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Time Series Fitting

Explore the Whipple mission's goals to study solar system objects beyond Neptune using occultation events and advanced telescope technology. Track thousands of stars to detect small bodies in the Kuiper Belt, Sedna region, and Oort Cloud. Investigate various fitting methods for event detection and analysis.

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Time Series Fitting

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  1. Time Series Fitting • Motivation: Solar system, occultation by outer solar system objects. • Surveys: TAOS, Pan-STARRS, Whipple

  2. Solar System • The Solar System comprises the Sun and the retinue of celestial objects gravitationally bound to it: • the eight planets • 162 known moons • three currently identified dwarf planets and their known moons (Pluto, Ceres and Eris) • thousands of small bodies. This last category includes asteroids, meteoroids, comets, and interplanetary dust. • Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, Neptune.

  3. Use occultations of background stars:

  4. A tantalizing example has been reported by Schlichting et al: the HST-FGS event:

  5. Whipple • Indirect exploration of the outer solar system • The primary goals of the Whipple mission are to detect and characterize objects in all of the major solar system populations beyond Neptune: • Kuiper Belt (and scattered disk …) • “Sedna region” (100 – 2,000 AU) • Oort Cloud (3,000 AU - ?) • Achieve these goals by monitoring >10,000 stars to look for occultations by small objects • 10,000 stars for 24 hours at 50Hz = 4*10^13 measurements

  6. PS1 Video GS ZONE LSST limit ASTEROIDs PS1 limit OCCULTATION EXLUSIVE ZONE KBOs Sedna Region Ooort Cloud Schlicting 2010 Protopapas PS1@Belfast

  7. Whipple: a Discovery Class mission to search for occultations • Original concept inspired by Kepler • Schmidt-Cassegrain telescope design • 37 square degree field of view • Earth leading orbit: • opposite direction from Spitzer & Kepler

  8. Whipple: a proposed spacecraft to search for occultations

  9. Whipple: a proposed spacecraft to search for occultations

  10. Whipple: a proposed spacecraft to search for occultations • Hybrid CMOS focal plane array • 10,000 (80,000) stars, 40 (5) Hz readout

  11. Anticipated Event Rates: • Oort Cloud: • 1012 objects (D>3 km) each in Inner and Outer Oort Clouds • N(>D) ~ D-1.8; randomized eccentricities • 10 – 100 events per year • “Sedna” population: • Take guidance from the Caltech survey (Meg Schwamb’s talk) • 100 AU < a < 1000 AU; q > 30 AU • 1-1000 per year. Very uncertain! • Kuiper Belt: • ~5,000 events per year (Schlichting et al 2009 event)

  12. Comparison between TAOS, Pan-STARRS, IMACS and Whipple:

  13. Scan statistics w r Idea: Given a time series find the region [sub sequence of measurements] that are not consistent with noise. Original idea originates from epidemiology time series: fi the value at time ti fi 0 10 20 30 40 50 60 70 80 work with Dan Preston and Iara Cury

  14. Part a: Event detection/Event fitting • First approach: Rank statistics. • Second approach: Alex Blocker’s method • What is the best method of fitting events

  15. Don’t fit it too much I hear your hypo-thesis but I think I heard enough My sh** is dead and outdated top notch to the top, I’m rated while you till tikin I’m wrong I know, I gotta reason to be so 44 years old, and no one seems to see that I’m worth my weight in gold but still no clue on stati-stics Just gimme a chance, show the problem, you’ll see if ya f** with me ya f**in with the whole time -e - series.

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