Editing Openai/6946e998-79f0-8007-9a65-19828450838d (section)

=== Assistant: Good, this is exactly how people try to make η⊕ less misleading: tighten the definition and explicitly subtract obvious… ===
Good, this is exactly how people try to make η⊕ less misleading: tighten the definition and explicitly subtract obvious “false positives.”

I’ll step through what your three constraints do and what the result probably looks like.

I’ll keep it qualitative-but-numerical, not Drake-equation baroque.

==== Take the conservative habitable zone (Kopparapu et al.-style): ====
* Inner edge: runaway greenhouse (well outside “recent Venus”)
* Outer edge: maximum greenhouse (well inside “early Mars”)

This already:
* Excludes orbits like modern Venus that are almost certainly over-irradiated even for Earth-like atmospheres.
* Excludes orbits like modern Mars that are too weakly irradiated even with optimistic CO₂.

Effect on η⊕:
* For Sun-like stars, going from “optimistic” HZ to “conservative” HZ tends to cut η⊕ roughly in half (very roughly; exact factor depends on the paper). You go from “maybe ~0.5–1 per star” to more like “~0.2–0.5 per star” as a typical ballpark.

So step (1) alone significantly reduces Venus-like and very Mars-like flux cases.

==== Now apply stricter physical filters instead of just “all 0.5–1.5 R⊕ in that band.” ====

You can reasonably do:
# Radius cut: - Only count 0.8–1.4 R⊕ (or even 0.8–1.2 R⊕) to avoid: - sub-Mars, likely to lose atmosphere - super-Earths / mini-Neptunes with deep volatile envelopes
# Mass-density cut (where known): - For planets with measured mass and radius, only keep rocky densities (say ≳ 4–5 g/cm³). - This explicitly rejects planets with large H/He envelopes that happen to be “Earth-size-ish.”
# Spectral-type cut: - If you want to be conservative regarding flares and pre-main-sequence stripping, you might: - focus on FGK stars (Sun-like and somewhat cooler/warmer), - or, at minimum, down-weight M-dwarfs, where a big fraction of nominal HZ planets may have had their atmospheres cooked off.

Together, these cuts likely:
* Reduce the raw η⊕ (FGK) to the lower end of typical estimates (say 0.1–0.3 per star, not 0.5–1.0).
* Reduce the effective contribution from M dwarfs by some factor (maybe treat their η⊕ as, say, 0.05–0.2 instead of 0.2–0.4, to reflect the risk that many are bare rocks).

The exact numbers are not well measured yet, but conceptually, that’s the effect.

==== You also suggested: “Take a random highball estimate for the number of mini-Neptunes… and thus not overcount.” ====

In practice:
* In the 1–4 R⊕ range, a lot of planets turn out to be low-density (volatile-rich) once you get mass measurements.
* In the 1–2 R⊕ range, there’s a known radius valley: planets below ~1.5–1.7 R⊕ are more likely rocky; above that, more likely to have gas envelopes. So if you cut off at ~1.3–1.4 R⊕, you’re already rejecting many mini-Neptunes.
* A “highball” correction might be: - Assume that, in the 1.0–1.4 R⊕ bin, maybe 30–50% are actually volatile-rich “stealth mini-Neptunes” you can’t yet identify individually. - Multiply your current η⊕ by ~0.5–0.7 to reflect that.

So if your conservative-HZ, tight-radius FGK η⊕ came out around 0.2 per star, and you then assume “maybe half remain after we eliminate hidden mini-Neptunes,” you get:
* Effective η⊕,rocky,conservative ≈ 0.1 per Sun-like star as a plausibly cautious number.

For M dwarfs, you’d likely apply even harsher penalties, both for volatile envelopes and for stellar activity stripping.

==== Let’s do a simple, pessimistic-but-not-crazy thought experiment: ====
'' Assume only FGK stars count, and they are ~10–20% of stars. Call it 0.15 × N_''.
'' Let N_'' ≈ 10¹¹ stars in the Milky Way → FGK stars ≈ 1.5×10¹⁰.
* Take η⊕,rocky,conservative ≈ 0.1 per FGK star after all your cuts.

Then:

N“good” HZ rocky planets≈1.5×1010×0.1≈1.5×109N_{\text{“good” HZ rocky planets}} \approx 1.5\times 10^{10} \times 0.1 \approx 1.5\times 10^9N“good” HZ rocky planets≈1.5×1010×0.1≈1.5×109
So even under:
# Conservative HZ boundaries,
# Strict radius cuts focused on truly Earth-like sizes,
# A highball “hidden mini-Neptune” subtraction,
# Ignoring (or heavily discounting) M dwarfs,

you still land at hundreds of millions to ~a billion “geometrically and bulk-composition-wise promising” planets in the Galaxy.

If you relax any of those pessimistic assumptions even a bit (include some fraction of K and M stars, allow slightly larger radii, use mid-range η⊕ instead of lower end), you go right back up into the several-billion to tens-of-billions range.

==== All you’ve done with this three-step tightening is: ====
* Make η⊕ more selective about obvious geometric/physical disqualifiers.

You have not yet accounted for:
* Long-term climate stability (billions of years vs. just 100 Myr)
* Plate tectonics vs stagnant lid
* Initial volatile inventory
* Early high-energy irradiation and atmosphere stripping
* Impact history and sterilizing events
* Deep waterworlds vs. dry worlds
* Biological probabilities (abiogenesis, evolution of complexity, evolution of intelligence)

So your modified η⊕ is still a “candidate planet count,” not a “likely inhabited planets” count.

But your suggestion (pessimistic HZ + strict radius + mini-Neptune penalty) is a perfectly reasonable way to:
* avoid obvious overcounting, and
* get a much harder lower bound on “worlds that are at least plausibly Earth-class from a coarse physical point of view.”

And even under that deliberately harsh haircut, you still get Galaxy-scale numbers that are enormous on human scales.