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the galaxy distribution in large spectroscopic surveys , such as sloan digital sky survey ( sdss ; * ? ? ? * ) , have revealed a complex hierarchical network of structure , called the cosmic web , composed of clusters , filaments , sheets , and voids ( e.g. * ? ? ? * ) . in the current paradigm of galaxy formation , these structures arise from the linear growth of gaussian density fluctuations in a nearly homogeneous early universe . dark matter tends to flow out of the voids , accretes onto the sheets , collapses to the filaments , and finally accumulates onto the clusters at the intersections of the filaments . due to the accretion history of the universe , the angular momentum of dark matter halos and galaxies are generated and affected by their large - scale environment .    according to the tidal torque theory ( ttt ) , protogalaxies acquire their angular momentum by the asymmetric interaction between their inertia tensor and the local tidal field @xcite . the galaxy and halo spin directions are expected to be correlated with the principal axes of the local tidal tensor . over the past decades , both numerical simulations and real redshift surveys have revealed such correlation between halos / galaxies and their local large - scale structure @xcite .    using numerical simulations , @xcite found that halo spin vectors are preferentially aligned with the intermediate axes of the tidal field , which is consistent with the theoretical prediction using the linear tidal torque theory . similar trends are also claimed from observational data . based on the real - space tidal field reconstructed from the 2mass redshift survey , @xcite claimed that there is a clear intrinsic alignment between the galaxy spins and the intermediate principal axes of the tidal tensor .    for halos in filaments from n - body simulations , recent studies reported a mass - dependence alignment signal between halo spins and filaments . the spins of low - mass halos tend to be parallel to filaments , while high - mass halos have orthogonal alignment @xcite . for halos in sheets , the spin vectors tend to lie in the plane of the sheets , independent of halo mass @xcite . observationally , the picture is not as clear because of limited statistics and because of the difficulty of properly defining cosmic filaments from observational data . several studies have endeavored to solve this problem but give partly contradictory results @xcite . for instance , while @xcite found alignment signals between the spin vectors of galaxies and the surrounding large - scale structures ( e.g. filament and sheet ) , @xcite found no statistical evidence for departure from random orientations . using 2dfgrs and sdss , @xcite found that spiral galaxies located on the shells of cosmic voids have their spins aligned preferentially in the void surface , whereas , @xcite , who used the sdss dr7 and galaxy zoo samples , found that the spins of spiral galaxies around voids tend to be perpendicular to the void surface . based on sdss dr7 , a recent study by @xcite showed that there is a different alignment between spiral and elliptical galaxies , arguing that the spin of spiral galaxies tends to lie parallel to their host filaments , whereas the spin of elliptical galaxies are aligned preferentially perpendicular to their filaments .    in short , observationally the spin alignment with the surrounding large - scale structure is still somewhat contradictory and inconclusive . in our previous paper @xcite , we examined the alignment between the major axes of galaxies and their surrounding large - scale structure . we found that red galaxies are very significantly aligned with their filaments , while blue galaxies are only marginally aligned with respect to their filaments . in this paper , we investigate the spin vectors of spiral galaxies with respect to the surrounding large - scale environments . here again we use the galaxy group catalog constructed from the sdss dr7 @xcite . the cosmic tidal field we used is directly reconstructed from the group catalog using the method described in @xcite . based on the signs of the eigenvalues of this tidal field , we classify the environments of groups into four categories : clusters , filaments , sheets , and voids . the morphologies of galaxies used here are those obtained from the galaxy zoo 2 catalog ( gz2 ; * ? ? ? we measure the spin vectors of spiral galaxies with respect to the principal axes of the local tidal tensor and study how these alignments depend on galaxy properties . the paper is organized as follows . in section [ sec_data ] , we present the observational data and the methodology used to measure the various alignment signals . the alignments of spiral galaxies with respect to cosmic web are present in section [ sec_result ] . we compare the observational results with dark matter halos from n - body simulations in section [ sec_sim ] . finally we summarize our results in section [ sec_summary ] . in what follows we describe the observational data we adopt to characterize the cosmic web and measure the alignment between the spin axes of galaxies relative to the large - scale structures . the galaxy sample we use here is the new york university value - added galaxy catalog ( nyu - vagc ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) , which is based on the multi - band imaging and spectroscopic survey sdss dr7 @xcite . as the completion of the survey phase sdss - ii , dr7 features an imaging survey in five bands over a continuous @xmath0 region in the northern galactic cap . the continuity over this large area is essential and critical to reconstruct the real - space tidal field from the sdss survey . from the nyu - vagc , we select @xmath1 galaxies in the main galaxy sample with an extinction - corrected apparent magnitude brighter than @xmath2 , with redshifts in the range @xmath3 and with redshift completeness @xmath4 . a small subset galaxies have redshifts adopted from the korea institute from advanced study ( kias ) value - added galaxy catalog @xcite .    using the adaptive halo - based group finder developed by @xcite , we construct a catalog of @xmath5 galaxy groups ( about @xmath6 groups with single galaxies ) . for each group , we assign a halo mass according to the ranking of its characteristic group luminosity , defined as the total luminosity of all group members with @xmath7 , where @xmath8 is the @xmath9-band absolute magnitude , @xmath10-corrected and evolution corrected to @xmath11 , using the method described by @xcite . in order to ensure sample completeness , in what follows we focus our analysis on the volume covering the redshift range @xmath12 , and within the largest continuous region in the northern galactic cap . using the complete galaxy groups with mass @xmath13 , @xcite constructed the mass , tidal and velocity ( sdss - mtv ) fields in this volume . we use the method developed by @xcite to correct for the peculiar motion of groups as well as the finger - of - god effect . we have tested that our alignment signals are insensitive to the boundary effect . the smoothing length scale we used to reconstruct the tidal field is @xmath14 , as this value provides the best agreement with the visual classification of the large - scale structure @xcite . the smoothing scale @xmath15 is related to the mass @xmath16 contained in the gaussian filter at mean density @xmath17 via @xmath18 , thus a smoothing scale @xmath19 corresponds to the mass @xmath20 . following @xcite , we calculate the tidal tensor using @xmath21 where @xmath22 and @xmath23 are indices with values of @xmath24 , @xmath25 , or @xmath26 , and @xmath27 is the peculiar gravitational potential , which can be calculated from the distribution of dark matter halos with mass @xmath28 above some threshold value @xmath29 through the poisson equation . at the position of each group , the tidal tensor is diagonalized to obtain the eigenvalues @xmath30 and @xmath31 ( @xmath32 ) , as well as the corresponding eigenvectors @xmath33 , @xmath34 , and @xmath35 .    according to the zeldovich theory @xcite , the sign of the eigenvalues of local tidal tensor can be used to classify the group s environment into one of four categories @xcite :    * : a point where all three eigenvalues are positive ; * : a point where @xmath36 has one negative and two positive eigenvalues ; * : a point where @xmath36 has two negative and one positive eigenvalues ; * : a point where all three eigenvalues are negative . the direction of a filament at the location of a group can be identified with the eigenvector corresponding to the single negative eigenvalue . likewise , the normal vector of a sheet for a group is the eigenvector corresponding to the single positive eigenvalue of the tidal tensor . central galaxies ; the dashed line shows the distribution for @xmath37 satellite galaxies.,scaledwidth=48.0% ]    we adopt the morphological classifications of galaxies from the galaxy zoo @xmath25 ( gz2 ) catalog @xcite , which provides robust classifications into elliptical and spiral for @xmath38 galaxies . in the following analysis , we only use spiral galaxies with @xmath39 strings beginning with s. this results in a sample of @xmath40 spirals in our survey volume . based on group catalog , the sample contains @xmath41 centrals and @xmath42 satellite galaxies , among which @xmath43 centrals and @xmath37 satellites have reliable halo masses . to compare with the results from n - body simulations , we focus on the @xmath43 central galaxies with reliable halo masses . based on local tidal fields described in the last subsection , @xmath44 galaxies ( @xmath45 ) are located in environments , @xmath46 ( @xmath47 ) in , @xmath48 ( @xmath49 ) in , and @xmath50 ( @xmath51 ) in .    in order to obtain a more reliable detection of the spin vectors @xmath52 of galaxies , in this paper we only use a sample of spiral galaxies . if a spiral galaxy were a thin circular disk , the inclination angle @xmath53 , between the plane of the disk and the line of sight , can be determined from the projected minor - to - major axis ratio @xmath54 . many studies used a simple model for the finite disk thickness to relate the apparent axis ratio @xmath54 and an intrinsic flatness parameter @xmath55 to obtain the inclination angles , is defined as the angle between the line of sight and the normal to the galaxy disk , so that @xmath56 . ] @xmath53 , of galaxies @xcite . here we follow the same practice and obtain @xmath53 through @xmath57 for @xmath58 and set @xmath59 for @xmath60 . according to @xcite , the intrinsic flatness @xmath55 depends on the morphological type of galaxies . however , we will use an average value of @xmath61 @xcite , since the variation of the flatness @xmath55 does not affect the calculation of the inclination angle @xmath53 significantly . we have repeated our entire calculation of the alignment assuming @xmath62 , and found that the results are very similar to those using @xmath63 . figure  [ fig : ia ] shows the probability distribution of the inclination angles of galaxies . we find that the distribution differs significantly from a uniform distribution . this is mostly likely due to the fact that spiral galaxies have bulges which distort the projected axis ratio . if the @xmath54 axis ratio is measured around an isophote where the bulge contributes significantly , then the result can be affected . this effect becomes more and more significant for systems that are close to edge - on . because of this , our following analysis will focus on galaxies with @xmath64 , which results in a sample of @xmath65 centrals and @xmath66 satellites .    from a two - dimensional image of a galaxy , projected on the sky , we can not decide which side of the galaxy is closer to us , which means that in the determination of @xmath53 using equation  ( [ incang ] ) , a single value of @xmath54 corresponds to two values of the inclination angle : @xmath67 . to avoid this problem , many studies constrain their analysis to edge - on ( @xmath68 ) and face - on ( @xmath69 ) galaxies , which usually results in small samples of about a few hundreds of galaxies ( e.g. * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) . in this paper , we use all the spirals selected from gz2 catalog . throughout we apply the positive sign of @xmath53 for all the spirals . we have tested and found no difference in the alignment signal if using the negative sign for @xmath53 . however , the sign ambiguity is expected to reduce the strength of the alignment signal , as we quantify in the following section .    following @xcite , we compute the components of the spin vector @xmath52 as @xmath70 where @xmath71 and @xmath72 are the right ascension and declination of a galaxy , respectively , @xmath53 is the inclination angle calculated from equation  ( [ incang ] ) . the position angle @xmath27 increases counterclockwisely from north to east in the plane of the sky , and is specified by the @xmath73 magnitudes per square arc - second isophote in the @xmath9-band .           to estimate the correlation between spin vectors of galaxies and the large - scale structure , we compute the cosine of the angle , @xmath74 , defined as the angle between the spin axis of the galaxy , @xmath52 , and the three principal axes @xmath33 , @xmath34 , and @xmath35 of the local tidal tensor . to quantify the alignments and their significance , we generate @xmath75 random samples in which the orientations of the principal axes of the tidal tensors are kept fixed , but the spin axes of the galaxies are randomized . the alignment strength is then expressed by the normalized pair count ( e.g. yang et al . 2006 ) : @xmath76 where @xmath77 is the number of pairs for each bin in @xmath78 , and @xmath79 is the average number of such pairs obtained from the @xmath75 random samples . we use @xmath80 , where @xmath81 is the s.d . of @xmath82 obtained from the 100 random samples , to assess the significance of alignment in each bin . since the significance is quantified with respect to the null hypothesis , we plot the error bars on top of the @xmath83 line . in addition to the normalized pair count , we also calculate the mean angle @xmath84 and @xmath85 , which is the standard deviation of @xmath86 for the @xmath75 random samples . in this paper , @xmath78 is restricted to the range @xmath87 $ ] . in the absence of any alignment , @xmath88 and @xmath89 . @xmath90 implies that the galaxy spin is parallel to the vector in question , while @xmath91 indicates it is perpendicular to it . but for central galaxies in halos ( groups ) of different masses . here results are shown only for galaxies with @xmath64 . , scaledwidth=50.0% ]     but for galaxies in clusters ( first row ) , filaments ( second row ) , sheets ( third row ) , and voids ( fourth row ) . here results are shown only for galaxies with @xmath64 . , scaledwidth=50.0% ]    figure  [ fig : tf ] shows the normalized pair count @xmath92 of the cosine of the angle between the galaxy spin vector and the eigenvectors @xmath33 , @xmath34 , and @xmath35 of the local tidal tensor . in the left panel , the calculation of the alignment is based on all @xmath43 centrals and @xmath93 satellite spiral galaxies selected from gz2 . in the right panel , we repeat the measurements for galaxies with @xmath64 . as expected , galaxies with @xmath64 have stronger alignment signals because of the reduced uncertainty in the values of @xmath53 . the average cosines and their errors are displayed for reference . figure  [ fig : tf ] shows that the galaxy spin vector has a weak tendency to be aligned with the intermediate axis @xmath34 , of the local tidal tensor , which is consistent with the theoretical prediction using the linear tidal torque theory @xcite . similar trends have been also found in simulation data . based on the tidal field traced by halos from n - body simulation , @xcite found that the spin vector of halos with masses larger than @xmath94 shows significant alignment with the intermediate axis of the tidal field . using a cosmological hydrodynamic simulation of galaxy formation in a cosmic filament , @xcite found that the spin vector has a weak alignment with the intermediate axis of the tidal field for their medium mass sample at @xmath95 ( see their figure  @xmath96 ) . we can also see that the galaxy spin tends to be perpendicular to the minor axis @xmath35 , which is consistent with the result shown in the right panel of figure  @xmath25 in @xcite . the alignment with the major axis @xmath33 is almost random . it is interesting to see that the alignment signal for satellites is as strong as that for centrals . this may suggest that satellites can preserve their alignment with the large scale tidal field after they have fallen into their host halos . since we have the halo mass for each central galaxy , we can investigate how the spin - tidal field alignment signal depends on the halo mass of groups . to that extent we split the central galaxies into four sub - samples of halo masses . figure  [ fig : tf_mass ] shows the alignment signals as a function of halo mass . as one can see , the alignment signals in middle panels appear to be slightly stronger for centrals in more massive halos . it s also interesting to see that there is a transition of the alignment signals in the lower left panel , although the error bars are very large due to the small number galaxies with halo mass larger than @xmath97 . figure  [ fig : tf1 ] shows the alignment between the three eigenvectors of the local tidal tensor and the spin vector of central galaxies which are located in cluster ( red ) , filament ( orange ) , sheet ( green ) , and void ( blue ) environments . here we see that for spiral galaxies in environments ( first row ) , the spin vectors have a significant alignment with the intermediate axis of the local tidal tensor . the upper right panel indicates that the spin vectors of galaxies in environments have a strong anti - alignment with the minor axis of the local tidal tensor . for galaxies in and environments , the alignments between spin vectors and the intermediate eigenvectors are rather weak . due to the small number of galaxies in environments , we can not obtain any useful information for these galaxies .    according to the definition of , the right panel in the second row in figure  [ fig : tf1 ] can be considered as the normalized pair count for the cosine of the angle between the spin vector and the direction of the filament in which the galaxy resides . there is a weak tendency that galaxies tend to have their spins preferentially perpendicular to their filaments , consistent with the prediction from the tidal torque theory . however , some of previous investigations found opposite alignments . using @xmath98 edge - on galaxies ( @xmath99 ) in filaments detected from sdss dr5 , @xcite found that only @xmath100 galaxies have their spin axes aligned perpendicular to their host filaments . this indicates that the spin of the edge - on galaxies tends to be parallel to their hosted filaments . however , as we have tested , if one only use edge - on or face - on galaxies , one needs to have a fairly large sample of filament directions to get statistically meaningful results . otherwise the signals may not be reliable . for example , if we have only one filament which lies along the line of sight direction , the edge - on or face - on galaxies will all have perfect perpendicular or alignment signals by selection . based on a galaxy sample constructed from sdss dr8 , @xcite found that the spin axes of spiral galaxies tend to align with the host filaments , which is opposite to our alignment signal . this discrepancy may be due to the different methods used to identify filamentary structures . in their investigation , filaments are traced by thin cylinders placed on the galaxy number density field , while the filaments in our samples are obtained from the continuous potential field constructed with the use of the method of @xcite .    for spiral galaxies in environments , the left panel in the third row in figure  [ fig : tf1 ] may be considered as the normalized pair count for the cosine of the angle between the spin and the normal of the sheet in which the galaxy resides . the results indicate that the spin vectors of galaxies have a very weak tendency to align along the normal of the sheet . using a sample of disk galaxies lying in the surfaces of voids obtained from sdss dr7 , @xcite found a significant tendency of galaxies around very large voids to have their spins aligned with the radial direction of the voids . this trend is consistent with our results . using @xmath101 edge - on and @xmath102 face - on galaxies from the 2dfgrs and sdss dr3 , @xcite found that spiral galaxies located on the walls of the largest voids have spins lying preferentially on the void surface . the disagreement may again be due to the small number of galaxies @xcite used . ( left ) , @xmath34 ( middle ) , and @xmath35 ( right ) of the tidal tensor field for fof halos . the dashed and solid line correspond to the original and control halo catalog , respectively . in the control sample , the spin vectors of @xmath103 halos have been changed ( see text for a detailed description ) . , scaledwidth=50.0% ]    , but for so halos with @xmath104 . , scaledwidth=50.0% ]    , but here spin vectors are estimated for inner halos within which the over density is @xmath105 . , scaledwidth=50.0% ]    to facilitate the interpretation of our results , we adopt two different n - body simulations using the massively parallel treesph gadget-2 code @xcite . the simulations evolved @xmath106 dark matter particles in @xmath107 and @xmath108 periodic boxes . the ` glass - like ' initial conditions @xcite were generate using the zeldovich approximation at redshift @xmath109 . the simulations adopted the cosmological parameters with @xmath110 , @xmath111 , @xmath112 , @xmath113 , @xmath114 and @xmath115 .    for the @xmath107 box simulation , the mass resolution and softening lengths are , respectively , @xmath116 and @xmath117 . this small volume simulation can give better statistics for halos with mass less than @xmath94 . the @xmath108 box simulation ( mass resolution of @xmath118 ) is used for computing the alignment signals for halos with mass larger than @xmath94 . dark matter halos are identified at redshift @xmath95 using the standard fof algorithm @xcite with a linking length of @xmath119 times the mean inter - particle separation . to obtain a reliable measurement , only halos with more than @xmath120 dark matter particles are included for further analysis , resulting in a catalog including @xmath121 ( @xmath122 ) halos with mass larger than @xmath123 ( @xmath124 ) for @xmath107 ( @xmath108 ) simulation . as comparison , we also use the so ( spherical over - density ) algorithm to identify halos . beginning with the most bound particles from the fof halos , a sphere is grown around the particle until the mean interior density is equal to the input value @xmath125 , where @xmath125 is the over - density within a sphere with respect to the critical density @xmath126 of the universe . here , we adopt @xmath104 and @xmath105 , representing the entire halo and the inner region , respectively .    to obtain a spin vector of a halo containing @xmath127 particles , we compute the total angular momentum @xmath128 using @xmath129 where @xmath130 is the mass of a dark matter particle , @xmath131 denotes the position vector of particle @xmath22 relative to the center of mass , and @xmath132 is the velocity relative to the bulk velocity of the halo .    as mentioned before , the spin vectors of galaxies in observation are not uniquely defined because we do not know which side of the galaxy is closer to us . in order to check this projection effect , we construct a control halo catalog in which we have changed the spin vectors of @xmath103 halos randomly selected from the original halo catalog . the changed spin unit vector @xmath133 is computed by @xmath134 where @xmath135 , @xmath136 is the original spin unit vector of a halo , and @xmath137 is the position unit vector of the halo , where we place a virtual observer at the corner of the simulation box . note that the original and changed spin vector of a halo are symmetric with respect to the line - of - sight direction @xmath138 .    in the simulation , we have classified the cosmic web environment of a dark matter halo using the density field hessian matrix method @xcite , similar to the method used above based on the tidal tensor . here , in order to compare with the alignment signals detected in the sdss data , we compute the probability distribution function @xmath139 , where @xmath140 is the angle between the halo spin and the eigenvectors of the tidal tensor .    figure  [ fig : fof ] shows the normalized pair count @xmath141 of the cosine of the angle between the halo spin and the eigenvectors of the tidal tensor . the solid line corresponds to the control sample , in which the spin vectors of @xmath103 halos have been changed to model the projection effect in observation . the dashed line denotes the alignment signal from the original halo catalog in the n - body simulation , which is consistent with the results described in @xcite . from figure [ fig : fof ] , we find that the alignment strength for control sample decreases about @xmath103 , which means the indetermination of the spin vector in observation can reduce the alignment strength significantly . the middle panels in figure  [ fig : fof ] show that the halo spin vector is aligned with the intermediate axis of the tidal tensor , and the strength of the alignment is stronger for higher mass halos . the results plotted in the right panels show that halo spin vector is aligned with the minor axis of the tidal field for low mass halos but tends to be perpendicular to it for massive halos . this mass dependence is consistent with recent results obtained for halo spin alignments with respect to filaments @xcite . as comparison , figure  [ fig : so200 ] shows the alignment signals for so halos with the over - density @xmath104 . the strength of the alignment signals is only slightly weaker than that for fof halos . the observational alignment signals shown in figure  [ fig : tf ] are in general agreement with n - body simulation results , in that only galaxies in halos with masses larger than @xmath142 show significant alignments with the intermediate axis . figure  [ fig : so2500 ] shows the alignment signals for so halos where spin vectors are calculated only by using the inner regions within which the over - density @xmath105 . here we see that the alignment signals are weaker than those for the entire halos . in particular the tendency that spin vectors are perpendicular to the major axis seen for the total fof and so halos is now replaced by a weak alignment . there is a stronger tendency for spin axes of the inner halos to be perpendicular to @xmath35 for halos with mass larger than @xmath94 . these results match better the observational results for spiral galaxies , suggesting that disk material may follow better the angular momentum of the halo material in the inner parts . using spiral galaxies selected from the sdss dr7 and the gz2 , we have investigated the alignment between the spin of galaxies and their surrounding large - scale structure , which is characterized by the local tidal tensor . based on the eigenvalues of the tidal tensor at the location of each galaxy group , we have classified the galaxy population into four different environments : , , and . we have found that the spin axes of central spiral galaxies selected from the gz2 have a weak tendency to be aligned with the intermediate direction of the local tidal tensor . this is consistent with the theoretical prediction using the linear tidal toque theory @xcite . there is almost no significant alignment between the spin axes of spiral galaxies and the major axis @xmath33 of the local tidal tensor , while the spins of spiral galaxies have a weak tendency to be perpendicular to the minor axis @xmath35 vector ( defined as the direction of the eigenvector of the tidal tensor associated with the single negative eigenvalue @xmath31 ) . the galaxies in environment show the most prominent alignment signals . for all spiral galaxies in environment , the spin axes show a weak tendency to be perpendicular to their filaments . for galaxies in environment , there is a weak tendency for their spins to align with the norm of the sheet .    using large n - body simulations , we check the projection effect in observation by constructing a control halo catalog , in which the spin vectors of @xmath103 halos have been changed to mimic the fact that it is impossible to determine which side of the galaxy is closer to us from the observed axis ratio . this indetermination can reduce the alignment strength significantly . the simulations also show that the spin vectors of the inner regions of halos have weaker alignments with the local tidal field than the spin vectors obtained for the whole halos . the observational results are consistent with the alignments obtained for the inner regions of halos , suggesting that the disk material traces the angular momentum of dark matter halos in the inner region . this work is supported by the 973 program ( no . 2015cb857002 ) , national science foundation of china ( grant nos . 11203054 , 11128306 , 11121062 , 11233005 , 11073017 ) , ncet-11 - 0879 , the strategic priority research program the emergence of cosmological structures " of the chinese academy of sciences , grant no . xdb09000000 and the shanghai committee of science and technology , china ( grant no . 12zr1452800 ) .
using a sample of spiral galaxies selected from the sloan digital sky survey data release 7 ( sdss dr7 ) and galaxy zoo 2 ( gz2 ) , we investigate the alignment of spin axes of spiral galaxies with their surrounding large scale structure , which is characterized by the large - scale tidal field reconstructed from the data using galaxy groups above a certain mass threshold . 
 we find that the spin axes only have weak tendency to be aligned with ( or perpendicular to ) the intermediate ( or minor ) axis of the local tidal tensor . 
 the signal is the strongest in a environment where all the three eigenvalues of the local tidal tensor are positive . 
 compared to the alignments between halo spins and local tidal field obtained in n - body simulations , the above observational results are in best agreement with those for the spins of inner regions of halos , suggesting that the disk material traces the angular momentum of dark matter halos in the inner regions .