eRO-ExTra: eROSITA extragalactic non-AGN X-ray transients and variables in eRASS1 and eRASS2

To build the sample of extragalactic transients, we first compiled the sample of variable sources selected based on the amplitude and the significance of the variability between eRASS1 and eRASS2. This allows the selection of all sources that brightened or faded significantly between eRASS1 and eRASS2. The flowchart of the included selection steps is presented in Fig. 1 and described in more detail in the following.

First, we crossmatched the eRASS1 (Merloni et al. 2024) and eRASS2 (unpublished, 1B: 0.2–2.3 keV, ver.221031, includes sources with $\mathrm{DET\_LIKE>6}$) source catalogs with a radius of 15″ and determined subsamples of sources which were detected in both eRASS (C12), only in eRASS1 (C1), or only in eRASS2 (C2). The eRASS2 catalog was processed with an updated version of the eROSITA standard data processing pipeline (ver.020). Comparing to that used for the DR1 (Merloni et al. 2024, ver.010), the new data processing version includes updates on the pattern and energy tasks, an improved boresight correction, a change in flaregti parameters, an improved low-energy detector noise suppression, and a better computation of the subpixel position. Subsequently, we applied a detection likelihood cut $\mathrm{DET\_LIKE>15}$ on the brighter detection of a source in either eRASS1 or eRASS2 to minimize spurious events. The chosen threshold corresponds to $\approx 0.03\%$ of false positives (see Seppi et al. 2022, Fig. 3). Extended sources were removed using the extension likelihood cut $\mathrm{EXT\_LIKE=0}$. The comprehensive description of the source detection parameters is provided in Brunner et al. (2022). The crossmatching radius was chosen based on eROSITA’s typical positional uncertainty (see Merloni et al. 2024, Fig. 5). Provided that a brighter detection has a detection likelihood of at least $\mathrm{DET\_LIKE=15}$, and that of a fainter detection can be as low as $\mathrm{DET\_LIKE=6}$, the chosen radius accounts for the combined positional error of more than 90 % of point sources. Since we searched for the closest match, we checked if there are cases in C12 where the crossmatch would have multiple counterparts within 15″ and found 98/348k sources. After applying the selection cuts (see Fig. 1), there remained only four potential spurious matches, for which we manually confirmed that the closest match is correct.

eROSITA’s scanning strategy (Merloni et al. 2024) results in a nonuniform exposure across the sky (see Fig. 2, left) with the highest exposure being reached near the ecliptic poles and the lowest near the ecliptic equator. For this study, we removed sources within 3° from the South Ecliptic Pole (SEP). At the SEP, the significantly larger exposure (up to 30 ks in each eRASS compared to $\sim 100$ s near the equator) and depth, leading to high source density and source confusion, require a very different data analysis from the rest of the sky. Results of the variability analysis of the SEP are presented in Bogensberger et al. (2024). To reduce the number of spurious sources, we also excluded regions in selected overdensities in the eRASS source catalogs. This includes, for example, regions near supernova remnants, very bright point sources, stellar clusters, and large local galaxies. The summary of the flagging procedure is provided in Merloni et al. (2024) in Table 5. Regions around nearby galaxy clusters were not excluded, since eROSITA’s resolving power is sufficient to distinguish between X-ray point sources associated with individual galaxies and diffuse cluster emission, and cluster member galaxies can host extragalactic transients and variables.

For sources in the C1 and C2 samples, we calculated the 3$\sigma$ upper limits for the nondetections at the X-ray detection positions in the 0.2–2.3 keV band, assuming the same spectral model as used in the eRASS catalogs (absorbed power law with $\Gamma=2$, N${}_{\rm H}=3\times 10^{20}$ cm^-2). The details of the upper limit computation can be found in Appendix A.

To characterize the variability, we determined the fractional amplitude, $\mathrm{A}$, and significance of the variability $\mathrm{S}$ for each source as:

where $F_{\rm max}$ and $F_{\rm min}$ are the maximum and minimum fluxes, corresponding to the integrated fluxes either in eRASS1 or eRASS2, and $F\_ERR\_\mathrm{max}$ and $F\_ERR\_\mathrm{min}$ are their 1$\sigma$ symmetric errors. For detections we used the catalog fluxes and their uncertainties. For sources for which the catalogs did not include error estimates (see the discussion in Merloni et al. 2024 for details), we assigned the median of the count error of all sources with counts and exposure time within 10 % of those of the source. This threshold provided at least 20 similar sources for each error estimation, with the exception of one high-count source, for which we assumed a $\mathrm{\sqrt{N}}$ error. To calculate the flux uncertainties in both cases, count rates were converted to fluxes using the standard catalog energy conversion factor ($\mathrm{ECF=1.074\times 10^{12}}$). For the nondetections in C1 and C2, $F_{\rm min}$ is the 3$\sigma$ upper flux limit and $\mathrm{F\_ERR\_\mathrm{min}=0}$. The final sample includes 2331 variable sources (C12: 1927; C1+C2: 404), which vary with $\mathrm{A>4}$ and $\mathrm{S>4}$, where 6 % (i.e., 147) have both amplitude and significance higher than 10.

An important step to determine the nature of an X-ray transient is to identify its multiwavelength counterpart. In this section, we describe the criteria by which optical counterparts were associated with the X-ray detections. The flowchart of the selection steps is shown in Fig. 3.

For the identification of the optical and near-infrared counterparts, we concentrated on the Legacy Survey DR10 area (LS10¹¹1https://www.legacysurvey.org/dr10/; Dey et al. 2019), since it provides extensive coverage of the eROSITA_DE sky (76 %) except in the Galactic Plane and several other small sky regions (see Fig. 2, right). From the 2331 sources in the variability sample, 1613 ($\approx 70$ %) are within the LS10 footprint. Sources not covered by the LS10 footprint are primarily concentrated in the Galactic Plane ($\mathrm{|b|\lessapprox 15^{\circ}}$) and were excluded from further study. As variability for sources in the Galactic Plane is heavily dominated by stellar phenomena, the exclusion of this region is expected to have minor impact on identifying the extragalactic transient and variable population presented in this work.

LS10 provides deep and homogenized photometry in the g, r, i, z and WISE W[1,2,3,4] bands. For sources located in areas within the LS10 mission footprint but where catalog data is not yet available in this data release, we used Gaia DR3 (Gaia Collaboration et al. 2016, 2023) and CatWise2020 (Marocco et al. 2021) independently to replace missing photometry results. However, we note that Gaia (G$<$20 mag) is shallower than LS10 and is biased against extended sources, such as nearby galaxies. While Catwise2020 is deeper than the LS10 W[1,2,3,4] bands (six times as many exposures), it suffers from blending. The counterparts were identified using NWAY (Salvato et al. 2018) by applying the procedure as described for the eROSITA eFEDS field (see Salvato et al. 2022, Sect. 3.1). Specifically, the geometrical distribution of sources (i.e., the distance from the X-ray position and positional uncertainty, the number density, and the similarity of their SEDs compared to those in a training sample) are taken into account. For details on the priors for LS10, Gaia DR3, and CatWise2020 and the agreement between the three surveys see Salvato et al. (in prep.), where the counterpart identification process for eRASS1 is described. The training sample was not specifically selected for the counterpart identification of X-ray transients and variables, but rather for typical X-ray emitters, due to the lack of previously discovered sources with suitable properties. The most complete to-date version of the NWAY/LS10 counterpart catalog for eROSITA is eRASS:5, a not-yet-published stacked source catalog for all eRASS. We associated NWAY/LS10 counterparts to the sources in the variability sample by crossmatching the X-ray position of the brighter detection in eRASS1 or eRASS2 with the eRASS:5 X-ray position with a radius of $\mathrm{r=15}$″.

Of the 1613 sources within the LS10 footprint, 1581 ($\approx 98$ %) have at least one possible counterpart in the NWAY catalog within 15″. The probability that for a given X-ray source one or more counterparts with properties typical for an X-ray emitter were found, is defined by the p_any parameter (Salvato et al. 2018). The optimal minimal value of p_any=0.17 was determined as the intersection of purity and completeness functions calculated for various p_any for our sample after the NWAY match. Henceforth, the counterparts with p_any¿0.17 are considered reliable. As shown in Fig. 4, the threshold of p_any¿0.17 corresponds to chance coincidences of $<5$ %. There are 1526 ($97\,\%$) sources with a counterpart with p_any$>$0.17; the remaining 55 sources ($3\,\%$) have a potential counterpart with a lower probability (0$<$p_any$<$0.17). The p_any values are provided in our final catalog, and users are advised to consider the association probability for their analysis. For 32 sources, no NWAY counterpart was found within $15^{\prime\prime}$ from the X-ray position. In addition, NWAY identified multiple counterparts in LS10 for 14/1581 sources. Multiple potential counterparts were kept during all further selection steps. For simplicity, we cited the numbers of unique X-ray sources in the description of the selection flow and in Fig. 3. After all cuts were applied, 11/14 X-ray sources were excluded as either stars or AGN (see Sect. 2.3 and Sect. 2.4). For another source, one LS10 counterpart was excluded as an AGN and another one remained in the catalog. For two remaining sources, multiple matches were associated with LS10 duplicates, which pointed to the same galaxy. In these cases, the closest match was selected for the catalog.

Finally, we visually inspected the X-ray images of all sources without an NWAY/LS10 counterpart. Here, 20/32 sources were removed from the sample by their association with extended X-ray cluster emission. These sources were not excluded by the EXT_LIKE cut earlier, since the extended emission is clearly identified in the compiled 4(5) eRASS only. Additionally, three sources were manually identified with NWAY/LS10 counterparts with p_any$>$0.17 using a larger crossmatching radius ($\mathrm{16\arcsec<r<20\arcsec}$). After the exclusion of clusters, the sample included 1593 unique X-ray sources.

To further reduce the contamination of the sample by Galactic objects, we made use of (1) the parallax significance estimates from Gaia DR3 (if p_any¿0.17) and (2) available classifications provided in the SIMBAD database (Wenger et al. 2000). The summary is shown in the sixth box in Fig. 3. First, the parallax significance cut of $\mathrm{par\_sig<3}$ was applied, where $\mathrm{par\_sig=parallax\times\sqrt{\mathrm{parallax\_ivar}}}$ with parallax_ivar being the inverse-variance of the parallax. This cut removed 449 sources.

Next, we excluded 50 known stars by crossmatching the remaining sources with SIMBAD, which contains names, positions, and known properties of more than 16 million objects and provides their classifications. For sources with reliable NWAY/LS10 counterparts (p_any$>$0.17), we searched around the LS10 counterpart position for SIMBAD sources, otherwise (p_any$<$0.17) around the X-ray position. In both cases, if a star is present in SIMBAD within 15″, we excluded the sources. Finally, we visually inspected the LS10 images and excluded 28 obvious stellar contaminants such as saturated bright stars and sources in densely populated stellar fields. One of these sources was identified as a Galactic nova in a fireball phase (König et al. 2022b, MGAB-V207). In total, additional 527 ( $\approx 30\%$) sources were removed from the eRASS1-eRASS2 variability sample as likely to be stars (see Fig. 3 for step-by-step numbers). At this step 1066 variable X-ray sources were left in the sample.

A large contribution to the extragalactic X-ray variable sky comes from AGN. In this section, we describe the identification of sources with properties matching those of regular AGN and how they were excluded. The applied selection criteria are shown in the second to last step of the flowchart in Fig. 3.

Firstly, we removed sources with major AGN contribution by applying a mid-IR color ($W1-W2$¡$0.8$ mag_Vega) cut from Stern et al. (2012) for sources with reliable counterparts. This discarded 483 sources ($\approx 30\,\%$ of all sources in LS10 footprint).

Secondly, we excluded sources classified as active galaxies in SIMBAD (124 sources), using the crossmatch described in Sect. 2.2. In addition, The Million Quasars Catalog (Milliquas; Flesch 2023) helped us to identify more contaminating AGN and QSOs in the sample. Milliquas contains 907,144 type-I QSOs and AGN, largely complete from the literature to 30 June 2023. We crossmatched our catalog and Milliquas using the same approach as for the SIMBAD catalog and excluded additional 12 AGN. To ensure the non-AGN nature of sources based on archival pre-flare data, we also visually inspected available archival optical spectra and excluded four sources which show characteristics of broad-line AGN. Finally, we crossmatched our sample with the eROSITA blazar catalog (Hämmerich in prep.²²2The eRASS1 blazar catalog includes known sources from the 4FGL (Ballet et al. 2023), ROMA BZCAT (Massaro et al. 2015), 3HSP (Chang et al. 2019), HighZ (Sbarrato et al., in prep), Milliquas (Flesch 2023), KDEBLLACS and WIBRaLS2 (D’Abrusco et al. 2019), ABC (Paggi et al. 2020), and BROS (Itoh et al. 2020) catalogs, found within 8″from the eROSITA position.) and excluded three sources.

Archival X-ray observations helped us further to exclude possible AGN which are not yet removed in previous steps, in particular, sources with significant archival X-ray detections, since their flaring is likely caused by long-term AGN variability. To characterize the history of the eROSITA transients and variables, we explored the archives of previous and operating X-ray missions. We used the web-based High-Energy light curve Generator (HILIGT³³3https://xmmuls.esac.esa.int/upperlimitserver; Saxton et al. 2022; König et al. 2022a) to retrieve flux and upper limits values estimated via aperture photometry with the Bayesian approach of Kraft et al. (1991) for archival observations from Neil Gehrels Swift X-ray Telescope (XRT; Burrows et al. 2005), ROSAT (Voges et al. 1999), and for the XMM-Newton Slew Survey (Saxton et al. 2008). For the flux estimation in the energy band 0.2-2.0 keV we chose a uniform spectral model of an absorbed power law with $\Gamma=2$ (same as in the eROSITA source catalogs), and a confidence interval (CL) of 99.87 %, corresponding to a one-sided 3$\sigma$ level.

All presented eROSITA transients and variables were covered by at least one of the above missions. Only upper limits estimates could be derived for 296 of sources. If an upper limit, $F_{\rm ul}$, constrained the historical flux to be fainter than the peak measured by eROSITA, $F$, so that $F_{\rm ul}\leq(F-F_{\rm err})_{\rm peak}$, where $F_{\rm peak}$ and $(F_{\rm err})_{\rm peak}$ refer to the maximum flux of the eROSITA light curve and its error, the source received $\mathrm{arch\_flag=1}$ (“constraining”) in our catalog. Otherwise, $\mathrm{arch\_flag=0}$, (“not constraining”).

In total 144 sources have archival detections. These detections can also constrain whether a source shows long-term variability or the eROSITA detection marks a brightening from a previously lower flux level. Archival detections performed at least one year before the eROSITA peak indicate X-ray long-term variability if one of the following criteria is true: 1) the significance of the source variability S (Eq. 2) between the archival detection and the fainter of the eRASS1 or eRASS2 flux constraints is $\geq 3$ ; 2) the significance of the variability S between the archival detection and the eROSITA peak is $\leq 3$; 3) the archival detection is brighter than the eROSITA peak. A source that fulfills at least one of these conditions received $\mathrm{arch\_flag=-1}$ (”variable”) in the catalog. Otherwise, the sources are flagged with $\mathrm{arch\_flag=2}$ (“not variable”). The latter group includes sources with archival detections fainter or comparable with the eROSITA minimum since they might indicate the pre-flare quiescent state of the system.

Overall, 136 sources identified as variable ($\mathrm{arch\_flag=-1}$) were excluded from the extragalactic variability catalog. Whereas all of these excluded sources were in the ROSAT footprint, 86 % of sources were also covered by XMM-Newton and 23 % by Swift pointed or slew observations. Although some bright archival detections might indicate a repeating transient, for example, as it was shown in Malyali et al. (2023) with a TDE candidate re-brightening on a scale of decades, a more likely explanation is long-term AGN variability. One the other hand, some AGN, which do not have significant archival detections, might have been missed in this cut due to the limitations in sensitivity and coverage of previous missions. All steps combined, 760/1068 sources were classified as AGN and were excluded to form the eRO-ExTra catalog.

A summary of the historical light curve classification is presented in Table 1. The archival fluxes with their uncertainties, instruments, and observing dates are provided in the catalog. Overall, 296/304 sources are not detected in archival observations and have only archival upper limits and, therefore, can be considered as genuinely new eROSITA transients.

The resulting catalog eRO-ExTra contains 304 transients and variables without a known pre-eROSITA AGN origin. All sources are associated with an optical LS10 counterpart. Since this study is focused on non-AGN sources, all further analysis was performed for the eRO-ExTra catalog. The summary of the catalog and its properties are discussed further in Sect. 6.

The eROSITA X-ray light curves were analyzed to characterize the long-term flux evolution. Each survey observes a source’s position multiple times (”visits”) with a cadence of $\approx 4$ hours (referred to as one ”eroday”). The number of visits, hence the accumulated exposure, depends on the proximity to the survey poles. It ranges from at least six visits near the survey equator to several tens near the poles. The long-term behavior can be assessed using the data of all four complete all-sky surveys (eRASS1-eRASS4) and eRASS5, if available. With each successive eRASS being $\approx 6$ months after the previous one, this provides a coverage of 1.5–2 years.

To analyze the long-term eROSITA behavior, we first crossmatched the eRASS:5 X-ray position with the detections in the eRASS3, eRASS4, and eRASS5 (v.221031, v.221031 and v.21101, respectively, unpublished, 1B: 0.2-2.3 keV, processing version 020) source catalogs using a matching radius of r=15^′′. The eRASS:5 coordinates are used for the crossmatch since the accumulated catalog contains the most accurate X-ray positions. Upper limits were computed following the procedure described in Appendix A if a source was not detected in an eRASS.

The light curves were then divided into four classes: ”flare,” ”decline,” ”brightening,” and ”other,” using an automated procedure considering general light curve trends and variability significance across eRASS measurements. The decision tree for the light curve classification is detailed in Fig. 5.

Sources peaking in eRASS1 are classified as either decline or other. The decline class includes sources, which peak in eRASS1 and decay onward. The light curve (or its part) is considered decaying if one of the following condition is satisfied (i.e., decay condition): for each pair of light curve points (m,n) after the peak, where m ¡ n: (1) flux(m) ¿ flux(n); or (2) flux(n) and flux(m) are consistent within 2$S$, where $S$ is defined by Eq. 2. Also, we require $S_{\rm decay}$, defined as the significance of the total decay from the peak to the last light curve point eRASS4(5), to be larger than two. Otherwise, the source is classified as other.

Sources peaking in eRASS2 or in later epochs belong to either brightening, flare or other light curve class. The brightening class shows a flux rise from eRASS1 to eRASS2 and then continues brightening, in agreement with the following condition (i.e., brightening condition): for each pair of light curve points (m,n), where m ¡ n: (1) flux(m) ¡ flux(n); or (2) flux(n) and flux(m) are consistent within 2$S$. Otherwise, the source is classified as other. The light curve has a flare if it first brightens from eRASS1 to eRASS2 and later decays. In order to have a flare class, the source should satisfy the decay condition after the peak epoch as well as have $S_{\rm decay}$¿2. If the latter condition is not satisfied (in other words if light curve decay is not sufficient) the source is classified as either brightening or other, depending on the agreement with the brightening condition.

Table 2 provides the light curve classification summary. Examples for each class are shown in Fig. 6. The light curve classification is included as flag LC_type in the final catalog. The distribution of sources in the sky color coded by their light curve class and scaled by their peak eRASS1 or eRASS2 flux is shown in the left panel of Fig. 7. A noticeable concentration of sources, including faint transients, in the southern Galactic hemisphere is caused by higher eROSITA exposure times near the SEP.

In addition, we separately searched for available X-ray observations by other missions, performed slightly earlier or during eROSITA epochs. The information about these observations is included in the catalog as well. Detections within a year before the eROSITA peak may have already been associated with the start of the event later found by eROSITA: 1eRASS J004058.3-683816 and 1eRASS J132252.1+182253 were detected by XMM-Newton Slew Survey a few days before the eROSITA peak, with the archival points being in agreement within 1.5$S$ with the eROSITA peak flux and the light curve decay trend. The archival classification of these sources ($\mathrm{arch\_flag=0}$) in Sect. 2.5 is based on their earlier archival observations. The X-ray mission archives also contained 150 eRO-ExTra sources where detections or upper limits constrain the behavior during or after the eROSITA observations. Mostly, additional points during or after eROSITA observations are nonconstraining upper limits. In addition, several detections and constraining upper limits are consistent with the expectations from the eROSITA light curve and their classifications. Only two sources should belong to a different light curve class taking into account the additional data, namely, 1eRASS J045457.8-652846 changes from a flare to other, and 1eRASS J102851.3+251439 - from decline to flare. For consistency, the catalog includes light curve classification based on the eROSITA points only.

For each source, we extracted spectra for the peak epoch using the eSASS task SRCTOOL (version eSASSusers_211214) with circular source and annular background regions centered on the X-ray positions. Utilizing SRCTOOL’s AUTO mode, the radii of the source and background regions were selected taking into account the source counts, the level of the background map model at the source position, the best fitting source extent model radius, as well as a model of the effective eROSITA PSF at the source position (averaged over the integration, and summed over all operating telescope modules).

X-ray spectra were analyzed using the Bayesian X-ray Analysis software (BXA; Buchner et al. 2014), which connects the nested sampling algorithm UltraNest (Buchner 2021) with the fitting environment XSPEC (Arnaud 1996). The spectra were fitted unbinned using C-statistic (Cash 1976), and the eROSITA background was modeled using the principal component analysis (PCA) technique described in Simmonds et al. (2018) and Liu et al. (2022). Each extracted eROSITA spectrum, which contains a contribution from both the source and background emission, was jointly fitted. The background spectrum was modeled with the fixed derived background model, and the source spectrum was modeled with a chosen source model convolved with the X-ray responses plus the background model convolved with a diagonal matrix response. Here, an absorbed power law model $\tt{tbabs*powerlaw}$ was used with fixed Galactic equivalent neutral hydrogen column density ($N_{\rm H,gal}$) extracted from the HI4PI survey (HI4PI Collaboration: et al. 2016) individually for each source. In addition to the free parameters of the source model (photon index and normalization), the background model has a free normalization parameter, which should equal to unity in the simultaneous source and background fitting. We assumed wide flat priors on the photon index and the logarithm of the normalization. The best-fit values of the photon index gamma $\Gamma$ and the corresponding 0.2–2.3 keV fluxes were both derived as medians from the BXA posterior distributions with uncertainties calculated as 68% percentile interval around the median (1$\sigma$). An example is shown in Fig. 8. The values of $\mathrm{N_{H,gal}}$, $\Gamma$, fluxes with errors and goodness of fit can be found in the eRO-ExTra catalog.

The sample includes sources with photon indices in the range $0.3<\Gamma<6.1$ (see Fig. 9) and a mean of $\Gamma=2.2$, dominated by 85 % of sources having $1<\Gamma<3$. The soft tail of the distribution includes 33 sources (11 %) with $\Gamma>3$, based on the mean posterior values. It is important to note that the best-fit results of the hard tail of the distribution with $\Gamma<1$ (4 % of sources) may be affected by the choice of the spectral model, particularly an underestimation of the intrinsic obscuration introduced by using a fixed $N_{\rm H,gal}$. However, due to the low photon counts for most sources, a more complex spectral modeling cannot be performed consistently. Similarly, the extremely steep photon index, namely, $\Gamma>6$, for one faint source (1eRASS J064449.4-603704), is due to the simple spectral model assumption. The distribution of sources in the sky color coded by $\Gamma$ is shown in the right panel of Fig. 7, illustrating how sources with various photon indexes are homogeneously distributed.

Spectroscopic redshifts are available for 79 sources, 27 of which are archival and 52 were obtained in our dedicated follow-up campaign of eROSITA X-ray transients. The summary of the follow-up observations is provided in Appendix B. For sources without spectroscopic redshifts, we provided reliable photometric redshifts (photo-z), which have accuracy 6% with a fraction of outliers estimated to be around 12%, see Salvato et al. (2024a, submitted) for more details. Also for a reliable photo-z we required all LS10 photometry bands (griz) to be available. For even more accuracy, one could also filter photo-z using LS10 parameters ANYMASK and ALLMASK, which denote sources that touch bad pixels; however, we did not exclude such photo-z from consideration. Also the values for sources p_any¡0.17 should be used only after confirming the counterpart. As a result, using only reliable redshifts and counterparts, the redshift completeness of the sample reaches 84 %.

Fig. 10 shows the total, spectroscopic, and photometric redshift distributions. The majority of sources are at $\mathrm{z<0.3}$ (64 %), and several sources (1 %) have $\mathrm{z>1}$. Photometric redshifts are typically higher than spectroscopic ones due to the limitations of optical spectroscopic follow-up redshift measurements.