3.1. Summary of principal datasets

The principal datasets discussed in our study are as follows:

• • POSS1-E plate scans: Publicly available plate images and metadata related to the POSS1 plates, which are the basis for all datasets described here. Solano et al. (Reference Solano, Villarroel and Rodrigo2022) used a software pipeline to measure the positions of SPFs from these scans. These scans and metadata are used in our study to investigate specific claims made in Solano et al. (Reference Solano, Villarroel and Rodrigo2022) and Villarroel et al. (Reference Villarroel2025a) about artefact removal, and in Bruehl & Villarroel (Reference Bruehl and Villarroel2025) about correlations between SPF occurrence and nuclear tests.

• • Set A: Unpublished dataset from Solano et al. (Reference Solano, Villarroel and Rodrigo2022), of unknown size, comprising the initial extraction of SPFs from the POSS1-E plate set.

• • Set S: Unpublished dataset from Solano et al. (Reference Solano, Villarroel and Rodrigo2022) derived from set A after removing optically visible catalogue stars (Gaia, Pan-STARRS), and used in Villarroel et al. (Reference Villarroel2025a) to search for clusters of aligned SPFs.

• • Set W: Published dataset from Solano et al. (Reference Solano, Villarroel and Rodrigo2022) containing SPFs from set S that are near NeoWISE infrared catalogue object locations. This was used in our study to examine alignments, spatial distributions of SPFs, and for reevaluation of correlations with nuclear tests and Earth’s shadow.

• • Set R: Published dataset from Solano et al. (Reference Solano, Villarroel and Rodrigo2022) used by our study as the most vetted dataset described in Solano et al. (Reference Solano, Villarroel and Rodrigo2022), Villarroel et al. (Reference Villarroel2025a), and Bruehl & Villarroel (Reference Bruehl and Villarroel2025). This is used in the present work to identify artefacts, examine spatial distributions of SPFs, and to revaluate the Earth shadow and nuclear test correlations.

• • Set V: Unpublished dataset derived from set S and used by Villarroel et al. (Reference Villarroel2025a) to explore SPF count deficits in Earth’s shadow, and used by Bruehl & Villarroel (Reference Bruehl and Villarroel2025) to explore correlations between SPFs and nuclear tests.

• • Set M: Published celestial catalogue from POSS1 plates by an independent research team, used in this study to examine characteristics of the spatial distribution of SPFs in R and W that are not apparent in M: i.e. that cannot be attributed to variations in the sensitivity of the optical system, the distribution of known celestial objects, or the astronomical viewing conditions on any given POSS1 observation day.

3.2. Dataset definitions

POSS1-E: The POSS1-E plates comprise 937 individual exposures using the red-sensitive Kodak 103a-E plate emulsion, whose sensitivity peaks at 640 nm with a limiting magnitude of 20 (Minkowski & Abell Reference Minkowski, Abell and Strand1963). This optical survey ran from November 11, 1949 to December 10, 1958 and covered the whole sky north of declination $-34^{\circ}$ . The $35.5$ cm $\times$ $35.5$ cm glass plates each have a $6.6^{\circ} \times 6.6^{\circ}$ field of view, and during the survey averaged 0.3 $^{\circ}$ of overlap on each edge; Pennington et al. (Reference Pennington, Humphreys, Odewahn, Zumach and Thurmes1993) and Villarroel et al. (Reference Villarroel2025a) recorded the positions of features in a footprint with dimensions of roughly $6^{\circ} \times 6^{\circ}$ , which is the approximate area usable for measurements following the scanning process. This survey captured exposures for 292 plates with footprints residing fully in the southern celestial hemisphere; 584 plates with footprints residing fully in the northern celestial hemisphere; and 61 with footprints that overlap the celestial equator. The POSS1-E metadata contains the observation details such as start date/time, exposure, plate centre, and hour angle for each plate that is required for all temporal correlation analyses. The DSS and SuperCOSMOS POSS1-E scans were made from two independent sets of glass copy negative plates made from a single set of glass copy positive plates, in turn made from the original glass negatives (Hambly & Blair Reference Hambly and Blair2024).

Set A (unknown size): Solano et al. (Reference Solano, Villarroel and Rodrigo2022) began with the DSS scans of the POSS1 survey and extracted an unpublished dataset A (see Figure 1) whose size was not reported, containing all SPFs that passed their initial automated detection pipeline including signal-to-noise thresholds, spike removal, high proper motion, and morphological symmetry constraints (see Solano et al. Reference Solano, Villarroel and Rodrigo2022).

Set S ( $N=298\,165$ ): To efficiently remove known stars while accounting for proper motion between surveys, each SPF in A within 5 $^{\prime\prime}$ of a catalogue object from Gaia DR3 (Vallenari et al. Reference Vallenari2023) or Pan-STARRS DR2 (Chambers et al. Reference Chambers2019) was removed from A to obtain the subset S (Solano et al. Reference Solano, Villarroel and Rodrigo2022). For the set of SPFs removed from A, it was not reported whether there was a 1:1 correspondence between the catalogue object locations and SPFs. Those plates whose footprints reside entirely within the southern celestial hemisphere were never sampled, or else SPFs from those plates were removed at this stage.

Set W ( $N=171\,753$ ): Dataset W is the publicly available subset of S containing features located within 5 $^{\prime\prime}$ of NeoWISE infrared catalogue objects (Mainzer et al. Reference Mainzer2011) that are not visible in the optical catalogs, and which are not expected to be visible in POSS1-E except in cases where these objects are flaring red dwarfs (Solano et al. Reference Solano, Villarroel and Rodrigo2022). We find a 1:1 correspondence between NeoWISE object locations and SPFs in W. Therefore, W is the result of using a spatially uniform-random distribution of positions (a starfield) to sample the set S, and is the focus of our analyses in Section 4. We determined that no SPFs in W derive from plates whose footprints reside entirely within the southern celestial hemisphere. Solano et al. (Reference Solano, Villarroel and Rodrigo2022) then filtered the set S by removing the set W, creating the intermediate set $P\ (N=126\,412)$ (i.e. $P\equiv S-W$ ).

Figure 1.

Diagram illustrating the relative sizes and overlap relationships of the SPF datasets defined in Table 1. The dashed line and ‘?’ here represent our uncertainty about the degree of overlap between V (the main focus of calculations in Villarroel et al. Reference Villarroel2025a and Bruehl & Villarroel Reference Bruehl and Villarroel2025) and W as well as R (the vetted ‘remainder’ of unidentified objects, defined in Solano et al. Reference Solano, Villarroel and Rodrigo2022). The shaded subsets R and W are publicly available.

Set R ( $N=5\,399$ ): In a series of stages, Solano et al. (Reference Solano, Villarroel and Rodrigo2022) removed SPFs from P to produce the published dataset we that have called set R for ‘remainder’. First, Solano et al. (Reference Solano, Villarroel and Rodrigo2022) removed all SPFs residing within 5 $^{\prime\prime}$ of stars in additional optical and additional infrared astronomical catalogs (as described in Solano et al. Reference Solano, Villarroel and Rodrigo2022). Then, likely asteroids and variable objects were removed. The remaining $9\,171$ SPFs were searched for digitisation-related artefacts (such as imaged dust or loose emulsion particles) by comparing separate scans of separate glass copy negatives (DSS and SuperCosmos) of the same field; an additional $3\,592$ SPFs ( $\sim40$ %) were identified and removed in this way. We expect that this step also removed endemic faults and ageing-related SPFs (such as plate corrosion) found on the DSS copy negative but not found on the SuperCosmos copy negative. On the other hand, this would not have removed plate defects whose source was the original glass plate or the copy positive glass plate. Next, SPFs identified as high proper motion stars and as obvious artefacts (by manual inspection) were also removed. The resulting set R ( $N=5\,399$ ) contains the unidentified SPFs least likely to be celestial objects, non-star-like plate artefacts, or digitisation artefacts, and comprises less than 2% of the SPFs in S.

Set V ( $N=107\,875$ ): Villarroel et al. (Reference Villarroel2025a) defined set V as set S with the NeoWISE-proximate SPFs removed ( $S-W$ ) and with SPFs in the southern celestial hemisphere removed; this appears to be the same definition as our $P \equiv S-W$ because W contains no SPFs from plates whose footprints completely reside within the southern celestial hemisphere. This cannot be correct, however, since the count of SPFs in V is short by 18 537 in light of the sizes reported for S and W in Solano et al. (Reference Solano, Villarroel and Rodrigo2022). Villarroel et al. (Reference Villarroel, Streblyanska, Bruehl and Geier2026) v2 has since reported that the definition of V in Villarroel et al. (Reference Villarroel2025a) was incorrect: instead, V derives from set S (which includes all of set W) with an undisclosed number of additional southern hemisphere SPFs, catalogue stars, and duplicate SPFs removed. Although the details of the sampling process have not been disclosed, a uniform sampling of S to get V would yield roughly 60 000 SPFs from W in V, of 107 295 in total.

Next, it can be inferred that removing the SPFs in the southern celestial hemisphere (on the equatorial plates) from set V yields set $V^{\prime}$ ( $N=106\,339$ ). Set $V^{\prime\prime}$ ( $N=22\,314$ ) is defined as $V^{\prime}$ with SPFs near the plate edges removed. Detailed motivations for these inferences are supplied in Sections 3.3 and Appendix A.

Villarroel et al. (Reference Villarroel2025a) and Bruehl & Villarroel (Reference Bruehl and Villarroel2025) did not use R in the analyses discussed therein. Villarroel et al. (Reference Villarroel2025a) used four datasets in its analyses (S, V, $V^{\prime}$ , and $V^{\prime\prime}$ ), which are generally not concordant with definitions in Solano et al. (Reference Solano, Villarroel and Rodrigo2022) and are ambiguously defined. Set S is tied to its definition in Solano et al. (Reference Solano, Villarroel and Rodrigo2022) by the reported size ( $N=298\,165$ ). Although Bruehl & Villarroel (Reference Bruehl and Villarroel2025) cited Solano et al. (Reference Solano, Villarroel and Rodrigo2022) as the source of its primary dataset, R was not used but instead the set V from Villarroel et al. (Reference Villarroel2025a) was used; this can be inferred from the reported size ( $N=107\,875$ ).

Set M: Nearly 90 million SPFs were recorded in the POSS1-E and POSS1-O plates by the MAPS project. MAPS discarded all features that did not appear in both the E (red band) and O (blue band) plates, in order to avoid recording plate artefacts; the Galactic plane was also occluded ( $|b|\gt 20^{\circ}$ ) to avoid features that blend together in crowded fields. We chose the MAPS project digitisation for comparison because it was independent of the DSS and SuperCOSMOS digitisations and because it records only very confident detections of celestial objects.

Our study makes use of the following datasets, all of which are publicly available: (i) set W ( $N=171\,753$ ), consisting of SPFs near NeoWISE object locations (and the associated sky coverage map)Footnote ^c ; (ii) set R, the most highly vetted SPF subset from Solano et al. (Reference Solano, Villarroel and Rodrigo2022) (and the associated sky coverage map)Footnote ^d ; plot of SPFs in set V on the sky (Figure 1 from Villarroel et al. Reference Villarroel, Streblyanska, Bruehl and Geier2026 v2); set M, the celestial catalogue generated from POSS1 plates (Pennington et al. Reference Pennington, Humphreys, Odewahn, Zumach and Thurmes1993; Cabanela et al. Reference Cabanela, Humphreys, Aldering, Larsen, Odewahn, Thurmes and Cornuelle2003).Footnote ^e We have also used the POSS1-E plate metadata (STScI 2026),Footnote ^f as well as POSS1-E imagesFootnote ^g in DSSFootnote ^h and SuperCosmos scansFootnote ⁱ (shown in Figures 2 and 9) and Pan-STARRS imagesFootnote ^j (shown in Figure 2). Finally, we use the three sources cited in Bruehl and Villarroel (Reference Bruehl and Villarroel2025) for nuclear test dates (NNSS 2023; Wikipedia 2025; CHERCA 2025).

Figure 2.

Examples of Selected POSS1-E Features (SPFs) in R ( $N=5\,399$ ), the most vetted subset of S ( $N=298\,165$ ) published by Solano et al. (Reference Solano, Villarroel and Rodrigo2022). The red crosses at the centre are $\sim10^{\prime\prime}$ in diameter. We have identified these features as follows: (i) clear artefacts or defects that do not resemble objects visible in a Pan-STARRS image of the same field (A (object 1092), B (object 1179), C (object 1223), D (object 1248)); and (ii) clear examples of an object that was incorrectly identified as having vanished (object 1043 in E vs. F, and object 1051 in G vs. H, where E and G are POSS1-E images and F and H are Pan-STARRS images), probably on account of displacement from high proper motion. Based on 540 objects examined, cases of this sort comprise 4–5% of R ( $N = 5\,399$ ). The images are available online from http://svocats.cab.inta-csic.es/vanish-possi/ .

Figure 1 illustrates the relationship between the A, S, W, P, V, and R datasets defined in Table 1, which are defined or implied in Solano et al. (Reference Solano, Villarroel and Rodrigo2022), Villarroel et al. (Reference Villarroel2025a), Bruehl & Villarroel (Reference Bruehl and Villarroel2025), and Villarroel et al. (Reference Villarroel, Streblyanska, Bruehl and Geier2026) v2. This also illustrates the ambiguity (dashed line and ‘?’) concerning the amount of overlap between the publicly available set R, which is the most vetted dataset from Solano et al. (Reference Solano, Villarroel and Rodrigo2022), and V, which has not been publicly released as of the time of this writing. None of the above papers describe the relationship between R and V. We stress that access to V is not necessary for our evaluation of the analysis and claims in Villarroel et al. (Reference Villarroel2025a) and Bruehl & Villarroel (Reference Bruehl and Villarroel2025).

3.3. Problems with data sources

In this section, we describe issues which, in principle, affect all of the SPF datasets, as well as issues that are dataset specific.

4.1. Variation in counts per plate

We examine the variation of counts per plate as part of assessing assumptions implicit in the analyses of Villarroel et al. (Reference Villarroel2025a) and Bruehl & Villarroel (Reference Bruehl and Villarroel2025) about what factors supposedly influence the distribution of SPF counts in time and space, such as the terrestrial shadow and nuclear tests. Primary sources of variation in counts per plate should be characterised, modelled, and subtracted before second-order effects are considered. In particular, we might expect the number of SPFs per plate to vary for two primary reasons. First, if the SPFs represent a population of stars not removed by prior filtering, then we expect (i) a roughly uniform-random distribution with an overall increase in number density with decreasing distance from the Galactic plane; and (ii) slight variations associated with variations in the astronomical viewing conditions (i.e. more stars are detected under favourable atmospheric conditions with less turbulence blur). Alternatively, if the SPFs represent plate artefacts, the distribution will depend on the processes that tend to create these features, and upon how the impact of these processes varies from plate to plate. This may in turn depend on how the plates were manufactured, exposed, developed, stored, and handled, and how often they have been accessed. Finally, we should consider that the digital scanning process may also introduce artefacts, such as by introducing images of dust or debris in the scanner or on the plate surface. Solano et al. (Reference Solano, Villarroel and Rodrigo2022) removed digitisation artefacts only after removing over 117 000 SPFs from set P (N=126 412) when constructing set R ( $N=5\,399$ ), whereas the removal of digitisation artefacts was neither explicitly described nor mentioned in Villarroel et al. (Reference Villarroel2025a) or Bruehl & Villarroel (Reference Bruehl and Villarroel2025) as part of the sampling of V ( $N=107\,875$ ) from S.

Since the published tables for R and W do not list the plate of origin for each SPF, we have determined this as follows: for each SPF, we find all plate centres within 3 $^{\circ}$ in declination, and then select the plate whose centre is nearest in horizontal separation. We have noted all SPFs whose positions are overlapped by the fields of view of multiple plates, and which cannot be unambiguously assigned to a single plate, so that we can remove these in the analyses discussed in later sections. This corresponds to about 10% of the SPFs in R and 12% in W.

We found that counts of SPFs per plate in both W and R exhibit enormous variation. In W, the number of SPFs per plate ranges from zero to 2 149 (plate ID 090R, label E1465), with an average of 257.5 and standard deviation of 337.2. In R, the number of SPFs per plate ranges from zero to 105 (Plate 08BW), with an average of 8.1 and standard deviation of 10.3. Figure 3 shows the cumulative fraction of SPF counts as a function of the total fraction of plates, ranked in order of decreasing counts from left to right. The first datum plots as $\sim0.012$ on the y axis because the first plate, being the most crowded, comprises over 1% of all the SPFs in the dataset. This figure illustrates that 50% of the plates contain nearly 90% of the SPFs in W.

Figure 3.

Cumulative distribution function of SPF counts as a function of the total fraction of plates, ranked in order of decreasing counts from left to right, for W, R, and M. In the case of W, roughly 20% of the most crowded plates contain over 60% of all SPFs. M is more uniform in terms of how SPFs are distributed across plates; this is partly because all SPFs in M are likely celestial objects, and because the Galactic plane was occluded when this dataset was sampled. The curve still represents a significant departure from a uniform-random distribution (dotted line), possibly associated with variations in astronomical viewing conditions. The discussions of spatial variability in Sections 4.2 and 4.3 suggest there may be multiple factors contributing to the spatial variation in SPF counts shown in R and W, arising from (i) how plates are manufactured, stored, scanned, and handled, or (ii) how datasets were constructed in Solano et al. (Reference Solano, Villarroel and Rodrigo2022).

We display the same plot for the M dataset in Figure 3, which shows a more gradual increase across the sample, but which still represents a significant departure from a uniform-random distribution (dotted line), possibly on account of variations in astronomical viewing conditions. Recall that all of the SPFs in M correspond to likely celestial objects, as these are apparent in both the E and O plates (red and blue bands). Another potential reason for the difference in distributions is that whereas M omits the bright zone within 20 $^{\circ}$ of the Galactic plane, S and its subsets (e.g. R and W) were sampled from throughout most of this region. That is, it is possible that the variation in SPF counts per plate in S has been more strongly affected by the increased number density near the Galactic plane. This could happen if (i) the SPF count comprises previously uncatalogued stars (e.g. flaring red dwarf stars), or (ii) the high number density of stars in this region result in blended objects with inaccurate centroid positions that frustrate the identification and removal of catalogue objects.

4.2. Distribution with respect to plate boundaries

We will focus in this section on spatial distribution of SPFs within plates in set W ( $N = 171\,753$ ) because (i) it is publicly accessible; (ii) it is large enough to clearly see patterns in relation to the plate centre and boundaries; and (iii) it is a majority subset of the set S used by Villarroel et al. (Reference Villarroel2025a) to search for linear clusters. Moreover, (iv) it will have retained some characteristics of S, the parent dataset of V, which is the focus of the analyses in Villarroel et al. (Reference Villarroel2025a) and Bruehl & Villarroel (Reference Bruehl and Villarroel2025). This is because W is effectively a dense, uniform-random sampling of the set S; i.e. it consists of SPFs residing within 5 $^{\prime\prime}$ of NeoWISE infrared catalogue object positions, which are not expected to be visible in POSS1-E plates unless they are flaring red dwarfs (Solano et al. Reference Solano, Villarroel and Rodrigo2022). Solano et al. (Reference Solano, Villarroel and Rodrigo2022) did not estimate the fraction of unidentified features consisting of actual flaring dwarf stars on account of the difficulty involved. This is not necessary for our analysis, however, since it suffices for our purposes to show that the spatial distribution of SPFs in W (and by implication S from which W and V were derived) departs dramatically from the spatially uniform-random distribution expected of a starfield (such as a catalogue of NeoWISE objects), which has been assumed in the shadow deficit calculation in Villarroel et al. (Reference Villarroel2025a). In summary, we focus here on the published dataset W because of what we can learn about characteristics of the unpublished sets S and V.

In Figure 4, we have plotted the positions of SPFs in W on selected plate fields that exhibit distinctive patterns, which in some cases bear a clear relationship to the plate boundaries. We have marked the SPFs with ambiguous plate assignments in red. These plates contain a wide range of SPF counts, most of them significantly exceeding the average of W’s 270 SPFs per plate. All SPFs in W reside within 5 $^{\prime\prime}$ of NeoWISE infrared catalogue star positions and were removed from S when constructing R for this reason (Solano et al. Reference Solano, Villarroel and Rodrigo2022). As Figure 4 shows, and as we demonstrate quantitatively later in this section, the distribution of SPFs from W is not spatially uniform-random, which is the expected spatial distribution of a star field. This suggests that the underlying distribution of SPFs in the parent set S is also strongly nonrandom and also bears a clear relationship to the plate boundaries. Furthermore, the fact that the intra-plate distribution of SPFs in W is far from uniform-random suggests that the large search radius (5 $^{\prime\prime}$ ) and large number density of NeoWISE objects has resulted in sampling many noncelestial SPFs that were incidentally matched.

Figure 4.

Scatter plots of SPFs from W on nine plates that exhibit distinctive patterns. Red dots signify SPFs that could not be assigned to a single plate because of overlap with the neighbouring plate’s field of view. These patterns are not visible in the dataset M of SPFs that appear in both E and O plates (i.e. likely celestial objects), suggesting that they are unrelated to nonuniform sensitivity of the instrumentation or photographic medium. The geometric patterns and relationship to plate boundaries strongly suggest (i) a physical process that has templated the spatial distribution of SPFs, such as a surface that has come into contact with the plate, or a region that has been preferentially exposed to processes that tend to degrade the medium over time; or (ii) a spatial filter applied when processing the data. We have plotted SPFs from W because (i) it is publicly accessible; (ii) it is large enough for these patterns to be visible, and (iii) because it is a dense, uniform-random sample and majority subset of S, the parent set of set V analysed by Bruehl & Villarroel (Reference Bruehl and Villarroel2025) and Villarroel et al. (Reference Villarroel2025a). Each plate is labelled with the plate ID, the number of SPFs on the plate, and the value of the Evans-Clark ratio $\rho$ , which is smallest for the most overdispersed (clustered) distributions. From left to right, the plate labels in each row are: E1465, E648, E976 (top); E65, E665, E1264 (middle); E971, E364, E1405 (bottom).

Figure 4 reveals that there is a strong spatial variation within individual plates that is distinct from the plate-to-plate variation in astronomical viewing conditions and proximity to the Galactic plane. Notably, on plates with large SPF counts, these appear to be sometimes concentrated in clusters. To characterise the spatial distribution of SPFs within plates in W, we have calculated the Clark-Evans ratio ( $\rho$ ) for each plate (Clark & Evans Reference Clark and Evans1954). This is defined as

(1) \begin{equation}\rho \equiv \frac{\bar{r}_\mathrm{obs}}{\bar{r}_{CSR}},\end{equation}

where $\bar{r}_\mathrm{obs}$ is the observed average nearest neighbour distance between SPFs in a given plate, and $\bar{r}_{CSR}\equiv 1/{2\sqrt{\lambda}}$ is the average nearest-neighbour distance for a special case of the uniform-random distribution (generated by a Poisson point process) with average number density $\lambda$ (Clark & Evans Reference Clark and Evans1954). The special case is that of complete spatial randomness (CSR), defined as the spatial distribution resulting from a homogeneous Poisson point process on an infinite domain. Because photographic plates have a finite extent, the nearest neighbour distance of SPFs near plate edges is larger than average, causing $\rho$ to be slightly more than 1 for points that are spatially uniform-random. The case $\rho \gg 1$ implies a spatially underdispersed distribution (relatively regular spacing), while $\rho \lt 1$ implies overdispersion (clustering).

We have computed $\rho$ on all of the plates containing SPFs for sets W and M. Set M was downsampled to 0.2% of its normal size to reduce computation time ( $N \sim 170\,000$ ), and so that its size is comparable to that of W ( $N = 171\,753$ ). Set R has been omitted from this analysis on account of its small size, with the result that $\rho$ becomes a noisy statistic. The scatter plots of SPFs in set W for the plates in Figure 4 have been labelled with estimates of $\rho$ , which ranges from 0.49 to 0.80 for these examples. Figure 5 contains a histogram of $\rho$ for plates in M and W. As expected, the spatial distribution of SPFs in the spatially uniform-random set M, consisting of SPFs that are very likely celestial in origin because they occur in both the O and E plates, usually result in values of $\rho$ slightly above 1 (modal value 1.04). By contrast, $\rho$ for plates in the set W are widely distributed, peaking at modal value 0.89. SPFs in W are mostly overdispersed and exhibit moderate to significant clustering. The scatter plots shown in Figure 4 are examples of significant overdispersion, sampled from the left-hand tail of the histogram in Figure 5 for set W.

Figure 5.

Histograms of the Evans-Clark ratio $\rho$ calculated for each plate, for SPFs in sets M and W. As expected for a uniform-random distribution of points on a finite domain, $\rho$ is typically slightly above 1 for set M, comprising SPFs of likely celestial origin because they appear in both the POSS1-E (red band) and POSS1-O plates (blue band). The distribution of SPFs in W is dominantly overdispersed (clustered), with $\rho \lt 1$ for most plates. See Figure 4 for examples of scatter plots of SPFs on individual plates with significant overdispersion, labelled with the estimated $\rho$ .

Next, we characterised the average spatial distribution within photographic plates. For the M, W, and R datasets, we computed the displacement in decimal degrees of SPFs with respect to the centre of each plate in declination and right ascension. The right ascension was multiplied by the cosine of the declination to compute true east-west displacement on the sky. These displacements were used to compute a normalised radial density profile in Figure 6 for sets M, W, and R. For each data set, we have also broken down the spatial distribution of the total SPF counts across all plate fields into a median background plus a nonrandom excess. In Figure 7, we have subtracted the median background SPF count within 2-D bins in order to visualise the excess SPF counts; this is shown in parts A, B, and C for sets M, W, and R, respectively. In plotting parts B and C, we have used only the SPFs that can be unambiguously assigned to plate footprints.

Figure 6.

Radial density profiles for the W (solid), R (dashed), and M (dotted) datasets. Densities were calculated in circular bins of $0.25^{\circ}$ with radii denoting the angular distance from plate centres. All distributions were normalised for easy visual comparison of their shapes. The W and R distributions show an increasing density of SPFs away from plate centres, in qualitative agreement with the experimental results of Greiner et al. (Reference Greiner, Flohrer, Wenzel and Lehmann1987), who found that the number density of endemic plate emulsion defects increases with distance from plate centres. By contrast, M exhibits a slight and gradual decline with increasing radius, indicating a mostly uniform number density combined with the effect of vignetting, as expected for a star field. A $\cos(\mathrm{ Dec.})$ correction was applied to RA to correctly estimate east-west displacements.

Figure 7.

Histograms (2-D) of SPF counts in excess of the median background as a function of offset from plate centres for (A) set M (likely celestial objects that appear in both O and E plates; see Cabanela et al. Reference Cabanela, Humphreys, Aldering, Larsen, Odewahn, Thurmes and Cornuelle2003); (B) set W, which reside within 5 $^{\prime\prime}$ of the positions of NeoWISE infrared catalogue objects (Solano et al. Reference Solano, Villarroel and Rodrigo2022); and (C) set R, comprising unidentified SPFs. The set M distribution peaks in the centre, possibly on account of the effects of vignetting at the margins. The distributions for set W and R peak in the edges and corners, and are qualitatively consistent with the expected pattern for endemic plate emulsion defects (Greiner et al. Reference Greiner, Flohrer, Wenzel and Lehmann1987). A $\cos(\mathrm{ Dec.})$ correction was applied to RA to correctly estimate east-west displacements.

The distribution for set M is consistent with expectations for telescopic observations of star fields: the centres of photographic plates tend to contain slightly more counts than the perimeter owing to the effect of vignetting near the margins. By contrast, the excess in W and R shows the opposite pattern, with the number density of SPFs increasing with distance from the centre of the plates, and is therefore highest at the corners and edges. The amplitude of this radial increase, as a fraction of total counts, is also much larger than the amplitude of the variation in M (Figure 6). Recall that R supposedly contains only features that are not identifiable as plate artefacts, digitisation artefacts, or celestial objects, and so it is difficult to form an expectation in advance about the intra-plate spatial distribution. By definition, all SPFs in W are located in close proximity to the positions of NeoWISE objects. Nevertheless, W exhibits a pattern that is inconsistent with the expectation of a uniform-random distribution for a star field on an individual plate: i.e. it does not resemble the distribution of SPFs in M.

The observed pattern for R and W instead suggests a distinct generative process that depends on proximity to plate boundaries. As part of the GRB-related efforts to understand plate faults, Greiner et al. (Reference Greiner, Flohrer, Wenzel and Lehmann1987) examined laboratory plates that had been exposed to diffuse light equivalent to sky background illumination, and which were then developed. Using different emulsions and plates, they found endemic faults at a rate that translates to 83 faults per area of a POSS1 plate (35.5 cm $\times$ 35.5 cm) that were difficult to distinguish from ideal stars or slightly distorted stars. These faults included point-like objects indistinguishable from stars, oblong objects indistinguishable from stars with trails, and objects with comas located on the outer edges of plates that resembled a normal star with slight distortion. The number of faults increased towards the edge of the plate and also with decreasing brightness. Other mechanisms for generating non-random excesses of SPFs on the edges of plates have not been experimentally examined; these include the contamination or degradation of the emulsion through handling of plates by the corners and edges. The distributions of SPFs shown here are plausibly related to the manufacture, processing, degradation, or digitisation of the plates and unrelated to luminous or illuminated objects in the telescope’s field of view.

Finally, we highlight that in all of our analyses, a $\cos(\mathrm{Dec.})$ correction was applied to RA to obtain accurate east-west displacements.

4.3. Templating and spatial filtering

In some cases, the distribution of SPFs within plates exhibits patterns and clusters that are qualitatively distinct from the mean pattern described in the previous section. A prominent example occurs very near the celestial meridian and equator in the plate with the largest number of SPFs (plate ID 090R, label E1465: $N = 2\,149$ , in part A in Figure 4), where the majority of SPFs are located between the boundaries of the plate and an oval that is partially inscribed within it. The origin of these patterns is not known. Other plates exhibit rectangular voids (part G) or band-like vertical gaps (parts E and F). We also find examples of tight clusters within central regions of a plate (part C) or at the corners (part D). A few plates exhibit a density gradient with highest density at one edge, decreasing towards the opposite edge (part H).

That some plates exhibit patterns bearing a clear relationship to plate boundaries (e.g. clustering near edges) and/or the celestial coordinate system (e.g. voids and clusters exhibiting horizontal and vertical edges, parallel to lines of constant right ascension or declination), suggests the action of generative mechanism(s) that relate to the manufacture, processing, curating, or digitising of the plates, rather than to lights in the sky.

The fact that some SPFs occur within regions with clear boundaries, or else avoid regions with clear boundaries, suggests that contact or exposure-based templating may play a role in the production of SPFs more generally. An example zone of avoidance is visible in the upper-left corner in part G of Figure 4. Based on inspection of multiple plates, the vertical stripes in parts E and F span the interval in right ascension from roughly $103^{\circ}$ to $107^{\circ}$ and cross plate boundaries; a second stripe from roughly $86^{\circ}$ to $98^{\circ}$ also crosses plate boundaries. Both of these features are further discussed in Section 4.4.

We emphasise the importance of answering the following questions. First, why do SPFs in some cases appear to reside in clusters or regions of higher number density with clear boundaries, and why do they sometimes appear to avoid regions with clear boundaries? Second, why do these overdense regions and empty regions in some cases appear related to the plate footprint or the celestial coordinate system (e.g. plate ID 090R, label E1465 in part A of Figure 4)? Third, what does this imply about the production of SPFs in these POSS1-derived datasets? These questions should be answered as part of the essential data validation process.

4.4. Distribution across the sky

In this section, we examine significant variation in SPF number density on the scale of the entire sky. We have graphed the on-sky distribution of the number density of SPFs from set M in part A of Figure 8 (i.e. likely celestial objects that appear in both O and E plates); we have graphed the number density of SPFs from W in part B and from R in part C. As mentioned, Cabanela et al. (Reference Cabanela, Humphreys, Aldering, Larsen, Odewahn, Thurmes and Cornuelle2003) occluded a buffer zone surrounding the Galactic plane to avoid blended objects in crowded fields when constructing M ( $|b| \gt 20^{\circ}$ ). By contrast, Solano et al. (Reference Solano, Villarroel and Rodrigo2022) does not specifically mention avoiding the Galactic plane while sampling.

Figure 8.

Plots of the number density of SPFs on the celestial sphere in (A) set M, (B) set W, and (C) set R. The Galactic plane was occluded in set M ( $|b|\gt 20^{\circ}$ ) to avoid features that blend together in crowded fields. The distribution of SPFs in parts B and C reveal a vertical band with a deficit of SPFs between 90 $^{\circ}$ and 105 $^{\circ}$ ; this remains apparent following aggressive filtering in R. There is also a marked deficit in a band surrounding the plane of the Galaxy; this is not explained in Solano et al. (Reference Solano, Villarroel and Rodrigo2022). The white boxes in (C) show the outlines of plates estimated to overlap Earth’s shadow during the observation window, as discussed in Section 5; their plate IDs are supplied below the plot. Villarroel et al. (Reference Villarroel2025a) reported a deficit of SPFs from set $V^{\prime}$ within these plates. The red line shows the ecliptic, the orange line is the Galactic plane, and the dashed white line highlights a marked depletion north of the celestial equator in the western hemisphere when compared to the eastern hemisphere.

We have shown the all-sky map of SPF number density in Figure 8 to call attention to the significant variation in this quantity across the sky in the Solano et al. (Reference Solano, Villarroel and Rodrigo2022) datasets, and especially the vertical stripe between roughly RA = 90 $^\circ$ and RA = 105 $^\circ$ for both R and W. Closer inspection of the plate-framed scatter plots (as shown in Figure 4, parts E and F) suggests that this stripe consists of two bands, from roughly RA = 87 $^{\circ}$ to RA = 98 $^{\circ}$ and a second, narrower band from RA = 103 $^{\circ}$ to RA = 107 $^{\circ}$ . This stripe lies largely in the galactic occlusion zone of set M, but no such stripe is visible in scatter plots of SPFs in M near the poles. Therefore, this feature in W and R does not appear to have resulted from a failure of the instrument to faithfully record astronomical objects in this region. There is also a notable band surrounding the Galactic plane, which is also not explained in Solano et al. (Reference Solano, Villarroel and Rodrigo2022) in terms of a specific filtering or sampling process. These large-scale spatial heterogeneities are also clearly visible in the published coverage maps of W and R (Solano et al. Reference Solano, Villarroel and Rodrigo2022), as well as the scatter plot of SPFs in V (Villarroel et al. Reference Villarroel, Streblyanska, Bruehl and Geier2026, v2).

We considered four possible explanations regarding the origin of the stripes: (i) The SPFs were incompletely sampled when the set A was assembled by Solano et al. (Reference Solano, Villarroel and Rodrigo2022) in the first place, or when the DSS or SuperCOSMOS scans were acquired. This appears unlikely because the stripes do not correspond to plate boundaries: they cross plate boundaries and only partially overlap some plates (see Figure 4, parts E and F). Note that plate boundaries become staggered as the sky area narrows near the pole, and yet the stripes span the full range of declinations: they are not offset or shifted at plate boundaries. Moreover, the striping did not affect set M, which was independently scanned; this suggests the stripes are not an intrinsic property of the plates themselves. (ii) The stripes are the result of how the plates were stored, maintained, and handled. This seems unlikely because it is hard to imagine how any of these activities could create a stripe that traces lines of roughly constant right ascension and which cross plate boundaries, especially given the staggered arrangement of plate footprints on the sky. (iii) The POSS1 telescope observations overlapping the stripe were captured during periods of time when SPFs, if they represent luminous or illuminated objects in the telescope’s field of view, were less abundant in the sky. This can be confidently ruled out because the plates overlapping the stripes were captured throughout the duration of the POSS1 survey (8 years). Also, as mentioned already, the stripes only partially overlap the plates, ruling out a time dependence. This leaves the least unlikely cause: (iv) SPFs within the stripes were filtered out during the processing steps that led from set A to sets W and R in Solano et al. (Reference Solano, Villarroel and Rodrigo2022). It is not clear why this interval would be singled out for suppression, intentionally or by accident.

We call attention to this feature of the on-sky distribution because analyses in Villarroel et al. (Reference Villarroel2025a) and Bruehl & Villarroel (Reference Bruehl and Villarroel2025) implicitly assume that V is completely and uniformly sampled (i.e. no part of the north celestial hemisphere was omitted when SPFs were selected) and faithfully records the distribution of SPFs across the sky. This assumption is essential for one of the key claims in Villarroel et al. (Reference Villarroel2025a), which reports a deficit of SPFs from set $V^{\prime}$ in the Earth’s shadow, as discussed in the next section. This is also significant for interpreting the background rate of SPFs estimated in the same paper. An incomplete or nonuniform sampling of the sky would affect correlation statistics between SPF occurrence and any other phenomena, such as nuclear tests in Bruehl & Villarroel (Reference Bruehl and Villarroel2025).

Table 2.

SPFs within quasilinear clusters reported in Table 3 of Villarroel et al. (Reference Villarroel2025a) with an angular separation ( $d_\mathrm{W}$ ) of less than 2 $^{\prime\prime}$ from an SPF in W. That is, 8 of 24 listed are probable matches to SPFs in W. Set W consists of SPFs whose celestial coordinates at the time of observation resided within 5 $^{\prime\prime}$ of a NeoWISE catalogue object. RA and Dec. coordinates (sexag.) are reported for the J2000 reference frame.

Table 2. Long description

The table presents data on celestial objects within quasilinear clusters. It has five columns: Cluster, Object, RA, Dec., and dW [as]. The table contains information for five clusters, each with multiple objects. Each row lists the cluster number, object number, right ascension (RA) in sexagesimal format, declination (Dec.) in sexagesimal format, and angular separation (dW) in arcseconds. Row 1: Cluster 1, Object 2, RA 02:29:21.38, Dec. 28:36:57.89, dW 1.7. Row 2: Cluster 1, Object 3, RA 02:29:21.76, Dec. 28:36:49.09, dW 1.8. Row 3: Cluster 4, Object 3, RA 21:24:47.62, Dec. 68:31:58.92, dW 0.7. Row 4: Cluster 4, Object 4, RA 21:24:39.72, Dec. 68:31:31.22, dW 1.1. Row 5: Cluster 4, Object 6, RA 21:24:03.94, Dec. 68:29:14.36, dW 0.8. Row 6: Cluster 5, Object 3, RA 19:16:45.73, Dec. 51:28:52.04, dW 1.8. Row 7: Cluster 5, Object 4, RA 19:16:40.13, Dec. 51:27:12.85, dW 1.7. Row 8: Cluster 5, Object 5, RA 19:16:40.27, Dec. 51:27:06.29, dW 1.7.

There are marked similarities and differences evident from comparing the spatial distributions of W and R (see parts B and C of Figure 8), which shows the effect of removing additional catalogue objects and scan artefacts from S by Solano et al. (Reference Solano, Villarroel and Rodrigo2022). Across the western celestial hemisphere, SPFs in the set R ( $N = 5\,399)$ tend to hug the plane of the Galaxy, suggesting that some fraction of these objects may be uncatalogued stars, including uncatalogued dwarf stars that were transiently flaring during the POSS1-E exposures. Alternatively, the high number density of stars in this region result in blended objects with inaccurate centroid positions that may frustrate the identification and removal of catalogue objects. There is also a marked depletion north of the celestial equator in the western hemisphere when compared to the eastern hemisphere in both W and R (white dashed outline in Figure 8). In the case of R, SPFs in the western hemisphere above the Galactic plane have been almost totally erased. Before using any of these datasets, R, W, or V, to search for images of unidentified objects, the origin of these patterns in the spatial distribution should be investigated and understood.

4.5. Clusters of aligned SPFs

Villarroel et al. (Reference Villarroel2025a) also searched for clusters of up to five SPFs exhibiting statistically significant alignments: i.e. that are unlikely to result from a Poisson point process for populations of comparable size. These were called ‘candidate alignments’ and were presented in Table 3 of that study. As already mentioned, there is no reason to expect that plate artefacts that give rise to SPFs should have a spatially uniform-random distribution (as if generated by a Poisson point process). We presented strong evidence that they are not uniform-random distributed, such as by highlighting SPFs in regions with clear linear boundaries (Section 4.3). In light of these observations, discovering clusters of aligned SPFs is not especially surprising. In this section, we focus on the nature of the specific SPFs that have been identified as belonging to the candidate linear clusters in Table 3 of Villarroel et al. (Reference Villarroel2025a).

Table 3.

Left column: reproduction of Table 1 from Bruehl & Villarroel (Reference Bruehl and Villarroel2025) for set V. Middle column: replication of Bruehl & Villarroel (Reference Bruehl and Villarroel2025) using set R, included to show that we are able to obtain approximately the same results. Right column: day counts for R obtained after properly normalising by the true observation window (the correct number of observation days). We have used the most vetted dataset R available from Solano et al. (Reference Solano, Villarroel and Rodrigo2022) instead of the unpublished set V. Due to smaller statistics overall, R contains only 289 days where SPFs were found as opposed to 310 days found by Bruehl & Villarroel (Reference Bruehl and Villarroel2025) in the V dataset. The nuclear testing window is defined in Bruehl & Villarroel (Reference Bruehl and Villarroel2025) as a day of nuclear testing $\pm1$ day. Percentages in parenthesis show the conditional probabilities of observing (or not observing) an SPF given the presence (or absence) of a nuclear test on that day. Observation days (‘plate days’ in Figure 12) relevant to this study are the days on which at least one plate is sampled from the northern celestial hemisphere and/or overlapping the celestial equator.

Long description

The table compares dataset analysis results from Bruehl & Villarroel (2025) and a new study. It has three columns: the first column reproduces Table 1 from Bruehl & Villarroel (2025) for set V, the second column replicates the analysis using set R, and the third column shows day counts for R after normalizing by the true observation window. The table includes rows for dataset used, normalization, time window, SPF observed, and within nuclear testing window. Each row provides specific data points and percentages for the comparisons. The table aims to show the consistency and differences in results between the two studies.

The start of Section 4 in Villarroel et al. (Reference Villarroel2025a) states that: ‘We base our analysis on the catalogue of 298 165 short duration transients presented in Solano et al. (Reference Solano, Villarroel and Rodrigo2022), detected in red POSS1 plates with typical exposure times of 45–50 min.’ This implies that the search for aligned SPFs made use of S ( $N=298\,165$ ), which according to Solano et al. (Reference Solano, Villarroel and Rodrigo2022) is 96.8% composed of features that reside within $5^{\prime\prime}$ of a catalogue star (including what we have called set W). Indeed, as shown in our Table 2, we find that 8 of the 24 SPFs belonging to candidate linear clusters in Table 3 of Villarroel et al. (Reference Villarroel2025a) reside within 2 $^{\prime\prime}$ of an object in W (a subset of S), suggesting that these features represent one and the same object. Villarroel et al. (Reference Villarroel2025a) recomputed the astrometric positions of SPFs in Table 3 (Villarroel et al. Reference Villarroel2025a) with respect to positions originally reported for SPFs in W from Solano et al. (Reference Solano, Villarroel and Rodrigo2022), which likely accounts for the $\lt 2^{\prime\prime}$ positional differences we see here. We have confirmed that 8 of 24 SPFs in Table 3 of Villarroel et al. (Reference Villarroel2025a) are located within 5 $^{\prime\prime}$ of a NeoWISE catalogue object position (a 9th is $\sim5.1^{\prime\prime}$ away). These members of set W were removed from S by Solano et al. (Reference Solano, Villarroel and Rodrigo2022) when constructing R because they were not confidently distinguished from NeoWISE objects. For the same reason, Villarroel et al. (Reference Villarroel2025a) also claims to have removed W from S to construct the set V (a claim since retracted in Villarroel et al. Reference Villarroel, Streblyanska, Bruehl and Geier2026 v2) used in other analyses. No reason is given in Villarroel et al. (Reference Villarroel2025a) for reverting to set S to search for SPF alignments representing satellite glints.

We manually examined the SuperCosmos and DSS images of all SPFs in Table 3 of Villarroel et al. (Reference Villarroel2025a) and show two comparisons in Figure 9. We have noted a marked qualitative asymmetry of some of these SPFs, indicating the need for a quantitative morphological analysis in addition to the symmetry-based filtering already applied in Solano et al. (Reference Solano, Villarroel and Rodrigo2022). (A morphological analysis is also recommended by the presence of the anomalous shapes of some SPFs in R as shown in Figure 2.) In Figure 8 of Villarroel et al. (Reference Villarroel, Solano and Marcy2025b), the lowermost member of the cluster of three SPFs (red arrows in part B of our Figure 9) is described as ‘slightly dubious in shape’. In our high-magnification view, this is clearly an asymmetrical feature and not representative of a star-like optical transient. These images also highlight two defects of the kind that can be removed by scan comparison, in this case appearing on the SuperCosmos scan and not the DSS scan (yellow arrows). These artefacts are also clearly identified as such in Figure 8 of Villarroel et al. (Reference Villarroel2025a). Parts C and D of our Figure 9 show another SPF from an aligned cluster (object 3 in cluster 5 of Table 3 in Villarroel et al. Reference Villarroel2025a) that also exhibits clear elongation, although is possibly a pair of overlapping sources.

Figure 9.

Magnified images of SPFs belonging to candidate linear clusters detailed in Table 3 of Villarroel et al. (Reference Villarroel2025a) (red arrows) and SPF scan artefacts present in SuperCosmos scans (B and D) and absent from DSS scans (A and C) of the same field (yellow arrows). Parts A and B represent ‘candidate 3’ and Parts C and D represent ‘candidate 5’. The noticeable departure from circular symmetry in the case of multiple objects marked with red arrows suggests that S should be aggressively filtered to remove features without an extremely high degree of radial symmetry, as expected for the point source glints hypothesised in Villarroel et al. (Reference Villarroel2025a), in order to avoid likely artefacts.

5.1. Shadow calculation

To assess the reported deficit of SPFs in the Earth’s shadow, we have simulated the shadowing of plates. Here we attempt to replicate the procedure by Villarroel et al. (Reference Villarroel2025a) as closely as possible. Because set V was not publicly available at the time of this writing, we used the W and R datasets, which were sampled from the same parent dataset as V and which, based on their sky coverage maps from Solano et al. (Reference Solano, Villarroel and Rodrigo2022) and in Figure 8, bear a strong resemblance to V at large spatial scales (see Figure 1 in Villarroel et al. Reference Villarroel, Streblyanska, Bruehl and Geier2026).

We model the Earth’s shadow using the earthshadow library (Nir Reference Nir2024), which computes the projected position of the shadow cone at geosynchronous altitude as a function of time. At that distance, the Earth’s shadow subtends an angular radius of approximately $8.696^\circ$ , which we adopt as a fixed shadow radius for all plates. For each of the 645 POSS1-E plates that have at least some area covering north of the celestial equator, we use the plate metadata to reconstruct the shadow trajectory across individual plates over an assumed 50-min exposure window (i.e. approximately the average over the northern hemisphere plates). Note that the set of in-shadow plates is a property of the POSS1-E survey, and is independent of the SPF datasets.

Each plate is cropped to a 6 $^{\circ} \times 6^{\circ}$ square aligned with the cardinal directions. Once the shadow coverage is calculated, SPFs are denoted as: (1) fully shadowed – inside the shadow at every time step throughout the entire exposure; (2) partly shadowed – inside the shadow at some point during the observation but not the entire time; and (3) unshadowed – never within the shadow. Of the 645 plates, five have a fully shadowed region (plates 728, 08L2, 08L9, 08RS, and 090W); six have only a partly shadowed region; and the remaining have no shadow interaction at all; one partially shadowed plate (0AVK) crosses the celestial equator. The total number of plates that are at least partially shadowed (11) is consistent with the total (‘ $\sim10$ ’) reported in Villarroel et al. (Reference Villarroel2025a). Following Villarroel et al. (Reference Villarroel2025a), both the fully shadowed and partly shadowed regions are combined for this analysis and considered to be ‘in-shadow’.

Figure 10.

The top bar chart shows the fraction of shadowed area for plates that are at least partly covered by Earth’s shadow. Notably, 08L9 is fully shadowed for the full 50 min observation window. The plates 08RV, 070P, 070S, and 0AVK have $\lt 2$ % shadow coverage and, therefore, a marginal effect on the statistics. The number of SPFs that are observed and expected in-shadow for W and R are shown in the middle and bottom panels, respectively.

The area fractions described above are shown in the top panel of Figure 10. There are a few notable cases: all SPFs in plate 08L9 lie within the shadow for the full exposure, while there are six plates with hardly any shadow coverage. Because one plate holds most of the SPFs, it dominates the statistical analysis. Villarroel et al. (Reference Villarroel2025a) used $\sim10$ plates, and claim therefore that a single outlier plate could not be driving their result – our results suggest the contrary is possible, and we show an example using the case of the related set W.

We use both the W and R datasets north of the celestial equator, and we only consider the SPFs that can be confidently assigned to a single plate; this yields 149 301 and 4 782 SPFs for the W and R samples, respectively. Each SPF is then assigned as in-shadow, or not, by testing its sky position against the computed shadow coverage.

Figure 11.

Signed Poisson statistics using the W (left) and R (right) datasets along with their Monte Carlo distributions for $10^{5}$ iterations. Upper axis is the ratio of SPF in-shadow counts: (observed-expected)/expected. The p-value given here is the fraction of trials with $\sigma$ to the left of the observed value (a one-sided test of the deficit hypothesis). The observed in-shadow deficit for W is not statistically significant, lying very near the null mean ( $p = 0.52$ ): i.e. almost any of the other samples results in a deficit or excess that is larger. By contrast, the observed in-shadow excess measured for R is moderately significant ( $p = 0.96$ ), since fewer than 4% of all samples exhibit a larger excess.

5.2. Statistics

The expected fraction of SPFs falling in shadowed regions under the null hypothesis of a spatially uniform-random distribution is simply the area-weighted fraction,

(2) \begin{equation}f_\mathrm{exp} = \frac{\sum_i A_{\mathrm{shadow},i}}{\sum_i \left( A_{\mathrm{shadow},i} + A_{\mathrm{unshadow},i} \right)},\end{equation}

where the sum includes all 645 plates; this means the fully-shadowed area is $f_\mathrm{exp} = 0.56\%$ . The expected number of in-shadow SPFs is then $N_\mathrm{exp} = f_\mathrm{exp} \times N_\mathrm{total}$ , where $N_\mathrm{total}$ is the total number of SPFs in the shadowed and unshadowed regions combined. We quantify the departure of the observed count $N_\mathrm{obs}$ from expectation using the signed Poisson significance,

(3) \begin{equation}\sigma = \frac{N_\mathrm{obs} - N_\mathrm{exp}}{\sqrt{N_\mathrm{obs} + N_\mathrm{exp}}},\end{equation}

where negative values indicate a deficit.

For W we find $N_\mathrm{obs} = 649$ against $N_\mathrm{exp} = 729.8$ , giving $\sigma = -2.18$ . For R, we find $N_\mathrm{obs} = 50$ against $N_\mathrm{exp} = 23.1$ , giving $\sigma = 3.15$ ; this is an excess rather than a deficit, driven largely by plate 08L9, which alone accounts for the bulk of the detections in the shadow region (see bottom panels of Figure 10).

5.3. Monte Carlo simulation

As established earlier in this paper, SPF number density varies significantly from plate to plate and clearly does not follow a Poisson process. Here we show that a naive application of the Poisson significance formula (Equation 3) can lead to a misinterpretation of the results. To construct a valid null distribution, we instead use a Monte Carlo procedure. For each of the in-shadow plates, we first construct their shadow templates: the geometry of how the shadow covers the plate; for example, the template of 08L9 is the full $6^{\circ} \times 6^{\circ}$ square while the template for 0AVK is a tiny sliver. Then we randomly select 11 of the 645 plates, randomly apply the 11 templates, and count the number of SPFs that would fall within the templated area. Summing these counts gives one null trial, from which we compute $\sigma$ using the same formula above. We repeat this procedure $10^5$ times and use the sampled distribution to calculate a p-value: i.e. the fraction of trials with $\sigma$ less than the observed value (a one-sided test of the deficit hypothesis).

The resulting distributions are shown in Figure 11. For W, we find a deficit of $\sigma = -2.18$ ; this result sits near the centre of the null distribution ( $p = 0.52$ ), indicating this deficit is not statistically significant: that is, about half of the samples exhibit a larger deficit, and about half exhibit a smaller deficit. For R, the observed Poisson significance is $\sigma = 3.15$ , which lies in the upper tail of the null distribution ( $p = 0.96$ ), indicating a statistically significant excess. That is, only 4% of the samples exhibit an excess as great as $\sigma = 3.15$ .

The distributions in Figure 11. reveal an important pitfall that arises when applying the Poisson approximation when it is not appropriate (i.e. when the features are not spatially uniform-random). For W, the randomly sampled distribution exhibits a wide range of possible Poisson significance values. Our results suggest there is a probability of $\approx30\%$ to observe at least $\sigma = -8$ deficit by chance (we note that $\sigma \approx 8$ deficit was estimated by Villarroel et al. Reference Villarroel2025a using V). This effect is more pronounced in W (compared to R) because its larger sample size amplifies the sensitivity to plate-to-plate density inhomogeneity. Thus, there is a greater chance of mistaking a random result to be significant under Poisson statistics with a larger sample size.

Even though we did not use the same dataset as Villarroel et al. (Reference Villarroel2025a), we demonstrate that their analysis is still subject to the effects presented here. Furthermore, Villarroel et al. (Reference Villarroel2025a) advocate for large data samples to increase their signal-to-noise ratio. Our results suggest this is a misapplication of Poisson statistics, and that using larger sample sizes amplifies the problem. The claim of a significant deficit of SPFs in Earth’s shadow should be reevaluated for V using a Monte Carlo framework for a more reliable signal-to-noise estimate.

Figure 12.

From top to bottom, plots of the observation dates (i) with POSS1-E plates solely residing completely in the southern celestial hemisphere; (ii) all remaining plate days (northern celestial hemisphere and/or overlapping the celestial equator); and (iii) the dates of nuclear test explosions.

For completeness, we ran the same Monte Carlo simulations for a few different scenarios. First, Villarroel et al. (Reference Villarroel2025a) ran a test that considered only the central parts of the plates (radius $=2^{\circ}$ ). Second, we determined whether there was an impact using only the fully shadowed regions (i.e. excluding the partially shadowed plates). The results vary, however, they are all consistent with the null hypothesis under the Monte Carlo approach. Therefore, we argue that any of the variations in the shadow calculation just mentioned do not alter our conclusion. It further strengthens our main argument: it is easy for a null result to masquerade as a significant detection using Poisson statistics when the underlying distribution is not spatially uniform-random.

We argue in many different ways throughout this paper that the spatial distribution of SPFs is not uniform-random. We do not know the expected distribution of plate- and digitisation-related artefacts, which depends on a host of poorly characterised processes related to the manufacture and degradation of the photographic medium, and the scanning of plates. A highly nonrandom distribution of these artefacts could significantly affect the relative proportion measured in a tiny fraction of the sky, such as the area covered by Earth’s shadow at geosynchronous altitudes. For example, consider the case where the distribution of SPFs is roughly uniform-random except that a handful of plates contains an enormous number of obvious plate artefacts: an example is plate 090R (label E1465) with its 2 149 SPFs in W, nearly 20 times the average SPF count per plate. If the few plates with the overdensity happen to reside outside of the shadow, then the few shadowed plates will contain fewer SPFs per square degree than the population as a whole. As we have seen for the case of set W, the in-shadow statistics appear to be dominated by a single plate (i.e. 08L9; see Figure 10).

Another important problem with the in-shadow frequency calculation is that set V was derived from S (Villarroel et al. Reference Villarroel, Streblyanska, Bruehl and Geier2026, v2) which, as we have seen, was determined by Solano et al. (Reference Solano, Villarroel and Rodrigo2022) to consist primarily of objects that have not been distinguished from catalogue stars and scan defects. At least 95% (i.e. $1 - N_{R}/N_{V}$ ) of SPFs in V were discarded by Solano et al. (Reference Solano, Villarroel and Rodrigo2022) to produce the aggressively vetted subset R (see Table 1).

In summary, in order to fully understand the source of the reported deficit of shadowed SPFs in V, it is important to understand the variations in SPF number density at a wide range of scales – from the scale of individual plates as seen in Figures 4 through 7, to the scale of the entire sky as seen in Figure 8. Plate degradation and digitisation, feature detection algorithms, as well as catalogue filtering and post-processing, all may affect the number density of the shadowed regions while being unrelated to the shadow itself. For example, it is essential to understand the origin of features like the western hemisphere void that we noted in R (part B of Figure 8), and the vertical stripe-shaped void between roughly RA = 90 $^\circ$ and RA = 105 $^\circ$ (part C of Figure 8) that we have noted in W and R, and then to examine how shadowed plate footprints and relative SPF counts are affected.

Finally, we call attention to Figure 1 of Villarroel et al. (Reference Villarroel, Streblyanska, Bruehl and Geier2026) v2 (upper left), which is a scatter plot of the positions of SPFs in set V, to shed light on the origin of the shadow deficit reported in Villarroel et al. (Reference Villarroel2025a). A comparison of this plot with our Figure 8(C) and its shadowed plate footprints (white boxes), indicates that at least three of the eleven shadowed plates (plate IDs 070P, 08RS, and 090W) overlap the large stripe-shaped void centred on RA $\approx45^{\circ}$ . This includes two of the most significantly shadowed plates (08RS and 090W; see Figure 10). These two plates are ranked second and fourth overall in terms of the duration and areal extent of shadowing (Figure 10). This particular stripe-shaped void is not present in R and W. This suggests that the incidental overlap of these plates with this stripe-shaped void in V, creates a spurious deficit of SPFs in the Earth shadow calculations in Villarroel et al. (Reference Villarroel2025a). This highlights the importance of characterising the underlying spatial variation in the data and using an appropriate statistical analysis.

6.1. Replication study

We start by attempting to replicate the measurement of the correlation between the dichotomous variable (SPFs observed or not) and nuclear tests (nuclear test date $\pm1$ day), as defined and reported in Bruehl & Villarroel (Reference Bruehl and Villarroel2025). The paper claimed there is a significant (Chi-Square = 6.94, $p = 0.008$ ) correlation between daily nuclear tests in the study time window and the daily occurrence of SPFs. The left part of Table 3 shows the resulting yes/no contingency table presented in Table 1 of Bruehl & Villarroel (Reference Bruehl and Villarroel2025) for dataset V. We attempted to replicate these results using the three sources cited in Bruehl & Villarroel (Reference Bruehl and Villarroel2025) (see Section 3) for nuclear test dates, the publicly available SPF dataset R, and properties of the publicly available dataset W. (The dataset, V, used by Bruehl & Villarroel (Reference Bruehl and Villarroel2025) was not publicly available at time of writing.) We find a slight count difference in nuclear test dates: Bruehl & Villarroel (Reference Bruehl and Villarroel2025) report 124 test dates while we account for 125 dates, likely due to differences in how we parsed the three sources of nuclear test dates.

Since R (the most vetted dataset available from Solano et al. Reference Solano, Villarroel and Rodrigo2022) and W (the largest dataset available from Solano et al. Reference Solano, Villarroel and Rodrigo2022) do not include plate identification numbers or timestamps, we had to match every detection from these datasets to a POSS1-E plate and its associated timestamp as described in Section 4.1. That is, we excluded SPFs from the datasets which have either no associated plate or ambiguous plate association using this method; this corresponds to about 10% of the SPFs in R and 12% in W. While there are discrepancies, both in the list of nuclear test dates and in the subset of SPFs that have unambiguous timestamps associated with them, these are trivial and do not change the outcome of the correlation analysis. This is shown in Table 3 by the good correspondence of the replication results using dataset R with the same (although incorrect) 2 718 days used by Bruehl & Villarroel (Reference Bruehl and Villarroel2025).

6.2. Normalisation by the true observation window

Now that we have successfully replicated the baseline results using dataset R, we can estimate the effects of normalising by just the days on which relevant observations were acquired by the telescope. SPFs were reported on 310 days out of the 2 718 days in the study period (Bruehl & Villarroel Reference Bruehl and Villarroel2025), of which 255 days occur outside any nuclear testing window and 54 days occur inside a nuclear testing window. The testing window is defined by Bruehl & Villarroel (Reference Bruehl and Villarroel2025) as a day of nuclear testing $\pm1$ day. In order to test for significant correlation between the detection of SPFs and the nuclear testing windows, Bruehl & Villarroel (Reference Bruehl and Villarroel2025) compared these numbers (255 days and 54 days, respectively) to the days with and without detected SPFs, that occur within the full time period of 2 718 days. In reality, the POSS1 survey did not record observations every single day out of this time period (Minkowski & Abell Reference Minkowski, Abell and Strand1963; STScI 2026). There are plates available for only 380 days, of which 368 fall within the study period.

In addition, we now use information about datasets R, W, and V to argue that the 368 days counted within the study period during which plates are available, can be further reduced if we account for the fact that none of these datasets contain SPFs that were sampled from plates fully in the southern celestial hemisphere (see Section 3.3.2). Therefore, days when the telescope only observed the southern hemisphere do not count as zero detection days, they count as no-data days, and must be removed from the total count of relevant observation days (Figure 12).

To calculate the number of plate dates to remove due to this overcounting, we use the POSS1-E metadata to see that the footprints of 292 of the 937 POSS1-E plates (31%) reside entirely in the southern celestial hemisphere without overlapping the celestial equator. However, as explained in Section 3.3.2, the equatorial plates do contribute a small amount of southern celestial hemisphere SPFs to W (less than 0.1%), R (1.4%), and V (1.4%) (Section 3.3.2 and Appendix A). Some of the fully southern hemisphere plates were acquired on days when northern hemisphere or equatorial plates were also taken, and these observation days should not be removed from the tally of relevant observation days. Hence, for the R, W, and V datasets, this leaves 56 days on which POSS1-E observations were taken fully and exclusively in the southern celestial hemisphere during the study period and are not relevant to this correlation analysis. Excluding these days, the maximum number of relevant observation days falls from 368 days to 312 days for all three datasets.

Separately, we find 289 unique observation days represented by SPFs in R, and 307 in W, after matching each of their SPFs to an unambiguous plate; Bruehl & Villarroel (Reference Bruehl and Villarroel2025) reports 310 days with SPFs for V. Thus, within the study time window, at least one SPF from W (respectively R) dataset was found on 98% (respectively 93%) of the days that the POSS1 survey imaged the northern sky. In the case of set V, this fraction of relevant POSS1 observation days on which SPFs were detected is 99%. This suggests that SPFs are not a rare event, they occur on almost every observation day, even within the most filtered set R, and their occurrences are almost entirely dictated by the POSS1 observation schedule.

If we repeat in Table 3 the correlation test by replacing the 2 718 days of the full time period with the effective 312 observation days of the POSS1 survey, using dataset R, which we have shown in Table 3 gives similar results to V when calculating correlation statistics, we see dramatically different conditional probabilities. The p-value for a correlation between SPF detection and nuclear testing window goes to $p = 0.1$ , which is no longer significant, and the relative risk ratio goes to 1.07 (95% confidence interval: 1.02–1.13). The relative risk ratio here is defined as the conditional probability $\mathbb{P}(\text{SPF detection} | \text{Nuclear test}) = 98.1\%$ divided by the conditional probability $\mathbb{P}(\text{SPF detection} | \text{No nuclear test}) = 91.5\%$ . A reasonable interpretation is that SPFs are 7% more likely to fall within a nuclear test window compared to outside of a nuclear test window (instead of 45% as claimed in Bruehl & Villarroel Reference Bruehl and Villarroel2025). However, even using the correct number of relevant observation days naively estimates the correlation between days with SPFs and days with nuclear tests. We haven’t yet considered the underlying baseline correlation between the nuclear tests and the telescope observation schedule itself.

6.3. Correlation between POSS1 observation schedule and nuclear test schedule

Normalising by the true observation time window (days on which the telescope was actually making observations of the northern celestial hemisphere) is still not satisfactory because it ignores the correlation between nuclear test windows and the observation schedule of POSS1, a correlation independent of plate content. The near-universal occurrence of SPFs on observation days (312), for V (310), R (289), and W (307), ensures that this effect will dominate correlations of SPFs with outside factors. The estimate of this baseline correlation is independent of SPF counts, so we compare the maximum possible relevant observation days (312) with the set of nuclear test windows in the full study period (2 718 days).

Using the same test of correlation between the dichotomous variables that was used for Table 3, we now compare the occurrences of nuclear test windows in the 2 718 days of the full study period with the 312 relevant observation days of the POSS1 survey to estimate the degree of correlation between the observation schedule and the nuclear test windows. We find the relative risk ratio is 1.35 (with a p-value of 0.03 and a 95% confidence interval: 1.03–1.78); in other words, a relevant POSS1 observation day is 35% more likely to fall within a nuclear test window compared to outside of a nuclear test window.

In summary, (i) normalising by the relevant POSS1 observation days (312) significantly dilutes the significance of the statistical effect between SPF detection and nuclear testing reported in both Bruehl & Villarroel (Reference Bruehl and Villarroel2025) and Villarroel et al. (Reference Villarroel, Streblyanska, Bruehl and Geier2026) v2; (ii) SPFs are reported by Bruehl & Villarroel (Reference Bruehl and Villarroel2025) on at least 99% of the days on which the POSS1 survey was observing. Out of 312 possible days relevant to these datasets, SPFs are found on 310 days for V, 307 days for W, and 289 days for R, suggesting near-universal occurrence of SPFs on observation days; and (iii) the POSS1 observation schedule has a non-negligible (35%) likelihood of falling within nuclear test windows compared to outside. We speculate that the correlation of the telescope schedule and nuclear tests may be due to seasonality, since both the timing of astronomical observations and nuclear testing rely on clear skies and low-wind weather conditions.