Varun Bhalerao

Dual Channel Photometerfor

KBO search by occultations

Varun Bhalerao

Advisor: Shri Kulkarni

24 Sep 2007

Varun Bhalerao

Motivation

• Kuiper Belt: 30 – 50 AU

• Remnants of protostellar disc

• Size distribution gives information about formation history

• Low mass end not well studied

• Aim: To build an instrument to detect small Kuiper Belt Objects

Slide 1 of 15

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Kuiper Belt• Broken power law

distribution

• Exact break radius rb unknown: 1~50 km

• Probe low mass end to place constraints on population

rb ~ 1 km

rb ~ 50 km

rb ~ 10 km

r -3

r -4

r / [km]

rq

dr

dN

Slide 2 of 15

Bernstein et al. 2004, Cooray & Farmer 2003, Trujillo et al. 2001, Pan & Sari 2005

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Detecting small KBOs

• Too faint for direct imaging: R≈30

• Detect by occultations

• KBO size: ~1 km– Angular size at 40 AU = 35 μas

• Stellar angular diameter:– A0V star, mv=12, angular size = 14 μas

– Projected diameter at 40 AU = 0.4 km

• Star may not be fully occulted

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Occultation Characteristics

• Diffraction ! (Fresnel scale= 1.5 km)

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Other effects

• Wavelength band of observation

• Background star: size, spectral type

• Omnipresent noise !

• Rate:– Opposition / quadrature – 1 event per night ~ 1 event per month

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Current Surveys

• Current surveys: CCD based– TAOS– Roques & Moncuquet

• Other surveys:– Georgevits: Fiber fed spectrograph– Chang et al.: RXTE data

• Limitations: Sampling rate, Sensitivity

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Instrument Design

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Reliable detection• Good signal to noise ratio (aim: 5)

• High speed sampling:– Ensure multiple data points on lightcurve– Sample at 100 Hz

• Rejection of false positives– Monitor two nearby stars simultaneously– Relative Photometry – Detect > 7% variation at R=6– Local effects show up in both lightcurves

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Detector

• APD – Avalanche Photodiode– CCD: readout noise, cost– PMT: quantum efficiency, ease of handling

• Noise characteristics:– NEP: 2 fW/Hz½

• Detection limit:– 0.2 pW R.M.S.– Limiting magnitude R≈8 (1 meter telescope)

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APD spectral response

• Peak 800 nm, FWHM 340 nm

• Peak quantum efficiency: 0.4

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Telescope• Table Mountain

Observatory– Pomona college– NASA

• Telescope:– 1 meter aperture– F/9.5– Useful FOV 11’– Plate scale 21”/mm

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Optical Design

• Direct focus not possible

• Pickoff mirrors to accommodate 2 modules

• Field lens to correct for tracking errors

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Mechanical Design

Adjusting screw

Diagonal mirror

Moving stage

APD / PMT

Light tight box

Blue indicates light path

Stage motion

Micrometer

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Testing

• Asteroid occultations– None at site in next year

• Optical pulsar: Crab– mv≈16

• Lunar occultations– Earthshine, star magnitude…

• Other rapid transients

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Current Status

• One APD module delivered, one awaited

• Optical design– Code-V simulations

• Observing time:– Second half of October– Second half of November

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Questions

Occultation Lightcurves

Motivation Detectors

Optical Design

TestingMechanical

Design

Slide 15 of 15

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Extra Slides

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Making a broadband lightcurve

KBO diameter: 0.6 kmStar diameter: 1.0 km

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Broadband lightcurves

(KBO radii)

Background sourcediameter: 1.0 km

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Monochrome point source

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Monochrome extended source

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Geometric regime

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Non-central occultations

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Size-distance degeneracy

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ORT: expected pattern

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ORT: Observations

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Fourier transform

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ORT: Reduced lightcurve

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Bessel and Lommel functions

m

m

m x

mmxJ

2

0 2)!(!

)1()(

)()1(),( 2

2

0

kn

kn

k

kn JU

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Lightcurve

)(2

cos),(2

)(2

sin),(2

),(),(1

)(

2222

2221

22

21

U

U

UU

I

),(),()( 21

20 UUI )(

)(

Fr

Fx Distance of KBO center from line of sight

KBO Radius2

aF

Fresnel scale atdistance a from observer

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Projected star sizes

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