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Masha Baryakhtar GRAVITATIONAL WAVES: FROM DETECTION TO NEW PHYSICS SEARCHES Masha Baryakhtar New York University Lecture 1 June 29. 2020 Today • Noise at LIGO (finishing yesterday’s lecture) • Pulsar Timing for Gravitational Waves and Dark Matter • Introduction to Black hole superradiance 2 Gravitational Wave Signals Gravitational wave strain ∆L ⇠ L Advanced LIGO Advanced LIGO and VIRGO already made several discoveries Goal to reach target sensitivity in the next years Advanced VIRGO 3 Gravitational Wave Noise Advanced LIGO sensitivity LIGO-T1800044-v5 4 Noise in Interferometers • What are the limiting noise sources? • Seismic noise, requires passive and active isolation • Quantum nature of light: shot noise and radiation pressure 5 Signal in Interferometers •A gravitational wave arriving at the interferometer will change the relative time travel in the two arms, changing the interference pattern Measuring path-length Signal in Interferometers • A interferometer detector translates GW into light power (transducer) •A gravitational wave arriving at the• interferometerIf we would detect changeswill change of 1 wavelength the (10-6) we would be limited to relative time travel in the two arms, 10changing-11, considering the interference the total effective pattern arm-length (100 km) • •Converts gravitational waves to changeOur ability in light to detect power GW at is thetherefore detector our ability to detect changes in light power • Power for a interferometer will be given by •The power at the output is • The key to reach a sensitivity of 10-21 sensitivity is to resolve the path- length difference in a tiny fraction, ie. 10-10 ICE 02/07/18 GW detection - M. Nofrarias 19 Measuring path-length Signal in Interferometers • A interferometer detector translates GW into light power (transducer) •A gravitational wave arriving at the• interferometerIf we would detect changeswill change of 1 wavelength the (10-6) we would be limited to relative time travel in the two arms, 10changing-11, considering the interference the total effective pattern arm-length (100 km) • •Converts gravitational waves to changeOur ability in light to detect power GW at is thetherefore detector our ability to detect changes in light power • Power for a interferometer will be given by •The power at the output is • The key to reach a sensitivity of 10-21 sensitivity is to resolve the path- length• differenceAdding multiple in a tiny fraction,`bounces’ ie. increases10-10 the effective length of the arms, giving a phase difference at the output of ICE 02/07/18 GW detection2N - M.L Nofrarias2πc 19 Δφ = h c λ Signal in Interferometers •A gravitational wave arriving at the interferometer will change the relative time travel in the two arms, changing the interference pattern •Converts gravitational waves to change in light power at the detector • The wavelength of the LIGO laser is 1064 nm and the arms are 4km • N ~100 2NL 2πc Δφ = h c λ • A change in phase of order 1 (light to dark) then corresponds to seeing strains of 10^-12 Signal in Interferometers •A gravitational wave arriving at the interferometer will change the relative time travel in the two arms, changing the interference pattern •Converts gravitational waves to change in light power at the detector • The wavelength of the LIGO laser is 1064 nm and the arms are 4km • N ~100 2NL 2πc Δφ = h c λ • A change in phase of order 1 (light to dark) then corresponds to seeing strains of 10^-12 • To see a difference in power at the level of distinguishing phases of 1 part in 10^10, need 10^20 photons (within measurement time)! Shot Noise: •Changes in the number of photons hitting the detector can looks like the power is changing, i.e. the phase difference is changing. • If on average the power is a kW, we have10^20 photons in 0.01 sec to measure 100 Hz frueqnecies • Then the flucuations in photon number are poissonian, i.e. dN ~10^10 photons Shot Noise: •Changes in the number of photons hitting the detector can looks like the power is changing, i.e. the phase difference is changing. • If on average the power is a kW, we Shot noisehave10^20 photons in 0.01 sec to measure 100 Hz frueqnecies • Then the flucuations in photon number are • Since we arepoissonian, measuring i.e. power dN ~10^10 fluctuations photons at the output, these fluctuations• Theseare indistinguishable looks like changes from in mirror arm lengthdisplacements of • And we are using mirror displacements to measure GW as the fractional length change in one arm • So brightness fluctuations are interpreted as equivalent gravitational wave noise ICE 02/07/18 GW detection - M. Nofrarias 22 Turn up the power? • Increasing length of the interferometer increases signal but not noise. decreasing wavelength can help Shot noise Shot noise • Clearly increasing power gets rid of this issue • Since we are measuring• Since power we are fluctuations measuring atpower the output, fluctuations these at the output, these fluctuations are indistinguishablefluctuations are from indistinguishable mirror displacements from mirror displacements • And we are using• mirrorAnd wedisplacements are using mirror to measure displacements GW as theto measure fractional GW as the fractional length change in onelength arm change in one arm • So brightness fluctuations• So brightness are interpreted fluctuations as equivalent are interpreted gravitational as equivalent gravitational wave noise wave noise ICE 02/07/18 ICE 02/07/18 GW detection - M. Nofrarias GW detection - M. Nofrarias 22 22 Turn up the power? • Increasing length of the interferometer increases signal but not noise. decreasing wavelength can help Shot noise Shot noise • Clearly increasing power gets rid of this issue • Since we are measuring• Since power we are fluctuations measuring atpower the output, fluctuations these at the output, these fluctuations are indistinguishablefluctuations are from indistinguishable mirror displacements from mirror displacements• However, increasing power increases the force on the mirror • For a perfect mirror, the radiation pressure • And we are using• mirrorAnd wedisplacements are using mirror to measure displacements GW as theto measure fractional GW force as the fractionalis equal to the power length change in onelength arm change in one arm • So brightness fluctuations• So brightness are interpreted fluctuations as equivalent are interpreted gravitational as equivalent gravitational wave noise wave noise ICE 02/07/18 ICE 02/07/18 GW detection - M. Nofrarias GW detection - M. Nofrarias 22 22 Turn up the power? • Increasing length of the interferometer increases signal but not noise. decreasing wavelength can help Shot noise Shot noise • Clearly increasing power gets rid of this issue • Since we are measuring• Since power we are fluctuations measuring atpower the output, fluctuations these at the output, these fluctuations are indistinguishablefluctuations are from indistinguishable mirror displacements from mirror displacements• However, increasing power increases the force on the mirror • For a perfect mirror, the radiation pressure • And we are using• mirrorAnd wedisplacements are using mirror to measure displacements GW as theto measure fractional GW force as the fractionalis equal to the power length change in onelength arm change in one arm • Fluctuations in the power give fluctuations • So brightness fluctuations• So brightness are interpreted fluctuations as equivalent are interpreted gravitational as equivalent in gravitational the force, and thus fluctuations in the wave noise wave noise Radiation pressure mirror position • The fluctuating force turns into a displacement in the test mass ICE 02/07/18 ICE 02/07/18 GW detection - M. Nofrarias GW detection - M. Nofrarias 22 22 • which can be expressed, as in the previous case, as an equivalent gravitational wave noise • Radiation pressure and shot noise are competing effects, what would be the noise if we minimise this two contributions, hrp(f,P) = hshot(f,P) ICE 02/07/18 GW detection - M. Nofrarias 24 Noise in Interferometers • As power is increased, tradeoff between shot noise and radiation pressure noise in interferometers • Attempting to measure system more precisely (more photons) eventually causes a backreaction and disturbs the system you’re trying to measure • `Standard quantum limit’ 16 Noise in Interferometers • As power is increased, tradeoff between shot noise and radiation pressure noise in interferometers • Attempting to measure system more precisely (more photons) eventually causes a backreaction and disturbs the system you’re trying to measure • `Standard quantum limit’ From original LIGO proposal (`89): 17 Gravitational Wave Signals Advanced LIGO sensitivity LIGO-T1800044-v5 18 Today • Noise at LIGO (finishing yesterday’s lecture) • Pulsar Timing for Gravitational Waves and Dark Matter • Introduction to Black hole superradiance 19 Pulsar Timing Arrays Credit: B. Saxton (NRAO/AUI/NSF) 20 Pulsar Timing Arrays •Pulsars: highly magnetized rapidly rotating neutron stars with a coherent source of radio waves. Millisecond pulsars are the special class of pulsars with a stable rotational period of ~ 1-10 ms and stable pulse frequency. •The stability (although not very well understood) of these millisecond pulsars can be used to make a galaxy-wide network of precise clocks, by measuring the arrival time of the pulses Vela Pulsar Cambridge University Lucky Imaging Group 21 Pulsar Timing Arrays • Parkes Pulsar Timing Array (PPTA) observing 25 pulsars • North American Nanohertz Observatory for Gravitational Waves (NANOGrav) observating 45 pulsars • European Pulsar Timing Array (EPTA) observing 42 pulsars • International Pulsar Timing Array (IPTA) collaboration of all three: new data release consists of 65 pulsars in 2019 22 Pulsar Timing Arrays • Astronomers know of a few thousand neutron stars, a subset of those pulsars, with varying levels of stability • Pulsar J1909-3744 has been observed Parkes Radio Telescope for 11 years. • During this time all 115,836,854,515 rotations can be fit • The rotational period of this star is known to 15 decimal places • One of the most accurate clocks in the universe! 23 Pulsar Timing Arrays •Pulsar timing arrays can detect low frequency gravitational waves (10−9 − 10−7 Hz), limited by observation time.
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