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astronomers have sought for two decades for dynamical evidence for the presence of massive black holes in galaxies by studying the dynamics of gas and stars in their nuclei . rapid motions provide the main signature of a black hole . if these are indeed observed , the main difficulty is to rule out alternative interpretations . gas motions can be due to hydrodynamical processes ( inflow , outflow , turbulence , etc . ) in addition to gravity . large stellar velocities in galactic nuclei can be the result of an overabundance of stars on radial orbits . the primary observational tool to discriminate between different models is to obtain data of the highest possible spatial resolution .    in recent years much progress has been made in all areas of this field . for active galaxies , the existence of a central dark mass in at least some galaxies is now well established . the rotation velocities of nuclear gas disks detected with the hst can be used to study the central mass distribution . this has yielded evidence for a central dark mass of @xmath9 in m87 ( ford 1994 ; harms 1994 ) , and of @xmath10 in ngc 4261 ( ferrarese , ford & jaffe 1996 ) . even higher spatial resolution vlba radio observations of water masers in the nucleus of the active galaxy ngc 4258 ( miyoshi 1995 ) have revealed a torus in keplerian rotation around a dark mass of @xmath11 . for the case of ngc 4258 , there are strong theoretical arguments that this mass is indeed a black hole ( maoz 1995 ) . the density of quasars at high redshifts suggests that many currently normal galaxies had an active phase in the past ( chokshi & turner 1992 ; haehnelt & rees 1993 ) . hence , black holes are believed to be common in quiescent galaxies as well . in these galaxies only stellar kinematics are generally available to study the nuclear mass distribution . the evidence for a black hole in our own galaxy is now very strong , due to proper motion measurements for individual stars near sgr  a@xmath12 ( eckart & genzel 1996 , 1997 ) . for a handful of other , nearby galaxies , evidence for a central dark mass was obtained from ground - based measurements of line - of - sight velocities ( see kormendy & richstone 1995 for a review ) , but it remained difficult to rule out all alternative models . it was always foreseen to be a main task for the hst to improve the evidence , by providing spectra of superior spatial resolution . stellar kinematical studies with hst became possible after the refurbishment mission in 1993 . the first results were presented by kormendy ( 1996a , b ) , for ngc 3115 and ngc 4594 . spectra near the nucleus with @xmath13 resolution confirmed previous arguments for black holes of @xmath14 and @xmath15 , respectively . the quiescent e3 galaxy m32 has long been one of the best - studied black hole candidate galaxies . the presence of a central dark mass of @xmath16@xmath17 has been argued on the basis of ground - based data with continuously increasing spatial resolution . the most recent work indicates a central dark mass of @xmath18@xmath19 ( van der marel et al . 1994b ; qian et al . 1995 ; dehnen 1995 ; bender , kormendy & dehnen 1996 ) . however , the best ground - based kinematical data still have a spatial resolution of ` only ' @xmath20 . goodman & lee ( 1989 ) showed that this is insufficient to rule out a cluster of dark objects , as opposed to a central black hole , on the basis of theoretical arguments . in addition , none of the previous dynamical studies has considered axisymmetric stellar dynamical models with fully general phase - space distribution functions . hence , it has not been shown convincingly that no plausible model can be constructed that fits the data without requiring a central dark mass . higher spatial resolution data are therefore highly desirable . this paper is part of a series in which we present the first hst spectra and new dynamical models for m32 . we obtained spectra of the nuclear region with the hst / fos , and we give here a detailed description of the acquisition and analysis of these data . dynamical models are presented in van der marel ( 1997b ) and cretton ( 1997 ) . the main results of the project are summarized and discussed in van der marel ( 1997a ) . the instrumental resolution of the fos has a gaussian dispersion of @xmath21 , while the wavelength scale can vary at the @xmath22 level from orbit to orbit . a study of a low mass galaxy such as m32 ( the main body of which has a velocity dispersion of @xmath23 and a rotation velocity amplitude of @xmath24 ) is therefore significantly more complicated observationally , than that of more massive galaxies ( which have higher dispersions ) . an additional complication is that the ` sphere of influence ' of the suspected black hole in m32 is smaller than that of most other candidate galaxies . it is thus necessary to use the smallest fos apertures , for which it is more difficult to do an accurate target acquisition . in addition , for a proper interpretation of the results it is necessary to determine the aperture position for each observation _ post facto _ , with an accuracy of @xmath25 . to deal with these complications it proved necessary to study the instrument and analyze the data in more than the usual detail . parts of this paper are therefore of a somewhat technical nature . readers interested mostly in the stellar kinematical results may wish to skip directly to section  [ ss : results ] . the paper is organized as follows . section  [ s : obsetup ] summarizes the observational setup and strategy . section  [ s : pos ] discusses the aperture positions for the observations . section  [ s : datareduc ] describes some aspects of the data reduction . section  [ s : lsf ] presents calculations of the line - spread function for each observation . section  [ s : temp ] discusses the template spectrum used in modeling the m32 spectra . section  [ s : kinematics ] discusses the kinematical analysis . section  [ s : discussion ] summarizes the main observational results . in the appendices , new calibrations and modeling are presented of the fos aperture sizes , point - spread - function ( psf ) and line - spread - functions , for which no sufficiently accurate determinations were previously available . we observed m32 with the red side detector of the hst / fos for nine spacecraft orbits on august 22 , 1995 ( project go-5847 ) . the costar optics corrected the spherical aberration of the hst primary mirror . telescope tracking was done in ` fine lock ' . the rms telescope jitter was typically @xmath26 milli - arcsec ( mas ) . each orbit consisted of @xmath27 minutes of target visibility time , followed by @xmath28 minutes of earth occultation . the first two orbits were used to accurately acquire the nucleus of m32 . subsequently , spectra were taken at various positions near the nucleus . the g570h grating was used in ` quarter - stepping ' mode , yielding spectra with 2064 pixels covering the wavelength range from 4572  to 6821  . periods of earth occultation were used to obtain wavelength calibration spectra of the arc lamp . in the last orbit of the observations the fos was used in a special mode to obtain an image of the central arcsec of m32 , to verify the telescope pointing . two different square apertures were used to obtain the spectra : the ` 0.1pair ' and the ` 0.25pair ' . these are the smallest apertures available on the fos . although they are paired ( two square openings separated by several arcsec ) , they were used exclusively in single - aperture mode . all data were collected through the upper aperture . the aperture names are based on their size in arcsec _ before _ the installation of costar . their nominal post - costar sizes are smaller : @xmath29 square and @xmath30 square , respectively . evans ( 1995a ) presented calibration observations in which the light throughput was measured for a point source as function of position in the apertures . models for these observations presented in appendix  [ s : appa ] indicate somewhat smaller aperture sizes : @xmath2 square and @xmath31 square , respectively . these sizes are adopted in the remainder of the paper . the natural coordinate system of the fos is the cartesian @xmath32 system defined in the fos instrument handbook ( keyes 1995 ) . the apertures have their sides parallel to the axes of this system . the grating disperses the light in the @xmath33-direction . the @xmath32 system is ` left - handed ' when projected onto the sky . in the following we adopt a more convenient ` right - handed ' system @xmath34 , defined through @xmath35 and @xmath36 . during the observations , the direction of the @xmath37-axis was fixed at a position angle of @xmath38 on the sky . this coincides with the major axis position angle of m32 ( cf . lauer 1992 ) . the position of the m32 center in the hst guide star coordinate system is ra @xmath39 0h 42 m 41.82s , @xmath40 . the positional uncertainty is dominated by that in the hst guide star catalog itself , which is @xmath20 rms . hence , some form of acquisition is required to properly position the galaxy in the small apertures . for an extended target with a sharp and well defined brightness maximum , such as m32 , the method of choice is a so - called ` peak - up ' acquisition , which consists of a number of ` stages ' . each stage adopts a rectangular grid of @xmath41 points on the sky , with inter - point spacings of @xmath42 and @xmath43 , respectively . an fos aperture is positioned at each of the grid points , and the total number of counts is measured in some exposure time . the grid point with the most counts is adopted as new estimate of the target position . subsequent stages in a sequence use smaller and smaller apertures , with each stage increasing the accuracy of the target positioning . various standard choices exist for the number of stages , and for the aperture , the grid and the exposure time for each stage in the acquisition ( keyes 1995 ) . these standard sequences work well for point - source targets . however , they have not been particularly well tested for extended sources , especially not for acquisitions into the small 0.1-pair aperture . therefore , as part of the preparation of the observations , a software package was developed to simulate fos peak - up acquisitions of arbitrary targets in a monte - carlo manner ( van der marel 1995 ) . guided by simulations done with this package , a non - standard 5-stage peak - up sequence was constructed for m32 . the parameters of this sequence are listed in table  [ t : peakup ] . the sequence was executed with the g570h grating in place , because m32 is too bright to be acquired with the fos mirror . the accuracy of the sequence is such that in an idealized situation ( no poisson noise , no telescope jitter , etc . ) @xmath44 and @xmath45 , where @xmath46 is the difference between the adopted pointing at the end of the acquisition and the true position of the galaxy center . the observed intensities in the acquisition stages can be analyzed _ post facto _ , to determine the extent to which the acquisition was successful . most important are the results of the fifth and final stage , in which the 0.1-pair aperture was sequentially positioned at the points of a @xmath47 grid on the sky , with spacing of @xmath48 between the grid points . the left panel of figure  [ f : peakup5 ] shows a grey - scale representation of the observations . the solid dot marks the position with the highest intensity , which was adopted by the telescope software as its best estimate for the position of the galaxy center .    to model the observed intensities , the ` cusp model ' for the unconvolved m32 surface brightness presented by lauer ( 1992 ) was used , which is based on pre - costar hst / wfpc images . the point - spread - function ( psf ) of the hst+fos was approximated by a sum of gaussians , as determined in appendix  [ s : appa ] . the total magnitude at each grid point was calculated using the equations in the appendix . the offset @xmath46 was varied to optimize the fit . the best fit is displayed in the right panel of figure  [ f : peakup5 ] . it has @xmath49 , with a formal error in either coordinate ( based on the chi - squared surface of the fit ) of approximately 1 mas . the target acquisition was thus successful . an fos image of the central region of m32 was obtained in the final orbit of the observations . the telescope was commanded to position the upper ` 1.0-pair ' aperture , which has a nominal post - costar size of @xmath50 square , on the galaxy center , after which the intensity on the photocathode was scanned with the diode array of the detector ( with no grating in the light path ) . the scan pattern was chosen to provide @xmath51 pixels . however , the spatial resolution of the image is poor , @xmath52 , corresponding to the size of one fos diode ( koratkar 1994 ; evans 1995b ) . the resolution can be improved by deconvolution . figure  [ f : grey_image ] shows the result of lucy deconvolving the raw image with a boxcar psf with the size of one diode . the cross marks the galaxy center , while the dot marks the aperture center , i.e. ,  the position where the telescope thought the galaxy center would be . the latter is offset from the actual galaxy center by @xmath53 ( with a formal error of 3 mas in each coordinate ) . this offset at the end of the observations is much larger than that achieved by the target acquisition . hence , positional errors must have accumulated during the observations . the reason for this is not well understood . however , the most likely cause is a drift of the telescope pointing due to thermal effects related to the heating and cooling of the spacecraft and fine guidance sensors ( fgss ) during the 14.4 hours of the observations . such thermal effects exist ( lupie , priv .  comm . ) , but were not previously reported to complicate observations with the fos ( keyes , priv . comm . ) . nine spectra were taken . those obtained with the 0.1-pair aperture are referred to as s1s4 , those obtained with the 0.25-pair aperture as l1l5 . table  [ t : obsetup ] summarizes the observational setup for each spectrum . it also lists the position with respect to the galaxy center at which the telescope was instructed to place the aperture . these _ intended _ aperture placements are illustrated in the left panel of figure  [ f : aper_plot ] .    in reality , the apertures were not placed exactly at their intended positions . the actual position is a sum of two vectors : ( i ) an intentional offset from the ( telescope s estimate of the ) galaxy center ( table  [ t : obsetup ] ) ; and ( ii ) an unintentional offset @xmath46 of the telescope s estimate of the galaxy center from the actual galaxy center . the intentional offsets are applied by slewing the telescope , which should be very precise ( @xmath54 mas positional error ) . to determine the actual aperture positions one thus needs to know the offset @xmath46 for each observation . these can be determined by modeling the observed intensities of the spectra , which are listed in table  [ t : applaces ] . the spectra s1 and s2 , taken in the subsequent orbits # 3 and # 4 , were scheduled to have identical aperture positions ( cf .  table  [ t : obsetup ] ) . the same holds for the observations l4 and l5 , taken in the subsequent orbits # 8 and # 9 . in both cases , however , the observed intensities in the two spectra are significantly different . this indicates that the aperture positions must have changed ( by @xmath55 mas , cf . figure  [ f : telpoint ] below ) between the orbits # 3 and # 4 , and between the orbits # 8 and # 9 . there was no motion of either the grating wheel or the aperture wheel of the instrument between the different observations . the guide star reacquisition at the beginning of each orbit is normally accurate to a few mas . hence , the inferred pointing drifts are indeed most likely due to thermal effects on the fgs . to proceed we make a number of simplifying assumptions about the offset @xmath46 : ( i ) the offset for the first spectrum , s1 , taken in orbit # 3 , was identical to the offset determined from the final peak - up stage ( figure  [ f : peakup5 ] ) , executed in orbit # 2 ; ( ii ) the offset for the last spectrum , l5 , taken in orbit # 9 , was identical to the offset determined from the fos image ( figure  [ f : grey_image ] ) , taken in that same orbit ; ( iii ) the observations s2s4 , taken in orbits # 4 , # 5 and # 6 , have a common offset ; and ( iv ) the observations l1l4 , taken in orbits # 7 and # 8 , have a common offset . these assumptions do not allow for positional errors between orbits # 4 and # 5 , between orbits # 5 and # 6 , and between orbits # 7 and # 8 . even though errors could have occurred , they are not required to fit the observed intensities . the assumptions do allow for an error between orbits # 6 and # 7 , when the 0.1-pair aperture was replaced by the 0.25-pair aperture . this is because these apertures might not be exactly concentric on the aperture wheel ( evans 1995 ) , and because the motion of the aperture wheel might have a positional non - repeatability ( dahlem & koratkar 1994 ) .    with these assumptions , the offset @xmath46 can be determined for each observation by fitting to the observed intensities , using the lauer ( 1992 ) cusp model for the m32 surface brightness , and the aperture sizes and psf determined in appendix  [ s : appa ] . the results are displayed in figure  [ f : telpoint ] . the corresponding aperture placements for the individual spectra are listed in table  [ t : applaces ] and are displayed in the right panel of figure  [ f : aper_plot ] . the fits to the intensities constrain only the absolute value of @xmath56 , and not its sign . this introduces an ambiguity for l1l4 , which was resolved by adopting the same sign for @xmath56 as measured in figure  [ f : grey_image ] ( so as to minimize the size of the positional error between orbits # 8 and # 9 ) . at the positions of the apertures ( along the major axis ) , the surface brightness changes more rapidly along the @xmath37 direction than along the @xmath57-direction hence , the observed intensities constrain the @xmath58 more tightly than the @xmath56 . other model assumptions to fit the observed intensities were also studied . in all cases the results for @xmath58 agreed to within a few mas , while the @xmath56 could differ by as much as @xmath59 . most of the necessary data reduction steps are performed by the hst calibration ` pipeline ' . for the m32 data , three issues required additional attention : ( i ) wavelength calibration ; ( ii ) absolute sensitivity calibration ; and ( iii ) flat - fielding . the wavelength scale provided by the calibration pipeline is not accurate enough for our project . arc lamp spectra were therefore obtained in each orbit during occultation . the emission line centers were determined , yielding for each arc spectrum @xmath60 and for each line @xmath61 with vacuum wavelength @xmath62 , the observed wavelength @xmath63 on the scale provided by the calibration pipeline . subsequently , the observed offsets @xmath64 were fit as @xmath65 the constant offset @xmath66 is the result of non - repeatability in the fos grating and aperture wheels , and was measured to be @xmath67 . the third order polynomial @xmath68 with zero mean accounts for a slight ( @xmath69 ) non - linearity of the wavelength scale . the offsets @xmath70 account for constant shifts of the wavelength scale from orbit to orbit , mostly due to the ` geo - magnetically induced image motion problem ' ( keyes 1995 ) . these shifts ranged between @xmath71 , and could be determined with @xmath72 ( @xmath73 ) accuracy . the wavelength scale of the m32 spectra was corrected using the above fits to the arc spectra . an additional shift of @xmath74 was applied to correct for the fact that the light path for external targets differs from that for the internal arc lamp ( keyes 1995 ) . for each m32 spectrum the @xmath70 were used that was / were determined from the arc spectrum / spectra obtained immediately preceding or following the m32 spectrum . the fact that the arc spectra are never obtained completely simultaneously with galaxy spectra introduces a slight additional uncertainty . the cumulative uncertainty in the mean streaming velocities of the stars as a result of uncertainties in the wavelength scale is estimated to be @xmath75 . this is always smaller than the formal errors in these velocities as a result of photon noise ( cf . table  [ t : kinresults ] below ) . after wavelength calibration ( and absolute sensitivity calibration and flat - fielding as described below ) the galaxy spectra were rebinned logarithmically in wavelength , as required for the stellar kinematical analysis . a scale of @xmath76pixel was used . the fos is a photon counting detector , so the formal errors in the spectra follow directly from poisson statistics . on average , the ( logarithmic ) rebinning decreases the formal errors , since it reduces the scatter between neighboring pixels . the decrease can be calculated for each pixel , and was taken into account in the subsequent analysis . the correlation between the errors in neighboring pixels induced by the rebinning was neglected . the calibration pipeline multiplies the observed count rate spectra by a so - called ` inverse sensitivity file ' ( ivs ) , to obtain fluxes in @xmath77@xmath78 . the pipeline ivs files contain a wavelength dependent aperture throughput correction , based on calibration observations of point sources . these , however , are not applicable to extended sources . therefore , instead of the standard pipeline ivs file a more recent ivs file with no aperture throughput correction was used , provided to us by fos instrument scientist tony keyes . each wavelength in the m32 spectra samples a slightly different region of the galaxy , because of the wavelength dependence of the psf . this influences only the continuum slope of the spectra , because the psf varies very slowly with wavelength . in the stellar kinematical analysis one is only interested in the absorption lines , which are not influenced . the underlying continuum is subtracted . hence , no attempt was made to construct aperture throughput corrections . ( in fact , this would require accurate knowledge of the wavelength dependence of the psf , which is not readily available for the fos ; see appendix  [ s : appa ] ) . a g570h flat - field based on multiple 0.25-pair ( upper ) aperture observations of a star was used , as provided to us by tony keyes . no flat - fields obtained explicitly with the 0.1-pair ( upper ) aperture were available . a star illuminates the photocathode of the detector differently than an extended source . to test the appropriateness of the flat - field for the m32 data it was cross - correlated with the continuum subtracted normalized galaxy spectra . this yielded clear peaks , indicating that the flat - field and the m32 spectra share the same features ( as they should ) . the peak was only @xmath7910% lower for the 0.1-pair spectra than for the 0.25-pair spectra . this indicates that the flat - field can be properly used for the 0.1-pair ( upper ) aperture as well , although a flat - field obtained specifically with that aperture would have been preferable . shifts between the galaxy spectra and flat - field were identified from the positions of the cross - correlation peaks , and were corrected for ( see also kormendy 1996a ) . the flat - fielding removes most of the pixel - to - pixel sensitivity variations , but some small residual variations might remain . the observed spectrum of a source is the convolution of its actual spectrum with the line - spread - function @xmath80 . the lsf can be written as the convolution of an ` illumination function ' @xmath81 and an ` instrumental broadening function ' @xmath82 ( cf . appendix  [ s : appb ] ) . the function @xmath81 is the normalized intensity distribution of the light that falls onto the grating . it depends on the target brightness and choice of aperture . the direction of dispersion is parallel to the @xmath57 direction . hence , @xmath81 is the integral over the @xmath37 direction of the two - dimensional brightness distribution that falls onto the grating . for the psf and aperture sizes derived in appendix  [ s : appa ] , @xmath81 is given by equations  ( [ blamdef ] ) and  ( [ bkernel ] ) in appendix  [ s : appb ] . it can be calculated for each observation upon substitution of the lauer ( 1992 ) cusp model for the m32 surface brightness , and the aperture positions in table  [ t : applaces ] . the normalized function @xmath82 accounts for the instrumental broadening due to the grating and finite size of a detector diode ( the resolution element ) . it was determined empirically from fits to the emission line shapes in the arc spectra , as discussed in appendix  [ s : appb ] . the lsf has zero mean if the galaxy light is distributed symmetrically within the aperture . this is not generally the case , because the aperture centers are not exactly at @xmath83 ( figure  [ f : aper_plot ] ) . calculations show that the intensity weighted mean position is within @xmath84 from the aperture center for all the observations . nonetheless , there are noticeable wavelength shifts , because @xmath84 projects onto @xmath85 in the wavelength direction ( @xmath86 at 5170 ) . table  [ t : applaces ] lists the lsf mean as calculated for each of the m32 spectra , both in  and in @xmath6 at 5170 . errors in these values due to errors in the aperture positions do not exceed 0.04 ( @xmath87 at 5170 ) . the width and shape of the lsf are determined mainly by the aperture size . the calculated lsfs for all the m32 spectra are shown in figure  [ f : lsf ] . the lsf shapes for the 0.1-pair observations are very similar to each other , as are the lsf shapes for the 0.25-pair observations . the shapes are also similar to the emission line shapes observed directly in arc spectra ( figure  [ f : arc ] ) . the 0.25-pair lsf can be well approximated by convolving the 0.1-pair lsf by a gaussian with a dispersion of @xmath88 ( @xmath89 at 5170 ) , as illustrated by the dotted curve in figure  [ f : lsf ] . the best - fitting gaussian to the 0.1-pair lsf has a dispersion of @xmath90 ( @xmath91 at 5170 ) . for the 0.25-pair lsf it has a dispersion of @xmath92 ( @xmath93 at 5170 ) . however , these numbers are of limited use in characterizing the lsfs , since these have noticeably broader wings than a gaussian . for stellar kinematical analysis a template spectrum is needed to compare the m32 spectra to . to avoid systematic errors it is important to minimize template mismatching . this is best done by constructing a composite template which contains an appropriate mix of spectral types . observing template stars with the hst is inefficient and time consuming ( mainly because of the lengthy target acquisitions that are required ) . to date less than a handful different template stars have been observed with the hst , all of similar spectral type . these hst spectra are insufficient to construct an optimal template . a ground - based template library of spectra of 27 stars of different spectral types was therefore used , obtained in february 1990 by m.  franx at the 4 m telescope of the kpno with the rc spectrograph ( as discussed previously by van der marel & franx 1993 ) . the lsf of these spectra is approximately gaussian with a dispersion of @xmath94 ( @xmath95 at 5170 ) . the spectra cover the spectral range from 4836 to 5547 , centered on the mg b triplet at @xmath96 . this is the most useful wavelength range for stellar kinematical analysis , so it is no drawback that this range is smaller than the full range covered by the fos g570h grating . the stellar spectra were similarly rebinned logarithmically as the galaxy spectra , and shifted to a common velocity . no attempt was made to construct a different composite template for each m32 spectrum ( which is reasonable , given that there are no strong color gradients in the central arcsec ; lugger 1992 ) . instead , the best fit was sought to a grand - total m32 spectrum , constructed by summing the hst spectra . the resulting composite template is a weighted mix of the individual templates , with the weights determined using the method outlined in appendix  a.3 of van der marel ( 1994a ) . the mix contains giants , sub - giants and dwarfs of spectral types  g and  k.    the composite template is used in the remainder of the paper . however , other templates were studied as well . for example , a stellar kinematical analysis was performed with a k - star template spectrum obtained from the hst data archive , taken with the fos circular 0.3 aperture ( @xmath97 diameter ) by h.  ford and collaborators before the installation of costar . this template provides a poor fit to the spectrum of m32 . nonetheless , the stellar kinematical properties inferred with this template were found to be consistent with those derived using the composite template . the stellar kinematical analysis was performed with the method presented in van der marel ( 1994a ) . it fits the convolution of a parametrized velocity profile and a template spectrum to a galaxy spectrum in pixel space , using chi - squared minimization . the formal errors in the fit parameters follow from the shape of the chi - squared surface near its minimum . the method has been well tested , and its results agree with those from other methods for extracting stellar kinematics from galaxy spectra . deviations of the line - of - sight velocity profiles from gaussians contain useful information on the dynamical structure of galaxies . unfortunately , the velocity resolution of the fos is too poor to extract any reliable velocity profile shape information from the m32 data . the analysis was therefore restricted to gaussian velocity profile fits . data obtained with the fos is time resolved . the red side detector reads and stores the data every @xmath98 minutes . between 6 and 20 spectra were therefore available per aperture position . the aperture positions for the observations l4 and l5 differ by @xmath99 , but both are at a distance of @xmath20 from the galaxy center , where kinematical gradients are small . in the kinematical analysis l4 and l5 were therefore treated as a single observation , referred to as l45 . especially for the 0.1-pair observations , the signal - to - noise ratio ( s / n ) of the individual read - outs is low . individual read - outs for a given aperture position were therefore added to achieve an average s / n of @xmath100 per ( logarithmically rebinned ) pixel . this resulted in 4 independent spectra for each of the observations s1s4 with the 0.1-pair aperture , and between 9 and 11 independent spectra for the observations l1 , l2 , l3 and l45 with the 0.25-pair aperture . a stellar kinematical analysis was performed on each of these spectra . the kinematical results for each aperture position were then averaged together , weighted with the errors . it was found that this yields slightly more accurate results than a kinematical analysis of the sum of the individual spectra for a given aperture position . no systematic trends with time in the orbit were found in the kinematical results . the stellar kinematical analysis was performed over the wavelength range 48595520 . regions influenced by so - called ` noisy ' diodes were masked . the fit to the galaxy spectrum includes a low order polynomial to account for continuum differences between the galaxy and template spectrum . this polynomial is fit simultaneously with the velocity profile . the parameters of the best - fitting velocity profile are virtually independent of the choice of polynomial order . a polynomial of order 5 was used .      the mean velocity and velocity dispersion of the best - fitting gaussian velocity profiles must be corrected for instrumental effects . the mean velocity is biased because the lsf mean is non - zero . this bias is removed by subtracting the corrections @xmath101 listed in table  [ t : applaces ] . these were calculated for the wavelength 5170 of the mg b triplet , but the wavelength dependence of the velocity corrections over the fit range is negligible ( @xmath102 in absolute value ) . further , to obtain velocities in the m32 frame one must subtract a constant offset , determined by the difference between the systemic velocity of m32 and the template velocity . these were not known accurately enough to determine the offset directly , and it was therefore estimated from the data itself . somewhat arbitrarily , it was fixed to the intercept of the best least - squares fit line in a plot ( see figure  [ f : allres]c below ) of rotation versus position @xmath37 along the m32 major axis for the observations s4 , s1 and s2 ( for which @xmath103 , @xmath104 and @xmath105 , respectively ) . the velocity dispersions @xmath106 of the best - fitting gaussians must be corrected for differences in the lsfs of the template and galaxy spectra . for this it is useful to consider not the observed dispersions themselves , but rather differences in the observed dispersions between two observations . let @xmath107 and @xmath108 be the best - fitting dispersions for observations at positions a and b. assume that the lsf of observation b can be obtained from the lsf of observation a through convolution with a gaussian of dispersion @xmath109 . the difference between the actual dispersions at positions a and b can then be estimated as : @xmath110 ( which uses the fact that the convolution of two gaussians is again a gaussian , the dispersion of which is the rms sum of the input dispersions ) . this approach has two important advantages . first , the lsf of the template influences the kinematical analysis at points a and b in the same way , so it does not enter into @xmath111 . second , the differences in the lsfs for the hst observations can in fact to good approximation be accounted for by convolution with a gaussian ( cf . figure  [ f : lsf ] ) . one does _ not _ have to assume that the lsfs themselves are gaussian , which would be a poor approximation .    in the following , the observation l45 at @xmath20 from the galaxy center is used as ` reference point ' . equation  ( [ sigdef ] ) then yields @xmath112 where @xmath113 for an observation with the 0.25-pair aperture , and @xmath114 for an observation with the 0.1-pair ( based on the results of section  [ s : lsf ] ) . the latter value was calculated for the wavelength 5170 of the mg b triplet , which is roughly at the center of the fit range . the actual value of @xmath115 varies from @xmath116 to @xmath117 over the fit range , which can be taken into account by assigning a ` formal ' error of @xmath118 to @xmath109 . equation  ( [ sigcor ] ) can be used to estimate the stellar velocity dispersion @xmath119 for any of the observations s1s4 and l1l3 , if one assumes that the dispersion @xmath120 at the position of observation l45 is known a priori . at @xmath121 along the major axis one is beyond the region most influenced by seeing in ground - based data . based on the data of van der marel ( 1994a ) and bender , kormendy & dehnen ( 1996 ) it was assumed that @xmath122 ( see figure  [ f : allres]d below ) . it is demonstrated in appendix  [ s : appc ] that the velocity dispersions thus obtained have no systematic biases , and that even velocity dispersions as small as @xmath23 can be measured reliably , in spite of the large fos instrumental dispersion of @xmath123 . the formal errors in dispersions @xmath119 obtained from equation  ( [ sigcor ] ) follow from the errors in @xmath106 , @xmath124 , @xmath125 and @xmath126 using a standard first order error analysis . systematic errors due to template mismatching are not likely to exceed a few @xmath6 , and are smaller than the formal errors in the measurements . table  [ t : kinresults ] lists the line strengths , rotation velocities and velocity dispersions , after correction for all instrumental effects . these results are discussed below . figure  [ f : allres ] displays the results as function of the position @xmath37 of the aperture center along the m32 major axis . the best spatial resolution ground - based m32 data are also shown . these are the data from van der marel ( 1994a ) obtained at the william herschel telescope ( wht ) , and those of bender , kormendy & dehnen ( 1996 ) obtained at the canada france hawaii telescope ( cfht ) . a comparison of these ground - based data to older ( lower spatial resolution ) ground - based data can be found in kormendy & richstone ( 1995 ) . the spatial resolution for each of the observations in figure  [ f : allres ] is characterized by a convolution kernel , which results from the psf and finite aperture size ( for ground - based long - slit data the effective aperture is the spatial ccd pixel size by the slit width ) . the top left - panel illustrates the difference in spatial resolution between the data sets . it displays the projection of the convolution kernel along the m32 minor axis , i.e. , the probability @xmath127 that a photon observed in a given aperture was emitted at distance @xmath37 from the center of that aperture , measured along the m32 major axis . these probability distributions have fwhm values of @xmath128 , @xmath129 , @xmath130 and @xmath131 , for the hst / fos/0.1-pair , hst / fos/0.25-pair , cfht and wht data , respectively . the hst data therefore provide a factor 5 increase in spatial resolution over even the best available ground - based data . the line strengths shown in figure  [ f : allres]b were normalized to an average of unity ( line strengths are measured with respect to the template spectrum , and are hence on an arbitrary scale ) . there is no obvious trend with radius . the observations with the 0.1-pair aperture closest to the nucleus have relatively low line strength , but this is unlikely to be real . metallicities and line strengths generally increase towards the centers of galaxies . the observed low values could be an artifact due to the presence of a black hole . the stars that move rapidly near the black hole produce broad velocity profile wings . these can be mistaken for an enhanced continuum , which causes the line strength to be underestimated ( van der marel 1994b ) . the broad - band colors of m32 are constant in the central arcsec ( lugger 1992 ) . the true line strengths in the central @xmath132 covered by the hst observations are therefore probably also close to constant . the observed line strengths have a sizable rms scatter of @xmath133 . this exceeds the formal errors , which are on average @xmath134 . the measurements are therefore not statistically consistent with a constant line strength ( as is confirmed by a chi - squared test ) . the scatter in the observed line strengths could be the result of minor inaccuracies in the data , such as unidentified bad pixels or flat - field errors , or it could be real , and due to shot noise in the contributions from individual stars . the total v - band luminosity inside the aperture varies from @xmath135 ( for observation s3 ) to @xmath136 ( for observation l3 ) . most of the observed light comes from giants , some of which can be as luminous as @xmath137 ( freedman 1989 ) . the luminosity of a ` typical ' giant as measured from surface brightness fluctuations ( tonry , ajhar & luppino 1990 ) is @xmath138 . this implies that there are @xmath139 typical stars in each hst aperture . therefore , @xmath140 fluctuations can be of order a few percent of the intrinsic line strength differences between stars . figure  [ f : allres]c shows the rotation velocities . the hst rotation curve is smooth . it is significantly steeper in the central @xmath141 than seen in the ground - based data , consistent with the presence of a central black hole . the rotation velocity is observed to be @xmath142 at @xmath1 from the nucleus . this is roughly twice the value measured from the ground at this distance . the scatter in the line strength measurements ( figure  [ f : allres]b ) induces scatter in the velocity dispersion measurements , because the velocity dispersion and line strength of a gaussian fit are statistically correlated . tests indicate that a line strength error @xmath143 induces an error @xmath144 in the velocity dispersion . rotation velocity measurements are not influenced . to avoid unwanted errors in the velocity dispersion measurements , they were determined by fitting gaussian velocity profiles to the data while keeping the line strength constant to the mean of the measurements in figure  [ f : allres]b . this yields velocity dispersions that differ only at the @xmath145 level from those obtained by gaussian fits with variable line strength , so the main results do not depend on this correction . figure  [ f : allres]d shows the resulting velocity dispersions . the dispersion measured with the 0.1-pair aperture closest to the nucleus is @xmath3 . the profile of the velocity dispersion with radius is smooth , with the exception of the measurement @xmath146 from observation s2 , which is significantly lower than that for the other observations in the central @xmath1 . we doubt the reality of this , but have not been able to attribute it to any known instrumental effect . the average of the four dispersion measurements inside @xmath1 is @xmath4 , with a rms scatter of @xmath5 . hence , the central velocity dispersion is definitely higher than the 8595@xmath6 determined from ground - based measurements . it thus appears that a keplerian increase in the velocity dispersion close to the center of m32 has been resolved . the difference in the dispersions measured for observations  s1 and  s2 , which were obtained with the same aperture at similar positions , indicates that uncertainties in the velocity dispersions are dominated by systematic errors , rather than poisson noise . systematic errors in the rotation velocity measurements are believed to be much smaller , primarily because these are less sensitive to the poor instrumental resolution of the fos . either way , the data clearly imply that the dispersion in the central @xmath1 is higher than measured from ground - based data . whether the nuclear dispersion seen through a small aperture is indeed as high as @xmath147 should await verification by observations with the future hst spectrograph stis . hst / fos spectra were obtained through small apertures centered on the nuclear region and major axis of m32 . kinematical analysis of these data is more complicated than it is for ground - based data : the fos is a low - resolution spectrograph , and is not particularly well suited for dynamical studies of low - dispersion objects such as m32 . one of the main results of this paper is therefore that stellar kinematical quantities _ can _ in fact be determined from the data , provided that a detailed study is made of various technical issues , including : calibration and modeling of the fos aperture sizes , psf and lsfs , determination of the aperture positions from the data , accurate wavelength calibration , template matching , and corrections for instrumental resolution . the resulting kinematical quantities are displayed in figure  [ f : allres ] . the main result is that in the central @xmath1 the m32 rotation curve is significantly steeper , and the velocity dispersion significantly higher , than measured from even the highest resolution ground - based data . these observational results are robust . they do not depend critically on the corrections made in the analysis ; even a rough analysis without any template matching and corrections for instrumental effects shows these main features . the results are exactly what would be expected if m32 does indeed have a massive dark object in its nucleus , as suggested previously on the basis of ground - based data . in the companion papers in this series ( van der marel 1997a , b ; cretton 1997 ) we construct dynamical models to address the presence of such a dark object quantitatively . we also address the question whether the dark object has to be a black hole , or whether plausible alternatives still exist . the authors are grateful to the fos instrument scientists tony keyes , anuradha koratkar and michael dahlem for helpful discussions , and to bill workman and jean surdej for successful scheduling and implementation of the observations . tony keyes provided preliminary instrument calibration data and marijn franx provided the template library . simon white helped with the early stages of the project . support for this work was provided by nasa through grant number # go-05847.01 - 94a , and through a hubble fellowship # hf-1065.01 - 94a awarded to rpvdm , both from the space telescope science institute which is operated by the association of universities for research in astronomy , incorporated , under nasa contract nas5 - 26555 . some calibrations exist of the hst+fos psfs and lsfs ( koratkar 1996 ) and of the fos aperture sizes ( evans 1995 ) , but these are too crude for the purposes of this paper . to obtain more accurate calibrations we present detailed models for the calibration observations obtained by evans ( 1995a ) after the installation of costar . he centered a star in fos apertures , and stepped the star across each aperture in the fos @xmath57 and @xmath37 directions , respectively . at each step the total intensity was measured . here the results are considered for the fos red detector with three apertures : the square upper aperture of the 0.1-pair , the square upper aperture of the 0.25-pair , and the circular 1.0 . the names of these apertures are based on their size in arcsec , _ before _ the installation of costar . their nominal post - costar sizes are smaller by a factor @xmath148 . figure  [ f : transmis ] shows for each aperture the observed intensity as function of distance from the aperture center , normalized by the observed intensity with the star at the center of the circular 1.0 aperture . the aperture length or diameter is easily determined from these data for apertures much larger than the psf core : it is then twice the radius at which the intensity has fallen to 50% of its central value . this was used by evans ( 1995 ) to estimate the size of all fos apertures . although this is reasonable for the larger apertures , it is not for the smaller apertures . for those a more careful analysis is required , in which the aperture sizes and psf are fitted to the data simultaneously .    for a target with surface brightness @xmath149 , the intensity @xmath150 observed through an aperture centered on @xmath34 is @xmath151 where @xmath152 is a convolution kernel that depends on the psf and the aperture size and geometry . the psf is assumed to be a circularly symmetric sum of gaussians , @xmath153 , \label{psfgauss}\ ] ] where the @xmath154 must satisfy @xmath155 . for a perfectly rectangular aperture with sides @xmath156 and @xmath157 the convolution kernel is then @xmath158             -\mathop{\rm erf}\nolimits              \left [ \fr{x-(a_x/2)}{\sqrt{2}\ > \sigma_i } \right ]       \right \rbrace \ >       \left \lbrace \mathop{\rm erf}\nolimits              \left [ \fr{y+(a_y/2)}{\sqrt{2}\ > \sigma_i } \right ]             -\mathop{\rm erf}\nolimits              \left [ \fr{y-(a_y/2)}{\sqrt{2}\ > \sigma_i } \right ]       \right \rbrace , \ ] ] while for a perfectly circular aperture with diameter @xmath66 it is @xmath159       \int_0^{d/2 }          \exp \left [ - \fr{1}{2 } ( \fr{r}{\sigma_i } ) ^2 \right ] \ >        i_0(\fr{r \rho}{\sigma_i^2 } ) \ > r \ > dr , \ ] ] ( van der marel 1995 ) . the function @xmath160 is the error function and @xmath161 is a bessel function .    this model was used to fit the data in figure  [ f : transmis ] . for a point source at @xmath162 , the intensity observed through an aperture centered at the origin is simply @xmath163 . the solid curves in the figure show the best chi - squared fit to the data for a psf that is a sum of three gaussians . the aperture sizes were treated as free parameters . the square apertures were assumed to have equal sizes in the @xmath57 and @xmath37 directions . the model was forced to fit 2 additional constraints , obtained from theoretical modeling ( as quoted in keyes 1995 ) : ( i ) the throughput ( for a centered point source ) of the circular 1.0 aperture is @xmath164 times that of a rectangular aperture of size @xmath165 ; and ( ii ) the absolute throughput of the @xmath165 aperture is @xmath166 . the best - fitting model parameters are listed in table  [ t : psfapfit ] . the fit is robust , in spite of the fact that the model parameters are highly correlated . in particular : ( i ) no good fit can be obtained if the aperture sizes are held fixed to their nominal post - costar values ( which are @xmath29 square , @xmath30 square , and @xmath50 circular , respectively ) ; and ( ii ) the fit does not improve significantly if the number of gaussians in the psf is increased . the formal errors in the best fit parameters are @xmath167 for the @xmath154 , and @xmath18% for the @xmath168 and aperture sizes . these numbers are not too meaningful , however , because systematic errors probably exceed the formal errors . figure  [ f : psffit ] shows the psf for the best fit , and the encircled flux curve @xmath169 . the latter is given by @xmath170 . \label{encircled}\ ] ] the psf has 73% of the light within a circle of radius @xmath1 . this is smaller than the 84% measured from star images at visual wavelengths obtained with the foc , but larger than the 65% measured with the wfpc2 ( which suffers from additional pixel scattering ) . it should be noted that the psf derived here pertains only to the upper position of the square paired fos apertures . the aperture transmissions , and thus the psf , are somewhat different at the lower positions of the square paired apertures ( evans 1995a ) . the above analysis ignores the effects of diffraction at the aperture edges . the derived aperture sizes are therefore not the geometrical apertures sizes . this might explain why the derived sizes are smaller than the nominal post - costar sizes . non - circularly symmetric features in the psf are also ignored . such features might in fact be present , given that the results of scanning a star across the aperture in the @xmath57 and @xmath37 directions differ slightly ( figure  [ f : transmis ] ) . either way , both the aperture sizes and the psf enter into the data analysis only through the convolution kernels @xmath152 . these kernels are adequately fit by the model , independent of whether or not the aperture sizes and psf of the model are unbiased estimates of their true values . the observations in figure  [ f : transmis ] were derived from so - called ` white light ' images , i.e. , with no grating in the light path . the psf with the parameters of table  [ t : psfapfit ] is therefore an average over all wavelengths to which the detector is sensitive . the m32 observations were obtained with the g570h grating . observations with this grating ( bohlin & colina 1995 ) show fractional throughputs for centered point sources that are larger by a few percent than those in figure  [ f : transmis ] . this indicates that the core of the psf for the g570h grating might be @xmath171% smaller than that of the psf derived here . on the other hand , in fitting the m32 peak - up acquisition observations ( section  [ s : acq_results ] ) by convolving the lauer ( 1992 ) cusp model for the m32 surface brightness , it was found that the chi - squared of the fit could be improved by _ increasing _ the width of the psf core by @xmath172% . this could mean that the psf does in fact have a broader core than derived here , or alternatively , that the lauer model , based on wfpc1 measurements , is not a perfectly adequate representation of the m32 surface brightness in the central @xmath1 . in the absence of theoretical constraints on the wavelength dependence of the psf from accurate wavefront modeling , it was decided not to make any corrections to the psf derived from the white light images ( table  [ t : psfapfit ] ) . the psf remains somewhat uncertain , but it was verified that changes in the psf core width between @xmath173% and 20% do not change any of the major conclusions of our paper(s ) . the observed spectrum @xmath174 of a source is the convolution of its actual spectrum @xmath175 with the line - spread - function @xmath80 , @xmath176 the lsf can be written as the convolution @xmath177 where the ` illumination function ' @xmath81 is the normalized intensity distribution of the light that falls onto the grating , and the normalized ` instrumental broadening function ' @xmath82 accounts for the broadening due to the grating and the detector . the @xmath34 coordinate system is defined such that the @xmath57 direction is parallel to the direction of dispersion . the function @xmath81 is therefore proportional to the integral over the @xmath37 direction of the two - dimensional brightness distribution that falls onto the grating . all the light in the aperture is detected , since the apertures used for the observations are smaller than the @xmath37-size of the diode array of the detector ( @xmath178 ) . for the case of observations of a target with surface brightness @xmath149 through an aperture centered on position @xmath162 , @xmath179 where @xmath180 is defined in equation  ( [ itot ] ) , and @xmath181 is a convolution kernel that depends on the psf and the aperture size and geometry . for the g570h grating the wavelength @xmath182 is related to the position @xmath57 according to @xmath183(x / arcsec )  . if the aperture is rectangular of size @xmath184 , and the psf is as given in equation  ( [ psfgauss ] ) , then @xmath185 \ >         \left \lbrace \mathop{\rm erf}\nolimits                \left [ { { y'+(a_y/2 ) } \over { \sqrt{2}\ > \sigma_i } } \right ]               -\mathop{\rm erf}\nolimits                \left [ { { y'-(a_y/2 ) } \over { \sqrt{2}\ > \sigma_i } } \right ]         \right \rbrace ,            & \quad \vert x \vert \leq { { a_x}\over2 }         ; \\       0 , & \quad \vert x \vert > { { a_x}\over2 }            . \end{array } \right . \label{bkernel}\ ] ]    the grating disperses the image of the aperture onto the photocathode of the detector , which is scanned using an array of diodes . a simple model for the instrumental broadening function @xmath82 is therefore : @xmath186 where @xmath187 is the normalized response function of a detector diode and @xmath188 is the normalized broadening function of the grating . let @xmath187 be a top - hat function with full width @xmath189 , and let the grating broadening function be @xmath190 , where @xmath191 is a normalized function , and @xmath192 is a free parameter that measures the width of @xmath193 . the notation @xmath194 is used for the primitives of @xmath191 . the function @xmath195 is then @xmath196 .\ ] ] it can be determined empirically by fitting to the emission lines in the arc spectra . if the arc lamp illuminates the aperture homogeneously , then @xmath81 is a normalized top - hat function of full width @xmath156 . for an emission line that is intrinsically a delta - function at @xmath197 , the observed line shape will be @xmath198 . \label{oarc}\ ] ] several functional forms were considered for @xmath191 . a gaussian did not yield good fits to the observed line shapes . satisfactory results were obtained with a lorentzian , for which @xmath199 .\ ] ] with this choice , the function @xmath195 has two parameters , @xmath192 and @xmath189 . the best fit is generally attained for values of @xmath189 that differ from the actual size of one diode , which is @xmath200 for the g570h grating . this probably indicates that the true diode response function is not a perfect top - hat . however , this does not invalidate the model . one is interested only in a fit to the function @xmath82 , not in a determination of either @xmath187 or @xmath188 . therefore , both @xmath192 and @xmath189 are treated as free fitting parameters . the best fits were determined to the emission line shapes in arc spectra obtained with the 0.1-pair and the 0.25-pair apertures , while keeping the values of @xmath156 fixed to their values in table  [ t : psfapfit ] . figure  [ f : arc ] shows the fits to the arc lines and the best - fitting function @xmath195 . no evidence was found for a wavelength dependence of the lsf over the wavelength range covered by the grating . the best - fit parameters are : @xmath201 and @xmath202 for the 0.1-pair aperture , and @xmath203 and @xmath204 for the 0.25-pair aperture . hence , the function @xmath82 is broader for the 0.25-pair aperture than for the 0.1-pair . the difference is too large to be attributed to small errors in the assumed aperture sizes . hence , the instrumental broadening is more complicated in reality than in our simplified model , in which one would have expected @xmath82 to be independent of the aperture size . however , the only important point for the interpretation of the m32 spectra is that an accurate empirical description of the lsf is available . the fits in figure  [ f : arc ] suggest that the model is satisfactory for this purpose . tests with artificial galaxy spectra were performed to determine whether systematic biases could be present in the velocity dispersion measurements . artificial galaxy spectra were created from each of the 27 stellar spectra in the template library , by broadening them with gaussian velocity profiles with dispersions @xmath205 . twenty copies were made of each broadened template , and noise was added to yield a s / n of 10 per pixel . a stellar kinematical analysis was then performed on each copy , using the composite spectrum discussed in section  [ s : temp ] as template . the twenty velocity dispersion measurements where then averaged to yield an output velocity dispersion @xmath206 . figure  [ f : kintest ] plots @xmath206 as function of @xmath205 for each of the input spectra . the results lie closely along the line @xmath207 . the minor deviations can be attributed entirely to the template mismatch in the simulations ( the input stellar spectra are giants , sub - giants and dwarfs of spectral types g , k and m ) . at dispersions below @xmath208 there is some tendency for the dispersion to be underestimated . however , for the m32 observations one is always in the situation where the difference in dispersion between the galaxy and template spectrum is @xmath209 ( because the lsf of the galaxy spectra is broader than that of the template , in addition to the kinematical doppler broadening ) . at these dispersions there are no significant biases in the results of the kinematical analysis , but only small ( @xmath210 ) errors due to template mismatching . these errors are nearly independent of the velocity dispersion . since the approach used in this paper for determining velocity dispersions relies on differences between velocity dispersion measurements at different positions , it is expected that even these small errors largely cancel out . a crude consistency check on our approach for determining velocity dispersions can be obtained by making the ( poor ) assumption that the lsfs of both the galaxy and template spectra are gaussian , with dispersions @xmath211 and @xmath212 , respectively . the stellar velocity dispersion @xmath119 then follows from the dispersion @xmath213 obtained by fitting to the galaxy spectrum , according to : @xmath214 for the observation l45 the dispersion measured directly from the spectra is @xmath215 . upon substitution in equation  ( [ sigcorgau ] ) of @xmath216 ( cf . section  [ s : temp ] ) , and @xmath217 ( cf . section  [ s : lsf ] ) one obtains the estimate @xmath218 for the stellar velocity dispersion at @xmath20 along the m32 major axis . this agrees reasonably well with the value of @xmath219 adopted in section  [ s : correc ] on the basis of ground - based measurements . this confirms the result of appendix  [ s : ctests ] that there are no systematic biases in the velocity dispersion measurements from the spectra , and that the differences in the lsfs of the template and galaxy spectra can be fully corrected for . evans , i.  n. , koratkar , a.  p. , keyes , c.  d. , & taylor , c.  j. 1995 , fos instrument science report cal / fos-138 , ` smov report vii : fos aperture alignments  ii . small apertures and adopted alignments ' ( baltimore : space telescope science institute )                        koratkar , a. , wheeler , t. , evans , i. , lupie , o. , taylor , c. , keyes , c. , & kinney , a. 1994 , fos instrument science report cal / fos-123 , ` smov report v : fos plate scale and orientation ' ( baltimore : space telescope science institute )                                                                                  ccccccccr 1 & 4.3 & 3.66 & 1.29 & 2 & 7 & 3.36 & 0.80 & 4.7 + 2 & 1.0pair & 0.86 & 0.86 & 6 & 2 & 0.61 & 0.65 & 7.4 + 3 & 0.5pair & 0.43 & 0.43 & 3 & 3 & 0.29 & 0.29 & 9.1 + 4 & 0.25pair & 0.215 & 0.215 & 3 & 3 & 0.143 & 0.143 & 8.5 + 5 & 0.1pair & 0.086 & 0.086 & 5 & 5 & 0.043 & 0.043 & 38.7 +    ccclcccc s1 & y2uf0107 t & 3 & 0.1-pair & @xmath220 & @xmath221 & @xmath222 & 2400 + s2 & y2uf0109 t & 4 & 0.1-pair & @xmath220 & @xmath221 & @xmath222 & 2400 + s3 & y2uf010bt & 5 & 0.1-pair & @xmath220 & @xmath221 & @xmath223 & 2400 + s4 & y2uf010dt & 6 & 0.1-pair & @xmath220 & @xmath221 & @xmath224 & 2400 + l1 & y2uf010gt & 7 & 0.25-pair & @xmath225 & @xmath221 & @xmath226 & 1105 + l2 & y2uf010ht & 7 & 0.25-pair & @xmath225 & @xmath221 & @xmath227 & 1105 + l3 & y2uf010jt & 8 & 0.25-pair & @xmath225 & @xmath221 & @xmath222 & 1395 + l4 & y2uf010kt & 8 & 0.25-pair & @xmath225 & @xmath221 & @xmath228 & 800 + l5 & y2uf010mt & 9 & 0.25-pair & @xmath225 & @xmath221 & @xmath228 & 1790 +    llcccccc s1 & 0.1-pair & 0.068 & 218.1 & @xmath229 & @xmath230 & @xmath231 & @xmath232 + s2 & 0.1-pair & 0.068 & 203.6 & @xmath233 & @xmath234 & @xmath233 & @xmath235 + s3 & 0.1-pair & 0.068 & 139.7 & @xmath233 & @xmath236 & @xmath233 & @xmath235 + s4 & 0.1-pair & 0.068 & 199.2 & @xmath233 & @xmath237 & @xmath233 & @xmath235 + l1 & 0.25-pair & 0.191 & 686.0 & @xmath238 & @xmath239 & @xmath240 & @xmath241 + l2 & 0.25-pair & 0.191 & 1133.7 & @xmath238 & @xmath242 & @xmath243 & @xmath244 + l3 & 0.25-pair & 0.191 & 1269.3 & @xmath238 & @xmath245 & @xmath246 & @xmath247 + l4 & 0.25-pair & 0.191 & 435.5 & @xmath238 & @xmath248 & @xmath249 & @xmath250 + l5 & 0.25-pair & 0.191 & 427.7 & @xmath251 & @xmath252 & @xmath253 & @xmath254 +    lrrrrrr s1 & 0.941 & 0.038 & @xmath255 & 10.0 & 156.4 & 10.2 + s2 & 0.957 & 0.033 & @xmath256 & 6.4 & 95.6 & 9.8 + s3 & 1.014 & 0.046 & @xmath257 & 9.7 & 111.9 & 11.7 + s4 & 1.049 & 0.039 & @xmath258 & 8.6 & 127.0 & 9.6 + l1 & 0.927 & 0.027 & @xmath259 & 5.3 & 78.3 & 11.0 + l2 & 0.989 & 0.022 & @xmath260 & 4.3 & 83.4 & 9.3 + l3 & 1.104 & 0.022 & @xmath261 & 4.8 & 124.2 & 7.0 + l45 & 0.973 & 0.022 & @xmath262 & 4.3 & 70.0@xmath12 & 5.0 +
we have obtained spectra through small apertures centered on the nuclear region and major axis of m32 , with the faint object spectrograph ( fos ) on the hubble space telescope ( hst ) . a detailed analysis and reduction of the data 
 is presented , including : ( i ) new calibrations and modeling of the fos aperture sizes , point - spread - function and line - spread - functions ; ( ii ) determination of the aperture positioning for each observation from the observed count rate ; and ( iii ) accurate wavelength calibration , template matching , and kinematical analysis of the spectra . 
 this yields measurements of the stellar rotation velocities and velocity dispersions near the center of m32 , with five times higher spatial resolution than the best available ground - based data . 
 the inferred velocities provide the highest angular resolution stellar kinematical data obtained to date for any stellar system . 
 the hst observations show a steeper rotation curve and higher central velocity dispersion than the ground - based data . 
 the rotation velocity is observed to be @xmath0 at @xmath1 from the nucleus . 
 this is roughly twice the value measured from the ground at this distance . 
 the nuclear dispersion measured through the smallest fos aperture ( @xmath2 square ) is @xmath3 . 
 the average of four independent dispersion measurements at various positions inside the central @xmath1 is @xmath4 , with a rms scatter of @xmath5 . 
 the nuclear dispersion measured from the ground is only 8595@xmath6 , whereas the dispersion outside the central arcsec is only @xmath7@xmath8 . 
 these results significantly strengthen previous arguments for the presence of a massive nuclear black hole in m32 . 
 detailed dynamical models are presented in a series of companion papers . 
 # 1#2