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it is well established that the measurement of the galaxy luminosity function ( lf ) is sensitive to the type of galaxy being sampled . morphologically early - type galaxies tend to be systematically brighter than their late - type counterparts , resulting in lf estimates with significantly brighter @xmath9 and shallower faint end slope @xmath2 ( e.g. efstathiou , ellis & peterson 1988 ; loveday et al . 1992 ; blanton et al . similar trends are also present if one selects galaxies based on h@xmath2 equivalent widths ( loveday , tresse & maddox 1999 ) , [ oii ] equivalent widths ( ellis et al . 1996 ) or colour ( lin et al . 1996 ; marzke & da costa 1997 ) . understanding and being able to quantify this variation in the lf is of great importance to a full understanding of galaxy formation and evolution .    up until now the greatest obstacle faced when attempting to determine how the lf varied with different galaxy properties was the fact that one was required to divide already small data sets , thereby losing much of the statistical significance in the lf estimations . in this paper we address this issue by making use of a subset of the galaxies observed to date in the 2df galaxy redshift survey ( 2dfgrs maddox 1998 ; colless 2001 ) . this subset is the largest single data set used in the calculation of lfs and can easily be divided several times whilst still maintaining very precise statistics . the 2dfgrs is a joint uk - australian effort to map the distribution of galaxies down to an extinction corrected @xmath0 magnitude of @xmath10 ( median redshift @xmath11 ) . in so doing we expect to obtain 250,000 galaxy spectra from which redshifts can be determined . this is a factor of 10 more than any previous redshift survey .    in order to divide our data set in a meaningful way we develop in this paper a classification of the galaxies based upon their observed spectra . as with other astronomical data , there are different approaches for analysing galaxy spectra ( see e.g. lahav 2000 and references therein ) . if one has a well defined physical model for galaxy spectra , then it is appropriate to estimate parameters of interest ( such as age and star - formation rate ) e.g. by maximum likelihood , directly using all the spectral bins , or via a compressed version of the data designed to give maximum information on the physical parameters of interest ( e.g. heavens , jimenez & lahav 2000 ) . if , on the other hand , one prefers to let the data ` speak for themselves ' , in a model - independent way , then it is more useful to look at the distribution of the galaxies in the high - dimensional space defined by the spectral bins . it is then possible to either look for distinct groups , e.g. early and late types , or more refined classes ( e.g. slonim et al . an alternative , which we present here , is to find a continuous ( sequence - like ) parameterisation of the spectral features , which can later be divided into subsets . the parameterisation we develop is denoted by @xmath1 and essentially represents a measure of the average absorption or emission line strength present in each galaxy s spectrum . this classification is robust to the known instrumental uncertainties and also has the advantage of being easily interpreted in terms of the current star - formation present in each galaxy . the set of galaxies we use in this paper comprises a sample of 75,000 galaxy spectra . this is more than 12 times larger than the one used in our previous analysis ( folkes et al . 1999 , hereafter f99 ) and is by far the largest sample used to date . as well as showing the latest lf determinations we will also present a new procedure for calculating self - consistent @xmath8-corrections and investigate possible fibre - aperture biases . the outline of this paper is as follows . section  [ section : data ] briefly summarises the 2dfgrs and describes the data set we are using , section  [ section : spectypes ] outlines our method for dividing the data set based on our parameterisation of the galaxy spectral type , @xmath1 . section  [ section : lumfunctions ] gives a detailed description of the calculations involved in estimating the lf and in section  [ section : discussion ] we discuss our results and future work . the 2dfgrs has already observed approximately 200,000 unique galaxies for which it has obtained redshifts . the survey , once complete , will cover approximately 2000@xmath12 on the sky , split between two independent strips : one in the northern galactic hemisphere and the other centred roughly on the south galactic pole . in addition to this there are 99 random fields in the southern galactic cap . the 2df instrument itself is capable of observing up to 400 galaxy spectra simultaneously ( lewis et al . , 2001 ) . each galaxy has been selected from a revised and extended version of the automated plate measuring ( apm ) galaxy catalogue ( maddox et al . 1990 ) in order to determine its position and magnitude . it is then observed as part of the survey through a 140@xmath13 m ( @xmath14 arcsec ) diameter optical fibre . the @xmath15 magnitudes we use in this analysis are total magnitudes derived from updated versions of the original apm scans . these magnitudes have been updated to take into account new ccd calibration data ( see colless et al . 2001 and norberg et al . , 2001 ) and are believed to have an rms error of approximately @xmath16 magnitudes . each of the spectra observed using the 2df instrument spans 1024 channels with a spectral scale of 4.3@xmath17 per pixel ; the fwhm is measured by arc lines to be of the order of 1.8 - 2.5 pixels . typically at the survey limit the observed spectra have an average signal - to - noise ratio of @xmath18 per pixel , sufficient for determining redshifts and performing spectral analyses . for the purposes of our spectral analysis we have restricted ourselves to the redshift range of @xmath19 so that we are left with a uniform sample of galaxy spectra in the rest - frame wavelength range spanning [ oii ] to h@xmath2 . a detailed outline of the spectral reduction pipeline is given in colless et al . ( 2001 ) and f99 which we follow with only minor modifications . the data that we have available for this analysis include all observations up until january 2001 . at this stage a total of 111404 and 60062 galaxy spectra had been obtained in the sgp and ngp regions respectively . from these objects we remove those which did not receive accurate redshifts ( @xmath20 , colless et al . 2001 ) , repeated observations and spectra with particularly low signal - to - noise ratio ( @xmath21 ) . this leaves us with 78994 ( sgp ) and 44937 ( ngp ) galaxies for use in our spectral analysis . because of interference from sky emission and atmospheric absorption we have made a further restriction to our redshift range such that @xmath22 . this cut ensures that the h@xmath2 line in our spectra is not corrupted . note that this is only a problem for the small redshift range @xmath23 , however , we have also excluded the galaxies with @xmath24 in order to simplify our analysis . imposing this cut and removing spectra observed in poor quality fields ( section  4.1 ) leaves us with 43449 ( sgp ) and 32140 ( ngp ) galaxies . a total of 75589 unique galaxies will therefore be used in our subsequent analysis and measurement of the lf . the spectral classification presented here is based upon a principal component analysis ( pca ) of the galaxy spectra . pca is a statistical technique which has been used with considerable success by multiple authors in the past ( e.g. connolly et al . 1995 ; folkes , lahav & maddox 1996 ; glazebrook , offer & deeley 1998 ; bromley et al . 1998 ; f99 ) to deal with large multi - dimensional data sets . a detailed mathematical formulation of the pca adopted here in is given in f99 . note that the most significant difference between this formulation and that used by other authors ( e.g. connolly 1995 ) is that our spectra have been mean - subtracted ( fig .  [ aver ] ) before constructing the covariance matrix . this makes no substantial difference to the analysis since using other methods simply yields the mean spectrum as the first component . we note that throughout the remainder of this paper we will denote the eigenvectors ( herein eigenspectra ) as @xmath25,@xmath26 etc . and the projections onto these axes by @xmath27 , @xmath28 etc . pca is a useful technique in that it allows us to easily visualise a multi - dimensional population in terms of just a handful of significant components . it does this by identifying the components of the data ( in this case the galaxy spectra ) which are the most discriminatory between each galaxy . the significance of each component is measured in terms of its contribution to the variance over the sample and is determined in the pca . this allows us to identify just the most significant components for future use . it is clear from such a formalism that any clustering in a space defined by the pca is indicative of distinct sub - populations within the sample in terms of reduced dimensionality we find , after applying the pca to our galaxy spectra , that rather than using the original 738 spectral channels to describe each spectrum we can use only two projections and still retain two thirds of the total variance within the population . indeed we can retain 50% of the total variance just from the first component ( the total variance of the population includes noise and hence this is an underestimate of the true fraction of variance in these projections ) . the significance of each successive principal component drops off very sharply so these first few components are by far the most important ( table  [ tabpc ] ) . .the relative importance ( measured as variance ) of the first 8 principal components . [ cols="^,^,^,^",options="header " , ]     [ tabres ]      f99 has performed similar calculations of the lf per spectral type using a subset of the data presented here . in fig . [ cpsf ] we compare their results with those presented here . note that in order to make this comparison we have recalculated the lfs assuming ( for consistency ) an einstein de - sitter universe ( @xmath29 , @xmath30 ) , and we have reduced the 5 classes of f99 to our 4 types by taking linear combinations of their lfs which give the same fractions of galaxies per type as our own . it can be seen from the figure that our results are in good agreement with those of f99 except for some small systematic shifts . these differences are due to four factors which we believe have significantly improved the accuracy of our analysis .    1 . we have used a considerably larger sample of galaxies in our calculations . we have adopted self consistent @xmath8-corrections , resulting in a small change in the predicted @xmath9 and @xmath31 . 3 .   taking into account recent advances in our ccd calibrations we have been able to update the catalogue @xmath0 magnitudes ( colless et al . 2001 ; norberg et al . , 2001 ) . this has also resulted in a small change in the number counts and hence @xmath31 . we have corrected for saturation effects in high surface brightness objects ( section  4.3 ) . this has a particularly large impact on our most late - type ( type 4 ) galaxies . the most similar independent analysis of the lf per spectral type has been conducted by bromley et al . ( 1998 ) , using the las campanas redshift survey . we also compare these results with our own in fig . [ cpsf ] . again , in order to compare the 6 clans with our 4 types we have had to combine their lf determinations in a way which yields the same fractions of galaxies per type as our own . in addition we have applied the transformation @xmath32 ( lin et al . 1996 ) to convert the lcrs gunn-@xmath33 magnitudes to @xmath0 . the trend of the galaxy lfs to become progressively fainter as one moves from passive to active star - forming galaxies is clear for both sets of results . however there appears to be some significant disagreement particularly in the faint end slope between the two lf determinations . given the poor fit of the schechter function to the faint end of the lf we would not expect these two sets of results to necessarily agree within their stated errors . the large differences observed are most probably due to the different selection effects ( e.g. surface brightness and @xmath0 versus @xmath33 selection ) which can be particularly prominent for fainter galaxies , hence adding more uncertainty to @xmath2 than can be estimated from a standard error analysis . our total luminosity density ( again assuming an einstein de - sitter universe ) is within 4% of the figure obtained in f99 and is 30% lower than the figure quoted by blanton et al . ( 2001 ) for the sloan digital sky survey early data release . the reasons for this discrepancy are discussed in norberg et al . ( 2001 ) , but in summary we believe that the blanton et al . figure is too high , partly owing to large - scale structure in their small initial sample , and also through the use of an inappropriate colour equation to predict 2dfgrs magnitudes . the spectra observed as part of the 2dfgrs are acquired through optical fibres with a diameter of 140@xmath13 m , corresponding to between @xmath34 and @xmath35 on the sky ( depending on plate - position , see lewis et al . , 2001 ) . in our assumed cosmology ( @xmath36=0.3 , @xmath37=0.7 ) this translates to an aperture width of approximately @xmath38  kpc at the survey median redshift of @xmath39 . the fact that fitted galaxy brightness profiles have scale lengths of the order of 3 - 4 kpc ( binney & merrifield 1998 ) raises the question of how representative the observed spectra are of the galaxies as a whole . however , with typical seeing ( @xmath40 ) and random fibre positioning errors ( rms @xmath41 ) the 2df fibre - aperture will in fact sample a much larger portion of each galaxy . if the effective fibre apertures were significantly smaller than the galaxies over a range of redshifts then the variation in this aperture with redshift would result in systematic biases in the determination of the lfs . these so - called ` aperture effects ' are difficult to quantify without an in depth knowledge of the spatially resolved spectral properties of the targeted galaxies . kochanek , pahre & falco ( 2000 ) recently suggested a test to estimate the influence of this fibre - aperture bias on the determination of type dependent lfs @xmath42 . the test involves comparing the observed fractional number counts of galaxies in each class to the fractional number counts predicted by our derived lfs . kochanek , pahre & falco found that for redshift surveys classified morphologically the two were generally consistent but that for surveys classified spectrally using fibre - aperture spectra the two were very inconsistent . we have performed this test on our data and found no substantial inconsistencies ( fig . [ aper ] ) . with the exception of small systematic offsets the observed type fractions were found to agree with those predicted by the lf to within 2@xmath43 over the entire range in @xmath0 magnitude . we note that as the number counts predicted by the lf are normalised by construction to the observed number counts this test is only necessary and not sufficient . for this reason more sophisticated tests such as comparisons with detailed models are necessary in order to isolate and analyse the competing effects on the data ( e.g. positional errors , seeing and evolution ) . we show the observed and predicted @xmath44 distributions for each spectral type out to @xmath45 in fig . [ nofzfig ] . it can be seen that the observed @xmath44 is well recovered by the lf for the first two types . there appears to be a significant over abundance of high-@xmath46 galaxies for the two highest star - forming types as well as a slight under abundance of low-@xmath46 galaxies . similar deviations in abundance could be explained by aperture effects . however , if this were the only explanation then we would also observe a significant over abundance of low-@xmath46 passive star - forming galaxies , which is not the case . a much more reasonable explanation for these deviations between the predicted and observed @xmath44 distributions is the presence of evolution ( see e.g. lin et al . 1999 ) . because these two effects affect the observed galaxy population in similar ways they will be difficult to dis - entangle in more detailed analyses . for the present we note that as far as the determination of the lf in broad bins of spectral type is concerned both of these biases have only a small effect on our calculations . in this paper we have applied a method of spectral classification , @xmath1 , based on the the relative emission / absorption line strength present in a galaxy s optical spectrum . this classification correlates well with morphology and we interpret it as a measure of the relative current star - formation present in each galaxy . based on this classification we have divided the galaxies observed to date in the 2dfgrs into 4 spectral types and calculated the lf for each . our results are consistent with previous determinations in that the faint end slope systematically steepens and the characteristic magnitude becomes fainter as we move from passive to active star - forming galaxies . in addition we have been able to show that the schechter function is a poor fit to the lf over a large range of @xmath47 magnitudes , perhaps as a result of sub - populations within the data . the calculations presented in this letter represent the most accurate determinations of the optical @xmath0 galaxy lf to date .    as @xmath1 is a continuous variable the next step in quantifying the variation of the lf with spectral type is to develop a bivariate formalism @xmath48 . such a result would be extremely valuable in that it would quantify the variation in the schechter parameters with galaxy type , @xmath49 and @xmath50 , allowing the results to be applied much more objectively to such things as semi - analytic models from which spectra as well as other galaxy properties can be derived ( e.g. slonim et al . 2001 and references therein ) . we can then also extend this approach of comparing the observed lfs with model lfs by mimicking the observational selection effects ( e.g. aperture bias ) . one of the key advantages of our spectral type , @xmath1 , is that it can easily be applied to any other set of galaxy spectra which occupy the relevant wavelength range . this will be invaluable when comparing results from the many different galaxy surveys currently underway ( e.g. sdss , virmos , 6df etc . ) . the 2df galaxy redshift survey has made available to the community 100,000 galaxy spectra and redshifts through their website , . additional information regarding the spectral classification and lfs presented here can be obtained from http://www.ast.cam.ac.uk/@xmath51twodfgrs/. dsm was supported by an isaac newton studentship from the university of cambridge and trinity college . we thank r. kaldare , s. ronen and r. somerville for many helpful discussions . the 2df galaxy redshift survey was made possible through the dedicated efforts of the staff at the anglo australian observatory , both in creating the two - degree field instrument and supporting it on the telescope . baldry i.k . , et al .  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we calculate the optical @xmath0 luminosity function of the 2df galaxy redshift survey ( 2dfgrs ) for different subsets defined by their spectral properties . these spectrally selected subsets 
 are defined using a new parameter , @xmath1 , which is a linear combination of the first two projections derived from a principal component analysis . 
 this parameter @xmath1 identifies the average emission and absorption line strength in the galaxy rest - frame spectrum and hence is a useful indicator of the present star formation . 
 we use a total of 75,000 galaxies in our calculations , chosen from a sample of high signal - to - noise ratio , low redshift galaxies observed before january 2001 . 
 we find that there is a systematic steepening of the faint end slope ( @xmath2 ) as one moves from passive ( @xmath3 ) to active ( @xmath4 ) star - forming galaxies , and that there is also a corresponding faintening of the rest - frame characteristic magnitude @xmath5 ( from @xmath619.6 to @xmath619.2 ) . 
 we also show that the schechter function provides a poor fit to the quiescent ( type 1 ) lf for very faint galaxies ( @xmath7 fainter than @xmath616.0 ) , perhaps suggesting the presence of a significant dwarf population . 
 the luminosity functions presented here give a precise confirmation of the trends seen previously in a much smaller preliminary 2dfgrs sample , and in other surveys . 
 we also present a new procedure for determining self - consistent @xmath8-corrections and investigate possible fibre - aperture biases . 
 [ firstpage ]    galaxies : distances and redshifts  galaxies : elliptical and lenticular , cd  galaxies : stellar content  galaxies : formation  galaxies : evolution