Localization capabilities of ground based interferometers Lee - - PowerPoint PPT Presentation

Localization capabilities of ground based interferometers

Lee Samuel Finn Penn State University

Goal, assumptions, outline

• Goal: How well can ground-based detectors localize

gravitational wave sources.

• Assumptions

– Simultaneous observation by at least four geographically distinct interferometric detectors

• Next 5y: LIGO (2) plus at least three of GEO, TAMA, Virgo
• > 5 yr horizon: LIGO (2) plus at least three of ACIGA, GEO,

LCGT, Virgo/Ego

• Outline

– Basic concepts – Methodology – Results

Basic concepts

• A single ground-based

interferometer has no directional sensitivity to inspiraling binaries

– NS/NS signal passes through band in ~ 20s

• Directional information

determined by time-of- arrival information at different detectors

– Two detectors: a circle in sky normal to axis between detectors

– Three detectors: intersection of two circles – Four (or more) detectors: a single point (patch)

• Arrival time?

– Define in terms of canonical feature of signal: e.g., when is instantaneous frequency 100Hz.

• Arrival time accuracy?

– No better than 0.1ms (8/SNR)

Methodology

• Wave incident direction n yields (relative) arrival

times T.

– T = A n

• N detectors? A is Nx3 matrix whose rows are detector location

vectors

• Pick point in sky & determine exact arrival times T
• Introduce timing errors dT

– Assume normally distributed, zero mean, σ ~ 1 ms

• Invert, in least squares sense, (T+dT) = A n’ to find

best-fit angle of incidence

• Find angle between n’, n
• Repeat to determine error distribution

Results

• GEO, LIGO, Virgo
• Median localization

error

– I.e., half time error is greater, half time less

• Error ranges by factor 2

– Maximum error when source direction normal to axis between detectors

Results: GEO, LCGT, LIGO, Virgo

• Maximum error

significantly reduced

– Minimum error slightly improved

• Mean error on sky

significantly reduced

Results: Add an Australian Detector

• ACIGA, GEO, LCGT,

LIGO, Virgo

• Maximum error

reduced again

• Mean sky error reduced

further

• Minimum error never

gets better than ~2 degrees

With, without Australian Detector

Caveats and Conclusions

• Assumption that all errors are the same

– GEO much less sensitive than LIGO, Virgo to binary inspiral and will have greater timing errors.

• Gravitational wave astronomy needs at least

four, large, well separated detectors

– Southern Hemisphere detector would be especially helpful