Where is everybody? · Working papers

Sixty years of radio searches, combined

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

Merging 29 published radio-survey components into one de-duplicated coverage function (Milky Way model: 7.5e10 stars), the null record limits always-on isotropic 1e17 W narrowband beacons to N < 4.4e5 (1.7e5 to 2.6e6) if the frequency is anywhere in 1-10 GHz.

Summary

Merging 29 published radio-survey components into one de-duplicated coverage function (Milky Way model: 7.5e10 stars), the null record limits always-on isotropic 1e17 W narrowband beacons to N < 4.4e5 (1.7e5 to 2.6e6) if the frequency is anywhere in 1-10 GHz. On the 21-cm line the limit is N < 5,600 only if META/META II are trusted at nominal thresholds and the carrier is drift-free; the defensible range is 970 to 3.7e5 (2,200 if SETI@home's unresolved candidates are all rejected, about 1e5 for a transmitter on a rotating planet without SETI@home). Kardashev-II beacons: N < 4.3 on the 21-cm line (the efficiency floor; 57 if only SETI@home plus post-2015 searches are trusted, 1,200 to 5,300 if neither legacy surveys nor SETI@home count) and N < 113 (55 to 18,000) in 1-10 GHz, where dedicated searches cover only 5.3% of stars x log-frequency, 94% of it via BETA at a nominal threshold. Arecibo-class radars and Earth-2025 leakage are unconstrained (limits exceed the number of stars), and the only published Dyson-swarm limits remain Suazo et al. 2022 (4.8e-2, 4.8e-4, 8.6e-5 of stars within 300 pc for covering fractions above 10%, 50%, 90%).

Key numbers

Quantity Value Uncertainty Note
N_max (95%), isotropic always-on 1e17 W narrowband beacon, log-uniform 1-10 GHz 4.35e5 transmitters in the Milky Way 1.7e5 to 2.6e6 (all in-range variants, both drift classes, efficiency 0.25-1) baseline: no SETI@home, drift-free, eta=0.5; N_eff = 1.04e6 stars, p = 6.9e-6 per transmitter; 81% of N_eff is in-beam stars of Breakthrough Listen pointings calibrated to Mason+ 2025
N_max (95%), isotropic 1e17 W beacon on the 21-cm line as received in our frame (1420.2-1420.6 MHz) 5.57e3 972 to 3.7e5; conditional: 2.2e3 if SETI@home counted; 6.9e4 (orbital drift) and 9.95e4 (surface drift) without SETI@home; 4.1e3 surface drift with SETI@home; 1.39e5 with no legacy sky surveys 94% of baseline N_eff is META + META II at nominal Technosearch thresholds; these lose a factor 11 (orbit) to 64 (surface) for drifting carriers
N_max (95%), isotropic 1e17 W beacon on the 21-cm line in the host star's rest frame 7.08e3 1.07e3 to 3.7e5 META velocity window (-41..+43 km/s) contains 34% of Milky Way stars; SETI@home window 95%
N_max (95%), isotropic K-II (3.83e26 W) beacon, 21-cm line our frame 4.32 <1 (eta=1) to 1.1e4; 57 if only SETI@home + post-2015 searches trusted; 1,200 (5,300 with Gajjar+ 2021 Galactic-centre star counts) if neither legacy surveys nor SETI@home count this is the efficiency floor ln(0.05)/ln(1-eta); detection chance for one such beacon is 50%, 5.1% or 0.25% in the three cases; 6.8 in the star's rest frame
N_max (95%), isotropic K-II beacon, log-uniform 1-10 GHz 113 55 to 1.8e4; 2.0e3 with post-2015 searches only (9.0e3 with Gajjar+ 2021 star counts) probably conservative: continuum surveys not included (such a beacon would be a 61-567 Jy NVSS source at 25-8.2 kpc)
Fraction of stars x log-frequency (1-10 GHz) covered at K-II power by dedicated narrowband searches 5.25% 0.30% from post-2015 searches alone; 3.4% for 0.1-100 GHz 94% of the 5.25% is the BETA survey at a nominal threshold
N_max (95%), Arecibo-class beam (2e13 W EIRP), random pointing, 5% duty, 1-10 GHz 3.4e17 1.3e17 to 1.9e18 p = 8.7e-18 per civilization; 6.6e-7 detections expected if every star hosted one; aimed at the Sun: N_max 1.7e10 (6.6e9 to 9.3e10)
Earth-2025 leakage, generous bound (all 4 GW in one narrowband carrier), 1-10 GHz N_max 3.1e11 (4x the number of stars) 1.5e11 to 1.2e12 0.72 detections expected if every star hosted one; literal case (4 GW over an assumed 20 MHz = 558 W per 2.79 Hz channel) is visible to FAST only to 427 AU, so N is unbounded
Posterior 95th percentile of N, log-uniform prior on [1, 7.5e10] (prior q95 2.2e10) 1,373 (1e17 W, 21 cm, baseline); 7.2e4 (1e17 W, 1-10 GHz); 46 (K-II, 1-10 GHz) 602 for 1e17 W 21 cm if SETI@home counted radar and leakage posteriors are essentially the prior
SERENDIP III share of 0.1-100 GHz N_eff at 1e17 W 88% one legacy survey (424-436 MHz) at a nominal threshold; tier-B thresholds x10 moves the 0.1-100 GHz limit from 1.4e5 to 8.0e5
In-beam star concentration (GBT L band, 1e17 W) top 10 pointings carry 44% (52% at S band); 80% within 10 deg of the plane; median distance 6.0 kpc unscaled model / Mason+ 2025 counts: 0.75-0.90 inside 3 kpc, 1.27 at <=1e17 W, 1.92 at <=1e18 W
Coverage fraction vs Grimaldi & Marcy 2018 idealised prior search (uniform 1-2 GHz) 1.2e-8, 4.3e-7, 5.4e-6 at 2e13, 1e15, 1e16 W ratio to their 2.6e-8 (L/L_Arecibo)^1.5: 0.46, 0.046, 0.019 theirs assumes the whole sky searched to 1e-23 W/m2 across the band
Dyson swarms at 300 K, published upper limits on fraction of stars within 300 pc (Suazo+ 2022) 4.8e-2, 4.8e-4, 8.6e-5 for covering fraction >10%, >50%, >90% sensitivity floor of a hypothetical 100%-complete WISE search: 2.5e-6 (10% bin, two unrefuted candidates), 7.1e-7, 1.2e-6; not a limit, no published completeness
Milky Way model normalisation 7.54e10 stellar objects, about 4.2e10 Msun about 25% below the usual 5-6e10 Msun; limits scale at most linearly

Data used

Method

For each of 33 radio survey components (16 tier A from the papers, 14 tier B legacy/nominal, 3 extragalactic never counted) N_cov(L) is the number of Milky Way stars inside the footprint closer than sqrt(L/4 pi S_min); stars are named targets with distances or come from an analytic Galaxy model (two discs, halo, bulge) normalised to the Gaia 100 pc sample. Components are merged zone by zone (max where footprints overlap, sum otherwise) and averaged over five frequency priors (21-cm line in our frame, 21-cm line in the star's rest frame with a kinematic model for survey velocity windows, water hole, log-uniform 1-10 and 0.1-100 GHz) to give N_eff(L). Per-survey drift losses max(1, drift x integration / channel width) are applied for three transmitter classes (drift-free, Earth-like orbit, Earth-like surface); SETI@home is excluded by default with a switch (barycentric or non-barycentric sensitivities). In-beam star counts use a Gaussian beam taper and are calibrated in five power shells to Mason et al. 2025. Limits use the exact binomial likelihood: p = eta x duty x beam fraction x N_eff/N_MW, N_max = ln(0.05)/ln(1-p); 24 robustness variants x drift classes x eta 0.25-1 define the quoted ranges; posteriors use a log-uniform prior on N. Dyson swarms: published Suazo et al. 2022 limits plus a WISE W3+W4 flux-limit sensitivity count on the Gaia Catalogue of Nearby Stars.

Closest prior work and what is new

Closest prior work. Wlodarczyk-Sroka, Garrett & Siemion 2020 and Mason, Garrett & Siemion 2025 (arXiv:2511.20231) count in-beam stars for Breakthrough Listen only; Price et al. 2020, Enriquez et al. 2017 and Margot et al. 2023 give per-survey transmitter fractions; Wright et al. 2018 and Tarter et al. 2010 give searched-volume fractions; Grimaldi & Marcy 2018 and Grimaldi 2023 do population inference from idealised search volumes; Lacki 2024 (arXiv:2405.04651) and 2025 (arXiv:2508.00249) bound broadcast populations including non-SETI radio data; Suazo et al. 2022/2024 for Dyson swarms.

What is new. (1) One cross-survey coverage function N_cov(L, nu) in units of Milky Way stars, de-duplicated across legacy sky surveys, targeted surveys, in-beam stars and fields, packaged as an exact-binomial per-behaviour likelihood module. (2) The explicit conditional structure of the 21-cm limit: SETI@home status x transmitter drift class x legacy thresholds changes it by a factor of 63. (3) For dedicated SETI searches only, the statement that above about 1e21 W frequency coverage rather than sensitivity sets the limit. Not new: the in-beam counting (a re-derivation calibrated to Mason et al. 2025) and the Dyson sensitivity count (the first-pass novelty claim for it is withdrawn).

Confidence that it is new: medium

Limitations

What it means for the Fermi question

The radio 'Great Silence' is a narrow observational fact that constrains behaviour, not abundance. It excludes a Galaxy with more than a handful of deliberate K-II 21-cm beacons (if legacy surveys are trusted), more than roughly 1e2 to 9e3 K-II beacons elsewhere in 1-10 GHz, or more than 1e3 to 4e5 planet-scale (1e17 W) 21-cm beacons; if a fraction f of civilizations run 1e17 W isotropic beacons somewhere in 1-10 GHz, then N x f < 4.4e5. It does not exclude a Galaxy in which every star hosts a civilization like Earth in 2025: the whole record would expect 0.7 detections under a generous leakage bound, zero under the literal one, and 7e-7 from randomly pointed planetary radars. An integrator should use seti_likelihood.log_likelihood (exact N ln(1-p)) with an explicit behaviour mixture, treating the drift class and the SETI@home switch as nuisance choices; for any population without loud, persistent, omnidirectional beacons the radio term is flat, so the paradox must be carried by other evidence (absence of settlement or artefacts, and waste heat, where fewer than about 1 in 1e4 nearby stars can host a near-complete Dyson swarm).

Changes made after the referee report

Referee points not accepted

Figures

Figure 1. What the radio searches that found nothing rule out: the 95% upper limit on the fraction of stars with a continuous narrowband transmitter, against the transmitter’s power, for six frequencies and for an unknown frequency between 1 and 10 gigahertz (black). The numbered symbols are the limits published by single surveys. At the power of the Arecibo radar the limit is still of the order of one star in a hundred, and towards the power of the Earth’s mobile-phone networks it rises to every star, which is no constraint.
Figure 1. What the radio searches that found nothing rule out: the 95% upper limit on the fraction of stars with a continuous narrowband transmitter, against the transmitter’s power, for six frequencies and for an unknown frequency between 1 and 10 gigahertz (black). The numbered symbols are the limits published by single surveys. At the power of the Arecibo radar the limit is still of the order of one star in a hundred, and towards the power of the Earth’s mobile-phone networks it rises to every star, which is no constraint. Open at full size.
Figure 2. The number of stars in the Milky Way around which a transmitter of a given frequency and power would have been detected by the dedicated radio searches. Grey has never been searched; lilac has been searched but with less than one star within reach. Coverage is deep only in a few narrow bands and only for very powerful transmitters.
Figure 2. The number of stars in the Milky Way around which a transmitter of a given frequency and power would have been detected by the dedicated radio searches. Grey has never been searched; lilac has been searched but with less than one star within reach. Coverage is deep only in a few narrow bands and only for very powerful transmitters. Open at full size.
Figure 3. Left: the 95% upper limit on the number of civilisations transmitting in the Milky Way, against the power of each transmitter, for several assumptions about its frequency. Above the dashed line the limit exceeds the number of stars, so there is no constraint. Right: how the limit for beacons of 10¹⁷ watts on the 21-centimetre hydrogen line moves, from about 2,000 to more than 100,000, depending on which surveys are trusted and how the transmitter drifts in frequency.
Figure 3. Left: the 95% upper limit on the number of civilisations transmitting in the Milky Way, against the power of each transmitter, for several assumptions about its frequency. Above the dashed line the limit exceeds the number of stars, so there is no constraint. Right: how the limit for beacons of 10¹⁷ watts on the 21-centimetre hydrogen line moves, from about 2,000 to more than 100,000, depending on which surveys are trusted and how the transmitter drifts in frequency. Open at full size.
Figure 4. The probability that more than a given number of civilisations of each kind are transmitting now, before the searches (grey dashed) and after them. Only loud, always-on transmitters that broadcast in all directions are constrained. For beams aimed at random and for leakage like the Earth’s, the searches leave the prior almost unchanged.
Figure 4. The probability that more than a given number of civilisations of each kind are transmitting now, before the searches (grey dashed) and after them. Only loud, always-on transmitters that broadcast in all directions are constrained. For beams aimed at random and for leakage like the Earth’s, the searches leave the prior almost unchanged. Open at full size.
Figure 5. Left: the published upper limits of Suazo and colleagues (2022) on the fraction of stars with a 300-kelvin swarm of collectors, by the share of starlight covered and the distance searched. The hatched bars show the best a complete search of the same infrared data could reach, which is not a limit. Right: the fraction of stars for which a swarm at 100, 300 or 600 kelvin would be bright enough to detect in those data.
Figure 5. Left: the published upper limits of Suazo and colleagues (2022) on the fraction of stars with a 300-kelvin swarm of collectors, by the share of starlight covered and the distance searched. The hatched bars show the best a complete search of the same infrared data could reach, which is not a limit. Right: the fraction of stars for which a swarm at 100, 300 or 600 kelvin would be bright enough to detect in those data. 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.

analysis.py common.py coverage.py fetch_data.py figures.py galaxy.py make_compilation.py make_report.py run_all.py seti_likelihood.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: yes.

Reran code/run_all.py --offline from a scratch copy (70 s). Ten output tables, including behaviour_limits, robustness_variants, dyson_limits, neff_table and key_numbers.json, are byte-identical to the analyst's, and every headline number matches them.

Three independent recomputations:

  1. HI-line coverage by my own Monte Carlo (6 million stars sampled directly from the density law, astropy coordinates, star-by-star survey footprints): N_eff at 1e17 W = 2.04e8 against the analyst's 2.05e8; N_max = 2.2e3; K-II N_max = 6.0; model star total 7.532e10 against 7.537e10.
  2. The 1-10 GHz limit at 1e17 W rebuilt from the published Besancon in-beam counts of Mason et al. 2025: N_max about 4.8e5 against the analyst's 3.2e5, a factor 1.5 and inside the quoted range.
  3. Dyson sensitivity counts with a separately typed luminosity relation and a plane-parallel disc: 225,738 / 261,523 / 217,842 within 100 pc (analyst 228,230 / 261,523 / 217,842) and 2.4e6 / 4.0e6 / 2.4e6 within 300 pc (analyst 2.5e6 / 4.2e6 / 2.5e6).

Citation spot-checks against cached full texts all match: SETI@home Table 8, Mason 2025 Table 1, Price 2020, Gajjar 2021, Margot 2023, Johnson 2023, Painter 2025 Table 7, Tao 2022, Tremblay 2025, Suazo 2022 Table 1, Wright 2018, Saide 2023, and the Technosearch thresholds. Thirteen arXiv identifiers, including the 2026 ones, resolve to the stated papers.

Strongest objection

The headline numbers are carried by the least-verified parts of the record. The well-characterised targeted surveys contribute almost nothing above 1e15 W. The limits come from three sources whose completeness for the assumed signal was never demonstrated end to end: SETI@home, whose roughly 200 candidates are still awaiting FAST re-observation; legacy sky surveys entered at nominal Technosearch thresholds, of which META and META II detect only drift-free carriers inside a +-42 km/s window; and several million model-predicted, uncatalogued stars at 3 to 11 kpc in about ten low-latitude Breakthrough Listen beams.

The conclusion survives qualitatively: under any reading, always-on isotropic beacons of 1e17 W or more are limited to between a few thousand and about a million in the Galaxy (under roughly 1e-5 of stars), and Earth-like emitters are unconstrained by many orders of magnitude. The specific figures do not all survive: the HI-line figure moves by up to 50 times (2,200 to about 1e5), the K-II figures by 3 to 15 times, and the 1-10 GHz figure by about 1.5 times.

Errors found

Overclaims

Novelty check

Novel: partly. I found no published work that combines the legacy sky surveys, SETI@home tiers, targeted surveys and in-beam stars into one de-duplicated, frequency-resolved coverage function in units of Milky Way stars, or that packages it as a per-behaviour likelihood. That synthesis is new. The ingredients are not: the in-beam counting re-derives Mason et al. 2025 (with a model 1.8 to 2 times higher at large distances); the finding that frequency coverage is the bottleneck restates Wright et al. 2018 and holds only for dedicated SETI searches; the Dyson sensitivity calculation is a coarser version of Suazo et al. 2022, so novelty claim (4) should be removed. Lacki 2024/2025 already bound Milky Way broadcast populations with non-SETI radio data and should be cited against claim (3). The honest description is a synthesis and extension of published limits, not a new measurement.

Required changes