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Dimmed elliptical galaxies: a fundamental-plane search for harvested starlight

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

For grey, spatially uniform dimming at fixed mass, two fundamental-plane samples with no outlier clipping (114,210 SDSS r-band and 8,856 6dFGSv J-band early-type galaxies) give 95% upper limits on the fraction of bright early types missing a fraction f of their light of 2.8% at f=0.5 (2.4-3.8% across selection variants), 0.29% at f=0.75 (0.24-0.45%; 1.4% under pessimistic S/N scaling) and 0.90% at f=0.9 (resting on only 689 nearby, bright, high-surface-brightness galaxies and vanishing under pessimistic S/N); a population spread over f=0.5-0.9 is bounded at 3.4-3.8%, and dropping the red …

Summary

For grey, spatially uniform dimming at fixed mass, two fundamental-plane samples with no outlier clipping (114,210 SDSS r-band and 8,856 6dFGSv J-band early-type galaxies) give 95% upper limits on the fraction of bright early types missing a fraction f of their light of 2.8% at f=0.5 (2.4-3.8% across selection variants), 0.29% at f=0.75 (0.24-0.45%; 1.4% under pessimistic S/N scaling) and 0.90% at f=0.9 (resting on only 689 nearby, bright, high-surface-brightness galaxies and vanishing under pessimistic S/N); a population spread over f=0.5-0.9 is bounded at 3.4-3.8%, and dropping the red colour edge gives 2.9%/0.34%/0.90%. These are limits on light, not stars: cloaking all dwarfs and subgiants of an old population removes only about 20-36% of the light (Lacki 2019), where the limit is 7-17% of galaxies or absent, and f above about 0.93 or physical removal of stars is unconstrained. Spheres dimmed by 50% (30%) and placed uniformly in volume fill less than 0.39/0.47/0.83% (2.9/2.7/1.2%) of the SDSS volume for R=5/10/20 Mpc, but for R<=10 Mpc this is extrapolated from the 0.05-3% of the volume (100-900 sphere volumes, mostly z<0.08) actually tested; galaxy-weighted, fewer than 0.1-1.2% of sample galaxies lie in such regions. The most significant dim spheres all sit on catalogued rich clusters; 44% of the Coma sphere's 0.10 dex deficit is finger-of-god plus photometry, the rest has the sign and rough size of the environmental offset of the plane (cause not established), and ACO 2593 keeps an unexplained ~15% deficit about twice that trend. The first-pass individual-galaxy numbers survive unchanged (the referee reproduced them); the claims around them are narrower.

Key numbers

Quantity Value Uncertainty Note
SDSS sample size (unclipped FP sample, z=0.02-0.12) 114,210 of 221,433 parent galaxies exact count 6dFGSv: 8,856 (36 outlier-clipped objects restored). SDSS FP intrinsic scatter 0.104 dex in log I_e, MAD 0.098; 6dFGSv 0.102 / 0.110.
95% upper limit on fraction of SDSS early types dimmed by f=0.5 (grey, uniform) 2.8% 2.4-3.8% across selection variants (mag limit, EW boost, S/N scaling); 1.9% with stricter quality cuts; 2.9% without red colour edge N_eff=57,746 (51% of sample, median z 0.073, r<=16.85); every outlier counted as a candidate (n_obs=111)
95% upper limit, f=0.75 0.29% 0.24-0.45% across variants; 1.4% if spectral S/N scales linearly with flux; 0.13% after vetting; 0.34% without red colour edge N_eff=14,853 (13% of sample, median z 0.050, r<=16.09)
95% upper limit, f=0.9 0.90% 0.75-2.1% across variants; no limit under pessimistic S/N scaling; 5.3% with stricter quality cuts rests on 689 galaxies (0.6% of sample), median z 0.030, 95% below z=0.049, r<=15.10, biased to high surface brightness (mean dI +0.13)
95% upper limits at f=0.3 / 0.4 / 0.6 / 0.95 (SDSS) 17% / 7.4% / 0.99% / 56% conservative (unvetted); f=0.6 vetted 0.47% weak below f=0.4, effectively no constraint above f~0.93 or below f~0.3
Mixture bound: total fraction of galaxies with any distribution of f over 0.5-0.9 <3.4% (per-threshold 95%), <3.8% (simultaneous) for f in 0.75-0.9: 0.77% / 1.1% linear programme over 28 thresholds; replaces the first-pass '2.8% for any f in 0.5-0.9'
6dFGSv J-band 95% limits at f=0.3/0.4/0.5/0.6/0.75/0.9 23% / 14% / 7.0% / 4.0% / 2.0% / 25% E/S0-only subsample 6.3% / 1.7% / 25% at f=0.5/0.75/0.9 independent survey, band and hemisphere; Faber-Jackson cross-check on SDSS much weaker (53/22/2.5/2.2%)
Tail asymmetry beyond 0.60 dex (dim / bright), both samples combined 11 dim vs 1 bright binomial p=0.003 SDSS 6/1, 6dFGSv 5/0; beyond 0.45 dex SDSS 52/59, 6dFGSv 10/2. Rates below -0.45 dex: 0.046% (SDSS), 0.11% (6dFGSv). Five objects at >=75% apparent deficit are not explained by vetting: S06 (157.816,+25.861), D02 (190.530,-43.371), D03 (300.367,-71.265), D04 (39.872,-19.842), D05 (144.756,-7.696)
Outlier vetting (dI<=-0.45 dex) SDSS 52 (35 explained, 17 not); 6dFGSv 10 (4 explained, 6 not) vetting is visual and partly manual none has mid-IR excess: for 23 unexplained outliers waste-heat ratio gamma(300 K)<=0.064 profile-fit, <=0.12 largest AllWISE aperture; gamma(150 K)<=0.18 / <=0.62; expected about 2 or more for f>=0.65
Red-side colour check (galaxies redder than the selection window) 1,222 of 132,662; 49 / 5 / 2 at dI<=-0.30/-0.45/-0.60; only 2 are >0.2 mag beyond the edge both of those 2 are photometric artefacts on inspection no population of reddened, under-luminous early types hidden by the colour cut
Howlett+22 clipped catalogue: eligible SDSS outliers expected vs present 9 eligible of 52, 6.1 expected, 0 present binomial p=3.3e-5, Poisson p=0.0021 confirms published FP catalogues remove dim outliers; at dI<=-0.30: 125 eligible, 85 expected, 48 present
SDSS region limit, 50% dimmed spheres, filling fraction (R=5/10/20 Mpc) <0.39% / <0.47% / <0.83% Monte Carlo 5% / 3% / 1%; weaker of rules A and B quoted tested share of survey volume 0.36% / 2.4% / 48% (762 / 643 / 1,590 sphere volumes); assumes spheres placed uniformly in volume; number density <7.5e3 / 1.1e3 / 250 per Gpc^3; galaxy-weighted <0.13% / 0.32% / 1.1%
SDSS region limit, 30% dimmed spheres, filling fraction (R=5/10/20 Mpc) <2.9% / <2.7% / <1.2% Monte Carlo 13% / 8% / 2% tested share 0.05% / 0.42% / 33% (103 / 111 / 1,093 sphere volumes; 90% of detections below z=0.08 for R<=10); galaxy-weighted <0.44% / 0.54% / 1.2%
SDSS region limit, 75% dimmed spheres, filling fraction (R=5/10/20 Mpc) <0.97% / <1.2% / <2.6% Monte Carlo 8% / 3% / 2% tested share 0.15% / 3.3% / 16%; such galaxies mostly drop out of the sample, so sensitivity is lower than for 50%
Most negative SDSS sphere statistic S_min (R=5/10/20 Mpc) -6.28 / -8.08 / -6.49 shuffle p=0.0033 each (1 of 300 at most) all on Coma (ACO 1656); after environment detrending -5.11 / -6.65 / -5.67; all 15 top dim spheres contain catalogued clusters
Coma scan-selected R=10 Mpc sphere mean residual -0.099 dex (N=90) +-0.009 finger-of-god -0.032, photometry -0.011+-0.005 (44% identified); remainder -0.055+-0.014 vs group-redshift environmental trend -0.031+-0.007; difference -0.025+-0.015
Catalogue-centred R=10 Mpc spheres (no scan selection) Coma -0.039 dex, ACO 2142 -0.020 dex, ACO 2593 -0.072 dex +-0.009 / +-0.008 / +-0.013 ACO 2593 corresponds to ~15% apparent dimming, about 2.8 sigma above the environmental trend, no group redshifts available; not explained
Coherent rms of FP residual on sphere scale (SDSS, R=5/10/20 Mpc) 0.016 / 0.015 / 0.010 dex shuffle-based linear-theory bulk flows give 0.02 dex at z=0.02 and 0.005 dex at z=0.08, so peculiar velocities account for a comparable amount

Data used

Method

Rebuilt two early-type samples without FP outlier clipping: SDSS DR-based r-band sample (de Vaucouleurs radii, sigma, colour/concentration/EW/S-N cuts; 114,210 galaxies, z=0.02-0.12) and the full 6dFGSv J-band table (8,856, clipped objects restored). Fitted the plane in the surface-brightness direction by truncated-normal maximum likelihood with a redshift term; residual dI shifts by log10(1-f) under dimming. For each f, every sample galaxy was dimmed and passed through all flux-dependent cuts (magnitude limit, S/N, sigma error, colour, EW) to get the number of surviving twins N_eff and the fraction recovered below four pre-specified thresholds; limits are Bonferroni-corrected Poisson upper limits on the observed count divided by the effective number, with all outliers counted as candidates (conservative) or after visual/catalogue vetting. Variants: magnitude limit, EW boost, linear S/N scaling, stricter quality cuts, no red colour edge, E/S0 only, Faber-Jackson. A linear programme bounds mixtures over f. Outliers were vetted with images, catalogue flags and AllWISE profile-fit and aperture photometry (waste-heat ratio). Regions: standardised residuals summed in spheres of 5/10/20 Mpc on a grid, shuffle null (300), 30k-300k injected dimmed spheres per case for sensitive volume; limits by rule A (beyond observed minimum) and rule B (fixed S<-5 with Poisson limit on observed count), quoting the weaker, with tested volume share, sphere volumes, detection redshifts, Monte Carlo errors and a galaxy-weighted version. Dim spheres were cross-identified with SIMBAD clusters, decomposed into finger-of-god (group redshifts from Howlett+22), photometry and remainder, and compared with catalogue-centred spheres and the environmental trend.

Closest prior work and what is new

Closest prior work. Annis (1999, JBIS 52, 33) used the fundamental plane of ~100 ellipticals (and Tully-Fisher for spirals) to find no galaxy dimmed by more than ~75%; Zackrisson et al. (2015, ApJ 810, 23) did the Tully-Fisher analogue for 1,359 spirals (<~3% with >=75% dimming) and Calissendorff (2013 thesis) its precursor; Lacki (2019, 'Sunscreen') modelled the non-grey colour and luminosity signature of partial cloaking; Chen & Garrett (2021) and Griffith et al. (2015) are the waste-heat counterparts; Howlett et al. (2022) and Campbell et al. (2014) are the FP catalogues used, which clip outliers for peculiar-velocity work.

What is new. To my knowledge the first FP dimming test at the 10^5-galaxy scale with (i) samples rebuilt without any FP outlier clipping (and a demonstration with expected counts that published catalogues remove exactly the objects sought), (ii) selection-corrected limits as a function of f with every flux-dependent cut modelled, a mixture bound, and a check for reddened objects outside the colour window, and (iii) a quantified search for coherently dimmed 5-20 Mpc regions with injection-based limits, tested-volume accounting and a galaxy-weighted version. I did not find a prior FP-based region search or selection-corrected FP dimming limit, but the literature search was limited to ADS/arXiv-level queries, so an unpublished or obscure equivalent cannot be excluded.

Confidence that it is new: medium

Limitations

What it means for the Fermi question

Within the local volume (z<0.12) and for bright early-type galaxies, a civilisation that has enclosed half or more of its galaxy's starlight in a grey, galaxy-wide way is rare: fewer than about 3% of such galaxies at f=0.5 and fewer than about 0.3-1.4% at f=0.75, independent of the temperature of the waste heat, which closes the cold-radiator loophole of mid-infrared searches for that regime. Combined with the mid-IR bounds on the surviving outliers, there is no candidate Kardashev-III early-type galaxy in ~120,000 objects. The constraint is much weaker than it sounds for the most plausible engineering path: enclosing only long-lived low-mass stars removes 20-36% of the light and reddens the galaxy modestly, and that regime is limited only to 7-17% of galaxies or not at all; complete cloaking (f>0.93) removes the galaxy from the sample altogether. Expanding spheres of dimmed galaxies of 5-20 Mpc radius with 30-50% dimming fill less than about 1-3% of the volume if placed at random, but the small-radius limits rest on a small tested volume and on the uniform-placement assumption, and rich clusters mimic the signal at the 5-15% level, so the FP cannot by itself exclude modest (<~20%) regional dimming. Net: the result removes the 'many galaxies are mostly harvested' branch for massive early types locally, and leaves partial, selective or complete harvesting open.

Changes made after the referee report

Referee points not accepted

Figures

The ten galaxies in the 6dFGSv sample whose surface brightness is at most about a third of what the fundamental plane predicts (the plane is the tight relation between an elliptical galaxy’s size, the speeds of its stars and its brightness). Each image carries the reason found on inspection, such as a spiral or a star-forming disc; those in bold have no such explanation. The main limits count every galaxy this faint, explained or not, and a tighter variant counts only those in bold.
The ten galaxies in the 6dFGSv sample whose surface brightness is at most about a third of what the fundamental plane predicts (the plane is the tight relation between an elliptical galaxy’s size, the speeds of its stars and its brightness). Each image carries the reason found on inspection, such as a spiral or a star-forming disc; those in bold have no such explanation. The main limits count every galaxy this faint, explained or not, and a tighter variant counts only those in bold. Open at full size.
The 52 galaxies in the SDSS sample whose surface brightness is at most about a third of what the fundamental plane predicts. Most are two overlapping galaxies, mergers, edge-on discs or bad measurements. Those labelled in bold have no such explanation. The main limits count every galaxy this faint, explained or not, and a tighter variant counts only those in bold.
The 52 galaxies in the SDSS sample whose surface brightness is at most about a third of what the fundamental plane predicts. Most are two overlapping galaxies, mergers, edge-on discs or bad measurements. Those labelled in bold have no such explanation. The main limits count every galaxy this faint, explained or not, and a tighter variant counts only those in bold. Open at full size.
Figure 1. How far each galaxy’s surface brightness lies above or below the fundamental plane, for the SDSS sample (left) and the 6dFGSv sample (right). The dashed lines show where galaxies missing 50, 75 or 90 per cent of their starlight would be centred. The published catalogues (orange) have lost much of the faint tail in which such galaxies would sit, most clearly in the SDSS sample, which is why the samples were rebuilt without clipping (blue).
Figure 1. How far each galaxy’s surface brightness lies above or below the fundamental plane, for the SDSS sample (left) and the 6dFGSv sample (right). The dashed lines show where galaxies missing 50, 75 or 90 per cent of their starlight would be centred. The published catalogues (orange) have lost much of the faint tail in which such galaxies would sit, most clearly in the SDSS sample, which is why the samples were rebuilt without clipping (blue). Open at full size.
Figure 2. Left: the 95% upper limit on the fraction of early-type galaxies that are missing a given fraction of their light, from each sample and cross-check, with the earlier results of Annis (1999) and Zackrisson and colleagues (2015) marked. Right: the fraction of each sample that would still pass the selection cuts after being dimmed, which falls steeply beyond 80 per cent.
Figure 2. Left: the 95% upper limit on the fraction of early-type galaxies that are missing a given fraction of their light, from each sample and cross-check, with the earlier results of Annis (1999) and Zackrisson and colleagues (2015) marked. Right: the fraction of each sample that would still pass the selection cuts after being dimmed, which falls steeply beyond 80 per cent. Open at full size.
Figure 3. The search for whole regions of dimmed galaxies. Left: a statistic measuring whether the galaxies inside spheres 10 megaparsecs in radius are jointly too faint, observed (blue) and with the values shuffled among galaxies (black). Centre: the 95% upper limits on the share of space filled by dimmed spheres, in each survey. Right: the share of each survey’s volume in which such a sphere would have been detected, which is small for the smaller spheres.
Figure 3. The search for whole regions of dimmed galaxies. Left: a statistic measuring whether the galaxies inside spheres 10 megaparsecs in radius are jointly too faint, observed (blue) and with the values shuffled among galaxies (black). Centre: the 95% upper limits on the share of space filled by dimmed spheres, in each survey. Right: the share of each survey’s volume in which such a sphere would have been detected, which is small for the smaller spheres. Open at full size.
Figure 4. Maps of the two surveys by position on the sky and redshift (distance), coloured by the mean departure from the fundamental plane of the galaxies within 10 megaparsecs; red is fainter than predicted. The circles mark the five most significant faint regions in each survey. In the SDSS map each of them contains a catalogued cluster of galaxies, and the most significant is the Coma cluster.
Figure 4. Maps of the two surveys by position on the sky and redshift (distance), coloured by the mean departure from the fundamental plane of the galaxies within 10 megaparsecs; red is fainter than predicted. The circles mark the five most significant faint regions in each survey. In the SDSS map each of them contains a catalogued cluster of galaxies, and the most significant is the Coma cluster. Open at full size.
Figure 5. Left: the more crowded a galaxy’s surroundings, the lower it lies against the fundamental plane, most clearly in the two SDSS samples, so a faint region in a cluster is not by itself unusual. Right: the most significant faint sphere, around the Coma cluster, broken into the part explained by the motions of galaxies inside the cluster, which distort their distances, the part explained by photometry, and the part that remains.
Figure 5. Left: the more crowded a galaxy’s surroundings, the lower it lies against the fundamental plane, most clearly in the two SDSS samples, so a faint region in a cluster is not by itself unusual. Right: the most significant faint sphere, around the Coma cluster, broken into the part explained by the motions of galaxies inside the cluster, which distort their distances, the part explained by photometry, and the part that remains. Open at full size.
Figure S1. The 1,222 galaxies that the colour cut excluded for being too red, by how far beyond the cut they lie and how far below the fundamental plane. A population dimmed by hiding its fainter stars would fall in the shaded region. Only two galaxies are there, and both turned out on inspection to be faults in the photometry.
Figure S1. The 1,222 galaxies that the colour cut excluded for being too red, by how far beyond the cut they lie and how far below the fundamental plane. A population dimmed by hiding its fainter stars would fall in the shaded region. Only two galaxies are there, and both turned out on inspection to be faults in the photometry. 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_individual.py analysis_regions.py build_samples.py download_data.py finalize_limits.py fpk_common.py make_figures.py region_checks.py report_numbers.py revision_checks.py run_all.py vet_candidates.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.

Full rerun: copied code/ to scratch, pointed FP_KIII_RAW at a fresh directory linked to the cached raw downloads, ran python3 run_all.py --no-download single-threaded: 495 s, exit code 0. All 16 output tables compared are byte-identical to the analyst's (limits_final, limits_individual, limits_individual_best, limits_regions, fp_fits.json, region_extreme_patches, env_trend, survey_volume, candidates_*_vetted, etc.). Every number I checked in the report matches those tables.

Raw data are re-downloadable: VizieR FPsample returns 11,102 rows, Zenodo answers, and a fresh SkyServer pull of the RA 0-4 chunk equals the cached copy after sorting (1,171 rows, max numeric difference 0). SkyServer returned HTTP 500 on 2 of 6 requests, so a first-time download relies on the retry loop.

Independent recomputation (own script from the 90 raw SDSS chunks; own cuts, astropy distances, crude k-correction, clipped least-squares plane instead of truncated ML, binned S/N table): sample 114,208 vs 114,210; tail at -0.45 / -0.60 dex 58 / 5 vs 52 / 6; N_eff 58,003 / 14,962 / 697 vs 57,746 / 14,853 / 689; 95% limits at f = 0.5 / 0.6 / 0.75 / 0.9 of 3.0% / 1.0% / 0.27% / 0.93% vs the analyst's 2.8% / 0.99% / 0.29% / 0.90%.

Independent region injections (own standardisation, sphere centred on the injection point): Coma is the most extreme sphere at all three radii; my sensitive volumes are 1.3-1.9 times the analyst's in 8 of 9 cases, so the analyst's region limits are on the conservative side.

Other checks that passed: units and zero points, 6dF RA in hours, 6dF radii against catalogue kpc/h (0.0000 dex), no duplicated specObjID, no chunk near a row cap, S/N model unbiased against the parent sample without the S/N cut, Bonferroni and Poisson limits applied correctly. The selection model is conservative: N_eff is set mainly by the analyst's own surface-brightness-range requirement (at f = 0.9, 8,442 pass the magnitude limit and 701 pass that requirement). Citations spot-checked in the source texts: Howlett+22 (34,059 galaxies; 503 outliers rejected at p < 0.01 after visual rejects), Zackrisson+15 (1,359 discs; 3% and 0.3%; "57 disk galaxies and 106 ellipticals" for Annis), 6dFGSv ReadMe (criterion 6 is chi2 < 12). Annis's "137 galaxies" comes from a web-search summary of the BIS abstract page; I did not open the page or the paper.

Strongest objection

The test measures missing light under a grey, uniform dimming model, while the plausible harvesting strategy in an old stellar population is neither grey nor light-weighted. Giants supply most of an elliptical's light and are the hardest stars to enclose. In Lacki's (2019) model, enclosing every dwarf and subgiant costs only about 20-36% of the light, where this study has little or no power (17% limit at f = 0.3, nothing below), and enclosing enough giants to reach f >= 0.5 makes the galaxy more than a magnitude redder than the red sequence, which the sample's colour window would exclude.

The conclusion survives in narrowed form. The numerical limits on the fraction of early-type galaxies missing >= 50% of their r-band light are correct for grey dimming, and my check of the 1,222 galaxies excluded on the red side found no reservoir of very red, under-luminous objects (49 at dI <= -0.30, only 2 of them more than 0.2 mag beyond the red edge), so the non-grey case at f >= 0.5 is covered to a similar level. What does not survive is the reading that galaxy-wide star harvesting in ellipticals is tightly bounded: harvesting of all main-sequence stars is essentially unconstrained here.

Errors found

Overclaims

Novelty check

Novel: partly. The method is Annis (1999); Zackrisson+15 did the disc-galaxy version with a selection correction and a WISE check of outliers. arXiv API and web searches (Kardashev with fundamental plane, Faber-Jackson, peculiar velocity, early-type galaxies, scaling relations) found no fundamental-plane search with a modern large sample and no observational limit on coherently dimmed multi-galaxy regions. So the FP limit from 1.1e5 galaxies with an explicit N_eff(f) is a new quantitative result with an old method; the clipping point is correct but is stated in the source papers themselves; the WISE check follows Zackrisson+15; the region limits appear new. Lacki 2019 (Sunscreen), which bears directly on the grey-dimming assumption, is missing from the prior-work list, as are Chen & Garrett 2021 and the Calissendorff thesis. The analyst's 'medium' confidence is fair.

Required changes