document: the m31 globular cluster ( gc ) b158 ( a.k.a . bo 158 ) , named following the revised bologna catalogue v3.4 @xcite , contains a bright x - ray source that was discovered by the einstein observatory @xcite , and has shown up in every x - ray observation of the region since ; we call this x - ray source xb158 . 
   xb158 exhibited strong intensity modulation on a 10017@xmath050 s ( @xmath12.78 hr ) period during the 2002 january xmm - newton observation @xcite . 
   @xcite found similar variation in the folded lightcurves from a 1991 june rosat observation and a 2000 june xmm - newton observation ; they found that the amplitude of modulation decreased with increasing source intensity . 
   they found no such modulation in the 2001 june xmm - newton observation , setting a 2@xmath3 upper limit of 10% modulation . assuming that this represents the orbital period 
   , @xcite found that this is probably a neutron star binary with a low mass donor with a separation @xmath510@xmath6 cm ( i.e. a low mass xb - ray binary , lmxb ) . 
   however , analysis of the unfolded 2000 june xmm - newton lightcurve revealed a single deep dip at the end of the observation , with no evidence for dips in the two previous orbital cycles @xcite . 
   furthermore , @xcite analyzed 3 proprietary xmm - newton observations over 2004 july 1719 , finding @xmath1100% dipping for one orbital cycle , and zero evidence for dips in other cycles ; we concluded that the disk was precessing , with dips only visible for some part of the super - orbital cycle . 
   such behavior is associated with the `` superhump '' phenomenon that is observed in accreting binaries where the mass ratio is smaller than @xmath10.3 @xcite . 
   superhumps were first identified in the superoutbursts of the su uma subclass of cataclysmic variables ( accreting white dwarf binaries ) , manifesting as a periodic increase in the optical brightness on a period that is slightly longer than the orbital period @xcite . 
   su umas are a subclass of dwarf novae with orbital periods @xmath72 hr , that exhibit occasional superoutbursts that last @xmath85 times as long as the normal outbursts @xcite . 
   @xcite proposed that these superoutbursts are enhanced by a tidal instability that occurs when the outer disk crosses the 3:1 resonance with the secondary ; the additional tidal torque causes the disk to elongate and precess , and also greatly enhances the loss of angular momentum ( and therefore the accretion rate ) . 
   the disk precession is prograde in the rest frame , and the secondary repeats its motion with respect to the disk on the beat period between the orbital period and the precession period , a few percent longer than the orbital period . 
   the secondary modulates the disk s viscous dissipation on this period , giving rise to the maxima in the optical lightcurve known as superhumps . some short period , persistently bright cvs exhibit permanent superhumps @xcite . 
   cccccccccccc obs & @xmath9 & ra & dec & xrt exp & @xmath10/@xmath11 & counts +   + 00032702001 & 0.0 & 00 43 00.81 & + 41 17 00.2 & 2234 & 10.0 & 57 + 00032702002 & 0.9 & 00 43 06.53 & + 41 16 54.6 & 2510 & 9.7 & 41 + 00032702003 & 2.0 & 00 43 03.73 & + 41 16 40.8 & 2299 & 9.5 & 13 + 00032702004 & 3.0 & 00 43 06.35 & + 41 16 51.3 & 2299 & 9.6 & 40 + 00032702005 & 3.1 & 00 43 13.10 & + 41 16 30.4 & 2489 & 9.2 & 43 + 00032702006 & 4.4 & 00 43 03.22 & + 41 13 58.5 & 2572 & 7.0 & 65 + 00032702007 & 5.4 & 00 43 10.44 & + 41 15 10.9 & 2511 & 7.9 & 51 + 00032702008 & 6.4 & 00 43 06.44 & + 41 16 06.4 & 2635 & 8.9 & 57 + 00032702009 & 7.3 & 00 43 11.97 & + 41 16 27.7 & 2476 & 9.1 & 29 + 00032702010 & 8.8 & 00 43 03.76 & + 41 16 15.5 & 2644 & 9.1 & 39 + 00032702011 & 9.5 & 00 43 08.40 & + 41 17 27.6 & 2405 & 10.2 & 53 + 00032702012 & 10.1 & 00 43 07.20 & + 41 16 29.8 & 2502 & 9.2 & 43 + 00032702013 & 11.2 & 00 43 03.63 & + 41 17 36.2 & 2514 & 10.5 & 48 + 00032702014 & 12.4 & 00 43 04.82 & + 41 17 00.3 & 2411 & 9.8 & 38 + 00032702015 & 13.2 & 00 43 07.68 & + 41 15 24.0 & 2490 & 8.2 & 11 + 00032702016 & 14.2 & 00 43 01.12 & + 41 15 11.3 & 2511 & 8.2 & 27 + 00032702017 & 15.1 & 00 43 06.35 & + 41 14 46.6 & 2273 & 7.6 & 54 + 00032702018 & 16.8 & 00 43 02.79 & 
   + 41 17 00.9 & 2314 & 9.9 & 55 + 00032702019 & 17.1 & 00 43 08.59 & + 41 15 26.4 & 1992 & 8.2 & 45 + 00032702020 & 18.1 & 00 43 04.88 & + 41 17 31.5 & 1389 & 10.3 & 13 + 00032702021 & 19.4 & 00 43 03.24 & + 41 17 28.0 & 2690 & 10.3 & 18 + 00032702022 & 20.2 & 00 43 02.68 & + 41 17 26.6 & 2686 & 10.3 & 42 + 00032702023 & 21.1 & 00 43 03.07 & + 41 17 07.0 & 2821 & 10.0 & 65 + 00032702024 & 22.3 & 00 43 04.56 & + 41 16 19.5 & 2659 & 9.2 & 50 + 00032702025 & 23.2 & 00 43 10.49 & + 41 16 54.1 & 2711 & 9.6 & 46 + 00032702026 & 24.3 & 00 43 07.86 & + 41 15 05.1 & 2740 & 7.8 & 35 + 00032702027 & 25.1 & 00 43 06.42 & + 41 16 41.0 & 2424 & 9.5 & 18 + 00032702028 & 26.1 & 00 43 10.04 & + 41 16 54.2 & 2550 & 9.6 & 49 + 00032702029 & 27.2 & 00 43 10.52 & + 41 17 33.9 & 2524 & 10.2 & 59 + 00032702030 & 28.4 & 00 43 06.50 & + 41 17 25.9 & 2331 & 10.2 & 41 +    4u 1916@xmath12053 is a high inclination neutron star lmxb with an x - ray period of 50.00@xmath00.08 min and an optical period 50.458@xmath00.003 min @xcite . 
   it exhibits periodic x - ray intensity dips due to absorption by material in the outer disk ; the amplitude of these dips varies over @xmath10 to @xmath1100% on a @xmath14 day period , the precession period of the disk @xcite . 
   @xcite showed that ns lmxbs with orbital periods shorter than @xmath14.2 hr are likely to exhibit superhumps , and identified 4u 1916 - 053 as a persistent superhumping source . 
   xb158 appears to be somewhat analogous to 4u 1916@xmath12053 @xcite .    in @xcite 
   we modeled the 2004 july 17 xmm - newton pn spectrum of xb158 with a blackbody and a power law , finding @xmath13 = 2.0@xmath00.2 kev , the photon index @xmath14 = 2.0@xmath00.3 , @xmath4/dof = 19/19 and the 0.310 kev luminosity was 1.5@xmath00.6@xmath15 erg s@xmath16 ; fitting a single power law emission model yielded a photon index of 0.57@xmath00.09 , which is harder than any black hole spectrum @xcite , meaning that the accretor is a neutron star . 
   we conducted three dimensional smoothed particle hydrodynamical ( sph ) modeling , assuming a 1.4 @xmath17 ns , a 2.78 hr period , a total system mass of 1.8 @xmath17 , and a luminosity @xmath180% of the eddington limit . as a result , we estimated the disk precession period to be 29@xmath01 times the orbital period , i.e. 81@xmath03 hr .    in @xcite we examined chandra observations of @xmath130 m31 globular cluster x - ray sources spanning @xmath112 years ( 89 acis and 45 hrc ) , including xb158 . 
   we observed 0.310 kev luminosities @xmath1420@xmath18 erg s@xmath16 , and proposed that this is due to varying accretion rates over the disk precession cycle . 
   since we expected a super - orbital period for xb158 over time - scales of a few days , we obtained a series of 30 swift observations , each with 2.5 ks exposure and spaced @xmath11 day apart . in this work we present our analysis of these swift results , and find evidence for a super - orbital period of @xmath16 days 
   we made 30 swift observations over 2013 february 8  march 9 ( obsids 00327020010032702030 , pi r. barnard ) . 
   xb158 was one of two main targets for this survey , and the pointing was chosen to optimize the results from both targets . 
   however , the actual pointings varied significantly over the 30 observations . 
   a journal of swift observations is provided in table  [ journ ] ; for each observation we give the time relative to the first observation , pointing , xrt exposure , and off - axis angle , along with the net source counts . 
   for each observation , we placed circular regions around xb158 and a suitable background region . 
   we obtained the net source counts using the `` counts in regions '' tool in the ds9 image viewer , and estimated the intensity by dividing the net counts by the exposure time . 
   these data were obtained in order to determine the extent to which the varying off - axis angles affected our results . 
   we also created spectra from the same extraction regions , created appropriate ancillary response files using xrtmkarf , and found the appropriate response file using the quzcif tool . 
   none of the spectra were suitable for free spectral fitting , hence we obtained luminosity estimates by assuming a model obtained from previous observations . for chandra acis observations with @xmath2200 net source photons , the mean line - of - sight absorption ( @xmath19 ) was 9@xmath04@xmath20 atom @xmath21 ( @xmath4/dof = 7/11 ) , and the mean power law index ( @xmath14 ) was 0.52@xmath00.03 ( @xmath4/dof = 5/11 ) . 
   this is consistent with the best absorbed power law fit to the 2004 july 17 xmm - newton observation ( @xmath19 = 0.1 , @xmath14 = 0.57@xmath00.09 , @xmath4/dof = 30/24 * ? ? ? 
   as we noted earlier , that xmm - newton spectrum was best described by a blackbody + power law model , but neither the chandra nor swift spectra were sufficient to constrain the two - component emission model . 
   however , we were able to estimate the luminosity for each observation by assuming a fixed emission model , allowing only the normalization to vary . 
   we fitted each spectrum using xspec 12.8.2b , fixing @xmath19 = 9@xmath20 atom @xmath21 and @xmath14 = 0.52 , to find the normalization required to make absorbed model intensity 1.00 count s@xmath16 . 
   we then calculated the unabsorbed flux for this model , allowing us to convert from intensity to flux . 
   multiplying the conversion by the background - subtracted intensity provided by xspec yielded the instrument - corrected , background - subtracted source flux . 
   the luminosity was calculated from the flux assuming a distance of 780 kpc @xcite . 
   we fitted the lightcurve with constant and sinusoidal components using the qdp program provided in heatools , performing a simple search for periodicity . 
   @xcite created a periodogram suitable for unbinned data with a mean of zero that produces exactly equivalent results to such least - squares fitting of sinewaves , but also allows comparison of the best period with other periods . 
   the likelihood that any peak in the periodogram is real is given by the false alarm probability ( @xmath22 ) , where a low value of @xmath22 indicates that the peak is likely to be significant . 
   if the highest frequency to be probed is @xmath23 times higher than the lowest frequency , then the power , @xmath24 , required for a false alarm probability @xmath22 is given by @xmath24 = @xmath25 $ ] ; for small @xmath22 , @xmath26 @xcite . 
   we present our 30 day , 0.310 kev swift xrt lightcurve of xb158 in figure  [ swiftlc ] . 
   we see that the 0.310 kev luminosity varied by a factor @xmath15 ; the luminosity dropped from @xmath12.3@xmath15 erg s@xmath16 to @xmath15@xmath18 erg s@xmath16 in @xmath12 days , assuming the mean chandra absorbed power law model . 
   we note that these swift observations are non - contiguous , spacing the 2.5 ks observing time over several hours ; the low intensities ( @xmath10.0050.025 count s@xmath16 ) meant that there was no appreciable variability within each observation . 
   we find no evidence for a dependence of luminosity on off - axis angle ; the luminosities for the observations when xb158 have the largest and smallest off - axis angles have consistent values , while observations at an off - axis angle of 8.2@xmath11 resulted in a factor @xmath15 range in luminosity . 
   the conversion factor for translating 1 count s@xmath16 into 0.310 kev flux ranged over 1.091.29@xmath27 erg @xmath21 count@xmath16 for all observations except the second one , where it was 1.79@xmath27 erg @xmath21 count@xmath16 . 
   this @xmath110% variation about the mean in instrumental correction is clearly not sufficient to account for the factor @xmath15 variation in luminosity . 
   fitting our lightcurve with a constant intensity yielded a best fit luminosity of @xmath11.3@xmath15 erg s@xmath16 , with @xmath4 = 181 for 29 degrees of freedom ( dof ) . 
   however , adding a sinusoidal variation component yielded a much improved fit , with @xmath4/dof = 43/26 ; for this model , the period is 5.65@xmath00.05 days , with an amplitude of 7.1@xmath00.6@xmath18 erg s@xmath16 around a mean luminosity of 1.43@xmath00.04@xmath15 erg s@xmath16 , and a phase of 88.1@xmath00.7 degrees . 
   all uncertainties in this work are quoted at the 1@xmath3 level . 
   this sinusoidal variability yielded @xmath28 = 138 for 30 bins , with 3 extra free parameters ; f - testing showed that the probability for this improvement being due to chance was 3@xmath29 , equivalent to a @xmath25@xmath3 detection . in figure  [ swift_per ] 
   we show our swift lightcurve folded on a 5.65 day period and fitted with the best fit sinusoid . 
   we present our lomb - scargle periodogram for the 0.310 kev swift xrt luminosity lightcurve of xb158 in figure  [ ls ] , and also indicate the power required for false alarm probabilities @xmath22 = 0.5 , 0.05 , and 0.005 for reference . 
   we tested 30 frequencies , and oversampled each frequency by a factor of 50 ; this resulted in a periodogram covering a wider range of periods than is interesting ( up to @xmath11500 days ) , so we show only part of the periodogram here . 
   the periodogram shows a single strong peak , with the maximum power of 10.4 at a period of 5.60 days , corresponding to @xmath22 = 0.0009 ; the range of periods which are detected at a @xmath23@xmath3 level is 5.45.8 days . while there is a small peak at the 3 day period , @xmath22 = 1 for this peak 
   xb158 is a high inclination x - ray binary associated with the m31 globular cluster b158 . 
   it exhibits deep intensity dips on a 2.78 hr period in some observations but not others , prompting @xcite to suggest that the disk is precessing , caused by the `` superhumping '' phenomenon observed in low mass ratio systems where the disk crosses the 3:1 resonance with the donor star . 
   @xcite predicted a disk precession period of 29@xmath01 times the orbital period , i.e. 81@xmath03 hr , inspiring a month of daily monitoring of the m31 central region by swift . fitting a sinusoid to 
   the lightcurve revealed a 5.65@xmath00.05 day super - orbital period ( 1@xmath3 uncertainties ) ; the 0.310 kev luminosity varied by a factor @xmath15 , which is consistent with the range of luminosities observed in the acis observations of our 13 + year chandra monitoring campaign @xcite . 
   the peak of the lomb - scargle periodogram is at 5.6 days , consistent with that obtained from least squares fitting of the lightcurve with a sinusoid . 
   the suggested super - orbital period is @xmath170% longer than predicted by our 3d sph simulations @xcite . 
   none of the authors of the current paper are experts in sph ; however , j.  r. murray stated in a private communication that the longer than expected super - orbital period is likely due to the mass ratio of the donor to the accretor being lower than assumed . 
   the mass of a roche lobe filling main sequence star , @xmath30 , may be approximated as @xmath30 @xmath31 0.11 @xmath32 , where @xmath32 is the orbital period in hours @xcite , and we originally assumed a donor mass of @xmath10.30 @xmath17 . 
   for the accretor , we assumed a 1.4 @xmath33 neutron star . 
   a power law emission model fit to the 2004 july 16 xmm - newton spectrum of b158 yielded a photon index of 0.57@xmath00.09 @xcite , which is considerably harder than any spectrum emitted by a black hole binary . 
   however , some neutron stars have masses @xmath22@xmath17 ( see e.g. * ? ? ? 
   * ; * ? ? ? 
   * ) , and it is possible that xb158 contains a particularly massive neutron star . 
   we noted in @xcite that other xbs such as xb146 exhibited strong luminosity fluctuations between fairly consistent maxima and minima during our chandra monitoring observations , and suggested that this long - term behavior could be indicative of a short period / low mass ratio system . 
   our new findings support this hypothesis . 
   we thank the anonymous referees for suggesting improvements to this work , in particular prompting more rigorous estimation of the super - orbital period . 
   we thank the swift team for making this work possible . 
   this work was funded by swift grant nnx13aj76 g .
summary: the m31 globular cluster x - ray binary xb158 ( a.k.a . bo 158 ) exhibits intensity dips on a 2.78 hr period in some observations , but not others . 
   the short period suggests a low mass ratio , and an asymmetric , precessing disk due to additional tidal torques from the donor star since the disk crosses the 3:1 resonance . 
   previous theoretical 3d smoothed particle hydrodynamical modeling suggested a super - orbital disk precession period 29@xmath01 times the orbital period , i.e. @xmath181@xmath03 hr . we conducted a swift monitoring campaign of 30 observations over @xmath11 month in order to search for evidence of such a super - orbital period . fitting the 0.310 kev swift xrt luminosity lightcurve with a sinusoid yielded a period of 5.65@xmath00.05 days , and a @xmath25@xmath3 improvement in @xmath4 over the best fit constant intensity model . 
   a lomb - scargle periodogram revealed that periods 5.45.8 days were detected at a @xmath23@xmath3 level , with a peak at 5.6 days . 
   we consider this strong evidence for a 5.65 day super - orbital period , @xmath170% longer than the predicted period . 
   the 0.310 kev luminosity varied by a factor @xmath15 , consistent with variations seen in long - term monitoring from chandra . 
   we conclude that other x - ray binaries exhibiting similar long - term behaviour are likely to also be x - ray binaries with low mass ratios and super - orbital periods .