Absolute model ages of lunar craters

I have been looking at several articles on the dating methods of craters, but I am wondering how exactly the "absoluteness" creeps into it. I came across several methods that link crater "freshness" (i.e. the 7 degrees of freshness by Pohn and Offield (1970), see e.g. Google ebook) to the number of superimposed craters to rock abundance to thermal inertia etc. and these are all supposed to be an indicator of age, but what is the gauge for that? How do you convert that to a number of years? The literature seems to call these "absolute model ages". I have seen it mentioned that you obtain them from fits to crater production functions.

So how do you obtain absolute model ages, really?

• I struggle to find (on scholar.google) the article you cite as 7 degrees of freshness by Posh and Offield (1970) - do you have exact title by any chance? Commented Mar 3, 2021 at 7:44
• @B--rian, I'm sorry, I misspelled his name, it's "Pohn" and the article is this one: Pohn, H. A., and T. W. Offield (1970), Lunar crater morphology and relative age determination of lunar geologic units—Part 1, Classification,U.S. Geol. Surv. Prof. Pap.,700-C, C153–C162. Commented Mar 3, 2021 at 7:52
• What exactly are you asking: Absolute model ages of individual craters, or absolute model ages of the lunar surface based on impact craters? There's a big difference there. ... if I have time before you respond, I'll write an answer that answers both. Commented Mar 3, 2021 at 17:15

First, Terminology: Age is how old something is. Relative age is how old something is when compared to another (older vs younger). Absolute age is putting a number on that age (I am XX years old). Absolute model age is an absolute age that is based on a model, but where the age has not been measured directly (based on this cat's tooth, its absolute model age is roughly 3 years old).

Second, the Lunar Crater Chronology, Relative: A generally known quantity (with some caveats that I'm not going to get into in this answer) is that impactors have been striking surfaces in the solar system since its formation. So, if a surface has more craters than another surface, on the same planetary body, then it can be assumed to be older than the surface with fewer craters. So by measuring the spatial density of impact craters on multiple surfaces, you can tell a relative age relationship of those surfaces.

Third, the Lunar Crater Chronology, Absolute Model: If we are able to tie a specific age, like 3.7 billion years, to a surface that has a specific crater spatial density, like 0.002 craters ≥1 km per square kilometer, then we have an anchor point. And, to within a factor of ~2 or so, we can say that any surface on that planetary body with 0.002 craters ≥1 km per square kilometer is going to be 3.7 billion years old. If we are able to anchor several surfaces, with different crater spatial densities, with different radiometric ages, then we can plot them on a graph (crater spatial density on the vertical, age on the horizontal) and fit some function to them. We can then use that function, or model - which has been calibrated based on absolute ages - to give us the absolute model ages of any lunar surface by measuring their crater spatial densities. We've done this with data from the Apollo and Luna sample returns. As the other answerer posted, I did a recent review and re-kajiggering of that function.

Fourth, Dating Individual Features: That lunar crater chronology can be used to date individual features even if they don't have 1 km craters on them. We measure smaller craters, and then use another model of how many small craters there are relative to large craters, to figure out how many there WOULD be on that surface if 1 km craters existed on it. Or, if it's a big or older surface, we have those 1 km craters there and can get the age via that lunar crater chronology function.

Fifth, Rock Abundance: The DIVINER instrument on the Lunar Reconnaissance Orbiter takes temperature measurements at different times of day and from those can model the rock abundance on the surface. Basically, a boulder holds onto its heat longer than sand, so the boulder is going to be warmer at midnight than the not-boulders. What the DIVINER team found, maybe a decade ago, is that young (<1 billion years old) lunar craters have high thermal inertias - large rock abundances - surrounding them. Rebecca Ghent (et al.) used a few craters that had absolute ages (from Apollo) and absolute model ages (from the chronology curve based on smaller superposed craters) and demonstrated there was a pretty good linear relationship, meaning that for craters <1 billion years old, we now have another method to date those individual features via the DIVINER rock abundance measurements, which, honestly, is easier than counting craters (or at least takes less time).

Sixth, Spectral Slope: A recent paper demonstrated that young craters also show rays in the far-ultraviolet light, and that removal of those far-UV rays follows a fairly parametrizable relationship, so they were able to get independent ages of young, large craters, too. Optical maturity studies is not new, but this is the first remember seeing it used in UV for this exact thing.

For an absolute calibration you need a sample of the rock you are trying to date, and put it into a mass spectrometer for isotopic analysis. This is done via the lunar cratering record (images) and corresponding samples collected by the Apollo missions. A recent re-analysis can be found here.