X-ray occultation of Scorpius X-1 by small trans-neptunian objects Liang, Jau-shian Institute of Physics, NTHU 2006/04/27

outline Introduction (1). trans-neptunian objects (2). the Idea of Occultation Survey (3). detection limit (4). Sco X-1 Data Searching method (1). Introduction (2). Results Further analysis (1). size distribution (2). event rate

trans-neptunian objects (TNOs) TNOs are objects in the outskirt of our solar system beyond the orbit of Neptune. The TNOs were first discovered in 1992.

The Idea of Occultation Survey

t0t0 t1t1 t2t2 t0t0 t1t1 t2t2 flux time Background star TNO

Distance (AU) Diameter of TNO (km) diffraction limit(Optical) m R = angular size of a target star    D ⊙ / 100 pc    D ⊙ / 1000 pc pencil-beam survey detection limit

Distance (AU) Diameter of TNO (km) diffraction limit(X-ray)    10 5 km/ 2.8 kpc detection limit

Sco X-1 the brightest persistent X-ray source in the sky low-mass X-ray binary system Z-track source X-ray quasi-periodic oscillator 6-20 Hz : 1%–5% amplitude (rms) ~45 Hz : ~1% amplitude (rms) ~ 800 Hz : 0.9% and 1.2% amplitude (rms) ~1100 Hz : 0.6%–1.2% amplitude (rms)

RA,DEC : , (J2000) Distance: 2.8  0.3kpc Orbital period: 18.9 hr Inclination angle: 40 o  6 o Luminosity: 2.3 × ergs s -1 Mass: 1.4M ⊙ and 0.42M ⊙ About 6 o to the north of the eciptic

Data RXTE/PCA archival data of Sco X-1 span over 7 years from 1996 to 2002 total exposure time : ~ 322 ksec count rate ~ 10 5 counts/sec S/N ~ 10 (for a millisecond bin)

Rossi X-Ray Timing Explorer (RXTE): December Altitude: 580 km orbital period: 90 minutes inclination: 23 degrees Instruments: Proportional Counter Array(PCA), High Energy X-ray Timing Experiment (HEXTE), All-Sky Monitor (ASM)

The Proportional Counter Array(PCA) The instrumental properties are: Detectors: 5 proportional counters Collecting area: 6500 square cm Time resolution: 1 microsec Energy range: keV Spatial resolution: collimator with 1 degree FWHM Sensitivity: 0.1 mCrab

searching method derived the difference between the photon counts of the time bin and mean counts in units of the standard deviation The mean counts and standard deviation are derived in a time window running with the time bin.

-  -1  11 22 Number x/  flux time

6.8  Number x/s Fluctuation distribution of flux

58 dip events with random probability lower than were found

Size distribution R = V xte-tno *  T R: diameter V xte-tno : relative projected speed on the sky  T: duration of event

TT flux time 11 -1  Flux drop

sun direction of Sco X-1

power law index: The numerical simulations of coagulation models for planet formation with collisional cascade predict a power index of 3.5 – 4.0 for TNOs smaller than 0.1 – 1 km, of 4.0 – 4.5 for those larger than 10 – 100 km, and a turnover size between 1 and 30 km 10,12.

the size distribution: power law Estimate of occultation rate total solid angle v: velocity,  : distance

the size distribution: broken power law

Relative velocity for a circular orbit

The main belt asteroids Based on the SDSS result, there are about objects with D>1 km. With D 0 = 5 km, b 1 =3, b 2 =1.3, we have  1 = 1.4 X 10 7 km -1 and  2 = 9.4 X 10 5 km -1.

Trans-Neptunian Objects b = 3and estimated total number of TNOs larger than 100km being about 3.8 X 10 4,we have  = 1.1 X km -1 For v = 25 km/s,  min = 30 AU In a 322-ksec data, the expected number of occultation is about 12. Our detection of 58 events is more than that number but not by orders of magnitudes.

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