarked that the solution with threemaxima led to short rotation periods, near the break-up barrier,which is a further argument for the longer periods and a lightcurve with six maxima.Two light curves in our data were found to show this kindof complexity. Asteroid (29628) 1998 TX30 was observed in theNereid field, during 16.7 hours. The peak-to-peak amplitude is0 m .
72, and the light curve suggests a triple or sextuple symme-try (Fig. 7). Assuming three humps, the rotational period is 8.04hours. Another solution with 16.08 h period is also possible.The overlapping region in the latter case (P = Article number, page 6 of 9. Szabó et al.: Uninterrupted optical light curves of main-belt asteroids from the K2 Mission a m p li t ude ( m ag ) log P (hr) Fig. 8.
Period-amplitude diagram of an unbiased sample of 35 asteroidsfrom the M35 field (red points). The small green dots represent 16000asteroids from the Asteroid Lightcurve Database (Warner et al. 2009),while the thick black line shows the binned average of that large sample.
Fig. 8 shows the period-amplitude diagram of our sample of 35asteroids with uninterrupted light curves from the M35 field. Fora comparison we plotted the parameters of over 16000 aster-oids taken from the Asteroid Lightcurve Database (Warner et al.2009) reflecting the status of the database as of 20 February,2016. We plot only the rotation frequencies above the Nyquist-frequency of K2 data, where the results are comparable. Thethick black line shows the binned average of the large sample.The distribution of our limited sample follows nicely that ofthe underlying bulk sample. The median rotational period in theM35 field (9.83 h) clearly shows that we are sensitive to asteroidswith relatively large periods compared to the bulk sample shownin Fig. 8, whose median rotational period is 7.00 h. This hints atthe possibility that ground-based observations are usually biasedtoward shorter rotational periods that are easier to detect fromthe ground. The average period depends on the size of the aster-oids (see e.g. Pravec (2000)) Our sample is composed by someof the smallest known asteroids, where the average rotation pe-riod is predicted to be shorter than for the largest bodies. Sincewe observe the opposite, the di ff erence in periods cannot be ex-plained by such selection biases, but it really shows the power ofspace observations in the long period range.We tested whether the K2 long cadence (30-min) samplinghas any e ff ect on the period (and amplitude) determination. Sincewe considered rotational periods that are longer the 2 hours (i.e.below the Nyquist frequency-limit), we expect that despite thelong integration, we still can retrieve the periods. This is indeedthe case, as is demonstrated by a series of Monte-Carlo simula-tion. In the course of these simulations we computed that in whatfraction of the cases our algorithm can find the right (injected)period, which was simulated by a pure sinus wave. In these teststhe photometric noise (depending on the brightness), the obser-vation length, the duty cycle, and the rotational period were var-ied. We found that our sensitivity does not decrease in the rel-evant period range ( > ff ect. The worst case scenario is a decreaseof the amplitude by 37% at a rotation period of 2 hours, whichis still detectable in our K2 data in the case of an assumed 0.1magnitude true variation down to the 20th magnitude.
4. Conclusions
We utilized the
Kepler space telescope for the first time to derivequasi-continuous light curves of a large number of main-belt as-teroids in long cadence mode (29.4 min sampling). The mainconclusions of this work are the following: – Out of 924 (96) asteroids in the M35 (Nereid) field in Cam-paign 0 (3), 867 (88) had twelve or more useful photomet-ric data points and only 23 (14) exhibited clear periodici-ties which is attributed to rotation. In addition, 12 (0) objectsshowed a slow trend or were observed through an incompleterotational cycle implying a long rotational period. – By comparing the M35 and Nereid samples we found a re-markable di ff erence regarding the number of main-belt aster-oids with detected rotational periods in the two fields. Whilein the dense M35 field only 4.0% of the asteroids showedclear periodicities or trend, in the Nereid field we recoveredperiodicities in 15.9% of the observed asteroids. The di ff er-ence is significant given the large number of observed aster-oids in both fields. To explain this di ff erence we propose twoarguments: – First, we conclude that the dense stellar field precluded thederivation of meaningful photometry in the case of many as-teroids, because too many points had to be discarded, dueto the disturbing e ff ects of stellar residuals along the pathsof the asteroids (see Fig. 4). This is partly explained by theundersampled PSFs delivered by the Kepler spacecraft. – Second, in Fig. 9 we plot the magnitude distribution of ourfull M35 asteroid sample (in blue) as seen from Kepler, andalso those that showed periodicities or long-term trends intheir light variations (red). The plot convincingly shows thatour sample is heavily dominated by faint targets ( >
20 mag).Together with Fig. 3 this clearly demonstrates that there isa rather low chance to pull out rotational signal of asteroidsbelow the 20 th magnitude brightness limit. This reasoninghelps to explain the relatively low rate of recovered rotationalperiods in our fields, especially in the M35 superstamp. – More sophisticated photometric methods may improve ourresults and provide more reliable and robust space photo-metric data of moving objects. Testing of such methods iscurrently is under way.
Acknowledgements.
This project has been supported by the Lendület LP2012-31 Young Researchers Program, the Hungarian OTKA grants K-109276 and K-104607, the Hungarian National Research, Development and Innovation O ffi ce(NKFIH) grants K-115709 and PD-116175, the GINOP-2.3.2-15-2016-00003grant, and by City of Szombathely under agreement no. S-11-1027. The researchleading to these results has received funding from the European Community’sSeventh Framework Programme (FP7 / / / NL / NDe and 4000109997 / / NL / KML,and the European Union’s Horizon 2020 Research and Innovation Programme,Grant Agreement no 687378. Gy. M. Sz., Cs. K. and L. M. were supported by theJános Bolyai Research Scholarship. Funding for the K2 spacecraft is providedby the NASA Science Mission directorate. The authors thank the hospitality of
Article number, page 7 of 9 & Aproofs: manuscript no. k2_asteroids_v09 N u m be r o f ob j e c t s Brightness (magnitude)
Fig. 9.
Magnitude distribution of the asteroids in the M35 field seen by
Kepler (924, blue columns), and the selected sample where significantrotational signal (period or trend) could be derived (35, red columns).Two brighter objects were omitted from the figure for the sake of clarity. the Veszprém Regional Centre of the Hungarian Academy of Sciences (MTAVEAB), where part of this project was carried out. We acknowledge the
Kepler team and engineers for their e ff orts to keep this fantastic instrument alive and forallocating the large pixel mosaics. All of the data presented in this paper wereobtained from the Mikulski Archive for Space Telescopes (MAST). STScI is op-erated by the Association of Universities for Research in Astronomy, Inc., underNASA contract NAS5-26555. Support for MAST for non-HST data is providedby the NASA O ffi ce of Space Science via grant NNX13AC07G and by othergrants and contracts. We thank the referee for his / her useful comments whichhelped to improve the paper significantly. References
Bailey, S. J., 1913, Ann. Harvard Coll. Obs. 72, 165Benishek, V., Coley, D., 2014, Minor Planet Bulletin, 41, 260Behrend, R., 2009, Observatoire de Genève web site, http: // / ∼ behrend / page_cou.htmlCellino A., Zappalà V., Farinella P., 1989, Icarus, 78, 298Chaplin, W. J., Kjeldsen, H., Christensen-Dalsgaard, J., et al. 2011, Science, 332,213Christiansen J. L., et al., 2013, Kepler Data Characteristics Handbook (KSCI-19040-004)Cooney, W. R., 2005, Minor Planet Bulletin, 32, 15Ditteon, R., Hirsch, B., Kirkpatrick, E., et al. 2004, Minor Planet Bulletin, 31, 54Ferrero, A., 2010, Minor Planet Bulletin, 37, 145Gehrels T., Owings D., 1962, ApJ, 135, 906Gilliland, R. L., Brown, T. M., Christensen-Dalsgaard, J., et al. 2010, PASP, 122,131Hanus, J., ˇDurech, J., Oszkiewicz, D.A., et al. 2016, A&A, 586, A108Harris A. W., Pravec, P., Galád, A. et al., 2014, Icarus, 235, 55Howell, S. B., Sobeck, C., Haas, M., et al. 2014, PASP, 126, 398Ivarsen, K., Willis, S., Ingleby, L., et al. 2004, Minor Planet Bulletin, 31, 29Kipping, D. M., Torres, G., Henze, C. et al. 2016, ApJ, 820, 112Kiss, C., Pál, A., Farkas-Takács, A. I. et al. 2016, MNRAS, 457, 2908Lenz, P., Breger, M., CoAst, 146, 53Michałowski T., 1996, A&A, 309, 970Molnár L., Pál A., Plachy E., Ripepi V., Moretti M. I., Szabó R., Kiss L. L., 2015,ApJ, 812, 2Pál, A., 2012, MNRAS, 421, 1825Pál, A., Szabó, R., Szabó, Gy. M. et al. 2015, ApJ, 804, L45Pál, A., Kiss, Cs., Müller, T. G. et al. 2016, AJ, 151, 117Polishook, D., 2009, Minor Planet Bulletin, 36, 104Pravec, P., Harris, A. W., 2000, Icarus, 148, 12Sanchis-Ojeda, R. Rappaport, S. Winn, J. N., Kotson, M. C., Levine, A., El Mel-lah, I. 2014, ApJ, 787, 47Ski ff , B. A., 2011, http: // / call.htmlSzabó, R., Kolláth, Z., Molnár, L., et al. 2010, MNRAS, 409, 1244Szabó, R., Sárneczky, K., Szabó, Gy. M. et al. 2015, AJ, 149, 112Van Cleeve J. E., Caldwell D. A., 2016, Kepler Instrument Handbook (KSCI-19033-002)von Oppolzer, E., 1901, AN, 154, 309Warner, B. D., Harris, A. W., Pravec, P. 2009, Icarus, 202, 134Waszczak, A., Chang, C.-K., Ofeck, E.O., et al. 2015, AJ, 150, A75Wisniewski, W. Z., Michałowski, T. M., Harris, A. W. et al. 1997, Icarus 126,395Zappalà V., Martino M. D., Scaltriti F., et al. 1983, A&A, 123, 326 Table 5.
Rotational signal detected in asteroids observed in the K2 M35superstamp.
ID period ampl. ref.[h] [mag]228 6.437 ± > > ± > > ± ff (2011)3903 28.09 ± > > > > ± ± ± ± ± ± ± > > ± ± > > ± ± ± > > ± > > ± ± > > ± > > ± > > ± > > ± Article number, page 8 of 9. Szabó et al.: Uninterrupted optical light curves of main-belt asteroids from the K2 Mission
Table 6.
Observed periods and amplitudes of the asteroids in the K2Nereid field.
ID period ampl. ref.[h] [mag]2954 4.691 ± ± ± ± ± ± ± ± ± ± ± ±0.24 0.270 this paper