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

t0

t1

t2

t0 t1 t2

flux

time

Background star

TNO

Distance (AU)

Dia

met

er o

f T

NO

(k

m)

diffraction limit(Optical)

mR= 20 25 30

angular size of a target star

D ⊙

/ 100 pc

D ⊙

/ 1000 pcpencil-b

eam surve

y

detection limit

Distance (AU)

Dia

met

er o

f T

NO

(k

m)

diffraction limit(X-ray)

105 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 : 16 19 55.07, -15 38 24.8 (J2000)• Distance: 2.8 0.3kpc• Orbital period: 18.9 hr• Inclination angle: 40o 6o

• Luminosity: 2.3 × 1038 ergs s-1

• Mass: 1.4M⊙ and 0.42M⊙

• About 6o 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 ~ 105 counts/sec

• S/N ~ 10 (for a millisecond bin)

Rossi X-Ray Timing Explorer (RXTE): December 1995 -

Altitude: 580 kmorbital period: 90 minutesinclination: 23 degreesInstruments: 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: 2 - 60 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

12

Num

ber

x/0 1 2 3-1-2-3

flux

time

6.8

Num

ber

x/s

Fluctuation distribution of flux

58 dip events with random probability lower than 10-3 were found

Size distribution

• R = Vxte-tno * T

R: diameter

Vxte-tno: relative projected speed on the sky

T: duration of event

T

flux

time

1

-1

Flux drop

)()( tnoxtetnoxte VVV

earthtnoearthtno ddVV //

xteV

)( xteVtnoV

)( tnoV

sun

direction of Sco X-1

AUdtno 43

power law index: 3.4 +- 0.5

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 km10,12.

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 670000 objects with D>1 km.With D0 = 5 km, b1=3, b2=1.3, we have 1= 1.4 X 107 km-1 and 2 = 9.4 X 105 km-1.

Trans-Neptunian Objects

b = 3and estimated total number of TNOs larger than 100km being about 3.8 X 104,we have = 1.1 X 1011 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.

Thank you