Thermal models of gravitational radiation?

Question

How is the background noise of gravitational waves modeled? Is it a thermal model, giving a stochastic distribution of the curvature tensor (field-strength tensor) in ambient space? That is, every binary star, every orbiting planet, every orbiting black hole or neutron star -- anything that accelerates -- is emitting gravitational radiation. The grand-total of all of these sums up to what looks like noise. Is there a "well-known" distribution for this noise? Some power law? Can an argument be made that this noise has a thermal profile? Are there specific equations describing this noise, and what are they? How do they scale?

Should one suppose that this varies from galaxy to galaxy, and depends on the local environment? Or can one argue for some generic form that is "typical"? Say, for binary clusters?

Somewhat related: what is the order of magnitude strength of this noise, compared to the instrument noise in current gravitational wave detectors? Yes, of course, its frequency dependent, so its a graph, but is this "natural noise" strong enough to be detectable? (Ignoring Earth-bound sources.)

Answer 1

Lets first focus on LIGO style ground based detectors. In order to produce background "noise" in the LIGO sensitivity band we need sources that produce gravitational waves in roughly the 10 Hz - 1000 Hz range. The only astrophysical sources that can contribute significantly to this, are unresolved compact binary mergers. To get a model for this background one typically considers the superposition of an ensemble of such sources, based on some population model (informed by resolved sources). This is a potentially observable stochastic gravitational wave signal, but no detection has been made to date, yielding an upper bound on this background.

At lower frequency bands more sources of astrophysical background gravitational waves may become relevant. E.g. LISA will be sensitive to the ensemble of millions of compact binaries in our own galaxy (of which it may only resolve about 10 000). Again such a background is modelled based on population models for these sources. For LISA this is expected to produce a significant source of noise that limits sensitivity curve at certain frequencies.

More typical astrophysical sources like stellar binaries have much lower frequencies than these detectors, and are incredibly weak. Even for pulsar timing arrays, they are not expected to play any role significance. If they would, their signal would be modelled based on astrophysical population models.

Note that for most of these sources it is not reasonable to assume that the populations are in some sort of thermal equilibrium. So, one would not expect any of these sources to have thermal profiles.