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x - ray binaries ( xbs ) represent the end - points of stellar evolution , and the xb population of a galaxy is informed by the star formation history of that galaxy . one way of characterizing such populations is the distribution of their orbital periods ; however , the estimation orbital periods for extra - galactic xbs is extremely challenging , unless they happen to be at high enough inclinations to exhibit dips and/or eclipses . the most accessible extra - galactic population for period studies is the m31 x - ray transient group . these are expected to be low mass x - ray binaries ( lmxbs ) with black hole ( bh ) primaries , since the galactic bh lmxbs are nearly all transient @xcite ; transient neutron star lmxbs also exist , but the majority of transients contain bh primaries ( see e.g. * ? ? ? * ) . x - ray and optical observations of these transients allow us to estimate their size , and therefore period , using the methods described below . comparing the period distributions of the m31 and galactic bh transient lmxbs may shed light on possible differences in the star formation and binary evolution histories of these galaxies . * hereafter vpm94 ) found the absolute v band magnitudes of 18 galactic lmxbs to vary between @xmath45 and + 5 , depending on the size of the accretion disk , and x - ray luminosity . to do this , they required a sample with well known distances , and therefore limited the sample to systems exhibiting x - ray bursts with radius expansion , soft x - ray transients and z - sources . the eddington limit was assumed to be 2.5@xmath5 erg s@xmath6 . they found that the optical counterparts to bursters were fainter than those of non - bursters ; this was a first clue that the optical and x - ray luminosities were linked , because bursters tend to have low x - ray luminosities , while the non - bursting z - sources operate near the eddington limit . furthermore , previous work suggested that @xmath7 was proportional to the orbital period ( e.g. * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) ; this led vpm94 to postulate that the relation between x - ray and optical luminosities ( @xmath8 and @xmath9 respectively ) was caused by x - ray reprocessing in the accretion disk . the vpm94 toy model suggested that @xmath9 @xmath10 @xmath11 , where @xmath12 is the binary separation . one might expect @xmath9 to be proportional to @xmath13 , since that is related to the area of the disk assuming that the disc radius is proportional to @xmath12 . however , the disk temperature decreases with radius : @xmath14 @xmath10 @xmath15 , and @xmath9 @xmath10 @xmath13 @xmath16 where @xmath17 @xmath02 for the observed temperature range in lmxbs ( vpm94 ) . kepler s third law gives @xmath12 @xmath10 @xmath18 ; vpm94 simplified this by assuming that the masses of the two stars were similar , and defined @xmath19 as @xmath20 . their empirical relation @xmath21 provided a good match to observations over 3 orders of magnitude in @xmath19 . however , their sample includes black hole and neutron star accretors , and a mix of different x - ray spectral states . more recently @xcite examined the correlations between optical / infra - red and x - ray luminosities for neutron star and black hole x - ray binaries separately , also factoring in the masses of the accretor and donor stars ( i.e. @xmath22 and @xmath23 ) . they found that the broadband bvri luminosity ( @xmath24 ) correlated well with @xmath25 over 8 orders of magnitude in @xmath8 for black hole binaries , and also neutron star binaries in the hard state ; the black hole normalization was @xmath010 times higher than the neutron star normalization , consistent with the expectation that black hole systems have larger disks for a given orbital period because @xmath26 is larger for black holes than for neutron stars . moss et al . ( 2012 , in prep , hereafter m12 ) focused on the @xmath7 vs. @xmath19 relation for black hole binaries in the high state at the peak of their outbursts , with the aim of providing the best period estimates for x - ray transients . they used x - ray and optical data for transients near their outburst maximum . their new empirical relation @xmath27 tends to result in a shorter period than the relation described in equation 1 . we note that the only significant difference between equations 1 and 2 is in the normalization , again caused by the larger disks in the black hole systems . we have conducted a 12 year campaign to monitor the central region of m31 for bright x - ray transients . over 130 chandra observations were made over this time , averaging one per month ; no observations are made when m31 is too close to the sun . bright new transients are followed up with hst acs wfc observations using the f435w filter that approximates the b band . one observation was made shortly after the transient outburst , and another observation was made @xmath06 months later , if there were no serendipitous coverage in an earlier observation ( see * ? ? ? * ; * ? ? ? * ; * ? ? ? * and nooraee et al . 2012 ) . in this work , we present our analysis of 12 x - ray transients observed with chandra acis and hst . herein we present the discovery of 2 new optical counterparts , and provide revised period estimates for all 12 systems . x - ray transient behaviour appears to be governed by thermal - viscous instability in the accretion disc , with hot and cold stable phases , along with an unstable transitional phase ( see e.g. * ? ? ? * and references within ) . the outbursts occur when the accretion disc enters the hot stable phase ; however , the resulting x - ray illumination prevents the disc from returning to the cold state until the x - ray luminosity is sufficiently diminished ( * ? ? ? * hereafter kr98 ) . kr98 showed that we may expect exponential decay lightcurves so long as the the whole disc is irradiated with x - rays ; otherwise , linear decay is expected . for long transient outbursts , kr98 expect the decay to switch from exponential to linear after a few e - folding times . @xcite analyzed the decay lightcurves of various transients , and found good agreement with the theory of kr98 ; furthermore , they found that systems with multiple outbursts tended to exhibit the same type of decay during each outburst . we provide a journal of hst observations in table  [ journ ] . for each hst acs observation we provide a number , the observation i d , the date , the exposure time , the pointing , and the target ( labeled t1t12 in order of increasing ra ) ; we also provide the closest acis observation , along with the time of observation with respect to the hst observation . if the transient is in a region that we have already observed , then a dedicated `` off '' observation is unnecessary . we have examined 90 chandra acis observations of the central region of m31 , spaced over @xmath012 years ; these observations comprise a monitoring programme that is designed to find transient x - ray sources in the central region of m31 . the roll - angle of each observation was unconstrained , resulting in an approximately circular field of view with 20@xmath28 radius . we determined the position of each source from a merged 0.37 kev acis image , using the iraf tool imcentroid . the merged acis image was registered to the field 5 b band image from the local group galaxy survey observations of m31 @xcite , using 27 x - ray bright globular clusters . we were unable to register the chandra positions with the hst observations directly because only a few of the hst fields contained x - ray bright globular clusters . after refining the positions of the globular cluster in the chandra and lgs b band images with imcentroid , we found the sky co - ordinates of the new positions with xy2sky , then registered the x - ray positions to the lgs b band image using the iraf task ccmap . the mean r.m.s . uncertainty in position due to registration was 0.11@xmath29 in r.a . and 0.09@xmath29 in dec . we extracted source and background lightcurves and spectra , along with the appropriate response files , for each observation of all 12 sources . source and background regions were circular , with the same radius ; the radius was optimized for crowding and off - axis angle , and ranged over @xmath0230@xmath29 . the location of each background region was chosen to be near to the source region , but not so close that it might be contaminated by source flux . we created long term , calibrated lightcurves for each source , obtaining a 0.310 kev unabsorbed luminosity for each observation . we used these lightcurves to determine the overall variability of each x - ray source , and the x - ray luminosity at the times closest to each hst observation . since we expect our transients to be black hole x - ray binaries in the high / soft state , we initially estimated the conversion from flux to luminosity by assuming a disk blackbody emission spectrum with inner disk temperature k@xmath30 = 1 kev , and @xmath31 = 6.7@xmath32 atom cm@xmath6 ( the galactic line of sight column density ) , then determining the unabsorbed 0.310 kev luminosity equivalent to 1 count s@xmath6 . after correcting for the exposure , vignetting and background , multiplying the source intensity by this conversion factor gave the source luminosity . source spectra with @xmath34200 net counts were freely fitted with disk blackbody models . when good spectral fits were found for a particular observation of a source , the parameters of these fits replaced the default parameters when estimating the source luminosity for observations of the source with @xmath2200 photons .      for each acs observation , we examined two types of images provided by the stsci . each observation had contained one drizzled ( drz ) image and 48 flat - fielded ( flt ) images . the drizzled image is the final product : the flat fielded images are combined , the sky background is subtracted , and cosmic rays are removed ; the image is scaled by intensity ( electron s@xmath6 ) . the flt images were corrected for instrumental effects ( dark , bias , and flat ) ; however , the sky was not subtracted , and cosmic rays were not removed ; furthermore , the image was scaled to the total number of electrons received over the observation . we used the drz images to create the difference images described below , but the flt files for photometry since daophot requires an accurate measurement of the sky background . each drizzled hst observation was registered to the lgs b band image , using the method described in the previous section . we then made a difference image for each pair of on / off observations . to achieve this , we first used the iraf task wregister to ensure that the pixels in each image had the same co - ordinate system and orientation . we then used the farith ftool to create the difference image . we examined the difference image for each observed variable x - ray source , looking for significant changes within a 3@xmath1 radius , including the uncertainty in the centroid position , and the r.m.s uncertainty in registration of the chandra image to the lgs b band image ; the r.m.s uncertainties in registering the hst images to the lgs image were negligible . if no counterpart was found in the difference image , then we estimated the 4@xmath1 upper limit to the b magnitude of an undetected star . to do this , we summed the counts in each of the flt images , within a circle with 2 pixel radius at the position of the x - ray source , for a total of @xmath35 counts over @xmath36 seconds . the maximum intensity of the counterpart is then 4@xmath37 , which we convert to vega b magnitude via @xmath38 + 25.76.\ ] ] in order to ensure that our b magnitude limits were believable , we ensured that daophot was able to detect several stars with similar or fainter magnitudes in the flt images . for images where the sky level varied significantly , we restricted the search for similarly faint stars to areas with similar sky levels as the target .    unfortunately , we did not have the simultaneous bvri observations to utilize the relation found by @xcite ; however , we did obtain period estimates using the vpm94 and m12 methods . both the vpm94 and m12 methods for estimating the orbital period require the absolute magnitude in the v band . we assumed that our f435w flux represented the b band flux , and used the relation b@xmath4v = 0.09 that was empirically derived for lmxbs @xcite . systematic studies of x - ray scattering halos around galactic lmxbs have shown that @xmath39 @xmath0 @xmath31 / 1.8@xmath40 atom @xmath41 @xcite while @xmath39/e@xmath42 @xmath03 ( see e.g. * ? ? ? * ) ; hence a@xmath43 @xmath0 @xmath44 . finally , the distance modulus for m31 is 24.47 @xcite . hence @xmath45      when calculating the periods derived from the m12 relation , we were able to include uncertainties in the relation . we achieved this by randomly altering the @xmath7 of every galactic black hole binary high state in the moss et al ( 2012 ) sample ten thousand times , drawn from a normal distribution scaled by the uncertainties , and obtaining a new @xmath7 vs. @xmath46 @xmath19 relation for each iteration ; these @xmath7 distributions had means and spreads that were consistent with the data . we then obtained the @xmath46 @xmath19 corresponding to the @xmath7 of each target in every iteration , and derived the mean log @xmath19 and uncertainties for each target by fitting a gaussian to the resulting log @xmath19 distribution . unfortunately , we did not have access to sufficient information to include uncertainties in the vpm94 relation ; instead , we propagated the uncertainties in @xmath7 and @xmath8 assuming that the relation was fixed . figure  [ btrans ] shows the locations of the 12 transients on a log - scaled b - band image of the central region of m31 , provided by the lgs ( massey et al . , 2006 ) . table  [ translist ] gives the positions of each target , and summarizes the results discussed later in this section ; we provide the 0.310 kev luminosity during the closest acis observation to the hst on observation , our estimated 0.310 kev luminosity at the time of the hst on observation , the b magnitude ( or 4 @xmath1 upper limit ) for the counterpart , and period estimates using the empirical relations of vpm94 and m12 . we present the @xmath012 year , 0.310 kev unabsorbed luminosity lightcurves of the 12 transients in fig . .      only four of the targets had @xmath34200 photons in the chandra observation that was closest to the hst on exposure : t1 , t2 , t5 , and t9 . spectral fit parameters are provided in table  [ spectab ] for absorbed disk blackbody models . the t9 spectrum was piled up ; we account for this in noorae et al . ( 2012 , submitted ) . only t1 apparently experienced greater than galactic absorption , with @xmath31 = 2.5@xmath31.9@xmath40 atom @xmath41 ( uncertainties are quoted at the 90% confidence level ) . we find that @xmath47 = 1.9@xmath31.4 for t1 , and 0.50 for the remaining transients . vpm94 obtained x - ray luminosities from the ariel v x - ray catalog , and ariel v employed the 210 kev band @xcite . hence we estimated the 210 kev luminosity of each target at the time of the hst observation . for those transients with freely fitted spectra , we used the @xmath48 factors provided in table  [ spectab ] . for transients with no freely fitted spectra , we assume k@xmath30 = 1 kev , giving @xmath48 = 0.48 .    however , it is possible that certain transients were in their low / hard state at the time of the hst on observation ; the transition from low state to high state during the rise of the outburst occurs at a luminosity @xmath4910% eddington @xcite , while the transition from high state to low state during the decay occurs at @xmath02% eddington due to hysteresis ( see e.g. * ? ? ? * and references within ) . the low state may be characterized by a power law with photon index @xmath50 @xmath0 1.7 ; assuming a power law with @xmath50 = 1.7 rather than a disk blackbody with k@xmath30 = 1 kev results in 210 kev luminosities that are @xmath075% higher , and periods that are @xmath035% shorter . since 8 of the 12 transients only yielded upper limits to their periods , we present the more conservative upper limits obtained by assuming high state spectra . we present the difference images for t1t12 in fig . [ difim ] , showing the difference in intensity between the drizzled images of the on and off observations ; white is positive , and black is negative . the 1@xmath1 and 3@xmath1 uncertainty ellipses are shown , including uncertainties in x - ray position , and x - ray registration to the lgs b image . north is up , east is left . each image shows a 5@xmath29@xmath515@xmath29 field . the background level varied considerably , with the nuclear region being drastically more crowded than the outer regions ; as a result , 4@xmath1 detection limits ranged over b@xmath02629 . [ [ t1 ] ] t1 ^^    chandra , swift , hst and einstein observations of t1 are discussed in detail by @xcite . t1 has no acs off image with the f435w filter , because the wfc was not in use at the time . instead , we used a serendipitous 81 s v band acs / wfc observation ( i d j92ga5naq , 2005 - 02 - 17 , pi crotts ) . there are many black stars in the difference image , because they are brighter in the v band than in the b band ; however , there are no white stars to signify the transient , and we estimate that b @xmath3428.7 . the sky background was extremely low , and we detected several stars over the image with b @xmath5228.7 at the 4@xmath1 level in one flt image . since there was no b band off image , we examined the 8 individual flt images to determine whether there were any detections of stars within the 3@xmath1 ellipse ; this allowed us to discriminate between stars and e.g. cosmic rays . we found no stellar candidates that were detected in @xmath343 out of 8 flt images , and conclude that there were no bright b band stars within the 3@xmath1 ellipse .    for t1 , the closest acis observation to the hst on image was obs 7139 ( day @xmath02500 in fig . 2 ) , taken 27 days previously ; however , t1 was not covered by any acis observations for @xmath34100 days either side of the 2006 outburst . in a later outburst ( day @xmath03900 ) , the 0.310 kev luminosity went from 8.6@xmath5110@xmath53 to 0.4@xmath5110@xmath53 erg s@xmath6 over 27 days . assuming exponential decay , the e - folding time was 8.8 days . we applied the same exponential decay to the 2006 outburst , and found a 0.310 kev luminosity of 0.5@xmath5110@xmath53 erg s@xmath6 at the time of the hst on observation . for the peak spectrum , we obtained a best fit k@xmath30 of 1.5@xmath30.3 kev ; as a result , @xmath48 = 0.55 . [ [ t2 ] ] t2 ^^    the t2 outburst ( day @xmath02550 ) lasted @xmath0150 days . the x - ray peak was during obs 7140 , 32 days prior to the hst on observation . fitting the lightcurve with exponential decay yielded an e - folding time of 38 days ; however , the residuals were large , and the @xmath54/dof was unacceptable ( 47/3 ) . we also fitted the lightcurve with power law and straight line models ; the best fit values had worse @xmath54/dof than the exponential fit . there was insufficient data to estimate the intensity for a model where the decay went from exponential to linear , hence the exponential decay model provided the best estimate of the 0.310 kev luminosity of t2 at the time of the hst on observation . using the best fit e - folding time of @xmath040 days , we obtained a 0.310 kev luminosity of @xmath06@xmath5110@xmath53 erg s@xmath6 for the hst on observation . the best fit disk blackbody model for the peak spectrum yielded k@xmath30 = 0.54 @xmath30.04 kev ; this results in a 210 kev luminosity of just 1.5@xmath55 erg s@xmath6 . the positioning of the t2 on observation was off by @xmath341@xmath28 , due to the misidentification of the guide star . as a result , it was impossible to accurately register the flt images to the drizzled image , and this limited our photometric accuracy . the difference image shows one particularly variable star ; its b magnitude changed from @xmath024.7 to @xmath025.6 between the on and off observations . we therefore consider this star to be the most likely counterpart . since the our optical counterpart to t2 had a b magnitude @xmath025.6 even after the x - rays had disappeared , we removed this component when calculating the period . [ [ t3 ] ] t3 ^^    t3 was first studied by @xcite , who found no counterpart and concluded that b @xmath3425.5 . however , our method of estimating the magnitude limit for the counterpart yielded b @xmath3427.2 . t3 exhibited two outbursts , @xmath02000 days apart ; the hst observations were triggered by the first outburst . this outburst had an observed peak 0.310 kev luminosity of 3.7@xmath30.3@xmath5110@xmath53 erg s@xmath6 , 22 days before the hst on observation ( day @xmath01700 ) ; however , the next observation of t3 was @xmath0150 days afterward , where the 0.3 - 10 kev luminosity had fallen to 0.35@xmath30.09 @xmath5110@xmath53 erg s@xmath6 . if we assume that these observations cover a single exponential decay , then the e - folding time is 68 days . the 0.310 kev luminosity would then be @xmath02.73@xmath5110@xmath53 erg s@xmath6 at the time of the hst on observation . [ [ t4 ] ] t4 ^^    t4 was mostly quiescent , but exhibited a @xmath01500 day period of x - ray activity , starting on day @xmath01500 where the intensity varied by a factor @xmath020 . the hst on observation was triggered at day @xmath02500 . the 0.310 kev luminosity of t4 was @xmath561.5@xmath55 erg s@xmath6 for the chandra observations closest to the hst on observation , and @xmath00.4@xmath55 erg s@xmath6 at the time of the off observation . we found no evidence for stellar variability in the difference image of t4 ; we set @xmath57 @xmath3428.9 .    [ [ t5 ] ] t5 ^^    t5 was first discussed by @xcite , who found no counterpart , and set a magnitude limit of b @xmath34 24.7 due to the high sky background caused by proximity to the nuclear region . our careful analysis of the flt images from this observation with daophot improved the magnitude limit to b @xmath34 26.6 . t5 exhibited a single outburst that was observed for @xmath080 days , starting at day @xmath01750 . exponential fits to the decay lightcurve were rejected ( @xmath54/dof @xmath5863/3 ) ; however the lightcurve was well described by linear decay with slope @xmath40.06 ( @xmath54/dof = 3.5/3 ) . the hst on observation occurred 29 days after the observed peak , hence we estimate the 0.310 kev luminosity to be 4.0@xmath55 erg s@xmath6 . the brightest observation yielded a spectrum with k@xmath30 = 1.1@xmath30.2 , yielding a 210 kev luminosity of 2.5@xmath55 erg s@xmath6 . [ [ t6 ] ] t6 ^^    we discovered from our long - term acis lightcurve of t6 that it is not a transient , but does vary by a factor @xmath5610 . fortunately , t6 was observed 6 times in our survey , and we were able to make a difference image from the two observations with the highest contrast in x - ray luminosity ( observations 3 and 4 in table 1 ) . we found no evidence for variability in the difference image within the 3@xmath1 ellipse ; instead , we estimate b to be @xmath3426.3 . we estimate that the 0.310 kev luminosity of t6 varied by a factor @xmath04 between hst observations 3 and 4 ( as described in table 1 ) , from @xmath00.9@xmath5110@xmath53 to @xmath00.2@xmath5110@xmath53 erg s@xmath6 . [ [ t7 ] ] t7 ^^    t7 exhibited a slow , faint outburst that lasted @xmath0250 days , starting at day @xmath02300 . the shape of the outburst was unlike the classical fast rise followed by exponential decay ( fred ) ; instead , the lightcurve was approximately flat for the four observations either side of the hst on image , with a 0.310 kev luminosity of @xmath0 0.6@xmath5110@xmath53 erg s@xmath6 . since the 0.310 kev luminosity of t7 did not significantly vary between its on and off observations , we can not expect to detect optical variability in the counterpart . as a result , we must set our magnitude limit to that of the brightest star within the 3@xmath1 position uncertainty ellipse , giving b @xmath3425.0 . [ [ t8 ] ] t8 ^^    t8 was initially quiescent , turned on around day 1400 , and has been active ever since . the 0.310 kev luminosity was @xmath00.4@xmath5110@xmath53 erg s@xmath6 at the time of the hst on observation , and also at the the time of the off observation . as with t7 , there was no significant difference between the x - ray luminosity of t8 at the times of the hst on and off observations . hence we set our magnitude limit to be fainter than the brightest star within 3@xmath1 of the x - ray position , i.e. b @xmath3423.9 . [ [ t9 ] ] t9 ^^    t9 was brightest x - ray source ever seen in m31 , and is discussed in detail in @xcite and noorae et al . the difference image shows a clear counterpart within the 1@xmath1 region . b = 23.91@xmath30.08 . no counterpart was observed in the `` off '' image , and b @xmath3427.8 at the 4@xmath1 level ; hence , we assume that all of the optical light comes from reprocessed x - rays . the closest acis observation was 14 days after the hst on image . however , the observed peak occurred in a hrc observation , 34 days before the hst on observation . the decay lightcurve appears to transition from exponential decay to linear decay ( see nooraee et al . , 2012 ) ; we estimate the 0.310 kev luminosity to have been @xmath050@xmath55 erg s@xmath6 at the time of the hst on observation . using a disk blackbody emission model , and correcting for pile - up effects , yielded k@xmath36 @xmath00.8 kev ; as a result , we estimate the 210 kev luminosity to have been @xmath018.6@xmath55 erg s@xmath6 at the time of the hst on observation . t10 is discussed in detail by @xcite , who used daophot and allstar to disentangle the counterpart from its bright neighbor . the counterpart dominated the blend for the on observation , but was significantly fainter in the off observation , allowing @xcite to obtain b = 24.90 for the other star . assuming the magnitude of the other star was 24.90 during the on observation yielded b = 24.52@xmath30.08 for the counterpart during the on observation , and 24.95@xmath30.08 during the off observation . as with t2 , we subtracted the `` off '' component of the optical emission when calculating the orbital period for t10 . the t10 outburst was captured in 5 acis observations over @xmath0180 days ; the shape is flat - topped , rather than the typical fast rise followed by exponential decay . the closest acis observation occurred 1 day before the hst on observation , with 0.310 kev luminosity 3.0@xmath30.2@xmath5110@xmath53 erg s@xmath6 ; given the slow evolution of the outburst , we assume the same luminosity at the time of the hst on observation .      the t11 outburst was significantly detected in 5 acis observations over 54 days . the decay was well described by an exponential with an e - folding time of 33 days ( @xmath54/dof = 2/5 ) . we calculated the 0.310 kev luminosity to be @xmath00.34@xmath5110@xmath53 erg s@xmath6 . the t11 difference image revealed a likely counterpart within the 1@xmath1 ellipse . we found that b = 24.87@xmath30.09 for the on observation . we found no trace of a counterpart in the `` off '' observation ; b @xmath3428.2 at the 4@xmath1 level . hence , we assume that all of the optical light comes from reprocessed x - rays . t12 was first discussed by @xcite , who identify a counterpart despite the fact that it is brighter in the off observation than in the on observation ; it appears as a black star in fig . [ difim ] . we disagree with this interpretation , since there is no scenario where the disc brightens during decay , and instead impose a 4@xmath1 upper limit of b @xmath34 27.9 . t12 exhibited an apparently double - peaked outburst over @xmath0200 days , with the second peak brighter than the first . however , the previous observation to include t12 was @xmath0150 days earlier , meaning that the true peak was not observed . the 0.310 kev luminosity fell from 2.4@xmath30.3@xmath55 to 0.26@xmath30.09@xmath55 erg s@xmath6 over 61.5 days ; if we assume exponential decay , then the 0.310 kev luminosity was @xmath00.9@xmath55 erg s@xmath6 at the time of the hst on observation . since the e - folding time for transient decay is @xmath02.2 times longer in the optical than in the x - ray lightcurves , the vpm94 and m12 relations only truly apply to the peak of the outburst , and get more inaccurate as the burst evolves . we made two sets of period calculations for each source : one set estimating the x - ray luminosity of each transient at the time of the hst observation , and one set estimating the optical luminosity at the time of the x - ray peak . comparison of the two sets of periods indicated the robustness of these estimates .    for t1 , the ns periods agreed within to within 30% , and the bh periods varied by 40% ; the e - folding time was particularly short for this system . for t9 there was a @xmath030% discrepancy between the periods . for t12 , the periods differed by a factor @xmath03 ; this large discrepancy may be due to the double - peaked nature of the t12 outburst . the two sets of periods agreed to within @xmath010% for all targets not previously specified . these results suggest that the observed peaks were generally close enough to the true peaks for the vpm94 and m12 relations to hold . the periods listed in table  [ translist ] are those obtained by estimating the x - ray luminosity at the time of the hst on observation ; we provide 1@xmath1 uncertainties for systems with identified counterparts , and 3@xmath1 upper limits to the periods for systems with magnitude limits . we note that some of the transients are rather x - ray faint , suggesting that they are more likely to be in the low / hard state , rather than the thermal high state ; the bolometric luminosities of these sources would then be somewhat higher , leading to shorter periods . however , most of these systems only have upper limits to the period already ; t11 is the only x - ray faint source with a counterpart . we note that @xcite fitted the acis spectra of t10 despite their low quality ( @xmath0120 net source counts ) . they favor power law emission models with n@xmath59 @xmath02@xmath40 atom @xmath41 ; they dismissed disk blackbody emission models because the @xmath31 was below the line - of - sight value instead of fixing @xmath31 . as a result , they found l@xmath60 = 6@xmath55 erg s@xmath6 , and @xmath7 = @xmath41.3@xmath30.5 , both a factor @xmath02 brighter than our values ( see table  [ translist ] ) ; these results give a @xmath0130 hr period , considerably longer than the @xmath050 hr period that we obtained . however , we checked these spectra and found @xmath31 to be consistent with the galactic line - of - sight absorption , and we prefer the results from our assumed spectral model .      in fig . [ perdist ] we order the transients by increasing bh period ; the y axis serves to separate them , but does not reflect any physical parameter . circles and stars represent ns and bh periods respectively , for systems with counterparts ; otherwise , we give the 3@xmath1 upper limits , represented by arrows . we show the period distribution of 15 milky way bh binaries listed in @xcite for comparison , represented by squares ; the three persistently bright bh hmxbs are excluded . our period distribution for the m31 transients is similar to that of the galactic bh lmxbs ; however the m31 transients may tend towards shorter periods . we have not included the period for t8 since its x - ray magnitude did not vary between the hst on and off observations , meaning that our b band magnitude limit was set by the brightest star within the 3@xmath1 positional uncertainty . this limit is brighter than most of the observed counterparts , and the resulting period limit is not useful . while the x - ray luminosity of t7 did not vary between the hst on and off observations either , the b magnitude limit was fainter than any of the observed counterparts so we have included t7 . we tested the possibility that the periods of the transients in m31 are consistent with those in the milky way using the tests for univariate data implemented in the asurv package ; this method allows us to compare a censored population , containing some systems with upper limits only , with an uncensored population , where all the values are known , within uncertainties ( see e.g. * ? ? ? * ; * ? ? ? we find that the two distributions are inconsistent at the @xmath09298% confidence level . in order to assess the effect of uncertainties on the orbital periods of the m31 systems we repeated the test several times by randomly sampling periods assuming that they follow a normal distribution with the mean and standard deviation calculated from the values in table 2 . in all cases the results give very similar confidence levels . our sample of m31 transients differs from the mw transients at the @xmath02@xmath1 level ; increasing the m31 transient population should amplify this result . @xcite discovered an enhanced population of x - ray binaries within @xmath0100@xmath29 of the m31 nucleus . the radial distribution of `` primordial '' , i.e. expected , lmxbs follows the distribution of stellar mass in the galaxy @xcite ; however , the surplus population appears to follow the @xmath61 distribution expected of dynamically formed binaries @xcite . dynamically formed lmxbs are normally very rare outside globular clusters ; however , @xcite propose that the bulge of m31 is sufficiently large and dense to allow the formation of a significant number of dynamically formed binaries . however , the stellar velocities in the m31 bulge are @xmath0510 times higher than in globular clusters ; hence @xcite expect only short period binaries to survive , with most of the survivors containing black holes . since the number of dynamically formed black binaries is strongly dependent on the distance from the center ( @xmath62 ) , one might expect to observe some correlation between orbital period and radial distance for our transients . in the top panel of fig . [ rvp ] we plot @xmath62 vs. @xmath63 for each transient , excluding t8 . the bottom panel of fig . [ rvp ] shows f435w ( @xmath0b band ) detection limit for each transient ; t7 lies in a diagonally - shaded region because it showed no x - ray variability between the hst on and off observations , hence the b magnitude was limited by the brightest star within the 3@xmath1 location ellipse rather than the local background . the sensitivity increased steadily with increasing @xmath62 , varying by 2.5 magnitudes ( i.e. a factor 10 ) . we employed the cox hazard test and the kendal tau test , both implemented in asurv to deal with bivariate data , to compare the population located 20@xmath29 @xmath2 @xmath62 @xmath2150@xmath29 with the population at 150@xmath29 @xmath2 @xmath62 @xmath2350@xmath29 ; the probability that these two populations were drawn from the same population ( @xmath64 ) is @xmath00.12 . limiting @xmath62 to 300@xmath29 , thereby removing t2 , and re - running the cox hazard and kendal tau tests produces the same result . by contrast , extending @xmath62 to 400@xmath29 for the second group , thereby including t1 , eradicates any trace of a correlation . therefore , a more substantial transient population is required to confirm this suspected correlation . x - ray transients are expected to exhibit exponential or linear decay , depending on whether or not the disc is fully ionized ; this depends on the orbital period and peak x - ray luminosity @xcite . hence we used fig . 1 of that paper to determine whether the decays of our targets should be exponential or linear .    with two exceptions , all of our targets are expected to exhibit exponential decay ; t7 is consistent with either linear or exponential decay , while t11 should decay linearly according to @xcite .    interestingly the decay of t11 was definitely more exponential ( @xmath54/dof = 2/5 ) than linear ( @xmath54/dof = 93/5 ) ; we suggest that the true peak luminosity of t11 was considerably higher than the observed peak 0.310 kev peak of @xmath04@xmath5110@xmath65 erg s@xmath6 . the true orbital period of t11 could then be significantly shorter than our estimate of 150@xmath330 hr . furthermore , the t5 outburst appears to have decayed linearly , even though exponential decay is expected ; no observations were made in the @xmath0170 days prior to the observed outburst , hence we may have caught the linear tail of a longer and brighter outburst . a brighter peak x - ray luminosity for t5 would mean a shorter period ; however , this would not affect our results , since we only have an upper limit for t5 . we report new orbital period estimates for 12 x - ray transients observed by chandra and hst . we have identified counterparts to 4 x - ray sources , 2 of those are new to this work ; we have estimated 4@xmath1 upper limits to the b magnitudes of the remaining 8 systems . period estimates were previously published for 5 sources ( t1 , t3 , t5 , t10 , t12 ) , using the vpm94 empirical relation @xcite , and noorae et al . ( 2012 ) have already applied the m12 relation to t9 . we obtained periods that ranged from @xmath20.17 hours to @xmath2175 hours for black hole lmxbs using the m12 relation , and @xmath20.4490@xmath390 hours for neutron star lmxbs using the vpm94 relation . the m31 transients that we have followed up appear to favor shorter periods than the galactic black hole transients ; if all of our transients contain bhs , then the probability for the m31 and mw binaries being drawn from the same population is @xmath20.08 . this result may be explained by an excess of x - ray binaries dynamically formed in the high density bulge of m31 ; such systems require short periods to survive @xcite . however , some of the transients with the shortest periods may contain neutron stars . we searched for a correlation between the period and distance from the nucleus that would further support the hypothesis of @xcite . we found a hint of a correlation , at the @xmath090% confidence level . further observations of m31 transients with chandra and hst will add significance to these relations . we thank the referee for their thoughtful comments that helped clarify this work . this research has made use of data obtained from the chandra data archive , and software provided by the chandra x - ray center ( cxc ) . is funded by chandra grant go9 - 0100x and hst grant go-11013 . m.r.g . and s.s.m are both partially supported by nasa contract nas8 - 03060 . , m. , isobe , t. , & feigelson , e. 1992 , in astronomical society of the pacific conference series , vol .  25 , astronomical data analysis software and systems i , ed . d.  m.  worrall , c.  biemesderfer , & j.  barnes , 245                                            cccccccccccc obs & i d & date & exp & ra & dec & target & chan obs & sep . + 1 & j8vp02010 & 2003 - 12 - 25 & 2200 & 00:42:56.03 & + 41:12:19.0 & t10 on & 4680 & + 2 days + 2 & j8vp03010 & 2004 - 01 - 23 & 2200 & 00:42:43.86 & + 41:16:30.1 & t6 on & 4681 & @xmath668 days + 3 & j8vp04010 & 2004 - 06 - 14 & 2200 & 00:42:33.39 & + 41:17:43.4 & t3 on & 4682 & @xmath422 days + 4 & j8vp05010 & 2004 - 08 - 15 & 2200 & 00:42:41.50 & + 41:17:00.0 & t5 on & 4719 & + 29 days + 5 & j8vp07010 & 2004 - 10 - 02 & 2200 & 00:42:56.04 & + 41:12:19.1 & t10 off & 4721 & + 2 days + 6 & j8vp08010 & 2004 - 11 - 02 & 2200 & 00:43:09.93 & + 41:23:32.6 & t12 on & 4721 & @xmath429 days + 7 & j8vp09010 & 2004 - 11 - 22 & 2200 & 00:42:41.49 & + 41:17:05.2 & t5 off & 4723 & + 13 days + 8 & j8vp10010 & 2005 - 01 - 01 & 2200 & 00:43:09.91 & + 41:23:32.5 & t12 off & 4723 & @xmath427 days + 9 & j9ju01010 & 2006 - 02 - 10 & 4360 & 00:42:52.38 & + 41:16:49.2 & t8 on & 7136 & @xmath435 days + 10 & j9ju02010 & 2006 - 07 - 09 & 4360 & 00:42:33.89 & + 41:23:31.1 & t4 on & 7139 & + 22 days + 11 & j9ju03010 & 2006 - 07 - 15 & 4352 & 00:42:51.17 & + 41:19:17.9 & t7 on & 7139 & @xmath416 days + 12 & j9ju04010 & 2006 - 08 - 27 & 4344 & 00:42:16.08 & + 41:19:26.1 & t1 on & 7139 & @xmath427 days + 13 & j9ju05010 & 2006 - 10 - 25 & 2148 & 00:42:17.34 & + 41:15:37.0 & t2 on & 7140 & @xmath432 days + 14 & j9ju06010 & 2007 - 01 - 10 & 4672 & 00:42:52.38 & + 41:16:49.2 & t8 off & 8183 & + 4 days + 15 & j9ju07010 & 2007 - 01 - 12 & 4672 & 00:42:33.88 & + 41:23:31.2 & t4 off & 8183 & + 2 days + 16 & j9ju08010 & 2007 - 01 - 12 & 4672 & 00:42:51.14 & + 41:19:18.0 & t7 off & 8183 & + 2 days + 17 & j9ud17010 & 2009 - 08 - 25 & 4360 & 00:42:17.31 & + 41:15:37.5 & t2 off & 10555 & @xmath455 days + 18 & jb9d15010 & 2010 - 01 - 21 & 4360 & 00:42:53.15 & + 41:14:22.9 & t9 on & 11278 & + 14 days + 19 & jb9d20010 & 2010 - 07 - 20 & 4360 & 00:42:53.15 & + 41:14:22.9 & t9 off & 11840 & @xmath43 days + 20 & jbdl01010 & 2010 - 12 - 09 & 5472 & 00:42:57.00 & + 41:20:05.0 & t11 on & 12162 & @xmath41 day + 21 & j9ju08010 & 2011 - 07 - 20 & 4672 & 00:42:51.17 & + 41:10:17.9 & t11 off & 12972 & @xmath45 days +    cccccccccccc targ & ra & @xmath67 & dec & @xmath68 & @xmath69 & @xmath70 & @xmath57 & @xmath7 & @xmath71 & @xmath72 + 1 & 00:42:16.106 & 0.015 & + 41:19:26.36 & 0.27 & 8.9@xmath32.3 & 0.3 & @xmath3428.7 & 2.45 & @xmath210.6 & @xmath211.6 + 2 & 00:42:17.330 & 0.012 & + 41:15:37.48 & 0.11 & 12.8@xmath31.2 & 2.89 & 24.7@xmath30.3 & @xmath40.2 & 120@xmath35 & 16@xmath73 + 3 & 00:42:33.426 & 0.012 & + 41:17:03.56 & 0.14 & 3.7@xmath30.3 & 1.59 & @xmath3427.2 & 2.3 & @xmath23.6 & @xmath24.5 + 4 & 00:42:33.883 & 0.016 & + 41:23:31.49 & 0.19 & 2@xmath30.2 & 0.88 & @xmath3428.9 & 4 & @xmath20.4 & @xmath20.97 + 5 & 00:42:41.805 & 0.010 & + 41:16:35.94 & 0.10 & 5.8@xmath30.8 & 2.52 & @xmath3426.6 & 1.7 & @xmath26.0 & @xmath25.6 + 6 & 00:42:43.834 & 0.011 & + 41:16:30.60 & 0.11 & 0.94@xmath30.12 & 0.53 & @xmath3426.3 & 1.4 & @xmath235 & @xmath231 + 7 & 00:42:51.199 & 0.012 & + 41:19:17.81 & 0.13 & 0.51@xmath30.1 & 0.35 & @xmath3425 & 2.9 & @xmath2380 & @xmath2175 + 8 & 00:42:52.433 & 0.010 & + 41:16:48.75 & 0.10 & 0.35@xmath30.08 & 0.29 & @xmath7423.9 & @xmath41 & @xmath22400 & @xmath21000 + 9 & 00:42:53.181 & 0.010 & + 41:14:22.83 & 0.10 & 38@xmath39 & 18.62 & 23.91@xmath30.08 & @xmath40.99 & 61@xmath311 & 18@xmath75 + 10 & 00:42:56.049 & 0.012 & + 41:12:18.64 & 0.13 & 3@xmath30.2 & 1.77 & 24.52@xmath30.02 & @xmath40.38 & 163@xmath38 & 9@xmath76 + 11 & 00:42:56.991 & 0.017 & + 41:20:05.35 & 0.31 & 0.39@xmath30.10 & 0.2 & 24.87@xmath30.09 & @xmath40.03 & 490@xmath390 & 140@xmath77 + 12 & 00:43:09.963 & 0.030 & + 41:23:32.56 & 0.43 & 1.65@xmath30.12 & 0.53 & @xmath34 27.9 & 3 & @xmath22.8 & @xmath24.8 +    cccccccccccc object & net source counts & @xmath31 / 10@xmath78 atom @xmath41 & k@xmath36 / kev & @xmath54/dof & @xmath79 + t1 & 374 & 2.5@xmath31.9 & 1.5@xmath30.3 & 10/15 & 0.55 + t2 & 756 & 0.67 & 0.54@xmath30.04 & 35/31 & 0.25 + t5 & 330 & 0.67 & 1.1@xmath30.2 & 4/12 & 0.59 + t9 & 1135 & 0.67 & 0.8 & 64/49 & 37 +
almost all galactic black hole binaries with low mass donor stars are transient x - ray sources ; we expect most of the x - ray transients observed in external galaxies to be black hole binaries also . obtaining period estimates for extra - galactic transients is challenging , but the resulting period distribution is an important tool for modeling the evolution history of the host galaxy . we have obtained periods , or upper limits , for 12 transients in m31 , using an updated relation between the optical and x - ray luminosities . we have monitored the central region of m31 with chandra for the last @xmath012 years , and followed up promising transients with hst ; 4@xmath1 b magnitude limits for optical counterparts are  2629 , depending on crowding . 
 we obtain period estimates for each transient for both neutron star and black hole accretors . 
 periods range from @xmath20.4 to 490@xmath390 hours ( @xmath20.97 to @xmath2175 hrs if all are bh systems ) . 
 these m31 transients appear to be somewhat skewed towards shorter periods than the milky way ( mw ) transients ; indeed , comparing the m31 and mw transients with survival analysis techniques used to account for some data with only upper limits yield probabilities of @xmath00.020.08 that the two populations are drawn from the same distribution . 
 we also checked for a correlation between orbital period and distance from the nucleus , finding a 12% probability of no correlation . 
 further observations of m31 transients will strengthen these results .