Definitions Flashcards
What are the foundations of general relativity?
Spacetime tells matter how to move, and matter tells spacetime how to curve.
What is general relativity?
GR is a generalisation of special relativity in which the laws of physics are valid in all inertial reference frames.
What are the postulates of relativity?
The speed of light in the vacuum will be the same for every inertial observer.
How are observers motion related?
Through lorentz transformations
Describe the spacetime interval between events.
It is independent of the observers reference frame.
What are the two forms of the equivalence principle?
The weak equivalence principle and the strong equivalence principle.
Describe inertial mass in Newtonian physics.
The inertial mass of a body is a measure of its resistance to acceleration.
What is the weak equivalence principle (WEP)?
The inertial mass and the gravitational mass are identically equal. Such that freely falling objects inhabits an inertial frame in which all gravitational forces have disappeared.
What is the local inertial frame (LIF)?
It is the reference frame inhabited by our freely falling object.
What is the strong equivalence principle (SEP)?
Locally all the laws of physics have their usual special relativistic form apart from gravity which disappears. Where there is no experiment that can distinguish between a LIF which is freely falling in a uniform gravitational field and an inertial frame which is in a region of the universe far from any gravitating mass.
What are the consequences of the equivalence principles?
- The empirically observed equality of gravitational and inertial mass is explained.
- The acceleration of a test mass in a gravitational field is entirely independent of its nature, mass and composition.
- The path of a light ray will be bent by the gravitational field of a massive body.
- A light ray emitted from the surface of a massive body will be redshifted - gravitational redshift - when its wavelength is measured by a distant observer
How can we describe space time rigorously?
Using physical quantities in terms of scalars and vectors to tensors.
What are geodesics?
The trajectories of freely falling particles in GR generalised to curved paths. They parallel transport their own tangent vectors.
What can geodesics not distinguish between?
Zero gravitational fields and a uniform gravitational field.
When do geodesic deviations accelerate?
They only accelerate for a non uniform or tidal gravitational field.
What are manifolds?
A manifold is a continuous space which is locally flat. They can be continuously parametrised.
What is a Riemannian manifold?
A differential manifold on which a distance, or metric has been defined.
What is a tensor?
A tensor of type (l,m) defined on an n dimensional manifold, is a linear operator which maps l one-forms and m vectors into a real number.
What is the covariant derivative?
A derivative which transforms covariently under a general coordinate transformation.
What do Christoffel symbols describe?
They describe how the basis vectors at different points in the manifold change as one moves across the manifold.
What does the Riemann Christoffel tensor or Riemann tensor describe?
The curvature of space time.
How can one derive the Riemann Christoffel tensor?
- by parallel transporting of a vector around a closed loop in our manifold
- by computing the deviation of two neighbouring geodesics in our manifold
What is the energy momentum tensor?
It is the source of space time curvature. Describing the presence and motion of gravitating matter.
What is a perfect fluid?
A mathematical idealisation but one which is a good approximate description of the gravitating matter in many astrophysical situations.
What is the simplest type of relativistic field?
Dust
What is the momentarily comoving rest frame?
The Lorentz frame where a collection of particles are all at rest.
What gives rise to pressure in the fluid?
The particles within a fluid element will face random motions giving rise to pressure in the fluid.
How can a fluid element exchange energy with its neighbours?
Via heat conduction
Describe viscous forces
Viscous forces are present between neighbouring fluid elements they are directed parallel to the interface between neighbouring fluid elements resulting in a shearing of the fluid
What is a perfect fluid?
A relativistic fluid element in its MCRF where the fluid element has no heat conduction or viscous forces,
What is an immediate consequence of the strong equivalence principle?
Any physical law which can be expressed as a tensor equation in SR has exactly the same form in a local inertial frame of a curved space time.
How can we describe the detection of gravitational waves?
With the weak field approximation. Gravitational wave results from deviations from the flat space time of SR which are small.
What do the free space solutions of the metric perturbations take the form of?
Free space solutions for the metric perturbations of a nearly flat space time take the form of a wave equation, propagating at the speed of light.
Give an example of a static metric
The schwarzschild solution for the space time exterior to a point mass is an example.
What are the conditions for a static metric?
- All metric components are independent of t
- The metric is unchanged if we apply the transformation t |-> -t
A weak gravitational field has what kind of space time?
‘Nearly’ flat space time
What explains the origin of the ‘transverse’ part of the transverse traceless gauge
There is no component of the metric perturbations in the direction of propagation of the wave
What are the two independent gravitational wave polarisation states
‘+’ and ‘x’
What is the polarisation of the distortion produced by a gravitational wave
It is quadrupolar due to the fact gravitational waves are produced by changes in the curvature of space time.
When is a gravitational wave invariant?
Under a rotation of 180 degrees about its propagation.
Describe the graviton
A spin, S = 2 particle
What is the dominant form of radiation from a moving charge in electromagnetic theory?
The electric dipole followed by magnetic dipole and electric quadrupole radiation.
What is the gravitational analogue of the electric dipole moment?
The mass dipole moment, d
What does a gravitational ‘mass dipole’ luminosity of zero mean?
There can be no mass dipole radiation from any sort of gravitational source.
The quadrupole from a spherically symmetric mass is zero. What does this suggest?
Metric perturbations which are spherically symmetric do not produce gravitational radiation. The collapse of a spherically symmetric star will generate no gravitational waves.
A non zero curvature gives rise to what?
Acceleration of geodesic deviation which gives rise to a non uniform gravitational field.
What are the characteristics of the traceless transverse gauge?
- Most components of the amplitude tensor vanish
- The trace reverse perturbation reduces to the perturbation
Why do we need to look at celestial bodies in order to appreciate gravitational forces?
Because gravitational forces are very weak.
What are gravitational waves emitted by?
Asymmetric, accelerating distributions of mass where M1 cannot equal M2.
How can we achieve appreciable amplitudes?
Using very large masses
Is it possible to generate gravitational waves?
No
What are examples of compact sources?
- Binary black hole mergers
- Binary Neutron star mergers
What is an example of a burst source?
- Core collapse supernovae
What is a pulsar?
A highly magnetised rotating compact star that emits beams of electromagnetic radiation out of its magnetic poles.
Describe the resonant bar detector.
A resonant bar detector was the first kind of gravitational wave detector. It used the natural frequencies of large aluminium bars which could be excited by passing gravitational waves. They are narrow band sensitive.
What is narrow band sensitivity?
Sensitivity is limited to the natural frequencies of the metallic bar. Detector is not sensitive at other frequencies.
How can interferometry be used to detect gravitational waves?
A laser is split equally down two perpendicular vacuum tubes. End test mass mirrors reflect laser light. It is thought that passing gravitational waves would warp the position of mirrors giving rise to constructive interference a measurable signal.
What are potential hazards with LIGO?
1.Alligators
2.Bad drivers
3.Tumbleweeds
4.Ravens
What does lower noise give?
Higher sensitivity
What is the optimum arm length?
Gravitational wave detection is a length measurement. The longer arms, the bigger the effect. The optimum arm length is when the wave stays in the detector for a half a wavelength for the entire round trip. Each arm length should be a quarter of the wavelength.
What are gravitational waves?
Perturbations in the metric of space time travelling at the speed of light.
Describe current gravitational wave detectors.
Current detectors are based on interferometers which can achieve a sensitivity of ~ x 10^{-19}
What was the size of the first detected gravitational wave signal?
ΔL ~ 10^{-18}
which is approximately ~ 1/1000th a proton diameter
What noise dominates at ultra-low frequencies?
Seismic noise
What noise dominates at frequencies where the detectors are most sensitive?
Mirror coating thermal (Brownian) noise.
What are the two parts of quantum noise?
Radiation pressure noise and photon shot noise
What are gravitational wave detectors mirrors made of?
High quality substrates of polished glass with a coating stack ontop to make them reflective where they are suspended with high quality glass.
How do you make highly reflecting coatings?
By stacking layers of different materials with different refractive indices.
What happens if the difference in the refractive index of the two materials becomes larger?
The more light gets reflected at each interface. Hence we can make the coating thinner.
What was indirect verification of the existence of atoms and molecules?
‘Jittering’ motion of pollen grains and dust suspended in water.
What is the origin of brownian motion?
The first time that random fluctuations, here random displacement of pollen grains, had been linked to a dissipative process, here the loss of energy due to the fluid viscosity.
What is the origin of Nyquist and Johnson noise?
Fluctuation-dissipation-theorem (FDT) which gives a link between spectral density of thermal fluctuations and mechanical impedance of the system.
Describe homogeneous loss?
It sums up thermal motion from all modes of the system to give the total thermal noise
What is fluctuating thermal energy?
Brownian thermal noise.
What is fluctuating temperature?
Thermo-elastic, thermo-refractive noise
What is mechanical loss?
The phase-lag between stress and strain in a real solid. The amount of energy lost when something vibrates.
How do we measure mechanical loss?
It is measured on disk resonators before and after coating by isolating them from external influences, and then vibrating them. Ringdown experiments.
Can we improve these coatings by coolings?
No, it causes serious limitations in achievable sensitivity in a cryogenically cooled GWD.
What do higher refractive indices offer
thinner coatings, thermal noise reduction and promising low loss and thermal noise reduction.
What is the proposed coating for the einstein telescope?
aSi based coating is employed to meet the ET coating thermal noise requirements.
What does thermal noise depend on?
Temperature and thickness
What does mechanical loss depend on?
Frequency and temperate.
What do low temperatures give rise to in two level systems versus high temperatures?
For low temperatures we get quantum tunnelling and for temperatures greater than 5K we get thermally activated transitions
What order is important in two level systems
Medium range order is important
What is ultrastable glass
Vapor deposited glasses that can reach ultrastable state. These can be grown at 0.8 Tglass
Why is it difficult to obtain ultrastable glasses?
It is not easy to know Tglass or to deposit at such temperatures without crystallising the material. aSi showed the most promise.
What is thin film deposition by Ion Beam Sputtering?
Ions sputter material off a target that then gets deposited on substrates. To grow oxides we need to add a background gas to the chamber - reactive ion beam sputtering.
What are the types of ion beam sources?
- Discharge vessel
- Kaufman-type
- RF-type
- ECR-type
Describe Kaufman type
Kaufman type is not gridded in this system. It generally has poor optical quality with low deposition rates.
Describe ECR-type
ECR-type has no requirements on targets. It has the highest extraction potential however it is not readily available in industry.
Describe RF-type
RF-type is a technique of choice for gravitational wave detection coatings. It has exceptional optical quality and is industry standard.
Why is bulk silica better than silica coatings.
Bulk silica has a much lower loss angle than silica coatings.
What tells us about how much we can anneal the coatings.
Studying the crystallisation temperature tells us how much we can anneal the coatings. We can only anneal at temperatures lower than the crystallisation temperature.
Why do we anneal?
It decreases the mechanical loss and optical absorption.
Why do we dope tantala with Titania?
We dope the tantala as it lowers the loss and increased crystallisation temperature compared to tantala
What is the material used in LIGO mirrors
Titania-doped germania is the material that will go in the high index layers
What are Rayleigh waves
Surface vertical waves where amplitude of ground vibration decreases with depth.
What are Love waves
Surface horizontal waves where the amplitude of ground vibration decreases with depth
Why are Earths Tides a problem?
Tidal deformation of Earth produces a ~0.4 mm arm length change which is far larger than the adjustment range of the in vacuum isolation system
How does an interferometer maintain lock?
The interferometer must maintain the same number of wavelengths in each arm to maintain lock. The common mode change is fixed by tweaking the laser frequency
What is a microseismic peak?
A micro seismic peak is generated by water waves pushing on the ocean floor. This makes it difficult to establish and maintain interferometer lock mostly remediated by external hydraulics.
What are the super sensors?
Super sensors or blend sensors helps overcome cross coupling
Why do we use a double over a single pendulum?
Two stage pendulum is good at tracking at low frequencies
How do we sense motion?
We sense motion with seismometers and actuate to drive their output to zero
What is the HEPI system
The hydraulic external pre isolator system has been designed to provide very low frequency active isolation and precision positioning.
What is a advantage of a HEPI system
To provide low frequency control. Reduces bandwidth but maintains low noise.
Why do we use counter wound coil springs
To reduce linear twist coupling
What is an accelerometer
Gives a flat response to acceleration below resonance
What is a geophone?
A geophone provides a flat response to velocity above resonance
Why do we use HAM/BSC isolators?
To provide isolation at a few Hz before passing isolation of the springs/pendulums kicks in
Example of a quadrupole approximation
A point source mass oscillating back and forth in one dimension with an amplitude and period.
What frequencies do different mass sources emit?
Low mass source - high frequency
High mass source - low frequency
What are neutron stars?
Product of a core collapse supernova. They have very high densities, rapidly rotating and are highly magnetised.
What are some neutron star observations?
Pulsars
Isolated neutron stars
Soft gamma ray repeaters / anomalous x-Ray pulsars
How do we detect pulsars?
From beamed radiation from magnetic poles
What are SGRs
A short burst of soft gamma rays
What are AXPs
They show X-Ray pulsations with a secular spin down rate
What are some similarities of SGRs and AXPs
They are magnetars with slow rotations. The bursts are thought to be from crystal reconfiguration and subsequent magnetic reconnection.
What are the types of black holes
Solar mass BHs - 10s solar masses
Intermediate mass BHs - 100-1000s solar masses
Supermassive BHs - >10^4 solar masses
Describe super massive black holes
Found in the centre of galaxies and power AGN.
What are the types of gravitational wave sources?
Modelled
- compact binary coalescence
- continuous
Unmodelled
- burst
- stochastic
What are the stages of a compact binary coalescences?
3 distinct phases
- inspiral (post Newtonian)
- merger (numerical relativity)
- ring-down
What is an inspiral?
The orbit loses energy through gravitational radiation, shrinks and period decreases.
What are the requirements for GW emission from a NS
Triaxial - have a bump - continuous emission
Vibrational modes - short burst emission
Precession - medium term emission
What is the spin down limit?
A limit at which all the rotational kinetic energy is lost via GWs. If the limit is beaten with GW observations then can start seeing GWs.
What is the best way to tune detection sensitivity?
Having a longer baseline
Objectives of LISA
- Survey massive black hole populations across cosmic time
- Confront general relativity with high SNR observations
- Explore the dynamics of galactic nuclei
- Probe new physics and cosmology
What does LISA aim to do?
Detect picometres changes in gigametre long arm lengths.
Methods to improve shot noise for future missions
- Larger mirrors
- More laser power
What forms an unequal arm interferometer?
The triangle changes shape and thus the arm lengths changes. The effects form unequal arm interferometers.
How do we calculate the length changes in the arm?
Time delay interferometry. Each arm is made up of two signals which are being relayed back and forth. Combining the time delays between the two laser signals.
How do we make time delay interferometry measurements.
We need gravitational references these are the test mass and mirrors in LIGO and test masses in LISA.
How do we make the test masses as inertial as possible.
Use drag free control. Shielding from external EM forces.
What did the LISA pathfinder test?
- Inertial sensors and their internal workings.
- Interferometry
- Space craft drag free control
When is LISA expected to launch?
Mid to late 2030s
Why do we use arm cavities on the arms?
To increase the circulating power and the effective arm length.
Why do we use Mode cleaner cavities?
To filter the input and output field. Reducing the laser noise improving the beam quality.
What does the power recycling mirrors do?
Recycles the light coming back to the laser
What does the signal recycling mirrors do?
Recycles the GW signal back to the interferometer.
Describe phase modulation from a moving mirror.
GW causes the mirror to move; this phase modulates the field reflected from the mirror.
How are GW signals read out?
By measuring beats in the detected light power. Where the beats arise due to interference near dark fringes.
What is the detector strain sensitivity?
The combination of the limiting noise sources and the detector response to GW.
What do interferometric improvements do?
The technique involves improving the detector response but not reducing noise.
What is a Fabry Perot interferometer?
A FP interferometer is a linear optical cavity.
Classify cavities
When T1 < Alpha the cavity is under coupled
When T1 = Alpha the cavity is impedance matched
When T1 > Alpha the cavity is over coupled
Which cavity case is the best?
Over coupling is the optimal case.
Why do we increase the finesse?
To increase the circulating power
What is gravitational wave detector noise?
A series of unknown fluctuations
What simplifications do we use when modelling the noise.
- It is stationary
- It is Gaussian
although the Gaussian assumption is far from the truth. There are many transient noises which must be removed.
Why and how do we use matched filtering?
We want to know whether signal, h, is present in data, d, or not. This is done by preparing a template bank and matching all of the templates with the data. Only works when we have wave form templates.
What are some techniques beyond matched filtering?
- 𝝌𝟐 test
- Coincidence test
- Astrophysical origin
How do we do an unmodeled search?
Search for GWs only using the coherence between detectors.
What are some intrinsic parameters?
- Chirp mass
- Component spins
- Tidal deformability parameters
What are the extrinsic parameters?
- Antenna response functions
- Luminosity distance
- Inclination angle
What is stochastic sampling and give some examples?
Stochastic sampling involves randomly sampling points in the parameter space and keeping the high likelihood points. MCMC and Nested sampling are widely used.
What is MCMC?
a set of random walkers make the next step with the probability determined by the posterior. The walkers trace will converge to a posterior distribution.
What is nested sampling?
A set of live points are generated from prior distributions. The point with the lowest likelihood will be abandoned. By the end the live points will eventually map to posterior samples.
What does the antenna pattern do?
Detectors have an antenna pattern which modulates the signal amplitude.
What are detector problems associated with non Gaussian noise?
CBCs have artefacts known as glitches while CWs have artefacts known as lines.
What are the 3 CW search methods.
- Targeted searches
- Directed searches
- All sky searches
What does the sensitivity of a single segment scale with?
Sensitivity of a single segment scales with the length of segment which you coherently analyse.
What are the steps of machine learning
- Simulate
- Neural network
- Train with some loss function, L
What statistical methods will be used for LISA?
A global fit
Bayesian methods
Reverse jump MCMC
What is multi messenger astronomy?
Astronomical observations which are made through multiple approaches, I.e gravitational waves and electromagnetic radiation.
What are good multi messenger sources.
Binary neutron star (BNS)
What are the two types of transient astronomy
Gamma ray burst observatories
- Swift BAT
- Fermi GBM
Optical surveys
- ESA Gaia
- ZTF
What is a gamma ray burst?
An intense beam of gamma ray radiation which is produced just after the merger.
What is a kilonova?
Decaying neutron rich material creates a glowing kilonova, producing heavy metals
What is a radio remnant
As material moves away from the merger it produces a shockwave in the interstellar medium. Producing emission which can last for years.
What are the detection stages following the emission of a gravitational wave signal
- Gamma ray burst
- Kilonova
- Radio remnant
When did we first observe gravitational waves?
14 September 2015 from a coalescence of a binary black hole
History of gravitational waves
1916 Einstein predicts gravitational waves
1974 indirect evidence of gravitational waves
2015 first observation
What is the gravitational wave catalogue made up of
A total of 90 candidates with p-Astro > 0.5
What is matched filtering?
Searching for signals using templates
What are the only type of gravitational waves that have been detected?
Compact binary coalescences
What is the chirp mass?
A combination of component mass that to leading order determines the rate of inspiral
What is the total mass
The total mass sets properties of merger and ring down
What can neutron star tides do?
Leave an imprint on the waveform
What does the equation of state describe?
The neutron star mass and radius are linked by the equation of state. They determine the tidal deformability.
What is the first discovery from O4a
GW230529 which is likely a neutron star black hole binary
Describe the black hole mass distribution
It exceeds electromagnetic observations
Why do we get a lower mass gap
Due to a core collapse supernova
Why do we get an upper mass gap
Due to pair instability supernova
why is the primary spin important
The primary spin is better measured and more important for dynamics
What is the search sensitivity quantified by
Search volume time
What are the magnitudes of spin
Small
What are the current theories of spin distributions
There is more support for aligned spins but still consistent with an isotropic distribution of spins
What are some tests of general relativity
Parametrised tests
Black hole spectroscopy
Kerr metric
What are the two important impacts on quantum noise
- Quantum shot noise - sensing noise
- Quantum radiation pressure noise - back action noise
What is quantum shot noise
Fluctuations in the photon arrival time
What is the quantum radiation pressure noise
Fluctuations in the photons incident on the mirror leading to fluctuations in the test mass motion
Difference between quantum shot noise and quantum radiation pressure noise
Frequency independent vs frequency dependent
Inversely proportional to laser power vs proportional to laser power
What is the standard quantum limit
The combination of shot noise and radiation pressure noise traces out a curve known as the standard quantum limit
Where does each quantum noise source dominate
Radiation pressure noise is the dominant effect at low frequency.
Shot noise is the dominant effect at higher frequencies.
What does Heisenberg’s uncertainty state
That two quadrature observable do not commute, the produce of the uncertainties is constrained.
Describe the ball on a stick picture
The stick is the mean parameters of the optical field and the ball is the statistical uncertainty in the parameters. HUP enforces a minimum area of the ball such that the produce of the uncertainties is constrained.
What happens in a squeezed state
The uncertainty in one quadrature is reduced while the other increases maintaining the area of the ball.
How can we beat the standard quantum limit
- Squeezed light injection - frequency dependent squeezing
- Variation readout
- Speedmeter interferometry
How do we achieve frequency dependent squeezing
By passing squeezed light through one or more filter cavities. This enforces rotation
How do we get arbitrary selection readout
By implementing balanced homodyne detection
What does speed meter interferometry do
It measures the relative speed of the mirrors as a proxy for momentum that commutes. It enforces two interactions with the moving test mass.
The Einstein telescope will be
Underground
Gravitational waves are produced by
Axisymmetric acceleration of matter
