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Register a new userStatistical Methods for Detecting Stellar Occultations by Kuiper Belt Objects: the Taiwanese-American Occultation Survey
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The Taiwanese-American Occultation Survey (TAOS) will detect objects in the Kuiper Belt, by measuring the rate of occultations of stars by these objects, using an array of three to four 50cm wide-field robotic telescopes. Thousands of stars will be monitored, resulting in hundreds of millions of photometric measurements per night. To optimize the success of TAOS, we have investigated various methods of gathering and processing the data and developed statistical methods for detecting occultations. In this paper we discuss these methods. The resulting estimated detection efficiencies will be used to guide the choice of various operational parameters determining the mode of actual observation when the telescopes come on line and begin routine observations. In particular we show how real-time detection algorithms may be constructed, taking advantage of having multiple telescopes. We also discuss a retrospective method for estimating the rate at which occultations occur.
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Results from the first two years of data from the Taiwanese-American Occultation Survey (TAOS) are presented. Stars have been monitored photometrically at 4 Hz or 5 Hz to search for occultations by small (~3 km) Kuiper Belt Objects (KBOs). No statistically significant events were found, allowing us to present an upper bound to the size distribution of KBOs with diameters 0.5 km < D < 28 km.
The Taiwanese-American Occultation Survey (TAOS) operates four fully automatic telescopes to search for occultations of stars by Kuiper Belt Objects. It is a versatile facility that is also useful for the study of initial optical GRB afterglows. This paper provides a detailed description of the TAOS multi-telescope system, control software, and high-speed imaging.
Here we present observations of 7 large Kuiper Belt Objects. From these observations, we extract a point source catalog with $sim0.01$ precision, and astrometry of our target Kuiper Belt Objects with $0.04-0.08$ precision within that catalog. We have developed a new technique to predict the future occurrence of stellar occultations by Kuiper Belt Objects. The technique makes use of a maximum likelihood approach which determines the best-fit adjustment to cataloged orbital elements of an object. Using simulations of a theoretical object, we discuss the merits and weaknesses of this technique compared to the commonly adopted ephemeris offset approach. We demonstrate that both methods suffer from separate weaknesses, and thus, together provide a fair assessment of the true uncertainty in a particular prediction. We present occultation predictions made by both methods for the 7 tracked objects, with dates as late as 2015. Finally, we discuss observations of three separate close passages of Quaoar to field stars, which reveal the accuracy of the element adjustment approach, and which also demonstrate the necessity of considering the uncertainty in stellar position when assessing potential occultations.
Kuiper belt objects (KBOs) are thought to be the remnant of the early solar system, and their size distribution provides an opportunity to explore the formation and evolution of the outer solar system. In particular, the size distribution of kilometre-sized (radius = 1-10 km) KBO represents a signature of initial planetesimal sizes when planets form. These kilometre-sized KBOs are extremely faint, and it is impossible to detect them directly. Instead, monitoring of stellar occultation events is one possible way to discover these small KBOs. Hitherto, however, there has been no observational evidence for the occultation events by KBOs with radii of 1-10 km. Here we report the first detection of a single occultation event candidate by a KBO with a radius of $sim$1.3 km, which is simultaneously provided by two low-cost small telescopes coupled with commercial CMOS cameras. From this detection, we conclude that a surface number density of KBOs with radii exceeding $sim 1.2$ km is $sim 6 times 10^5 {rm deg^{-2}}$. This surface number density favours a theoretical size distribution model with an excess signature at a radius of 1-2 km. If this is a true detection, this implies that planetesimals before their runaway growth phase grow into kilometre-sized objects in the primordial outer solar system and remain as a major population of the present-day Kuiper belt.
Here we measure the absolute magnitude distributions (H-distribution) of the dynamically excited and quiescent (hot and cold) Kuiper Belt objects (KBOs), and test if they share the same H-distribution as the Jupiter Trojans. From a compilation of all useable ecliptic surveys, we find that the KBO H-distributions are well described by broken power-laws. The cold population has a bright-end slope, $alpha_{textrm{1}}=1.5_{-0.2}^{+0.4}$, and break magnitude, $H_{textrm{B}}=6.9_{-0.2}^{+0.1}$ (r-band). The hot population has a shallower bright-end slope of, $alpha_{textrm{1}}=0.87_{-0.2}^{+0.07}$, and break magnitude $H_{textrm{B}}=7.7_{-0.5}^{+1.0}$. Both populations share similar faint end slopes of $alpha_2sim0.2$. We estimate the masses of the hot and cold populations are $sim0.01$ and $sim3times10^{-4} mbox{ M$_{bigoplus}$}$. The broken power-law fit to the Trojan H-distribution has $alpha_textrm{1}=1.0pm0.2$, $alpha_textrm{2}=0.36pm0.01$, and $H_{textrm{B}}=8.3$. The KS test reveals that the probability that the Trojans and cold KBOs share the same parent H-distribution is less than 1 in 1000. When the bimodal albedo distribution of the hot objects is accounted for, there is no evidence that the H-distributions of the Trojans and hot KBOs differ. Our findings are in agreement with the predictions of the Nice model in terms of both mass and H-distribution of the hot and Trojan populations. Wide field survey data suggest that the brightest few hot objects, with $H_{textrm{r}}lesssim3$, do not fall on the steep power-law slope of fainter hot objects. Under the standard hierarchical model of planetesimal formation, it is difficult to account for the similar break diameters of the hot and cold populations given the low mass of the cold belt.
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