Questions: Gravitational Waves from Compact Object Mergers

Question 1

The first LIGO detection (GW150914) showed a signal that increased in both frequency and amplitude, reached a peak, then rapidly faded. Which physical process does this 'chirp' waveform represent?

• A. A rapidly rotating neutron star losing energy as its spin slows and its magnetic field decays
• B. Two compact objects spiraling together as gravitational wave emission drains their orbital energy, then merging and ringing down
• C. A supernova core collapse releasing a burst of gravitational radiation as the star's inner layers implode
• D. A single black hole oscillating in response to a close gravitational encounter with another massive object

Answer: (B)

The inspiral-merger-ringdown waveform is the gravitational wave signature of a compact binary coalescence. As the two objects spiral inward, losing orbital energy to gravitational radiation, the orbital period decreases and both frequency and amplitude rise — the 'chirp.' At merger, strain peaks. The ringdown is the final settling of the merged remnant into a stable configuration, radiating away its remaining asymmetries. This full waveform is precisely calculated from general relativity, making it both a detection template and a direct test of GR.

Question 2

The 2017 event GW170817 was accompanied by electromagnetic observations across the spectrum. Which major conclusion did this single multi-messenger event provide?

• A. That black hole mergers produce short gamma-ray bursts visible across cosmological distances
• B. That gravitational waves travel slightly faster than light, consistent with certain modified gravity predictions
• C. That neutron star mergers are a primary site of r-process nucleosynthesis, explaining the cosmic origin of heavy elements such as gold and platinum
• D. That neutron stars always collapse directly to black holes during mergers, with no intermediate kilonova phase

Answer: (C)

GW170817 was a landmark event in astrophysics. The coincident kilonova (optical/infrared transient) showed spectroscopic signatures of freshly synthesized heavy r-process elements, confirming the long-hypothesized but unproven mechanism for producing gold, platinum, uranium, and other heavy elements. The event also constrained the neutron star equation of state, confirmed that gravitational waves travel at the speed of light (the gamma-ray burst arrived ~1.7 s after the GW signal, consistent with zero mass for gravitons), and provided an independent Hubble constant measurement.

Question 3

Gravitational waves detected by LIGO produce spacetime strains on the order of 10⁻²¹, meaning the instrument must measure differential length changes thousands of times smaller than the diameter of a proton.

• T. True
• F. False

Answer: True

A strain of h ~ 10⁻²¹ means ΔL/L ~ 10⁻²¹. For LIGO's 4 km arms, ΔL ~ 4 × 10⁻¹⁸ meters, compared to a proton diameter of ~10⁻¹⁵ meters — so LIGO measures changes ~1000 times smaller than a proton. This extraordinary sensitivity required decades of development in laser interferometry, vibration isolation, quantum noise suppression, and mirror technology. The tininess of the signal is why gravitational waves were predicted in 1916 but not detected until 2015.

Question 4

Gravitational waves from a binary merger compress and stretch spacetime equally in most directions, like a spherical pressure wave expanding outward from the source.

• T. True
• F. False

Answer: False

Gravitational waves have a quadrupole pattern: they stretch spacetime in one transverse direction while simultaneously compressing it in the perpendicular transverse direction, then reverse. This is fundamentally different from a spherical (monopole) sound wave or even a dipole electromagnetic wave. The quadrupole nature arises because gravitational wave emission requires a changing quadrupole moment — a changing distribution of mass. A perfectly symmetric explosion produces no gravitational waves; a spinning dumbbell or orbiting binary does.

Question 5

Why are compact binary mergers — rather than, say, individual rapidly rotating stars — the primary detectable sources of gravitational waves, and what determines the frequency and amplitude of the signal?

Model answer: Gravitational wave power scales steeply with mass and orbital velocity. Compact objects (neutron stars, black holes) can orbit at relativistic speeds while being separated by only a few stellar radii — ordinary stars would be torn apart at such separations. The frequency of the gravitational wave is twice the orbital frequency, so the wave sweeps from millihertz into the audio band (tens to hundreds of hertz) as the binary tightens. The amplitude (strain) depends on the masses and distance: more massive and closer mergers produce larger strains. An isolated spinning star produces negligible waves because its mass distribution is nearly symmetric.

The key physics: gravitational wave luminosity ∝ (mass)⁵ × (orbital speed)⁶ / (separation)⁵. Only the extreme compactness and masses of neutron stars and black holes push this into a detectable range. Single stars, even rapidly rotating ones, are insufficiently asymmetric and too low-velocity to produce detectable waves at current sensitivity.