A New Sample of Transient Ultraluminous X-Ray Sources Serendipitously Discovered by Swift/XRT

Swift J130456.1-493158 was first detected in a Swift/XRT observation taken on 2021 February 8 (obsID: 00013908005). The target of the Swift observation was NGC 4945 X-1 (Brandt et al. 1996), a ULX hosted by NGC 4945, a barred spiral galaxy in the constellation Centaurus. The enhanced position given by the online tool was R.A. = 19623411, −4953306 (=13^h 04^m 5619, −49°31'590) with an error radius of 32 (90% confidence). The position of Swift J130456.1-493158 appears to place the source in the outskirts of the galaxy (Figure 1). No X-ray source has been reported at this position previously, despite multiple Chandra, XMM-Newton, Suzaku, NuSTAR, and Swift observations, the last of which was by Swift only 2 weeks prior to the new X-ray source being detected, as shown in the lightcurve in Figure 2. After the source was initially detected, it declined in brightness from its peak, becoming undetected by Swift/XRT 60 days after its initial detection, even in stacked observations.

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We used the online tool to extract the stacked Swift/XRT spectrum of the source from six observations during which the source was detected. The total exposure time was 12.9 ks. The online tool fitted the spectrum with an absorbed power-law model, which yielded W = 53.02 with 62 DoFs, where N_H = ${1.33}_{-0.76}^{+1.12}\times {10}^{22}$ cm⁻² and ${\rm{\Gamma }}={2.63}_{-0.87}^{+1.06}$, assuming a Galactic column density of 2.2 × 10²¹ cm⁻² (Willingale et al. 2013). The 0.3–10 keV unabsorbed flux from this model was ${1.0}_{-0.6}^{+4.2}\times {10}^{-12}$ erg cm⁻² s⁻¹, which implies a luminosity of 1.7 × 10³⁹ erg s⁻¹ at 3.7 Mpc. The count rate to flux conversion factor was 1.37 × 10⁻¹⁰ erg cm⁻² count⁻¹, which we used to determine the luminosity axis in Figure 2.

The deepest upper limit on the flux of Swift J130456.1-493158 prior to its detection is from Chandra observations, which have a sensitivity of 1.1 × 10⁻¹⁵ erg cm⁻² s⁻¹ in the 0.5–8 keV band listed in CSC2 (Evans et al. 2010). This is 3 orders of magnitude lower than the flux measured above. The deepest upper limit from XMM-Newton observations is <7.4 × 10⁻¹⁵ erg cm⁻² s⁻¹ in the 0.2–12 keV band listed in the XMM-Newton Science Archive (XSA).

We also obtained a Chandra Director's Discretionary Time (DDT) observation of the source, which took place on 2021 March 10 (obsID: 24986), with ACIS-S at the aimpoint in VFAINT mode. The source was well detected, with a count rate of 1.52 × 10⁻² counts s⁻¹ in the 10 ks exposure. We extracted the Chandra spectrum with specextract from circular regions of radius 15 for the source and 75 for the background. The spectra were grouped with a minimum of one count per bin with the tool grppha.

We fitted the Chandra spectrum of the source with the same model used to fit the Swift/XRT spectrum described above. Since we did not find evidence for spectral variability between Swift/XRT and Chandra, we fitted the joint Swift/XRT and Chandra spectrum of the source in xspec, with a constant to account for cross-calibration uncertainties and the flux variability of the source. This yielded W = 120.10 for 174 DoFs. The cross-calibration constant for the Swift/XRT spectrum is set to unity, and the constant for the Chandra spectrum is ${0.70}_{-0.16}^{+0.21}$. We find N_H = ${1.13}_{-0.38}^{+0.45}\times {10}^{22}$ cm⁻² and ${\rm{\Gamma }}={2.82}_{-0.51}^{+0.56}$. The log of the 0.3–10 keV unabsorbed flux from this model corresponding to the time of the Chandra observation is $-{11.84}_{-0.28}^{+0.38}$, which implies a luminosity of 2 × 10³⁹ erg s⁻¹ at 3.7 Mpc. The spectrum is shown in Figure 3.

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We also trialed a diskbb model in place of the powerlaw one, which produced W = 122.14 for 174 DoFs, a slightly worse fit for the same number of DoFs. We find N_H = ${5.18}_{-2.22}^{+2.72}\times {10}^{21}$ cm⁻² and ${T}_{\mathrm{in}}={1.03}_{-0.17}^{+0.24}$ with a normalization, $N={1.67}_{-1.00}^{+2.40}\times {10}^{-2}$. The normalization is related to the inner-disk radius by ${R}_{\mathrm{in}}={D}_{10}\times \sqrt{N/\cos \theta }$, where R_in is the inner-disk radius in kilometers, D₁₀ is the distance to the source in units of 10 kpc, and θ is the inclination angle of the disk. Assuming a face-on disk (θ = 0) yields R_in = 48 km, which is the innermost stable orbit of a 5 M_⊙ black hole. We note that the luminosity estimate would be a factor of 3.5 lower if this model is assumed and integrated over all energies.

We also used the Chandra data to acquire a more precise position of Swift J130456.1-493158. We compiled an X-ray source list of the Chandra observation in the 0.5–8 keV band using wavdetect with default parameters and crossmatched this with a Gaia Early Data Release 3 source list of the region (Gaia Collaboration et al. 2018), selecting sources within 10 of each other, which produced four Chandra/Gaia-matched sources. We define the astrometric shifts as the mean difference in R.A. and decl. between these matched sources, which is δR.A. = 034 and δdecl. = −044. The corrected position is R.A. = 13^h04^m 56350 (19623479), decl. = −49° 31' 5966 (−49533239, J2000), which lies in the middle of the Swift error circle. The mean residual offset between the corrected Chandra positions and the Gaia positions is 053, which we use as our positional error. There are no sources cataloged at other wavelengths within the Chandra error circle. The closest source is a near-IR J = 18.9 source cataloged by the VISTA Hemisphere Survey (McMahon et al. 2013) and lies 168 from the Chandra position, and is therefore unlikely to be related. Despite numerous HST observations of NGC 4945, none of them covered the region of the source.

We ran the tool uvotsource on the Swift/UVOT images to obtain photometry of the source in the UV bands using a 2'' radius circular region centered on the X-ray position. The source was not detected, and we obtained upper limits of UVW2 > 22.7, UVM2 > 22.5, and UVW1 > 21.5 taken from observations when the X-ray source was bright.

This X-ray source was also detected in a Swift/XRT observation of NGC 4945 X-1, and was first detected on 2021 September 24 (obsID: 00013908017), 7 months after Swift J130456.1-493158, as described in Section 2.1 above. The astrometrically corrected position given by the online tool from the first 22 obsIDs where the source was detected was 196.2985°, −49.4928° (=13^h05^m1165, −49° 29' 343) with an error radius 24 (90% confidence); we henceforth refer to this source as Swift J130511.5-492933. No X-ray source has previously been reported within the positional error circle of Swift J130511.5-492933. The Swift/XRT lightcurve of the source produced by the online tool is shown in Figure 4, which shows the source declining in brightness until ∼250 days after its initial detection, after which the source was undetected by Swift/XRT. The XRT, UVOT, and R-band images are shown in Figure 1, which show that, similarly to Swift J130456.1-493158, Swift J130511.5-492933 appears to be in the outskirts of NGC 4945.

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We ran the tool uvotsource on the Swift/UVOT images to obtain photometry of the source in the UV and optical bands using a 2'' radius circular region centered on the X-ray position. The source was not detected, and we obtained upper limits of UVW2 > 20.9, UVM2 > 21.2, UVW1 > 20.8, U > 20.2, B > 19.5, and V > 18.8, taken from obsID 00015017005 when the source was X-ray bright.

As with Swift J130456.1-493158, no source at any wavelength is cataloged within the error region for this X-ray source, and none of the Hubble Space Telescope (HST) observations of NGC 4945 cover the region. Once again, the closest source is a J = 14.6 mag near-IR source, which lies 47 from the astrometrically corrected position of the X-ray source, outside the 90% error circle (24 radius).

We used the online tool to extract the stacked Swift/XRT spectrum of the source (first 26 observations since detection) with a total exposure time of 45.1 ks. The online tool fitted the spectrum with an absorbed power-law model, which yielded W = 259.57 with 252 DoFs, where N_H = ${6.7}_{-1.7}^{+2.1}\times {10}^{21}$ cm⁻² and ${\rm{\Gamma }}={2.23}_{-0.27}^{+0.30}$, assuming a Galactic column density of 2.2 × 10²¹ cm⁻² (Willingale et al. 2013). The 0.3–10 keV unabsorbed flux from this model was ${1.02}_{-0.17}^{+0.31}\times {10}^{-12}$ erg cm⁻² s⁻¹, which implies a luminosity of 1.7 × 10³⁹ erg s⁻¹ at 3.7 Mpc. The count rate to flux conversion factor was 7.71 × 10⁻¹¹ erg cm⁻² count⁻¹, which we used to determine the luminosity axis in Figure 4.

Fitting in xspec, we found an improvement in the fit could be found with a multicolor disk component (diskbb) in the place of the power-law component, which yielded W = 246.11 with 252 DoFs. The best-fit parameters of this model were N_H = ${2.7}_{-1.0}^{+1.3}\times {10}^{21}$ cm⁻², T_in = 1.0 ± 0.2 keV, and $N\,={2.3}_{-1.0}^{+1.7}\times {10}^{-2}$. As for Swift J130456.1-493158, if we assume a face-on disk we find R_in = 56 km, which is the innermost stable orbit of a 6 M_⊙ black hole. We note that the luminosity estimate would be a factor of 1.9 lower if this model is assumed and integrated over all energies. We plot the spectrum of Swift J130511.5-492933 in Figure 5.

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Unfortunately, the Chandra observation taken of Swift J130456.1-493158 as described above did not have Swift J130511.5-492933 in the field of view. The deepest upper limit on the flux of Swift J130511.5-492933 prior to its detection with Swift/XRT is from other Chandra observations, which have a sensitivity of 6.5 × 10⁻¹⁶ erg cm⁻² s⁻¹ in the 0.5–8 keV band listed in CSC2. This is >3 orders of magnitude lower than the flux measured above. The deepest historical upper limit from XMM-Newton observations is <1.1 × 10⁻¹⁴ erg cm⁻² s⁻¹ in the 0.2–12 keV band listed in XSA.

A 150 ks XMM-Newton observation of NGC 4945 took place on 2022 July 5, 284 days after Swift J130511.5-492933 was detected. The XMM data were reduced using a pipeline that utilizes v 19.1.0 of the Science Analysis Software (SAS). The cifbuild command was used to create a current calibration file corresponding to the observations, and the odfingest command was used to produce a SAS summary file. The data were reduced and MOS and pn event files were created using the emproc and epproc commands, respectively. We first identify periods of high background by creating a lightcurve of the events in the 10–12 keV band, creating good time intervals where the rate was <0.4 counts s⁻¹ in this band in the pn detector, leaving 99 ks for the pn and 101 ks for the MOS. Events were selected with PATTERN ≤ 4 for the pn and PATTERN ≤ 12 for the MOS.

Upon inspection of the images, a faint X-ray enhancement appears at the source location in both the pn and MOS1 data. To test whether this is a detection, spectra were extracted using the specextract command with circular source regions of radii 16''. Local background was accumulated from annuli of the same area just around the source regions. The resulting spectra are heavily background dominated, which requires extensive modeling. We therefore calculate an upper limit on the flux of the source by assuming that the spectrum does not change and applying the best-fitting Swift/XRT model of a multicolor disk component (diskbb) with N_H = 2.7 × 10²¹ cm⁻² and T_in = 1.0 keV to the source+background spectrum in xspec. This yields an upper limit on the 0.3–10 keV flux of 7.5 × 10⁻¹⁵ erg cm⁻² s⁻¹, which implies a 0.3–10 keV unabsorbed luminosity of L_X = 1.2 × 10³⁷, well below the luminosity measured by Swift/XRT only 30 days prior (Figure 4).

This X-ray source was first detected in a Swift/XRT observation taken on 2018 April 28 (obsID: 00094097003) and not found in our real-time search, rather a search through archival data. The target of the Swift observation was NGC 7793 P13, a ULX hosted by NGC 7793 (Read & Pietsch 1999) known to be a ULX pulsar (Fürst et al. 2016; Israel et al. 2017b). The enhanced XRT position given by the online tool was R.A. = 35960774, decl. = −3260254 (=23^h58^m2586, −32°36'092) with an error radius of 25 (90% confidence; see Figure 6).

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The source is listed in the 2SXPS catalog as 2SXPS J235825.7-323609 with a mean count rate of 5.37 ± 0.76 × 10⁻⁴ counts s⁻¹, detected in a stack of data over the date range 2010 August 16–2018 July 28. This average count rate was 2 orders of magnitude below the newly detected count rate. We note that this average flux is from a date range that covers periods both when the source was undetected in individual observations and when it was detected in individual observations.

Since this source was first cataloged in 2SXPS, we henceforth refer to it by its cataloged name, 2SXPS J235825.7-323609. The lightcurve produced by the online tool is shown in Figure 7. This shows that prior to 2018 April 28 the source was not detected in stacked observations with upper limits consistent with the 2SXPS count rate. The source was not detected in the XRT observation immediately preceding April 28 on April 22. After reaching its peak, the source declined monotonically until it was no longer detected by Swift/XRT 180 days afterwards.

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We used the online tool to extract the stacked Swift/XRT spectrum of the source from 22 individual observations, with a total exposure time of 24.4 ks. The online tool fitted the spectrum with an absorbed power-law model, which yielded W = 166.19 with 171 DoFs, where N_H = ${2.11}_{-0.99}^{+1.20}\times {10}^{21}$ cm⁻² and ${\rm{\Gamma }}={2.03}_{-0.30}^{+0.33}$, assuming a Galactic column density of 1.2 × 10²⁰ cm⁻² (Willingale et al. 2013). The 0.3–10 keV unabsorbed flux from this model was ${7.3}_{-1.0}^{+1.5}\times {10}^{-13}$ erg cm⁻² s⁻¹, which implies a luminosity of 1.3 × 10³⁹ erg s⁻¹ at 3.8 Mpc. The count rate to flux conversion factor was 4.55 × 10⁻¹¹ erg cm⁻² count⁻¹, which we used to determine the luminosity axis in Figure 7.

A diskbb model in place of the powerlaw one produced an improvement in the fit of ΔC = −9, where N_H < 5.9 × 10²⁰ cm⁻² and ${T}_{\mathrm{in}}={1.03}_{-0.16}^{+0.21}$ with a normalization, $N={1.72}_{-0.87}^{+1.65}\,\times {10}^{-2}$. The normalization corresponds to R_in = 50 km, which is the innermost stable orbit of a 6 M_⊙ black hole when assuming a face-on disk. We note that the luminosity estimate would be a factor of 1.7 lower if this model is assumed and integrated over all energies.

An XMM-Newton observation took place on 2018 November 27, 213 days after the initial detection by Swift/XRT (obsID: 0823410301). We filter the data in the same way as described for Swift J130511.5-492933, which results in 17.6 ks of data. A circular region with a radius of 15'' was used to extract the source spectrum, and an annulus with inner radius 25'' and outer radius of 45'' was used to extract the background spectrum. The data were grouped with a minimum of one count per bin using grppha. The source was background dominated above 1 keV so we excluded these channels, and the resulting average count rate in the 0.2–1 keV band was 2.5 ± 0.5 × 10⁻³ counts s⁻¹.

Due to the narrow bandpass, we fit the XMM-Newton spectrum with the same model as for the Swift spectrum, with all parameters fixed with the exception of the normalization, which yielded N = 1.4 × 10⁻⁵ with W = 73.04 with 54 DoFs. The 0.3–10 keV flux is ${4.6}_{-1.5}^{+1.6}\times {10}^{-14}$ erg cm⁻² s⁻¹, which implies a luminosity of ${7.9}_{-2.6}^{+1.8}\times {10}^{37}$ erg s⁻¹ at 3.8 Mpc (Sabbi et al. 2018). We plot this flux in Figure 7. The source was not detected in an observation only 1 month after the above XMM-Newton observation (obsID: 0823410401 on 2018 December 27). The upper limit on the 0.2–10 keV flux is listed as 5.9 × 10⁻¹⁵ erg cm⁻² s⁻¹ in 4XMM from this observation, with similar upper limits provided by further observations since then. We show the Swift and XMM-Newton spectra in Figure 8.

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The deepest upper limit from XMM-Newton observations prior to the Swift detection is <5.0 × 10⁻¹⁵ erg cm⁻² s⁻¹ in the 0.2–12 keV band listed in XSA. This is 2 orders of magnitude lower than the peak flux measured above.

4XMM Data Release 11 lists the source from obsID 0823410301 as 4XMM J235825.9-323610 at R.A. = 23^h58^m2598 and decl. = −32°36'105 with a positional error of 10, which is an improvement on the XRT position.

Fortuitously, HST has observed the region of 2SXPS J235825.7-323609 as part of the GHOSTS survey (Radburn-Smith et al. 2011) with the ACS and F606W and F814W filters. However, no source is listed in the Hubble Source Catalog (HSC, v3) within the XMM-Newton positional error and the closest source lies 21 away.

We ran uvotsource on the mostly U-band UVOT data but did not detect the source in any observation to a limiting magnitude of U ∼ 21.5.

This X-ray source was also detected in a Swift/XRT observation of NGC 7793 P13, and was first detected on 2022 September 25 (obsID: 00031791173), 4 yr and 5 months after 2SXPS J235825.7-323609 (see Section 2.3 above). The enhanced position given by the online tool from the first nine obsIDs where the source was detected was 359.458°, −32.590806° (=23^h57^m4992, −32° 35' 269) with an error radius 25 (90% confidence), and we henceforth refer to this source as Swift J235749.9-323526 (Figure 9). A faint Chandra source, 2CXO J235749.7-323527, has previously been reported within the positional error circle of Swift J235749.9-323526 with a flux of 2.2 × 10⁻¹⁵ erg cm⁻² s⁻¹ in the 0.5–7 keV band, 3 orders of magnitude lower than the inferred XRT flux, which is also coincident with the Gaia nuclear position of the galaxy (Figure 9). The Swift/XRT lightcurve of the source produced by the online tool is shown in Figure 10, which shows the source declining in brightness from its initial detection. A lightcurve binned by snapshot rather than observation is also shown to highlight some short-term variability seen.

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We used the online tool to extract the stacked Swift/XRT spectrum of the source (first nine observations since detection) with a total exposure time of 14 ks. The online tool fitted the spectrum with an absorbed power-law model, which yielded W = 176.66 with 204 DoFs, where N_H = ${2.1}_{-0.8}^{+0.9}\times {10}^{21}$ cm⁻² and ${\rm{\Gamma }}={2.02}_{-0.24}^{+0.25}$, assuming a Galactic column density of 1.2 × 10²⁰ cm⁻² (Willingale et al. 2013). The 0.3–10 keV unabsorbed flux from this model was ${1.72}_{-0.20}^{+0.26}\times {10}^{-12}$ erg cm⁻² s⁻¹, which implies a luminosity of 3.0 × 10³⁹ erg s⁻¹ at 3.8 Mpc. The count rate to flux conversion factor was 4.86 × 10⁻¹¹ erg cm⁻² count⁻¹, which we used to determine the luminosity axis in Figure 10.

We obtained a NuSTAR DDT observation of Swift J235749.9-323526, which occurred on 2022 October 7 (obsID: 90801526002), with an exposure time of 53 ks. We used heasoft v 6.28, nustardas v 2.0.0, and caldb v 20211115 to analyze the data. We produced cleaned and calibrated event files using nupipeline with the default settings on mode 1 data only. We used nuproducts to produce spectral data, including source and background spectra, and response files. A circular region with a radius of 40'' was used to extract the source spectra and a radius of 80'' was used to extract the background spectra, taking care to extract the background from the same chip as the source. The source is detected with a count rate of 5 × 10⁻³ counts s⁻¹ in the 3–10 keV band in each focal plane module (FPM), above which the background dominates the source. We used the absorbed power-law model described above to determine the flux plotted in Figure 10.

We also obtained a Chandra DDT observation of the source, which took place on 2022 October 27 (obsID: 27481), with ACIS-S at the aimpoint in VFAINT mode. The source was well detected, with a count rate of 4.09 × 10⁻² counts s⁻¹ in the 10 ks exposure. We extracted the Chandra spectrum with specextract from a circular region of radius 20 for the source and an annulus radii of 31 and 62 for the background. The spectra were grouped with a minimum of one count per bin with the tool grppha. Again we used the absorbed power-law model from the Swift data to determine the flux plotted in Figure 10.

We then fitted the Swift, NuSTAR, and Chandra data simultaneously initially with an absorbed power-law model in xspec, with a constant to account for cross-calibration uncertainties and the flux variability of the source. This yielded W = 580.10 for 611 DoFs. However, this revealed structure in the data to model residuals, indicating that a more complex model was required. We then trialed the addition of a high-energy cutoff to the power-law model (cutoffpl), which lead to an improved W = 534.30 for 610 DoFs. A multicolor disk blackbody model, diskpbb, similarly produced W = 534.00 for 610 DoFs, which we select as our best-fit model due to the slightly better fit statistic. The best-fit parameters are intrinsic line-of-sight column density N_H = ${1.2}_{-0.8}^{+0.7}\times {10}^{21}$ cm⁻², inner-disk temperature ${T}_{\mathrm{in}}={1.24}_{-0.16}^{+0.17}$ keV, disk temperature index $p={0.54}_{-l}^{+0.10}$ (where −l indicates the lower bound uncertainty reaching the lower limit of 0.5 for the parameter), and normalization $N={8}_{-5}^{+15}\times {10}^{-3}$. The total luminosity of this model is 3.7 × 10³⁹ erg s⁻¹. Given the normalization of the diskpbb model and assuming a face-on inclination of the disk (θ = 0°), the implied black hole mass is 4 M_⊙ for a nonspinning black hole. The spectra fitted with this model are shown in Figure 11. We also checked for variation of the parameters between observations by untying them in the fit, but did not find any evidence for this.

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We also used the Chandra data to acquire a more precise position for Swift J235749.9-323526 in the same way as was done for Swift J130456.1-493158, which produced seven Chandra/Gaia-matched sources. The astrometric shifts were δR.A. = +034 and δdecl. = +022. After subtracting these shifts, the corrected position is R.A. = 23^h57^m49903 (35945793), decl. = −32° 35' 2797 (−32591104, J2000), which lies within the Swift error circle. The mean residual offset between the corrected Chandra positions and the Gaia positions is 057, which we use as our positional error. With this improved positional uncertainty, 2CXO J235749.7-323527 and the nucleus of NGC 7793 are excluded as counterparts to this new X-ray source since they lie 20 away (Figure 9). 2CXO J235749.7-323527 was not detected in this observation, however. Its reported flux was around the limiting flux of the new observation, which is the likely reason for the nondetection. There are also no other sources cataloged at other wavelengths within the Chandra error circle for Swift J235749.9-323526, with the exception of eight HSC sources (Whitmore et al. 2016), which we will discuss in Section 4.1.

Finally, due to the possibility that Swift J235749.9-323526 was a nuclear transient, we obtained radio follow-up of the source with the Very Large Array (VLA). The VLA observations were carried out on 2022 October 27 in the X band (8–12 GHz), in its C configuration. The angular resolution was 59 × 23, slightly larger than the nominal one due to the low declination of the source. The field of view included the entire host-galaxy structure. We did not detect radio emission at the position of the source obtained by Chandra, resulting in a 3σ upper limit of 18 μJy beam⁻¹. An emitting region is visible starting ∼3'' toward west from the transient position (Figure 9), with an angular size of about 13'' corresponding with optical emission from the nuclear star cluster (e.g., Carson et al. 2015; Mondal et al. 2021).

This X-ray source was first detected in a Swift/XRT observation taken on 2022 April 3 (obsID: 00096886002). The target of the Swift observation was M81, a Seyfert 2 galaxy. The enhanced position given by the online tool was 148.83625°, 69.06692° (=09^h55^m2070, +69° 04' 009), with an error radius of 32 (90% confidence), which appeared to place the source within the galaxy 11 from the nucleus (Figure 12). We will henceforth refer to this source as Swift J095520.7+690401. No X-ray source had been reported at this position previously, despite multiple Chandra, XMM-Newton, NuSTAR, and Swift observations, the last of which was by Swift 2 days prior to the new X-ray source being detected, albeit in a short (<200 s) observation.

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Since this source is close to the bright nucleus of M81, we do not use the automated online tool to generate the spectrum and lightcurve as for the other sources. This is to ensure that the nucleus is properly accounted for. We therefore download the observations and extracted events of the source using the heasoft v 6.25 tool xselect (Arnaud 1996). Source events were selected from a circular region with a 25'' radius centered on the above coordinates. Background events were also selected from a circular region with a 25'' radius placed at the same distance from the nucleus as the source in order to sample the point-spread function at its position. For each source spectrum, we constructed an auxiliary response file using xrtmkarf. The relevant response matrix file from the CALDB was used. All spectra were grouped with a minimum of one count per bin for spectral fitting purposes.

We start by simultaneously fitting the Swift/XRT spectra from the first 15 observations where the source was detected. We fitted the spectra with an absorbed power-law model with a constant applied to account for the variability of the source from observation to observation. This yielded W = 78.24 with 94 DoFs, where N_H < 5.2 × 10²¹ cm⁻² and ${\rm{\Gamma }}={2.0}_{-0.6}^{+1.9}$. To produce the lightcurve, we stack the individual observations in time bins of 10 days using the tool addascaspec and again group the stacked spectra with a minimum of one count per bin. We then fit these with the above model, where N_H and Γ are frozen. We plot the flux and implied luminosity in Figure 13.

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We also obtained a Chandra DDT observation of the source, which took place on 2022 June 4 (obsID: 24621), with ACIS-S at the aimpoint in FAINT mode. The source was well detected, with a count rate of 3.89 × 10⁻² counts s⁻¹ in the 10 ks exposure. We extracted the Chandra spectrum with specextract from a circular region of radius 20 for the source and an annulus radii of 25 and 12'' for the background. The spectra were grouped with a minimum of one count per bin with the tool grppha. We fitted the spectrum with an absorbed power-law model as done for the Swift/XRT data, which yielded W = 27.66 with 35 DoFs, where N_H < 2.8 × 10²² cm⁻² and ${\rm{\Gamma }}={4.6}_{-2.6}^{+3.5}$, consistent with Swift/XRT, albeit with large uncertainties. If we fit the stacked Swift/XRT data and the Chandra data together, we find W = 109.49 with 128 DoFs, where N_H < 6.8 × 10²¹ cm⁻² and ${\rm{\Gamma }}={2.6}_{-1.1}^{+1.6}$. We show these spectra in Figure 14.

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A diskbb model in place of the powerlaw one produced a worsened fit with ΔC = 10, where N_H < 5 × 10²⁰ cm⁻² and ${T}_{\mathrm{in}}={1.03}_{-0.16}^{+0.18}$ with a normalization, $N={1.17}_{-0.52}^{+1.20}\times {10}^{-2}$. The normalization corresponds to R_in = 40 km, which is the innermost stable orbit of a 5 M_⊙ black hole when assuming a face-on disk. We note that the luminosity estimate would be a factor of 1.8 lower if this model is assumed and integrated over all energies.

The deepest upper limit on the flux of Swift J095520.7+690401 prior to its detection with Swift/XRT is from Chandra observations, which have a sensitivity of 9.8 × 10⁻¹⁶ erg cm⁻² s⁻¹ in the 0.5–8 keV band listed in CSC2. This is 3 orders of magnitude lower than the flux measured above. The deepest upper limit from XMM-Newton observations is <1.7 × 10⁻¹² erg cm⁻² s⁻¹ in the 0.2–12 keV band listed in XSA and is from a slew.

We also used the Chandra data to acquire a more precise position for Swift J095520.7+690401 in the same way as was done for Swift J130456.1-493158 and Swift J235749.9-323526, which produced nine Chandra/Gaia-matched sources. The astrometric shifts were δR.A. = −085 and δdecl. = −075. After subtracting these shifts, the corrected position is R.A. = 09^h55^m20873 (14883697), decl. = +69° 04' 0253 (+6906737, J2000), which lies toward the edge of the Swift error circle. The mean residual offset between the corrected Chandra positions and the Gaia positions is 033, which we use as our positional error. There are no sources cataloged at other wavelengths within the Chandra error circle, with the exception of three HSC sources (Whitmore et al. 2016), which we will discuss in Section 4.1.

If these transient X-ray sources are within our Galaxy, the implied peak luminosities would be ∼10³³ erg s⁻¹ if assuming a distance of 10 kpc. On the timescale–luminosity plot of Polzin et al. (2022) the source types most consistent with this luminosity and timescales of 10² days are classical/dwarf novae; however, novae are usually accompanied by optical/UV emission (e.g., Page et al. 2020). This luminosity is comparable to X-ray flares from stars, but the X-ray activity lasted much longer than typical stellar flares, which are not normally longer than a few hours (e.g., Pye et al. 2015). Furthermore, the lack of any stellar counterpart at other wavelengths, particularly in the HST observations of 2SXPS J235825.7-323609, make the association with a star in our Galaxy unlikely. These HST observations contained sources down to m_F814W ∼ 26, which when applying a distance modulus of 15 corresponding to 10 kpc implies M_F814W ∼ 11. This does not rule out a white dwarf or cool main-sequence star, however.

With the exceptions of Swift J235749.9-323526 and Swift J095520.7+690401, which appear to be in the disks of NGC 7793 and M81, respectively, and therefore not likely to be in the background of these galaxies, the other sources may be in the background of the galaxy they appear to be associated with. If so, their timescales and fluxes compare well with TDEs (e.g., Auchettl et al. 2017). Assuming a typical TDE X-ray luminosity of 10⁴⁴ erg s⁻¹, this puts the sources at z ∼ 0.1. At this distance, all known TDE host galaxies (e.g., French et al. 2020) have a V-band magnitude of 17.5–21.5. The HST observation of 2SXPS J235825.7-323609 would have detected a background galaxy where the F606W (wide V-band) observations reach m_F606W ∼ 26. Furthermore, TDEs are usually also bright in the optical/UV, so the lack of a UVOT counterpart also argues against a TDE. Gamma-ray bursts also have much shorter timescales than these X-ray transients, of the order of hours (e.g., Tarnopolski 2015). The afterglows of gamma-ray bursts are longer, but are usually accompanied by emission at other wavelengths.

As mentioned in Section 2, HST has observed the regions of 2SXPS J235825.7-323609, Swift J095520.7+690401, and Swift J235749.9-323526. 2SXPS J235825.7-323609, which is in the outskirts of NGC 7793, was observed as part of the GHOSTS survey (Radburn-Smith et al. 2011) with the ACS and F606W and F814W filters. While none of the sources detected in these observations are within the X-ray positional uncertainty region, several are nearby, the properties of which may yield clues as to the environment of the source. The position of the X-ray source is 76 from the center of NGC 7793, which implies a projected distance of 8.4 kpc, assuming a distance of 3.8 Mpc to the galaxy (Figure 6). The HST observations were all taken many years before the X-ray transients, so the photometry is unlikely to be contaminated by the accretion disks.

In Figure 15 we present color–magnitude diagrams (CMDs) with all stars in the vicinity of the ULX plotted in the black histogram in the background. The green star (or green arrows) on each CMD indicates the star closest to the ULX source position and the blue squares indicate stars within the positional error circle (with the exception of 2SXPS J235825.7-323609, where we show the stars within 10''). Some stars had nondetections in the HST filters we plot here, and these nondetections are indicated with arrows. In the middle panel, we have two stars plotted with nondetections. The green arrows indicate a star that was not detected in either band plotted, and the star plotted with a horizontal arrow was detected in the F814W band but not the F606W band.

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We include isochrones from the Padova stellar models (Marigo et al. 2008, 2017; Bressan et al. 2012) at different ages, which are listed in the figure legend. The purple lines represent isochrones of various ages with no dust extinction applied (A_V = 0.0), and the orange lines represent isochrones with 1 magnitude of dust extinction (A_V ) applied using the reddening coefficients from Schlafly & Finkbeiner (2011) in the HST filters presented in each CMD.

For 2SXPS J235825.7-323609 the closest stars lie on the red giant branch (RGB) of the CMD described in Radburn-Smith et al. (2011). The closest source falls in a region identified by Radburn-Smith et al. (2012) as belonging to old RGB stars with ages of 1–10 Gyr. Our isochrones imply they could be 100–300 Myr or 1–30 Myr with 1 A_V of extinction. The case is similar for Swift J095520.7+690401. For Swift J235749.9-323526, the closest star lies on the main sequence with an age of 1–10 Myr. The other stars within the positional error circle may have ages of up to 30 Myr.

While other transient ULXs have previously been presented in the literature, many, if not all, of these sources were discovered serendipitously, and not in real time. As far as we know, this is the first study to carry out a systematic search for transient ULXs outside of our Galaxy in real time, allowing us to conduct a more detailed study with follow-up observations, such as with Swift to get well-sampled lightcurves, Chandra to obtain more precise positions, and NuSTAR to obtain a broadband spectrum.

We have reported on two transient ULXs in NGC 4945. However, two other transient X-ray sources, Suzaku J1305-4931 and Suzaku J1305-4930, with ULX or close-to-ULX luminosities were reported by Isobe et al. (2008) and Ide et al. (2020) from Suzaku observations of the galaxy. The sources were detected at positions of 13^h05^m055, −49° 31'' 39'' and 13^h05^m170, −49° 30' 15'', respectively. Suzaku J1305-4931 was active in 2006 January and Suzaku J1305-4930 was active in 2010 July, and lasted less than 6 months. Both Suzaku sources were close to our Swift/XRT sources (∼1' from either), but closer to the plane of the galaxy.

In addition to 2SXPS J235825.7-323609 and Swift J235749.9-323526 in NGC 7793, Quintin et al. (2021) reported the discovery of another transient ULX in that galaxy found while looking for long-term variability of XMM-Newton sources in the 4XMM Data Release 9 catalog. The source, which they name NGC 7793 ULX-4, was active for 8 months from 2012 May–November. The ULX had a position of 23^h57^m479–32° 34' 57'', which is close to the center of the galaxy, ∼8' from 2SXPS J235825.7-323609, and ∼40'' from Swift J235749.9-323526. They also reported a pulsation signal at 2.52 Hz from the XMM-Newton data, making it the second ULX pulsar in that galaxy.

Examples of other transient ULXs presented in the literature are ones in M31 (Middleton et al. 2012, 2013), M51 (Brightman et al. 2020), M83 (Soria et al. 2012), M86 (van Haaften et al. 2019), NGC 55 (Robba et al. 2022), NGC 300 (Carpano et al. 2018), NGC 821 (Dage et al. 2021), NGC 925 (Earnshaw et al. 2020), NGC 1365 (Soria et al. 2007), NGC 3628 (Strickland et al. 2001), NGC 4157 (Dage et al. 2021), NGC 5907 (Pintore et al. 2018), NGC 6946 (Earnshaw et al. 2019a), and NGC 7090 (Liu et al. 2019; Walton et al.2021).

One of the best-studied transient ULXs is NGC 300 ULX1, which was classified as a supernova imposter in 2010, with an observed X-ray luminosity of 5 × 10³⁸ erg s⁻¹ (Binder et al. 2011). The source was observed at lower fluxes in observations made in 2014 (Binder et al. 2016) but then reached ULX luminosities during observations made in 2016 with L_X ∼ 5 × 10³⁹ erg s⁻¹ during which pulsations were detected (Carpano et al. 2018), identifying it as a ULX pulsar powered by a NS. Regular Swift monitoring of the source in 2018 revealed that the source initially persisted at these luminosities but then went into decline. Spectral analysis showed a hard spectrum.

Another source, Swift J0243.6+6124, was an X-ray transient found in our own Galaxy, identified by Swift/BAT (Cenko et al. 2017) and with no previously reported activity. The source reached an X-ray luminosity of 2 × 10³⁹ erg s⁻¹ in a period of around 30 days, before steadily declining over a period of ∼100 days (Wilson-Hodge et al. 2018). The detection of pulsations also identified it as a NS accretor (Kennea et al. 2017), and Kong et al. (2022) reported the detection of a cyclotron resonance scattering feature at 146 keV with the Hard X-ray Modulation Telescope, allowing for the estimation of the magnetic field strength to be ∼1.6 × 10¹³ G. The source exhibited rebrightenings in the X-ray after the decline, albeit to peak luminosities around 2 orders of magnitude less than the initial outburst (van den Eijnden et al. 2019). The companion star is a known Be type.

RX J0209.6-7427 is a Be XRB in the SMC and also briefly became a ULX pulsar in 2019 (Chandra et al. 2020; Coe et al. 2020; Vasilopoulos et al. 2020). The spin period was 9.3 s and reached a luminosity of 1–2 × 10³⁹ erg s⁻¹, similar to the super-Eddington outburst of SMC X-3 (Tsygankov et al. 2017). Karino (2022) discussed the possibility that a large number of ULXs are formed of Be high-mass XRBs.

We also note that the peak luminosities of these sources, disk temperatures, and implied inner-disk radii are similar to the brightest outbursts from Galactic XRBs such as GRO J1655-40, GX 339-4, and XTE J1550-564 when considering fits with the disk model.

As described above, many well-known ULX transients are Be XRBs in outburst, therefore it is reasonable to ask if these new systems are also Be XRBs. The peak luminosities of 2–3 × 10³⁹ erg s⁻¹ are consistent with the Type II outbursts from these sources; however, Be XRBs typically have longer rise times, up to 50 days from detection to peak, whereas our ULX transients have rise times of 10 days or less where the the lightcurves are well sampled (Reig & Nespoli 2013). Furthermore, Be stars are young and massive, at odds with the older stellar population that 2SXPS J235825.7-323609 and Swift J095520.7+690401 are found in. For Swift J235749.9-323526, the potential stellar counterparts are young and massive, therefore we cannot rule out a Be star in this case.

A model was presented in Hameury & Lasota (2020) to explain the transient ULX phenomenon with a disk-instability model, previously used to explain dwarf novae and other X-ray transients. There, the super-Eddington outbursts can be explained by thermal-viscous instabilities in large unstable disks with outer radii greater than 10⁷ km. They showed that this model can successfully reproduce the lightcurve of the transient ULX M51 XT-1 presented in Brightman et al. (2020), with derived accretion rates of 6–15 × 10¹⁹ g s⁻¹ depending on the mass of the accretor.

We fit the observed transient ULX lightcurves using these models. Hameury & Lasota (2020) provides analytical formulas that accurately approximate the observable properties of the outbursts. According to this model, the accretion disk in outburst is brought into a fully hot state, then the disk mass decreases until the surface density at the outer edge of the disk becomes inferior to the critical value below which quasi-stationary hot states can no longer exist. This results in a cooling wave, propagating into the disk from its outer edge, bringing the whole disk back into a low state. When the disk is fully in the hot state, it is close to steady state, with a mass-accretion rate that is constant with radius and larger than the mass transfer rate from the secondary. Hameury & Lasota (2020), following Ritter & King (2001; see also Lipunova & Shakura 2000) have shown that during this phase the accretion rate does not decrease exponentially, but according to

$$\begin{eqnarray}&&\dot{M}={\dot{M}}_{\max }{\left[1+\displaystyle \frac{t}{{t}_{0}}\right]}^{-10/3},\end{eqnarray} \tag{ 1 }$$

where $\dot{M}={\dot{M}}_{\max }$ is the initial mass-accretion rate and t₀ is a characteristic timescale, which depends on ${\dot{M}}_{\max }$ and the disk parameters (size, viscosity):

$$\begin{eqnarray}&&{t}_{0}=3.19{\alpha }_{0.2}^{-4/5}{M}_{1}^{1/4}{r}_{12}^{5/4}{\dot{M}}_{\max ,19}^{-3/10}\ \mathrm{yr},\end{eqnarray} \tag{ 2 }$$

where ${\dot{M}}_{\max ,19}$ is ${\dot{M}}_{\max }$ measured in units of 10¹⁹ g s⁻¹, r₁₂ is the disk size in units of 10¹² cm, M₁ the accretor mass in solar units, and α_0.2 the Shakura–Sunyaev viscosity parameter normalized to 0.2. Therefore, for given binary parameters and disk viscosity, the initial time evolution of the disk depends only on one free parameter, the initial accretion rate. Conversely, the determination of t₀ from observations (at time t = t₀, the mass-accretion rate is one-tenth of its initial value) enables one to determine the disk size. This phase lasts until the accretion rate falls below the critical rate, ${M}_{\mathrm{crit}}^{+}$, at which the hot solution can no longer exist at the outer radius. Using Equations (1) and (2) and the fits for ${M}_{\mathrm{crit}}^{+}$ provided by Hameury & Lasota (2020) in their Equation (9), one finds that the duration of this phase is

$$\begin{eqnarray}&&{\rm{\Delta }}{t}_{1}={t}_{0}[1.38{t}_{0}^{-0.50}{M}_{1}^{0.25}{\dot{M}}_{19,\max }^{0.15}{f}_{\mathrm{irr}}^{0.15}{\alpha }_{0.2}^{-0.4}-1],\end{eqnarray} \tag{ 3 }$$

and is followed by a rapid decay phase during which the accretion rate drops steeply; the duration of this final phase is

$$\begin{eqnarray}&&{\rm{\Delta }}{t}_{2}=0.74\ {M}_{1}^{0.37}{f}_{\mathrm{irr}}^{0.15}{\alpha }_{0.2}^{-0.8}{r}_{12}^{0.62}\ \mathrm{yr},\end{eqnarray} \tag{ 4 }$$

where f_irr ∼ 1 is a parameter describing the effect of irradiation on the disk.

The above equations describe the time evolution of the mass-accretion rate as a function of only four parameters: the initial (i.e., peak) mass-accretion rate, t₀, M₁, and α_0.2, to which one could add f_irr, which enters only via ${f}_{\mathrm{irr}}^{0.15}$. The parameters Ψ and ξ, as defined in Hameury & Lasota (2020), were taken to be equal to 1.3 and 6.3, respectively, since, as discussed in Hameury & Lasota (2020), these values provide the best agreement between the numerical results and their analytical approximations. Ψ accounts for deviations of the opacities from the Kramers' law and ξ is the ratio between the rate at which the inner, hot disk mass decreases and the accretion rate at the inner edge; it is larger than unity because of the strong mass outflow at the cooling front.

In order to compare the model predictions with observations, one must convert mass-accretion rates into luminosities; we used ${L}_{{\rm{X}}}=(1+\mathrm{ln}\dot{m})[1+{\dot{m}}^{2}/b]{L}_{\mathrm{Edd}}$ for luminosities larger than the Eddington value, where b is a constant which differs from, but is related to, the beaming parameter (see King 2009). This relation differs somewhat from the formula derived by King (2009), valid only for strong beaming; we modified it in order to account for a smooth transition with the case where beaming is negligible, as explained in Hameury & Lasota (2020).

If the final decay is not observed, one cannot determine the viscosity parameter, since the disk radius, which enters Equation (2), is not known a priori. One can nevertheless obtain upper limits on α_0.2 because the observed duration of the outbursts sets a lower limit on Δt₁. Moreover, one expects significant degeneracies between t₀, ${\dot{M}}_{\max }$, and M₁ when the lightcurve does not deviate much from an exponential (i.e., when t never becomes larger than t₀), which is defined by two parameters only. On the other hand, useful constraints can be obtained when the final decay is observed and therefore the duration of the hot phase is measured. Because of the rapid drop off during the final decay, one does not expect to get significant constraints from the shape of this phase, but one at least gets a determination of Δt₁, and some constraint, usually in the form of an upper limit, on Δt₂. This basically sets three strong constraints on four parameters, implying that degeneracies should still exist that preclude the simultaneous determination of M₁ and α_0.2, unless observational uncertainties are very low.

Table 1 shows the results of the fitting procedure, both when using the powerlaw model to convert from count rate to flux and the diskbb model. As expected, the viscosity parameter α can be determined only when the final decay has been observed, i.e., in the case of 2SXPS J235825.7-323609 and Swift J130511.5-422933. In this case, the value of α we obtain is large, and typically much larger than the value α ∼ 0.1–0.2 determined when fitting the lightcurves of cataclysmic variables (Smak 1999; Kotko & Lasota 2012). This should not come as a surprise, since Tetarenko et al. (2018b) found that much larger values of α, in the range 0.2–1, are obtained when considering low-mass XRBs; they attributed this large value of the viscosity parameter to the existence of strong winds in these systems that carry away matter and also angular momentum. We take b = 73, as in King (2009), but because of the relatively large size of the error bars the fits are not sensitive to the value of the beaming parameter. For M51 XT-1, with two data points with relatively small error bars, Hameury & Lasota (2020) were able to exclude b = 20, but found that b = 200 gave an acceptable fit.

Table 1. Fits of the Outburst Lightcurves

		powerlaw Model				diskbb Model
Source Name	M1	t0	${\dot{M}}_{\max }/{\dot{M}}_{\mathrm{Edd}}$	α	χ2/DOF	t0	${\dot{M}}_{\max }/{\dot{M}}_{\mathrm{Edd}}$	α	χ2/DOF
		(days)				(days)
Swift J130456.1-493158	1.4	159.8	18.67	<1.4	0.90/6	78.4	8.97	<1	0.61/6
	10	74.9	4.23	<7	0.86/6	96.0	0.89	<3	0.79/6
Swift J130511.5-422933	1.4	395.2	20.89	0.37	19.06/21	309.6	14.93	0.33	15.55/21
	10	164.2	5.33	1.39	18.52/21	199.3	2.20	1.06	18.51/21
2SXPS J235825.7-323609	1.4	365.0	13.75	0.35	15.78/12	271.6	10.07	0.33	12.34/12
	10	335.3	1.56	1.06	18.02/12	322.9	0.96	0.90	16.63/12
Swift J235749.9-323526	1.4	216.4	19.49	<1	10.71/11	184.9	15.67	<0.9	9.62/12
	10	89.4	4.72	<6	14.72/11	102.5	2.45	<4	14.60/12
Swift J095520.7+690401	1.4	61.6	9.98	<0.5	4.59/5	65.6	4.83	<0.4	5.80/5
	10	81.2	0.90	<1.5	5.36/5	81.2	0.49	<1	5.36/5

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We also note that, again as expected, the primary mass cannot be determined from fitting the observed lightcurves. The fits are equally good for NSs and for 10 M_⊙ black hole accretors. The only difference is that the lower the M₁, the shorter the duration Δt₁ of the main outburst phase, and long outbursts may require unrealistically low values of α in the NS case.

The maximum accretion rate is in all cases is close to or larger than the Eddington limit, except in the case of Swift J095520.7+690401 for large primary masses.

The fit quality, as measured by the χ² compared to the number of degrees of freedom, is quite good in all cases, except for 2SXPS J235825.7-323609. The reason for this is the existence of a low data point at t ∼ 50 days, and, to a lesser extent, a slightly steeper final decay than predicted by the model. Although the χ² value is good for Swift J130511.5-422933, the observed drop between t = 250 days and t = 284 days is too sharp to be accounted for by the model. The detection at t ∼ 284 days is somewhat marginal, and the estimate of the X-ray luminosity becomes questionable because of uncertainties in the spectral model; it is, however, unlikely that the current model can reproduce the sharp cutoff observed in this source. This would mean mean that the cooling front propagates faster than expected when the propagation is controlled by irradiation with a constant efficiency. Dropping this hypothesis might solve this problem, at the expense of a new and uncontrolled parameter; given other oversimplifying assumptions of the model, notably about winds, this would be of limited interest. One should note that similar problems are encountered when modeling outbursts of sub-Eddington X-ray transients (Tetarenko et al. 2018a). Although the χ² value is also good for Swift J235749.9-323526, the model does not reproduce what appears to be a plateau or rebrightening at t ∼ 50 days, which is unlikely due to changes in the accretion disk. The short drop at t ∼ 10 days is also not accounted for by the model, and the NuSTAR data point has not been included in the fit. We show the fits to all sources in Figure 16.

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We summarize the properties of the sources in Table 2. We find that the average N_H = 5.7 × 10²¹ cm⁻², with a standard deviation of 3.8 × 10²¹ cm⁻². The average Γ is 2.3, with a standard deviation of 0.4. This is consistent within the standard deviations of the sample of persistent sources from Gladstone et al. (2009), where the average N_H = 2.8 × 10²¹ cm⁻² with a standard deviation of 1.7 × 10²¹ cm⁻² and the average Γ is 2.3 with a standard deviation of 0.5. Therefore, we do not see any significant spectral differences between our transient sources and their persistent counterparts. For Swift J235749.9-323526, where we obtain NuSTAR data to extend the spectral coverage to higher energies, the diskpbb model was preferred over the power-law one, typical of ULX spectra as shown by Walton et al. (2018b). Again, the parameters of this model were consistent with those seen in the persistent sources.

Table 2. Summary of Source Properties

Source Name	Host Galaxy	Best Position	Decl.	Uncertainty	NH	Γ	LX (peak)
		R.A. (deg)	(deg)	('')	(cm−2)		(erg s−1)
Swift J130456.1-493158	NGC 4945	196.23479	−49.53324	0.53	${1.1}_{-0.4}^{+0.5}\times {10}^{22}$	${2.8}_{-0.5}^{+0.6}$	2 × 1039
Swift J130511.5-492933	NGC 4945	196.2985	−49.4928	2.4	${6.7}_{-1.7}^{+2.1}\times {10}^{21}$	2.2 ± 0.3	2 × 1039
2SXPS J235825.7-323609	NGC 7793	359.60828	−32.60291	1.0	${2.0}_{-1.0}^{+1.2}\times {10}^{21}$	2.0 ± 0.3	3 × 1039
Swift J235749.9-323526	NGC 7793	359.45793	−32.59110	0.57	${2.1}_{-0.8}^{+0.9}\times {10}^{21}$	2.0 ± 0.3	3 × 1039
Swift J095520.7+690401	M81	148.83697	+69.06737	0.33	<6.8 × 1021	${2.6}_{-1.1}^{+1.6}$	2 × 1039

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We have found that two of our sources appear to lie in a population of old RGB stars. Interestingly, Wiktorowicz et al. (2017) predicted that the majority of NS ULXs have low-mass (<1.5 M_⊙), red-giant donors. According to Wiktorowicz et al. (2017), red-giant donor NS ULXs form at late times, and start with the primary becoming an oxygen-neon white dwarf. When the secondary becomes a red giant and fills its Roche lobe, the primary accretes additional mass and forms a NS due to an accretion-induced collapse (AIC). Following this, the red giant refills its Roche lobe and a short (0.1 < Δt < 0.2 Myr) ULX phase occurs. We have not unambiguously identified the donor stars of these sources as red giants, and neither do we know they are NSs, but these properties do match well, albeit the timescales are much shorter than suggested by Wiktorowicz et al. (2017).

It has been suggested that fast radio bursts (FRBs) may be associated with ULXs (Sridhar et al. 2021). In this model, the accreting compact object is a black hole or a nonmagnetar NS, as in King (2009). One FRB with an intriguing similarity to our transient ULXs is FRB 20200120E, which was found in the outskirts of M81 (Bhardwaj et al. 2021). The FRB was localized to a globular cluster with an old stellar population, which challenged the magnetar models that invoke young magnetars formed in a core-collapse supernova but would be consistent with the Sridhar et al. (2021) scenario. The AIC of a white dwarf was also suggested as a possible formation channel (Kirsten et al. 2022). However, to date, no FRB has been reported at the position of a ULX.

In addition to the five transient ULXs we have presented here, three further transient ULXs were serendipitously discovered in the same galaxies from previous observations, implying that the rates of these sources is potentially high. While our sample of five sources is small, we next attempt to estimate the rates of transient ULXs in these galaxies, and compare these to their persistent counterparts.

For NGC 4945, we found two transient ULXs in searches of observations over 3.0 yr from 2019 December to 2022 December, implying a rate of 0.7 ± 0.5 yr⁻¹. Using the same technique to identify the transient sources, and in the same period, we found four persistent sources classified as ULXs identified in SIMBAD as [CHP2004] J130518.5-492824, [BWC2008] U31, [CHP2004] J130521.2-492741, and [BWC2008] U32.

For NGC 7793, we found two transient ULXs in searches of observations over 5.0 yr from 2017 December to 2022 December, implying a rate of 0.4 ± 0.3 yr⁻¹. In the same period, we found two persistent sources classified as ULXs, P9 and P13.

For M81, we found one transient ULX in searches of observations over 9 months from 2022 April to 2022 December, implying a rate of 1.3 yr⁻¹. In the same period, we found one persistent source classified as a ULX, [LB2005] NGC 3031 ULX2.

If we compare the number of transient ULXs in any one snapshot to the number of persistent ULXs, as would be done when computing the X-ray luminosity function of a galaxy (e.g., Lehmer et al. 2019), the persistent sources would dominate the high end. However, if we take the total number of sources that have exceeded 10³⁹ erg s⁻¹ over the time period of our searches, the transient ULX numbers roughly equal those of the persistent ones. Further, if we integrate the derived transient ULX rates over the timescales in which the persistent source have been detected, several decades, then the transient ULX numbers would dominate the persistent ones. In other words, the number of systems that exhibit ULX luminosities in each of these galaxies is dominated by transient rather than persistent sources.

Since we have only considered galaxies where a transient ULX has been identified in our searches, we cannot extend this conclusion to all galaxies. The rates are also biased by the Swift targeting and our incomplete search of observations. A more systematic search using eROSITA data could reveal the true rate. However, we note that the 6 months scanning pattern of eROSITA means some of the sources we identified can be missed.

While the duration of the transient sources studied here is well determined, the duration of the persistent sources is not well known. However, evidence points to their far longer duration. For example, the collisionally ionized bubbles surrounding Holmberg IX X-1, NGC 1313 X-1 and X-2, NGC 7793 S26, and NGC 5585 ULX have estimated dynamical ages of ∼10⁵ yr (Pakull & Mirioni 2002; Pakull et al. 2010; Moon et al. 2011; Weng et al. 2014; Soria et al. 2021; Gúrpide et al. 2022).