LISA. William Joseph Weber Dipartimento di Fisica, Università di Trento. 4 th VESF School on Gravitational Waves VIRGO Cascina 28 May 2009

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1 LISA William Joseph Weber Dipartimento di Fisica, Università di Trento LISA / LISA Pathfinder Project 4 th VESF School on Gravitational Waves VIRGO Cascina 28 May 2009

2 Laser Interferometer Space Antenna NASA / ESA Mission, to be launched in 2018

3 LISA: Laser Interferometer Space Antenna 2 semi-independent km Michelson interferometers with laser transponders (measurement noise 40 pm/hz 1/2 ) 3 pairs of free falling test masses in 3 Drag-Free spacecraft shields ( acceleration noise < m/s 2 /Hz 1/2 ) km LISA goals: GW Band: 0.1 mhz 1 Hz Sensitivity: S 1/2 h ~10-20 Hz -1/2 at 1 mhz (h)~ for 1 year integration

4 LISA Constellation 5 million km equilateral triangle 60 tilt with respect to ecliptic 1 AU from sun, 20 behind earth

5 LISA Orbits 3 phased orbits with eccentricity ε.01 and inclination θ INC 1 Maintains equilateral configuration within 1 Sweeps antenna sensitivity through the sky, frequency and amplitude modulation for source location

6 LISA Interferometry 3 5 million km arms: 33 sec 2-way light time (1 st interferometry null at 30 mhz) L 1 L 2 Laser divergence: Telescope D ~ 30 cm YAG 1.06 µm Arriving Beam ~20 km SEND RECEIVE 1 W ~200 pw (< 100 pw final) Shot Noise: S 1/ 2 δl = hc λ 2π P received = 2 hc λ λ L 4 4π P η D sent 2 10 pm/hz 1/2 Laser transponding: outgoing light phase locked to incoming beam Goal: keep all optical path errors within 40 pm/hz 1/2

7 LISA astronomy: source location θ f, h, kˆ, hˆ φ Axis of max sensitivity Constellation orbital velocity (v/c~10-4 ) sensitivity lobes of antenna pattern sweep through sky 2 f ~ ± (T= 1 year) T signals doppler shifted by orbital velocity of observatory v f ~ ± fgw c Use frequency and amplitude modulation to locate sources in the sky Synthetic aperture telescope with diameter D=2 AU!! λ GW θ For S/N = 1 D

8 LISA astronomy: wave polarization ( L1 L2 ) L 2 L ( L + L 2L ) independent interferometry signals Measure both gravitational wave strain polarizations h + h x L 1 Other combination relatively insensitive to gravity wave signal (L 1 + L 2 + L 3 ) Discriminate instrumental noise from a noisy GW background! (ie, we can turn off the gravitational wave signal)

9 Ground and Space GW Observatories Complementary

10 LISA Signals: mass, separation, chirp time, and distance [equal mass binaries with circular orbits] Keplerian orbit frequency ( x 2) Energy decay time τ GM a 2 ( 2πf ) = 3 TOT Black hole merger h~ c ( 2πf ) 2 τ r GW Product of measured strain and measured decay time gives distance to source!

11 LISA Gravitational Wave Astronomy: Compact Object Mergers Astronomers tell us... Most stars are in binary systems Many stars collapse to compact relativistic stars: Neutron stars, White dwarfs, black holes... but they are hard to see electromagnetically Only 5 merging NS-NS systems have been found (need to be lucky to see the pulsar) Only roughly 50 ultra-compact binaries observed (mostly WD- WD)

12 LISA and Galaxial Binaries Known calibration signals Signal guaranteed for a functioning LISA! Verification of GR predictions for GW strain

13 Recent binary neutron star discovery PSR J neutron stars (M TOT ~ 2.8 M ) 2.4 hour orbital period 3 times faster than HT, doubles strain signal, easier detection at higher frequency.25 mhz 2006 orbital decay detected, confirms GR at 1 % level only 2000 light years away 10 times closer than HT possibly detectable by LISA (strain of order at 0.25 mhz)? changes estimates of population of galaxial NS-NS binary mergers 1 / 5000 years in our galaxy 200 with τ < 1 million years (f > 2 mhz) LISA should provide a real measurement of populations of galactic binaries

14 Stochastic GW noise: galaxial binaries and primordial backgrounds 1 year measurement: f 1 1 year.03 µhz 10 5 frequency bins up to 3 mhz many galactic white dwarf binaries (perhaps 10 8 ), lots per frequency bin below 3 mhz, produces noisy background

15 Discrimination of noisy confusion limited galactic binary foreground Sagnac variable to characterize instrument noise from noisy gravitational foreground Annual modulation of noisy from galactic center Sample data with instrument noise

16 Gravitational Wave Astronomy: Massive Black Hole Mergers Astronomers tell us... Many galaxies have massive black hole at core Most galaxies merge... but we can t see them Our Milky Way appears to have a M black hole at its core

17 Quasar OJ287: gravitational radiation in a massive black hole system Observation of quasi-periodic (12 year) quasar light bursts since 1913, occuring in pairs Valtonen et al, Nature, 2008 Optical bursts from an orbiting object penetrating accretion disk of a massive black hole Mass M determined by geodesic precession of eccentricity, 39 / orbit September 2007 burst without gravitational radiation, burst would arrive 20 days later! 10 %-level validation of general relativity description of gravitational radiation orbit apogee roughly 10 R BH The next major periodic outburst is expected in early January 2016, by which time there may be methods to measure the gravitational waves directly. -- Valtonen, et al, Nature, 2008

18 Coalescence of Massive Black Hole Pairs Massive black hole binaries from cores of merging galaxies ( M ) expect to see tens in a 5 year mission SNR up to 2000 in one year at z 1 3 observable anywhere in the universe visibility up to one year before merger chirp rate and amplitude combine to give the luminosity distance (0.2 % -1% uncertainties) frequency and amplitude modulation combine to give angular resolution (to within a square degree) well calibrated source distances formation of MBH as function of redshift with optical counterpart, measure distance redshift relationship

19 Simulated strain time series for a MBH merger at redshift z= 5 S/N ratio >> 1 even for single cycles near the end of a MBH merger ( M at z= 5) High S/N observation of MBH mergers anywhere in the relevant universe!

20 Sources: Black Hole Gravitational Captures Gravitational capture of compact object (1-10 M BH, NS) High rate (order 10 per year) SNR Trajectory of point particle near event horizon of a BH test of relativity in strongly relativistic limit

21 Gravitational waves physics Gravitational wave observation (phase, polarization, amplitudes) can probe general relativity in limit of strong gravitational fields, near black hole event horizons Gravitational waves drive dynamics in such systems need compact test particle NS or BH not tidally disrupted near MBH Example: small test particle black hole falling into a massive black hole

22 High precision tests of GR demand high precision GR radiation solutions!! New result in numerical relativity: complete GW waveform of BH-BH merger Successfully bridged the gap between inspiral and ringdown phases

23 LISA Gravitational Wave Astronomy: Cosmic Gravitational Wave Background? Early universe opaque to EM radiation until recombination of neutral atoms liberated the cosmic microwave background photons (400,000 years after Big Bang) Universe transparent to GW since much earlier BOOMERANG map of CMB Gravitational waves could allow study of big bang, inflation, early universe phase transitions

24 LISA Sensitivity Curve Test mass acceleration noise Photon shot noise Decreased interferometer response Sensitivity curve for 1 year integration and S/N=5

25 LISA Interferometry: TM separation as 2 part measurement long interferometer and (2) short interferometer *** pm precision requires subtracting nm spacecraft motion (thruster noise) Gerhard Heinzel, AEI

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27 LISA Optical Bench Astrium Germany design, ESA study 3 interferometers Light from 2 lasers L1 to remote SC (1 W), local TM L2 (beam for 2nd arm) local oscillator for incoming beam and TM readout TM readout (L1, L2 as LO) Remote beam readout (far laser, L2 as LO) L1 L2 measurement of relative phase noise

28 Interferometry challenges: Keplerian breathing of orbital formation Classical orbital dynamics do not produce rigid rotation of equilateral triangle φ~ 1 L ~ km v~ 20m/s telescopeangle mustbreathe unequal arm interferometer relativevelocitycausesdopplershiftup to20 MHz(fringerates) interferometer signals are RF beat notes, with science signal as a mhz phase modulation

29 Interferometry challenges: frequency noise with unequal arm IF x f f L With L ~ km, need f~ µhz/hz 1/2 (relative stability of /Hz 1/2 ) More than 7 orders of magnitude improvement from cavity stabilized laser!

30 Unequal arms Time Delay Interferometry km length difference 7 orders of magnitude too big Instead of reducing Lto order 10 m, measure Lto 10 m precision Recombine phase data with opportune delays to cancel laser phase noise synthesize an effectively equal arm interferometer [Tinto& Armstrong, PRD, 1999] Can synthesize different combos (including Sagnac) Can also handle relative SC motion 2L2 2L1 z1 t z1 ( t) z2 t z2 ( t) c c

31 Interferometry challenges: further frequency stabilization to relax TDI Cavity pre-stabilization is limited by the optical cavity length stability. δl/l ~ / Hz Take advantage of 5 million km LISA arm stability: δl/l ~ / Hz Daniel Shaddock, JPL + arm locking

32 LISA Low Frequency Sensitivity: Importance of free-fall Stray acceleration noise (1/f 2 ) for flat spectrum h min L L min L 1 T S 1/ 2 f 2 mω h min ~ at 1 mhz (S/N=5)requires S f 1/2 /m ~ m/s 2 / Hz 1/2

33 Purity of free-fall critical to LISA science Example: massive black hole (MBH) mergers Integrated SNR at 1 week intervals for year before merger Assuming LISA goal: S a 1/2 < 3 fm/s 2 /Hz 1/2 at 0.1 mhz Acceleration noise at and below 0.1 mhz determines how well, how far, and how early we will see the most massive black hole mergers. do we see the merger for long enough to use orbital modulation to pinpoint it? To search with optical telescopes?

34 LISA differential accelerometry performance Measurement of tidal accelerations between 2 or more geodesic reference test masses 2 a ω Lh 2 a ω x measure h n effective GW acceleration distance measurement noise a force f m Stray force noise imperfect geodesic motion LISA differential accelerometry represents a large leap in performance requires significant design changes requires experimental verification Free-fall at low frequencies difficult to test on ground Dedicated geodesic motion flight mission LISA Pathfinder

35 Stray forces and drag-free control Solar radiation pressure would give 10 nm / s 2 acceleration to 1 kg test mass Spacecraft shield (mass M) Relative position measurement x m µnewton Thrusters Drag Free loop gain Mω DF 2 m internal stray forces f str Springlike coupling to spacecraft ω p motion( stiffness ) mω p 2 external forces on satellite F str Common problem for several precision space experiments: LISA, GPB, STEP...

36 LISA Drag-free Control Residual acceleration noise: a res f str 2 F = + ω str p xn + 2 m Mω DF Relative spacecraft TM motion Role of LISA drag-free control is to reduce test mass acceleration noise, with respect to distant test mass NOT to minimize relative spacecraft motion NOT to produce most precise spacecraft orbit

37 LISA control: spacecraft follows 2 masses at once

38 LISA control: spacecraft follows 2 masses at once

39 LISA control: spacecraft follows 2 masses at once

40 LISA control: spacecraft follows 2 masses at once 1: Move the spacecraft and centre the masses along laser beams

41 LISA control: spacecraft follows 2 masses at once 1: Move the spacecraft and centre the masses along laser beams

42 LISA control: spacecraft follows 2 masses at once 1: Move the spacecraft and centre the masses along laser beams

43 LISA control: spacecraft follows 2 masses at once 1: Move the spacecraft and centre the masses along laser beams

44 LISA control: spacecraft follows 2 masses at once 2: Re-center the masses along orthogonal axes using electrostatic forces

45 LISA control: spacecraft follows 2 masses at once 2: Re-center the masses along orthogonal axes using electrostatic forces

46 LISA control: spacecraft follows 2 masses at once 2: Re-center the masses along orthogonal axes using electrostatic forces

47 LISA control: spacecraft follows 2 masses at once Need to sense all 6 degrees of freedom of the test mass Need to apply (electrostatic) actuation forces on non-interferometry degrees of freedom

48 Key LISA test mass acceleration noise sources Gap d x Springlike coupling to spacecraft: sensor readout stiffness (ω p2 x n ~ d) gravity gradients 10-6 N/m Residual acceleration noise: a res gas damping magnetic noise readout back action (~ d -2 ) Stray electric fields + charge/dielectric noise (~ d -1,d -2 ) T radiation pressure, radiometric, outgassing effects Local gravitational noise Control force noise (leakage) 6 fn/hz 1/2 External forces on SC, finite control loop bandwidth f str 2 F = + ω str p xn + 2 m Mω DF Sensor noise Low frequency stability! 2.5 nm/hz 1/2

49 Gravitational Reference Sensor Design Defines TM environment Provide nm/hz 1/2 measurement on all axes Provides electrostatic voltages (force, measurement) 46 mm cubic Au / Pt test mass (1-2 kg) 6 DOF gap sensing capacitive sensor Contact free sensing bias injection Resonant inductive bridge readout (100 khz) ~ 1 nm/hz 1/2 thermal noise floor Audio frequency electrostatic force actuation avoid DC voltages Large gaps (2 4 mm) limit electrostatic disturbances High thermal conductivity metal (Mo) / sapphire construction limit thermal gradients V AC 100 khz L V M C s1 C p C s2 C p L V ACT1 V ACT2

50 Completing the GRS Caging (2000 N load during launch) UV light photoelectric TM discharge system Vacuum chamber + getter pumps (10-5 Pa) Optical windows for IFO readout

51 What do we know about LISA free-fall performance? experimental verification LISA differential accelerometry represents a large leap in performance requires significant design changes requires experimental verification Two approaches... Torsion pendulum small force testing (Low frequency free-fall difficult to test on ground) Dedicated geodesic motion flight mission LISA Pathfinder LISA LPF LPF is a single interferometry arm of LISA squeezed into a single spacecraft

52 LISA Pathfinder (2011): Einstein s Geodesic Explorer Mostly ESA test mission for freefall in LISA and other future precision space missions Shrink 1 LISA arm from 5 million km to 30 cm Flight test of LISA free-fall at 30 fm/s 2 /Hz 1/2 level at 1 mhz Flight test of LISA local interferometry measurement at 10 pm/hz 1/2 level

53 LISA Pathfinder Mission Launch mid-2011 Roughly 2 month journey to Lagrange point 1 Commissioning + 3 months LTP (ESA), 3 months DRS (NASA) VEGA Launcher

54 Free-fall flight test: LISA Pathfinder (2011) drag-free TM1 X base ~ 30 cm TM2 electrostatically suspended x 12 x 2 -x 1 x Optical interferometer Differential displacement x 12 Compare relative noise in orbits of two free-falling test masses 1 spacecraft, 1 measurement axis (30 cm baseline) Relative displacement x 12 measured with interferometer to probe drag-free performance LTP Goal: demonstrate a res < m/s 2 /Hz 1/2 for f > 1 mhz (relaxed from LISA by factor 10 in both acceleration noise and frequency)

55 LPF primary measurement: stray force noise f str TM1 x 12 TM2 Differential force noise Satellite follows TM1 with sensor x 1 and µn thrusters TM2 forced to follow TM1, using differential x 1 x 2 IFO and sensor 2 electrostatic actuation Open-loop differential acceleration in differential IFO signal (calibrate transfer function) Baseline stability (Zerodur) 1 f f F x ω ω δxω x ω 2 = ω IFO 1 x str + 2 2, 2 ω 2 ω 2 ω 2 m n1 ω 1p p p n opt p + 2 p ES M 2 DF Satellite coupling (can be tuned to zero) IFO readout noise LPF f f a 2 LPF = 1 + x 1 ω 2 ω δxω x ω ω m 2 p + 2 p n, opt 2 p 1p LISA a res f str 2 Fstr = + ω p xn + 2 m Mω DF

56 LPF Hardware: Interferometry Readout Mach Zehnder heterodyne interferometer on Zerodur optical bench 10 pm/hz 1/2 precision Relative (x 1 x 2 ) and x 1 measurement IFO, + frequency IFO, reference IFO, amplitude stabilization Quadrant photodiodes for wavefront sensing angular readout F. Steir et al, CQG 26 (2009) LISA LPF performance already reached with fixed mirrors

57 LPF Hardware: MicroNewton Thrusters Need to provide roughly 10 µn thrust (radiation pressure compensation) Need to allow nm/hz 1/2 SC centering 0.1 µn/hz 1/2 Important for minimizing satellite coupling (measurement axis), limiting IFO cross-talk (other axes) Cs-Slit FEEP (Alta, Italy) Colloidal thrusters for LISA Pathfinder (Busek, USA) Colloidal thruster noise not detectable in thrust stand measurement FEEPs: successful life test (1000 Ns total impulse) Performance test results expected soon

58 LISA Pathfinder: performance limited by 2 TM in 1 SC gravitational balancing and applied forces g 1 g 2 F S SC can only follow 1 TM along x (2 TM, 1 sensitive axis) (UNLIKE LISA!!) Any differential DC acceleration must be balanced by applied (electrostatic) forces Noise in applied voltage gives noisy force V 2 = 2FS 1/ 2 1/ 2 F δv / V S = 2 g S 1/ 2 1/ 2 a DC δv / V 2 g < 1.3 nm/s 1/ 2 6 1/2 S δ V / V < 2 10 /Hz GRS compensation masses reduce 30 nm/s 2 to 0.1 nm/s 2 Modelling accuracy, positioning

59 LISA Pathfinder: performance limited by 2 TM in 1 SC gravitational balancing and applied forces 2 F V g < 1.3 nm/s S = 2FS 1/ 2 1/ 2 F δv / V S = 2 a S 1/ 2 1/ 2 a DC δv / V 1/ 2 6 1/2 S δ V / V < 2 10 /Hz 2 Actuation voltage carrier amplitude measured to be stable to 3 ppm/hz 1/2 at 1 mhz Less than 10 fm/s 2 /Hz 1/2 acceleration noise (electronics Contraves Space, test U. Trento / ETH Zurich)

60 LISA Pathfinder: avoiding actuation instabilities with free-fall mode compensate average DC force imbalance by applying a large impulse followed by free-fall (parabolic flight!) x Grynagier, CQG 26(2009) Example: Apply 300 x average needed force for 1s, followed by 300 s free-fall Keep displacement to 10 micron range Analyze force spectrum, without applied actuation forces, even to lower frequencies, with windowed spectrum estimation

61 Preparing for LISA Pathfinder: Ground testing of free-fall with prototype GRS and torsion pendulum small force measurements Mo / Shapal (2 mm gaps) 1-mass torsion pendulum (torques) Mo / Shapal EM (4 mm gaps, LPF geometry) Mo / Sapphire LPF EM LPF materials 4-mass torsion pendulum (direct force sensitivity) Lightweight TM test surface forces Bulk forces (gravitational, magnetic) tested separately and with LISA PF

62 Torsion pendulum testing with replica of flight model GRS electrode housing + replica of FM electronics Starting in Trento (as we speak!)

63 Torsion pendulum ground testing of LISA Free-fall Light-weight test mass suspended as inertial member of a low frequency torsion pendulum, surrounded by sensor housing Measure stray surfaces forces as deflections of pendulum angular rotation to within < 100 LISAgoal <10 LTP goal Precision coherent measurement of known disturbances

64 Multiple degree of freedom torsion pendulum for testing free-fall Sensitive force measurements on (at least) 2 TM degrees of freedom Can we achieve femto-g free fall in one axis while actively controlling another TM along another axis? How does control along some axes leak into forces and force gradients along other axes? Can we perform pm measurements with a TM that is moving in all 6 degrees of freedom? PETER (pendolo roto-traslazionale) In development at U. Firenze and U. Roma Tor Vergata soft torsional and translational degrees of freedom

65 Single mass torsion pendulum for LISA ground testing 110 gm TM + mirror (hollow Al, Au coated) 25 µm, 1 m long W fiber 2 mhz resonant frequency, Q 3000 NEW! Fused silica fiber, Q (τ E 2 years) Passive magnetic damping of swing mode (τ100 s for swing mode) Autocollimator and capacitive readouts On demand electrostatic damping /actuation of swing mode Turbo vacuum pump 10-7 mb Thermally controlled foam room (50 mk long term stability)

66 Upper limits on GRS force noise: 1 mass pendulum, deflection monitored with capacitive and optical autocollimator for 3 days Period 591 s, Q = k B T Γ Typical thermal peakpeak pendulum oscillation Near 1 mhz, close to thermal noise High frequencies readout noise Low frequency excess

67 Upper limits on GRS force noise: Distinguish true torque on pendulum from background SN = R{ SN, } sensor noise with cross-correlation analysis: AC NS Less than factor 2 in power from Brownian noise for decade of frequency around 1 mhz Unexplained excess at lower frequencies (coupling to environment? Sensor itself?) Excess at higher frequencies rotational motion of apparatus (order 10 nrad/hz 1/2 ) desire to improve sensitivity with lower thermal noise and better (interferometric) readout

68 Torsion pendulum upper limits on GRS force noise: Mo / sapphire sensor + EM FEE, 1TM pendulum Angular deflection measurement with two readouts (GRS and autocollimator) distinguish true torque noise floor from background readout noise S = R { S, } N N N AC S Recent upgrade of torsion fiber from Tungsten (Q =3000) to Fused Silica (Q = )

69 Upper limits on GRS force noise: conversion from torque force (acceleration) rule out large class of TM surface disturbances at level of 50 fm/s 2 /Hz 1/2 at 1 mhz within factor 2 of LPF goal achieving similar acceleration noise levels with LISA would allow observation of galactic binaries

70 Measure force gradient for satellite coupling a res f m = str + ω 2 p x Sensor OFF stray stiffness Sensing electrostatic stiffness Sensor stiffness (modeled): ~ 100 nn / m LPF sensor bias Measured stray stiffness (sensor OFF) ~ 5 nn / m (DC bias? δv RMS ~ 90 mv) Total LISA stiffness budget: ~ 1000 nn / m Unexpected stiffness likely not an issue for LISA (4 mm gaps!) LISA Pathfinder will perform full stiffness measurement (including gravity gradients)

71 Thermal gradient-induced forces radiometric T Fradiom = AP κ 4 T 18 pn/k κ RAD RAD κrad 1.25 PRD, (2007) radiation pressure F rad press 3 8 σ AT = T κ 3 c 27 pn/k κ RP RP κ RP 0.3 ( r=95%) outgassing F outgas T T ΘQ??? 2 outgas T Numerical simulations for finite size calculations df/d T ~ 100 pn / K need S T 1/2 < 10 µk / Hz 1/2 outgassing hard to predict need a measurement

72 Thermalgradient-induced forces Direct measurement of force coupling df x /d T relevant to LISA force noise Much easier analysis of temperature distribution Preliminary results: Verify radiometric model (10%) 309 K 298 K LISA goal (100 pn / K) Outgassing observed (pre-bake) Zero pressure data increase faster than radiation pressure s T 3 Measure roughly 100 pn/k at 10-5 Pa / 25 C LISA pressure 10-5 Pa Looks OK for LISA Experiment to be repeated on LPF Will characterize thermal environment on-board

73 Brownian force noise from residual gas damping S = 4k T β Viscous gas damping coefficient F x B Order of magnitude estimate: F x imbalance thermal rate of impacts momentum 2 kbt n L V m 0 m 0 m k T [ β ] 2 0 pl V V B F S = 4k T β 4 pl m k T 2 F B 0 B F More accurate (normal + shear forces, correlated incoming + reemission : 512 π = 1+ π 8 2 SF pl m0k BT Enclosure inside sensor amplifies force noise Correlations between impulses from repeated impacts of same molecule slower averaging out of force noise Flow impedance of small channels around TM cause pressure build-up with TM motion

74 z Brownian force noise from gas damping: Numerical simulation Maxwell-Boltzmann velocity distribution inelastic collisions, random cosine-law reemission calculation of force and torque spectra from mean square momentum transfer y x

75 Brownian acceleration noise: estimates for LISA Equal gaps Actual sensor: d x = 4 mm, d y = 2.9 mm, d z = 3.5 mm, holes Factor 13 increase in noise power Infinite gap model Acceleration noise for LISA / LPF S 1/ 2 1/ 2 2 p m0 a 5 fm/s 5 Need to improve to 10-6 Pa pressure with LISA 10 Pa 30 1/ 4

76 Gas damping: experimental results dβ dp SIM 1TM dβ dp EXP 1TM = 3 43 nm s = ± nm s Differential measurement (with and without GRS) SIM d β4tm 3 = 4.6 µ m s dp d β dp EXP 4TM = ± µ m s Simulation and experimental results consistent at 15% level (pressure gauge calibration level)

77 Noise source: stray low frequency electrostatics δv 1 δv 2 V M x / 2 TM charge Q Stray electrostatic potentials δv 2 F 1 Ci k = = V 2 i V x 2 x i ( ) TM 2 2 Q δv 2 Electrostatic stiffness F Q C i = Vi TOT C δ x S S 1/ 2 2 F = 1/ 2 F = Q C T e 2 λ ωc T C x EFF S 1/ 2 x C x x Random charge noise mixing with DC bias ( x ) Noisy average DC bias (S x ) mixing with mean charge S 2 1/ 2 Ci 2 F = δvi S Noisy DC biases interacting δ x V i with themselves

78 Noise source: Cosmic ray charging Randomly arriving charged particles interact with any net field to produce force noise Q F Q Q V Expect λ EFF ~ e/s [Araujo, 2004] V V +V COMP -V COMP +VCOMP -V COMP δv 1Β δv 2Β Calculated and measured force noise with large photoelectric currents (+/ e / s) and largeapplied field ( φ = 12 V) Measurement and compensation of DC bias to within φ < 1 mv uncompensated 50 mv, Mo/sapphire sensor test with charge modulation shows compensation works to within several mv

79 Measured noise in stray DC biases Voltage fluctuations Measurement noise floor (quad phase) Measurement noise floor (theory) LISA goal 50 µv/hz 1/2 1/2 160 µhz 200 µ V/Hz 1+ f 3 No excess voltage fluctuation noise observed above 0.1 mhz 1σ-limit of measurement: 200 µv/ Hz 1/2 white noise near 0.2 mhz fit to 1/f 3/2 excess at lower frequencies

80 Noise budget for charge stray voltage interaction NB: worst case for stray voltage fluctuations is measurement limited (true noise likely falls off with increasing frequency)

81 Noise source: Cosmic ray charging To compensate the deterministic charging of test mass, need a discharging system UV light photoelectric discharging With appropriate biasing of electrodes, can both measure and remove TM charge 254 nm Hg lamp hν= 4.9 ev φ Au = ev Charge becomes important for LISA at level of 10 6 e UV light fibers illuminating TM and electrode surfaces

82 Bipolar UV photoelectric discharge test Measure charge with applied voltages and coherent torque detection (as in flight) Alternately expose TM and electrodes to produce charge rates of +/ e/s enough to discharge 1 day s worth of charge in 10 minutes

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85 This document is the property of Astrium. It shall not be communicated to third parties without prior written agreement. Its content shall not be disclosed. Astrium Satellites LTP Progress Meeting #12, ASD, 23/24 April 2008 p85

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87 ESA LTP Collaboration Trento LISA Team Stefano Vitale (LPF PI) Matteo Benedetti, Daniele Bortoluzzi, Antonella Cavalleri, Giacomo Ciani, Rita Dolesi, Mauro Hueller, Daniele Nicolodi, David Tombolato, Peter Wass, Bill Weber

88 Going beyond LISA: The Big Bang Observer Exploiting frequencies near 1 Hz --- few signals from galactic binaries Look for an extra-galactic cosmic gravitational wave background produced by the big bang and inflation

89 The Big Bang Observer Shorter arms ( km, not km) More light (300 W, not 1 W) Bigger telescopes (3 m, not 30 cm) Better force isolation (.03 fm/s 2 /Hz 1/2, not 3 fm/s 2 /Hz 1/2 ) Multiple constellations for noise discrimination Need to subtract off signals from ALL NS-NS, BH-BH mergers in universe in order to see background of gravitational radiation from big bang... Wow! year 2025 (????)