First Results from the rapid-response spectrophotometric characterization of Near-Earth Objects
Samuel Navarro-Meza, Michael Mommert, David Trilling, Nathaniel Butler, Mauricio Reyes-Ruiz, Barbara Pichardo, Tim Axelrod, Robert Jedicke, Nicholas Moskovitz
DDraft version March 21, 2019
Typeset using L A TEX manuscript style in AASTeX62
First results from the rapid-response spectrophotometric characterization of Near-Earth Objectsusing RATIR
S. Navarro-Meza,
1, 2
M. Mommert,
3, 2
D.E. Trilling, N. Butler,
4, 5
M. Reyes-Ruiz, B. Pichardo, T. Axelrod, R. Jedicke, and N. Moskovitz Instituto de Astronom´ıa, Universidad Nacional Aut´onoma de M´exico, Ensenada B.C. 22860, M´exico. Department of Physics and Astronomy, Northern Arizona University, Flagstaff, AZ 86001, USA Lowell Observatory, Flagstaff, AZ 86001, USA School of Earth and Space exploration, Arizona State University, Tempe, AZ 85287, USA Cosmology Initiative, Arizona State University, Tempe, AZ 85287, USA Instituto de Astronom´ıa, Universidad Nacional Aut´onoma de M´exico, Ciudad Universitaria, D.F. 04510, M´exico. Steward Observatory, University of Arizona, Tucson, AZ 85721, USA Institute for Astronomy, University of Hawaii at Manoa, Honolulu, HI 96822, USA
ABSTRACTAs part of our multi-observatory, multi-filter campaign, we present r-i color observa-tions of 82 Near-Earth Objects (NEOs) obtained with the RATIR instrument on the1.5 m robotic telescope at the San Pedro Martir’s National Observatory in Mexico. Ourproject is particularly focused on rapid response observations of small ( (cid:46)
850 m) NEOs.The rapid response and the use of spectrophotometry allows us to constrain the taxo-nomic classification of NEOs with high efficiency. Here we present the methodology ofour observations and our result, suggesting that the ratio of C-type to S-type asteroids
Corresponding author: S. [email protected] a r X i v : . [ a s t r o - ph . E P ] M a r in a size range of ∼ Keywords: asteroids: individual (near-Earth objects) — minor planets — surveys INTRODUCTIONSolar System minor bodies are tracers of the Solar System’s formation and evolution, and hencecan be used as current samples of the processes that occurred in the early days of the system and itsformation (Delsemme 1991; Malhotra 1997). Therefore, studies with numerous samples, focused onanalyzing colors, taxonomies, orbital and physical properties of asteroids from different populationshave been made (see for example Ivezi´c et al. 2001; Carvano et al. 2010; Carry et al. 2016).Near Earth Objects (NEOs) are of particular interest for their potential to explain the disagree-ment between the composition of meteorite falls on Earth and the composition observed in asteroids(Mommert et al. 2016). Furthermore, the Chelyabinsk event in 2013 showed us that there existNEOs with the potential to cause moderate to devastating damage to our communities (Brown etal. 2013). It is worth to remark that events like this can happen in any point on the globe. Thisevent has motivated projects aimed to characterize those asteroids that could impact the Earth andthat have enough energy to compromise its safety.Discovery and characterization efforts aimed at NEOs have significantly increased in the last years.However, due to their general faintness, characterization of small NEOs lags behind. The mosteffective way to constrain NEO compositions is spectroscopy, which allows for the identification ofboth the overall continuum shape and diagnostic band features and enables their taxonomic clas-sification. However, spectroscopy is very expensive in terms of telescope time, and is only possiblewith relatively bright objects, which generally are the largest objects. Only few small asteroids (withdiameters smaller than 100 m) get bright enough to be observed spectroscopically (e.g. Moskovitz etal. 2015). Currently, DeMeo et al. (2009) offer the most complete taxonomic classification system.Photometric measurements at a few key wavelengths - spectrophotometry - can be sufficient to esti-mate asteroid taxonomies (see Mommert et al. 2016, and references therein). This technique has theadvantage of making faint targets accessible because the light is collected within a broad bandpassinstead of being dispersed as a function of wavelength. Furthermore, spectrophotometry can beperformed with smaller telescopes than the ones necessary for spectroscopy. Here we present a com-bination of spectrophotometry and rapid-response observations, i.e., observations that are obtainedshortly after the discovery of the target, when it is still relatively bright. This article constitutesthe third of a series of papers oriented to taxonomically classify hundreds of small NEOs usingspectrophotometry.C- (organic rich) and S- (siliceous rock) taxonomic types are the dominant constituents of the dis-tribution of large asteroids (Stuart & Binzel 2004; Thomas et al. 2011). However, the compositionaldistribution of small NEOs appears to be different from that of Main Belt asteroids, as well as fromlarge NEOs. Mommert et al. (2016) find S and C+X complexes to be the main components of theirsample of small NEOs. Also as pointed out by them, the compositional distribution of meteoritefalls does not match the observed NEO distribution, a fact that can yield information on asteroidstrength. This fact needs to be studied with better statistics on the small asteroid range in order tobetter understand the threat to Earth from impactors. It is important to remark that according toThomas et al. (2011, 2014), Q-type asteroids can be an important component of a magnitude biasedNEO sample, due to their relatively high albedos. There are other teams interested in this sametopic (see for example Popescu et al. 2018; Ieva et al. 2018). Results from Mommert et al. (2016) make no distinction between the C and the X taxonomic complexes. Forcomparison purposes the notation C+X will be used here, which stands for the set of objects corresponding to both,the C and the X complexes.
This study is part of a worldwide systematic survey of NEO compositions. With the use of the 3.8m United Kingdom Infrared Telescope (UKIRT) and KMTNet-SAAO telescope, we provide detailedinformation on the compositional distribution of NEOs with absolute magnitudes up to H ∼ RATIRObservations were performed with the Reionization And Transients InfraRed camera (RATIR,Butler et al. 2012), on the San Pedro Martir (SPM) 1.5 m telescope at the National Mexican As-tronomical Observatory (Observatorio Astron´omico Nacional). This telescope is a Ritchey-Chr´etientype, operated by the Universidad Nacional Aut´onoma de M´exico. The instrument is equipped withtwo optical and two near-infrared (NIR) detectors, all of them 2048x2048 pixels. Each of these detec-tors corresponds to a different channel with specific filters, as shown in Table 1. RATIR takes fourimages of an object in a single shot . To minimize dark current and thermal background effects, theoptical detectors are water cooled, while the NIR detectors are operated in a helium-cooled cryostat. See detailed information in RATIR’s web page: http://ratir.astroscu.unam.mx
Channel Detector Field size Filters(arc minute square)C0 CCD 5 . . Table 1.
Channels of the RATIR instrument. All detectors are 2048x2048 pixels. C0 and C1 channels holdthe visual range filters (observations reported in this paper were taken with the r and i filters). C2 and C3channels contain the near infrared filters; H2RG (HAWAII-2RG) are Teledyne mercury-cadmium-telluridedetectors. RATIR was designed to study gamma ray bursts (e.g. Butler et al. 2017a,b,c), but other uses arepossible as shown here (see also Tapia et al. 2014; Garc´ıa-D´ıaz et al. 2014; Ricci et al. 2015). Obser-vations are executed in an automated queue mode (Watson et al. 2012) if no gamma ray burst eventsare ongoing. The results that we present are the first asteroid observations made with the instrument. OBSERVATIONSThe observations we present here were taken during 2014 and 2015. During most part of 2015 and2016, RATIR’s channels C2 and C3 (see Table 1) were not available due to technical problems. Inthis work, we analyze the set of optical-only data. Since the second half of 2016 we are obtainingobservations in all four channels, which will be presented in a future publication.Our rapid response approach is the key feature of this project. We trigger rapid response spec-trophotometric observations of NEOs within a few days of their discovery when the objects aregenerally still bright enough to be observed with a 1.5 m aperture. We can observe and characterizeobjects as faint as V ∼
20. Such rapid response is generally not feasible through classical observingprograms. The first results of NEO observations made by our team are presented in Mommert et al.(2016) and Erasmus et al. (2017).Potential targets are identified and uploaded into the RATIR queue on a daily basis. Accessibletargets are identified among those NEOs that have been discovered within the last four weeks; thisduration is partially arbitrary , but the method usually leads to a number of well-observable andbright potential targets. A target is considered accessible if it has a visible brightness V ≤
20 andan air-mass ≤ H V (small sizes) andlarge values of H V -V, where V stands for the apparent magnitude of the target of the upcomingnight. A high value of H V -V ensures that our target is observed when it is close to the Earth.RATIR queue observing scripts are automatically created for the selected targets, using the latestorbital elements of the objects of interest provided by JPL Horizons. The exposure time of eachframe, as well as the total integration time in each band per visit are a function of the object’sbrightness. Exposure times usually ranges between 5 and 30 seconds, while the total integrationtime per target is usually less than 1 hour.Our observations are biased in favor of bright objects. At a given distance from Earth, for objectsof a given diameter, objects with higher albedo are easier to observe. For targets close to our limitingmagnitude, only those with relatively high albedos will be observed. Hence, our sample may containa higher fraction of S and Q objects than the actual asteroid population. DATA ANALYSIS After the closest approach, NEOs fade at a rate of typically 0.5 mag within one week and 5 mag within 6 weeks(Galache et al. 2015).
Object Obs. Midtime Dur. H V r-i error(UT) (hr) (mag) (mag) (mag)2014 MK6 2014-07-22 09:30 1.7 21.00 0.29 0.012014 MP5 2014-07-21 05:25 1.5 21.80 0.27 0.022014 OZ337 2014-08-04 08:13 0.3 22.50 0.35 0.022014 QQ33 2014-08-25 10:20 1.3 22.10 0.30 0.022014 TT35 2014-10-18 03:49 0.1 26.00 0.49 0.012014 TZ 2014-10-23 05:12 1.1 22.60 0.33 0.012014 UT192 2014-11-10 09:03 0.2 19.60 0.46 0.032014 UZ116 2014-11-03 06:41 1.6 20.90 0.36 0.042014 WX4 2014-11-20 07:16 0.5 26.40 0.40 0.022014 WZ4 2014-11-20 03:42 0.5 23.50 0.29 0.032014 YE35 2015-01-15 08:32 0.5 20.30 0.38 0.012014 YW34 2015-01-15 06:53 1.6 21.60 0.25 0.062015 EL7 2015-04-05 10:19 0.4 22.70 0.38 0.032015 EL7 2015-04-09 07:40 0.2 22.70 0.39 0.062015 EL7 2015-04-11 07:22 0.1 22.70 0.36 0.032015 EZ 2015-03-15 05:56 0.4 20.30 0.40 0.012015 FG120 2015-04-10 09:12 1.1 22.90 0.36 0.022015 FG120 2015-04-11 09:20 0.2 22.90 0.29 0.032015 FG120 2015-04-12 09:35 1.0 22.90 0.30 0.022015 FG120 2015-04-13 08:07 0.9 22.90 0.38 0.022015 FG120 2015-04-17 11:09 0.7 22.90 0.37 0.022015 FG37 2015-04-15 10:53 1.1 21.70 0.41 0.022015 FG37 2015-04-22 11:25 0.1 21.70 0.29 0.042015 FL290 2015-04-09 05:11 1.1 22.20 0.36 0.022015 FL290 2015-04-10 04:53 1.1 22.20 0.37 0.022015 FL290 2015-04-11 04:46 1.2 22.20 0.39 0.01 Table 2.
This table presents each of the reported targets according to their number or designation, obser-vation midtime of the observing run, and the duration of it. Also presented are, the measured color indices(solar colors have been subtracted) and corresponding uncertainties.
Object Obs. Midtime Dur. H V r-i error(UT) (hr) (mag) (mag) (mag)2015 FQ 2015-03-29 05:43 0.9 22.30 0.40 0.022015 FT118 2015-04-20 10:50 0.6 20.40 0.30 0.042015 FY284 2015-04-02 07:13 0.5 21.60 0.37 0.052015 GS13 2015-05-14 09:26 0.4 21.00 0.51 0.032015 GS 2015-04-15 09:34 1.1 20.60 0.35 0.022015 GS 2015-04-16 09:53 1.2 20.60 0.33 0.022015 GY 2015-04-15 05:14 0.6 21.70 0.41 0.012015 GY 2015-04-19 07:16 0.5 21.70 0.27 0.022015 HA1 2015-04-25 09:04 0.9 21.20 0.46 0.012015 HA1 2015-05-05 07:50 0.5 21.20 0.45 0.012015 HP171 2015-05-12 09:32 0.3 20.10 0.34 0.022015 HR1 2015-05-06 08:59 0.7 24.30 0.35 0.062015 HR1 2015-05-07 09:00 0.4 24.30 0.34 0.062015 HR1 2015-05-13 09:39 0.7 24.30 0.26 0.032015 HV171 2015-05-08 08:55 0.1 18.10 0.36 0.012015 HW11 2015-05-12 07:04 1.1 23.30 0.41 0.022015 JQ1 2015-05-18 05:03 1.0 20.30 0.26 0.052015 JQ1 2015-05-19 05:45 1.0 20.30 0.28 0.022015 KL122 2015-06-05 09:19 0.5 22.30 0.47 0.072015 KQ120 2015-05-30 10:10 0.1 26.70 0.43 0.042015 KQ57 2015-05-26 05:17 0.0 22.20 0.40 0.042015 KV18 2015-05-23 09:41 0.8 23.80 0.42 0.032015 KV18 2015-05-24 09:28 0.8 23.80 0.37 0.042015 KV18 2015-05-25 07:40 0.2 23.80 0.31 0.022015 KV18 2015-05-26 07:40 0.1 23.80 0.41 0.032015 LA2 2015-06-14 06:35 1.0 23.10 0.33 0.012015 LG14 2015-06-22 06:22 1.0 23.20 0.40 0.032015 LG14 2015-06-23 06:03 0.8 23.20 0.52 0.042015 LG2 2015-06-18 07:18 1.0 20.30 0.40 0.03 Table 2. (continued).
Object Obs. Midtime Dur. H V r-i error(UT) (hr) (mag) (mag) (mag)2015 LG2 2015-06-21 08:41 0.8 20.30 0.37 0.022015 LJ24 2015-06-18 05:11 0.2 20.00 0.42 0.032015 LJ 2015-07-04 06:43 0.8 24.70 0.45 0.052015 LJ 2015-07-04 07:50 0.8 24.70 0.33 0.072015 LJ 2015-07-13 05:21 0.8 24.70 0.27 0.032015 LJ 2015-07-25 06:54 0.9 24.70 0.29 0.062015 LQ21 2015-06-21 05:01 0.1 24.50 0.50 0.032015 MC 2015-06-20 06:18 0.2 24.10 0.45 0.022015 MC 2015-06-26 06:49 0.9 24.10 0.30 0.042015 ME116 2015-07-14 04:57 0.3 22.30 0.38 0.062015 ME116 2015-07-25 04:49 0.4 22.30 0.27 0.042015 MQ116 2015-07-15 08:09 0.8 23.40 0.35 0.052015 MS59 2015-07-13 10:15 0.9 21.00 0.25 0.012015 MS59 2015-07-14 09:26 0.9 21.00 0.49 0.022015 MS59 2015-07-15 09:25 1.0 21.00 0.41 0.022015 MS59 2015-07-23 09:48 0.9 21.00 0.37 0.042015 MU59 2015-07-09 10:01 0.8 20.00 0.31 0.022015 MU59 2015-07-13 09:15 0.8 20.00 0.44 0.012015 MU59 2015-08-04 08:44 0.6 20.00 0.39 0.012015 MX103 2015-07-04 05:13 0.5 24.40 0.46 0.022015 MX103 2015-07-06 06:16 0.6 24.40 0.38 0.022015 MY53 2015-07-03 05:59 0.5 25.40 0.39 0.062015 MY53 2015-07-03 06:49 0.2 25.40 0.52 0.032015 NK13 2015-08-04 07:07 0.8 21.00 0.40 0.032015 NK3 2015-08-04 05:56 0.8 21.30 0.26 0.032015 NK3 2015-08-07 06:57 1.0 21.30 0.28 0.012015 NU2 2015-07-21 07:10 0.6 20.90 0.28 0.042015 NU2 2015-07-24 05:15 1.1 20.90 0.35 0.04 Table 2. (continued) Object Obs. Midtime Dur. H V r-i error(UT) (hr) (mag) (mag) (mag)2015 OF26 2015-08-07 05:37 0.3 21.60 0.32 0.022015 OM21 2015-07-24 09:55 0.7 22.50 0.38 0.032015 OM21 2015-08-06 08:00 0.9 22.50 0.45 0.032015 OM21 2015-08-07 08:05 1.0 22.50 0.48 0.022015 PA229 2015-08-21 09:39 1.0 21.40 0.41 0.022015 PA229 2015-09-05 08:55 1.0 21.40 0.39 0.052015 PQ56 2015-09-03 07:59 0.9 22.60 0.46 0.042015 PQ 2015-09-07 07:52 0.7 22.70 0.48 0.012015 QB 2015-08-21 08:32 1.0 24.20 0.39 0.012015 QG 2015-08-22 05:17 0.3 23.80 0.33 0.022015 QM3 2015-08-23 04:45 0.4 20.40 0.28 0.052015 QN3 2015-08-23 04:20 0.4 19.50 0.28 0.012015 QN3 2015-08-24 04:56 0.4 19.50 0.40 0.012015 QO3 2015-08-24 07:05 0.6 19.40 0.38 0.012015 RH36 2015-09-18 09:57 0.5 23.60 0.37 0.062015 RO36 2015-09-18 05:36 0.3 22.90 0.24 0.032015 RQ36 2015-09-16 07:25 1.0 24.50 0.36 0.012015 RQ36 2015-09-19 09:05 0.6 24.50 0.35 0.022015 SO2 2015-09-26 09:01 0.3 23.90 0.37 0.032015 SO2 2015-09-27 09:33 0.3 23.90 0.29 0.032015 SO2 2015-09-28 10:57 0.3 23.90 0.50 0.032015 SO2 2015-10-02 11:21 0.4 23.90 0.32 0.032015 SV2 2015-09-29 05:31 0.9 20.80 0.33 0.032015 SY 2015-10-01 06:35 0.7 23.30 0.44 0.022015 SY 2015-10-02 06:09 0.8 23.30 0.33 0.032015 SZ 2015-10-02 05:22 0.4 23.50 0.36 0.012015 TE 2015-10-08 04:26 0.5 22.50 0.43 0.02 Table 2. (continued) Object Obs. Midtime Dur. H V r-i error(UT) (hr) (mag) (mag) (mag)2015 TF 2015-10-10 05:15 0.6 22.20 0.39 0.012015 TW178 2015-10-26 04:18 0.9 21.20 0.28 0.042015 TY144 2015-10-26 10:14 0.5 21.30 0.48 0.052015 TY178 2015-11-06 06:52 0.7 21.80 0.32 0.042015 UJ51 2015-10-27 07:41 0.7 21.40 0.38 0.032015 US51 2015-10-28 04:54 0.6 22.40 0.44 0.022015 US51 2015-11-01 05:02 0.8 22.40 0.43 0.012015 US51 2015-11-02 04:35 0.8 22.40 0.44 0.012015 UT52 2015-11-05 07:40 0.8 20.90 0.45 0.032015 UT52 2015-11-11 10:56 0.6 20.90 0.40 0.042015 VJ2 2015-11-10 09:36 0.4 19.60 0.44 0.022015 VJ2 2015-11-18 10:50 0.2 19.60 0.37 0.032015 VJ2 2015-11-19 10:06 0.6 19.60 0.26 0.012015 VO66 2015-11-14 10:06 0.4 20.60 0.25 0.032015 VO66 2015-11-19 08:20 0.5 20.60 0.28 0.012015 VZ2 2015-11-19 04:15 0.9 22.70 0.46 0.042014 OT338 2014-08-17 11:10 1.4 21.40 0.45 0.022014 TX32 2014-10-16 05:35 1.1 20.20 0.42 0.012015 DE176 2015-02-28 06:18 1.0 19.70 0.35 0.032015 JV 2015-05-19 07:35 0.8 21.50 0.33 0.012015 KJ19 2015-05-24 04:53 0.6 22.50 0.28 0.07 Table 2. (continued)
Taxonomic classification
We use the Bus-DeMeo classification scheme (DeMeo et al. 2009) to classify our sample. This isa widely used taxonomic scheme that combines the visible and near infrared ranges, covering from2
Figure 1.
All r-i indices considered in this work according to the Bus-DeMeo taxonomies. Orange linesare the subtypes that are most distant from the C- and S-type respectively, thus defining the limits of thesecomplexes . Notice that the C- and S-subtype are in the middle of their complexes. . µ m. The taxonomy includes 24 classes, most of which correspond to the C-, S- andX-complexes that include the majority of the known asteroids (see DeMeo et al. 2009, and Section1). For this reason, we considered these 3 complexes in our analysis, as well as the Q-type, which,as described by Thomas et al. (2011, 2014), can be an important component of a magnitude biasedNEO sample like ours. Other taxonomic types were not considered, as they are not expected to bea significant part of the distribution (perhaps up to 20%: Mommert et al. (2016); Erasmus et al.(2017); Perna et al. (2018); Lin et al. (2018)) and due to the simplicity of our model. We revisit thisassumption below.We obtain the characteristic color of each taxonomic type from a sample of measured asteroidspectra . For each object from the sample, its reflectance spectrum is convolved with the spectralresponse of each RATIR’s filter and the solar spectrum. Details of the process can be found at http://smass.mit.edu/minus.html r-i color.4.2. Photometry
Image reduction and photometry is carried out using a pipeline developed for GRB observations(see, e.g. Becerra et al. 2017; Littlejohns et al. 2015). Briefly, the pipeline reduces, sky-subtracts, andaligns input frames. These frames are then stacked into a sky image. The stellar PSF is determinedand fit using custom python scripts to determine the photometric zero point in comparison withSDSS, 2MASS, and/or USNO photometric catalogs. After finishing the GRB pipeline reduction,we create a source mask using the sky image. By then coadding the frames in the moving frameof the target, keeping track of the exposure per pixel, the non-moving sources are removed and weretain only the signal from the target. The PSF determined from the sky image is then fit to themoving-target image and the zero point from the sky image is applied to normalize the photometry.The magnitude of an object as a function of the observing time is generated by dyadically combin-ing the masked frames, selecting a sufficiently long time interval for each photometric epoch as toadequately fill in masked pixels prior to PSF fitting. In principle, single frame photometry is possiblebecause we propagate the exposure pixel by pixel; however the accuracy can depend strongly on thestability of the PSF.Therefore, the pipeline yields photometry on the original image, on a set of stacked images, andon the overall visit’s stacked frame. The stacking creates new images with different virtual exposuretimes which are integer multiples of the real exposure time. The result of this procedure is availablein data tables and through a graphical display in a website. In our analysis we use the photometrymeasured in individual r band and i band images. With this information we measure the r-i colorindex. The Solar r-i was subtracted from our measurements in order to make them compatible withthe synthetized colors (see Section 4.1).4 4.3. Outlier rejection
In order to reject photometric outliers we performed a 10 − σ clipping on the r-i index for eachvisit: a weighted mean of the r-i index was taken, then any measurement further than 10 σ from themean was rejected and the weighted mean calculated again. This process was carried out 3 times.Each time the photometric errors from the individual measurements were propagated to obtain theweights (Taylor 1997). Therefore, the corresponding error on the r-i index from a visit is: ς = 1 √ Σ w k , (1)where w k = 1 e ≡ e r + e i (2)where e k is associated with the r-i from each of the non-rejected data points of that visit and e r and e i are the photometric errors from the r and i band measurements. The values of ς are plotted inFigure 2. 4.4. Selection of the best observations
We only consider measurements of those objects that passed through all of our selection criteria,the first of which is a clean visit-stacked image: a well defined source and a successful removal ofthe not moving sources (see Section 4.2 for details on the photometry). Note that we use the visitstacked image only to check the quality of the photometry and of the observation itself, e.g., withrespect to background sources confusion. Also, a limit on the color index’s error due to photometricuncertainty must be set. The difference in color index between the C- and S-type asteroids is 0.084,hence it is convenient that we only consider the objects that have an error lower than this threshold.Based on the discussion on Section 6.2, we decide to use 0.075 as an upper error limit on the colordetermination. We require a minimum of 4 measurements per visit.5
Figure 2.
Error distribution of the color from our sample. The vertical line shows the upper error limitset for the sample. See Section 4.4 for details on the selection criteria used.
The outcome of this selection process is 82 different objects observed in 131 visits.4.5.
Probability density
After the selection process described in the previous section, we have one r-i index and its asso-ciated error for each visit in our clean sample. These indices are shown in Figure 3. In order toanalyze the taxonomic distribution of our sample, we model it based on the known asteroid colors.We consider every count in Figure 3 as a normalized Gaussian centered at the r-i value of that objectwith the width of the Gaussian equal to the error on the r-i index (the height is therefore a freeparameter). For objects observed more than once, the Gaussian’s normalization factor is divided bythe number of visits each object has. That way an object observed in more than one visit will berepresented by different Gaussians all of which add up an area of unity. The Gaussians correspond-ing to all objects were added up to obtain the Probability Density Function (PDF), shown in Figure 4.6
Figure 3.
Color distribution of our sample. Color indices were obtained after performing the rejectionprocess described in the text. The main subtypes from the C- and S-complex are shown (see Figure 1).
Monte Carlo simulation
In order to measure the compositional distribution from the PDF, we conducted a Monte Carlo(MC) simulation, which consists of creating 10 samples of synthetic asteroids, each sample with thesame number of objects as our data sample but with different taxonomic distributions. In each runthe S-, C-, X- complexes and the Q-type are considered, and the number of objects in each taxonomyis set with a pseudo-random number generator. We call the resulting color index distribution fromeach run the Random Probability Density Function, RPDF, to distinguish it from the PDF from ourdata. The process to generate each distribution is the same. The details of our MC simulation areas follows.82 synthetic objects were used in each MC run in order to directly compare the RPDF with thePDF. From Mommert et al. (2016) and Erasmus et al. (2017), we expect the C- and S-type asteroidsto be the main components of our sample, and to find a C/S ratio of ∼
1. However, we take intoaccount the possibility that our sample is composed of any combination of the taxonomic types con-7sidered. This is achieved by using a pseudo-random number generator under a uniform distributionwith equal weights for the 3 complexes and the Q-type. The process to obtain the composition oneach of the runs is as follows.The order in which the number of elements is set for each complex and the Q type is randomlysorted. Each of them is labeled as n a , n b , n c or n d . The assignation of number of elements isalways in alphabetical order, however the correspondence between the types and n a − d is given by thepseudo random number generator. Then n a can be assigned with any number between 0 and 82, theavailability for n b is 82- n a , and similar for n c and n d .The main subtypes of the complexes, respectively C-type, S-type and X-type, are the most likelyto be present in our sample (Binzel et al. 2015). Therefore, in each of the random generated samples,half of the elements assigned to each complex are given to the main subtype, while the other halfis uniformly distributed among the other subtypes (see Figure 1 for the r-i index of each of themembers of these complexes). The number of elements in the second half will likely not be an integermultiple of the number of subtypes. For example, if 36 elements are assigned to the S-complex,18 will correspond to the main type, the S-type. The remaining 18 will correspond to the other 4subtypes of the complex, but 18 over 4 is not an integer. The procedure is therefore as follows: ifthe number of elements assigned to the 4 subtypes are n S1 , n S2 , n S3 , n S4 , then: n S1 = round(18/4) = 5; 18-5 = 13 elements available for the 3 other subtypes, n S2 = round(13/3) = 4; 13-4 = 9, n S3 = round(9/2) = 5; 9-5 = 4, n S4 = 4.In each run, the correspondence between the n S − and the 4 subtypes is randomly sorted, so thatover the 10 samples generated, none of the 4 subtypes is favored. The same criteria apply for the8C- and the X-complex. The main processes of the simulation are represented in Figure 5.After applying all the selection criteria (see Section 4.4), some of the objects that were observedduring different visits showed a different r-i index. This fact was not considered in the building ofthe RPDF. In the simulation, the elements that are not members of the C- or the S-complex aredefined as “pollution”.Once the number of elements of each type in a single run is determined, it is necessary to add anerror to them in order to emulate the photometric uncertainty. In order to take this into account,we fitted a Gaussian function to the distribution from Figure 2 and created a random distributionunder that function. 82 errors from that distribution were assigned to the r-i indices of each ofthe determined types. This completes our generated sample. 82 elements were randomly selectedfollowing a distribution based on current NEOs observations. Each of the elements has an associatederror, based on the error distribution of our observations. Having these, the RPDF was built up.After creating the 10 samples, the PDF was compared to each of the 10 RPDFs. RESULTSIn order to extract the results from the simulations, we calculated the reduced χ ( χ ) betweenthe RPDF and the PDF. Since we are allowing the simulation to create any possible combinationof the taxonomies considered, the χ range is wide as can be seen in Figure 7. We took the firstpercentile of simulations in terms of the χ . This is a set of 88 simulations ( ∼ − from the total).The difference in χ between the best and the second to the best case is minimal. Both present 36elements of the S-type, the first one suggest 38 C-types, while the second 39. The main differenceis in the number of X- and Q-type objects. To analyze the behavior of the best cases we calculatedthe distribution of the ratio C/S , which is shown in Figure 8. Our best case corresponds to a valueof 1.06 in this space. Notice that value is well within 1 standard deviation from the mean, but notin the bin where mean of the distribution is. We ascribe this to the fact the histogram is skewed9
Figure 4.
Probability Density Function of the color in our sample. Every visit is considered as a Gaussiancentered in the color index obtained. Vertical lines represent the limits of the C and S complexes. See textfor full explanation. to the left, which is discussed in the next Section. Table 4 shows the percent compositions of the4 taxonomic types considered according to our best case. The errors correspond to the standarddeviation of the individual distribution of each class within the 1st percentile. Although we presentresults on the 3 complexes and the Q-type, the scope of this analysis is restricted to suggest a
C/S ratio. All of our targets have a subkilometer diameter. We don’t report subdivisions in size sincethere was not a clear trend on the results by doing so. DISCUSSION6.1.
Limitations and comparison with previous studies
The strongest bias in our sample is the one presented by albedo. Our rapid-response approach isbased on optically discovered objects, hence the sample targets are more likely to have moderate tohigh surface albedos. This can lead to an over-estimated fraction of S objects, which means the realfraction of C / S can be higher than the estimated here. Hence, our sample is biased, and although0 total objects=82 n '= total n C = n C /2 comp n X = n X /2 n S = n S /2 compcomp determine the number of elements of the reminding subtypes in each complex assign a random error toeach element build the RPDF n' = n'- n a determine n a determine n b determine n c n = n' n bc d Each run n, n, n & n are randomly determined and can be any of C, X, S or Q. a b c d comp compcompcomp n' = n'-n' = n'- n
Figure 5.
Main processes in the Monte Carlo simulation. Particularly the procedure for setting the numberof objects of each type in the synthetic sample. Every box including the word “determine” involves a randomprocess. n is the number of objects of a certain type or complex in a single run; the subindex indicates thereferred taxonomy. Since there are C-, S- and X- complexes, as well as a C-, S- and X-types, a super index“comp” indicates when the variable is associated to the complex. n ’ is the number of objects available forthe unassigned taxonomies at a certain point.Taxonomic type PercentageC 46 ±
9S 44 ±
8X 8 ±
9Q 2 ± Table 4.
Compositional fractions found in our Monte Carlo simulation. Figure 6.
Probability Density Function (red) of the color in our sample. Equivalent to Figure 4, this timethe best result from our MC simulation is overplotted (Random Probability Density Function, orange). AGaussian fit to the PDF is also overplotted (blue). Both, the RPDF and the Fit make a good match withthe data, as can be seen on the residuals (dashed orange and blue). See Sections 5 and 6.2 for details. debiasing of NEOs had been carried out (Stuart & Binzel 2004; Hinkle et al. 2015) we will addressit in a future work.Our full sample contains observations in up to 6 different bands in the optical and near infraredrange. However, the results presented here correspond to our control sample using only the r-i color. Hence, one the main goals of this article is to describe the methodology we are using for ourobservations. Our future work will include data in all bandpasses.The distribution in Figure 8 is skewed to the left due to the feature at r-i ∼ . − .
30 in Figures3 and 4. It is likely due to a systematic error in the observations causing a bluer color. The analysisof the complete sample will allow us to test this idea.2
Figure 7. χ from the 10 MC simulations. Vertical line shows the domain of the first percentile ofsimulations in terms of the χ . Our full sample is one of the largest for small NEOs. The analysis of it as well as the work fromother teams is needed for a comprehensive classification of this kind of objects. (As a comparison,Ivezi´c et al. (2001) made a study of the Main Belt including ∼ ∼
61% of S-types. Lin et al. (2018), presents 51 subkilometer NEOs. Withthis sample they found an S fraction of ∼ ∼ ∼
40% with 40 NEOs in Mommert et al. (2016), while Erasmus et al. (2017), with asample of 45 objects, obtained an S fraction of ∼ Figure 8.
C/S distribution from the 1st percentile of our MC simulations in terms of χ . Note: the elementin the far right is the 66th best fit, therefore not considered an issue but still considered in the estimationof the mean and standard deviation. (2004) found an S-type fraction of 22%. This number is a reference for the distribution of NEOs,but is not directly comparable with our results since they performed bias correction, their sampleincludes Mars Crossing asteroids, and includes objects up to the 10 km scale. Binzel et al. (2018) (inpress) uses a sample of 1040 objects, with a median of 0.7 km and finds an S fraction of ∼ ∼
46% we suggest.6.2.
Gaussian Fit
With the purpose of getting a result independent from the MC simulation, we performed a Gaussianfit on the PDF, for which, we considered two components with fixed mean: one centered on the color4index of C-type asteroids (0.335), and the other one centered on the color index of S-type asteroids(0.418).The result from our fit is overplotted to the PDF and RPDF in Figure 6. The two componentsof the fit are equivalent to 48% of S-type objects and 52% of C-type objects yielding
C/S = 1 . −∞ , ∞ ](b) Integrating under the limits of the taxonomic types plus the maximum error allowed in color(0.075).(c) [ −∞ ,mid z ] for the C Gaussian and [mid z , ∞ ] for the S Gaussian.where mid z is the middle point between the r-i index of the C and S taxonomic complexes in termsof the z-score.5 Figure 9.
Integration limits considered for the Gaussian components of the fit. The fit is equivalent to theone showed in Figure 6. Vertical dotted shows the position of the main subtype of the C- and S-complex,thus the center of the Gaussian components. The width of the Gaussians is related to the error of theindividual elements, the ordinate axis has no practical meaning. See text for more details.
The three integration limits are shown in Figure 9. They yield a similar C / S ratio, but, method (b)proved to be more stable as a function of the pollution in test runs of the MC analysis. With theuse of this method we made a cut in the tails of the Gaussians, obtaining more localized components.Notice from Figure 1 that the main types of the C- and S-complex are positioned nearly at the centerof their corresponding complex range, making the integration reliable.We explored the C / S ratio (obtained in Section 4.5) as a function of the upper error allowed in theclean sample. This dependence is shown in Figure 10. Excluding the extremes of the abscissa rangeon this plot, the C / S ratio does not present a strong dependence on the error limit. Additionally,more than % of the objects that passed our other selection criteria have an error lower than 0.075 We used Equations 3 - 5 presented in Section 6.3 to compare the results. Figure 10.
C-type to S-type ratio found with a Gaussian fit to the PDF after using different upper errorselection criteria. Notice that this figure is a comparison of different error limits for our sample and it doesnot represent our main results. (and most of the asteroids in our full sample too, see Figure 2).6.3.
Accuracy
The composition of the RPDF is generated during the simulation, therefore it is known per se.Hence, by applying a Gaussian fit to the RPDF, such as the one described in Section 4.5, we canobtain the reliability of the fit in a particular case with the relative error: e = f m − f k f k , (3)where f k stands for the known compositional fraction of a certain type in the RPDF, and f m for thefraction measured through the Gaussian fit. Then we can consider all of the instances of a fixed k inthe 10 runs with: (cid:15) = e, (4)7and the spread of Equation 4 is measured with: σ = (cid:112) e − e . (5)Equations 3 -5 are identical for the three complexes and the Q-type.As a general trend, (cid:15) was larger for the C complex than for the S one. This suggests that ifobjects of the X-complex and Q-type are present in the data sample, is more likely for them to beidentified as members of the C-complex than the S-complex by performing a Gaussian fit. This wasalso observed in test runs where only the main type of each complex was used. In terms of the r-i index, the Q-type is closer to the C-complex, while the X-complex is closer to the S (see Figure 1).It is possible that this behavior is due to the relative width of the C- and S-complexes and not tothe position of the X-complex itself.The errors reported in Table 4 were obtained by taking the standard deviation of each complex/typefrom the set of 12 best matches from the MC simulation described in previous subsection.The Gaussian fit is not as robust as the MC analysis for obtaining the results, therefore we canexpect lower accuracy. Having a fit centered on the C and S taxonomic components, the ratio ofthe area under the corresponding Gaussians is directly related to the compositional fraction of thesample. The fraction of S-type elements obtained through a Gaussian fit is more reliable than theC-type one. For this reason, from the fit we focus on the S-type fraction obtained: 48%, which withinthe error bars is compatible with our MC result.Although in our simulations we allowed for a wide range of variation in the randomly generatedsample, our results partially rely on the assumptions described in Section 4.6. CONCLUSIONS AND FUTURE OUTLOOK8With the use of spectrophotometry on a 1.5 m robotic telescope, we performed rapid-responseobservations of small Near Earth Objects. Here we present the results from our optical sample.Measurements were simultaneously made in the r and i band. After applying selection criteria, oursample consisted on 131 observations of 82 different NEOs within the size range of ∼ / S = 1 .
06. Together, these two asteroid types represent ∼
90% of our sample, with the restlikely to be Q- and X-type asteroids. This compositional fraction is in agreement with the results ofour previous publications (Mommert et al. 2016; Erasmus et al. 2017) which are based on UKIRTand KMTNet-SAAO observations.Observations from our program are ongoing. The facility used in this study is now observing withthe
Z, Y, J and H near infrared bands in addition to the optical r and i . By analyzing the dataset presented here, we created the tools to analyze the observations from the rest of the campaign(2016-ongoing). Future publications from this study will include observations from multiple photo-metric bands, which will improve the accuracy of the results. ACKNOWLEDGMENTSWe would like to thank Carlos Roman for his help on scheduling RATIR ' s observations. We thankthe anonymous referee for their valuable comments on this work. SNM wants to dedicate this paperto coauthor, professor and friend B´arbara Pichardo, RIP.The data used in this paper were totally or partially acquired using the RATIR instrument, fundedby the University of California (UC) and NASA Goddard Space Flight Center (GSFC), on the 1.5meter telescope at Observatorio Astron´omico Nacional, San Pedro Martir, operated and maintainedby OAN-SPM and IA-UNAM. This project was supported in part by the National Aeronautics andSpace Administration under the Grant No.NNX15AE90G issued through the SSO Near Earth Object9Observations Program. SNM also acknowledges the grant UNAM- DGAPA PAPIIT IN107316.REFERENCES Becerra, R. L., Watson, A. M., Lee, W. H., et al.2017, ApJ, 837, 116Binzel, R. P., Reddy, V., & Dunn, T. L. 2015,Asteroids IV, 243R.P. Binzel and F.E. DeMeo and S.J. Bus and A.Tokunaga and T.H. Burbine and C. Lantz andD. Polishook and B. Carry and A. Morbidelliand M. Birlan and P. Vernazza and B.J. Burtand N. Moskovitz and S.M. Slivan and C.A.Thomas and A.S. Rivkin and M.D. Hicks andT. Dunn and V. Reddy and J.A. Sanchez andM. Granvik and T. Kohout 2018, IcarusBrown, P. G., Assink, J. D., Astiz, L., et al. 2013,Nature, 503, 238Butler, N., Klein, C., Fox, O., et al. 2012,Proc. SPIE, 8446, 844610Butler, N., Watson, A. M., Kutyrev, A., et al.2017, GRB Coordinates Network, CircularService, No. 21915, McAdam, M. M., Sunshine, J. M., Howard, K. T.,et al. 2018, Lunar and Planetary ScienceConference, 49, 2081Mommert, M., Trilling, D. E., Borth, D., et al.2016, AJ, 151, 98Moskovitz, N., Thirouin, A., Binzel, R., et al.2015, IAU General Assembly, 22, 2255616Popescu, M., Perna, D., Barucci, M. A., et al.2018, MNRAS, 477, 2786Ricci, D., Ram´on-Fox, F. G., Ayala-Loera, C., etal. 2015, PASP, 127, 143Stuart, J. S., & Binzel, R. P. 2004, Icarus, 170, 295Perna, D., Barucci, M. A., Fulchignoni, M., et al.2018, Planet. Space Sci., 157, 82 Ryan, E. L., Mizuno, D. R., Shenoy, S. S., et al.2015, A&A, 578, A42Tapia, M., Rodr´ıguez, L. F., Tovmassian, G., etal. 2014, RMxAA, 50, 127Taylor, John R. 1997, An introduction to erroranalysis, 2nd Ed, p. 176Thomas, C. A., Trilling, D. E., Emery, J. P., et al.2011, AJ, 142, 85Thomas, C. A., Emery, J. P., Trilling, D. E., et al.2014, Icarus, 228, 217Watson, A. M., Richer, M. G., Bloom, J. S., et al.2012, Proc. SPIE, 8444, 84445LWarner, B. D., Harris, A. W., & Pravec, P. 2009,Icarus, 202, 134 ll Authors and Affiliations
S. Navarro-Meza,
1, 2
M. Mommert,
3, 2
D.E. Trilling, N. Butler,
4, 5
M. Reyes-Ruiz, B. Pichardo, T. Axelrod, R. Jedicke, and N. Moskovitz Instituto de Astronom´ıa, Universidad Nacional Aut´onoma de M´exico, Ensenada B.C. 22860, M´exico. Department of Physics and Astronomy, Northern Arizona University, Flagstaff, AZ 86001, USA Lowell Observatory, Flagstaff, AZ 86001, USA School of Earth and Space exploration, Arizona State University, Tempe, AZ 85287, USA Cosmology Initiative, Arizona State University, Tempe, AZ 85287, USA Instituto de Astronom´ıa, Universidad Nacional Aut´onoma de M´exico, Ciudad Universitaria, D.F. 04510, M´exico. Steward Observatory, University of Arizona, Tucson, AZ 85721, USA8