REVIEW 5 major objections 5 minor 22 references
The Growth and Decay of Individual Sunspots and Pores
T0 review · 5 major / 5 minor · reviewed 2026-08-06 · deepseek-v4-flash
Pith's one-line read Sunspot growth and decay rates are piecewise power laws that change slope near 50 and 150 millionths of a solar hemisphere.
desk verdict Large spot-level dataset with a plausible but poorly constrained non-monotonic decay law; the specific power laws need proper error analysis before being trusted. read the letter →
The pith
A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.
The reading
What carries the argument
The load-bearing machinery is the chain-tracking procedure. Sunspots and pores are detected in SDO/HMI continuum images five times per day; objects in consecutive images are linked into evolution chains if they share magnetic polarity, sit at the minimal combined distance d_ij = $\sqrt$((φ_i - φ_j)^2 + (θ_i - θ_j)^2 + (ΔS)^2) (with longitude corrected for differential rotation), and fall within coordinate windows of ±(2 + Δ/2) degrees. Each chain's maximum-area time separates the growth stage from the decay stage, and every intra-chain 5-hour area change contributes to the average rates. This machinery supplies the large statistics needed to resolve small spots and to see the breakpoints at 50 and 150 µsh.
What would settle it
Run the same chain-tracking on synthetic SDO/HMI-like images with injected spots whose growth and decay laws are known, and check whether the recovered dS/dt versus S curve reproduces breakpoints at 50 and 150 µsh with the claimed exponents; alternatively, apply a more conservative association requiring spatial overlap of umbral boundaries and see if the non-monotonic features survive.
Extended reading notes
Core claim
The central discovery is a non-monotonic, piecewise power-law relation between sunspot area S (in millionths of a solar hemisphere, µsh) and the rates dS/dt. For growth, dS_gr ≈ 0.2 $S^{1}$.35 µsh/day for S < 50 µsh, and dS_gr ≈ 11.9 $S^{0}$.32 µsh/day for S > 50 µsh. For decay, the paper finds dS_dc ≈ 0.28 $S^{1}$.26 for S < 50, dS_dc ≈ 11 $S^{0}$.15 for 50 < S < 150, and dS_dc ≈ 0.14 $S^{0}$.96 for S > 150 µsh/day. Pores, by contrast, show a simple linear relation, dS_gr ≈ 19 + 1.2 S and dS_dc ≈ -2.5 + 1.8 S µsh/day. Spots of trailing magnetic polarity grow and decay about two to three times faster than leading-polarity spots in the 50 to 200 µsh range, while pores show no polarity dependence. The combined growth-decay curve resembles a hysteresis loop, and at areas near $10^{3}$ µsh decay catches up with growth, suggesting a ceiling of a few thousand µsh for spot area.
Load-bearing premise
The results assume that objects linked across consecutive 5-hour images are the same physical sunspot or pore, identified by same polarity and minimum distance; if many links are wrong during splits, merges, or rapid area changes, the piecewise rates are distorted.
Editorial extensions
If this is right
- The Gnevyshev-Waldmeier plateau observed for sunspot groups appears for individual spots only in the 50 to 150 µsh range; outside this range decay accelerates roughly as the first power of area.
- No single decay model, whether turbulent diffusion or turbulent erosion, can cover the whole observed size range; the data require at least two regimes.
- Individual sunspots of area around 100 µsh decay at about 20 µsh/day, roughly twice the group rate, so group lifetimes are about twice the lifetime of a single spot of the same area.
- The hysteresis-like asymmetry between growth and decay rates, with decay approaching growth near 10^3 µsh, implies a natural upper limit of a few thousand µsh for spot areas.
- Trailing-polarity spots evolve faster than leading-polarity spots in the 50 to 200 µsh range, linking magnetic configuration to spot dynamics.
Reading between the lines
- If the 50 and 150 µsh breakpoints reflect penumbra formation thresholds, the same breakpoints should appear in other solar cycles and in numerical simulations; that is a testable prediction beyond the paper's 2010 to 2025 sample.
- The apparent hysteresis loop suggests the rate depends on evolutionary state (growing versus decaying), not just current area; a two-branch or state-dependent model could unify the piecewise fits.
- The chain-association criterion may mislink spots during splitting or merging; injecting synthetic spots with known growth and decay laws into the same tracking pipeline would test whether the piecewise exponents are recovered.
- Because the decay rate at 100 µsh is 20 µsh/day for individual spots versus roughly 11 µsh/day for groups, flux-budget models of active regions should use spot-level rather than group-level decay rates.
Editorial analysis
A structured set of objections, weighed in public.
Referee Report
Summary. The paper uses SDO/HMI continuum and magnetogram images from May 2010 to March 2025 to detect about 108,000 sunspots and 250,000 pores and to track their evolution in 5-hour cadence chains. For each object, growth and decay rates are computed relative to the time of maximum area. The central empirical claim is that the area-change rates of sunspots are non-monotonic functions of area: growth is steep for S < 50 µsh and shallow for S > 50 µsh, while decay is steep for S < 50 µsh, nearly flat for 50–150 µsh, and steep again for S > 150 µsh. The paper also reports linear area dependences for pores and systematic differences between leading- and trailing-polarity sunspots.
Significance. If the central claim holds, the paper is significant: it would show that no single area-rate law describes sunspot evolution across the full size range, that the Gnevyshev-Waldmeier rule applies only in an intermediate area band, and that any unified model of sunspot decay must reproduce a regime change near S ≈ 50–150 µsh. The dataset is unusually large (~350,000 objects) and the paper provides confidence intervals for the pore-rate averages, which is a genuine strength. The polarity-resolved analysis is also a useful addition. However, the quantitative foundations are not fully reported: the piecewise fits lack uncertainties, the breakpoints are introduced without a stated selection procedure, and the tracking-association rules are not validated. These omissions leave the central non-monotonicity claim unproven as stated and require attention before publication.
major comments (5)
- [Section 3.1, Figures 1–2 and Abstract] The central claim of non-monotonic decay rests on three disjoint power-law fits whose segments do not join at the breakpoints. Evaluating the stated expressions at S = 50 µsh gives about 38.7 µsh/day for the S < 50 segment and about 19.7 µsh/day for the 50–150 segment; at S = 150 µsh the second segment gives about 23.3 µsh/day and the third about 17.2 µsh/day. These downward jumps are the entire basis for the 'non-monotonic' wording, yet no physical discontinuity in the rate function is argued. If the binned means actually vary smoothly, independent straight-line fits on log-log axes will produce spurious drops at the segment boundaries. The authors should either fit with continuity constraints, fit a smooth function with a changepoint model, or at minimum display the binned data with error bars and demonstrate that the segments are statistically separated.
- [Section 3.1, equations for dS_gr/dt and dS_dc/dt] No uncertainties are reported for any of the fitted coefficients or exponents (0.2 ± ?, 1.35 ± ?, 11.9 ± ?, 0.32 ± ?, 0.28 ± ?, 1.26 ± ?, 11 ± ?, 0.15 ± ?, 0.14 ± ?, 0.96 ± ?). Without standard errors, covariance information, or a description of the fitting method on the binned averages, the reader cannot assess whether neighboring exponents such as 1.26 and 0.96 are actually different, or whether the claimed regime change at S = 50 and S = 150 is statistically significant. This is a load-bearing omission for the central claim.
- [Section 3.1, definition of the three decay regimes] The breakpoints S = 50 µsh and S = 150 µsh are introduced in the text and used in the abstract, but the manuscript never states how these values were chosen, whether they were fixed a priori or estimated from the data, or what uncertainty they carry. If the breakpoints were selected by eye from the same data used to fit the slopes, the quoted power laws and the non-monotonicity claim are affected by post-selection bias. A changepoint or model-comparison analysis (e.g., BIC over candidate breakpoint positions) would be necessary.
- [Section 2, chain-tracking criteria] The entire rate analysis depends on the association of objects in consecutive 5-hour images using the thresholds |θ_i − θ_j| < 2 + Δθ/2, |φ_i − φ_j| < 2 + Δφ/2, minimum dij, and the area-difference term in dij. The manuscript provides no validation of this tracking procedure, no discussion of how splitting, merging, fast area changes, or brief disappearances are handled, and no sensitivity study of the resulting rates to the matching thresholds. Since the central claim concerns how rates depend on area, systematic misassociation concentrated in particular area ranges could distort the apparent piecewise behavior. At minimum, the authors should quantify the fraction of chains that are ambiguous under the matching rule and perform a robustness test with stricter and looser thresholds.
- [Section 3.2, Figures 4–5 and polarity claims] The quantitative claims that trailing-polarity sunspots grow at about 80 µsh/day versus 30 µsh/day for leading polarity in the 50–200 µsh range, and decay at about 30 versus 10 µsh/day, are given without confidence intervals, sample sizes per area bin, or fit details. Given that the number of trailing-polarity sunspots is about half that of leading-polarity sunspots (34,356 versus 74,383), the apparent polarity asymmetry in the 50–200 µsh range could be affected by small-number statistics or by the same tracking issues noted above. The authors should report uncertainties for these rates and test whether the asymmetry is significant.
minor comments (5)
- [Section 3.1, pore fits] The pore decay fit dS_dc/dt ≈ −2.5 + 1.8·S µsh/day has a negative intercept, which would imply negative decay rates for very small S. The authors should state the area range over which this fit is intended and whether the linear fits are extrapolations at small S.
- [Section 2, data period] The period is written as '05.2010-03-2025'; this should be normalized to a consistent date format, e.g., May 2010 – March 2025, to avoid ambiguity.
- [References] Several references contain corrupted or malformed entries, including the Dalla, Fletcher & Walton (2008) entry with extra author text and journal symbols, and the Muraközy (2020) entry with an encoding artifact. These should be cleaned.
- [Figures 1–2] The figures show 'dotted lines are the approximation lines', but the axis labels, bin widths, and the number of objects per bin are not described in the text. Adding these details would help readers reproduce the fits.
- [Section 4, Discussion] The mention of vertical velocities from hmi.V.45s is interesting but Figure 7 is discussed only briefly; no uncertainties or quantitative comparisons are given for the velocity difference between growth and decay stages. This part could be expanded or clearly labeled as preliminary.
Circularity Check
No circular derivation; empirical fits stand on the measured area time series, with only minor non-load-bearing self-citations.
full rationale
The paper is an observational fitting study, not a derivation. Growth and decay rates are computed directly from chained SDO/HMI area measurements (dSgr/dt = (S_{l+1} - S_l)/dt, dSdc/dt = (S_l - S_{l+1})/dt), and the quoted power laws are explicitly approximations of binned averages ('can be approximated as', 'the dotted lines are the approximation lines'). The central non-monotonicity claim is thus an empirical description of the current data, not a consequence of any prior result containing that conclusion. The in-text self-citations are not load-bearing in a circular way: Tlatov et al. (2014, 2019) and Tlatov & Tlatova (2024) support the sunspot/pore boundary-detection procedure, which is independent methodological tooling; Tlatov (2023) is invoked in the Discussion as an interpretive comparison ('In a study of the lifetime of sunspots... different dependencies were also found') rather than as the proof of the rate laws. The model-selection issue that the segment fits are discontinuous at S=50 and S=150 microsh, with no continuity constraint or breakpoint uncertainties, is a statistical robustness concern, not a circularity: the fitted segments are not equivalent to their inputs by construction, and the paper does not dress the fits up as predictions from a fitted parameter. No equation is shown to reduce to an input, and no uniqueness claim is imported from the authors' prior work. Hence no significant circularity.
Assumptions & free parameters
free parameters (17)
- Growth coefficient (S<50 µsh) =
0.2
- Growth exponent (S<50 µsh) =
1.35
- Growth coefficient (S>50 µsh) =
11.9
- Growth exponent (S>50 µsh) =
0.32
- Decay coefficient (S<50 µsh) =
0.28
- Decay exponent (S<50 µsh) =
1.26
- Decay coefficient (50-150 µsh) =
11
- Decay exponent (50-150 µsh) =
0.15
- Decay coefficient (S>150 µsh) =
0.14
- Decay exponent (S>150 µsh) =
0.96
- Pore growth intercept =
19 µsh/day
- Pore growth slope =
1.2 day^-1
- Pore decay intercept =
-2.5 µsh/day
- Pore decay slope =
1.8 day^-1
- Growth/decay regime breakpoint =
50 µsh
- Decay regime breakpoint =
150 µsh
- Matching thresholds (theta, phi) =
2 + half-extent degrees
assumptions (4)
- domain assumption Changes in continuum area measured from HMI white-light images represent physical emergence/decay of sunspots and pores.
- domain assumption The tracking criterion (same polarity, minimal d_ij, thresholds in Section 2) uniquely identifies the same physical spot between consecutive 5-hour images.
- domain assumption Hale polarity assignment by co-aligned HMI magnetograms is correct for each tracked spot.
- standard math Power-law fitting of binned means to log-transformed data yields unbiased estimates of the scaling exponents.
Cite this review
Pith. "Pith review of The Growth and Decay of Individual Sunspots and Pores." pith.science (2026). https://pith.science/paper/CAGQUKCR
@misc{pith2026250621698,
author = {Pith},
title = {Pith review of: The Growth and Decay of Individual Sunspots and Pores},
year = {2026},
howpublished = {\url{https://pith.science/paper/CAGQUKCR}},
note = {Machine review of arXiv:2506.21698}
}
abstract
An analysis of the photometric growth and decay rates of sunspots and pores was carried out. According to the \textit{Solar Dynamics Observatory/Helioseismic and Magnetic Imager} (SDO/HMI) data for the period 05.2010-03-2025, $\approx 3.5\cdot 10^{\rm 5}$ sunspots and pores were detected and their evolution tracked. The growth and decay rates of sunspots depend non-monotonically on the area. For small-area sunspots $S \lesssim 50$ $\mu$sh, a rapid increase in velocity is observed with increasing the area for the growth stage $dS^{\rm gr}_{\rm sp}\approx 0.2 \cdot S^{\rm 1.35}$ and for the decay stage $dS^{\rm dc}_{\rm sp}\approx 0.28 \cdot S^{\rm 1.26} $ $\mu$sh/day. For sunspots $S\gtrsim 50$ $\mu$sh, the growth rate depends weakly on the area: $dS^{\rm gr}_{\rm sp}\approx 11.9 \cdot S^{\rm 0.32}$ $\mu$sh/day. For the decay stage of sunspots with an area of $S\approx 50\,-\,150$ $\mu$sh, the decay rate also depends weakly on the area and can be approximated as $dS^{\rm dc}_{\rm sp}\approx 11 \cdot S^{\rm 0.15} $. For sunspot areas $S\gtrsim 150$ $\mu$sh, the decay rate accelerates with increasing area: $dS^{\rm dc}_{\rm sp}\approx 0.14 \cdot S^{\rm 0.96} $ $\mu$sh/day. For solar pores, the growth and decay rates of solar pores are linearly related to the area. The growth and decay rates for the spots of the leading and trailing polarities are determined. In the range of spot areas $S\approx 100\,-\,200$ $\mu$sh, the growth and decay rates of sunspots of trailing polarity are higher than those of sunspots of leading polarity.
Figures
Figures from the paper (4 more)
Reference graph
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Reviewed August 6, 2026 · model on record in the stance chip above.
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