Chandra probes the X-ray variability of M51 ULX-7: evidence of propeller transition and X-ray dips on orbital periods
G. Vasilopoulos, F. Koliopanos, F. Haberl, H. Treiber, M. Brightman, H. P. Earnshaw, A. Gúrpide
DDraft version February 17, 2021
Typeset using L A TEX twocolumn style in AASTeX63
Chandra probes the X-ray variability of M51 ULX-7: evidence of propeller transition and X-ray dips on orbitalperiods
Georgios Vasilopoulos, Filippos Koliopanos, Frank Haberl, Helena Treiber,
1, 4
Murray Brightman, Hannah P. Earnshaw, and Andr´es G´urpide Department of Astronomy, Yale University, PO Box 208101, New Haven, CT 06520-8101, USA Universit´e de Toulouse; UPS-OMP; IRAP, 31058 Toulouse, France Max-Planck-Institut f¨ur extraterrestrische Physik,Giessenbachstraße, 85748 Garching, Germany Department of Physics and Astronomy, Amherst College, C025 New Science Center, 25 East Dr., Amherst, MA 01002-5000, USA Cahill Center for Astronomy and Astrophysics, California Institute of Technology, 1216 East California Boulevard, Pasadena,CA 91125,USA (Received February 17, 2021)
Submitted to ApJABSTRACTWe report on the temporal properties of the ULX pulsar M51 ULX-7 inferred from the analysis of the2018-2020
Swift /XRT monitoring data and archival Chandra data obtained over a period of 33 daysin 2012. We find an extended low flux state, which might be indicative of propeller transition, lendingfurther support to the interpretation that the NS is rotating near equilibrium. Alternatively, this offstate could be related to a variable super-orbital period. Moreover, we report the discovery of periodicdips in the X-ray light curve that are associated with the binary orbital period. The presence of thedips implies a configuration where the orbital plane of the binary is closer to an edge on orientation,and thus demonstrates that favorable geometries are not necessary in order to observe ULX pulsars.These characteristics are similar to those seen in prototypical X-ray pulsars like Her X-1 and SMC X-1or other ULX pulsars like NGC 5907 ULX1.
Keywords: editorials, notices — miscellaneous — catalogs — surveys INTRODUCTIONUltra luminous X-ray (ULX) sources (Kaaret et al.2017) are off-nuclear extra-galactic X-ray binary sys-tems with an apparent isotropic luminosity that exceedsthe Eddington limit for an accretion powered, stellarmass black hole (i.e. L X > erg s − ). Given theirhigh luminosity ULXs were thought to host the elusiveintermediate-mass black holes. Remarkably, within thelast years there has been undisputed evidence that atleast a few of these systems are powered by accretinghighly magnetized neutron stars (NS); these are knownas ULX pulsars (ULXPs, Bachetti et al. 2014; F¨urstet al. 2016; Israel et al. 2017; Israel et al. 2017; Carpanoet al. 2018; Rodr´ıguez Castillo et al. 2020). This discov-ery is consistent with theoretical predictions (e.g. Basko Corresponding author: Georgios [email protected] & Sunyaev 1976; Mushtukov et al. 2015) that argue thatNSs can break the barrier set by the Eddington limit( L Edd ∼ . × M/M (cid:12) erg/s) for strong magneticfields ( B ). Moreover, an increasing number of authorshave put forward the proposition that a major fractionof ULXs are powered by NSs rather than black holes(e.g. King et al. 2017; Koliopanos et al. 2017; Waltonet al. 2018).For a standard accretion disk (Shakura & Sunyaev1973), as the accretion rate reaches the Eddington limit,the radiation pressure dominates the inner part of theaccretion disk, causing a large fraction of the accretedmaterial to be lost through outflows (Poutanen et al.2007). Material is expelled inside the spherization ra-dius R sph , and the outflow is not spherical but formsa funnel-like structure (see Fig. 1). In the context ofULXPs, the disk is truncated at the magnetospheric ra-dius R M . For high B values, truncation can thereforeoccur outside R sph . However, it has been proposed that a r X i v : . [ a s t r o - ph . H E ] F e b Vasilopoulos et al.
Figure 1.
Schematic of outflows from an accretion disk during super-Eddington accretion. Outflows can start from the disk(i.e. orange shade), or even inside the magnetosphere (i.e. cyan shade) given the super-Eddington luminosity. The walls of theoutflow create a funnel and an observer can see the central source if it is in a favorable orientation (i.e. left panel). The pulsedemission is shown with blue dotted lines, while reprocessed emission is shown with red dotted lines. Given the extent of thefunnel, coherent pulsations are diluted, while the spectral shape of the emission should also alter. If the disk precesses, thefunnel also follows the same motion, and thus the observer sees a super-orbital modulation. If the observer’s line of sight isobscured by the funnel walls, then only non-pulsating emission from the funnel walls should be visible (i.e. right panel). outflows could form in a similar manner inside R M , asmaterial is accreted onto the NS via the magnetic fieldlines (King et al. 2017).Super-orbital modulation of ULXs is possible throughprecession of the funnel (Dauser et al. 2017). For threeknown ULXPs (M51 ULX-7, M8 2 X-2 and NGC 5907ULX1) super-orbital periodicities (40 d, 60 d and 78 d,respectively) are evident in their X-ray light curves (seeBrightman et al. 2020, and references therein). The ob-served flux ( F X ) during a super-orbital cycle can varyby a factor of 100, but there has been no concreteevidence for spectral changes indicating accretor-to-propeller transitions (Illarionov & Sunyaev 1975). Thesetransitions occur when the inner disc radius (i.e. themagnetosphere of the NS) becomes larger than the coro-tation radius of the NS, the centrifugal drag causes ma-terial to be propelled away instead of accreted. Alter-natively, the changes in F X can be due to obscurationby a precessing accretion disk and a funnel formed byoptically thick outflows (Middleton et al. 2018). A firmconfirmation of this scenario has been shown in the caseof NGC 300 ULX1, where a stable spin-up rate has beenmaintained during epochs of variable F X (Vasilopouloset al. 2019). However, the engine behind precession isstill unclear; it could be the tidal force from the massivecompanion star, the interaction with the magnetosphereof the NS, the irradiation of the warped disc, or even theNS free precession (see Vasilopoulos et al. 2020a, and ref- erences within). Constraints in theoretical models canonly be derived by monitoring ULXPs and their super-orbital periodicity, the study of the stability of this peri-odicity, and the occurrence of on and off states. One ofthe unanswered fundamental questions about ULXPs isif their X-ray emission is beamed towards the observer,and what is the beaming factor, i.e. apparent luminosityis larger than the true on L app = bL . For a narrow fun-nel (see Fig. 1) beaming could be very strong, while forwide funnels the beaming factor could be smaller than2. This means that the bolometric X-ray emission of thesource is only overestimated by a small factor. Given thelack of physically self-consistent spectral models and thedegeneracy of phenomenological ones (e.g. Koliopanoset al. 2017, 2019), we should perhaps look at temporalproperties for observational constraints on b .G´urpide et al. (2021) have processed archival dataof 17 ULXs to investigate their long-term X-ray spec-tral evolution. Motivated by their work and usingthe products of their analysis, we studied the variabil-ity of M51 ULX-7, the only ULXP with an orbit thatcan be continuously monitored by X-ray observatories(Townsend & Charles 2020). M51 ULX-7 is a ULXP(Rodr´ıguez Castillo et al. 2020) hosting a NS rotatingwith a spin period of ∼ Swift /XRT monitoring revealed the presence ofa super-orbital modulation with a period of ∼
51 ULX-7: off states and X-ray dips Figure 2.
X-ray light curve of M51 ULX-7 based on the 2018-2020
Swift /XRT monitoring of the region. Points below 0.005c/s may be considered as non-detection or upper limits as they correspond to less than ∼ Figure 3.
X-ray lightcurve of Fig. 2 folded for the super-orbital period of 38.9 days. Blue dotted curve is same as Fig.2. Red line is scaled to match the lower flux points throughthe super-orbital cycle. Most points follow the super-orbitaltrend, while few outliers are mainly from observations be-tween MJD 58900-59000 d (see shaded area in Fig. 2). we report on the discovery of an irregular off-state withinthe super-orbital cycle of M51 ULX-7 and the discov-ery of periodic dips in the X-ray light curve computedfrom archival Chandra data. The detection of eclipsesoffers new insights onto the geometrical configuration ofULXPs, and could provide an independent constraint onthe beaming factor of M51 ULX-7. DATA ANALYSIS & RESULTS2.1.
Probing the super-orbital modulation
For this study we used X-ray data from the M51monitoring (Brightman et al. 2020) by the Neil Gehrels
Swift
Observatory (Gehrels et al. 2004) X-ray Telescope(XRT, Burrows et al. 2005).
Swift /XRT data wereanalysed following the pipeline developed by Brightman et al. (2020). To estimate an updated super-orbital pe-riod we computed the Lomb-Scargle (LS) periodogram(Scargle 1982) for the 2018-2020 data shown in Fig.2. A period of ∼ Swift /XRT. By following Vasilopoulos et al. (2020a)many low flux points are consistent with upper limits.By ignoring all lower flux points with rates smaller than0.005 c/s, the LS periodogram yields a periodicity of38.94 d. The difference between the two methods may beconsidered as an estimate of the uncertainty of the super-orbital period. Thus the super-orbital period should be ∼ ± N × ∼
20 ks) andthus only contribute to the study of the variability ofM51 ULX-7 on timescales of a few hours (i.e. 2 hourlong dips reported by Liu et al. 2002). M51 was ob-served by Chandra between 2012 September 9 and Oc-tober 10 (PI: Kuntz) with a few long visits (i.e. > Vasilopoulos et al. in Table 1 of Earnshaw et al. (2016). Data reduc-tion was performed with the
CIAO software (Fruscioneet al. 2006). For creation lightcurves, the source (back-ground) events were extracted from circular regions with3 (20) arcsec radius (following Earnshaw et al. 2016).We used standard
FTOOLS scripts to perform event se-lection and create light curves. For the light curve weused a 6000 s binning to compromise between getting ac-ceptable statistics and sufficient timing resolution (seeFig. 4). To investigate spectral changes we estimatedthe spectral Hardness Ratio (HR) from each 6000 s in-terval. We define HR as the ratio of the difference overthe sum of the number of counts in two subsequent en-ergy bands: HR=(R i+1 − R i ) / (R i+1 + R i ), where R i isthe background-subtracted count rate in a specific en-ergy band (i.e. 0.3-1.5 keV and 1.5-8.0 keV). HRs werecomputed with a Bayesian estimator tool ( BEHR ; Parket al. 2006).In Fig. 4 we plot the X-ray light curve obtained fromthe Chandra observations in September 2012. The mod-ulation looks consistent with the reported 38.9 d super-orbital modulation of M51 ULX-7 (Vasilopoulos et al.2020a). To test this we extrapolated the super-orbitalsolution derived by fitting a sinusoidal function to the
Swift /XRT monitoring data, as shown with a blue linein Fig. 2. We scaled the function by a factor of 3,which is the ratio of the ACIS-S to XRT spectral re-sponse given the spectral properties reported by Earn-shaw et al. (2016), i.e. an absorbed power-law withΓ=1 . N H =1.5 × cm − . The result is shownin Fig. 4 by the dashed blue line. For clarity, we alsoplot a sinusoidal function computed for the upper limitof the super-orbital period, i.e. 38.94 d. The agree-ment with the Chandra data is good for the first partof the light curve. However, during the final Chandraobservation (obsid: 15553) the flux remained at a lowlevel. To further investigate the drop in flux within thelast observation we derived accurate count rates for eachChandra pointing. We performed source detection us-ing the CIAO wavdetect tool that implements a waveletanalysis on the X-ray images. The resulted count ratesare given in Table 1. The drop in flux seen around MJD56210 (obsid: 15553) can be compared with observationstaken about 15 days earlier (obsid: 13815), when the fluxshould have been similar according to the super-orbitalmodulation. Thus we find that on MJD 56210 the fluxof M51 ULX-7 is ∼
80 times lower than expected.2.2.
Detection of periodic X-ray dips
The Chandra light curve shows fast variability ontimescales of a few 1000 s, which is consistent with otherstudies of the system (Earnshaw et al. 2016; Liu et al.
Table 1.
Chandra Observing logObsid ( a ) Date Exposure Rate ( b ) ks 10 − c/s13812 2012-09-12 159 5.07 ± ± ± ± ± ± ± (a) All data were obtained by ACIS-S camera. (b)
Net count rates(0.3–8 keV band) derived from the wavdetect tool. χ test, or a maximizationof variance. We used the normalised ratio light curveproduced from the three observations where the dipsare distinguished (obsids: 13812-4). We folded the ratiolight curve for test periods between 0.5 and 3.5 days.Then we binned the folded profile to obtain 20 averagemeasurements (similar to the smoothed profile in Fig. 5)and we calculated the variance of these average values.Finally, we repeated the procedure for 10000 simulated
51 ULX-7: off states and X-ray dips Figure 4.
Upper panel:
X-ray light curve (0.3-8.0 keV) of M51 ULX-7 based on Chandra data obtained in 2012. Events arebinned every 6000 s. The vertical dotted lines are phased with the binary orbit of 1.9969 d. There is an indication of periodicflux drops occurring at the same orbital phase. The blue dashed line marks the 38.9 d super-orbital modulation similarly to Fig.2 and Fig. 3. The dotted line marks the extrapolated solution for a 38.94 d period (see text for details).
Middle panel:
Ratiobetween Chandra data and a linear model fit to the first 15 days of the Chandra monitoring.
Lower panel:
Spectral hardnessevolution estimated by HRs. There is only a marginal indication of spectral softening in the first dip.
Figure 5.
Left:
Chandra X-ray ratio light curve of M51 ULX-7 folded for the orbital period of the binary. We only used datafrom obsids 13812-4. Normalised rates were calculated in reference to a linear model fitted to the data. The shaded region marksthe approximate duration of the dips.
Right:
Result of epoch-folding method. The maximum variance is found for exactly theorbital period of the system.
Vasilopoulos et al. data-sets to estimate the false alarm probability. Theresult is plotted in the right panel of Fig. 5.Given that the statistical significance of the X-raydips has been established we should address whetherthese can be associated with a specific phase of the or-bital period. The orbital ephemeris of the system wasdetermined using
XMM-Newton data obtained betweenMJD 58251 and 58281 d (Rodr´ıguez Castillo et al. 2020).Given that the Chandra data were obtained about 1100orbits before that, the ephemeris cannot be extrapolatedwith enough accuracy to actually compare the predictedtransitions of the optical star in front of the NS (i.e.time of ascending nodes: T asc ) with the X-ray dips. Forsuch comparison we used the the Swift /XRT data fromthe 2018-2020 monitoring of the system (MJD 58000-59125 d). Given that individual observations can spanup to one day, we performed source detection to individ-ual snapshots and folded the resulting light curve withthe orbital period. We found no evidence of X-ray dipsin the
Swift /XRT orbit-folded light curve. Nevertheless,this should be expected due to the low effective areaof XRT and the short exposures that resulted in highuncertainties for individual detections. Specifically forthe 170 snapshots where the source was detected, theuncertainties were of the order of 38 ± DISCUSSIONFollowing the discovery of pulsations originating fromthe NS in M51 ULX-7, it has been shown that in or-der to model the spectral and temporal properties ofthe system self-consistently, the NS should have a verystrong magnetic field and should be in the fast rotatorregime (Vasilopoulos et al. 2020a). Vasilopoulos et al.(2020a) also argued that the ∼
39 d super-orbital modu-lation of the ULXP could be triggered by (or related to)free precession of the NS, which surprisingly requires aNS magnetic field of 3-4 × G, in quantitative agree-ment with the spin equilibrium predictions. As a con-sequence, strong outflows are not expected from the ac-cretion disk (since R M >R sph ). Thus the opening funnelof any outflow should be large, and as a result we do notexpect strong beaming by the system and accretion ontothe NS is indeed 10-30 times above the Eddington limit(Vasilopoulos et al. 2020a). In the following paragraphs,we will discuss how the newly reported patterns of X-ray variability can be interpreted and address some ofthe open questions for M51 ULX-7 and ULXPs, like in-vestigating beaming and the engine behind super-orbitalmodulation. 3.1. Propeller transition or an unstable super-orbitalclock
In terms of super-orbital variability, the agreement be-tween the modulation seen in the Chandra data andthe phase of the expected maximum of the super-orbitalperiod computed by the
Swift /XRT monitoring data isremarkable. Especially considering that the
Swift andChandra data are separated by about 50 super-orbitalcycles. Thus, the drops may be related to a transition tothe propeller state, as it is speculated for similar dropsin flux seen in NGC 5907 ULX1 (F¨urst et al. 2017). Thisdrop in flux is in agreement with the behavior seen by
Swift /XRT around MJD 55715 d (see Vasilopoulos et al.2020a), where during a 70 day monitoring M51 ULX-7was not detected in the final 20 days of the monitor-ing, when the rise of its flux was expected accordingto the super-orbital period. However, in both epochs,there are no additional monitoring data to determinethe duration of the off state, or investigate if the super-orbital period was different than the one determined bythe 2018-2020 monitoring. A similar “off-state” is seenin the
Swift /XRT data around MJD 58900 d (see Figs.2, 3), where the flux dropped near zero for 3 consecu-tive visits. In that case although the super-orbital cycleseemed to be disturbed the super-orbital period returnedto its normal beating pace after a few cycles.A stable super-orbital period would also be in agree-ment with the requirements of the NS free precessionmechanism, as the ratio of super-orbital and NS spinperiod should be proportional to the NS B field. Sincea transition to the propeller regime can occur with min-imal change in mass accretion if the accretion disk istruncated near the NS corotation radius, this drop influx lends further support to the findings of Vasilopou-los et al. (2020a), who proposed that the NS has a mag-netic field ∼ − × G and is rotating near its equi-librium period. Nevertheless, a variable super-orbitalperiod cannot be excluded for M51 ULX-7. If a vari-able period is confirmed with future monitoring data thiswould reveal a similar observational behavior to HMXBpulsars like SMC X-1 (Trowbridge et al. 2007).Assuming that the off-state is associated with pro-peller transition, we can derive the NS magnetic field B that would be required for the transition to occur.Following Campana et al. (2018) we find that: B = 10 (cid:18) L X,min × erg/s ( P/ s ) / ξ − / (cid:19) / G, (1)where ξ is a normalization factor with typical value of 0.5(however see case of ULXs Chashkina et al. 2019, where ξ can be higher), and L X , min is the minimum luminositybefore the propeller transition. Given that the super-
51 ULX-7: off states and X-ray dips L X is similar to the maximum X-ray luminositywithin the super-orbital cycle. For M51 ULX-7 this isof the order of 7 × erg s − in the 0.3-10.0 keV band(Rodr´ıguez Castillo et al. 2020; G´urpide et al. 2021),however for ULXPs the bolometric luminosity could beof a factor of 2 higher (Koliopanos et al. 2017; G´urpideet al. 2021). Moreover, it has already been establishedthat the observed L X is only boosted by small beaming(Vasilopoulos et al. 2020a), of the order of 2 or less (seealso § L X , min ∼ × erg s − forpropeller transition (but we caution the reader for theabove mentioned uncertainties), thus based on equation1 we find B ∼ − × G. We note that, dependingon the torque model used the propeller transition canoccur very close (factor <
2) to the L X that probes spinequilibrium for a given magnetic field (see comparisonsParfrey et al. 2016; Vasilopoulos et al. 2018). Thus,equation 1 yields a similar magnetic field estimate tothe value derived by just assuming the NS is rotatingnear equilibrium (see discussions for M51 ULX-7 andM82 X-2 Vasilopoulos et al. 2020a; Eksi et al. 2015).So far we have connected the “off-states” ofM51 ULX-7 with the source transitioning from accre-tor to propeller regime. Thus, during the “off-state” thesource has moved way down on the Luminosity gap forX-ray pulsars (i.e., Corbet gap; Corbet 1996). However,given the spin period of ∼ in L X of the order of ∼ ∼
80. This discrepancy may be explainedif we assume that even at the propeller regime, there isstill some residual accretion that can penetrate the mag-netophseric barrier (Spruit & Taam 1993), a mechanismthat has been supported by theory and simulations (e.g.,D’Angelo & Spruit 2012; Parfrey & Tchekhovskoy 2017;Romanova et al. 2018).An opposing view would be that during the “off-state”,M51 ULX-7 is still in the accretor regime. This limitmay be used to put a lower limit to the propeller stageassuming that the source is then on the propeller line.By using equation 1 we find B ∼ × G. However, thislow B field value posses difficulties in explaining the verylow NS spin-up rate ( ˙ P NS ) observed during maximum X-ray luminosity (Rodr´ıguez Castillo et al. 2020). Givenall the observational evidence, to account for this low B value and the observed ˙ P NS , we would need change ourbasic assumptions (for the accretion disk) in order to Luminosity jump is propotional to the ratio of the dynamical en-ergy at the NS surface over the corotation radius (Corbet 1996),i.e. ∼ × (P/1 s) / decrease the rate of angular momentum transfer. Ineffi-cient angular momentum transfer may be achieved if theaccretion disk is miss-aligned with the N S rotation axis,or the inner disk velocity significantly deviates from theKeplerian approximation.3.2.
M51 ULX-7 as an ULXP analog of Her X-1
The study of ULXPs has revealed not only that somehost strongly magnetized NSs, but also that this mightbe the norm for a large fraction of ULXs (Koliopanoset al. 2017; King et al. 2017). Thus, it is natural to lookfor similarities (and also differences) between individualULXPs and HMXBs, which host the majority of X-raypulsars. The NS spin period as well as the orbital andsuper-orbital periods of M51 ULX-7 (2.8 s, 1.99 d and ∼
40 d), are close to the values (1.24 s, 1.7 d and ∼
35 d)of the prototypical X-ray pulsar Her X-1 (Tananbaumet al. 1972; Katz 1973). In regards to the super-orbitalmodulation, for both systems it has been proposed thatNS free precession could play an important role (Truem-per et al. 1986; Staubert et al. 2009; Vasilopoulos et al.2020a). Another characteristic feature of Her X-1 is thepresence of eclipses that coincide with the orbital pe-riod of the binary. Our study of M51 ULX-7 found ev-idence of similar features that occur periodically andcould help to further constrain the properties of the sys-tem. In order to understand the nature of the X-raydips in M51 ULX-7 we can thus refer to the plethoraof theoretical models proposed for Her X-1. In Her X-1full eclipses occur when X-rays are obscured by the com-panion star, however in its X-ray light curve there arecharacteristic X-ray dips, commonly referred to as pre-eclipse or anomalous dips . The pre-eclipse dips (2-5 hlong) occur before the eclipse and gradually march back-ward in phase within the super-orbital cycle. Anoma-lous dips (1-2 h long) occur at the same orbital phase,while there is evidence of cold matter absorption, in con-trast to the pre-eclipse dips (Reynolds & Parmar 1995).Theoretical explanations of these dips include dynam-ical, hydrodynamic and radiative interactions betweenthe accretion stream, the warped accretion disk and thecompanion star (e.g. Schandl 1996; Shakura et al. 1999).If the stream falls into the warped disk with an angle,the formation of a cold clumpy spray is possible, that inturn will cover the central source once per orbit (Schandl1996). In this scenario, a turbulent thickening of thewarped disk is also possible.A different cause for the X-ray dips is obscuration bythe stellar wind of the companion. For X-ray binariesit is important to take into account the strong X-rayillumination of the companion star that can affect thegeometry of the stellar winds. It has been shown that Vasilopoulos et al.
X-ray illumination can cause the formation of a so-called“shadow wind” by the companion in luminous HMXBs(Blondin 1994). By performing 2D hydrodynamic sim-ulations, Blondin (1994) found that for high X-ray lu-minosities the gas that resides on the stellar surface ex-posed to the X-ray source will be highly photoionized,and thus halt the formation of a radiative driven windfrom that side (see Haberl et al. 1989, for an applicationto 4U 1700-37). Given that stellar wind can still escapefrom the other side of the star, enhanced column den-sity is still possible at favorable orientations and orbitalphases. In fact, the shadow wind model has been of-fered as a possible mechanism to explain periodic dipsseen during a super-Eddington outburst of SMC X-2 (Liet al. 2016). For systems like Her X-1, the irradiationof the companion star can also depend on the binaryorbital phase (Shakura et al. 1999). In this scenario, the(phase dependent) shadowing of the companion by thedisk leads to the formation of flows coming out from theorbital plane and could in principle shadow the centralsource once per orbit.For M51 ULX-7 it is possible to imagine a similar sce-nario, where either (or all) of the above mechanisms canprovide the necessary conditions to form the X-ray dipsunder a favorable orientation. Nevertheless, the lack ofsignificant spectral change during the dips (see HRs inFig. 4), could be an indication of obscuration from afully ionised material rather than cold matter.3.3.
Constraints on orbit inclination and ULX beaming
At this point, and without further observations ofM51 ULX-7 during full orbital cycles, it is not possi-ble to test different models such as those introduced insection 3.2. However, we might test the extreme casewhere the dips are caused by partial obscuration by ma-terial very close to the Roche lobe radius, that perhapscould be at the Lagrangian points or the inner wind ofthe companion star. The Roche lobe radius, from thevantage point of the NS, will subtend an area on the skywith an angular radius θ , i.e.:tan( θ ) ≈ R RL a = 0 . q / . q / + ln(1 + q / ) , (2)where R RL is the donor radius that has filled its Rochelobe, a is the separation between the donor and theNS, and their ratio depends only on the mass ratio q = M donor /M NS (Eggleton 1983). The mass ratio inM51 ULX-7 is (cid:38) i ( i =0, refers to a face-on system), θ is actually weaklydependent on it. Assuming the companion always fillsits Roche lobe, for i o -45 o we find θ ∼ . o − . o . Given that a (cid:39) R RL , the duration of an eclipse in a2 day circular orbit would last ∼ ∼ o (full opening of ∼ o ). However, giventhe known super-orbital modulation in M51 ULX-7 andULXPs in general, the funnel orientation should changewithin the super-orbital cycle. Thus this would not ex-clude smaller opening angles for the funnel. Neverthe-less, a large opening angle is consistent with the largetruncation radius of the disk in M51 ULX-7, that wasderived from its temporal properties and is consistentwith the NS rotating near equilibrium (e.g. Vasilopou-los et al. 2020a; Erkut et al. 2020). Similar findingsthat suggest low or no beaming at all have been dis-cussed based on spectro-temporal properties of ULXPs(e.g. NGC 300 ULX-1 Vasilopoulos et al. 2018, 2019), orpulse profile evolution of X-ray pulsars during super-Eddington outbursts (e.g. Koliopanos & Vasilopoulos2018; Vasilopoulos et al. 2020b). This would mean thatthe proposed relation between mass accretion rate andbeaming factor b , i.e. b (cid:39) ( ˙ M / ˙ M edd ) /
73 (King et al.2017), would need to be revisited in the context ofULXPs. Small beaming is also consistent with the de-tection of pulsations in ULXPs, as large beaming fac-tors would otherwise result in very small pulsed fractions(Mushtukov et al. 2020). The above suggest that strongbeaming is not needed for ULXPs, and this should beconsidered in the framework of ULX population syn-thesis (e.g. Kuranov et al. 2020; Misra et al. 2020; Ab-dusalam et al. 2020), and perhaps gravitational waveprogenitors, that are thought to go through a ULX phase(Marchant et al. 2017).An important consequence of the discovery of the X-ray dips is that, regardless of assumptions about beam-ing, it is now evident that ULXPs can be seen evenas near edge-on systems. In the literature, ULXs thatshow X-ray eclipses are often assumed to host BHs (e.g.Urquhart & Soria 2016). Nevertheless, for another con-firmed ULXP, NGC 7793 P13, it has been speculatedthat X-ray dips that appear during its orbital light curvewere also evident of an edge-on system (Motch et al.2014). Thus, future search for pulsations should not bediscouraged even for eclipsing ULXs. Finally, another
51 ULX-7: off states and X-ray dips
Implications for orbital modulation
Our findings suggest that the mass accretion rate inM51 ULX-7 is indeed super-Eddington. An implicationof high accretion rates in ULXs is the change of thebinary orbital period over time (Bachetti et al. 2020).According to Bachetti et al. (2020) the orbital periodderivative should be:˙ P orb ≈ − . × − (cid:18) M NS . M (cid:12) (cid:19) − (cid:32) ˙ M
100 ˙ M Edd (cid:33) s/s (3)Given that mass accretion rate for M51 ULX-7 is about30 ˙ M Edd , the binary orbit should change by ∼ ∼
180 revolutions per year whichwould translate to a drift in the epoch of T asc of the orderof 30 s/year, or about 250 s between 2012 and 2020. Fu-ture observations with X-ray telescopes could help con-strain this drift by tracking the eclipses, or pulsar timingtechniques (e.g. Bachetti et al. 2020; Rodr´ıguez Castilloet al. 2020). CONCLUSIONBy analysing archival Chandra and
Swift /XRT datawe investigated the super-orbital and orbital variabil-ity of M51 ULX-7. The 2012 Chandra data obtainedwithin 33 days show an extended low flux state, in con-trast to the super-orbital clock the system. A similar lowflux state is also seen in the 2020
Swift /XRT monitor-ing data. These off-states might be related to propeller transition similar to ULXP NGC 5907 ULX1. Alterna-tively they could be indicative of a variable super-orbitalperiod like those in other accreting pulsars (see Her X-1, SMC X-1). Moreover, we have reported the pres-ence of periodic dips in the Chandra X-ray light curveof M51 ULX-7. Although X-ray dips are also seen inbright X-ray binaries (Marelli et al. 2017) and ULXs(Wang et al. 2018), this is the first evidence of such prop-erty in ULXPs. The physical origin of the dips remainunclear, however they could be related to a plethora ofmechanisms that have been proposed to explain similarfeatures in HMXBs. Our finding demonstrates the needfor developing numerical simulations of HMXB systemsin the context of super-Eddington accretion and inves-tigating these intriguing phenomena. From an observa-tional point of view, it demonstrates the need for longmonitoring observations of ULXPs and ULXs to identifyand confirm the presence of features related to orbitalmodulation. Such combined efforts would help to de-velop a physically motivated, self-consistent model ableto explore the central engines of ULXPs.ACKNOWLEDGEMENTSThe authors would like to thank the anonymous ref-eree for their comments and suggestions that helpedimprove the manuscript. We would like to thank theorganizers of the “Chandra Frontiers in Time-DomainScience” meeting that was held virtually in October2020. Presentation of M51 monitoring data and discus-sions that followed resulted in the current work.GV acknowledges support by NASA Grantnumbers 80NSSC20K1107, 80NSSC20K0803 and80NSSC21K0213.Software used: HEASoft v6.26, CIAO v4.12.1, Pythonv3.7.3, IDL ® REFERENCES
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51 ULX-7: off states and X-ray dips11