Where is everybody? · Working papers

How much of a head start did other planets have?

Revised after a second, separate analysis run for this project tried to break it. Neither analysis is an outside expert.

About 70% of the Sun-like (0.8-1.2 Msun) stars now residing in the solar cylinder are older than the Sun, but the first-pass precision did not survive review.

Summary

About 70% of the Sun-like (0.8-1.2 Msun) stars now residing in the solar cylinder are older than the Sun, but the first-pass precision did not survive review. The primary LAMOST subgiant sample gives 0.725 (0.692-0.759, statistical plus young-fraction prior); the two well-characterised subgiant samples (LAMOST and the newly added Nataf+24 primary sample) on four published age scales span 0.66-0.74, and two weaker bracketing samples widen the systematic range to 0.64-0.78. That is consistent with Lineweaver's 74 +/- 9% and does not test it more sharply; published star-formation histories give 0.55-0.74. Older stars lead the Sun by a mean of 4.1 Gyr (3.4-4.4 Gyr across estimates) and 16-31% of all Sun-like stars lead by more than 5 Gyr. The Fermi-clock consequence is robust to all of this: if no settlement has occurred and a settled Galaxy would be evident, p < 1.0e-9 to 1.2e-9 (95%) for the fiducial 2.5-2.9e9 planets, or 3.4e-9 to 7.9e-9 once the uncertainty in star count and eta_Earth is marginalised.

Key numbers

Quantity Value Uncertainty Note
Fraction of Sun-like stars now in the solar cylinder that are older than the Sun (adopted) 0.70 systematic range 0.64-0.78; core range 0.66-0.74 (10 estimates from LAMOST and Nataf+24 primary on four published age scales) Adopted value is the midpoint of the core envelope. Lower edge of the full range: Gaia 200 pc sample rescaled to the Nataf+24 scale (0.636). Upper edge: Nataf+24 primary + metal-poor annex on the X&R scale (0.779).
Primary estimate: LAMOST subgiants, Xiang & Rix ages, dynamical column weights 0.725 0.692-0.759 (16-84%, bootstrap plus young-fraction prior only) 8,525 stars, 100 bootstrap resamples. This interval is statistical; it is not the uncertainty of the result.
Nataf+24 primary sample (new in revision) 0.678 own ages; 0.708 on the X&R scale; 0.661 FLAME scale; 0.722 StarHorse scale; 0.655 with tracers older than 3 Gyr 0.649-0.709 (own ages); 0.678-0.746 (X&R scale) 17,107 stars. Agrees with LAMOST to 0.02 once on one age scale.
Nataf+24 primary + metal-poor annex (bracketing, upper) 0.757 own ages; 0.779 on the X&R scale 0.712-0.798 (own ages) Annex selection modelled approximately; combined sample is kinematically colder at old ages than the primary (rms v_z 26 vs 32 km/s at 10-12 Gyr), suggesting contamination.
Gaia 200 pc subgiants, this study's own ages (bracketing, lower) 0.703 as computed (biased); 0.644 on the X&R scale (mid-plane 0.543); 0.636 on the Nataf+24 scale; 0.654 on the StarHorse scale 0.607-0.686 on the X&R scale No longer called an independent replication. Lower than LAMOST by 0.07-0.08 on each of three common age scales; cause not established. 32% of the sample has RUWE > 1.4.
Age-scale offsets for the same stars (median ratio to Xiang & Rix) Nataf+24 0.950 (31,782 stars, -0.33 Gyr); StarHorse 1.040 (486, +0.27 Gyr); Gaia FLAME 0.926 (525, -0.55 Gyr); this study's Gaia-only ages 1.146 (475, +0.97 Gyr) The Gaia-only ages are also 1.167x Nataf+24 and 1.125x StarHorse (+0.79 Gyr, 9,879 stars), and put 22% of their weight in the last age bins.
Star-by-star age swap (LAMOST stars given Nataf+24 ages, same weights) -0.056 1,583 stars in common: 0.758 with X&R ages, 0.701 with Nataf+24 ages. Larger than the constant-ratio rescaling (0.703 vs 0.725) because 7% of the weight crosses the Sun's age downward and 0.5% upward.
Systematics of the primary estimate: age scale 0.689-0.739 for published scales (x0.93 to x1.04); 0.679-0.758 for +/-10%; 0.664 and 0.771 for x0.87 and x1.146 x0.87 and x1.146 are the scale of this study's own Gaia-only ages and are not supported by any published catalogue. The x1.146 value differs from the referee's 0.759 because a first-pass bug that dropped stars rescaled beyond 14 Gyr was fixed.
Systematics of the primary estimate: vertical structure star-count scale heights 0.659-0.698; column counted to 0.8 / 1.3 / 2 kpc 0.687 / 0.708 / 0.717; alternative potentials 0.715-0.729 Star-count variants are disfavoured by the layer test but lie inside the full range anyway.
Systematics of the primary estimate: other young fraction 0.06 / 0.13 / 0.15 gives 0.757 / 0.701 / 0.685; bright-limit correction 0.716; selection geometry 0.714-0.729; tracer weights (isochrone shifts, IMF slope) 0.708-0.737 0.13 is the young fraction the tracers imply for a flat recent rate.
Layer test, LAMOST: tracer fraction older than the Sun at |Z| 200-350 / 350-500 / 500-800 pc observed 0.783 / 0.867 / 0.939; dynamical weights predict 0.771 / 0.869 / 0.918; star-count heights (exp) predict 0.722 / 0.758 / 0.801 about 0.004-0.008 per cell Orbit-based weights reproduce the observed age mix above the slab to within 0.02; star-count heights miss by 0.06-0.14. For Nataf+24 the dynamical prediction is high by 0.02-0.05 (observed 0.671 / 0.744 / 0.845).
Scale heights: dynamical vs Mazzi+24 star counts agree below 4 Gyr (240/267/296 vs 211/264/296 pc); dynamical 7-25% larger at 4-10 Gyr; 1166 vs 368 pc in the oldest bin Implied high-alpha share of Sun-like stars: 24% in the column, 10% in the mid-plane.
Mean head start of the stars older than the Sun 4.13 Gyr 4.06-4.20 statistical; 3.4-4.4 across core and bracketing estimates; 3.3-5.1 including disfavoured variants Median 4.03 Gyr (3.2-4.3 across estimates).
Fraction of all Sun-like stars older than the Sun by more than 1 / 3 / 5 Gyr 0.629 / 0.456 / 0.289 (primary) ranges across estimates 0.54-0.69 / 0.34-0.51 / 0.16-0.31 Primary statistical intervals 0.602-0.656 / 0.433-0.477 / 0.271-0.306.
Mean age minus the Sun's age, all Sun-like stars (Lineweaver's 1.8 +/- 0.9 Gyr statistic) 2.43 Gyr 1.5-2.9 across estimates Consistent with Lineweaver's value.
With a metallicity floor (LAMOST) [M/H] > -0.5: 0.681; [Fe/H] > -0.5: 0.651; [M/H] > -0.3: 0.623; [Fe/H] > -0.3: 0.585 0.647-0.720; 0.614-0.688; 0.582-0.663; 0.539-0.628 Lower bounds on the head start: small planets show no sharp metallicity floor (Buchhave+ 2012, 2014; Kepler-444). Nataf+24 primary: 0.669 and 0.646 for [Fe/H] > -0.5 and > -0.3.
Living main-sequence Sun-like stars older than the Sun 0.636 (LAMOST); 0.608 (Nataf+24 primary) Stars formed, weighted by the fraction still on the main sequence.
Column minus mid-plane fraction +0.04 to +0.12 depending on sample and method LAMOST dynamical +0.12 (mid-plane 0.606); star-count heights +0.05 to +0.09; Nataf+24 +0.06 to +0.09; Gaia subgiants +0.08 to +0.10; FLAME dwarfs +0.04; GCS 40 pc dwarfs +0.24.
Published star-formation histories re-integrated 0.55-0.74 (seven column solutions; Mazzi+24 0.688) Mid-plane literature values: 0.50 (Gallart+24, 100 pc) and 0.76 (Alzate+21 as fitted by Madau 2023, who quotes 77%).
N_eff: habitable-zone rocky planets with enough head start (fiducial 1.07e10 Sun-like stars, eta_Earth 0.37) 2.48e9 at 1e-4 c; 2.86e9 at 0.1 c 1.9e9-2.6e9 and 2.2e9-3.0e9 across 16 age distributions; factor of several from star count and eta_Earth 1.6e9 at 3e-5 c (56% of maximum); zero below about 1.1e-5 c.
95% upper limit on per-planet probability of a Galaxy-settling civilisation, conditional on fiducial N_eff 1.05e-9 (0.1 c) to 1.21e-9 (1e-4 c) 1.0e-9-1.6e-9 across age distributions; 1.3e-9-2.7e-9 with metallicity floors; 1.3e-10-5.6e-9 at the joint extremes of star count and eta_Earth Premise: no settlement has occurred and a settled Galaxy would be evident; Earth-clock emergence.
Same limit with the uncertainty of N_eff marginalised (log-normal, sigma_ln 0.8-1.08, flat prior on p) 3.4e-9 to 7.9e-9 at 0.1 c; 3.9e-9 to 9.1e-9 at 1e-4 c Loosening factor 3.2-7.6. Upper end exceeds the referee's 6e-9 because 'factor 2 either way' in star count read as 1 sigma gives sigma_ln 1.08.
Galaxy-wide fraction (illustrative assumptions, not measurements) 0.71-0.80 with a bulge assumption; 0.76-0.82 using Xiang+25's high-alpha disc mass plus the local low-alpha age mix Local low-alpha stars alone: 0.65 older than the Sun.
Selection cut-flow LAMOST 247,104 -> 245,301 (age >= 2 Gyr) -> 45,043 (shell) -> 33,151 (annulus) -> 8,534 (|Z| < 200 pc) -> 8,525 (J_z > 0); Nataf+24 401,819 -> 17,107; Gaia 200 pc 117,677 -> 28,388 451 LAMOST stars get zero column weight (no-zero weighting gives 0.729); bright-limit completeness of 2-3 Gyr tracers 0.84 (-0.009); 14% of Gaia candidates lack a radial velocity, flat with age.

Data used

Method

Subgiant tracer estimator: each subgiant in a survey's colour-magnitude selection box stands for I0/G(age,[M/H]) Sun-like stars born at the same time, where G is the IMF-weighted mass interval of a MIST v1.2 isochrone inside the box. Stars are taken from a 0.3-0.8 kpc shell (age mix flat with distance), within 0.5 kpc of the solar radius and |Z| < 200 pc, and each is weighted by the inverse of the fraction of its vertical orbit spent in the slab to convert mid-plane to column. The weighted age histogram is deconvolved for age errors by EM; stars younger than 2 Gyr are added with a share of 0.10 +/- 0.04 from published star-formation histories; intervals come from 100/50/30 bootstrap resamples. Three samples: LAMOST with Xiang & Rix 2022 ages (primary), the Nataf+24 primary sample with Gaia kinematics (added in revision, plus its metal-poor annex modelled approximately), and a Gaia-only 200 pc sample with this study's own ages (cross-check, rescaled onto published scales). Revision additions: star-by-star age comparison between catalogues and a paired age-swap test; a layer test in which slab-star orbits predict the age mix observed at 200-800 pc, compared with star-count scale heights; a systematics table; [M/H] floors; estimates classified as core, bracketing or excluded with reasons. Cross-checks: seven published column star-formation histories re-integrated, GCS and Gaia FLAME dwarfs, solar twins. Fermi clock: N_eff(v) = N_Sun-like x eta_Earth x fraction of stars whose age minus settling time (1e5 ly / v) exceeds the emergence time; 95% limit p < 3.0/N_eff, also marginalised over a log-normal N_eff with a flat prior on p.

Closest prior work and what is new

Closest prior work. Madau 2023 (analytic fit to a Gaia mid-plane star-formation history within 100 pc combined with planet occurrence: 77%); Lineweaver 2001 (74 +/- 9%) and Lineweaver+ 2004 (75%) from models; Legassick 2015 (arXiv:1509.02832: 77% of potentially habitable systems older than the Sun, by 3.13 Gyr on average); Behroozi & Peeples 2015 (80%); Zackrisson+ 2016; Robles+ 2008 (53 +/- 2%). Data products: Xiang & Rix 2022 and Nataf+ 2024 (subgiant ages), Mazzi+ 2024 and Gallart+ 2024 (local star-formation histories; integrating Mazzi+24's published column history gives 0.69 in a few lines), Xiang+ 2025 (selection-corrected model of the same LAMOST subgiants).

What is new. The answer itself is not new: this is a reproduction of the known 'about three quarters' with newer data and an honest systematic range. What I did not find published: (i) the statistic taken from individual subgiant ages in three samples rather than from a model or fitted history; (ii) an explicit orbit-based mid-plane-to-column correction, checked by a layer test that discriminates it from star-count scale heights; (iii) an age-scale budget from stars shared between catalogues, including a star-by-star age swap; (iv) head-start distribution and metallicity-floor variants on both [Fe/H] and [M/H]; (v) the Fermi clock computed from a measured distribution with conditional and marginalised limits. The Fermi limit is standard Hart-Tipler arithmetic.

Confidence that it is new: medium

Limitations

What it means for the Fermi question

The head start Fermi's argument needs is real and large: 64-78% of Sun-like stars near the Sun's orbit are older than the Sun, by a median of 3.2-4.3 Gyr, and 16-31% by more than 5 Gyr. Under an Earth-clock emergence model, travel time alone cannot explain the silence for front speeds above about 3e-5 c: the number of planets with enough head start is already 56% of its maximum at 3e-5 c and 87% at 1e-4 c. The resulting 95% limit on the per-planet probability of producing a Galaxy-settling civilisation is about 1e-9 for the fiducial planet count and 3e-9 to 8e-9 with the count's uncertainty marginalised, and holds only if no settlement has occurred and a settled Galaxy would be evident. The census fixes the size of the clock; it does not say which explanation (rarity, short lifetimes, no expansion, undetected presence) is right, and it says nothing about emergence times longer than Earth's. Even the hardest metallicity floor considered ([Fe/H] > -0.3) leaves the limit at 2.7e-9 at 1e-4 c. The uncertainty in the age census (which changes N_eff by under 25%) is small next to the factor-of-several uncertainty from the assumed star count and eta_Earth.

Changes made after the referee report

Referee points not accepted

Figures

Figure 1. Left: when the Sun-like stars now in the Sun’s part of the Galaxy formed, from three samples of this study and from published star-formation histories (grey). Right: the fraction of those stars with at least a given head start over the Sun. About 70 per cent are older than the Sun (range 64 to 78 per cent), in line with Lineweaver’s 2001 estimate of 74 ± 9 per cent.
Figure 1. Left: when the Sun-like stars now in the Sun’s part of the Galaxy formed, from three samples of this study and from published star-formation histories (grey). Right: the fraction of those stars with at least a given head start over the Sun. About 70 per cent are older than the Sun (range 64 to 78 per cent), in line with Lineweaver’s 2001 estimate of 74 ± 9 per cent. Open at full size.
Figure 2. The fraction of Sun-like stars older than the Sun, from every sample and age scale used here, from models in the literature and from published star-formation histories. The dark blue band is the core range, 0.66 to 0.74, and the light band the full range, 0.64 to 0.78. Filled points are the main samples, open points the weaker bracketing samples, and crosses were not used.
Figure 2. The fraction of Sun-like stars older than the Sun, from every sample and age scale used here, from models in the literature and from published star-formation histories. The dark blue band is the core range, 0.66 to 0.74, and the light band the full range, 0.64 to 0.78. Filled points are the main samples, open points the weaker bracketing samples, and crosses were not used. Open at full size.
Figure 3. Four checks on the method. (a) The mix of ages is steady across the range of distances used (shaded). (b) The heights above the Galactic plane reached by stars of each age, from this study and from star counts, agree for stars younger than 4 billion years. (c) Which model of those heights reproduces the ages seen above the plane. (d) Two catalogues of ages for ordinary dwarf stars disagree star by star, which is why the study uses subgiants.
Figure 3. Four checks on the method. (a) The mix of ages is steady across the range of distances used (shaded). (b) The heights above the Galactic plane reached by stars of each age, from this study and from star counts, agree for stars younger than 4 billion years. (c) Which model of those heights reproduces the ages seen above the plane. (d) Two catalogues of ages for ordinary dwarf stars disagree star by star, which is why the study uses subgiants. Open at full size.
Figure 4. Left: the number of rocky planets in habitable zones that are old enough for a settlement wave starting there to have crossed the Galaxy by now, against the speed of the wave. Right: the 95% upper limit this puts on the chance per planet of producing such a wave, if none has happened. The limit applies only on that condition and widens when the uncertainty in the number of planets is included (orange).
Figure 4. Left: the number of rocky planets in habitable zones that are old enough for a settlement wave starting there to have crossed the Galaxy by now, against the speed of the wave. Right: the 95% upper limit this puts on the chance per planet of producing such a wave, if none has happened. The limit applies only on that condition and widens when the uncertainty in the number of planets is included (orange). Open at full size.
Figure 5. Left: three published age scales and this study’s own, compared star by star with the one used as the baseline; they differ from it by up to about 15 per cent. Right: how far each source of uncertainty moves the fraction of Sun-like stars older than the Sun, starting from the main sample’s 0.725; the headline value across all samples is about 0.70.
Figure 5. Left: three published age scales and this study’s own, compared star by star with the one used as the baseline; they differ from it by up to about 15 per cent. Right: how far each source of uncertainty moves the fraction of Sun-like stars older than the Sun, starting from the main sample’s 0.725; the headline value across all samples is about 0.70. Open at full size.

Code

Every number above is produced by these scripts from public data. The data tables themselves are not hosted here; the scripts download them.

age_scales.py analysis_gaia_sg.py analysis_ms.py analysis_nataf.py analysis_xr.py common.py fermi_clock.py fetch_data.py figures.py make_report.py published_sfh.py run_all.py sgweights.py tracer.py

Referee report

A second, separate analysis re-ran the code, recomputed the main numbers by its own route and tried to break the result. Like the first, it was run by Claude for this project; it is not an outside expert. In its report “the analyst” is the first analysis, which wrote the paper, and file names that are not linked on this page are its own working files. The paper above is the version revised in response.

Verdict: sound with fixes. Results reproduced: partly.

Rerun: exact. I ran a scratch copy of run_all.py --no-fetch (515 s, single thread); all 17 derived CSV tables match the analyst's with zero numerical difference (headline 0.725, floors 0.651/0.585, living MS 0.636, Gaia-only 0.703, Fermi clock table). Fermi arithmetic reproduced by hand (Kroupa fraction 0.0533 -> 1.07e10 stars; N_eff 2.48e9 at 1e-4c, 2.86e9 at 0.1c; p95 1.21e-9 and 1.05e-9; extremes 1.3e-10 and 5.6e-9; v_half 2.5e-5c). Mazzi+24 Table 4 re-integrated by hand: 0.688. Independent routes for the headline come out LOWER than 0.725: (a) same LAMOST stars and 1/G weights but star-count scale heights (Mazzi+24 Table 3) instead of the dynamical J_z weights give 0.666 (exp), 0.660 (sech2), 0.699 with canonical thick-disc heights at old ages, bootstrap sd 0.005; (b) the analyst's Gaia 200 pc sample put on the Xiang & Rix age scale gives 0.644 column / 0.544 mid-plane. So the pipeline reproduces exactly, but the headline value sits at the top of what independent routes support (0.64-0.73).

Strongest objection

The data cannot fix this fraction to better than about +/-0.06, so they do not test Lineweaver's number; they are merely compatible with it. The Sun's age falls where the cumulative age distribution is steep, so the statistic is hostage to the absolute isochrone age scale and to the weight given to the thick disc. The measured disagreement between age scales for the same stars (Xiang & Rix vs StarHorse vs the analyst's MIST ages: 4-15%) moves the answer by 0.035-0.06; replacing dynamical column weights with star-count scale heights moves it by 0.03-0.06; the two subgiant samples disagree by 0.06-0.08 once on one age scale; published column SFHs span 0.55-0.74. An expert would accept 'somewhere in 0.6-0.75' and reject '72.5% (69-76%)' and 'confirms'. The Fermi-relevant conclusion survives: across f = 0.55-0.76 N_eff runs 2.2e9-3.0e9 and the conditional limit 1.4e-9 to 1.0e-9, against a factor-6 uncertainty from star count and eta_Earth; multi-Gyr head starts for a majority of Sun-like stars and insensitivity to expansion speed above about 3e-5 c are secure. The specific headline number, its error bar, the word 'confirms' and the 'independent replication' label do not survive.

Errors found

Overclaims

Novelty check

Novel: partly. The assembled calculation (subgiant tracers with explicit column weighting, metallicity floors, Fermi clock from a measured distribution, uniform comparison across catalogues) is not published in this form as far as I could find. The answer is not new: Madau 2023 already used an empirical Gaia SFH and got 77% (mid-plane); integrating Mazzi+24's published column SFH gives 0.69 in a few lines; Legassick 2015 (not cited) reports 77% of habitable systems older than the Sun by 3.13 Gyr on average from a chemical-evolution model. The p < 3/N limit is standard Hart-Tipler arithmetic. Best described as a careful reproduction of the known 'about three quarters' with newer data, whose useful new element is the explicit mid-plane-to-column correction. Two relevant datasets were missed: Nataf et al. 2024 (Gaia ages for ~400,000 subgiants, a ready replacement for the home-made Gaia ages) and Xiang et al. 2025 (selection-function-modelled high-alpha disc mass, a better basis for a Galaxy-wide statement). All spot-checked citations (Lineweaver 2001, Madau 2023, Robles+ 2008, Behroozi & Peeples 2015, Zackrisson+ 2016, Bryson+ 2021) say what the analyst claims; table transcriptions from Mazzi+24, del Alcazar-Julia+25, Mor+19 and Xiang & Rix match the papers.

Required changes