JuanCastillo29/space-mission-intelligence-data huggingface dataset:
pipeline implementation appears to be associated with a combination of low target brightness and high levels of photometric contamination.

We note, however, that PSF-fitting photometry is generally expected to outperform aperture photometry in crowded fields and for faint sources.

This has been demonstrated for Kepler – which used similarly undersampled PSFs – by Libralato et al. (2016a,b).

We therefore expect comparable improvements to be achievable.

The PSF-fitting method used in the present work was primarily developed for and tested against stars with 𝑉≤11 mag, which may contribute to the reduced performance observed for dimmer targets.

However, given that the faint (𝑉≤16 mag) P4 M-dwarf sample stars will receive the same 25-second imagette data product as the bright P1/P2 samples, we expect the final implementation of the PSF-fitting routine to more effectively handle dim, crowded targets.

Despite the limitations of the current PSF-fitting photometry implementation, aperture photometry was successfully extracted for the entire sample.

Each of the four CCDs in a PLATO camera is read out with a 6.25second offset, allowing an effective cadence finer than 25 seconds.

In principle, this enables a combined light curve with 6.25-second resolution when data from all four camera groups are used.

However, only transits with very high signal-to-noise ratios would significantly benefit from such high temporal resolution, which was not the case for the overwhelming majority of our targets.

Additionally, each camera group produces an independent light curve that would require separate detrending before combination, with the risk of introducing additional noise.

Thus, we chose to average the light curves from the four groups to produce a final light curve with a uniform 25second cadence, which remains superior to the shortest cadence of the Kepler data (58.85 seconds).
We chose to use the biweight detrending method implemented in wotan (Hippke et al. 2019) with a window length of one day based on its good performance in Canocchi et al. (2023). Since we knew from the simulation inputs the transit times and durations, we masked out all of the transits before detrending. This work focuses on the measurement and detectability of known transits, making this approach readily applicable to real data. For each star, we applied this method to both the aperture photometry and, where available, the PSF-fitting photometry 25-second cadence light curves.
ometric noise. (b) The number of contaminating stars within 45 arcsec brighter than 5 magnitudes dimmer than the targets. (c) The mean ratio of contaminant to target flux within the photometric apertures. (d) The mean size in pixels of the Marchiori et al. (2019) derived photometric apertures. (e) The noise redness factor 𝛽1hr as defined in Eq. 1 for each photometry method. For each star, the value associated with the photometry method that yields the lower 1-hour noise is shown with greater opacity.]

of magnitude, ranging from 0.23 (PSF lower noise) to 76 (aperture lower noise), as shown in panel (a) of Fig. 3. The relative performance of the two methods varies from star to star and reflects a combination of target brightness and local crowding (see panels (b) and (c) of Fig. 3 showing the variation of the number of contaminants and the relative amounts of contaminating flux with host brightness). Because the L1 PSF-fitting pipeline is under active development, we do not attempt to interpret these differences in detail, but we note that relative performance is most strongly correlated with the number of contaminants, rather than the contamination ratio. For each target, we adopt the photometry method that yields the lower 1-hour noise. This ensures that our timing forecasts reflect the best-performing extraction method available for each star within the current simulation framework. In total, 28 stars achieve better precision with PSF-fitting photometry and the remaining 124 stars achieve better precision with aperture photometry.
1 The noise model of Cabrera et al. (2026) is parameterized in PLATO P magnitudes. To maintain consistency with the use of V magnitudes throughout this work, we adopt the V magnitude to electron-flux conversion given in Appendix A, Eq. 1 of Rauer et al. (2025).
In Fig. 4, we show the 1-hour noise-to-signal ratio (NSR) as a function of host brightness and camera number, along with the beginning-of6 N-Cams 12 N-Cams 18 N-Cams 24 N-Cams 6 N-Cams (5.14)

12 N-Cams (3.77) 18 N-Cams (2.91) 24 N-Cams (2.68)
Obs. / Model 1-hour NSR
Number of Stars
Observed = Modelled
0.5
10−3 10−2 10−1 100 Contamination Ratio
β1hr (Noise Redness)
2 0
0.5 1 2 5 10 20 PLATO / Kepler 1-hour NSR

[Figure: Figure 6. Distribution of the relative noise performance of PLATO and Kepler for the sample stars by number of co-pointing cameras. Vertical dashed lines indicate the median noise ratio for each number of cameras (numerically shown in the legend).]

White Noise Expectation 10−3 10−2 10−1 100 Contamination Ratio

[Figure: Figure 5. Top: Ratio of the measured 1-hour noise-to-signal ratios to those predicted by the model of Cabrera et al. (2026), shown as a function of the contamination ratio. The stars observed by 6, 12, 18, and 24 cameras are denoted by triangles, circles, squares, and diamonds, respectively. Bottom: Noise redness, 𝛽1hr, as defined in Eq. 1, shown as a function of the contamination ratio (the mean ratio of contaminant to target flux in the photometric apertures).]
Under the assumption of white noise, binning by a factor 𝑛, or meanaveraging every consecutive 𝑛data points, lowers the root-meansquare (RMS) scatter by a factor √𝑛. As defined by Winn et al. (2007), we take as a measure of correlation in the noise the ratio of the measured noise in the 1-hour binned out-of-transit light curve to the level expected by reducing the 25-second noise by a factor √𝑛= 12. Formulaically,
In the following section, we describe the procedure used to infer midtransit times from simulated PLATO light curves. Our aim is not to detect transits independently, but instead to quantify the precision with which individual transit epochs can be measured given strong prior knowledge of the systems from Kepler or from combining transits from PLATO. Accordingly, we treat the transit shape and ephemeris as known to a good approximation, and focus on the conditional inference of the mid-transit time for each observed transit.
For each planet, we prepared up to ten individual transit light curves for fitting, balancing statistical completeness against computational cost. Using the injected mid-transit times, we extracted segments from the detrended 25 s cadence light curves spanning ±1.5 transit durations around each expected transit centre, for all transits occurring within the two-year observing window. This window size provides a sufficient out-of-transit baseline for normalization while avoiding the inclusion of unnecessary stellar variability. For each star, we adopted the photometric extraction method that yielded the lowest 1-hour noise metric. Within each extracted window, we masked any transits of other known planets in the same system to avoid contamination. We then constructed a vetted sample of transit windows by requiring at least 95 per cent temporal coverage of the transit itself and at least 50 per cent temporal coverage of both the pre- and post-transit baseline regions. From this vetted set, we selected up to ten transits per planet, approximately uniformly distributed over the observing baseline. For planets with fewer than ten suitable transits, all vetted transits were retained. Finally, we applied a 5𝜎clip to the injectedmodel-normalized flux to correct for the effect of cosmic rays, which is particularly impactful on aperture photometry. We note that this is a simplified, ad hoc approach to outlier detection that does not reflect the most up-to-date methods in the photometry pipelines.
For each extracted transit window, we model the observed flux using a fixed-shape limb-darkened transit light curve computed with the batman package, adopting a quadratic limb-darkening law. All orbital and geometric parameters are held fixed at their injected values, including the orbital period, scaled semi-major axis, scaled planet radius, inclination, eccentricity, argument of periastron, and limbdarkening coefficients. This approach isolates the inference of the mid-transit time while avoiding degeneracies with poorly constrained shape parameters. The free parameters in the fit are the mid-transit time 𝑡0, a multiplicative scaling factor applied to the transit depth 𝑑, a multiplicative flux baseline 𝐵, and an additive jitter term 𝑠that accounts for potential underestimation of the nominal photometric uncertainties. Allowing for a depth scaling accommodates small mismatches between the injected and observed transit depths due to residual uncorrected contamination. Assuming Gaussian-distributed photometric errors, the likelihood for a set of flux measurements 𝑓𝑖at times 𝑡𝑖is given by � ( 𝑓𝑖−𝑚𝑖)2
ln L = −1
∑︁
+ ln � 2𝜋(𝜎2 𝑖+ 𝑠2) ��
, (2)
𝜎2 𝑖+ 𝑠2
𝑖
where 𝑚𝑖≡𝑚(𝑡𝑖; 𝑡0, 𝑑, 𝐵) is the model flux and 𝜎𝑖are the nominal
per-point uncertainties. In the case of the PSF-fitting photometry, the per-point uncertainties are formally estimated by – and a direct output of – the L1 proto-pipeline. Conversely, uncertainties were estimated for the aperture photometry derived using the method of Marchiori et al. (2019) by calculating, for each mask update, the 3𝜎-clipped standard deviation of the detrended, transit-masked light curves, since formal uncertainties were not provided. The additional variance term 𝑠2 is fitted simultaneously to ensure that timing uncertainties are not artificially underestimated in the presence of imperfect noise estimation. Priors are imposed as follows. The mid-transit time 𝑡0 is assigned a uniform prior within a window of ± duration around the predicted ephemeris. This choice reflects reasonable prior knowledge obtained either through the propagation of Kepler ephemerides or the stacking of PLATO transits while allowing the posterior to be dominated by the likelihood function. The jitter parameter is sampled uniformly in ln 𝑠 over the range [−20, 1]. The depth scaling factor 𝑑follows a Gaussian prior centred close to unity, with an exact mean and width calibrated empirically from high signal-to-noise simulated transits and separately for the PSF-fitting and aperture photometry. This strong prior on the depth reflects confidence in both the knowledge of the transit shape and the accuracy of the contamination correction, and is necessary to prevent the sampler from focusing on high-likelihood but physically implausible solutions. The baseline parameter 𝐵is assigned a uniform prior over the interval [0.9, 1.1].
Posterior distributions for the model parameters were explored using Markov Chain Monte Carlo (MCMC) sampling. For each transit window, we employed the ensemble sampler implemented in the emcee package (Foreman-Mackey et al. 2013). The sampler was initialized with 32 walkers distributed around an initial parameter estimate corresponding to the injected mid-transit time, unit depth scaling, unit baseline, and a jitter term set by the median photometric uncertainty in the window. Each chain was evolved for 10,000 steps, with the first 1000 steps discarded as burn-in. Convergence was assessed by verifying that the autocorrelation lengths of all parameters were at most 1/50 the retained chain length (satisfied by ∼99 per cent of fits). For each parameter, posterior summaries are reported using the median and central credible intervals. In particular, the uncertainty on the mid-transit time is quantified using half the interval between the 16th and 84th percentiles of the marginal posterior distribution. We retain the full posterior samples for subsequent analysis, including the assessment of posterior structure and model support described in the following sections.
CLASSIFICATION ACROSS SNR

In the following section, we refer to the transit signal-to-noise ratio (SNR), which we define in the canonical, albeit simplistic (Kipping 2023), fashion:
𝑡duration/1hr 𝜎1hr
SNR = 𝑑transit √︁
, (4)
where 𝑑transit is the maximum transit depth, 𝑡duration is the total (first to fourth contact) transit duration, and 𝜎1hr is the photometric noise-to-signal ratio in one hour.
The distribution of expected SNRs across the planet sample is shown in panel (a) of Fig. 7. In the Kepler mission’s Transiting Planet Search, folded transit features with detection statistics greater than 7.1𝜎were designated ‘Threshold Crossing Events’ (Jenkins et al. 2010). Although the simple transit SNR does not exactly map to their detection statistic, we use SNR ≥7.1 as a heuristic benchmark for whether a transit is independently detectable. Of the 360 sample planets, which are broadly representative of Kepler planets overall, only 66 have an expected individual SNR ≥7.1. When combining all the expected transits within PLATO’s expected two-year stare, and assuming white-noise scaling, the number of SNR ≥7.1 planets rises to 267. We emphasize again that the goal of this work is not to determine whether PLATO can detect these planets independent of prior knowledge from Kepler, but instead to assess the achievable timing precision for known systems.
Panel (b) of Fig. 7 illustrates how the achievable timing precision for individual transits depends on SNR. As expected, higher SNR transits tend to yield tighter timing constraints. However, at fixed SNR there remains a substantial spread in the inferred timing precision, even for transits of the same planet, which reflects that the quality of an individual timing is stochastic in nature. A best-fit log-log regression to members of the two high-significance classes yields the relation along with the 1𝜎residual scatter:
𝜎𝑡0 𝑡duration
�
� = −1.1122 log10 (SNR) −0.3962 ± 0.1578. (5)
log10 We note that using the analytic result of Carter et al. (2008) or linear transformations thereof to predict timing precisions from SNR, ingress time, and transit duration yields a lower proportion of explained variance in the measured uncertainties than the above relation. This is likely a result of idealized noise assumptions that are not realized in the present SNR regime. Hence, we prefer our linear fit. In total, of the 3399 transit fits, 1716 fall into the prior-limited class, 594 into the low-significance class, 142 into the asymmetric significant class, and 947 into the symmetric high-significance class. Panel (c) of Fig. 7 shows the fraction of transit fits in each classification as a function of SNR. At low SNR, most transits are either prior-limited or fail to achieve significant support over a flat model, whereas at higher SNRs the population becomes increasingly dominated by high-significance solutions. The dashed vertical lines indicate characteristic SNR values at which at least 50 per cent of transits reach a given minimum classification. Specifically, half of all transits achieve at least a low-significance but not prior limited timing constraint at SNR ≃2.1 (50.83 per cent of sample planets have at least this SNR), half yield at least asymmetric high-significance solutions by SNR ≃3.8 (33.61 per cent of planets), and symmetric high-significance timing dominates beyond SNR ≃4.3 (28.61 per cent of planets). These thresholds indicate that, given realistic prior knowledge from Kepler, transits can be timed with significantly less significance than is required for independent detection.

recovered transit times. The dispersion of 𝑍𝑡0 depends systematically on classification: prior-limited fits exhibit sub-unity dispersion (𝜎𝑍𝑡0 ≃0.7), reflecting conservatively large uncertainties imposed by the prior boundaries, while low-significance fits are consistent with unit variance. High-significance fits show a marginally inflated dispersion (𝜎𝑍𝑡0 ≃1.1), attributable to residual non-Gaussianity and posterior asymmetry. We conclude that for all but the prior-limited fits, the extracted uncertainties reasonably reflect the true timing uncertainties.
(a)
SNR per Transit 2 Year Combined SNR
Number of Planets
Best Fit (High Significance) Prior Limited Low Significance Asymmetric/High Significance Symmetric/High Significance
Timing Uncertainty / Duration
(b)
It has been shown, e.g. by Price & Rogers (2014), that finite light curve sampling leads to greater timing uncertainty than instantaneous sampling. In the preceding analysis, we analysed PLATO’s native 25-second cadence output. Per Rauer et al. (2025), the P5 𝑉≤13 mag sample stars will predominantly receive 10-minute cadence data product, with a subset receiving 50-second cadence data, and an even smaller subset receiving 25-second data. To investigate the impact of realistic lower-frequency sampling, we repeated the fitting process of Section 4 on the same data, but mean-average binned to 50-second and 10-minute cadence. We supersampled the batman fits to the original underlying 25-second cadence to account for smearing from finite integration times and to avoid introducing timing bias. Panel (d) of Fig. 7 shows the ratio of retrieved precisions arising from data of each sampling cadence. Across the range of SNRs, we find little difference between the uncertainties in the 25- and 50-second cadence data. The 16th, 50th, and 84th percentiles of this ratio are [0.980, 1.000, 1.021]. Similarly, the 10-minute cadence data achieves near-identical performance to the 25-second cadence data on average, although the uncertainty ratio shows more scatter. The corresponding 16th, 50th, and 84th percentiles are [0.947, 1.013, 1.104]. We repeated the analysis of Section 5.3 on the slower cadence data to search for evidence of additional uncertainty underestimation and, in both cases, found almost identical distributions of 𝑍𝑡0 to the 25second cadence analysis. Furthermore, the number of fits falling into each classification does not deviate in either case by more than 1 per cent of the total number of fits compared to the 25-second cadence analysis. Thus, we conclude that neither 50-second nor 10-minute cadence data seriously degrades performance relative to native cadence in the studied SNR regime.
10−1
10−2
10−3
1.0
(c)
Prior Limited Low Significance Asymmetric/High Significance Symmetric/High Significance
0.8
Fraction of Transits
0.6 0.4 0.2 0.0
(d)
600 s vs 25 s 50 s vs 25 s
2.0
Precision Ratio
1.5
1.0
0.5
10−1 100 101 102 103 Transit SNR

[Figure: Figure 7. (a) Histogram distribution of the expected transit signal-to-noise ratios within the planet sample, both from one single transit and also when combining all the transits expected in a two-year window. (b) The ratio of the mean timing uncertainty (half the 16th–84th percentile range) to the transit duration for each individual transit fit. A linear (log-log) fit to the two highsignificance classes is shown as a solid line. (c) The (non-cumulative) fraction of transit fits falling into each class as a function of transit SNR. The SNR at which 50 per cent of transit fits achieve at least a given class are shown as vertical dashed lines. (d) The ratio of the timing precisions arising from 600and 25-second sampled and 50- and 25-second sampled data.]
A majority of the planets’ transits in our sample cannot be timed individually at a high level of significance. Under the SNR ≥3.8 highsignificance criterion adopted in Section 5.2, 121 of the 360 sample planets exceed the threshold for well-constrained single-transit timing measurements. This does not imply that the remaining systems are uninformative. Leleu et al. (2021) developed a deep-learning method to detect and measure TTVs from river diagrams that remains effective for planets with low per-transit SNR, provided the TTV amplitude is sufficiently large. They demonstrate their approach on Kepler-1705 b and c, which each have a transit SNR ≃1. In our sample, 272 of the 360 planets have an individual SNR ≥1. Additionally, in multi-planet systems exhibiting TTVs, even modest additional timing constraints on one planet can improve the dynamical characterization of the entire system through coupled orbital interactions. Of the 360 planets, 189 reside in systems where at least one planet has an expected transit SNR ≥3.8, and 332 reside in
For each class, we investigated the relationship between the injected and extracted best-fit transit times to search for evidence of bias or underestimation of uncertainties. For each transit fit, we calculated the ratio of the difference between the injected and extracted times to the relevant uncertainty, resulting in a Z-score for each transit midtime. Under the assumption of Gaussian posteriors, a distribution, 𝑍𝑡0 ∼N (0, 1) is expected. Across all timing classes, the mean values of 𝑍𝑡0 were found to be consistent with zero to 2𝜎, indicating no significant bias in the systems where at least one planet has an expected SNR ≥1.

The degree to which timing information can be recovered from lower-SNR transits depends sensitively on the amplitude and morphology of the TTV signal (see e.g. Holczer et al. 2016) and requires system-specific dynamical modelling beyond the scope of this work. However, these results suggest that a significantly larger fraction of the planets in these systems could receive additional dynamical constraints than the fraction whose transits can be individually timed. Another alternative to individual transit fitting is the photodynamical approach, introduced by Ragozzine & Holman (2010), and later applied to a variety of often multiple stellar systems, including KOI-126 (Carter et al. 2011), Kepler-16 (Doyle et al. 2011), and Kepler-47 (Orosz et al. 2012). In contrast to the conventional twostep procedure – in which individual transit times are first measured and subsequently fit with an independent 𝑁-body model – photodynamical analyses simultaneously model the system dynamics and photometric observations within a single self-consistent model. This allows the full information content of the light curve to be utilized directly, rather than compressing the observations into a set of measured transit times. A key advantage of the photodynamical approach is that it can remain effective even when individual transits have low signal-tonoise (see Langford & Agol 2025). By using the entirety of the data, information from many transits can be combined to constrain the orbital architectures and transit parameters, even when individual events are difficult to identify or characterize in isolation. Thus, the opportunity of this approach sparks further optimism that a much larger fraction of the planet sample remains tractable than their transit SNRs would initially suggest.

[Table: Table 1. Properties of the 42 planets in the 15 systems from the sample identified by Jontof-Hutter et al. (2021) that were included in our analysis, selected as systems in which the projected TTVs of at least one planet diverge by more than 90 minutes by BJD 2460900. Orbital periods are the default values reported in the NASA Exoplanet Archive. Transit SNRs were calculated in this work, and the projected transit-timing uncertainties for the first transit occurring after BJD 2460900 (𝛿TTV) are taken from Jontof-Hutter et al. (2021). Transit SNRs exceeding the individual timing threshold of 3.8 are shown in bold.] 𝛿TTV (min)
Period (d)
Transit SNR

95 KOI-1783.02 284.21
18.96
562 KOI-3503 b 21.18 0.40 390 KOI-3503 c 31.83 0.44 432 Kepler-29 b 10.34 1.42 238 Kepler-29 c 13.29 1.34 310 Kepler-36 b 13.87 2.26 144 Kepler-36 c 16.22
28.76
256 Kepler-49 b 7.20 2.52 18 Kepler-49 c 10.91 2.41 33 Kepler-49 d 2.58 0.81 24 Kepler-49 e 18.60 1.07 278 Kepler-54 b 8.01 1.14 76 Kepler-54 c 12.07 0.42 131 Kepler-54 d 21.00 0.71 49 Kepler-60 b 7.13 1.00 143 Kepler-60 c 8.92 1.28 53 Kepler-60 d 11.90 1.47 230 Kepler-81 b 5.96 2.73 74 Kepler-81 c 12.04 2.94 31 Kepler-81 d 20.84 0.83 364 Kepler-176 b 5.43 0.47 18 Kepler-176 c 12.76 1.81 61 Kepler-176 d 25.75 1.90 >1 day Kepler-176 e 51.17 0.71 >1 day Kepler-177 b 36.86 3.02 52 Kepler-177 c 49.41
13.86