Calibration of the gravitational wave signal in the LIGO detectors Gabriela Gonzalez (LSU), Mike Landry (LIGO-LHO), Patrick Sutton (PSU) with the calibration team: Rana Adhikari (LIGO-MIT), Brian O’Reilly (LIGO-LLO), and many others…

Gravitational Wave Signal Originates in a photodetector at the antisymmetric port. It is a demodulated photocurrent: (L1,H1,H2):LSC-AS_Q It is proportional to the differential length of the arm cavities, and thus the gw strain. In the frequency domain, AS_Q(f)=C(f)h(f) C(f): calibration function (complex)

Detector control system Gravitational wave strain: h=X ext /L Detected signal: H(f)=open loop gain=G(f)A(f)C(f) interferometer digital filters pendulum calibration

Calibrated spectrum Calibration lines

Open Loop Gain: Fits Simulink model (R. Adhikari)

Open Loop Gain: Fits Parameters in the fit: - Time delays - Optical gain

Changing optical gain  =scale factor for open loop gain

Changing optical gain

Scale factor for open loop gain

Scale factor for Open Loop Gain

Interferometer sensitivity and alignment Carrier power in the arm cavities Sideband Power in the recycling cavity Signal  carrier x sideband

Changing optical gain

LIGO Autocalibrator Tcl script to expedite calibration Calls to DTT (ifo transfer function, psd estimate), Root and/or Matlab manipulation Output (web-navigable) data in ascii, xml, pdf (transfer functions, noise data, olg, sensing functions) Pole-zero fitting useful for rapid commissioning New version interpolates TF, no fits

Autocalibrator vs S1 analyses

V2 Autocalibrator Latest version does Interpolation of transfer Function (no fit problems) Not as flexible for Commissioning Adding matlab fit and DTT cal record shortly

Autocalibrator for S2 S2 run ~per day per ifo In addition to noise curves, output open loop gain and sensing function as a check on point calibration/alpha propagation method Brian O’Reilly has version running at LLO

online resources online resources include the calibration homepage – history (ascii strain and displacement vs time, elog pointers) commissioning (online autocalibration automatic storage of data) science (S1) and engineering (E2-E9) runs And the official page on LIGO sensitivity –

E9 & S2 Calibrations from SenseMonitor SenseMonitor: A DMT program which provides real-time estimates of the average range to which an IFO is sensitive with SNR > 8 to the inspiral of a M o neutron-star binary. Runs continuously at LLO, LHO. Tracks the response function of the IFO to make its range estimate, therefore is a natural tool for providing near-real-time calibration information.

What SenseMonitor Needs Reference calibration information supplied to SenseMonitor: – Measured/modelled open-loop gain H(f) and sensing function C(f) of the IFO, supplied in ASCII data files. – RMS amplitude of the 1kHz calibration line in AS_Q during calibration run. – Injected amplitude of the 1kHz calibration line in EXC during calibration run. – Digital gain (`GW_K' ®  during S1) during calibration run.

What SenseMonitor Gives For each 60 sec of AS_Q data, SenseMonitor: – measures the current amplitude of the 1kHz calibration line. – using the current line amplitude and the reference data, computes the new value of calibration parameter `  '. – exports , , range data to DMTViewer. Once per hour: – exports , , range data to trend frames.

at start 1/minute SenseMonitor ampl AS_Q = ampl EXC = 0.25 beta = 1.0 H(f), C(f): 3.00e1 5.28e e e3 2.45e e-2 Reference Calibration: AS_Q Data: 1/minute 1/hour , range,... Trend frames: , range,... DMTViewer:

Caveats Up to 1-hour latency in writing trend frames. Reference calibration data (open loop gain, sensing function, etc.) not available in trend frames. Calibration lines are not robust (sometimes crash); alpha is not updated if the line amplitude is 150% nominal. Alpha, beta set to zero if IFO is not locked in common mode.

Expectations for S2 Good models Frequent checks (autocalibrators) Automatic on-line calibration and reach measurement (SenseMon)