Eta-Earth Revisited II: Deriving a Maximum Number of Earth-like Habitats in the Galactic Disk

Helmut Lammer; Laurenz Spro{\ss}; Manuel Scherf

REVIEW 3 major objections 4 minor 298 references

Eta-Earth Revisited II: Deriving a Maximum Number of Earth-like Habitats in the Galactic Disk

T0 review · 3 major / 4 minor · reviewed 2026-08-11 · deepseek-v4-flash

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Pith's one-line read At most 250,000 Earth-like habitats exist in the galactic disk

desk verdict A transparent and useful synthesis that delivers concrete numbers, but the 'maximum' label is undercut by evaluating XUV stability at the mean rather than the outer HZCL distance. read the letter →

arxiv 2412.05002 v1 pith:NURIYMUI submitted 2024-12-06 astro-ph.EP astro-ph.GAastro-ph.SR

Manuel Scherf , Helmut Lammer , Laurenz Spro{ss} This is my paper · ORCID

classification astro-ph.EPastro-ph.GAastro-ph.SR

keywords Earth-likeHabitatshabitablezoneofcomplexlifeN2-O2atmosphereatmosphericescapegalacticstellarXUVfluxexoplanetoccurrencerateastrobiology

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper sets out to put an upper bound on how many planets in the Milky Way's disk can be Earth-like Habitats: rocky planets in the habitable zone of complex life that can hold an N$_2$-O$_2$-dominated atmosphere with only minor CO$_2$. Applying its maximum-count formula to the present-day disk-star population, with filters for galactic metallicity and supernova sterilization, stellar XUV-driven atmospheric escape, rocky-planet occurrence, water and land availability, and large moons, it finds maxima of $2.5^{+71.6}_{-2.4}\times10^5$ planets for atmospheres with at most 10% CO$_2$ and $0.6^{+27.1}_{-0.59}\times10^5$ for at most 1% CO$_2$. The consequence is that Earth-like habitats are rare: on average, at least roughly $10^3$ to $10^6$ rocky HZCL planets are needed for one Earth-like habitat to exist. These are maxima, the paper emphasizes, because several requirements that are not yet quantifiable, such as the origin of life, are set to unity.

What carries the argument

The load-bearing object is the inequality $N_{\mathrm{EH}} \le N_\star \times \eta_\star \times \eta_{\mathrm{EH}}$, where $N_\star$ is the number of disk stars with masses between $0.1$ and $1.25\,M_\odot$, $\eta_\star$ is the fraction of those stars offering a habitable galactic and stellar environment, and $\eta_{\mathrm{EH}}$ is the fraction of their rocky planets that meet the planetary requirements. Each fraction is a product of requirement probabilities: supernova survival, metallicity threshold, XUV/X-ray atmospheric stability, bolometric-luminosity upper limit, rocky-planet occurrence, water plus subaerial land, and large-moon frequency. The physical hinge is the atmospheric stability threshold: for a one-Earth-mass planet at the middle of the HZCL, an N$_2$-dominated atmosphere with 10% CO$_2$ is assumed to survive only if the stellar XUV surface flux stays below $F_{\mathrm{XUV,max}} = 35\ \mathrm{erg\,s^{-1}\,cm^{-2}}$ (with $F_{\mathrm{X,max}} = 5\ \mathrm{erg\,s^{-1}\,cm^{-2}}$ in the minimum case), and lower thresholds for the 1% CO$_2$ case. Applying this threshold with stellar evolution tracks across the rotational distribution removes most M dwarfs and shifts the surviving sample toward K and G stars.

What would settle it

A spectroscopic survey of rocky planets in the HZCL around M and late-K dwarfs that receive mean XUV surface fluxes above $35\ \mathrm{erg\,s^{-1}\,cm^{-2}}$ would test the central threshold: finding even a few long-lived N$_2$-dominated or N$_2$-O$_2$ atmospheres on such planets would contradict the assumed maximum.

Watch

Extended reading notes

Core claim

The central claim is that the number of Earth-like Habitats in the galactic disk, while not known, is bounded above by a few hundred thousand, and that most rocky planets in the habitable zone of complex life do not become Earth-like habitats. The calculation reaches this bound by filtering the disk-star population stepwise: a star must lie in a galactic environment with sufficient metallicity and low enough supernova exposure; at the mean HZCL distance, the star's XUV and X-ray fluxes must be low enough for an N$_2$-O$_2$ atmosphere to survive thermal escape; and its luminosity must not yet have pushed the planet through the inner habitable-zone boundary. The paper then multiplies by the rocky-planet occurrence rate and by the requirement of surface water with subaerial land and a large moon, using literature minima and maxima for each factor. The result is a plausible maximum range of $2.5^{+71.6}_{-2.4}\times10^5$ Earth-like Habitats for the 10% CO$_2$ case and $0.6^{+27.1}_{-0.59}\times10^5$ for the 1% CO$_2$ case, with the statement that the actual number is likely lower, since several biological and geological requirements are not included. The authors conclude that the Copernican Principle cannot be used to infer that complex animal-like life is common in the Galaxy.

Load-bearing premise

The load-bearing premise is that the XUV and X-ray surface-flux thresholds that define atmospheric stability, taken from simulations for roughly one-Earth-mass N$_2$-dominated atmospheres, are representative of real planets; if additional cooling agents, higher planetary masses, or different atmospheric histories allow such atmospheres to survive around late K or M dwarfs at fluxes above $35\ \mathrm{erg\,s^{-1}\,cm^{-2}}$, the viable stellar sample grows substantially and the stated maximum is no longer an upper bound.

Editorial extensions

If this is right

At most a few hundred thousand Earth-like Habitats exist in the galactic disk, and the actual number is likely smaller.
On average, at least $\sim 10^3$ to $10^6$ rocky planets in the habitable zone of complex life are needed for one Earth-like Habitat to exist.
Most M dwarfs, especially late M dwarfs, are strongly disfavored: for the stricter 1% CO$_2$ atmosphere case essentially no M dwarfs remain in the viable stellar sample.
Extraterrestrial intelligence, if it requires an Earth-like Habitat, would be much rarer than the population of rocky habitable-zone planets suggests, and the Copernican Principle cannot be invoked to infer that such life is common.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

If the atmospheric-stability thresholds hold, the model predicts a sharp stellar-type signature: N$_2$-dominated atmospheres should be found preferentially around K-type and early M stars in a restricted birth-age window, while late M dwarfs should be systematically empty of them.
The same filter chain could be applied to other habitat definitions by replacing the atmospheric-stability and HZCL terms, which would shift the upper bound by orders of magnitude for, say, CO$_2$-dominated or H$_2$-dominated habitats.
The paper's spatial distribution of EHs could be integrated over any survey volume to build a target list for future atmospheric spectroscopy, so that observed atmospheric compositions would test the filter chain region by region.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Colleague,

The headline is that this paper gives the first concrete quantitative upper limit for Earth-like habitats in the galactic disk: about 2.5e5 and 0.6e5 planets for 10% and 1% CO2 atmospheres, implying EHs are rare relative to ~1e11 stars. It's a transparent, caveat-heavy synthesis of Paper I's formula with literature models for star formation, metallicity, XUV-driven atmospheric escape, planet occurrence, water, and moons. The step-by-step application is careful, and they run nominal/min/max cases across a wide parameter range. The qualitative claim—that not every star or rocky HZCL planet can host an Earth-like N2-O2 atmosphere—is well supported.

The main soft spot is internal to the 'maximum' claim. They evaluate XUV stability at the mean HZCL distance, not at the outer edge where incident flux is lowest. For a true upper bound, you'd take the most favorable orbit. At the nominal threshold, this choice excludes all stars below ~0.44 Msun; many of those low-mass stars could host stable atmospheres at the outer HZCL. So the headline numbers are not guaranteed maxima—they are maxima conditional on a particular orbital averaging. The paper acknowledges the simplification but doesn't address its implications for the upper-bound claim. The stress-test concern holds up on reading, and it's a genuine methodological flaw, though it doesn't necessarily overturn the rarity conclusion.

Second, the atmospheric stability thresholds (e.g., FXUV,max=35 erg/s/cm2) come from Johnstone et al. 2021 for 1-Earth-mass planets. If CO2 cooling or higher masses allow survival around late K/M dwarfs, the viable stellar sample grows substantially. That's an external uncertainty, and the paper is admirably upfront about it. Still, the numbers are model-dependent.

Minor issues: the asymmetric ranges (e.g., +71.6/-2.4) are parameter ranges presented in the style of error bars, which can mislead; and no code/data are provided, which hurts reproducibility. The correlation between parameters is discussed but not resolved.

Who's this for? Astrobiologists and SETI researchers who want a concrete, if conditional, estimate of Earth-like habitats. It deserves a serious referee—the topic is important, the work is extensive, and the flaws are identifiable and fixable. I'd recommend sending it out with a request to address the mean-vs-outer-edge issue and to reframe the numbers as 'plausible' rather than strict maxima.

Referee Report

3 major / 4 minor

Summary. The paper applies the Earth-like Habitat (EH) framework developed in Paper I to the Galactic disk. It constructs a model of present-day main-sequence stars with masses 0.1–1.25 M_sun from an IMF, a star formation history, and a Galactic disk mass model, then sequentially applies supernova-sterilization, metallicity, XUV-driven atmospheric stability, bolometric-luminosity, rocky-planet occurrence, ocean/subaerial-land, and large-moon requirements. Six model cases spanning two CO2 limits (10% and 1%) and nominal/minimum/maximum input choices yield maximum counts of 2.5^{+71.6}_{-2.4} x 10^5 and 0.6^{+27.1}_{-0.59} x 10^5 EHs, implying that roughly 10^3–10^6 rocky HZCL planets are needed per EH. The authors conclude that EHs are rare and that the Copernican Principle cannot be used to infer that complex animal-like life is common in the Galaxy.

Significance. If established as an upper bound, the result would be a valuable quantitative update to Eta-Earth estimates because it combines stellar evolution, Galactic environment, and atmospheric stability in a single framework. The paper has real strengths: it uses the public Mors stellar evolution code, documents literature-based parameter ranges in tables, separates quantifiable from currently unquantifiable requirements, and is unusually candid about its caveats. It also makes falsifiable statements about the expected rarity of N2-O2-dominated atmospheres in the HZCL. However, the central 'maximum' claim is not yet supported, because several load-bearing choices are not conservative in the direction of maximizing the count. The result is better described as a plausible central estimate under a specific set of assumptions rather than a demonstrated upper bound.

major comments (3)

[§5.2.1.1, Eq. (15)] The XUV stability filter is applied at the mean HZCL distance d<HZCL> rather than at the outer HZCL boundary, where the incident XUV flux is smallest. The text explicitly notes that planets farther out receive less FXUV, but then averages over the zone. For a claimed maximum, a star should be counted if there exists any orbital position within the HZCL at which an N2-O2 atmosphere is stable; that position is the outer edge. This choice is not neutral: under the nominal FXUV,max = 35 erg s^-1 cm^-2 threshold, all stars below about 0.44 M_sun are removed, and a 0.35 M_sun star that fails at d<HZCL> can pass at the outer edge because the flux is lower by roughly (d_outer/d_mean)^2. The same issue applies to the upper bolometric limit in §5.2.2.1, where using the mean distance makes the Seff cutoff stricter than an outer-edge criterion. The headline NEH values are therefore not guaranteed maxima; the maximum case should evaluate atmospheric stability at the outer HZCL boundary and should apply the bolometric upper limit at the same outer location.
[§5.2.1.1 and Appendix A2] The atmospheric stability thresholds (FXUV,max = 35 erg s^-1 cm^-2 for 10% CO2, FX,max = 5 erg s^-1 cm^-2 for the minimum case) are taken from Johnstone et al. (2021) simulations for 1 Earth-mass planets. The manuscript states this choice and notes that higher-mass planets may be more stable, but it does not provide a maximum-case analysis with the most favorable planetary mass or with CO2 cooling effects included. Since these thresholds are the main reason that M and late-K dwarfs are excluded from the sample, an upper-bound claim requires either adopting the most favorable threshold values that are still consistent with the adopted atmospheric models or demonstrating that the maximum case already brackets them. As written, the result depends on this unvalidated atmospheric assumption and is not a formal upper bound.
[§3.2.3 and Eq. (4)] Equations (2)–(4) multiply independently estimated fractions, but the paper itself notes that requirements may be positively correlated. If two necessary requirements are positively correlated, the fraction satisfying both is at least as large as the product of the individual fractions; treating them as independent can therefore lower the estimate and break the 'maximum' property. The paper handles the metallicity–βHZCL correlation by weighting, but it does not establish that all remaining implemented fractions are independent or that positive correlations cannot increase NEH. The text should either derive the maximum under an explicit independence assumption or replace 'maximum' with 'plausible estimate under nominal assumptions' in the abstract and conclusions.

minor comments (4)

[§4.2.4] The notation M̄⊙ is used where the mean stellar mass is meant; this should be M̄⋆ to avoid confusion with the solar mass symbol.
[Eq. (8)] The piecewise main-sequence lifetime relation is taken from Westby & Conselice (2020), but the units of the numerical coefficients should be stated explicitly; as written, terms such as 7.1M^{-2.5} appear dimensionally inconsistent.
[Abstract and §8 tables] The asymmetric ranges quoted for NEH (e.g., 2.5^{+71.6}_{-2.4} x 10^5) are not labeled; please state explicitly whether these are 1σ errors, full min–max ranges, or something else, and make the same distinction in the tables.
[Figure 16 and §5.2.2.1] The caption and text describing the direction in which the minimum and maximum stable HZCL boundaries are shifted appear contradictory; please check whether the minimum case shifts the boundaries inward or outward and make the figure and text consistent.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the EH count is a product of independently sourced literature fractions and physical stability thresholds, not a refit of the target result.

full rationale

The derivation chain multiplies separately sourced quantities: the stellar census N* uses IMF/SFH models (Sections 4.2-4.3), the stellar fraction eta* uses GHZ models, metallicity distributions, and XUV/luminosity thresholds from external atmospheric simulations (Sections 5.1-5.2), and the planetary fraction etaEH uses occurrence rates and water/moon frequencies from the literature (Section 6). The core formula NEH <= N* x eta* x etaEH (Section 2) is presented as a definitional decomposition taken from Paper I, not as a fitted relation, and the result is not used to infer any input parameter. The atmospheric stability thresholds (e.g., FXUV,max = 35 erg/s/cm2 for 10% CO2, Section 5.2.1) come from Johnstone et al. (2021a,b) simulations with stated assumptions (1 Earth-mass planets, CO2 as infrared coolant) and are varied across nominal/minimum/maximum cases, so the final counts are not forced by construction. The skeptical concern about evaluating XUV stability at the mean HZCL distance rather than the outer edge is a methodological point about whether the result is truly a maximum, not a circularity: it does not make the output equivalent to an input or to a fitted parameter. Self-citations to Paper I and to Johnstone et al. are present and provide the framing and thresholds, but they are not invoked as a uniqueness theorem, and the inputs remain externally based, so no circular step rises to the level of the defined patterns.

Assumptions & free parameters 8 free parameters · 8 assumptions · 1 invented entities

The calculation rests on a Drake-like product of independently estimated fractions, with unknown biological factors set to 1. The numerical output is therefore an upper bound conditional on the validity of the stellar evolution, atmospheric escape, and GHZ models. Many threshold values are chosen from literature ranges, and the planetary occurrence, water, and moon fractions are the dominant uncertain multipliers.

free parameters (8)

Metallicity threshold Zmin = 0.3 nominal; 0.1 max; 0.5-0.75 min
Defines the minimum stellar metallicity for rocky planet formation; directly sets the stellar sample in Section 5.1.2.
XUV flux threshold for 10% CO2 atmospheres = FXUV,max = 35 erg/s/cm2 nominal; FX,max = 5 erg/s/cm2 min; FXUV,max = 56 erg/s/cm2 max
Sets the lower stellar age limit for atmospheric stability; drives exclusion of M dwarfs in Section 5.2.1.
XUV flux threshold for 1% CO2 atmospheres = FXUV,max = 15 erg/s/cm2 nominal; FX,max = 2.5 erg/s/cm2 min; FXUV,max = 35 erg/s/cm2 max
Stricter atmospheric stability threshold for the low-CO2 case.
Upper stellar flux limit Seff,max = 1.107 Seff,sun nominal; 1.0512 min; 1.21 max
Defines when a star's brightening makes HZCL planets uninhabitable; Section 5.2.2.
Rocky planet occurrence rate in HZCL (beta_HZCL) = Literature range approximately 0.01-0.3 (nominal, min, max cases)
Scales from Eta-Earth; central planetary factor in Section 6.1; exact values in Table B1 not in reviewed excerpt.
Water/ocean-subaerial land requirement fraction = Literature min/max/nominal values
Fraction of rocky HZCL planets with enough water and subaerial land (Appendix C); discussed in Section 6.2.
Large moon requirement fraction = Literature min/max/nominal values
Fraction of planets with a large moon (Appendix D); debated requirement, implemented in Section 6.3.
Stellar mass range for Mors model = 0.1-1.25 Msun
Limits sample because Mors stellar evolution tracks are only valid in this range; excludes lower-mass M dwarfs.

assumptions (8)

domain assumption Multiplicative decomposition NEH <= N* x eta_star x eta_EH is a valid upper bound (Eq. 2).
Imported from Paper I; assumes requirements multiply and all probabilities are <=1.
domain assumption Unknown factors (life origin, biological cycles) are set to 1.
Explicitly stated in Section 2; yields a maximum only among modeled factors.
domain assumption Mors stellar evolution tracks are valid for 0.1-1.25 Msun and rotational percentiles.
Section 5.2.1; limits the stellar sample.
domain assumption Johnstone et al. (2021) atmospheric escape thresholds apply to N2-O2 atmospheres with 1% and 10% CO2.
Appendix A2; central to alpha^XUV_at.
domain assumption GHZ survival probabilities from Gowanlock et al. (2011) and metallicity MDFs from Hayden et al. (2015) are representative of the disk.
Sections 5.1.1 and 5.1.2.
ad hoc to paper All HZCL planets are placed at the mean HZCL distance and have 1 Earth mass.
Sections 5.2.1 and 6.1; simplifying assumption for atmospheric stability.
domain assumption CO2 toxicity limits for terrestrial metazoans define HZCL boundaries and apply to putative alien complex life.
Section 3.2.5; follows Schwieterman et al. 2019b and Ramirez 2020.
domain assumption The N2-O2 atmosphere acts as a biosignature, so Blife factors are necessary and set to 1.
Section 2; life is assumed present if conditions allow.

invented entities (1)

Earth-like Habitat (EH) definition
purpose: Defines the counted objects as rocky HZCL planets with N2-O2-dominated atmospheres with minor CO2
A stipulated classification, not an independently observed entity; it determines what is counted.

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Pith. "Pith review of Eta-Earth Revisited II: Deriving a Maximum Number of Earth-like Habitats in the Galactic Disk." pith.science (2026). https://pith.science/paper/NURIYMUI

@misc{pith2026241205002,
  author       = {Pith},
  title        = {Pith review of: Eta-Earth Revisited II: Deriving a Maximum Number of Earth-like Habitats in the Galactic Disk},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/NURIYMUI}},
  note         = {Machine review of arXiv:2412.05002}
}

abstract

In Lammer et al. 2024, we defined Earth-like Habitats (EH) as rocky planets in the habitable zone of complex life (HZCL) on which Earth-like N$_2$-O$_2$-dominated atmospheres with minor amounts of CO$_2$ can exist and derived a formula for estimating their maximum number in the Galaxy. Here, we apply this formula by considering only requirements that are already scientifically quantifiable. By implementing models for star formation rate, initial mass function, and galactic mass distribution, we calculate the spatial distribution of disk stars as functions of stellar mass and birth age. We apply models for the GHZ and evaluate the thermal stability of Earth-like atmospheres with various CO$_2$ mixing ratios by implementing the newest stellar evolution and upper atmosphere models. In addition, we include the rocky exoplanet frequency, the availability of oceans and subaerial land, and the potential large moon requirement by evaluating their importance and implementing these criteria from minima to maxima values. We also discuss factors that are not yet scientifically quantifiable but may be requirements for EHs to evolve. We find that EHs are rare by obtaining maximum numbers of $2.5^{+71.6}_{-2.4}\times10^{5}$ and $0.6^{+27.1}_{-0.59}\times10^{5}$ planets that can potentially host N$_2$-Earth-like atmospheres with maximum CO$_2$ mixing ratios of 10\% and 1\%, respectively, implying that a minimum of $\sim 10^3 - 10^6$ rocky HZCL planets are needed for 1 EH to evolve. Their actual number, however, may be substantially lower as several requirements are not included in our model; this also implies ETIs are significantly rarer still. Our results illustrate that neither every star can host EHs, nor that each rocky HZCL planet evolves such that it may be able to host complex animal-like life. The Copernican Principle therefore cannot be applied to infer that such life is common in the Galaxy.

Figures

Figures reproduced from arXiv: 2412.05002 by the authors.

**Figure 1.** Different cumulative stellar mass distributions for different Initial Mass Functions (IMFs), i.e., of an initial population of stars, as calculated through the empirical power laws by Salpeter (1955), Miller & Scalo (1979), Kroupa (2001)/Kroupa et al. (2013), and Chabrier (2003), displayed for stellar masses up to 2.0 M⊙. The solid lines were calculated between stellar mass limits of 0.07 − 100 M⊙, while the dashed … view at source ↗

**Figure 3.** Upper panel: The normalized best-fit SFH for inner (solid black line) and outer disk (dashed black line) by Snaith et al. (2015), the reconstructed SFH of the Milky Way by Naab & Ostriker (2006), the cosmic SFH (green line) by Madau & Dickinson (2014), and the SFH of a 2 kpc wide bubble around the Sun (grey line) by Ruiz-Lara et al. (2020). Lower panel: Inner and outer SFH by Snaith et al. (2015) renormalized (dott… view at source ↗

**Figure 4.** Upper panel: The relative fraction of today’s mainsequence stars between 0.1-1.25 M⊙ as a function of birth age and stellar mass within bins of 50 Myr and 0.01 M⊙ for our nominal case. The varying densities at different ages are an effect of the implemented SFR by Snaith et al. (2015) and depict higher and lower star formation rates. The dashed orange lines indicate the birth age and mass of the Sun. Lower panel: T… view at source ↗

Figures from the paper (27 more)

**Figure 5.** Figure 5: The radial and vertical distribution of disk stars from r0 = 2000 pc to r1 = 21000 pc, and z0 = 0 pc to z1 = 2500 pc. The Sun is located at a distance from the center of r⊙ = 8178 ± 35 pc (Gravity Collaboration et al. 2019) and z⊙ = 17 ± 5 pc above the galactic mid-pla…

**Figure 6.** Figure 6: Upper panel: Galactic habitable zones (GHZ) from various studies, which show the probability of being habitable as a function of galactocentric distance. The black lines show the fraction of stellar systems that are not sterilized by SNs in two of the GHZ models (bot…

**Figure 7.** Figure 7: shows the mean values for the metallicity distribution according to Hayden et al. (2015) with the extensions discussed in this paragraph. Within r = 3 − 15 kpc and z = 0 − 2 kpc, the range for which these authors provide ob- Sun Sun [PITH_FULL_IMAGE:figures/full_fig…

**Figure 8.** Figure 8: Upper panel: The present-day probability for a certain star to be above a metallicity threshold of Zmin = 0.3 (nominal case) as a function of galactocentric distance r and height z. This probability is based on the metallicity distribution functions by Hayden et al. (2…

**Figure 9.** Figure 9: Upper panel: The fraction of stars above the different metallicity thresholds Zmin as a function of stellar mass. Lower panel: The number of stars above Zmin, again as a function of stellar mass. minimum case34. If we also vary SFH, IMF, etc., we obtain a total range o…

**Figure 10.** Figure 10: The inner HZ boundary (thick grey line) of the HZ according to the Runaway Greenhouse threshold and several different outer boundaries, i.e., the HZCL for pCO2 = 0.1 bar (green line) and pCO2 = 0.01 bar (green dashed line), both according to Schwieterman et al. (2019b…

**Figure 11.** Figure 11: Upper panel: The stellar X-ray surface flux, FX, in the middle of the HZCL for moderately rotating stars (i.e., the 50th percentile of the stellar rotational distribution) with stellar masses between M⋆ = 0.1 − 1.25 M⊙ as a function of stellar mass and age, calculated…

**Figure 12.** Figure 12: The stellar ages at which the X-ray (upper panel) and XUV surface flux (lower panel) at d⟨HZCL⟩ will fall below threshold values of FX,max = 5.0 erg s−1 cm−2 (upper panel) and FXUV,max = 35.0 erg s−1 cm−2 (lower panel), respectively, for each percentile (from 0th to 1…

**Figure 14.** Figure 14: Upper panel: The number of remaining GHZ stars that are above the lower limit, α XUV at , for our nominal case with FXUV,max = 35.0 erg s−1 cm−2 as a function of birth age and separated into spectral classes. Here, cutoff birth ages can be seen for each spectral clas…

**Figure 15.** Figure 15: Our nominal case for an N2-O2-dominated atmosphere with xCO2,max = 1% and for FXUV,max = 15.0 erg s−1 cm−2 (upper and middle panels). The upper panel shows the distribution of remaining stars as a function of birth age and stellar mass, while the middle panel illustr…

**Figure 16.** Figure 16: The stable HZCL boundaries for slow, moderate, and fast rotators with M⋆ = 0.1 − 1.25 M⊙, as well as for our nominal (nontransparent lines), minimum (transparent, shifted to the right) and maximum (transparent, shifted to the left) cases. These boundaries define the …

**Figure 18.** Figure 18: The distribution of remaining stars as a function of stellar mass and age, including α Seff at as the upper limit, for our nominal (upper), minimum (middle) and maximum (lower panel) cases. All plots are for N2-O2-dominated atmospheres with xCO2,max = 10%. threshold t…

**Figure 19.** Figure 19: The minimum case for an N2-O2-dominated atmosphere with xCO2 = 1%. The upper panel shows the same as [PITH_FULL_IMAGE:figures/full_fig_p035_19.png]

**Figure 20.** Figure 20: The number of remaining stars as a function of necessary requirements feeding into η⋆. The x-axis shows the stellar fraction (including error bars) remaining after implementing each criterion. The figure starts at the top with the entire number of disk stars (orange)…

**Figure 21.** Figure 21: The distribution of the remaining stars that are potentially able to host EHs, i.e., of N⋆ × η⋆, as a function of stellar mass for N2-O2-dominated atmospheres with xCO2 ≤ 10% (solid lines) and xCO2 ≤ 1% (dotted lines) for our nominal (orange), maximum (green) and min…

**Figure 22.** Figure 22: Different values for planet occurrence rates around solar-like stars from the literature (black points and error bars) for the same studies and boundary conditions as listed in Table B1. The orange points and error bars display the calculated values for βHZCL for a so…

**Figure 23.** Figure 23: Planet occurrence rates for our nominal (upper), minimum (middle) and maximum (lower panel) cases for an N2-O2- dominated atmosphere with xCO2 ≤ 10%. The big red and orange crosses with the black outlines show the initial planet occurrence rates from the literature f…

**Figure 24.** Figure 24: The same as [PITH_FULL_IMAGE:figures/full_fig_p042_24.png]

**Figure 25.** Figure 25: The frequency of planets with an appropriate water mass fraction as a function of stellar mass for our nominal (black), maximum (blue) and minimum (red) cases. The dotted lines show occurrence rates for which we assumed a simple linear correlation with FXUV (nominal a…

**Figure 26.** Figure 26: The distribution of remaining planets with the right amount of water that can in principal host an N2-O2-dominated atmosphere with xCO2,max = 10% as a function of stellar mass and age for our nominal (upper), minimum (middle) and maximum (lower panel) cases. crucial r…

**Figure 27.** Figure 27 [PITH_FULL_IMAGE:figures/full_fig_p046_27.png]

**Figure 28.** Figure 28: The distribution of planets with N2-O2-dominated atmosphere containing xCO2,max = 10% that meet all implemented requirements, including βmoon env , for our nominal (upper panel), minimum (middle panel) and maximum cases (lower panel). culated survival rates from Dobo…

**Figure 30.** Figure 30: Maximum values for ηEH (upper panel) and NEH (lower panel) as a function of stellar mass for both N2-O2- dominated atmospheres with xCO2,max = 10% (solid lines) and xCO2,max = 1% (dotted lines), respectively. While the upper panel shows the fraction of rocky exoplanet…

**Figure 29.** Figure 29: Same as [PITH_FULL_IMAGE:figures/full_fig_p049_29.png]

**Figure 31.** Figure 31: further illustrates the distribution of NEH as a function of galactic distance (upper panel) and stellar birth age (lower panel). From the upper panel, one can see that the maximum number of EHs slightly increases from the outskirts of the galaxy towards its center u…

**Figure 32.** Figure 32: The birth age of all remaining planets within our sample by spectral class for an N2-O2-dominated atmosphere with a maximum of 10% CO2 (upper) and 1% CO2 (lower panel), respectively. Here, the different colors illustrate the various spectral classes (with black as t…

**Figure 33.** Figure 33: Upper panel: The minimum average distance, dEH,SN,10%, between EHs in the Solar Neighborhood for our nominal (black cross), maximum (blue cross) and minimum (red cross) cases with xCO2,max = 10%, as well as the average distance, dEH,d,10%, for the entire galactic dis…

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