ARDOR in Solar & Exoplanet Studies

• ARDOR is a term in astrophysics with two separate applications: Active Region Degree of Rogueness for solar-cycle prediction and a Bayesian flare-detection pipeline for exoplanet studies.
• The solar ARDoR method ranks active regions by quantifying deviations in tilt and separation to efficiently reconstruct the Sun’s axial dipole moment with minimal data.
• The ardor pipeline uses multi-tier Bayesian inference to detect low-amplitude stellar flares and assess phase-dependent clustering indicative of star–planet magnetic interactions.

Searching arXiv for the cited papers to ground the article. ARDOR denotes two unrelated technical constructs in contemporary astrophysical literature. In solar-cycle theory, ARDoR stands for Active Region Degree of Rogueness, a descriptor introduced to reduce the data burden of reconstructing the Sun’s axial dipole moment at sunspot minimum by isolating a small number of unusually influential active regions (Nagy et al., 2020). In exoplanet and stellar-activity studies, ardor denotes a multi-tier, Bayesian flare-detection and characterization pipeline designed to identify low-amplitude, short-duration stellar flares and test whether their occurrence is phase-correlated with planetary periastron, as expected under some star–planet magnetic interaction models (Whitsett et al., 26 Sep 2025). The shared spelling reflects nomenclature coincidence rather than conceptual continuity; the two uses belong to different subfields, rely on different observables, and solve different inference problems.

1. ARDoR in solar-cycle prediction

ARDoR was introduced in the context of an algebraic method for reconstructing, and potentially predicting, the solar dipole moment value at sunspot minimum, a quantity treated as a good predictor of the amplitude of the next solar cycle (Nagy et al., 2020). The central problem is that a direct summation of the ultimate dipole moment contributions of individual active regions would, in principle, require detailed and reliable input data for thousands of active regions in a cycle. ARDoR addresses this by ranking regions according to how strongly their actual properties depart from an expected, reduced-stochasticity baseline.

The descriptor’s name, Active Region Degree of Rogueness, encodes its intended role. It quantifies the extent to which a given active region deviates from expected properties such as mean tilt and polarity separation, conditioned on latitude and flux, and thereby changes its ultimate contribution to the Sun’s axial dipole moment at minimum (Nagy et al., 2020). Physically, it is a measure of the influence of “rogue” active regions with atypical tilt, separation, or polarity characteristics on the final polar field built through surface flux transport. Statistically, it is defined as the signed difference between the ultimate dipole contribution computed from the actual, fully stochastic properties of an active region and that computed from a reduced-stochasticity representation in which tilt and separation are replaced by their expected mean values.

The sign convention is intrinsic to the descriptor. Positive ARDoR indicates that the actual active region increases the end-of-cycle axial dipole magnitude relative to the reduced-stochasticity expectation; negative ARDoR indicates a reduction. Large absolute values therefore identify the active regions that dominate the mismatch between a mean-field baseline and the realized cycle evolution (Nagy et al., 2020).

2. Algebraic formulation underlying ARDoR

The ARDoR construction is embedded in an algebraic representation of the solar axial dipole moment. The axisymmetric photospheric radial field $B(\lambda,t)$ produces an axial dipole moment

$$D(t) = \frac{3}{2} \int_{-\pi/2}^{\pi/2} B(\lambda, t)\,\sin\lambda\,\cos\lambda\,\mathrm{d}\lambda.$$

Here $\lambda$ is heliographic latitude, $B$ is the azimuthal average of the large-scale radial field in Gauss, and $D(t)$ is commonly reported in Gauss (Nagy et al., 2020).

The end-of-cycle change in dipole moment is written as a sum over the ultimate contributions of all active regions that emerged during cycle $n$:

$$\Delta D_n \equiv D_{n+1} - D_n = \sum_{i=1}^{N_{\mathrm{tot}}} \delta D_{U,i} = \sum_{i=1}^{N_{\mathrm{tot}}} \delta D_{\infty,i}\, \exp\!\left(\frac{t_i - t_{n+1}}{\tau}\right) = \sum_{i=1}^{N_{\mathrm{tot}}} f_{\infty,i}\, \delta D_{1,i}\, \exp\!\left(\frac{t_i - t_{n+1}}{\tau}\right).$$

In this formulation, $N_{\mathrm{tot}}$ is the total number of active regions in the cycle, $t_i$ the emergence time of active region $i$, $$D(t) = \frac{3}{2} \int_{-\pi/2}^{\pi/2} B(\lambda, t)\,\sin\lambda\,\cos\lambda\,\mathrm{d}\lambda.$$0 the time of cycle minimum, and $$D(t) = \frac{3}{2} \int_{-\pi/2}^{\pi/2} B(\lambda, t)\,\sin\lambda\,\cos\lambda\,\mathrm{d}\lambda.$$1 a radial diffusion timescale. The quantities $$D(t) = \frac{3}{2} \int_{-\pi/2}^{\pi/2} B(\lambda, t)\,\sin\lambda\,\cos\lambda\,\mathrm{d}\lambda.$$2, $$D(t) = \frac{3}{2} \int_{-\pi/2}^{\pi/2} B(\lambda, t)\,\sin\lambda\,\cos\lambda\,\mathrm{d}\lambda.$$3, and $$D(t) = \frac{3}{2} \int_{-\pi/2}^{\pi/2} B(\lambda, t)\,\sin\lambda\,\cos\lambda\,\mathrm{d}\lambda.$$4 denote, respectively, the ultimate contribution at sunspot minimum, the asymptotic contribution for $$D(t) = \frac{3}{2} \int_{-\pi/2}^{\pi/2} B(\lambda, t)\,\sin\lambda\,\cos\lambda\,\mathrm{d}\lambda.$$5, and the initial contribution at insertion. The factor $$D(t) = \frac{3}{2} \int_{-\pi/2}^{\pi/2} B(\lambda, t)\,\sin\lambda\,\cos\lambda\,\mathrm{d}\lambda.$$6 is a retention or amplification factor due to surface transport and depends mainly on emergence latitude (Nagy et al., 2020).

For a single active region, the initial dipole contribution is

$$D(t) = \frac{3}{2} \int_{-\pi/2}^{\pi/2} B(\lambda, t)\,\sin\lambda\,\cos\lambda\,\mathrm{d}\lambda.$$7

where $$D(t) = \frac{3}{2} \int_{-\pi/2}^{\pi/2} B(\lambda, t)\,\sin\lambda\,\cos\lambda\,\mathrm{d}\lambda.$$8 is the solar radius, $$D(t) = \frac{3}{2} \int_{-\pi/2}^{\pi/2} B(\lambda, t)\,\sin\lambda\,\cos\lambda\,\mathrm{d}\lambda.$$9 is the magnetic flux in the northern polarity patch, $\lambda$0 is the latitudinal separation between polarities, $\lambda$1 is the full angular polarity separation, $\lambda$2 is the bipole tilt angle relative to east–west, and $\lambda$3 is the emergence latitude (Nagy et al., 2020). The transport factor is approximated by

$\lambda$4

with $\lambda$5 and $\lambda$6 encapsulating surface transport physics. In the baseline $\lambda$7D setup, $\lambda$8 and $\lambda$9 (Nagy et al., 2020). Because $B$0 is largest at low latitudes, rogueness at low latitudes carries disproportionate leverage.

3. Formal definition, ranking, and performance of ARDoR

ARDoR is defined relative to two representations of an active region. In the reduced-stochasticity (RS) representation, the measured latitude $B$1 and flux $B$2 are retained, but the tilt $B$3 and separation $B$4 are replaced by their expected mean values for that latitude and flux. In the fully stochastic (FS) representation, the actual tilt $B$5, separation $B$6, and other realized properties are used (Nagy et al., 2020).

For active region $B$7,

$B$8

This is a signed deviation, not a normalized index (Nagy et al., 2020). Large $B$9 values typically arise for large-flux active regions at low latitudes with strong tilt deviations, anti-Hale orientation, or unusual polarity separation.

The operational procedure is to compute the RS baseline,

$D(t)$0

rank active regions by descending $D(t)$1, and then form an ARDoR-corrected reconstruction using only the top $D(t)$2 regions:

$D(t)$3

where $D(t)$4 indexes the ranking by $D(t)$5 (Nagy et al., 2020). The remaining regions are represented by RS, equivalently setting their ARDoR values to zero.

The statistical validation used 647 synthetic cycles from a hybrid $D(t)$6D Babcock–Leighton dynamo with an average of $D(t)$7 active regions per cycle (Nagy et al., 2020). The central quantitative result is that only a small number of rogue regions is needed to recover most of the FS–RS deviation. For the fraction of cycles with dipole reconstruction error exceeding $D(t)$8, the RS baseline ($D(t)$9) yields $n$0, ARDoR with $n$1 yields $n$2, and the full FS algebraic sum yields $n$3 (Nagy et al., 2020). The standard deviation of fractional residuals falls from 0.212 at $n$4 to 0.128 at $n$5, 0.120 at $n$6, and 0.101 for the full FS sum (Nagy et al., 2020).

For cycles in which the total ARDoR sum exceeds 15% of $n$7, the top 10–20 active regions by $n$8 explain 80–90% of the FS–RS deviation (Nagy et al., 2020). The single most rogue region explains on average $n$9 of the deviation, while the top five explain $$\Delta D_n \equiv D_{n+1} - D_n = \sum_{i=1}^{N_{\mathrm{tot}}} \delta D_{U,i} = \sum_{i=1}^{N_{\mathrm{tot}}} \delta D_{\infty,i}\, \exp\!\left(\frac{t_i - t_{n+1}}{\tau}\right) = \sum_{i=1}^{N_{\mathrm{tot}}} f_{\infty,i}\, \delta D_{1,i}\, \exp\!\left(\frac{t_i - t_{n+1}}{\tau}\right).$$0. This supports the interpretation that intercycle variability is dominated less by the aggregate effect of numerous small active regions than by a low-number subset of large, low-latitude outliers.

4. Practical use and limitations of ARDoR

ARDoR was proposed specifically to reduce detailed input requirements for solar-cycle reconstruction and prediction. The minimal inputs for the RS baseline are emergence time $$\Delta D_n \equiv D_{n+1} - D_n = \sum_{i=1}^{N_{\mathrm{tot}}} \delta D_{U,i} = \sum_{i=1}^{N_{\mathrm{tot}}} \delta D_{\infty,i}\, \exp\!\left(\frac{t_i - t_{n+1}}{\tau}\right) = \sum_{i=1}^{N_{\mathrm{tot}}} f_{\infty,i}\, \delta D_{1,i}\, \exp\!\left(\frac{t_i - t_{n+1}}{\tau}\right).$$1, latitude $$\Delta D_n \equiv D_{n+1} - D_n = \sum_{i=1}^{N_{\mathrm{tot}}} \delta D_{U,i} = \sum_{i=1}^{N_{\mathrm{tot}}} \delta D_{\infty,i}\, \exp\!\left(\frac{t_i - t_{n+1}}{\tau}\right) = \sum_{i=1}^{N_{\mathrm{tot}}} f_{\infty,i}\, \delta D_{1,i}\, \exp\!\left(\frac{t_i - t_{n+1}}{\tau}\right).$$2, flux $$\Delta D_n \equiv D_{n+1} - D_n = \sum_{i=1}^{N_{\mathrm{tot}}} \delta D_{U,i} = \sum_{i=1}^{N_{\mathrm{tot}}} \delta D_{\infty,i}\, \exp\!\left(\frac{t_i - t_{n+1}}{\tau}\right) = \sum_{i=1}^{N_{\mathrm{tot}}} f_{\infty,i}\, \delta D_{1,i}\, \exp\!\left(\frac{t_i - t_{n+1}}{\tau}\right).$$3 or a proxy such as sunspot area, and mean relations for tilt and separation. Detailed measurements of actual tilt and separation are then required only for the top-$$\Delta D_n \equiv D_{n+1} - D_n = \sum_{i=1}^{N_{\mathrm{tot}}} \delta D_{U,i} = \sum_{i=1}^{N_{\mathrm{tot}}} \delta D_{\infty,i}\, \exp\!\left(\frac{t_i - t_{n+1}}{\tau}\right) = \sum_{i=1}^{N_{\mathrm{tot}}} f_{\infty,i}\, \delta D_{1,i}\, \exp\!\left(\frac{t_i - t_{n+1}}{\tau}\right).$$4 candidate rogue regions (Nagy et al., 2020). Suggested data sources include synoptic magnetograms such as Kitt Peak, SOLIS, and SDO/HMI, and white-light sunspot catalogues with tilt estimates such as Debrecen and Mt. Wilson/MDI.

The recommended workflow is a rolling RS reconstruction of $$\Delta D_n \equiv D_{n+1} - D_n = \sum_{i=1}^{N_{\mathrm{tot}}} \delta D_{U,i} = \sum_{i=1}^{N_{\mathrm{tot}}} \delta D_{\infty,i}\, \exp\!\left(\frac{t_i - t_{n+1}}{\tau}\right) = \sum_{i=1}^{N_{\mathrm{tot}}} f_{\infty,i}\, \delta D_{1,i}\, \exp\!\left(\frac{t_i - t_{n+1}}{\tau}\right).$$5 during the cycle, combined with continuous provisional ARDoR estimates for newly emerged large, low-latitude active regions. The top $$\Delta D_n \equiv D_{n+1} - D_n = \sum_{i=1}^{N_{\mathrm{tot}}} \delta D_{U,i} = \sum_{i=1}^{N_{\mathrm{tot}}} \delta D_{\infty,i}\, \exp\!\left(\frac{t_i - t_{n+1}}{\tau}\right) = \sum_{i=1}^{N_{\mathrm{tot}}} f_{\infty,i}\, \delta D_{1,i}\, \exp\!\left(\frac{t_i - t_{n+1}}{\tau}\right).$$6 rogue regions are then explicitly assimilated to update the predicted end-of-cycle dipole $$\Delta D_n \equiv D_{n+1} - D_n = \sum_{i=1}^{N_{\mathrm{tot}}} \delta D_{U,i} = \sum_{i=1}^{N_{\mathrm{tot}}} \delta D_{\infty,i}\, \exp\!\left(\frac{t_i - t_{n+1}}{\tau}\right) = \sum_{i=1}^{N_{\mathrm{tot}}} f_{\infty,i}\, \delta D_{1,i}\, \exp\!\left(\frac{t_i - t_{n+1}}{\tau}\right).$$7 (Nagy et al., 2020). Anti-Hale regions and unusually tilted or unusually separated regions are explicitly prioritized.

Several caveats constrain interpretation. The results are based on synthetic cycles rather than full historical validation, although the emergence statistics were tuned to observations (Nagy et al., 2020). Both RS and FS representations treat active regions as single bipoles introduced instantaneously; highly complex active regions with morphological asymmetries may not be perfectly captured in that approximation. The transport parameters $$\Delta D_n \equiv D_{n+1} - D_n = \sum_{i=1}^{N_{\mathrm{tot}}} \delta D_{U,i} = \sum_{i=1}^{N_{\mathrm{tot}}} \delta D_{\infty,i}\, \exp\!\left(\frac{t_i - t_{n+1}}{\tau}\right) = \sum_{i=1}^{N_{\mathrm{tot}}} f_{\infty,i}\, \delta D_{1,i}\, \exp\!\left(\frac{t_i - t_{n+1}}{\tau}\right).$$8, $$\Delta D_n \equiv D_{n+1} - D_n = \sum_{i=1}^{N_{\mathrm{tot}}} \delta D_{U,i} = \sum_{i=1}^{N_{\mathrm{tot}}} \delta D_{\infty,i}\, \exp\!\left(\frac{t_i - t_{n+1}}{\tau}\right) = \sum_{i=1}^{N_{\mathrm{tot}}} f_{\infty,i}\, \delta D_{1,i}\, \exp\!\left(\frac{t_i - t_{n+1}}{\tau}\right).$$9, $N_{\mathrm{tot}}$0, and $N_{\mathrm{tot}}$1 are model-calibrated rather than directly measured for the real Sun. The paper notes that sensitivity to tilt scatter amplitude, flow speed, diffusivity, and flux calibration is not exhaustively quantified. A plausible implication is that the optimal value of $N_{\mathrm{tot}}$2 is not universal, though the reported results suggest that the reduction in data complexity is substantial even under parameter uncertainty.

5. ardor as a flare-detection pipeline for star–planet magnetic interaction

A separate 2025 study introduced ardor, stylized in lowercase, as a multi-tier, Bayesian flare-detection and characterization pipeline for time-series photometric data, with emphasis on recovering flares near the photometric noise floor and testing whether those flares cluster with orbital phase in a manner consistent with star–planet magnetic interactions (Whitsett et al., 26 Sep 2025). No acronym expansion is given.

The scientific motivation is the use of induced stellar flares as an indirect probe of planetary magnetic fields. The paper situates the problem within the context of the radius irradiation valley, the underabundance of close-in planets with radii $N_{\mathrm{tot}}$3, often attributed to photoevaporation and/or core-powered mass loss. In that framework, planetary magnetism may modulate atmospheric retention. If a close-in planet enters the sub-Alfvénic region of its host star, magnetic coupling can perturb coronal fields and potentially trigger flares preferentially near periastron, where the interaction is strongest (Whitsett et al., 26 Sep 2025).

The pipeline ingests TESS SPOC PDCSAP flux products at 2-minute and 20-second cadence. The reported data volume comprises 2,083 confirmed hosts represented by 10,558 light-curve files and 3,519 TOI hosts represented by 17,423 files (Whitsett et al., 26 Sep 2025). The objective is not merely flare discovery but a linked inference chain: detect candidate flares, characterize them with a physically motivated model, map flare epochs to orbital phase, and test for phase-dependent clustering.

The physical model adopted is the sub-Alfvénic, dipole–dipole interaction picture of Lanza (2018). The field superposition is written as

$N_{\mathrm{tot}}$4

and the corresponding field-energy expressions are used to derive an energy change that scales as $N_{\mathrm{tot}}$5, implying a periastron-peaked perturbation (Whitsett et al., 26 Sep 2025). The magnetospheric obstacle radius is given as

$N_{\mathrm{tot}}$6

and the interaction timescale near periastron is written as

$N_{\mathrm{tot}}$7

To estimate whether a planet lies inside the stellar Alfvén surface at periastron, the study uses the magnetic confinement parameter

$N_{\mathrm{tot}}$8

and the Alfvén-radius scaling

$N_{\mathrm{tot}}$9

with the dipolar specialization

$t_i$0

and an empirically rescaled relation

$t_i$1

The paper notes that these Alfvén-surface estimates carry $t_i$2 typical uncertainties (Whitsett et al., 26 Sep 2025).

6. Detection architecture, statistical tests, and reported candidates

ardor is organized into a sequence of detection and vetting tiers. Tier 0 performs detrending with a Savitzky–Golay filter through Lightkurve flatten,

$t_i$3

using window size 401, polynomial order $t_i$4, and local outlier rejection at $t_i$5 (Whitsett et al., 26 Sep 2025).

Tier 1 identifies candidates with a local $t_i$6 threshold above the median baseline in a sliding 100-point window updated every 10 points. For 2-min cadence, the criterion is one point above $t_i$7 followed by two points above $t_i$8; for 20-s cadence, one point above $t_i$9 followed by five above $i$0 (Whitsett et al., 26 Sep 2025). This explicitly relaxes the classic three-consecutive-$i$1 heuristic to improve short-flare recall.

Tier 2 uses a coarse model fit based on the log-linearized decay law

$i$2

with propagated errors

$i$3

and goodness-of-fit assessed by reduced chi-square,

$i$4

Candidates with $i$5 are retained (Whitsett et al., 26 Sep 2025). Tier 3 performs Bayesian model comparison between a single-peak flare template and a hybrid spline noise model using dynamic nested sampling in allesfitter, with threshold

$i$6

Posterior sampling over $i$7, amplitude $i$8, and FWHM $i$9 is then performed via MCMC (Whitsett et al., 26 Sep 2025).

The pipeline evaluates orbital-phase clustering through both goodness-of-fit tests and unbinned likelihood analysis. The empirical CDF is

$$D(t) = \frac{3}{2} \int_{-\pi/2}^{\pi/2} B(\lambda, t)\,\sin\lambda\,\cos\lambda\,\mathrm{d}\lambda.$$00

with the KS, AD, and Kuiper statistics

$$D(t) = \frac{3}{2} \int_{-\pi/2}^{\pi/2} B(\lambda, t)\,\sin\lambda\,\cos\lambda\,\mathrm{d}\lambda.$$01

$$D(t) = \frac{3}{2} \int_{-\pi/2}^{\pi/2} B(\lambda, t)\,\sin\lambda\,\cos\lambda\,\mathrm{d}\lambda.$$02

$$D(t) = \frac{3}{2} \int_{-\pi/2}^{\pi/2} B(\lambda, t)\,\sin\lambda\,\cos\lambda\,\mathrm{d}\lambda.$$03

For likelihood-based phase models, ardor tests an inhomogeneous Poisson process parameterized either by a von Mises phase density,

$$D(t) = \frac{3}{2} \int_{-\pi/2}^{\pi/2} B(\lambda, t)\,\sin\lambda\,\cos\lambda\,\mathrm{d}\lambda.$$04

or by an inverse-cubic periastron weighting,

$$D(t) = \frac{3}{2} \int_{-\pi/2}^{\pi/2} B(\lambda, t)\,\sin\lambda\,\cos\lambda\,\mathrm{d}\lambda.$$05

combined with a uniform background through

$$D(t) = \frac{3}{2} \int_{-\pi/2}^{\pi/2} B(\lambda, t)\,\sin\lambda\,\cos\lambda\,\mathrm{d}\lambda.$$06

The test statistic is

$$D(t) = \frac{3}{2} \int_{-\pi/2}^{\pi/2} B(\lambda, t)\,\sin\lambda\,\cos\lambda\,\mathrm{d}\lambda.$$07

with significance reported as $$D(t) = \frac{3}{2} \int_{-\pi/2}^{\pi/2} B(\lambda, t)\,\sin\lambda\,\cos\lambda\,\mathrm{d}\lambda.$$08 (Whitsett et al., 26 Sep 2025).

The principal reported systems are summarized below.

System	Reported evidence	Notes
TOI-1062 b	$$D(t) = \frac{3}{2} \int_{-\pi/2}^{\pi/2} B(\lambda, t)\,\sin\lambda\,\cos\lambda\,\mathrm{d}\lambda.$$09, $$D(t) = \frac{3}{2} \int_{-\pi/2}^{\pi/2} B(\lambda, t)\,\sin\lambda\,\cos\lambda\,\mathrm{d}\lambda.$$10	$$D(t) = \frac{3}{2} \int_{-\pi/2}^{\pi/2} B(\lambda, t)\,\sin\lambda\,\cos\lambda\,\mathrm{d}\lambda.$$11, six flares, $$D(t) = \frac{3}{2} \int_{-\pi/2}^{\pi/2} B(\lambda, t)\,\sin\lambda\,\cos\lambda\,\mathrm{d}\lambda.$$12 AU
Gliese 49 b	$$D(t) = \frac{3}{2} \int_{-\pi/2}^{\pi/2} B(\lambda, t)\,\sin\lambda\,\cos\lambda\,\mathrm{d}\lambda.$$13, $$D(t) = \frac{3}{2} \int_{-\pi/2}^{\pi/2} B(\lambda, t)\,\sin\lambda\,\cos\lambda\,\mathrm{d}\lambda.$$14	$$D(t) = \frac{3}{2} \int_{-\pi/2}^{\pi/2} B(\lambda, t)\,\sin\lambda\,\cos\lambda\,\mathrm{d}\lambda.$$15, 14 flares
HD 163607 b	$$D(t) = \frac{3}{2} \int_{-\pi/2}^{\pi/2} B(\lambda, t)\,\sin\lambda\,\cos\lambda\,\mathrm{d}\lambda.$$16	$$D(t) = \frac{3}{2} \int_{-\pi/2}^{\pi/2} B(\lambda, t)\,\sin\lambda\,\cos\lambda\,\mathrm{d}\lambda.$$17, non-significant

Injection–recovery analyses quantify photometric-limit performance. Tier 1 precision–recall curves yield PR AUC $$D(t) = \frac{3}{2} \int_{-\pi/2}^{\pi/2} B(\lambda, t)\,\sin\lambda\,\cos\lambda\,\mathrm{d}\lambda.$$18 for M dwarfs and $$D(t) = \frac{3}{2} \int_{-\pi/2}^{\pi/2} B(\lambda, t)\,\sin\lambda\,\cos\lambda\,\mathrm{d}\lambda.$$19 for G dwarfs, while Tier 2 yields PR AUC $$D(t) = \frac{3}{2} \int_{-\pi/2}^{\pi/2} B(\lambda, t)\,\sin\lambda\,\cos\lambda\,\mathrm{d}\lambda.$$20 on visually vetted flare-rich light curves (Whitsett et al., 26 Sep 2025). In direct comparison with AltaiPony near the noise floor, ardor recovers substantially more short-duration, low-amplitude flares. The injection counts reported are 232,851 for ardor and 468,000 for AltaiPony (Whitsett et al., 26 Sep 2025).

The strongest candidate is TOI-1062 b, which exhibits flaring during periastron consistent with induced activity, with $$D(t) = \frac{3}{2} \int_{-\pi/2}^{\pi/2} B(\lambda, t)\,\sin\lambda\,\cos\lambda\,\mathrm{d}\lambda.$$21 and a fitted clustering offset from periastron of approximately $$D(t) = \frac{3}{2} \int_{-\pi/2}^{\pi/2} B(\lambda, t)\,\sin\lambda\,\cos\lambda\,\mathrm{d}\lambda.$$22, reported elsewhere in the same study as $$D(t) = \frac{3}{2} \int_{-\pi/2}^{\pi/2} B(\lambda, t)\,\sin\lambda\,\cos\lambda\,\mathrm{d}\lambda.$$23 (Whitsett et al., 26 Sep 2025). Monte Carlo sampling suggests a $$D(t) = \frac{3}{2} \int_{-\pi/2}^{\pi/2} B(\lambda, t)\,\sin\lambda\,\cos\lambda\,\mathrm{d}\lambda.$$24 chance of sub-Alfvénic periastron. Gliese 49 b is a moderate candidate, and the paper estimates that $$D(t) = \frac{3}{2} \int_{-\pi/2}^{\pi/2} B(\lambda, t)\,\sin\lambda\,\cos\lambda\,\mathrm{d}\lambda.$$25 additional days of photometry may be required to confirm it at $$D(t) = \frac{3}{2} \int_{-\pi/2}^{\pi/2} B(\lambda, t)\,\sin\lambda\,\cos\lambda\,\mathrm{d}\lambda.$$26. For HD 163607 b, $$D(t) = \frac{3}{2} \int_{-\pi/2}^{\pi/2} B(\lambda, t)\,\sin\lambda\,\cos\lambda\,\mathrm{d}\lambda.$$27 additional days are estimated for a potential $$D(t) = \frac{3}{2} \int_{-\pi/2}^{\pi/2} B(\lambda, t)\,\sin\lambda\,\cos\lambda\,\mathrm{d}\lambda.$$28 detection (Whitsett et al., 26 Sep 2025).

7. Ambiguity of the term and broader significance

The term ARDOR therefore has an intrinsically ambiguous status in astrophysical usage. In solar physics, ARDoR is a descriptor attached to an algebraic reconstruction of the solar axial dipole and is motivated by dimensionality reduction in active-region data requirements (Nagy et al., 2020). In exoplanetary time-domain analysis, ardor is a data-analysis pipeline that integrates flare detection, Bayesian model comparison, orbital-phase mapping, and forward models of star–planet magnetic interaction (Whitsett et al., 26 Sep 2025). The former ranks solar active regions by their contribution to dipole-moment uncertainty; the latter ranks flare-based hypotheses for phase-dependent stellar activity.

This ambiguity can generate a superficial misconception that both uses refer to a unified framework. They do not. Their commonality lies only in an emphasis on isolating rare, high-leverage events from large populations: rogue active regions in one case, low-amplitude and potentially induced flares in the other. This suggests a methodological parallel—sparse identification of dominant contributors within noisy astrophysical populations—but that parallel is interpretive rather than terminological.

Both constructs were proposed as practically useful reductions of otherwise data-intensive inference. ARDoR reduces the need for detailed inputs from thousands of solar active regions by showing that a top-$$D(t) = \frac{3}{2} \int_{-\pi/2}^{\pi/2} B(\lambda, t)\,\sin\lambda\,\cos\lambda\,\mathrm{d}\lambda.$$29 set of rogues can dominate dipole reconstruction error (Nagy et al., 2020). ardor pushes flare detection toward the noise floor while embedding the detections in a phase-domain likelihood framework capable of testing periastron-clustered star–planet interaction scenarios (Whitsett et al., 26 Sep 2025). In both cases, the technical contribution lies less in introducing a new observable than in reorganizing inference around the subset of events that carry the largest posterior leverage.