The Astrophysical Journal, 594:L63–L66, 2003 September 1 䉷 2003. The American Astronomical Society. All rights reserved. Printed in U.S.A.
A SEARCH FOR SMALL KUIPER BELT OBJECTS BY STELLAR OCCULTATIONS F. Roques, M. Moncuquet, N. Lavillonie`re, M. Auvergne, M. Chevreton, F. Colas, and J. Lecacheux Observatoire de Paris, 92195 Meudon Cedex, France;
[email protected] Received 2003 April 11; accepted 2003 July 23; published 2003 August 7
ABSTRACT We report the conditions and results of an observation campaign organized in 2000 September at the Pic du Midi Observatory, and dedicated for the first time to the study of Kuiper belt objects (KBOs) by stellar occultations. The observation consisted of recording the flux of a well-chosen star with a fast photometer (20 Hz) and counting occultations of this star by passing KBOs. The campaign provided 15 hr of good-quality signal (rms j ∼ 1.8%) and zero detections of KBOs at a 4 j detection level. For a KBO differential size distribution assumed to vary as r⫺q, this first result suggests a slope q ⱗ 4.5. A refined analysis of the data, studying diffraction patterns, allowed us to find an event at a 3 j detection level compatible with a 150 m KBO. More generally, observation campaigns of stellar occultation by KBOs on ≥2 m class telescopes could statistically constrain the slope and the expected turnover radius due to collisional erosion of the subkilometer KBO size distribution. Subject headings: Kuiper Belt — occultations — solar system: formation — techniques: photometric their total mass to only ∼0.1 M丣 (see Luu & Jewitt 2002 and references therein). In contrast, the simple extrapolation of the surface mass density of the solar system outside 35 AU yields several Earth masses. Moreover, KBO accretion models need to work (i.e., to produce objects with radius larger than 100 km) for an initial Kuiper belt 100 times more massive than the current (observed) belt (Kenyon & Luu 1999). These authors argued that the primitive KB has been collisionally depleted over the age of the solar system. In this KB evolution scenario, the collisional erosion should have cleared the 0.1–10 km main population and left untouched the 1%–2% of objects of radius greater than 50 km which should form the present-day KB. Indeed, we think this point deserves further observational investigation: the collision frequency between small-size objects, which leads to their destruction to dust, depends on their size/age, and thus a turnover radius is expected in the slope of the KBO size distribution (Kenyon 2002), depending on the age of the belt and other badly known parameters, such as the KB surface density and the KBO mean density. A rough estimation leads to a turnover radius of about 0.1 km, and in this case the 0.1– 10 km population should make up the greater part of the KB total mass up to now. If we may observe this population of small KBOs, we could determine or constrain the slopes and the expected turnover radius of the size distribution.
1. INTRODUCTION
The stellar occultation method is commonly used to study dark matter in the solar system, planetary atmospheres, or rings (see, e.g., Sicardy, Roques, & Brahic 1991). The method consists of recording the flux of a star with a fast photometer. A dip in the photometer signal is then detected when an object passes in front of the star. This method is able to detect small objects invisible by direct observation: an object of radius r, passing in front of a star of angular radius r, creates a signal decay DF ≈ [r/(rD)]2, where D is the object-Earth distance. For example, with D p 40 AU and a well-chosen star (r ∼ few # 10⫺3 mas), there is full extinction for an occulting object of about 100 m. This DF expression is quite approximate (see Roques, Moncuquet, & Sicardy 1987 and Roques 2000 for further computations including diffraction effects) but gives an idea of the power of occultations to detect small objects orbiting in the outer solar system, especially beyond the Neptune orbit. Since the discovery of Pluto in 1930, several people guessed that the region beyond Neptune might not be empty, and the discovery since 1992 of hundreds1 of objects orbiting from 30 to 50 AU and between 50 and a few hundred km radius have confirmed this conjecture. The good idea was partially ascribed to G. Kuiper, and these objects are now often referred to as Kuiper belt objects (KBOs). Up to now, the large magnitude of the KBOs and telescopes’ capabilities limit the detection of the reflected solar flux to objects with radii larger than a few tens of kilometers. However, several facts suggest that there exists a huge number of smaller (kilometer and subkilometer) sized objects in the disk: the Triton surface craters show that a large number of small KBOs have recently riddled this moon (Stern & McKinnon 2000). The near-Earth asteroids (Rabinowitz et al. 1994) exhibit an almost continuous size distribution from kilometers to 5 m scale objects. When limiting the minimum radius of the existing KBOs to 1 km, and assuming that the KBO differential size distribution (i.e., the number of objects with radius in km between r and r ⫹ dr) varies as a power law ∝ r⫺q dr with a slope q ≈ 4, the total KBOs number may be estimated at ⱗ1011 and
2. STELLAR OCCULTATIONS APPLIED TO KUIPER BELT OBJECT DETECTION
The work presented here is a first attempt to detect small KBOs by the method of “serendipitous” stellar occultations. Serendipity means here that we observe with a telescope a well-chosen star and we wait for occultations of this star by passing KBOs. Note that the observation of such an occultation is not the discovery of a KBO because it is not possible to retrieve the object: it allows one only, by accumulation of observations, to build a statistical sample of the KBO population. The number of detected KBOs depends on the effective density of KBOs in the sky plane (connected to their size distribution). It also depends on the smallest KBO radius we are able to detect with our given star/telescope. Moreover, the KBO occultation light curves depend strongly on Fresnel diffraction effects, especially for observations made with very
1 About 800 KBOs have been discovered by direct detection by mid-2003; see http://cfa-www.harvard.edu/iau/lists/TNOs.html.
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Fig. 1.—Two data samples (top) of 500 s from the TBL data and their histograms (bottom, gray areas) with the best Gaussian fit superposed. The left histogram is Gaussian (j p 1.8%), but the right one is not Gaussian and the corresponding sample has been rejected.
good signal-to-noise ratio (Roques 2000). The simulation of the occultation profiles by KBOs taking into account diffraction effects, the estimation of the smallest observable KBO, and the deduced occultation rates for miscellaneous observation conditions are done in Roques & Moncuquet (2000, hereafter R&M2000). In addition, R&M2000 have estimated occultation rates by using two hypotheses on the size distribution slope of subkilometer KBOs (q p 3 or 4) as functions of the star radius and the depth of the events. These authors have also shown that monitoring stars with large telescopes (≥2 m diameter telescopes) allows the search for occultation by subkilometer objects. In particular, when assuming a subkilometer KBO size distribution with slope q p 4, the estimated occultation rate is high enough (∼1 event per night) to attempt the method on 2 m class telescopes: this is the starting point of the observation campaign presented here. 2.1. Requirements, Provisos, and Data Processing
1. The judicious choice of the target star is critical, especially concerning its apparent size because, as shown in R&M2000, the smaller the occulted star, the smaller the detectable KBO, and because small KBOs are more numerous, the larger the occultation rates. Indeed, the star radius projected at 40 AU can be hundreds of kilometers down to few meters depending on the star spectral class and magnitude. For a given magnitude, the blue stars are smaller than the red ones: an O5 star of m V p 12 has a projected radius of 100 m at 40 AU. With the same magnitude, an M5 star has a projected radius of 10 km. On the other hand, KBOs are mainly orbiting in the ecliptic plane, so the target star must have an ecliptic latitude as small as possible. 2. High-speed photometry is necessary to record the star flux because occultations by a KBO are very brief events, a fraction of a second (see point 3 below). Observations with a photometer are better because they allow a frequency acquisition larger than 10 Hz (see below). Observation with a CCD does not allow an acquisition frequency larger than a few Hz. The optimal instrumentation is a multiobject photometer. 3. The observations done in the direction of the opposition increases the apparent velocity of the KBO in the sky plane and, hence, the probability of occultation. However, the oc-
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cultation length is reduced and the profile is smoothed on the integration interval. An object at 40 AU from the Sun has a velocity in the sky plane of 25 km s⫺1. An occultation has a minimum width of the order of 2 Fresnel scale Fs p (lD/2)1/2 (Fig. 3 of R&M2000). In the case of an observed wavelength l p 4 mm and D p 40 AU, this yields Fs p 1.1 km. Then, the minimum radius of the shadow is 2.2 km if the star is smaller than the Fresnel scale. Toward the opposition, this corresponds to 0.1 s, and then the minimum acquisition frequency is 10 Hz. If the star is larger than Fs, the minimum depth of the event is defined by the star size. 4. It is critical to observe a comparison star nearby the target star. The comparison of the light curves of the target star and the comparison star allows elimination of “false events” due to observation problems (technical or human problems) and to atmospheric events (clouds, birds, satellites, etc.). If an event is observed simultaneously or quasi-simultaneously on the two stars, it is due to an Earth-connected cause. Objects of a few centimeters’ size in the Earth’s atmosphere, passing in front of the stars, generate simultaneous dips in the two light curves. 5. When observations are done with two nearby telescopes, the comparison of the light curves allow confirmation that the events are due to the occultation by a distant object. Simultaneous events detected on the target star fluxes from two nearby telescopes, with no simultaneous event on comparison star, confirm that the occulting object is extraterrestrial. As mentioned in point 3, for small objects, the size of the shadow is larger than twice the Fresnel scale. Then simultaneous observations from telescopes separated by L means that the occulting object is at a distance ≥L2/2l. For example, at the Pic du Midi Observatory, where telescopes are separated by 200 m, the simultaneous observation of an event means that the object is at a distance larger than 4 # 10 6 km. 6. Occultations by asteroids are possible. However, the extrapolation of the distribution size of known asteroids to smaller objects allows estimation of a probability of occultation more than one-hundredth smaller than occultation by KBOs (R&M2000). Moreover, the observation of the diffraction fringes allows us to know the Fresnel scale and, hence, the distance of the occulting object. Data processing.—In order to compare the number of events with the predictions done in R&M2000, it is important to accumulate observations to form a significant statistical sample. Moreover, for further statistical exploitation, well-defined and homogeneous methods of data processing are required. The noise on the star flux is generated by scintillation for m V ≤ 12. Theoretical analysis of the scintillation shows that the rms fluctuation of the light curve (Young 1967) depends in particular on the telescope size and the frequency of observation. This noise is normally distributed (i.e., has a Gaussian distribution). We fix the limit between noise and events to a 4 j level. This corresponds to nine fortuitous one-point dips during 8 hr of observation, for a frequency acquisition of 10 Hz. For a frequency acquisition of 20 Hz, the probability of two consecutive points beyond 4 j is less than 10⫺3. The data processing may be divided into four steps. (i) Normalization.—The first step is to remove the sky flux and to normalize the stellar fluxes of the target star and the comparison star. (ii) Validation.—The rms signal fluctuations j is computed on 5 minute intervals. Intervals with non-Gaussian noise are
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with the 1 m telescope (T1m), located 200 m away from the TBL. 3.1. Observation Conditions and Results
Fig. 2.—Normalized fluxes of the target star and of the comparison star (shifted of 0.2) as functions of time. A possible occultation by a KBO is detected at 3 j around 03:02:43 UT. This dip with diffraction fringes was found by the equivalent width method on the TBL light curve, and no dip is observed simultaneously on the comparison star flux.
rejected (see Fig. 1). The size of the detectable KBO is deduced from j. (iii) Search for events.—The research method is similar to the equivalent width method used by Sicardy et al. (1991) when these authors were searching for the Neptune ring profile by occultation. The method is well adapted to search for a brief occultation profile with no hypothesis on its shape, depth, and location. Around the point i, a small window is fixed in the middle of a large window. The mean flux AFS on the large window is computed. The equivalent width of the small window is defined as E(i) p S [1 ⫺ (F(i)/ AF S)], S being the sum over the small window. When the star is occulted in the small window, E is a maximum. The size of the small window, n, is defined by the minimum duration of the event we want to detect. Since the minimal depth of the events is fixed to 4 j, we search for points i where E(i) 1 4jn. (iv) Elimination of false events.—Among these selected points, false events are eliminated with the help of the light curve of the comparison star and the other telescope. 3. THE PIC DU MIDI CAMPAIGN IN 2000
Observations have been organized at the Bernard Lyot 2 m telescope (TBL) of the Pic du Midi Observatory from 2000 September 4 to 11. Simultaneous observation was organized
We summarize in Table 1 the circumstances of observations for the Pic du Midi Observatory. The target star has been chosen from the catalog Tycho-2 (Hog 2000) near the ecliptic plane (0⬚. 2 ecliptic latitude) and such that the star diameter projected at 40 AU is ≤50 m. The target is identified as 181210-1 (a p 14⬚06⬘28⬙. 54 and d p 5⬚45⬘0⬙. 38) with m V p 12.03. The acquisition frequency of the four-channel Chevreton’s photometer (see § 3.2) was set to 20 Hz. The four channels correspond to the target star, the reference star, and the sky on two channels (the two sky fluxes are averaged before being removed from the star’s flux). Unfortunately, a problem in the recording of time at the TBL has limited the two telescopes’ synchronization to several seconds and so has made difficult the search for simultaneous events on the two telescopes’ light curves. The analysis of the Pic du Midi observations concerns four nights, corresponding to 18 hr of data. During these nights, the search for events is done on the intervals with stable sigma. The Figure 1 shows for illustration the signal fluctuation (top) and the histograms (bottom) of two data samples. Outside very noisy intervals (Fig. 1, right), which exhibit numerous absorption structures, we were able to select large intervals with stable values of j between 0.03 and 0.018 (Fig. 1, left). This corresponds to 15 hr of exploitable observation. Note that equation (15) of R&M2000 yields the theoretical rms signal fluctuation for the light curve observed with the TBL: j p 0.02. The value of 0.018 (6 hr on 15 hr) is then better than the value given by the theoretical formula. This is also the case for the rms signal fluctuation of the T1m, which is 0.027, when the theoretical value is 0.032. The minimum width of an event, fixed by the diffraction, is 2.2 km. As the observation is done toward the opposition, v p 25 km s⫺1 and the minimum duration of an event is 0.1 s, corresponding to two points. The program searches points where the equivalent width is larger than 8 j. For j p 0.018, the simulation of profiles done in R&M2000 shows that such an event corresponds to a ∼200 m KBO. Results.—There is no validated detection at 4 j. Actually, one event deeper than 4 j, observed during the first night, is eliminated because there is no similar event in the T1m light curve (even within the rather large periods where they should occur, owing to our TBL timing problem). This nondetection can be compared with the occultation rates given by equation
TABLE 1 Conditions of Observations for Occultations by Kuiper Belt Objects on the Two Sites and Their Results Results
Conditions
Observatory ⫹Telescope Ø Pic du Midi 2 m . . . . . . Pic du Midi 1 m . . . . . . Teide 1m54 . . . . . . . . . . . a b c
Star Radiusa (m)
Ecliptic Latitude (deg)
Acquisition Frequency (Hz)
rms j
Elapsed Time (hr)
c
18-1210-1 Comp. star 18-1210-1
50 … 50
0.2 … 0.2
20 20 20
0.018 0.02 0.027
18 18 28
BN Cancri Comp. star
900 …
0.87 …
50 50
0.017 0.012
8.3 8.3
Target Star
Validated Data Time (hr) 15
6.7
Projected at 40 AU. Predicted number of events are given for q p 4.5, 4, or 3 size distribution slope, respectively. From the Tycho-2 catalog.
Number of Events at 4 j
Number of Events at 3 j
Detected
Predictedb
Detected
Predictedb
0
2, 1 or 0.25
1
4, 1.7, or 0.3
0
0.1, 0.07 or 0.02
…
…
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(14) in R&M2000. Computed for the 15 hr of exploitable data with j p 0.02, the estimated occultations rate is 0.2 if q p 3, 1 if q p 4, and 2 if q p 4.5. While we cannot yet constrain q with this sole observation campaign, the lack of detection at 4 j is a first indication that the slope of the differential size distribution is probably less than 4.5. The search for less deep events can be done, but keeping in mind that events less deep than 4 j may happen in Gaussian noise: during the 12 hr of selected data where j ≤ 0.02, we expect three fortuitous two-point dips deeper than 3 j. This is of the order of the expected occultations rate, which is 0.3 if q p 3, 1.7 if q p 4, and 4 if q p 4.5. Of 15 events detected, seven events are eliminated because simultaneous dip is visible on the comparison star light curve. The remaining eight possible events are not deep enough to be confirmed by the T1M light curve. However, comparisons of these dips with simulated light curves (R&M2000) show that none but one exhibit the diffraction fringes visible in the simulated profiles. So only this event, shown in Figure 2, could be due to occultation by a KBO. The event depth of 0.06 is compatible with a ∼150 m radius KBO. 3.2. Comparison with One Other Star and Site One other data set of fast photometry observations of a star (see Table 1) has been revisited, especially for testing the same data processing than used on the Pic du Midi data. The d Scuti star BN Cancri (HD 73763) in the Praesepe constellation (M44) has been observed on 1992 February 2 during 8 hr and 20 minutes, on the 1.54 m Carlos Sa´nchez telescope at the Observatorio del Teide (OT, Tenerife, Spain) by M. Chevreton, with one of his four-channel STEPHI network photometers (Belmonte et al. 1994). BN Cnc is a star of visual magnitude 7.80 and A9 V spectral class. Its diameter projected at 40 AU is then 0.9 km and its ecliptic latitude is ⫹0⬚. 87. Two comparison stars were recorded, and the acquisition frequency was 50 Hz. On the 8.3 hr of data, cloudy data are removed, leaving 6.7 hr of data. The rms signal fluctuation is 0.017. The two reference stars are brighter with j equal to 0.012 and 0.015. The minimum width for one event is 2 points, and the minimum depth is 0.068. Results.—No occultation by KBO was detected in these data. This is in agreement with the very small predicted occultation rate of a few hundredths for these 6.7 hr of exploitable data, whatever the value of q (see Table 1). Indeed, BN Cnc is not suitable for occultation by KBO mainly because it has too large an angular radius. These data were difficult to analyze because,
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all night long, clouds generated brief events, sometimes as brief as a real event. Most of them were eliminated because they appeared simultaneously in the three stars’ flux, but some were visible in two or only one light curves. However, because these remaining candidates were all embedded in a train of identified false events, they were rejected as well. This shows the advantage of using a nearby redundant telescope in order to confidently validate such events. Having made this comparison, we may also suggest revisiting in this way all archived star flux data in accordance with the four following criteria: target star of angular radius less than few # 10⫺3 mas, close to the ecliptic (!2⬚), and flux acquired with a rapid enough photometer (≥20 Hz) with a good signal-to-noise ratio (j ⱗ 2%). 4. FINAL REMARKS
Observations organized at the Pic du Midi Observatory in 2000 September to search for KBOs led to a first trend on the slope q of the differential size distribution: the nondetection of occultation at 4 j during this period suggests that q ⱗ 4.5 for objects in the range 0.1–1 km. Moreover, a 3 j dip, which exhibits diffraction fringes, may be ascribed to an occultation by a 150 m radius KBO. The main conclusion of this first occultation by KBOs campaign is that the detection of hectometric KBOs is possible with medium-size class telescopes. It needs to accumulate observations in good conditions using a well-defined and homogeneous analysis method. More generally, observation campaigns of stellar occultation by KBOs on larger telescopes (so scanning smaller objects) could statistically constrain the slope and the expected turnover radius due to collisional erosion of the small KBO size distribution. Finally, why is it so important to explore the size distribution of KBOs? Mainly because the Kuiper belt is probably the most primitive part of the solar system, so any new observational data about its structure, mass, and size gives a clue to understanding the formation of the solar system. In particular, the small size distribution measurement could give an estimation of the protoplanetary disk mass beyond 30 AU and then possibly constrain the timescale of formation of the outer planets. For all these reasons, we must try harder to deeply scan the Kuiper belt with all the means at our disposal: it is high time to begin KBO hunting with stellar occultations. This work has been supported by the “Programme National de Plane´tologie” (PNP, France).
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Roques, F. 2000, in Minor Bodies in the Outer Solar System, ed. A. Fitzsimmons, D. Jewitt, & R. M. West (Berlin: Springer), 171 Roques, F., & Moncuquet, M. 2000, Icarus, 147, 530 (R&M2000) Roques, F., Moncuquet, M., & Sicardy, B. 1987, AJ, 93, 1549 Sicardy, B., Roques, F., & Brahic, A. 1991, Icarus, 89, 220 Stern, A., & McKinnon, W. B. 2000, AJ, 119, 945 Young, A. T. 1967, AJ, 72, 747
