A Search for Subkilometer-sized Ordinary Chondrite Like Asteroids in the Main-Belt

A Search for Subkilometer-sized Ordinary Chondrite Like Asteroids in the Main-Belt

H. W. Lin Fumi Yoshida Y. T. Chen W. H. Ip C. K. Chang Institute of Astronomy, National Central University, Taoyuan 32001, Taiwan National Astronomical Observatory of Japan, 2-21-1 Osawa, Mitaka, Tokyo 181-8588, JAPAN Institute of Astronomy and Astrophysics, Academia Sinica, P. O. Box 23-141, Taipei 106, Taiwan Space Science Institute, Macau University of Science and Technology, Taipa, Macau
Abstract

The size-dependent effects of asteroids on surface regolith and collisional lifetimes suggest that small asteroids are younger than large asteroids. In this study, we performed multicolor main-belt asteroid (MBA) survey by Subaru telescope/Suprime-Cam to search for subkilometer-sized ordinary chondrite (Q-type) like MBAs. The total survey area was 1.5 deg near ecliptic plane and close to the opposition. We detected 150 MBAs with 4 bands (, , , ) in this survey. The range of absolute magnitude of detected asteroids was between 13 and 22 magnitude, which is equivalent to the size range of kilometer to sub-kilometer diameter in MBAs.

From this observation, 75 of 150 MBAs with color uncertainty less than 0.1 were used in the spectral type analysis, and two possible Q-type asteroids were detected. This mean that the Q-type to S-type ratio in MBAs is 0.05. Meanwhile, the Q/S ratio in near Earth asteroids (NEAs) has been estimated to be 0.5 to 2 (Binzel et al., 2004; Dandy et al., 2003). Therefore, Q-type NEAs might be delivered from the main belt region with weathered, S-type surface into near Earth region and then obtain their Q-type, non-weathered surface after undergoing re-surfacing process there. The resurfacing mechanisms could be: 1. dispersal of surface material by tidal effect during planetary encounters (Binzel et al., 2010; Nesvorný et al., 2010), 2. the YORP spin-up induced rotational-fission (Polishook et al., 2014) or surface re-arrangement, or 3. thermal degradation (Delbo et al., 2014).

keywords:
Asteroids, surfaces, Asteroids, composition, Asteroids, Regoliths
journal: Icarus

1 Introduction

The taxonomic type of asteroid has been studied extensively to understand the mineral composition of asteroids. It is mostly based on the asteroid’s colors and spectra in optical wavelength. Numerous types (such as S, C, D, B and V) have been identified (Bowell et al., 1978; Tholen, 1984; Zellner et al., 1985; Bus and Binzel, 2002a, b; DeMeo et al., 2009; DeMeo and Carry, 2013, 2014). Space weathering effects and related color-spectrum correlations for the main-belt asteroids (MBAs) and near-Earth asteroids (NEAs) have also been studied (Chapman, 1996; Binzel et al., 2001; Chapman, 2004; Clark et al., 2001; Jedicke et al., 2004; Nesvorný et al., 2005; Willman et al., 2008, 2010; Willman and Jedicke, 2011; Thomas et al., 2012). These studies have been primarily based on relatively larger asteroids; only few studies done for kilometer to sub-kilometer asteroids because of the requirement of large telescopes to determine their colors or spectra, have been conducted.

Asteroids with sizes below the kilometer range are most likely collisional fragments of large asteroids (Davis et al., 2002; Morbidelli et al., 2009). Therefore, their surfaces should have lower degree of space weathering compared with larger asteroids, which have survived throughout the history of the solar system (Binzel et al., 2001, 2004; Bus and Binzel, 2002b). Some small, several hundred meter sized NEAs observed in detail while during close approach to the Earth, showed Q-type spectra which are similar to those of the ordinary chondrite (OC) with low degree of space weathering (Tholen, 1984). Researchers also reported that a spectral transition could occur between S-type and Q-type asteroids (Binzel et al., 1996, 2004; Dandy et al., 2003). These results indicated that S-type asteroids are likely Q-type asteroids, with their surface materials originally characterized by OC-like spectra, but modified by space weathering to the present-day darker and redder spectra. Laboratory experiments (Sasaki et al., 2001; Brunetto et al., 2006)) and observations conducted by the NEAR and Hayabusa space missions (Clark et al., 2002; Ishiguro et al., 2007) ) supported this theory.

A large number of Q-type asteroids have been detected in the near-Earth region (Binzel et al., 2001; Dandy et al., 2003; Stuart and Binzel, 2004; DeMeo and Carry, 2013), the ratio of Q/S in NEAs is 0.5 to 2. If Q-type NEAs were produced by collisions, we should also detect Q-type MBAs because the collisional rate in main-belt is higher than that in near-Earth region. While, Q-type asteroids were missing in the main-belt in the earlier studies (Bus and Binzel, 2002a, b; Lazzaro et al., 2004), more recent observations have detected several Q-type MBAs in the extremely young asteroid family “Datura dynamical cluster” (Mothé-Diniz and Nesvorný, 2008) and the older Koronis family (Rivkin et al., 2011; Thomas et al., 2011). Carvano et al. (2010) classed 3296 of 62576 asteroids as Q-type-like objects in SDSS Moving Object Catalog (SDSSMOC4). Polishook et al. (2014) also detect two Q-type asteroids, (19289) 1996 HY12 and (54827) 2001 NQ8, in the unbound asteroid pairs. These results show that Q-type taxonomy is not limited to the NEA population. However, the abundance of Q-type asteroids in the main-belt is still low comparing with that in the near-Earth region. A simple explanation for this low ratio of Q/S in MBAs is that the survey of small MBAs is incomplete, many of Q-type MBAs might be discovered if the observations are able to detect the sub-kilometer-sized MBAs.

The collisional formation model of Q-type NEAs (hereafter, “standard model”) could be challenged by the rapid process of space weathering effect with solar wind implantation (Hapke, 2001; Vernazza et al., 2009), which timescale could be as short as to years. Two arguments have been presented. First, kilometer-sized or large asteroids with collisional lifetimes exceeding years (Bottke et al., 1993, 1994) should not display Q-type spectra under long-term space weathering effect. However, the existence of kilometer-sized Q-type NEAs, such as (1862) Apollo (Stuart and Binzel, 2004), contradicts the prediction of the “standard model”. Second, the high collisional rate in the main-belt region can produce asteroids with fresh surfaces more efficiently. On the other hand, the time scale of transport processes, such as the Yarkovsky effect and small resonances, that insert collisional fragments into the planet-crossing space also exceeds years (Rabinowitz, 1997; Morbidelli and Vokrouhlický, 2003; Migliorini et al., 1998; Bottke et al., 2002; Binzel et al., 2004). Therefore, Q-type NEAs should not be present if they were primarily transferred from the main-belt with a Q-type spectra. This contradicts the observations made in near-Earth space.

An alternative scenario involves a possibility that the surfaces of Q-type NEAs have been reset during planetary encounters, from which the surface materials were removed (Nesvorný et al., 2005) or re-arranged (Binzel et al., 2010) by tidal effect. This hypothesis has been tested by several theoretical and observational studies. For example, Marchi et al. (2006) determined that the spectral slope of Q-type asteroids is correlated with planet-crossing frequency. Binzel et al. (2010) and Nesvorný et al. (2010) suggested that the Q-type NEAs have experienced encounters with the Earth, Venus and then the tidal forces from these terrestrial planets could refresh the asteroidal surfaces. DeMeo et al. (2014) proposed the possibility that this mechanism might also be valid for Mars. As a corollary, the planetary encounter models predicts that Q-type asteroids are rare among MBAs because of the low planetary encounter rate in the main-belt.

Nevertheless, the timescale of space weathering on asteroid surface is still in debate. Willman and Jedicke (2011) studied 95 asteroids for which span a size and age range of about 1-20 km and 100-3000 Myr, respectively, and measured a space weathering time of years. This is much longer than the result of fast space weathering (Hapke, 2001; Vernazza et al., 2009). Polishook et al. (2014) also detected a Q-type asteroid in main-belt with age years indicating that the space weathering timescale should be no less than years.

The other mechanisms to create Q-type asteroids are correlated with fast rotation and YORP effect: 1. rotational-fission results in the exposure of material from the covered surface of parent asteroid (Polishook et al., 2014), and 2. rotational re-arrangement of asteroid surface material via landslips (Scheeres, 2015; Walsh et al., 2012) and partial removal of weathered regolith. These two mechanisms are able to uncover non-weathered materials and display the fresh Q-type spectra. Since the rotation of the smaller astroids are easier to be accelerated by YORP effect, we expect to detect more small size Q-type MBAs if rotational effects are the dominant mechanism of the Q-type asteroid formation.

Delbo et al. (2014) reported recently that thermal degradation induced by diurnal temperature variation is able to break up rocks on the asteroid surface rapidly into new regolith layer. They also suggested that asteroids with large diurnal temperature difference (i.e., NEAs) can be cover by fresh regolith characterized by the Q-type spectra. This scenario predicts that more Q-type asteroids should be detected in near Earth space than in main-belt because of the larger diurnal temperature variation of NEAs. Note that the regolith formation by thermal fragmentation does not depend on asteroid size; it may also imply that there is no color-size relation in the NEA population.

From the discussion above, the multicolor observation of kilometer to sub-kilometer diameter MBAs becomes critical to understand the space weathering on S-complex asteroid surface and the formation of Q-type asteroids. We should detect a comparable or even higher fraction of Q-type asteroids in the main-belt than the near-Earth region, if the space weathering timescale is years, and the collisional “standard model” dominate the formation of Q-type asteroids. By contrast, if the Q-type asteroid fraction in the main-belt is very low, the Q-type NEAs must form in-situ and other mechanism like the planetary encounter models, rotational-fission/re-arrangement or thermal degradation should be responsible of the formation of Q-type NEAs.

2 Observations and Data Reduction

To find sub-kilometer asteroids in the main-belt, we used the data taken by Subaru telescope with Suprime-Cam, which is a prime focus camera with a wide field of view (34’ x 27’) that consists of 10 CCD chips (Miyazaki et al., 2002). The observational dates were August 9 and 10, 2004 (UT).

Three fields were surveyed each night for approximately 3.5 hours from the midnight of Hawaii. The seeing size was 0.54-0.70 arcsecond on the first night and 0.77-1.06 arcsecond on the second night. The observational fields were near opposition and close to the ecliptic plane. The center of the coordinates of each observed field is listed in Table 1.

The images were obtained using four broadband filters: , , and . The exposure times were 120 sec for the -, - and -bands and 180 sec for the -band. The observations followed the color sequence ----- for each fields. The time interval of the first -band set and the second -band set was approximately 80 min. The interval between the second -band set and the third -band set was approximately 60 min. We used this three sets of -band observations to interpolate the R magnitude in the epoch of and -band observations to avoid possible color uncertainty due to the asteroid rotational effect. Detailed description of photometric calibration can be found in Sections 2.2 and 2.3 in detail.

Aug. 09, 2004
Field ID RA DEC
F1-1 21:18:24 -15:11:00 317.306 0.488
F2-1 21:18:24 -15:41:00 317.154 0.011
F3-1 21:18:24 -16:11:00 317.003 -0.465
Aug. 10, 2004
Field ID RA DEC
F1-2 21:22:12 -14:54:00 318.266 0.478
F2-2 21:22:12 -15:24:00 318.112 0.002
F3-2 21:22:12 -15:54:00 317.959 -0.474
Table 1: Coordinates of the surveyed fields

2.1 Detection of Moving Objects

To detect moving objects in relatively crowded fields, we first stacked all 12 exposures in each field to obtain deep images. We then used these deep images as the source images to generate the reference stationary catalogs and remove all stationary sources in every exposure.

After removing the stationary sources, we used the KDTree-based nearest neighborhood search method to identify the detection pairs in every two consecutive exposures. The pairs detected in the first set of consecutive exposures were used to determine the main vectors for predicting the possible locations in the other five exposure pairs. We then searched for the corresponding pairs at the predicted locations of the other set of consecutive exposure. Once the entire set of six pairs (i.e., 12 detections in total) was identified, the complete set was passed to the code (Bernstein and Khushalani, 2000) to ensure that the orbital solution are reasonable; the semi-major axis was between 2 AU and 5 AU, and the fitting residual was smaller than 0.5”. Under these stringent conditions, all moving objects detected are real and complete color measurements were performed for all of them. The asteroid detection list is summarized in Table 2.

RA () DEC () Epoch (MJD) a (AU) i () H B B V V R R I I A A Comment a (AU) e i (
319.48272 -15.40419 53226.529043 2.84 2.31 18.103 22.561 0.014 21.690 0.002 21.277 0.011 20.926 0.008 0.088 0.011
319.39225 -15.22197 53226.529043 2.90 4.69 19.612 24.146 0.021 23.320 0.002 22.981 0.017 22.584 0.001 0.004 0.106
319.69678 -15.20883 53226.529043 3.21 0.03 18.980 23.970 0.025 23.231 0.037 22.980 0.038 22.661 0.001 -0.119 0.053
319.46102 -15.20154 53226.529043 3.09 16.65 19.088 23.911 0.008 23.141 0.003 22.749 0.017 22.246 0.016 0.002 0.034
319.46236 -15.19466 53226.529043 2.25 5.50 18.683 21.583 0.030 20.930 0.012 20.607 0.014 20.563 0.027 -0.130 0.024
319.58996 -15.18535 53226.529043 2.55 8.45 19.353 23.149 0.001 22.336 0.026 21.922 0.013 21.560 0.012 0.048 0.048
319.57579 -15.16933 53226.529043 2.84 9.71 18.900 23.027 0.012 22.493 0.006 21.859 0.012 21.519 0.023 0.006 0.020
319.38260 -15.16018 53226.529043 3.05 0.16 19.211 23.882 0.087 23.200 0.015 23.056 0.032 22.667 0.020 -0.236 0.140
319.34533 -15.16815 53226.529043 2.56 23.00 21.014 25.138 0.016 24.025 0.023 23.339 0.240 22.887 0.050 0.452 0.351
319.63049 -15.14830 53226.529043 2.92 1.07 20.022 24.513 0.255 23.774 0.046 23.602 0.048 23.087 0.125 -0.176 0.245
319.86432 -15.11508 53226.529043 2.53 11.95 15.351 19.177 0.002 18.279 0.003 17.823 0.003 17.423 0.009 0.138 0.003
319.37775 -15.09740 53226.529043 2.85 2.08 19.851 24.105 0.030 23.461 0.012 23.022 0.064 22.618 0.041 -0.054 0.050
319.82910 -15.09154 53226.529043 3.46 0.68 18.449 23.810 0.041 23.106 0.028 22.772 0.037 22.467 0.009 -0.086 0.044
319.58372 -15.09950 53226.529043 2.61 19.12 18.133 22.075 0.010 21.258 0.003 20.762 0.013 20.367 0.004 0.109 0.008
319.81048 -15.08243 53226.529043 2.99 13.25 19.227 23.837 0.042 23.096 0.028 22.738 0.049 22.321 0.026 -0.042 0.040
319.72990 -15.05428 53226.529043 2.91 0.46 19.240 23.795 0.052 22.967 0.004 22.727 0.051 22.365 0.019 -0.065 0.104
319.31365 -15.03409 53226.529043 2.71 7.15 19.777 23.905 0.011 23.108 0.006 22.726 0.015 22.375 0.057 0.014 0.045
319.86975 -15.03411 53226.529043 2.91 4.80 15.174 19.783 0.008 18.904 0.000 18.410 0.003 17.941 0.002 0.151 0.008
319.32668 -15.01941 53226.529043 2.92 1.91 17.177 21.680 0.006 20.918 0.002 20.463 0.007 20.018 0.020 0.041 0.006
319.70512 -14.98392 53226.529043 2.29 5.76 19.579 22.853 0.033 21.928 0.013 21.657 0.003 21.035 0.024 0.025 0.031
319.76720 -15.30467 53226.529043 3.28 10.14 17.388 22.444 0.001 21.760 0.002 21.409 0.008 21.071 0.003 -0.089 0.027
319.88038 -15.29547 53226.529043 2.41 2.13 19.033 22.554 0.020 21.687 0.012 21.228 0.008 20.831 0.008 0.118 0.019
319.74818 -15.28862 53226.529043 2.68 4.36 15.391 19.505 0.001 18.654 0.003 18.189 0.001 17.780 0.020 0.111 0.003 (62523) 2000 SW24 2.7 0.07 4.28
319.30847 -15.28169 53226.529043 3.16 10.69 18.476 23.424 0.028 22.650 0.021 22.377 0.022 21.998 0.011 -0.080 0.041
319.86194 -15.28194 53226.529043 2.97 8.94 19.373 23.631 0.085 23.205 0.163 22.552 0.029 22.227 0.050 -0.057 0.208
319.71990 -15.27244 53226.529043 3.03 14.48 20.092 25.335 0.035 24.039 0.074 23.739 0.039 23.551 0.052 0.308 0.075
319.35283 -15.27298 53226.529043 2.72 4.47 20.254 24.188 0.004 23.599 0.053 23.245 0.020 22.988 0.002 -0.153 0.064
319.83410 -15.23152 53226.529043 3.01 9.89 17.812 22.470 0.004 21.713 0.015 21.393 0.016 21.670 0.434 -0.058 0.025
319.62572 -15.22084 53226.529043 2.91 1.49 13.441 17.950 0.005 17.165 0.011 16.909 0.039 16.808 0.028 -0.084 0.018
319.69906 -15.22543 53226.529043 3.06 0.96 19.460 24.116 0.056 23.453 0.063 23.019 0.036 22.602 0.004 -0.045 0.067
320.70343 -15.12162 53227.533671 2.54 0.60 19.229 23.109 0.009 22.184 0.009 21.719 0.019 21.398 0.002 0.163 0.035
320.65551 -15.05483 53227.533671 2.99 1.51 16.549 21.252 0.001 20.414 0.004 19.955 0.004 19.528 0.005 0.097 0.004
320.68576 -15.01347 53227.533671 2.88 3.55 18.366 22.788 0.006 22.040 0.021 21.655 0.020 21.333 0.004 -0.019 0.016
320.59647 -15.00993 53227.533671 3.03 10.02 19.492 24.327 0.030 23.437 0.034 23.172 0.025 22.874 0.016 -0.003 0.047
320.33657 -14.97422 53227.533671 3.04 2.47 17.160 22.045 0.004 21.123 0.012 20.678 0.007 20.248 0.002 0.146 0.015 (252718) 2002 CQ194 3.01 0.08 3.47
320.66292 -14.89674 53227.533671 3.05 0.55 19.167 24.113 0.025 23.148 0.110 22.830 0.077 22.386 0.042 0.087 0.092
320.44262 -14.85440 53227.533671 2.64 3.27 19.728 24.209 0.063 22.907 0.191 22.512 0.049 22.306 0.037 0.380 0.220
320.58374 -14.84279 53227.533671 3.12 0.43 16.584 21.393 0.009 20.680 0.009 20.331 0.005 19.975 0.001 -0.069 0.016
320.26807 -14.82940 53227.533671 2.88 2.04 16.242 20.761 0.006 19.912 0.001 19.504 0.005 19.183 0.003 0.069 0.015 Q-type candidate
320.54242 -14.80967 53227.533671 2.94 9.75 19.503 23.711 0.160 23.289 0.049 22.955 0.029 22.512 0.023 -0.285 0.152
320.52186 -14.78980 53227.533671 3.11 2.37 18.405 23.366 0.013 22.495 0.016 21.906 0.078 21.411 0.022 0.213 0.031
319.51576 -15.68548 53226.534619 2.50 9.54 20.173 23.905 0.032 23.036 0.001 22.675 0.011 22.290 0.010 0.050 0.033
319.85629 -15.67499 53226.534619 2.57 6.24 20.294 24.496 0.009 23.330 0.062 23.168 0.013 22.646 0.090 0.119 0.062
319.75825 -15.67583 53226.534619 2.31 0.80 21.302 24.414 0.004 23.709 0.069 23.215 0.022 22.703 0.048 0.028 0.108
319.67486 -15.66787 53226.534619 2.14 1.03 22.288 24.940 0.189 24.237 0.004 23.481 0.063 23.408 0.000 0.212 0.158
319.67821 -15.66154 53226.534619 3.23 2.79 19.251 23.904 0.309 23.531 0.024 23.224 0.036 22.888 0.035 -0.339 0.221
319.38817 -15.64510 53226.534619 2.68 8.59 20.630 24.276 0.162 23.901 0.102 23.324 0.039 23.055 0.008 -0.146 0.141
319.50101 -15.63361 53226.534619 2.41 3.41 14.861 18.618 0.007 17.524 0.012 17.207 0.014 16.954 0.012 0.178 0.013
319.70150 -15.63029 53226.534619 2.19 7.19 16.856 19.749 0.004 18.932 0.003 18.346 0.043 18.092 0.003 0.172 0.005 (204290) 2004 PV21 2.17 0.1 6.36
319.72054 -15.60861 53226.534619 2.60 3.43 17.202 21.007 0.002 20.289 0.006 19.983 0.006 19.638 0.000 -0.095 0.005
319.36405 -15.57624 53226.534619 2.92 7.74 18.437 22.750 0.010 22.180 0.111 21.635 0.008 21.247 0.008 -0.031 0.106
319.30469 -15.51043 53226.534619 2.93 1.91 19.062 23.533 0.026 22.831 0.012 22.508 0.013 22.208 0.022 -0.095 0.063
319.30965 -15.50791 53226.534619 2.52 3.71 21.024 24.562 0.079 23.941 0.050 23.454 0.096 23.684 0.008 -0.037 0.143
319.36096 -15.50186 53226.534619 2.54 17.38 19.236 22.934 0.044 22.198 0.017 21.540 0.014 21.088 0.000 0.166 0.040
319.54940 -15.87029 53226.534619 2.43 6.49 19.608 23.105 0.043 22.312 0.003 21.859 0.025 21.406 0.009 0.062 0.034
319.35954 -15.87175 53226.534619 2.69 0.02 20.663 24.784 0.009 23.956 0.019 23.692 0.048 23.171 0.112 -0.048 0.022
319.60794 -15.85584 53226.534619 2.61 14.67 20.238 24.104 0.094 23.357 0.063 22.864 0.014 22.486 0.017 0.057 0.101
319.84755 -15.86667 53226.534619 3.00 13.01 18.785 23.621 0.263 22.670 0.008 22.254 0.023 21.901 0.009 0.147 0.187
319.80565 -15.84336 53226.534619 3.13 8.43 15.163 20.077 0.000 19.285 0.011 18.832 0.007 18.504 0.002 0.061 0.012
319.74746 -15.84407 53226.534619 2.65 0.94 19.940 23.945 0.002 23.142 0.029 22.692 0.020 22.297 0.038 0.066 0.027
319.49048 -15.83221 53226.534619 2.84 2.87 17.144 21.536 0.010 20.732 0.007 20.299 0.004 19.942 0.002 0.055 0.009
319.61032 -15.82195 53226.534619 2.64 2.77 20.579 24.493 0.038 23.763 0.031 23.312 0.033 22.931 0.013 0.015 0.060
319.46590 -15.82367 53226.534619 3.11 1.35 17.336 21.778 0.003 21.417 0.001 20.367 0.399 20.501 0.008 0.177 0.009
319.70470 -15.80420 53226.534619 2.43 6.59 20.853 24.404 0.020 23.553 0.026 23.061 0.040 22.749 0.013 0.130 0.029
319.47202 -15.79704 53226.534619 2.77 5.62 20.608 24.561 0.061 24.058 0.024 23.762 0.068 23.680 0.044 -0.255 0.061
319.59842 -15.79135 53226.534619 2.77 3.68 19.621 23.884 0.015 23.078 0.008 22.683 0.032 22.294 0.047 0.030 0.048
319.61758 -15.79291 53226.534619 2.23 4.60 20.205 22.574 0.211 22.403 0.213 21.716 0.010 21.393 0.017 -0.213 0.232
319.45546 -15.78328 53226.534619 2.49 4.66 17.988 21.554 0.000 20.831 0.004 20.460 0.005 20.094 0.001 -0.047 0.005
319.75107 -15.77375 53226.534619 2.71 3.71 20.252 24.560 0.019 23.586 0.039 23.325 0.037 22.823 0.042 0.053 0.048
319.71019 -15.75217 53226.534619 2.47 1.68 19.898 23.581 0.031 22.691 0.014 22.219 0.011 21.775 0.044 0.143 0.042
319.39739 -15.74895 53226.534619 2.77 6.53 18.324 22.572 0.030 21.779 0.007 21.291 0.007 20.898 0.001 0.086 0.022
319.43563 -15.73506 53226.534619 2.64 1.59 20.248 24.317 0.005 23.435 0.014 23.026 0.017 22.388 0.156 0.093 0.037
319.35384 -15.72188 53226.534619 2.80 5.80 18.519 22.810 0.017 22.026 0.005 21.627 0.028 21.333 0.010 0.017 0.013
320.42609 -15.57531 53227.539246 2.22 3.42 15.012 17.950 0.005 17.171 0.005 16.604 0.007 16.435 0.037 0.132 0.008 (6919) Tomonaga 2.26 0.1 5.16
320.79772 -15.55019 53227.539246 2.72 4.30 18.238 22.254 0.019 21.593 0.014 21.240 0.014 20.890 0.024 -0.103 0.024
320.71232 -15.53839 53227.539246 3.04 2.51 18.195 22.782 0.007 22.164 0.023 21.677 0.063 21.371 0.003 -0.039 0.029
320.82430 -15.53347 53227.539246 2.54 3.91 19.103 22.670 0.042 22.071 0.034 21.274 0.062 20.832 0.022 0.167 0.085
320.32744 -15.53627 53227.539246 2.28 3.97 17.616 20.842 0.008 19.942 0.017 19.459 0.004 19.066 0.003 0.158 0.014
320.33516 -15.52610 53227.539246 2.38 3.91 18.111 21.565 0.002 20.702 0.018 20.258 0.005 19.823 0.014 0.104 0.013
320.67588 -15.49924 53227.539246 3.16 10.05 18.341 23.253 0.030 22.519 0.004 22.227 0.004 21.915 0.009 -0.094 0.034
320.41969 -15.47944 53227.539246 2.37 7.19 20.047 23.933 0.117 22.608 0.009 22.424 0.060 22.051 0.018 0.247 0.091
320.58908 -15.46737 53227.539246 3.30 4.38 15.615 20.736 0.013 20.020 0.001 19.653 0.023 19.338 0.013 -0.054 0.009
320.28343 -15.45079 53227.539246 2.72 5.32 17.285 21.499 0.001 20.642 0.010 20.278 0.007 19.797 0.055 0.043 0.010
320.80845 -15.38456 53227.539246 3.00 7.79 15.556 20.261 0.008 19.456 0.002 19.141 0.005 18.844 0.005 -0.028 0.006
320.49664 -15.38502 53227.539246 2.89 2.26 19.593 24.077 0.132 23.271 0.006 22.923 0.216 22.194 0.003 -0.004 0.099
320.63919 -15.37706 53227.539246 3.30 14.74 17.682 23.284 0.057 22.088 0.092 22.118 0.010 21.781 0.005 0.004 0.090
320.63703 -15.38200 53227.539246 2.57 10.28 18.101 22.082 0.130 21.137 0.001 20.780 0.011 20.310 0.012 0.100 0.093
320.54423 -15.37073 53227.539246 2.68 6.37 19.424 23.435 0.044 22.698 0.013 22.313 0.014 21.963 0.012 -0.027 0.083
320.32559 -15.33817 53227.539246 3.05 1.41 17.527 22.273 0.004 21.516 0.019 21.192 0.005 20.675 0.000 -0.055 0.014
320.76977 -15.30567 53227.539246 3.02 0.90 17.848 22.515 0.017 21.767 0.024 21.427 0.007 21.112 0.009 -0.051 0.024
320.70791 -15.28156 53227.539246 2.34 1.87 18.318 21.534 0.002 20.805 0.001 20.412 0.006 20.038 0.007 -0.027 0.005 (2014) AR8 2.4 0.14 1.72
320.45096 -15.27708 53227.539246 2.24 1.83 17.172 20.377 0.005 19.389 0.008 18.891 0.010 18.554 0.021 0.231 0.009 (151733) 2003 BA88 2.32 0.15 2.64
320.64892 -15.22799 53227.539246 2.45 2.77 19.498 23.051 0.010 22.241 0.035 21.872 0.023 21.580 0.041 0.014 0.030
320.63783 -15.20756 53227.539246 2.72 0.08 18.807 22.916 0.029 22.153 0.025 21.774 0.014 21.434 0.021 -0.012 0.037
319.35421 -16.19792 53226.540177 3.11 0.65 18.054 22.743 0.020 22.135 0.010 21.703 0.009 21.590 0.001 -0.084 0.024
319.60419 -16.39941 53226.540177 2.42 4.00 20.306 23.827 0.051 22.981 0.184 22.668 0.397 22.918 0.070 0.000 0.173
319.34255 -16.38858 53226.540177 3.78 13.11 17.136 23.051 0.021 22.249 0.008 21.799 0.021 21.476 0.024 0.065 0.021 Q-type candidate
319.62069 -16.37934 53226.540177 2.82 9.67 18.962 23.206 0.054 22.507 0.026 22.084 0.015 21.272 0.299 -0.027 0.047
319.33731 -16.17518 53226.540177 2.84 2.81 20.090 24.511 0.038 23.689 0.048 23.318 0.080 23.047 0.076 0.024 0.098
319.57251 -16.37746 53226.540177 2.62 2.94 18.422 22.469 0.004 21.555 0.006 21.091 0.008 20.694 0.008 0.155 0.015
319.86114 -16.36801 53226.540177 2.35 1.14 20.808 24.117 0.028 23.307 0.025 22.627 0.025 22.147 0.018 0.234 0.047
319.64018 -16.13018 53226.540177 2.98 12.47 18.580 23.257 0.085 22.428 0.008 22.049 0.007 21.657 0.002 0.035 0.061
319.54882 -16.12899 53226.540177 2.77 6.70 19.475 23.585 0.022 22.919 0.019 22.515 0.041 22.737 0.081 -0.064 0.036
319.32721 -16.11899 53226.540177 2.95 15.29 16.878 21.484 0.003 20.680 0.007 20.161 0.011 19.713 0.002 0.115 0.014
319.60643 -16.12420 53226.540177 2.59 3.05 18.688 22.621 0.009 21.759 0.003 21.339 0.008 20.964 0.009 0.087 0.014
319.82640 -16.10238 53226.540177 2.59 3.40 20.109 23.909 0.049 23.185 0.051 22.704 0.034 22.295 0.010 0.032 0.064
319.51692 -16.09192 53226.540177 3.02 7.10 18.453 23.231 0.004 22.387 0.012 21.858 0.017 21.456 0.011 0.150 0.025
319.83680 -16.07527 53226.540177 2.35 2.16 19.252 22.467 0.011 21.753 0.005 21.402 0.014 21.058 0.002 -0.067 0.011
319.76208 -16.06889 53226.540177 2.96 11.26 18.247 22.939 0.010 22.072 0.096 21.766 0.015 21.404 0.007 0.009 0.103
319.72250 -16.06501 53226.540177 2.67 7.38 18.203 22.303 0.007 21.451 0.013 21.008 0.007 20.626 0.008 0.096 0.019
319.36741 -16.05471 53226.540177 3.06 7.98 18.246 23.006 0.009 22.250 0.034 21.893 0.009 21.517 0.008 -0.033 0.067
319.47395 -16.04208 53226.540177 3.07 8.63 19.673 24.456 0.005 23.684 0.012 23.343 0.016 22.974 0.008 -0.033 0.055
319.85396 -16.35700 53226.540177 2.91 1.61 18.683 23.172 0.046 22.411 0.039 22.125 0.032 21.742 0.005 -0.080 0.046
319.72944 -16.02779 53226.540177 2.52 6.36 19.079 22.897 0.021 22.000 0.007 21.660 0.026 21.253 0.010 0.055 0.024
319.73087 -16.35587 53226.540177 2.75 1.16 16.955 21.061 0.009 20.376 0.012 19.827 0.005 19.377 0.020 0.052 0.014
319.76130 -16.02214 53226.540177 2.68 1.49 20.524 24.626 0.030 23.783 0.031 23.335 0.025 23.170 0.004 0.093 0.108
319.58537 -16.01515 53226.540177 2.65 1.79 20.121 24.249 0.022 23.332 0.076 22.790 0.057 22.347 0.099 0.212 0.083
319.61491 -16.00706 53226.540177 2.75 4.22 19.611 23.959 0.006 23.030 0.025 22.592 0.022 22.195 0.011 0.147 0.021
319.43173 -16.00280 53226.540177 3.02 0.46 13.083 17.621 0.007 17.015 0.005 16.939 0.030 16.792 0.008 -0.338 0.007
319.72263 -16.35138 53226.540177 2.98 5.89 19.868 24.295 0.106 23.729 0.042 23.196 0.029 22.892 0.087 -0.043 0.107
319.62979 -15.96643 53226.540177 2.81 2.03 17.485 21.699 0.010 21.014 0.007 20.651 0.617 20.661 0.320 -0.079 0.014
319.51548 -15.97303 53226.540177 2.39 6.87 17.151 20.531 0.005 19.769 0.002 19.490 0.010 19.097 0.002 -0.083 0.004
319.69070 -15.97569 53226.540177 3.02 9.71 14.657 19.295 0.004 18.576 0.005 18.222 0.006 17.868 0.002 -0.061 0.005
319.45615 -16.33313 53226.540177 2.99 12.99 18.454 23.144 0.004 22.319 0.009 21.933 0.025 21.498 0.031 0.036 0.015
319.69838 -16.32601 53226.540177 2.51 0.48 20.177 24.522 0.018 23.069 0.406 23.014 0.050 22.693 0.037 0.247 0.303
319.69109 -16.28867 53226.540177 2.63 6.04 20.354 23.898 0.198 23.519 0.050 23.163 0.021 22.787 0.005 -0.300 0.147
319.85657 -16.27948 53226.540177 3.12 0.50 19.148 23.844 0.026 23.243 0.003 22.847 0.027 22.483 0.043 -0.115 0.024
319.85490 -16.26903 53226.540177 2.68 2.55 20.756 24.994 0.056 24.023 0.117 23.626 0.089 23.131 0.099 0.147 0.167
319.56316 -16.23162 53226.540177 3.22 4.24 15.270 20.221 0.006 19.547 0.020 19.088 0.012 18.382 0.013 -0.019 0.021
319.42440 -16.20991 53226.540177 2.96 0.96 20.773 25.443 0.034 24.592 0.056 24.029 0.040 23.412 0.061 0.179 0.079
320.79963 -16.11936 53227.544813 2.99 1.87 18.126 22.710 0.008 21.997 0.018 21.638 0.034 21.361 0.009 -0.062 0.041
320.56040 -16.08520 53227.544813 2.04 5.53 21.185 23.541 0.010 22.824 0.023 22.194 0.017 21.742 0.022 0.132 0.024
320.64800 -16.03000 53227.544813 2.87 17.42 17.010 21.444 0.009 20.651 0.006 20.265 0.005 19.901 0.006 0.014 0.009
320.27458 -16.02996 53227.544813 3.05 7.99 17.404 22.289 0.046 21.376 0.014 20.940 0.011 20.564 0.024 0.134 0.035
320.40652 -16.01986 53227.544813 2.29 12.74 20.260 23.424 0.047 22.600 0.020 22.209 0.028 21.855 0.002 0.039 0.047
320.31635 -16.00107 53227.544813 2.25 0.53 19.489 22.591 0.019 21.726 0.000 21.300 0.008 20.938 0.004 0.093 0.026
320.82385 -15.98608 53227.544813 2.44 3.24 18.920 22.623 0.021 21.652 0.010 21.032 0.009 20.621 0.007 0.305 0.021
320.71048 -15.93982 53227.544813 2.64 4.53 19.094 23.258 0.031 22.283 0.004 21.818 0.010 21.453 0.019 0.198 0.028
320.65166 -15.91541 53227.544813 2.33 7.10 20.093 23.306 0.004 22.550 0.007 22.065 0.029 21.109 0.511 0.057 0.006
320.62216 -15.91270 53227.544813 3.13 3.21 16.622 21.451 0.007 20.738 0.007 20.321 0.004 19.957 0.001 -0.021 0.008
320.39658 -15.87950 53227.544813 2.56 2.40 19.464 23.241 0.008 22.462 0.062 22.075 0.010 21.649 0.004 0.004 0.062
320.41451 -15.86789 53227.544813 2.72 3.93 18.944 22.866 0.126 22.304 0.055 21.900 0.047 21.499 0.038 -0.137 0.119
320.39999 -15.85829 53227.544813 3.10 0.75 18.993 23.920 0.041 23.057 0.044 22.648 0.020 22.590 0.149 0.079 0.048
320.70450 -15.85786 53227.544813 2.64 1.98 19.097 23.084 0.035 22.283 0.010 21.895 0.013 21.556 0.000 0.021 0.040
320.66966 -15.78510 53227.544813 3.22 1.12 15.826 20.814 0.018 20.095 0.006 19.707 0.004 19.393 0.004 -0.037 0.014
320.65956 -15.74312 53227.544813 2.91 24.42 17.230 21.705 0.018 20.951 0.000 20.661 0.006 20.222 0.001 -0.082 0.015
320.51081 -15.74918 53227.544813 2.69 6.83 19.273 23.438 0.014 22.559 0.000 22.276 0.032 21.796 0.000 0.002 0.018
320.65568 -15.73321 53227.544813 2.51 3.04 19.194 23.230 0.011 22.099 0.010 21.434 0.127 21.270 0.001 0.450 0.027
320.32995 -15.71095 53227.544813 3.08 12.77 18.356 23.137 0.015 22.386 0.037 22.007 0.007 21.630 0.004 -0.021 0.032
320.30033 -15.68513 53227.544813 3.15 10.08 18.531 23.528 0.019 22.691 0.000 22.247 0.010 21.592 0.191 0.086 0.030

Note. – Estimated by using Equation 6, 7,8 and 9 under assuming e=0. Note. – See Equation 13. Note. – Orbital elements of known asteroids are provided by JPL Small-Body Database.

Table 2: Asteroid list

2.2 Flux Calibration

The Suprime-Cam image data were calibrated chip by chip in every exposure by identifying Pan-STARRS 1 (hereafter PS1) catalogue stars in the observed field; the data were calibrated using “uber-calibration” (Magnier et al., 2013). Uber-calibration is an algorithm used to photometrically calibrate wide-field optical imaging surveys, and it was first applied to the Sloan Digital Sky Survey imaging data. It can be used to simultaneously solve for the calibration parameters and relative stellar fluxes through the use of overlapping observations (Padmanabhan et al., 2008). Those uber-calibrated catalogues have a relative precision (compared with the SDSS) of 10 mmag in , , and , and approximately 10 mmag in and (Schlafly et al., 2012). Since we used the , , , filters in our survey, we transferred those PS1 catalogue stars from the PS1 photometry system to our Johnson-Cousins system by using the transformation equation and parameters obtained by Tonry et al. (2012). The transformation error was approximately 0.03 in the -band and 0.01 to 0.02 in the -, -, -bands.

2.3 Trail Fitting

Two problems occur when using the traditional photometry methods for asteroid flux measurements: First, the flux would be contaminated by nearby stars if aperture photometry is used to measure the asteroid flux within crowded fields. Second, PSF fitting fails to yield accurate results if the asteroid image is not point-source-like object under long exposure. Therefore, we applied the trail fitting technique to measure the asteroid flux.

The trail function chosen is an axisymmetric Gaussian PSF-convolution trail function given in equation (3) of Vereš et al. (2012):

(1)

where

(2)

and

(3)
(4)

where is the background level, is the length of the trail, is the total integrated flux in the trail, is the standard deviation of the PSF Gaussian, and are the coordinates of the centroid of the trial. is the angle between the long axis of the trail and the  axis.

We used the Levenberg-Marquardt least-squares fitting technique to minimize the variance between the image and trail function. Figure 1 shows an example of an asteroid trail and its fitting residue. Clearly, the asteroid trail can be completely subtracted by using the trail function. The photometric error of the asteroid flux was estimated from the flux difference between two consecutive exposures of the asteroid; we considered the flux difference to be closer to the actual uncertainty compared with the estimation derived from the fitting result. We expect that the SNR of trail fitting photometry decreases with (/()). Thus the faster mover have larger photometry uncertainty. Fortunately, there is no systematic effect related to the trail length (See Vereš et al. (2012) for more detail), and the photometry results should be independent with the semi-major axis of asteroids.

Figure 1: An example of an asteroid trail in our sample before (top) and after (bottom) subtracting its fitting result (contour).

2.4 Detection Efficiency and De-biasing

For testing the detection efficiency of moving objects in the observations, we planted 500 non-trailing artificial stars with a brightness between 22.5 to 25.5 magnitude in each CCD chip. The artificial objects were generated by task by modeling the stars in each CCD chip in each exposure. The limiting magnitude also depends on the trailing rate of asteroids. Assuming that the moving rate of asteroids is about 0.01”/s in average. We expect that the trail length is around 1.2” in the 120s exposure. For the average 0.7” seeing size of our data, the SNR of the asteroid trail is roughly 60 of the non-trailing source with the same brightness. Therefore, we increased the detection threshold of artificial non-trailing stars to 5 sigma to simulate the limiting magnitude of 3 sigma asteroid detections.

We counted the number of detected artificial objects with a function of magnitude and plotted a diagram of magnitude vs. fractional detection as shown in Figure  2, and fitted a detection efficiency function, which was a function with double hyperbolic tangents (Petit et al., 2006), to the test result:

Figure 2: An example of fractional detection as a function of the R-magnitude. The best-fit detection efficiency function is illustrated.
(5)

Here, the fitted parameters A, R, and are the filling factor (or maximal efficiency), roll-over magnitude ( of the maximal efficiency), and widths of the two components, respectively. An exemplary result for the R-band, Chip2, took on August 10, 2004 was the detectability of approximately 23.7 magnitude, and the filling factor was approximately 83 (see Figure 2).

Using this detection efficiency function, we assigned a weight for each asteroid detection; the weight was the multiplicative inverse of the product of the detection efficiency of every chip and exposure of the asteroid that passed. The weight of the object with the highest detectability is 1, and fainter objects, which have a low detection probability, have a higher weighting value. Therefore, we eliminated the observational bias in the detection of objects and tested the completeness of the survey.

3 Results

3.1 Absolute Magnitude and Completeness

We extracted a total of 150 asteroids with 12 detections from the six fields and measured their apparent velocities. Assuming that their orbital eccentricities were zero and they located around opposition during the observations, we estimated the semi-major axes and inclinations by using the following equations (Bowell and Lumme, 1979; Nakamura and Yoshida, 2002; Yoshida and Nakamura, 2007):

(6)
(7)
(8)
(9)

where and are the moving rate along the ecliptic longitude and latitude, respectively; and are the semi-major axis and inclinations, respectively; and k is the Gaussian gravitational constant. The semi-major axis and inclinations estimated using the aforementioned equations included errors of approximately 0.1 AU and 5 because the actual eccentricities of the asteroids were not zero. We compared the orbital elements of known asteroids in Table 2 with our estimated elements. The result shows that the estimate elements are generally accurate; the difference between known and estimated semi-major axes, inclinations are less than 0.1 AU, 2, respectively.

The absolute magnitude of each asteroid at opposition can be estimated using the following equation:

(10)

where m is the apparent magnitude of the asteroid and and r are geocentric distance and heliocentric distance, respectively. For simplicity, and because of the and nearly opposition assumptions.

Figure 3 shows the absolute magnitude () distribution of our samples. The black spikes are the raw distribution, and the gray boxes shows the weighted result. Based on the results of Yoshida and Nakamura (2007), we plotted two power laws (N () ) to the distribution, with power law indices b of 1.29 (for the range from 17.8 to 20.2 mag) and 1.75 (14.6 to 17.4 mag). Here b = 5 . This plot clearly indicates that our samples have power law indices consist with the results of Yoshida and Nakamura (2007) and satisfactory completeness of up to , which corresponds to asteroids with diameters smaller than 590 meter for the C-complex asteroids (assuming an albedo of 0.05) and smaller than 270 meter for the S-complex asteroids (assuming an albedo of 0.25).

Figure 3: Weighted (Grey) and unweighted (black) cumulative absolute magnitude () distributions of the asteroids sample. Solid and dashed lines show the power laws distribution with power law indices of 1.29 (for the range 17.8 to 20.2 mag) and 1.75 (14.6 to 17.4 mag), respectively.

3.2 Colors and Estimated Taxonomic Types

From our sample (150 asteroids), 75 asteroids with the range from 16 to 20 magnitude, the color errors smaller than 0.1, 0.2 and 0.6 1 was selected. These asteroids have satisfactory completeness and photometric accuracy which made them suitable for taxonomic estimations. The color errors are propagated from the uncertainly of BVRI photometry of asteroids in Table 2. Figure 4 shows the relative reflectances in our asteroid samples overlap with the transmission curve of the Suprime-Cam filter system. The C-complex asteroids generally have a flat reflectance across the four filters, and the S-complex and V/Q/R-type asteroids exhibit similar slopes in the region but different reflectances near the I-band; the V/Q/R-type asteroids demonstrated a stronger absorption feature at 1 m. Therefore, while and color are used to separate S-complex and C-complex asteroids, the color is needed to distinguish S-type asteroids from V/Q/R-type-like asteroids in the following sense. The S-type asteroids are those with (0.332 0.008, according to Holmberg et al. (2006)); otherwise the V/Q/R-type-like asteroids.

Figure 4: Spectrophotometry of three types of asteroid spectra: S-complex, C-complex and V/Q/R-type-like asteroids. The background shows the transmission curves of the Suprime-Cam filter system.

We also separated our sample into large and small asteroids by , which approximately corresponds to a diameter of 1 km for C-complex asteroids. Figure 5 shows vs. color-color diagram for part of our large asteroid sample (). The bimodular distribution corresponds to the color difference between the C-complex and S-complex asteroids.

Figure 5: The and color-color diagram for our large asteroid sample (). The solid line shows the direction of new axis (A) of the color-color distribution.

Moreover, we identified principal components (the uncorrelated variables) for the large asteroid sample in and space by prcincipal component analysis to separate S-complex asteroids and C-complex asteroids and resulted two linear combinations of and colors:

(11)

and

(12)

The result shows that and axes become PC1 and PC2, respectively, after rotating 45 counterclockwise.

Furthermore, there is a dip at PC1 = 0.82 in the histogram of PC1 and can be the boundary of C and S-complex asteroids. Therefore, we define a new axis ‘’:

(13)

Asteroids with 0 should belong to S-complex, otherwise are C-complex. The new axis ’A’ is shown as a solid line in Figure 5.

Figure 6 shows the color-color diagram of axis vs. . Each dot represents an asteroid. A value of 0.332, which is corresponding to the solar color, was subtracted from the axis to separate S-complex and V/Q/R-type. Two major points can be made based on Figure 6: (1) only two objects can be certified as Q-type MBA candidates; (2) the small sample () appeared to be more concentrated at , though the C- and S-complexes are clearly separated in large sample ().

Figure 6: The vs. color-color diagrams of the large (upper) and small (bottom) asteroid samples in the present Subaru data. The regions corresponding to three types of asteroids are shown in the plots. The average colors of B, C, D, F, G, S, T, V, Q, R and X-type asteroids from Dandy et al. (2003) are also marked.

3.3 Fraction of Each Estimated Taxonomic Type

To estimate the taxonomic type of asteroids, we considered as C-complex asteroids, and as S-complex and and as V/Q/R like asteroids. Four objects locate around D/T type region were removed by visually selection. Figure 7 shows the semi-major axis vs inclination distribution of the 75 asteroids with estimated taxonomic type. The distribution looks normal; there are more C-complex than S-complex asteroids in outer main-belt. There is a possible V/Q/R-type candidate located on 3.8 AU. It could because of wrong estimation in semi-major axis.

Figure 7: Semi-major axis (a) vs inclination (i) distribution of the 75 asteroids with estimated taxonomic type. Gray dots show the a, i distribution of of known asteroids.

To calculate the fraction of each estimated taxonomic type, we took the uncertainly of boundaries of and axes, which are 0.02 from the bin-size of histogram and 0.008 from the uncertainty of , respectively, and the uncertainly of asteroid color measurements into account. We use 2D gaussian distribution with a covariance matrix equal to

to represent the probability distribution of each object in , space. Therefore, the fraction of a object in a specific taxonomic type is its probability distribution multiply a Complementary Error Function, which is the cumulative function of a gaussian distribution with the mean value equal to boundary value and standard deviation equal to the uncertainty of boundary. Figure 8 shows the fraction of asteroid types in our weighted and unweighted sample.

Since our sample exhibits a range similar to that of the near-Earth asteroid sample used by Dandy et al. (2003), it is worth to compare the fraction of asteroid’s type to that of NEA population. The Q/S ratio in our observation is less than 0.05 in the main-belt region. By contrast, the Q/S ratio in the near earth space is about 0.5 (Binzel et al., 2004) to 2 (Dandy et al., 2003), which is much higher than in the main-belt.

Finally, we tested the correlation between and of S-complex asteroids. As shown in Figure 9, unlike the result of Dandy et al. (2003) in which the absorption band depth was correlated with S-complex NEA size, we did not find any evidence that color has significant correlation with the size of S-complex MBA.

Figure 8: Histograms of the fractions of estimated asteroid spectral types. C and S are C-complex and S-complex asteroids, respectively, and V/Q/R indicates V/Q/R-type-like asteroids.
Figure 9: Variation of color (an indicator of absorption band depth) as a function of the absolute magnitude, , for the observed S-complex MBAs.

4 Discussion

There are only two possible Q-type asteroids candidates in our km to sub-km sized MBA sample (see Figure 6). This fact indicates that the Q-type asteroids are rare in the main-belt. The Q/S ratio is less than 0.05, which is significantly lower than the value of NEAs ( in Binzel et al. (2004) and in Dandy et al. (2003)). This result is also comparable with the Q-type-like fraction in Carvano et al. (2010), which the main belt Q/S ratio is for the good classified asteroids in SDSSMOC4.

Since most of S-complex MBAs are weathered, we can estimate the upper limit of space weathering timescale in main belt by using the collisional size-age relation in Bottke et al. (2005) and Willman and Jedicke (2011):

(14)

The H range of our MBA samples are between 16 to 20 magnitude, and their corresponding collisional ages are between to years. We can safely conclude that the space weathering timescale in main belt should be less than years.

The lack of Q-type MBAs also suggests two facts: 1. Most of the Q-type NEAs did not come from main-belt, they must form in-situ, and 2. collision is not the main mechanism of the formation of Q-type NEAs due to the collision rate being lower in the near Earth region. There must exist other mechanisms to generate such large amount of Q-type NEAs, and these mechanisms are more effective in the near Earth region than the main-belt. The planetary encounter model (Binzel et al., 2010; Nesvorný et al., 2010) advocating the recent resetting of S-type asteroid surfaces by the effects of tidal stress is one of the possible mechanisms.

Another possible mechanism that could be responsible for the formation of Q-type NEAs is YORP effect spin-up induced rotational-fission or surface re-arrangement of asteroids. The acceleration rate of asteroid spin by the YORP effect is inversely proportional to the square of semi-major axis and more effective in the near Earth region than in the main-belt due to the smaller heliocentric distance (Rubincam, 2000; Scheeres, 2007). Thus, if rotational-fission mechanism or rotational re-arrangement is also several times more effective to create Q-type NEAs than Q-type MBAs, it may be able to explain why the Q/S ratio in NEAs is about 10 to 40 times larger than Q/S ratio in MBAs.

The YORP spin-up can also explain the existence of main-belt Q-type asteroids (see Polishook et al. (2014) for detail). It indicates the size-color (or size-S/Q ratio) dependence of S-complex MBAs, because the smaller asteroid is easier to be accelerated to near the break-up limit resulting in the Q-type-like color. However, such relation is not shown in our sample. There are two possible effects that may cause the lack of size dependence:
1. The “secondary fission” of rotational-fission models provided by Jacobson and Scheeres (2011) may be the more likely model to create main-belt Q-type asteroids. This model implies the destruction of the secondary of pair asteroids by primary’s tidal forces. For the km to sub-km sized asteroid pair, the gravity may be too small to deform secondary and produce Q-type surface.
2. A size-dependent strength for asteroids in addition to gravity (Holsapple, 2007) can prevent the break-up of small asteroids. The existence of sub-km sized super-fast rotator, such as (29075) 1950 DA (Rozitis et al., 2014) and (335433) 2005 UW163 (Chang et al., 2014), might be the evidence of the existence of this internal strength.

The other mechanism is thermal degradation of the rocks on asteroid surface from Delbo et al. (2014). This process is strongly dependent on the value of diurnal temperature difference, which is a function of perihelion distance; it takes yrs in near Earth region and yrs in the main-belt to break of 3 centimeter diameter size rocks. If thermal degradation dominates the formation of Q-type asteroids, space weathering must have timescale yrs to keep low Q/S ratio in the main-belt.

5 Summary

We surveyed kilometer- to sub-kilometer-sized asteroids in the main belt by using the Subaru telescope. A total of 150 asteroids with BVRI colors were detected and 75 of them exhibited satisfactory photometry accuracy. The main results can be summarized as follows:
1. Q-type asteroids are rare in the main-belt; only two Q-type candidates were detected in our sample, and the Q-type to S-type ratio is less than 0.05 in main-belt.
2. Unlike the size-color dependence of NEAs found by Dandy et al. (2003), we did not found any evidence of that in MBA population.
3. The space weathering timescale in the main belt should be less than years.
4. Re-arrangement of surface material of S-type asteroid by tidal stress during planetary encounters and thermal degradation are possible mechanisms of Q-type NEAs formation. YORP spin-up induced rotational-fission or surface re-arrangement of asteroids could be responsible for both Q-type MBAs and NEAs formation.

Acknowledgments

We also acknowledge the anonymous referees’ useful suggestions for improving the manuscript. This work is based on data collected at Subaru Telescope, which is operated by the National Astronomical Observatory of Japan. This work was supported in part by NSC Grant: NSC 101-2119-M-008-007-MY3 and NSC 102-2119-M-008-001. The Pan-STARRS1 Surveys (PS1) have been made possible through contributions by the Institute for Astronomy, the University of Hawaii, the Pan-STARRS Project Office, the Max-Planck Society and its participating institutes, the Max Planck Institute for Astronomy, Heidelberg and the Max Planck Institute for Extraterrestrial Physics, Garching, The Johns Hopkins University, Durham University, the University of Edinburgh, the Queen’s University Belfast, the Harvard-Smithsonian Center for Astrophysics, the Las Cumbres Observatory Global Telescope Network Incorporated, the National Central University of Taiwan, the Space Telescope Science Institute, and the National Aeronautics and Space Administration under Grant No. NNX08AR22G issued through the Planetary Science Division of the NASA Science Mission Directorate, the National Science Foundation Grant No. AST-1238877, the University of Maryland, Eotvos Lorand University (ELTE), and the Los Alamos National Laboratory.

References

  • Bernstein and Khushalani (2000) Bernstein, G., Khushalani, B. 2000. Orbit Fitting and Uncertainties for Kuiper Belt Objects. The Astronomical Journal 120, 3323-3332.
  • Binzel et al. (1993) Binzel, R. P., Xu, S., Bus, S. J., Skrutskie, M. F., Meyer, M. R., Knezek, P., Barker, E. S. 1993. Discovery of a Main-Belt Asteroid Resembling Ordinary Chondrite Meteorites. Science 262, 1541-1543.
  • Binzel et al. (1996) Binzel, R. P., Bus, S. J., Burbine, T. H., Sunshine, J. M. 1996. Spectral Properties of Near-Earth Asteroids: Evidence for Sources of Ordinary Chondrite Meteorites. Science 273, 946-948.
  • Binzel et al. (2001) Binzel, R. P., Harris, A. W., Bus, S. J., Burbine, T. H. 2001. Spectral Properties of Near-Earth Objects: Palomar and IRTF Results for 48 Objects Including Spacecraft Targets (9969) Braille and (10302) 1989 ML. Icarus 151, 139-149.
  • Binzel et al. (2004) Binzel, R. P., Rivkin, A. S., Stuart, J. S., Harris, A. W., Bus, S. J., Burbine, T. H. 2004. Observed spectral properties of near-Earth objects: results for population distribution, source regions, and space weathering processes. Icarus 170, 259-294.
  • Binzel et al. (2010) Binzel, R. P., Morbidelli, A., Merouane, S., DeMeo, F. E., Birlan, M., Vernazza, P., Thomas, C. A., Rivkin, A. S., Bus, S. J., Tokunaga, A. T. 2010. Earth encounters as the origin of fresh surfaces on near-Earth asteroids. Nature 463, 331-334.
  • Bottke et al. (1993) Bottke, W. F., Jr., Nolan, M. C., Greenberg, R. 1993. Collision lifetimes and impact statistics of near-Earth asteroids. Lunar and Planetary Science Conference 24, 159-160.
  • Bottke et al. (1994) Bottke, W. F., Nolan, M. C., Greenberg, R., Kolvoord, R. A. 1994. Velocity distributions among colliding asteroids. Icarus 107, 255-268.
  • Bottke et al. (2002) Bottke, W. F., Morbidelli, A., Jedicke, R., Petit, J.-M., Levison, H. F., Michel, P., Metcalfe, T. S. 2002. Debiased Orbital and Absolute Magnitude Distribution of the Near-Earth Objects. Icarus 156, 399-433.
  • Bottke et al. (2005) Bottke, W. F., Durda, D. D., Nesvorný, D., Jedicke, R., Morbidelli, A., Vokrouhlický, D., Levison, H. 2005. The fossilized size distribution of the main asteroid belt. Icarus 175, 111-140.
  • Bottke et al. (2005) Bottke, W. F., Durda, D. D., Nesvorný, D., Jedicke, R., Morbidelli, A., Vokrouhlický, D., Levison, H. F. 2005. Linking the collisional history of the main asteroid belt to its dynamical excitation and depletion. Icarus 179, 63-94.
  • Bowell et al. (1978) Bowell, E., Chapman, C. R., Gradie, J. C., Morrison, D., Zellner, B. 1978. Taxonomy of asteroids. Icarus 35, 313-335.
  • Bowell and Lumme (1979) Bowell, E., Lumme, K. 1979. Colorimetry and magnitudes of asteroids. Asteroids 132-169.
  • Brunetto et al. (2006) Brunetto, R., Vernazza, P., Marchi, S., Birlan, M., Fulchignoni, M., Orofino, V., Strazzulla, G. 2006. Modeling asteroid surfaces from observations and irradiation experiments: The case of 832 Karin. Icarus 184, 327-337.
  • Bus and Binzel (2002a) Bus, S. J., Binzel, R. P. 2002. Phase II of the Small Main-Belt Asteroid Spectroscopic Survey. The Observations. Icarus 158, 106-145.
  • Bus and Binzel (2002b) Bus, S. J., Binzel, R. P. 2002. Phase II of the Small Main-Belt Asteroid Spectroscopic Survey. A Feature-Based Taxonomy. Icarus 158, 146-177.
  • Carvano et al. (2010) Carvano, J. M., Hasselmann, P. H., Lazzaro, D., Mothé-Diniz, T. 2010. SDSS-based taxonomic classification and orbital distribution of main belt asteroids. Astronomy and Astrophysics 510, AA43.
  • Chang et al. (2014) Chang, C.-K., Waszczak, A., Lin, H.-W., Ip, W.-H., Prince, T. A., Kulkarni, S. R., Laher, R., Surace, J. 2014. A New Large Super-fast Rotator: (335433) 2005 UW163. The Astrophysical Journal 791, L35.
  • Chapman (1996) Chapman, C. R. 1996. S-Type Asteroids, Ordinary Chondrites, and Space Weathering: The Evidence from Galileo’s Fly-bys of Gaspra and Ida. Meteoritics and Planetary Science 31, 699-725.
  • Chapman (2004) Chapman, C. R. 2004. Space Weathering of Asteroid Surfaces. Annual Review of Earth and Planetary Sciences 32, 539-567.
  • Chapman (2010) Chapman, C. R. 2010. Asteroids: Stripped on passing by Earth. Nature 463, 305-306.
  • Clark et al. (2001) Clark, B. E., and 11 colleagues 2001. Space weathering on Eros: Constraints from albedo and spectral measurements of Psyche crater. Meteoritics and Planetary Science 36, 1617-1637.
  • Clark et al. (2002) Clark, B. E., Helfenstein, P., Bell, J. F., Peterson, C., Veverka, J., Izenberg, N. I., Domingue, D., Wellnitz, D., McFadden, L. 2002. NEAR Infrared Spectrometer Photometry of Asteroid 433 Eros. Icarus 155, 189-204.
  • Dandy et al. (2003) Dandy, C. L., Fitzsimmons, A., Collander-Brown, S. J. 2003. Optical colors of 56 near-Earth objects: trends with size and orbit. Icarus 163, 363-373.
  • Davis et al. (2002) Davis, D. R., Durda, D. D., Marzari, F., Campo Bagatin, A., Gil-Hutton, R. 2002. Collisional Evolution of Small-Body Populations. Asteroids III 545-558.
  • Delbo et al. (2014) Delbo, M., Libourel, G., Wilkerson, J., Murdoch, N., Michel, P., Ramesh, K. T., Ganino, C., Verati, C., Marchi, S. 2014. Thermal fatigue as the origin of regolith on small asteroids. Nature 508, 233-236.
  • DeMeo et al. (2009) DeMeo, F. E., Binzel, R. P., Slivan, S. M., Bus, S. J. 2009. An extension of the Bus asteroid taxonomy into the near-infrared. Icarus 202, 160-180.
  • DeMeo and Carry (2013) DeMeo, F. E., Carry, B. 2013. The taxonomic distribution of asteroids from multi-filter all-sky photometric surveys. Icarus 226, 723-741.
  • DeMeo and Carry (2014) DeMeo, F. E., Carry, B. 2014. Solar System evolution from compositional mapping of the asteroid belt. Nature 505, 629-634.
  • DeMeo et al. (2014) DeMeo, F. E., Binzel, R. P., Lockhart, M. 2014. Mars encounters cause fresh surfaces on some near-Earth asteroids. Icarus 227, 112-122.
  • Hapke (2001) Hapke, B. 2001. Space weathering from Mercury to the asteroid belt. Journal of Geophysical Research 106, 10039-10074.
  • Holmberg et al. (2006) Holmberg, J., Flynn, C., Portinari, L. 2006. The colours of the Sun. Monthly Notices of the Royal Astronomical Society 367, 449-453.
  • Holsapple (2007) Holsapple, K. A. 2007. Spin limits of Solar System bodies: From the small fast-rotators to 2003 EL61. Icarus 187, 500-509.
  • Ishiguro et al. (2007) Ishiguro, M., and 18 colleagues 2007. Global mapping of the degree of space weathering on asteroid 25143 Itokawa by Hayabusa/AMICA observations. Meteoritics and Planetary Science 42, 1791-1800.
  • Ivezić et al. (2001) Ivezić, Ž., and 32 colleagues 2001. Solar System Objects Observed in the Sloan Digital Sky Survey Commissioning Data. The Astronomical Journal 122, 2749-2784.
  • Jacobson and Scheeres (2011) Jacobson, S. A., Scheeres, D. J. 2011. Dynamics of rotationally fissioned asteroids: Source of observed small asteroid systems. Icarus 214, 161-178.
  • Jedicke et al. (2004) Jedicke, R., Nesvorný, D., Whiteley, R., Ivezić, Ž., Jurić, M. 2004. An age-colour relationship for main-belt S-complex asteroids. Nature 429, 275-277.
  • Lantz et al. (2013) Lantz, C., Clark, B. E., Barucci, M. A., Lauretta, D. S. 2013. Evidence for the effects of space weathering spectral signatures on low albedo asteroids. Astronomy and Astrophysics 554, A138.
  • Lazzaro et al. (2004) Lazzaro, D., Angeli, C. A., Carvano, J. M., Mothé-Diniz, T., Duffard, R., Florczak, M. 2004. S OS : the visible spectroscopic survey of 820 asteroids. Icarus 172, 179-220.
  • Magnier et al. (2013) Magnier, E. A., and 13 colleagues 2013. The Pan-STARRS 1 Photometric Reference Ladder, Release 12.01. The Astrophysical Journal Supplement Series 205, 20.
  • Marchi et al. (2006) Marchi, S., Magrin, S., Nesvorný, D., Paolicchi, P., Lazzarin, M. 2006. A spectral slope versus perihelion distance correlation for planet-crossing asteroids. Monthly Notices of the Royal Astronomical Society 368, L39-L42.
  • Migliorini et al. (1998) Migliorini, F., Michel, P., Morbidelli, A., Nesvorny, D., Zappala, V. 1998. Origin of Multikilometer Earth- and Mars-Crossing Asteroids: A Quantitative Simulation. Science 281, 2022.
  • Miyazaki et al. (2002) Miyazaki, S., and 14 colleagues 2002. Subaru Prime Focus Camera – Suprime-Cam. Publications of the Astronomical Society of Japan 54, 833-853.
  • Morbidelli and Vokrouhlický (2003) Morbidelli, A., Vokrouhlický, D. 2003. The Yarkovsky-driven origin of near-Earth asteroids. Icarus 163, 120-134.
  • Morbidelli et al. (2009) Morbidelli, A., Bottke, W. F., Nesvorný, D., Levison, H. F. 2009. Asteroids were born big. Icarus 204, 558-573.
  • Mothé-Diniz and Nesvorný (2008) Mothé-Diniz, T., Nesvorný, D. 2008. Visible spectroscopy of extremely young asteroid families. Astronomy and Astrophysics 486, L9-L12.
  • Nakamura and Yoshida (2002) Nakamura, T., Yoshida, F. 2002. Statistical Method for Deriving Spatial and Size Distributions of Sub-km Main-Belt Asteroids from Their Sky Motions. Publications of the Astronomical Society of Japan 54, 1079-1089.
  • Nesvorný et al. (2005) Nesvorný, D., Jedicke, R., Whiteley, R. J., Ivezić, Ž. 2005. Evidence for asteroid space weathering from the Sloan Digital Sky Survey. Icarus 173, 132-152.
  • Nesvorný et al. (2010) Nesvorný, D., Bottke, W. F., Vokrouhlický, D., Chapman, C. R., Rafkin, S. 2010. Do planetary encounters reset surfaces of near Earth asteroids?. Icarus 209, 510-519.
  • Padmanabhan et al. (2008) Padmanabhan, N., and 23 colleagues 2008. An Improved Photometric Calibration of the Sloan Digital Sky Survey Imaging Data. The Astrophysical Journal 674, 1217-1233.
  • Petit et al. (2006) Petit, J.-M., Holman, M. J., Gladman, B. J., Kavelaars, J. J., Scholl, H., Loredo, T. J. 2006. The Kuiper Belt luminosity function from m= 22 to 25. Monthly Notices of the Royal Astronomical Society 365, 429-438.
  • Polishook et al. (2014) Polishook, D., Moskovitz, N., Binzel, R. P., DeMeo, F. E., Vokrouhlický, D., Žižka, J., Oszkiewicz, D. 2014. Observations of fresh and weathered surfaces on asteroid pairs and their implications on the rotational-fission mechanism. Icarus 233, 9-26.
  • Rabinowitz (1997) Rabinowitz, D. L. 1997. Are Main-Belt Asteroids a Sufficient Source for the Earth-Approaching Asteroids?. Icarus 127, 33-54.
  • Rivkin et al. (2011) Rivkin, A. S., Thomas, C. A., Trilling, D. E., Enga, M.-t., Grier, J. A. 2011. Ordinary chondrite-like colors in small Koronis family members. Icarus 211, 1294-1297.
  • Rozitis et al. (2014) Rozitis, B., Maclennan, E., Emery, J. P. 2014. Cohesive forces prevent the rotational breakup of rubble-pile asteroid (29075) 1950 DA. Nature 512, 174-176.
  • Rubincam (2000) Rubincam, D. P. 2000. Radiative Spin-up and Spin-down of Small Asteroids. Icarus 148, 2-11.
  • Sasaki et al. (2001) Sasaki, S., Nakamura, K., Hamabe, Y., Kurahashi, E., Hiroi, T. 2001. Production of iron nanoparticles by laser irradiation in a simulation of lunar-like space weathering. Nature 410, 555-557.
  • Schlafly et al. (2012) Schlafly, E. F., and 16 colleagues 2012. Photometric Calibration of the First 1.5 Years of the Pan-STARRS1 Survey. The Astrophysical Journal 756, 158.
  • Scheeres (2007) Scheeres, D. J. 2007. The dynamical evolution of uniformly rotating asteroids subject to YORP. Icarus 188, 430-450.
  • Scheeres (2015) Scheeres, D. J. 2015. Landslides and Mass shedding on spinning spheroidal asteroids. Icarus 247, 1-17.
  • Stuart and Binzel (2004) Stuart, J. S., Binzel, R. P. 2004. Bias-corrected population, size distribution, and impact hazard for the near-Earth objects. Icarus 170, 295-311.
  • Tholen (1984) Tholen, D. J. 1984. Asteroid taxonomy from cluster analysis of Photometry. Ph.D. Thesis .
  • Thomas et al. (2011) Thomas, C. A., Rivkin, A. S., Trilling, D. E., Enga, M.-t., Grier, J. A. 2011. Space weathering of small Koronis family members. Icarus 212, 158-166.
  • Thomas et al. (2012) Thomas, C. A., Trilling, D. E., Rivkin, A. S. 2012. Space weathering of small Koronis family asteroids in the SDSS Moving Object Catalog. Icarus 219, 505-507.
  • Tonry et al. (2012) Tonry, J. L., and 13 colleagues 2012. The Pan-STARRS1 Photometric System. The Astrophysical Journal 750, 99.
  • Vereš et al. (2012) Vereš, P., Jedicke, R., Denneau, L., Wainscoat, R., Holman, M. J., Lin, H.-W. 2012. Improved Asteroid Astrometry and Photometry with Trail Fitting. Publications of the Astronomical Society of the Pacific 124, 1197-1207.
  • Vernazza et al. (2009) Vernazza, P., Binzel, R. P., Rossi, A., Fulchignoni, M., Birlan, M. 2009. Solar wind as the origin of rapid reddening of asteroid surfaces. Nature 458, 993-995.
  • Walsh et al. (2012) Walsh, K. J., Richardson, D. C., Michel, P. 2012. Spin-up of rubble-pile asteroids: Disruption, satellite formation, and equilibrium shapes. Icarus 220, 514-529.
  • Willman et al. (2008) Willman, M., Jedicke, R., Nesvorný, D., Moskovitz, N., Ivezić, Ž., Fevig, R. 2008. Redetermination of the space weathering rate using spectra of Iannini asteroid family members. Icarus 195, 663-673.
  • Willman et al. (2010) Willman, M., Jedicke, R., Moskovitz, N., Nesvorný, D., Vokrouhlický, D., Mothé-Diniz, T. 2010. Using the youngest asteroid clusters to constrain the space weathering and gardening rate on S-complex asteroids. Icarus 208, 758-772.
  • Willman and Jedicke (2011) Willman, M., Jedicke, R. 2011. Asteroid age distributions determined by space weathering and collisional evolution models. Icarus 211, 504-510.
  • Yoshida and Nakamura (2007) Yoshida, F., Nakamura, T. 2007. Subaru Main Belt Asteroid Survey (SMBAS) - Size and color distributions of small main-belt asteroids. Planetary and Space Science 55, 1113-1125.
  • Zellner et al. (1985) Zellner, B., Tholen, D. J., Tedesco, E. F. 1985. The eight-color asteroid survey - Results for 589 minor planets. Icarus 61, 355-416.
Comments 0
Request Comment
You are adding the first comment!
How to quickly get a good reply:
  • Give credit where it’s due by listing out the positive aspects of a paper before getting into which changes should be made.
  • Be specific in your critique, and provide supporting evidence with appropriate references to substantiate general statements.
  • Your comment should inspire ideas to flow and help the author improves the paper.

The better we are at sharing our knowledge with each other, the faster we move forward.
""
The feedback must be of minimum 40 characters and the title a minimum of 5 characters
   
Add comment
Cancel
Loading ...
334861
This is a comment super asjknd jkasnjk adsnkj
Upvote
Downvote
""
The feedback must be of minumum 40 characters
The feedback must be of minumum 40 characters
Submit
Cancel

You are asking your first question!
How to quickly get a good answer:
  • Keep your question short and to the point
  • Check for grammar or spelling errors.
  • Phrase it like a question
Test
Test description