A Possible 250 s X-Ray Quasi-periodicity in the Fast Blue Optical Transient AT2018cow

Recent optical time-domain surveys have discovered a new population of fast-rising blue optical transients (FBOTs). These objects are characterized by rapid rise to their peak brightness within ≲10 days and blue colors (g − r < − 0.2) near the peak, followed by fading away of emission within ≲100 days (Drout et al. 2014; Pursiainen et al. 2018; Ho et al. 2021). AT2018cow is one of the most extreme FBOTs, hosted in the dwarf spiral galaxy CGCG 137-068 at a luminosity distance of 66 Mpc (z = 0.0141, Prentice et al. 2018). After its discovery by the ATLAS survey on 2018 June 16, AT2018cow received prompt and extensive multi-wavelength observations spanning from radio to γ-rays (Rivera Sandoval et al. 2018; Ho et al. 2019; Kuin et al. 2019; Margutti et al. 2019; Perley et al. 2019; Roychowdhury et al. 2019; Mohan et al. 2020; Sun et al. 2022; Huang et al. 2019), confirming it to be the brightest FBOT known so far with a peak bolometric luminosity of 4 × 10⁴⁴ erg s⁻¹, that is located outside the nucleus of the host galaxy with a positional offset of 1.7 kpc. At the explosion site of AT2018cow, a young star population in a dense gas environment was inferred, indicating active star formation (Morokuma-Matsui et al. 2019; Lyman et al. 2020). Despite its physical origin remaining controversial, the multi-wavelength analysis, especially in the X-ray bands, indicates that AT2018cow could be powered by a compact object (Margutti et al. 2019), either a newly formed stellar-mass black hole (BH) or neutron star in a supernova, or tidal disruption of a star by an intermediate-mass black hole (IMBH, a few 10⁴–10⁵ solar masses) (Kuin et al. 2019; Perley et al. 2019). The detection of 4.4 ms quasi-periodic oscillation (QPO) from NICER observations argues further for the presence of a compact object in AT2018cow (Pasham et al. 2021), but the study is limited to only the soft X-ray band (0.25–2.5 keV) because of the high background contamination beyond ∼2.5 keV. It is still not conclusive whether the compact object is a neutron star or a BH powering AT2018cow.

In this paper, we report the detection of a possible X-ray QPO signal at 4.07 ± 0.39 mHz from XMM-Newton and Swift observations of AT2018cow when its X-ray emission is in the relatively bright phase (L_{0.3–10 keV} ≳ 10⁴² erg s⁻¹). We also propose a model with the tidal disruption by an IMBH with mass of ∼10⁴ M_⊙ to explain the unusual X-ray light curve of AT2018cow. In Section 2, we describe the observations and data reduction. Section 3 presents the detailed timing analysis and results. Possible origins of the QPO at ∼4.1 mHz and its implications on the central engine of AT2018cow are discussed in Section 4.

AT2018cow has been observed by XMM-Newton on three epochs, about 37, 82, and 218 days after the optical discovery. However, only the data from the first XMM-Newton observation have enough photons for detailed timing analysis. We used principally the data from the EPIC PN camera, which have a much higher sensitivity. We processed data using Science Analysis Software version 17.0.0, with the latest calibration files. We extracted the event files from a circular region with a 35'' radius centered on the source position from optical observations (R.A.: 16^h16^m0022, decl.: +22°16'048, Prentice et al. 2018) and the background was extracted from four source-free circular regions with 35'' radius near the source position. Both the source spectrum and light curve in the energy range of 0.3–10 keV were selected, and only the good events with PATTERN ≤ 4 were used in generating the light curve. Then we utilized the epiclccorr tool to correct the light curve for instrumental effects. By examining the background light curve, we found that background flares were present at the beginning of the observation. We ignored the first ∼3 ks to remove the time interval that may be affected by the high particle background, resulting in a net exposure of ∼27 ks. We assessed the extent of photon pile-up utilizing the SAS task epatplot, and found that such an effect is negligible.

AT2018cow was also intensively observed by Swift-XRT covering a period of t = 3–70 days since the optical discovery. ⁷ Totally there are 95 individual Swift-XRT observations in which AT2018cow is detected, which provide critical constraints on the long-term evolution of its X-ray emission. For Swift-XRT data, we executed the task xrtpipline to generate the event files, and then used XSELECT in HEASoft to extract the source spectrum in a circular region with a radius of 40'', and the background spectrum in an annulus with an inner radius of 60'' and outer radius of 110''. All spectra were extracted in the energy of 0.3–10 keV. The light curves were corrected for bad time intervals using the task xrtlccorr and the background was subtracted by applying the standard FTool lcmath. Owing to a few counts in individual observations, we cannot derive the source's flux through spectral fittings. We used the WebPIMMS tool to convert the Swift-XRT count rates to flux by assuming an absorbed power-law model (Margutti et al. 2019) with photon index Γ = 1.6 modified by a Galactic HI column density of N_H = 0.05 × 10²² cm⁻².

The PN light curve was rebinned to have a time binsize of 10 s. Given the mean count rate of 0.62 cts s⁻¹, this ensures that there are enough photons in each time bin for meaningful timing analysis. We then Fourier transformed the light curve into a power density spectrum (PDS) which was normalized by the Leahy method (Leahy et al. 1983) to have a mean Poisson noise level of 2. The Leahy-normalized PDS was then rebinned by a factor of 21, which gives a frequency resolution of ∼0.8 mHz. Figure 1 (left panel) depicts the resulting PDS, which reveals an apparent QPO component at a frequency of 4.07 ± 0.39 mHz, corresponding to a period of 246 s. We repeated the above analysis by changing the size and position of both source and background extraction areas, and found that the PDS is basically unchanged. In addition, we also checked the PDS of the background light curve and found that there is no QPO signal, so we excluded the possibility that the QPO signal at 4.07 mHz comes from background fluctuations. Furthermore, we checked that the power value (ξ_obs = 4.2) at the frequency of ∼4.1 mHz does not change if the PDS was constructed from the light curve with smaller time binsizes (<10 s). The QPO signal appears to be present over the entire energy band of our interest (0.3–10 keV), as its power increases gradually if more photons at higher energies are included (Figure A1 in Appendix). However, if focusing on only the hard X-ray bands at >2 keV, the QPO feature disappears, suggesting that the signal is dominated by photons at soft bands.

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In order to confirm the QPO detected in the XMM-Newton data, we also performed PDS analysis for data taken from Swift-XRT because its effective energy band is similar to that of XMM-Newton. Due to the individual Swift-XRT observations being short and most having an exposure less than 1 ks, we selected the observations with continuously effective exposure time of >1.25 ks and count rates >0.1 cts s⁻¹ to ensure enough counts for timing analysis. This results in a total of 13 useful light curves (Table B1 in Appendix). We further restricted all individual light curve segments to have the same exposure of 1.25 ks for stacking the PDS. The reason to choose the length of 1.25 ks is to ensure that the frequency width of PDS (1/1250 s) is close to that of PN (21/27000 s). Since most of the usable Swift-XRT observations have a length of 1.3–2 ks, we uniformly chose the initial 1.25 ks in each light curve. This will help to avoid the effect of arbitrarily selected light curve segments that may cause false signals in the PDS. Note that we split one light curve that has enough exposure length (2.8 ks) into two 1.25 ks segments. The light curve segments were rebinned to have a time binsize of 10 s, resulting in at least 1 count per bin, which is sufficient for a reliable timing analysis. By stacking the PDS from totally 13 individual light curve segments, each with 1.25 ks, we extracted an average PDS for the Swift-XRT data. The Leahy-normalized PDS is displayed in Figure 1 (right panel) where an obvious feature is observed at 4.0 ± 0.4 mHz, which is consistent with the QPO frequency obtained with the XMM-Newton data within errors. Note that the Leahy-normalized PDS was produced without weighting by flux for the Swift-XRT data, as it is not clear whether there is a strong dependence of QPO strength on the X-ray flux.

We also used the light curve analysis tool efold in HEASoft to fold the PN light curve with the period of 246 s, which is shown in Figure 2. The fractional root mean square (rms) amplitude calculated by the folded light curve is 6.0% ± 1.3%. The light curves from individual Swift observations do not have enough signal-to-noise ratio values to perform the folded analysis. Therefore, we did not estimate the QPO rms amplitude for the Swift data.

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To estimate the statistical significance of the QPO detected at ∼4.1 mHz which depends on the underlying distribution of the noise powers, an important question is to test whether the noise at other frequencies (except for the frequency where the QPO is located) in the PDS is consistent with white noise which is relatively flat, or red noise whose strength depends on frequency. A direct way to distinguish the type of noise is to examine whether the noise powers are χ² distributed as expected for white noise. We removed the three frequency bins centered at 4.1 mHz, and generated a cumulative distribution function (CDF) of the powers at all other frequencies. We then compared it with a χ² distribution (with 2 × 21 degrees of freedom, d.o.f.) scaled by a factor of 1/21, where the number 21 is the factor by which the PDS was rebinned, as displayed in Figure C1 in the Appendix. In addition, we also analyzed the probability density distribution of these powers and compared it with the expected values from a χ² distribution. Both tests yield consistent results that the powers of the noise can be described with a χ² distribution, i.e., dominated by white noise. For the Swift PDS, we also tested that the noise powers are χ² distributed (Figure C1 in the Appendix). Therefore, for the white noise distribution of the underlying continuum in the PDS, the significance of the QPO at ∼4.1 mHz can be analytically estimated using the χ² distribution. For the XMM-Newton data, we found that the probability to observe a power value larger than measured (ξ_obs = 4.2) is P (>21ξ_obs; d.o.f.) = 3.9 × 10⁻⁵ = p₁. By taking into account the search for all frequency bins over the range of interest (N = 64), the global significance is 1 − p₁ × N =99.75%. Similarly, for the Swift PDS, the probability to observe a power value larger than measured (ξ_obs = 4.18) is P (>13ξ_obs; d.o.f.) = 9.26 × 10⁻⁴ = p₂. The global confidence level for N = 62 frequency trials is 1 − p₂ × N = 94.26%.

The above assessment of noise distribution in the PDS is only qualitative. It is still possible that a weak or unknown red noise component is present in the data. To estimate the QPO significance by properly accounting for the underlying noise, we then employed a Monte Carlo approach, by generating a series of light curves following a given power spectral distribution (Uttley et al. 2002). We used the power-law plus constant model, P(f) = Nf^−α + C, to fit the unnormalized and unbinned PDS of XMM-Newton, where N is the normalization factor, α is the power-law index and C is a constant indicating the Poisson noise level. The power-law component was used to account for a possible effect of weak red noise on the simulation results. Using the maximum likelihood estimation method (Vaughan 2010), we first obtained the best fitting parameters, where N = −0.71, α = −1.1 × 10⁻⁵ and C =5.04. Then we utilized the best-fit PDS model to generate a series of simulated light curves (Timmer & Koenig 1995), which were resampled to have the same duration, mean count rate and variance as the real light curve. To eliminate the possible effect of red noise leakage at the edge of the light curve, we chose a length of 5 × 27,000 s which is five times longer than the real data. Then we intercepted the middle 27 ks as the final light curve for simulations. We repeated this process and obtained 100,000 simulated light curves. The same power spectral analysis on these simulated light curves was performed as we did on the real data, producing 100,000 simulated PDS.

With the 100,000 simulated PDS, we computed the significance level of a QPO peak by scanning all frequency bins below 0.05 Hz, the highest frequency in the PDS. We averaged the power of the 100,000 PDSs at each frequency bin and obtained the where i is ith number of bins (i = 1,...,n). For each simulated PDS, we divided the power value at each frequency by the average value at the corresponding frequency, and recorded the largest value as , yielding 100,000 at a given frequency. Averaging the power distribution has the advantage of eliminating the possible effect of red noise (Pasham et al. 2019). Using the 100,000 values of , we calculated the cumulative distribution of probability to exceed a given (Figure 3). By comparing with the observed value of , we obtained the global confidence level of 99.76% for the QPO at ∼4.1 mHz. Using the same Monte Carlo approach, we obtained that the statistical significance of the QPO signal in the Swift PDS is 94.38%. The results from Monte Carlo simulations are in good agreement with those obtained with the χ² analysis of white noise distribution, indicating that the red noise component (if present) is negligible. Considering that the QPO was detected at the same frequency in two independent detectors, its combined confidence level is 99.986%, making the signal statistically significant. Note that we did not detect the QPO signal in either individual or combined EPIC MOS data, possibly due to the relatively low count rates in the individual MOS light curves, which are a factor of ∼3.5 less than those in PN. In addition, the fractional rms amplitude is only 6%, implying that the QPO signal (if present) could be more affected by noise fluctuations in the MOS data. In order to test this possibility, we performed detailed simulations in Appendix D, and found that the chance of the same QPO signal detected at a level of 99.76% in the MOS data is indeed low (<0.1%). We also performed the PDS analysis by combining PN and MOS light curves, and found that the power value at 4.1 mHz comes down, probably due to the fact that QPO signal is not detectable in the MOS data. In this case, the global confidence level for the QPO in the combined light curve is reduced to 92.81% (Figure D2).

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Having established that the QPO is statistically significant, we now place its constraint on the origin of the X-ray emission and the central engine of AT2018cow. On the basis of the soft X-ray QPO identified at 224 Hz, a compact object for the origin of X-ray emission was proposed (Pasham et al. 2021). The discovery of ∼4.1 mHz QPO provides further evidence for the presence of a compact object, which could be either a neutron star or an accreting BH. mHz QPOs have been detected in a few neutron-star low-mass X-ray binaries (Revnivtsev et al. 2001; Tse et al. 2021), which are generally explained as thermonuclear burning on the neutron star surface. As a result, these QPOs are transient behavior occurring only in a narrow range of X-ray luminosity during outbursts. This contradicts the constant frequency of the QPO at ∼4.1 mHz in AT2018cow, as the stacking analysis of Swift data suggests that the QPO frequency may be stable over a period of 30 days, during which the luminosity declined by a factor of >5. The QPO's stability may also challenge other models involving a neutron star (Pasham et al. 2021), such as spin-down of an isolated millisecond magnetar or magnetar-accretion driven outburst.

If the compact object was a stellar-mass BH, the 4.1 mHz QPO is unlike typical low-frequency QPOs (LFQPOs), as the frequency is lower than most of the type-A (∼8 Hz), type-B (∼5–6 Hz) and type-C (∼0.1–15 Hz) QPOs (Casella et al. 2005; Remillard & McClintock 2006; Ingram & Motta 2019). The QPO's frequency is also far less than a few 10–100 Hz for high-frequency QPOs (HFQPOs) (Morgan et al. 1997; Belloni et al. 2012). Although several accreting stellar-mass BHs have exhibited QPOs with frequency in the mHz range (Cheng et al. 2019), most of these sources are believed to have high orbital inclinations. This is inconsistent with the weak or no X-ray absorption in observations on timescales of hours to days (Margutti et al. 2019). Furthermore, almost all these sources have shown the red noise PDS at below 1 mHz. These properties distinguish them from the 4.1 mHz QPO found in AT2018cow, which appears with weak or absent red noise. Two BH sources, GRS 1915+105 and IGRJ17091–3624, show mHz QPOs in the so-called "heartbeat" state (Belloni et al. 2000; Altamirano et al. 2011). However, these QPOs are characterized by high harmonic content and accompanied with flat-top noise in the PDS where low and high frequency breaks are evident. On the other hand, if isotropically emitted, the peak luminosity of AT2018cow is ≳10⁴ times the Eddington limit for a stellar-mass BH (M_BH ∼ 10 M_⊙), challenging standard models of BH accretion. Therefore, if the mHz QPO of AT2018cow was due to a process similar to that operating in stellar-mass BHs, the underlying physical mechanism would be extreme and have never been seen before.

The observed frequency, if it is related to the Keplerian period of the innermost circular stable orbit, would correspond to a BH mass of between 5 × 10⁵ M_⊙ and 6 × 10⁶ M_⊙, for a non-rotating and maximally rotating BH, respectively. Alternatively, the 4.1 mHz QPO could represent a scaled-down analog of the typical LFQPOs or HFQPOs of stellar-mass BHs, but occurring at a lower frequency if a more massive BH or IMBH is at work in AT2018cow. The frequencies of HFQPOs appear to be stable and scale inversely with mass, f₀ = 931(M/ M_⊙)⁻¹ Hz (Remillard & McClintock 2006). Assuming the 4.1 mHz corresponds to the stronger 2 × f₀ frequency, the scaling relation yields a BH mass of 4.4 × 10⁵ M_⊙ in AT2018cow (Figure 4). As we mentioned above, different types of LFQPOs are observed in the frequency range of ∼0.1–20 Hz. The QPO frequency can be variable and correlated with the energy spectral parameters, i.e., the flux and shape of a power-law spectral component (Remillard & McClintock 2006). During the first 37 days, the 0.3–10 keV spectrum of AT2018cow can be described by a simple power-law with little absorption (Margutti et al. 2019), with a photon index in the range ∼1.6–1.7, indicating no evident spectral evolution. Following the method outlined in previous works (Dewangan et al. 2006; Strohmayer & Mushotzky 2009), we used the relation between the QPO frequency and power-law index obtained for six systems with dynamic mass constraints (Vignarca et al. 2003; Shaposhnikov & Titarchuk 2009; Strohmayer & Mushotzky 2009) to find the possible range of QPO frequencies with power-law indices between 1.6 and 1.7. Under the assumption that QPO frequency scales inversely in proportion to BH mass (Remillard & McClintock 2006), we can estimate the BH mass in AT2018cow to be M_BH ∼2.2 × 10³ M_⊙ (Figure 4). The above estimates of the BH mass (∼10³–10⁵ M_⊙) suggest that AT2018cow may harbor an IMBH.

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In order to explain its fast evolving ultraviolet (UV) and optical emission, Perley et al. (2019) suggested that AT2018cow could be powered by the TDE of a main sequence star by an IMBH. They used the MOSFit TDE model (Mockler et al. 2019) to fit the UV and optical light curves and obtained a best-fit BH mass of 1.9 × 10⁴ M_⊙ disrupting a star of 0.6 M_⊙. However, it is possible that the early UV and optical emission originates from the circularization process (Piran et al. 2015), rather than accretion, posing a challenge to apply the MOSFit model which assumes the TDE UV/optical emission is related to the reprocessed accretion luminosity. We attempted to develop a TDE accreting model to fit its X-ray light curve obtained from Swift-XRT observations. In this framework, after a star is disrupted by the BH, its debris will fall back to the pericenter on a timescale (Rees 1988)

where M_BH is the BH mass, M_* is the mass of the disrupted star and R_* is its radius. In the late time, the fallback rate drops with an asymptotic power-law index −5/3 (Ramirez-Ruiz & Rosswog 2009; Chen & Shen 2018). However, the power-law index can approach −9/4 rather than the canonical value of −5/3, if the stellar core survives after the pericentric encounter (Guillochon & Ramirez-Ruiz 2013; Coughlin & Nixon 2019) or the disrupted star is in its late age (Golightly et al. 2019). The luminosity history will trace the mass fallback rate if the fallback mass is rapidly accreted by the BH. In this case, accretion rate will be close to the fallback rate , and the luminosity is , where η ≪ 1 is the efficiency of converting accretion power to luminosity. However, this might not be occurring if the accretion timescale is longer than the fallback timescale. In this case, the relation between the accretion rate and the mass fallback rate can be given by Kumar et al. (2008); Lin et al. (2017); Chen & Shen (2018); Mockler et al. (2019)

where τ_acc is the so-called "slowed" accretion timescale.

Here we approximate the overall debris fallback history as follows. The fallback rate remains constant at between t_fb and 1.5t_fb, and after 1.5t_fb it starts to decay as t^−5/3, i.e.,

For the case of full disruption, . The luminosity history is . If the "slowed" accretion timescale is τ_acc = 0, it becomes . We used the parameter η, BH mass M_BH and TDE start time t₀ to fit the X-ray light curve. The disrupted star is assumed to be solar-type. The best fitting result yields M_BH ∼ 10⁴ M_⊙, t₀ ∼ 58,281 (Modified Julian Date days), τ_acc ∼ 9 days and η ∼ 10⁻⁵. The corresponding fallback timescale is t_fb ∼ 4 days. The best-fit light curve is depicted in Figure 5 for the late-time luminosity evolution parameterized with t^−5/3 decline law (black), and with t^−9/4 decline law (red).

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The best-fit TDE model yields a BH mass of ∼10⁴ M_⊙, which is consistent with the mass range constrained by the QPO analogy, as well as that obtained by fitting the MOSFit model to the UV/optical emission of AT2018cow (Mockler et al. 2019). Given the observed peak bolometric luminosity of ∼4 × 10⁴⁴ erg s⁻¹ (Margutti et al. 2019), such a BH mass requires that the system be radiating at about 100 times the Eddington limit. On the other hand, the X-ray emission may be anisotropic and beamed, given the detections of fast-evolving radio radiation (Margutti et al. 2019; Bietenholz et al. 2020; Mohan et al. 2020). The X-ray timing and spectral properties, i.e., QPO frequency, rms amplitude and power-law dominated X-ray spectrum, make AT2018cow similar to the jetted TDE Sw J1644+57 (Reis et al. 2012), though the latter has a much higher luminosity, indicating that similar processes may operate in two objects.

We note that Pasham et al. (2021) identified a soft X-ray QPO at a much higher frequency of 224 Hz, setting a tight mass limit for the compact object in AT2018cow to be less than 850 M_⊙ if due to a BH. If the signal were true, the tension could be alleviated by introducing a binary compact object system instead of a single neutron star or BH. Such an exotic system comprised of a stellar-mass compact object orbiting around an IMBH with mass ∼10³–10⁵ M_⊙ , if confirmed, would be a valuable gravitational wave source for future space-based missions such as the Laser Interferometer Space Antenna (Babak et al. 2017). In conclusion, our results suggest that the FBOT AT2018cow may be powered by an IMBH residing in young star clusters off-center from its dwarf host galaxy (Morokuma-Matsui et al. 2019). Although a variety of searching strategies has been proposed (Noyola et al. 2008; Farrell et al. 2009; Lin et al. 2018; Greene et al. 2020), the existence of IMBHs is still in dispute. Luminous FBOTs are promising candidates in future search for IMBHs, which will provide further insights into their formation mechanisms.

This research made use of the HEASARC online data archive services, supported by NASA/GSFC. We thank the P.I. who proposed the XMM-Newton and Swift observations of AT2018cow for making the data available. This work is supported by the National Natural Science Foundation of China (NSFC, Grant Nos. 11822301, 12192220, 12192221 and 11833007). X.S. acknowledges support by the science research grants from the China Manned Space Project through No. CMS-CSST-2021-A06. L.T. acknowledges support from the NSFC (Grant No. 12122306). J.Q. acknowledges support from the NSFC (Grant Nos. 11733009 and U2031205).

Figure A1 shows the XMM/PN PDS extracted in different energy bands.

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Table B1 lists Swift data used in the PDS analysis (Section 3). For the observation of S11, the light curve can be divided into two segments with 1.25 ks. All other ≥2.5 ks observations cannot be divided into two segments due to the presence of a gap in the light curve. Note that we extracted the average PDS from the light curve segments for the NuSTAR and NICER observations, but did not detect the QPO signal at 4.1 mHz. This is possibly due to the fact that the QPO signal is dominated by photons at soft bands (Figure A1), while only data in the hard X-ray band at >3 keV can be used for NuSTAR observations. For NICER observations, most light curve segments have too short exposures (≲1 ks) to be used effectively in searching for the QPO signal through stacking PDSs. Hence, we do not display the NuSTAR and NICER data in this paper.

Figure C1 (upper row) shows the CDF (left) and probability density function (right) of noise powers in the PDS of XMM-Newton data.

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It is evident that the observed noise powers are consistent with a χ² distribution (with 2 × 21 d.o.f., see Section 3 for details) scaled by a factor of 1/21, i.e., consistent with white noise. Note that we performed similar analysis of noise properties in the PDS of Swift/XRT data, and found the noise power values are also χ² distributed (lower row).

We reduced the data from XMM-Newton/MOS observations (MOS1 and MOS2) following the standard procedures utilizing the XMM-Newton SAS v17.0.0, with the latest calibration files. Similar to PN, the source light curves in the energy range of 0.3–10 keV were extracted using a circular region with a radius of 35'', while the background light curves were extracted from source-free areas on the same CCD using four identical circular regions. No strong background flares were present during the MOS observations. Figure D1 (upper panel) displays the MOS1, MOS2 and MOS1+MOS2 light curves. Then we produced the corresponding Leahy-normalized PDS with a frequency resolution of 0.8 mHz (Figure D1, lower panel), where no strong feature at 4.1 mHz can be seen, with the power values being consistent with the noise level of ∼2. This suggests that even if we combine the PN and MOS data, the signal would not necessarily be getting stronger (Figure D2).

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Furthermore, we performed simulations to assess whether the 4.1 mHz QPO signal of AT2018cow seen in the PN data (at 99.76%) is indeed not detectable by MOS. We generated a fake MOS1 light curve as follows. We first divided the observed source light curve of PN by a factor of 3.5 (the ratio of mean count rates between PN and MOS1), and added the observed background light curve of MOS1 to resemble the expected source+background light curve of MOS1. By assuming a Poisson distribution, we then re-sampled the expected counts in each time bin. Finally, we subtracted the observed background counts from the expected counts to produce a fake source light curve of MOS1. We also generated a fake MOS2 light curve in a similar way. We repeated the procedures 10⁴ times and obtained 10⁴ simulated MOS1+MOS2 light curves and PDSs. Among 10⁴ PDS, only seven have power values at 4.1 mHz reaching the 99.76% level as detected in PN (Figure D3). This suggests that the chance of QPO detection in the MOS data is indeed low (<0.1%).

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