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A Wide-Field CCD Survey for Centaurs and Kuiper Belt Objects

A modified Baker-Nunn camera was used to conduct a wide-field survey of 1428 square degrees of sky near the ecliptic in search of bright Kuiper Belt objects and Centaurs. This area is an order of magnitude larger than any previously published CCD survey for Centaurs and Kuiper Belt Objects. No new objects brighter than red magnitude m=18.8 and moving at a rate 1"/hr to 20"/hr were discovered, although one previously discovered Centaur 1997 CU26 Chariklo was serendipitously detected. The parameters of the survey were characterized using both visual and automated techniques. From this survey the empirical projected surface density of Centaurs was found to be SigmaCentaur(m<18.8)=7.8(+16.0 -6.6)x10^-4 per square degree and we found a projected surface density 3sigma upper confidence limit for Kuiper Belt objects of SigmaKBO(m<18.8)<4.1x10^-3 per square degree. We discuss the current state of the cumulative luminosity functions of both Centaurs and Kuiper Belt objects. Through a Monte Carlo simulation we show that the size distribution of Centaurs is consistent with a q=4 differential power law, similar to the size distribution of the parent Kuiper Belt Objects. The Centaur population is of order 10^7 (radius>1 km) assuming a geometric albedo of 0.04. About 100 Centaurs are larger than 50 km in radius, of which only 4 are presently known. The current total mass of the Centaurs is 10^-4 Earth Masses. No dust clouds were detected resulting from Kuiper Belt object collisions, placing a 3sigma upper limit<600 collisionally produced clouds of m<18.8 per year.


Introduction
The outer Solar System has recently been found to be populated by a vast number of minor bodies (e.g., Jewitt, Luu, & Chen 1996, Jedicke & Herron 1997, Jewitt, Luu, & Trujillo 1998. As of June 2000 there are 20 objects, known as Centaurs, which have semi-major axes and perihelia between Jupiter and Neptune and over 300 objects, known as Kuiper Belt objects (KBOs), which have semi-major axes greater than that of Neptune. Centaurs are believed to have originated from the Kuiper Belt and are now in dynamically unstable orbits that will lead either to ejection from the solar system, an impact with a planet or the Sun, or evolution into a short period comet. The brightest known KBO, other than Pluto-Charon, has apparent red magnitude m R ∼ 20, whereas several Centaurs are brighter than this. With current technology, physical and chemical properties of only the biggest and brightest minor bodies in the outer solar system can be studied. Centaurs and KBOs could be the most primitive bodies in the solar system and represent a unique opportunity to probe the early history of the local solar nebula.
The Cumulative Luminosity Function (CLF) describes the sky-plane surface density of objects brighter than a given magnitude. Little work has been done on the CLF of Centaurs (Jewitt et al. 1996, Levison & Duncan 1997, but the CLF of KBOs is well-defined between magnitudes 20 ∼ < m R ∼ < 26 (Gladman et al. 1998, Chiang & Brown 1999. The bright end of the KBO CLF is very uncertain because bright KBOs are rare and a limited amount of sky has been searched. The extrapolated CLF currently predicts about one KBO of m R ≤ 19 per 500 square degrees of sky. Observations with possible bearings on large bodies in the outer Solar System include the high eccentricities and inclinations of KBOs which could have come from massive planetesimals in the outer Solar System (Morbidelli & Valsecchi 1997) and the obliquity of Uranus's spin axis that might imply a collision with a massive body (Singer 1975). Evolution of the outer Solar System suggests a more massive disk was needed in the primordial Kuiper Belt to explain its current population size structure (Stern 1996a). A detailed accretion model of the early Kuiper Belt by Kenyon & Luu (1999) showed several Pluto sized objects could form within the age of the Solar System. Direct evidence for large objects in the outer Solar System includes the large irregular satellite Triton, as well as the Pluto-Charon system. To constrain the CLF of both the Centaurs and KBOs at m R ≤ 20 requires searches covering large sky areas. To date large surveys have been conducted using photographic plates which are difficult to parametrize. A list of surveys which have covered > 50 deg 2 and which had temporal sampling sufficient to detect Centaurs and/or KBOs is given in Table 1. Considering that relatively little of the sky has been searched for these Slow Moving Objects (SMOs), and that recent advances in CCD technology have made large area surveys feasible, this is an excellent time to search for bright SMOs. Accordingly, we undertook a wide-field survey in search of bright objects in the outer Solar System.

Observations
The 0.5 meter diameter Automated Patrol Telescope (APT) at Siding Spring Observatory in Australia was used during 3 observing runs in early 1999. The APT is a modified Baker-Nunn camera using a 3-element lens to achieve a corrected wide field of view (Carter et al. 1992). It was originally designed to track satellites in Earth orbit. We used a 770 × 1152 pixel CCD manufactured by EEV with 22.5 µm pixels and a pixel scale of 9.41 ′′ /pixel at the f/1 focal plane for imaging. The quantum efficiency of the detector is 0.46 in the R-band. The detector has a 3 • × 2 • rectangular field of view with the east-west direction aligned parallel to the long axis. Exposures were taken using a Johnson R-band filter and the telescope was tracked at sidereal rate. The APT site is exceptionally dark. The seeing was usually around 1.5 ′′ as measured from other telescopes on the mountain. At the APT the large pixel scale did not allow us to directly measure the seeing and moderate variations in seeing were not noticeable. The data were undersampled which made it difficult to distinguish between galaxies and stars ( Figure 1).
A total of 238 independent fields covering 1428 deg 2 of sky were imaged during observing runs centered around new moon in January, February, and March 1999 (Table 2). A map of the sky areas searched is shown in Figure 2 and the specific field centers are given in Table 3 (the complete extended Table 3 is provided in the electronic version of this paper). The fields were selected to be observed at an airmass ≤ 1.5 and be within 30 degrees of the ecliptic. Selection of the fields was made with no prior knowledge of known SMOs in the area. The search was made between +10 and −30 degrees of the ecliptic. The observational strategy was to search within ±1.5 hr of opposition. At opposition the movement of an object is simply related to heliocentric distance by where R(AU) is the heliocentric distance and dθ/dt (arcsec hr −1 ) is the rate of change of apparent position of the SMO on the CCD. From Equation 1, KBOs with R > 30 AU will have dθ/dt ≤ 4 ′′ hr −1 (≤ 10 pixels per day) and Centaurs with 5 < R < 30 AU have 4 ′′ hr −1 ≤ dθ/dt ≤ 20 ′′ hr −1 (between 10 and 50 pixels per day). Therefore we sought KBOs and Centaurs by comparing images taken on successive nights, allowing the detection of objects moving at rates between 1 ′′ hr −1 and 20 ′′ hr −1 . Trailing of both KBOs and Centaurs was negligible due to the large pixels, slow movement of the objects, and short integration times.
Three consecutive exposures of 200 seconds each were taken on each of 3 separate nights yielding 9 images per field. Weather permitting, the fields were imaged on consecutive nights. The images were bias and dark subtracted, then flat fielded with median twilight skyflats. The 3 images of a field taken during a single night were registered, then combined using the IRAF "crreject" cosmic ray rejection algorithm to remove cosmic rays and increase signal-to-noise. These 3 images were taken consecutively so there was little or no telescope motion between them. Landolt (1992) standard stars were used for photometric calibration.
Field centers differed by up to 50 arcseconds from night to night due to APT pointing variations. We aligned the fields from different nights by eye. The data were analyzed in two complementary ways, a) by visual "blinking" and b) using an automated search algorithm. For the visual analysis, four criteria were used for SMO identification: (1) the object must appear in all three frames, (2) it must have linear motion, (3) it must have a steady brightness in all 3 frames, and (4) it must have constant velocity appropriate for an SMO (< 20 ′′ hr −1 ). Many asteroids between magnitudes 10 and 19 were quickly identified and rejected by their large motions (>50 pixels in 24 hours). They were not followed up with further observations because of limited telescope time. Centaur 10199 Chariklo (provisional designation 1997 CU26) was at m V = 17.8 when detected serendipitously ( Figure 1). It was discovered independently by the visual and automated procedures with no knowledge of its location in the field. No other known SMOs in the area searched were bright enough to be detected by our survey. It should also be noted that the January fields were crowded due to the close proximity of the Galactic plane to opposition, while the March fields were hampered by bad weather. During poor weather, the few fields with gaps of 2 or 3 days were observed on 4 nights instead of the usual 3 to ensure that SMO identification efficiency was not significantly reduced compared to fields taken on 3 consecutive nights.
The limiting magnitude of the survey was found by randomly placing 100 artificial SMOs onto a subset of the images. A Moffat profile (Moffat 1969) matched to the point spread function of the APT was used to generate the artificial SMOs. The visual detection efficiencies for KBOs and Centaurs are shown as a function of magnitude in Table 4. A KBO detection efficiency equal to half the maximum efficiency was reached at m R = 18.8, which we take as the limiting magnitude of this survey. The Centaur detection efficiency equal to half the maximum efficiency was also reached near m R = 18.8.
As a complement to the visual SMO search, a moving object detection program was used to flag potential SMO candidates for scrutinization. The algorithm was optimized for our undersampled data. Objects were detected in each image by searching for maxima in the center of a 3 × 3 pixel box. An approximate signal-to-noise and flux for the object was then determined using all pixels within the 3 × 3 pixel box with flux more than 1.5σ above the sky background. While this underestimated the flux of extended objects, it provided a good estimate of the flux of faint undersampled stellar images, which occupied 1 to 4 pixels depending on the location of the image centroid with respect to the pixel grid. Using catalogues of objects in each field with signal-to-noise greater than 4, the software removed stationary objects by searching for objects within ±1 pixel of the same position in multiple images. Stationary objects with fluxes that varied by more than a factor of 2 are retained in the catalogue as these could be blended objects. The program then flags "objects" with a consistent rate of motion between 1 ′′ hr −1 and 12 ′′ hr −1 within 20 • of the projected direction of the ecliptic. Candidates with fluxes varying by more than a factor of 5 were rejected as these were dominated by spurious objects and variable stars.
The software successfully detected Centaur Chariklo, which was not unexpected as it was more than a magnitude brighter than the survey limit. As with searching for candidates by eye, the detection efficiency was determined by searching for artificial SMOs. The average detection efficiency as a function of magnitude is summarized in Table 5. The KBO detection rate of half the maximum value was reached at m R = 18.5 and is the limiting magnitude for the automated detection technique. The code is not as effective as the eye at deblending merged objects, so the ∼ 50% magnitude limit is ∼ 0.3 magnitudes brighter than that determined by eye. However, in high Galactic latitude fields, the efficiency of the code improved significantly with ∼ 70% of m R < 18.5 KBOs being detected.

Results and Discussion
A total of 238 fields were examined covering 1428 square degrees of sky (about 3.5% of the whole sky). No new SMOs were detected. One previously discovered Centaur (Chariklo) was serendipitously detected. From the one detected Centaur and the efficiency of this survey we found the empirical projected surface density of Centaurs to be Assuming Poisson statistics, the 3σ upper confidence limit for the projected surface density of KBOs from our survey is We plot these and cumulative surface density measurements from other surveys for Centaurs and KBOs in Figures 3 and 5, respectively. Error bars were calculated at 1σ confidence from detection efficiencies and Poisson error statistics when not explicitly given in the published papers (Gehrels 1986). Quoted upper limits are Poisson 3σ confidence limits. The CLF is modeled by where Σ(m R ) is the number of objects per square degree brighter than m R , m o is the magnitude at which Σ = 1 deg −2 , and 10 α describes the slope of the luminosity function.

The Centaurs
The current state of the CLF of Centaurs is shown in Figure 3. Almost half of the known Centaurs have been found by the Spacewatch program (Jedicke & Herron 1997, McMillan 1999. The parameters of the Spacewatch survey have changed with time as the detector and observing strategy have been modified. Dr. Robert McMillan, head of the Spacewatch program, kindly provided estimates of the Spacewatch survey parameters (Table 1). Spacewatch points in Figures 3 and 4 were calculated using the total area searched with the number of Centaurs found. They are lower limits since the effective area searched is less than the reported total area searched due to some observations in marginal observing conditions and some areas covered multiple times. Kowal's (1989) Centaur constraint is plotted with a sizeable uncertainty because of the large trailing losses incurred in long (75 minute) photographic integrations on (relatively) fast moving Centaurs. The CLF of the Kuiper Belt (c.f. section 3.2) is overplotted on the Centaur data in Figure 3. A line of the same slope has been vertically shifted to run through the points having one or more Centaur detections. The offset line is consistent with every observational point shown in Figure 3, within the uncertainties of measurement. The Centaurs reach Σ = 1 deg −2 at m R = 24.6 ± 0.3. Thus, Centaurs have an apparent sky-plane-density about 10 times less than that of the KBOs at a given magnitude.
The CLF represents the convolved effects of the size and distance distributions of the objects. A Monte Carlo simulation was used to determine the total number of Centaurs larger than a certain radius. The Centaurs were assumed to follow a differential power-law radius distribution of the form n(r)dr = Γr −q dr, where Γ and q are constants, r is the radius of the Centaur, and n(r)dr is the number of Centaurs with radii in the range r to r + dr. The radii of the Centaurs were assumed to lie between r min and r max . To find the total number of Centaurs, we adopted r min = 1 km (since the smaller short period comets are about this size), and r max = 1000 km (about the size of the largest known Trans-Neptunian body, Pluto). The derived total number of Centaurs is insensitive to r max . The surface density distribution of Centaurs in the plane of the ecliptic varies with heliocentric distance and was assumed to be a power law of the form n(R)dR = Σ o R −γ dR, where Σ o and γ are constants, R is the heliocentric distance, and n(R)dR is the number of objects with heliocentric distance in the range R to R + dR. The heliocentric distance was taken between 10 and 30 AU. A γ = −1.3 was chosen as the most likely Centaur distance distribution based on the simulation by Levison and Duncan (1997).
The Monte Carlo simulation was performed by randomly choosing a distance and radius for up to 10 8 Centaurs from the two power law equations above. Each Centaur's apparent magnitude at opposition was then calculated using in which r is in km, R is in AU, ∆ is the geocentric distance in AU taken here to be ∆ = R − 1, m ⊙ is the apparent red magnitude of the sun (−27.1), m R is the apparent red magnitude of the Centaur, p R is the geometric red albedo assumed to be 0.04, and φ(α) is the phase function in which the phase angle α = 0 deg at opposition and thus φ(0) = 1.
The results of the Monte Carlo simulation using q = 3.5, 4.0, and 4.5 are shown in Figure 4. We obtained the total number of Centaurs with r > 1 km by normalizing the simulation to the CLF of the Centaurs at m R = 22.0. We assumed the inclination distribution extends to ±30 degrees in latitude from the ecliptic: the total sky area occupied by Centaurs is then about 20000 deg 2 . We used the relation N(> r) = Γ/(q − 1)r q−1 where N is the cumulative number of Centaurs with radius greater than r to find Γ. Table 6 shows the results for the number of Centaurs using different assumed values of the main parameters. For the q = 4 index we found there are about 1 × 10 7 Centaurs with r > 1 km. Uncertainties in q of ±0.5 correspond to uncertainties in the population of factors 3 to 4. Plausible uncertainties in γ have a smaller effect ( Table 6).
The q = 3.5, 4.0 and 4.5 curves are all consistent with the Centaur CLF (Figure 4). If we use the closest fit q = 4 simulation we obtain N(r > 50 km) ∼ 100 (Table 6). The number of Centaurs with r > 50 km is comparable to the 300 main-belt asteroids (Tedesco 1989) in this size regime but much smaller than the 7 × 10 4 KBOs expected with r > 50 km ). Our result is about an order of magnitude smaller than the result obtained by Jewitt et al. (1996). These authors detected 2 Centaurs in a narrow field survey and crudely estimated the Centaur population based on only 1 of the Centaurs and in the absence of a model of the Centaur radial distance distribution. Jedicke & Herron (1997) found, at the 99% confidence level, that there must be fewer than 250 Centaurs with r > 50 km (we scaled the quoted value for r > 25 km in Jedicke & Herron (1997) to r > 50 km using a q=4 index for the size distribution) and they also concluded there are 3 or fewer Centaurs with r > 100 km. Although all three results are consistent, our simulation using the CLF in Figure 3 presumably provides a superior estimate of the population since more Centaurs are now known and a model of the distance distribution has been incorporated.
Assuming the Centaurs are supplied by the KBOs, in steady-state we should have N c ∼ N k t c /t k where N c is the number of Centaurs, N k is the number of KBOs, t c is the average Centaur lifetime, and t k is the average KBO lifetime. For KBOs t k ≈ 10 10 years (Quinn et al. 1990) and for Centaurs t c ≈ 10 6 to 10 7 years (Hahn & Bailey 1990, Asher & Steel 1993, Levison & Duncan 1997. With N k ≃ 70000 (r > 50 km) KBOs , we expect N c ≃ 7 to 70 (r > 50 km) Centaurs based on the steady state assumption. This is consistent with N c ∼ 100 estimated here from the CLF, and consistent with the Kuiper Belt supplying the Centaur population. Since the average Centaur lifetime expressed in years is similar to the number of Centaurs with radii greater than 1 km (N(r > 1km)/t c ∼ 1), about one Centaur with r ≥ 1 km must be delivered to the gas giant region per year. Duncan et al. (1995) found the fraction of KBOs which leave the Kuiper Belt from planetary interactions is 5 × 10 −11 per year. Assuming that half of the KBOs which leave the Kuiper Belt end up as Centaurs, then with 7 × 10 4 KBOs of r >50 km and a Centaur lifetime of 10 6 to 10 7 years we would expect between 2 to 20 Centaurs to be present with radii > 50 km, consistent with our results.
For a q = 4 size distribution the total mass is M = 4 × 10 9 πρΓ 3 0.04 p R 3/2 ln r max r min (6) where ρ (kg m −3 ) is the bulk density. Using ρ = 1000 kg m −3 (similar to cometary nuclei), p R = 0.04, r min = 1 km, and r max = 200 km (about the size of the largest known Centaur), we obtain M ≈ 8 × 10 20 kg (∼ 10 −4 M ⊕ ) for the current total mass of the Centaurs. Assuming Centaurs have a lifetime of 5 × 10 6 years and are in steady state we find that 0.1 M ⊕ has been cycled through the Centaurs during the 4.5 × 10 9 year age of the solar system. If objects as large as Pluto (r max = 1200 km) with ρ = 2000 kg m −3 are considered then the mass cycled through the Centaurs during the age of the solar system is about 2.5 times greater than the above result. Either way it is comparable to the inferred total mass currently in the Kuiper Belt of ∼0.2 M ⊕ ).
Centaurs are close enough to the Sun to show cometary activity (e.g., Chiron), which can lead to an overestimate of their size if assuming a constant albedo, as we have done.
Observationally, most surveys are only sensitive to bright (large) Centaurs. Thus the smaller Centaur population was obtained by extrapolating from larger Centaurs which may not follow the same distribution. No survey has been specifically targeted at detecting Centaurs. Most surveys which have found Centaurs are optimized instead for finding KBOs or asteroids. This makes it hard to assess the sensitivity to Centaurs of some published surveys. Surveys plotted in Figure 3 are those which were capable of finding Centaurs in at least the range of heliocentric distances 10 AU to 30 AU. Our survey was sensitive to Centaurs from 5 to 30 AU. Only 4 of the 20 currently known Centaurs could have radii > 50 km (assuming geometric albedo 0.04) and our simulation predicts ∼ 100 such objects in the whole sky. Most of them would be located near but inside the orbit of Neptune, with apparent red magnitudes near 23. They would have naturally escaped detection in most wide field surveys conducted to date.

The Kuiper Belt
Surface densities of KBOs from different surveys are in reasonable agreement between 20 ∼ < m R ∼ < 26 ( Figure 5). A weighted least squares fit to the CLF for all the data with at least one detection is shown in Figure 5 (we used only the middle of the three Tombaugh points in the fit), yielding α = 0.59 ± 0.05, m o = 23.0 ± 0.2. The fit is consistent with the fits found by Jewitt et al. (1998) Chiang & Brown (1999) [α = 0.52 ± 0.02, m o = 23.5 ± 0.06]. Our survey's 3σ upper limit is consistent with the constant slope of the CLF but does not rule out a steepening in the CLF for m R < 19.
The above and some other previous works have improperly calculated the surface density from Tombaugh's (1961) survey (see Table 1 for the correct results of Tombaugh's survey). They used Tombaugh's follow up survey which was conducted to search for satellites or other objects that might be near Pluto. This survey reached m R = 16.8 and covered 1530 square degrees of sky. However, Pluto was discovered in a survey which reached only m R = 15.5 and covered about 28000 deg 2 , initiated earlier and continued later ( Table 1). The 1530 square degree survey should be interpreted as a null result since Pluto was not detected serendipitously. Therefore, the Tombaugh datum used in some earlier works should be shifted to brighter magnitudes and lower surface densities.

Collision Clouds
The Kuiper Belt was first thought to be collisionless though it now appears collisional effects might be very important (Davis & Farinella 1997). This has the result of removing the primitive and possibly unprocessed material from KBOs and might allow for dust to be observed in the Kuiper Belt. The collision products might be seen directly by the detection of dust clouds around the KBOs (Alcock & Hut 1993, Stern 1996b. Assuming there are 10 9 KBOs with r > 1 km and that the Kuiper Belt extends ±30 degrees from the ecliptic, Stern (1996b) and Alcock & Hut (1993) predicted between 1 and 100 collisions per year producing detectable (m R ∼ < 15) dust clouds.
The characteristic expansion time of a cloud is t ≈ r/v, where v is the expansion velocity and r is the radius of the expanding cloud. The velocity of the ejected material depends on the energy of the impact and size of the projectile and target. KBOs have Keplerian velocities of a few kilometers per second and escape velocities for 1 km objects are around 1 m s −1 . The cloud should reach peak brightness in reflected light when its optical depth is unity. The time to reach peak brightness is t ≈ c/v, where c is the critical radius at which optical depth unity is reached. The critical radius depends on the size distribution of ejected particles. If constant density is assumed then the critical radius is just the square root of the geometric cross-section of the particles (c = a[a i /a] 1.5 where a is the average radius of particles created from the initial projectile radius of a i ). The duration of visibility depends on the limiting magnitude. Using typical values of v = 1 to 5 km s −1 (the approximate expansion velocity of gas produced by impact vaporization) and a constant size of 0.1 to 10µm for particles in the cloud we find that a dust cloud should reach optical depth unity in only a few days and be brighter than red magnitude 19 for about 20 to 100 days. If 100 clouds are produced in one year and each is visible for 50 days about 14 clouds should be visible at any instant. With 14 clouds in 20,000 square degrees, we expect to find one cloud for every 1430 square degrees of sky. Owing to the large pixels of the APT our survey would not resolve one of these collision clouds if in our field of view, though we would detect the KBO type movement of any clouds brighter than m R = 18.8. No dust clouds brighter than m R = 18.8 were detected in 1428 square degrees of sky searched in this survey. Assuming Poisson spatial distribution this gives a 3σ confidence limit that there are < 82 clouds for 20,000 square degrees at any given time or less than 1 cloud per 244 square degrees of sky with m R < 18.8. This also puts a 3σ limit of < 600 clouds produced per year with m R < 18.8.
More sky must be searched to determine if Pluto is just one of several other large KBOs waiting to be discovered. If the amount of sky searched for slow moving objects were doubled, strong constraints on the bright end of the KBO CLF would be obtained. This survey was hindered by the large pixel size of the CCD. Currently CCDs four times as large and with pixels half the size are routinely available. It is our goal to continue to survey the sky for bright SMOs with a bigger CCD and smaller pixels. This will improve the efficiency of the survey and allow the data to be better sampled.

Summary
1. A total of 1428 square degrees of sky were searched for KBOs and Centaurs to a limiting magnitude of m R = 18.8. One previously discovered Centaur was detected serendipitously (1997 CU26 Chariklo), and no KBOs were detected.
2. This survey, the largest published CCD survey to date sensitive to Centaurs and Kuiper Belt Objects, was analyzed both by an automated technique and by eye. The survey parameters were well established.
3. The cumulative surface density is Σ C = 7.8( +16.0 −6.6 ) × 10 −4 deg −2 for Centaurs at m R = 18.8 with error bars at the 1σ level. The Centaur cumulative luminosity function (CLF) has a slope (α ∼ 0.6) similar to the Kuiper Belt CLF but shifted about 1.5 magnitudes fainter. The number of Centaurs per unit sky area is about 1/10th the number of KBOs, at any given magnitude.

A Monte
Carlo simulation was performed to obtain the expected number distribution of Centaurs. Differential power-law size distribution indices between q=3.5 and 4.5 are consistent with the Centaur CLF. Using q=4, we find there are about 1 × 10 7 Centaurs with radii larger than 1 km and ∼ 100 larger than 50 km in radius, of which only 4 (Chiron, Pholus, Chariklo(1997 CU26), and 1995DW2) are presently known. The combined mass of all Centaurs is 10 −4 M ⊕ . Assuming a steady state this implies that 0.1 M ⊕ has been cycled from the Kuiper Belt through the Centaurs during the age of the solar system. 5. The surface density of Kuiper Belt objects at m R = 18.8 is Σ K < 4.1 × 10 −3 deg −2 at the 3σ confidence level. This result is consistent with the previously determined CLF for Kuiper Belt objects but does not rule out a steepening in the slope for m R < 19.
6. No collisionally produced dust clouds were observed in the Kuiper Belt. We place a 3σ upper limit of < 600 visible collisional clouds (m R < 18.8) produced per year.        Note. -Centaur Chariklo was found in field f0409.
Note. -The complete version of this table will be in the electronic edition of the Astronomical Journal. The printed edition contains only a sample. a Artificial KBOs moved between 8 and 10 pixels per day (3 to 4 ′′ hr −1 ). b Artificial Centaurs moved between 15 and 30 pixels per day (6 to 12 ′′ hr −1 ).