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.

### 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.

### 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):

 g[x′,y′]=b+FL12σ(2π)1/2exp[−y′22σ2]⎧⎨⎩erf⎡⎣x′+12Lσ√2⎤⎦−erf⎡⎣x′−12Lσ√2⎤⎦⎫⎬⎭, (1)

where

 erf[z]=2π∫z0exp[t2]dt (2)

and

 x′ = (x−xc)cosθ+(y−yc)sinθ, (3) y′ = −(x−xc)sinθ+(y−yc)cosθ, (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.

### 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:

 η(R)=A4[1−tanh(R−RcΔ1)][1−tanh(R−RcΔ2)] (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):

 a = 12γ(γ−2kλ±√∣κ∣), (6) tanI = ∣β∣λ+k/(a−1), (7) γ = λ2+β2, (8) κ = γ2−4kλγ−4k2β2, (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:

 HV=m−5log(Δr) (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).

### 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.

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.

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:

 PC1≡0.7071(B−V)+0.7071(V−R), (11)

and

 PC2≡0.7071(B−V)−0.7071(V−R) (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 ‘’:

 A≡0.7071(B−V)+0.7071(V−R)−0.82 (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 ().

### 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.

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

 ($A$2err00$(R−I)$2err)

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.

## 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):

 Ts(yr)=3.23×10(11.0−0.18Hv) (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.

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