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Time Series Fitting

Time Series Fitting. Motivation: Solar system, occultation by outer solar system objects. Surveys: TAOS, Pan-STARRS, Whipple. Solar System. The Solar System comprises the Sun and the retinue of celestial objects gravitationally bound to it: the eight planets 162 known moons

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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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