基于LIGO引力波测定宇宙膨胀率：中子星碰撞观测原理问询

Hey there, let's break this down clearly—using neutron star mergers (the events LIGO detects) to calculate the Hubble constant (and thus cosmic expansion rate) is a brilliant trick that combines gravitational wave astronomy with traditional electromagnetic observations. Here's the play-by-play:

The Key Advantage: Neutron Star Mergers Are "Standard Sirens" #

Unlike other cosmic distance markers (like Type Ia supernovas, our go-to "standard candles"), neutron star mergers act as standard sirens. Here's what that means:

• We can use general relativity to predict the absolute gravitational wave brightness of a neutron star merger. Because we understand the physics of these compact objects (their mass ranges are well-constrained), the gravitational wave signal's waveform tells us exactly how much energy the merger emits as gravitational waves.
• The amplitude of the gravitational wave we detect here on Earth drops off with the square of the distance to the merger. So if we know the absolute brightness, we can reverse-engineer the luminosity distance (how far the merger is from us) directly from the detected signal's strength.

Step 1: Grab the Distance from Gravitational Waves #

When LIGO (and Virgo, KAGRA, etc.) detects a gravitational wave from a neutron star merger, the data gives us:

• The waveform shape, which lets us confirm it's a neutron star merger and calculate the system's total mass.
• The signal's amplitude, which we pair with the predicted absolute brightness to compute the luminosity distance to the merger. No guesswork here—just pure general relativity math.

Step 2: Get the Redshift from Electromagnetic Signals #

Neutron star mergers don't just emit gravitational waves—they also produce a bright electromagnetic "afterglow":

• First, a short gamma-ray burst (GRB) that telescopes like Fermi can spot quickly.
• Then, a longer-lasting optical/infrared glow that we can observe with ground-based telescopes (like the Hubble Space Telescope or large observatories on Earth).
• By analyzing the spectrum of this optical glow, we can measure the cosmological redshift (z) of the merger. Redshift tells us how much the universe has expanded since the light (and gravitational waves) left the source—higher redshift = more expansion = farther away in cosmic time.

Step 3: Calculate the Hubble Constant #

Now we have two critical numbers:

• The luminosity distance (d) from the gravitational wave.
• The redshift (z) from the electromagnetic signal.

We plug these into the Hubble-Lemaître law (the updated version of Hubble's original law) which relates cosmic distance to redshift and the Hubble constant (H₀, the current expansion rate of the universe). For most cases (especially for relatively nearby mergers, which LIGO detects well), we can use the simplified relation:
v = H₀ * d
Where v is the recession velocity, calculated from redshift using v ≈ c * z (c is the speed of light, and this approximation works for low to moderate redshifts).

Solving for H₀ gives us H₀ = v / d—a direct, independent measurement of the cosmic expansion rate, no reliance on the "distance ladder" that traditional methods use (which can introduce cumulative errors).

Why This Matters #

This method is a game-changer because it bypasses the systematic errors that have plagued previous Hubble constant measurements (like the tension between values from the Planck satellite and local observations). It gives us a completely independent check on how fast the universe is expanding, using two entirely different types of signals from the same event.

内容的提问来源于stack exchange，提问作者John