a r X i v :a s t r o -p h /9809168v 2 18 S e p 1998Clustering of Galaxies in a Hierarchical Universe:II.
Evolution to High Redshift
Guinevere Kau?mann,J¨o rg M.Colberg,Antonaldo Diaferio &Simon D.M.White Max-Planck Institut f¨u r Astrophysik,D-85740Garching,Germany Abstract In hierarchical cosmologies the evolution of galaxy clustering depends both on cos-mological quantities such as ?,Λand P (k ),which determine how collapsed structures –dark matter halos –form and evolve,and on the physical processes –cooling,star formation,radiative and hydrodynamic feedback –which drive the formation of galax-ies within these merging halos.In this paper,we combine dissipationless cosmological N-body simulations and semi-analytic models of galaxy formation in order to study how these two aspects interact.We focus on the di?erences in clustering predicted for galax-ies of di?ering luminosity,colour,morphology and star formation rate,and on what these di?erences can teach us about the galaxy formation process.We show that a “dip”in the amplitude of galaxy correlations between z =0and z =1can be an impor-tant diagnostic.Such a dip occurs in low-density CDM models,because structure forms early and dark matter halos of mass ～1012M ⊙,containing galaxies with luminosities ～L ?,are unbiased tracers of the dark matter over this redshift range;their clustering amplitude then evolves similarly to that of the dark matter.At higher redshifts bright galaxies become strongly biased and the clustering amplitude increases again.In high density models,structure forms late and bias evolves much more rapidly.As a result,the clustering amplitude of L ?galaxies remains constant from z =0to z =1.The
strength of these e?ects is sensitive to sample selection.The dip becomes weaker for galaxies with lower star formation rates,redder colours,higher luminosities and ear-lier morphological types.We explain why this is the case and how it is related to the variation with redshift of the abundance and environment of the observed galaxies.We also show that the relative peculiar velocities of galaxies are biased low in our models,but that this e?ect is never very strong.Studies of clustering evolution as a function of galaxy properties should place strong constraints on models of galaxy formation and evolution.
Keywords:galaxies:formation;galaxies:halos;cosmology:large-scale structure;cosmology:dark matter
1Introduction
Local galaxies are highly clustered.On large scales they are organized into a network of sheets and?laments which surround large underdense regions,usually referred to as voids. On smaller scales galaxies are found in gravitationally-bound groups and clusters.Accord-ing to the standard theoretical paradigm,the structures observed today were formed by the gravitational ampli?cation of small perturbations in an initially gaussian dark matter density ?eld.Small scale overdensities were the?rst to collapse,and the resulting objects subse-quently merged under the in?uence of gravity to form larger structures such as clusters and superclusters.Galaxies formed within dense halos of dark matter,where gas was able to reach high enough overdensities to cool,condense and form stars.
In this hierarchical formation picture,the clustering of the dark matter,as measured by the amplitude of the matter correlation functionξm(r),increases monotonically with time. The precise evolution ofξm(r)with redshift has been studied extensively using both N-body simulations(e.g.Jenkins et al.1998)and analytic methods(Hamilton et al1991;Peacock& Dodds1994;Jain,Mo&White1995).Ifξm(r,z)were observable,it would be straightforward to use its behaviour to determine?,Λand the power spectrum of linear density?uctuations. What one measures in practice,however,is the clustering of galaxies,and the interpretation then requires an understanding of how these objects trace the underlying dark matter density ?eld.
If galaxies form at the centre of dark matter halos,considerable insight may be gained by using N-body simulations to study the clustering of halos(Brainerd&Villumsen1994;Mo &White1996;Roukema et al1997;Jing&Suto1998;Wechsler et al1998;Bagla1998a,b; Ma1998).Mo&White(1996)tested an approximate analytic theory against their numerical results,and this theory and its extensions can also be used to analyse the evolution of halo clustering with redshift(Matarrese et al1997;Coles et al1998).An important conclusion from all these studies is that the clustering of halos of galactic mass(～1012M⊙)evolves much more slowly than the clustering of the dark matter.This is because at high redshifts,such halos correspond to rare peaks in the initial density?eld,and are thus more strongly clustered than the dark matter(Kaiser1984).Another important conclusion is that more massive halos are more strongly clustered than less massive halos.If the luminosity of a galaxy is correlated with the mass of its halo,more luminous galaxies ought to be more strongly clustered.A detailed comparison with observational data requires a model for the observable properties of the galaxies present within halos of given mass at each epoch.
Precise measurement of the clustering amplitude of galaxies at high redshift has just re-cently become https://www.doczj.com/doc/fa2210550.html,ually this is done by calculating the angular two-point correlation function w(θ)as a function of apparent magnitude.In order to assess how clustering has evolved,w(θ)must be deprojected using Limber’s equation under the assumption of some speci?c model for the redshift distribution of the observed galaxies.In future large surveys of faint galaxies with photometric and/or spectroscopic redshifts will be available(see,for exam-ple,Connolly et al1995).It will be possible to classify the galaxies in these surveys according to absolute magnitude,spectral type,star formation rate and colour,and to investigate how clustering evolution depends on these properties.
At present,most of the data indicate that the clustering amplitude of galaxies decreases from z=0to z=1.Di?erent analyses,however,yield very di?erent estimates for the strength of this decrease.Le F`e vre et al(1996)analyzed the clustering of591galaxies with I<22.5in the?ve10arcminute?elds of the CFRS survey.They?nd that clustering has evolved dramatically,quoting a comoving correlation length at redshift0.5of r0=2h?1Mpc (q0=0.5).More recently,Carlberg et al(1998)presented a preliminary analysis of clustering in the CNOC2?eld galaxy redshift survey.Their sample is spread over four patches of sky with a total area of1.5square degrees.They estimate that the comoving correlation length of galaxies with M R
The clustering of Lyman break galaxies at z～3has now been measured with surprising precision(Steidel et al1998a;Giavalisco et al1998;Adelberger et al1998).The comoving correlation length of these objects is comparable to that of L?galaxies today,implying,as expected from models of halo clustering,that Lyman break galaxies are highly biased tracers of the dark matter distribution at these redshifts.In addition,Giavalisco et al(1998)?nd that the fainter Lyman break galaxies are less strongly clustered.This accords well with a simple model in which the star formation rates in these objects increase with the mass of their halos.More detailed theoretical modelling of the observed properties of Lyman break galaxies at z=3,including analysis of their abundances,sizes,luminosities,colours,star formation rates and clustering properties,has been carried out by Mo&Fukugita(1996),Baugh et al (1998),Governato et al(1998),Somerville,Primack&Faber(1998)and Mo,Mao&White (1998)
In this paper,we combine cosmological N-body simulations and semi-analytic modelling of galaxy formation to study the evolution of galaxy clustering as a function of redshift. Our methods for incorporating galaxy formation in the simulations are discussed in detail in Kau?mann et al(1998,Paper I).Two variants of a cold dark matter(CDM)cosmology are analyzed here:a high-density model with?=1,Γ=0.2and H0=50km s?Mpc?1 (τCDM),and a low-density?at model with?=0.3,Λ=0.7and H0=70km s?1Mpc?1 (ΛCDM).Paper I was concerned with the global properties of the galaxy distribution at z=0, including B and K-band luminosity functions,the I-band Tully-Fisher relation,galaxy two-point correlation functions,colour distributions,star formation rate functions and peculiar velocity distributions.Here we focus on clustering evolution in the two models.We study the predicted di?erences in clustering evolution for galaxies of di?erent magnitude,type and star formation rate,and we outline how future observational data will clarify the galaxy formation process.
2What can be learned from the evolution of halo clus-tering?
Because galaxy formation is complex and involves many poorly-understood physical processes, for example,star formation and radiative and hydrodynamical feedback,it is worthwhile to ask whether the clustering of dark matter halos can be used to constrain cosmological parameters directly.
In?gure1we plot the correlation length r0as a function of redshift for halos of di?erent mass in our two simulations.Here,as in the rest of the paper,all length scales are expressed in comoving units.Since the correlation functions in the models are not exact power laws,we de?ne r0as the radius whereξ(r)=1.The smallest halos resolved in the simulations contain 10particles and have virial masses～2×1011M⊙.For these objects,r0initially decreases with redshift,reaches a minimum,and then increases again.The redshift of this minimum is di?erent for the two cosmologies:z～0.7forτCDM and z～1.5forΛCDM.Massive halos do not exhibit the same“dip”in correlation length;their r0remains constant for a while,then increases at high redshift.Once again,the redshift at which the evolution becomes strong is lower forτCDM than forΛCDM.This is simply because structure formation occurs later in theτCDM model.
With10metre telescopes,it is now possible to measure the rotation curves of disk galaxies at redshift～1(Vogt et al1996).It will be many years,however,before such samples are both large enough and complete enough for an analysis of the clustering evolution of galaxies as a function of their halo mass.In all likelihood,we will have to deal with?ux-limited surveys of galaxies for some time to come.
Let us now make the simplifying assumption that each simulated dark matter halo contains one observable galaxy,and that the luminosity of the galaxy increases with the mass of its halo.The correlation function of a?ux-limited sample of galaxies of known abundance at redshift z may then be calculated by evaluatingξ(r)for the mass-limited set of simulated halos which has the same abundance.This is illustrated in?gure2,where we plot the correlation length of halos versus their number density(in units of h3Mpc?3)at a series of redshifts.As expected,r0decreases as the number density increases,because the correlation signal becomes dominated by low-mass halos,which are more weakly clustered.Note that the di?erences between theτCDM and theΛCDM models are small at all redshifts.Mo,Mao& White(1998)show a similar plot for halos at z=3for four di?erent CDM cosmologies and ?nd that they all give similar results.There thus appears to be a“cosmic conspiracy”that makes it impossible to infer information about cosmological parameters from the clustering of halos of given abundance.On the other hand,the uniformity seen in?gure2can be used as a test of the entire class of hierarchical models and of the hypothesis that there is a one-to-one correspondence between halo mass and galaxy luminosity.As discussed by Steidel et al(1998b)and by Mo,Mao&White(1998),this hypothesis works well for the Lyman break population at z～3.At low redshifts,the assumption of a one-to-one correspondence between halos and galaxies must break down,because the abundance of high mass halos is larger,and more and more bright galaxies are grouped together in each such halo.The values of r0plotted in?gure2are then lower limits on the true values.
0123
2
3
4
5
6
7
Figure 1:The evolution of the co-moving correlation length of halos as a function of redshift in the τCDM and ΛCDM simulations.The solid line is for halos with log(M vir /M ⊙)in the range 11.0?11.5,the dotted line for 11.5?12,the short-dashed line for 12?12.5and the long-dashed line for 12.5?13.
34
5
6
00.5
34
5
6
1 1.5
-2.8-2.6-2.4-2.2-2-1.83
4
5
6
2-2.8-2.6-2.4-2.2-2-1.8
3Figure 2:The co-moving correlation length r 0of halos is plotted against comoving number density at redshifts 0,0.5,1,1.5,2and 3.The solid line shows results for the τCDM simulation and the dotted line for the ΛCDM simulation.
3The evolution of galaxy clustering
In this section,we study the evolution of galaxy clustering in theΛCDM andτCDM simu-lations.We use the star formation and feedback recipes that resulted in the best?ts to the observational data at z=0.As discussed in Paper I,extremely e?cient feedback was required in theτCDM model in order to obtain a reasonable?t to the correlation function on scales below1h?1Mpc and to avoid producing too many galaxies with luminosities below L?.Even so,the model failed to?t the observed bright end of the luminosity function and the clustering amplitude was too low on large scales.TheΛCDM model with relatively ine?cient feedback resulted in a better overall?t to most of the data at z=0.For simplicity,we do not consider dust extinction in the analysis of this paper because it is very uncertain how the empirical recipes we adopted in Paper I should be extended to high redshift.This neglect has little e?ect on ourΛCDM model but means that ourτCDM model now substantially underpredicts galaxy clustering at z=0.We concentrate below on the relative evolution of r0rather than on its absolute value,so this problem does not strongly a?ect our conclusions.
In?gure3results are shown for galaxies with rest-frame B-band magnitudes brighter than ?19+5log h in theΛCDM simulation.At redshift zero,this corresponds to selecting galaxies brighter than～L?.The?rst three panels in the plot show the evolution ofξ(r)evaluated at r=2,3and8h?1Mpc(co-moving units).The fourth panel shows the evolution of the co-moving correlation length r0.For comparison,the dotted line in each panel shows the evolution of the corresponding quantity for the dark matter.Results forτCDM are given in ?gure4.In each case the redshift extends to the point at which the abundance of L?galaxies becomes too low for reliable estimation of the correlation function.
In theΛCDM model,the clustering amplitude decreases from z=0to z=1.5,remains approximately constant from z=1.5to z=2.5and then increases again at higher redshift. The dip in clustering amplitude is stronger on small scales:ξ(r)decreases by a factor of3 at2h?1Mpc and by a factor1.5at8h?1Mpc.The correlation length r0decreases from 5.5h?1Mpc at z=0to3.9h?1Mpc at z=1.5.This agrees remarkably well with the parametrization of r0as a function of z quoted by Carlberg et al(1998).In theτCDM model the clustering amplitude remains?xed from z=0to z=1and then rises steeply at higher redshifts.Note,as mentioned above,that the correlation length at z=0is low(～3h?1 Mpc)in this model.
In?gure5,we plot the evolution of the bias b,de?ned as the square root of the ratio between the galaxy and the dark matter correlation functions:
b(r)= ξg(r)
0123450246
8012345
01
2
3
4
01234500.2
0.4
0.6012345
23
4
5
6
Figure 3:Evolution of clustering the the ΛCDM model.In the ?rst 3panels,the clustering amplitude is plotted against redshift for galaxies with rest-frame B-band magnitude brighter than ?19+5log h (solid lines)and for the dark matter (dotted line).Results are shown for ξ(r )evaluated at r =2,3and 8h ?1Mpc ?1.In the fourth panel,the comoving correlation length r 0is plotted against redshift both for the galaxies and for the dark matter.
0123024
6
0123
01
2
3
012300.2
0.4
0.60123
12
3
4
5
Figure 4:As in ?gure 3,except for the τCDM model.
2
4
6
Figure 5:Evolution of the bias for galaxies with rest-frame B-band magnitude brighter than ?19+5log h in the ΛCDM and τCDM models.Solid,dotted,short-dashed and long-dashed lines show results evaluated on comoving scales of 2,3,5and 8h ?1Mpc respectively.
4Dependence on luminosity,star formation rate and
morphological type
In ?gures 6and 7,we demonstrate that the clustering evolution depends on the way in which galaxies are selected in the simulations.The ?rst panel compares the clustering evolution of galaxies selected in the rest-frame B-band with that of galaxies selected in the rest-frame I-band.The second panel compares the clustering evolution of galaxies with M (B )
In the ΛCDM model,we ?nd that the strength of the “dip”in clustering between z =0
and z =1.5is sensitive to sample selection.The dip is weaker for more luminous galaxies and for galaxies selected in the I-band,but stronger for galaxies selected by star formation rate.The clustering amplitude of early-type galaxies is stronger than that of the population as a whole and evolves very little with redshift.In the τCDM model,clustering evolution is less sensitive to sample selection.The clustering always remains ?xed out to z ～1and then rises steeply at higher redshifts.Early-type galaxies are also very strongly clustered in this model,particularly at high redshifts.
01234524
6
8I < -21
B < -19.5
012345
246
8
B < -21B < -19.5012345246
80123
24
6
8
early type
Figure 6:The dependence of clustering evolution on sample selection in the ΛCDM model.The comoving correlation length r 0is plotted as a function of redshift for:a)L ?galaxies selected in the rest-frame I-band (solid)and L ?galaxies selected in the rest-frame B-band (dotted);b)very bright galaxies (solid)and L ?galaxies (dotted);c)galaxies with star forma-tion rate greater than 3M ⊙yr ?1(solid)and 1M ⊙yr ?1(dotted);d)early-type galaxies with stellar masses greater than 3×1010M ⊙.
01232345
6
I < -22
B < -20.5
0123
23
4
5
6 B < -22B < -20.501232345
600.51 1.52 2.5
23
4
5
6
early type Figure 7:As in ?gure 6,except for the τCDM model.
4.1What can be learned from these dependences?
We now explain why the evolution of clustering depends on sample selection and what can be learned about galaxy formation by studying the observed evolution as a function of morpho-logical type,luminosity,colour and star formation rate.
For a given cosmology,the clustering amplitude predicted for a sample of galaxies depends on the masses of the dark matter halos they inhabit.The evolution of clustering depends on how the mass distribution of these halos changes with redshift.Additional relevant and observationally accessible information comes from the variation with redshift of the abundance of galaxies in the sample.
As an example,let us suppose that galaxies with?xed star formation rate are found in smaller halos at high redshift than at the present day.We would expect the clustering amplitude of a SFR-selected sample to show a stronger dip than a sample of galaxies that tracked halos of the same mass at all redshifts.We would also expect the abundance of galaxies in a SFR-selected sample to increase more strongly with redshift,because there are many more small halos than large ones.
As a second example,let us suppose that early type galaxies are found primarily in massive halos at all redshifts.As seen in?gure1,these galaxies should not exhibit any dip in clustering and their abundances should decrease strongly at high redshifts because massive halos are rare objects at early times.
These points are illustrated in detail in?gure8,where we plot the evolution of the median halo mass and the comoving number density of galaxies in samples selected in di?erent ways from theΛCDM simulation.The top3panels show results for galaxies selected according to rest-frame B-magnitude,rest-frame I-magnitude and star formation rate.At z=0,all three galaxy samples have the same abundance and occur in halos of roughly the same mass. Galaxies selected according to star formation rate move to smaller halos at higher redshift. This e?ect is simply a result of the parametrization of star formation in our models.Following Kennicutt(1998),we have adopted a star formation law of the form˙M?=αM cold/t dyn,where M cold is the mass of cold gas in the galaxy and t dyn is the dynamical time of the galaxy.Since t dyn decreases at higher redshifts,the star formation rates are higher in halos of the same cold gas content.Galaxies selected in the B-band exhibit a weaker trend towards low-mass halos.In the case of the I-band selection,galaxies trace halos of roughly the same mass at all redshifts below2.This is because the I-band magnitude of a galaxy is a measure of its total stellar mass,rather than its instantaneous star formation rate.We thus conclude that SFR-selected samples show the strongest dip in clustering in?gure6because this selection procedure favours galaxies in lower mass halos at high redshift.Note that galaxies in the SFR-selected samples also exhibit the strongest increase in abundance from z=0to z=1.5.
The bottom two panels in?gure8show that very bright galaxies and early-type galaxies in the simulation are found in halos with masses～1013M⊙.As seen in?gure1,the clustering of these objects evolves very little from z=0to z=1.
In?gure9,we show the evolution of galaxy abundances and median halo masses for samples selected in the same way from theτCDM simulation.The results are qualitatively similar to those found forΛCDM.L?galaxies occur in halos of roughly the same masses
Figure 8:The evolution of the comoving number density (left column)and the median halo mass (right column)of galaxies selected from the ΛCDM simulation.Error bars indicate the upper and lower quartiles of the halo mass distributions.Results are shown for the selection criteria described in the caption to ?gure 6.
(～1012M⊙)in both models.The reason why no dip is seen in theτCDM model is because
halos of these masses are more strongly biased at z=1than in theΛCDM model and the decrease in halo mass with redshift for the SFR-selected sample is less pronounced.Note also that the redshift at which the abundance curves peak is higher forΛCDM than forτCDM.In
theΛCDM simulation,the abundance of early-type galaxies only decreases substantially at redshifts greater than1.5,whereas in theτCDM simulation,the abundance of ellipticals has already declined by a factor of3by z=1.
5Evolution of the slope ofξ(r)
Figure10shows the evolution of the slopeγof the two-point correlation function for galaxies
with rest-frame B-magnitudes brighter than?19+5log h in theΛCDM andτCDM models. We have?t a power-law toξ(r)over three di?erent ranges in scale:r=1?5h?1Mpc, r=5?10h?1Mpc and r=1?10h?1Mpc.
In theΛCDM model,the evolution of the slope is stronger on small scales.Over the range 1?5h?1Mpc,γevolves from?2at z=0to?1.5at z=1.On large scales,γremains
approximately constant.Over the range1?10h?1Mpc,γevolves from?1.85at z=0to ?1.6at z=1and then remains constant.These results appear to be in qualitative agreement with the observations(Postman et al1998).These au thors?nd no dependence ofγon
magnitude for the bright(I<21)galaxies in their survey.At fainter magnitudesγ?attens, reaching a value of?1.6at I=22.5.They also?nd that the?attening is stronger on smaller angular scales.Neuschae?er&Windhorst(1995)?nd similar results from an independent survey carried out at a di?erent wavelength.In theτCDM model,there is very little change in the slope with redshift on any scale.
6Evolution of pairwise peculiar velocities
Estimates of dynamical quantities such as?or cluster M/L ratios from galaxy data require knowledge not only of the spatial bias in the galaxy distribution,but also of any possible bias in the kinematics of the galaxies relative to those of the dark matter.In Paper I we explored this“velocity bias”for our z=0models using pairwise velocity statistics,and in Paper III (Diaferio et al1998)we will do the same using group and cluster velocity dispersions.Here we brie?y explore the predicted evolution of velocity bias using pairwise statistics.The thin solid lines in?gure11show the redshift evolution of the pairwise peculiar velocity dispersionσ12 evaluated at relative separations r=0.5,1and2h?1Mpc(co-moving units)for galaxies with rest-frame B-band magnitudes less than?19+5log h in theΛCDM andτCDM simulations. The thick solid lines show the evolution ofσ12for the dark matter.In order to compare the relative change inσ12as a function of redshift in the two models,we scale the results by dividing by the value ofσgal12at z=0.As shown in?gure13of Paper I,σgal12?800km s?1 (r=1h?1Mpc)in both theΛCDM andτCDM models at the present day.
The pairwise peculiar velocities of the galaxies follow those of the dark matter quite closely in both models.The galaxy velocities are10-40%lower than those of the dark matter at
Figure 9:As in ?gure 8,except for the τCDM simulation.
-1.4
-1.6-1.8
00.51 1.52
-1.4
-1.6
-1.8
Figure 10:The evolution of the slope of the correlation function of galaxies with M (B )
Figure11:Redshift evolution of the pairwise velocity dispersionσ12at relative comoving separations of0.5,1and2h?1Mpc for galaxies with rest-frame B-magnitudes brighter than ?19+5log h(thin lines)and for dark matter(thick lines)in theΛCDM andτCDM simula-tions.The results are scaled by dividing by the value ofσgal12at z=0.
z=0.(Note that the“antibias”in galaxy peculiar velocities at z=0is stronger than that shown in?gure13of Paper I,because the models presented in this paper do not include dust extinction.Dust reduces the contribution of star-forming?eld galaxies in a B-selected sample, but has little e?ect on early-type galaxies in rich groups and clusters.Models that include dust extinction thus give values ofσgal12that are10-25%larger).The di?erence between the galaxy and dark matter peculiar velocities decreases at higher redshift.In contrast to the spatial distributions,galaxy peculiar velocities in our models are never very strongly biased. In theτCDM model,there is nearly a factor2decrease inσgal12from z=0to z=0.5.In the ΛCDM models,σgal12remains roughly constant out to z=0.5,before decreasing at higher redshift.
7Discussion and Conclusions
In a hierarchical Universe,the evolution of galaxy clustering depends on the following:
1.Cosmological parameters,such as?,Λandσ8,because these determine the rate at
which structure grows and the epoch at which halos of given mass change from being rare objects,and thus biased tracers of the dark matter distribution,to being“typical”
objects with clustering properties similar to that of the mass.
2.The relationship between the mass of a dark matter halo and the properties of the
galaxies that form within it.Note that this relationship depends only on halo mass and is independent of the environment in which the halo?nds itself(Lemson&Kau?mann
1998).
3.The evolution of the galaxy population with redshift(and hence the evolution of the
relationship between galaxy properties and halo mass).
In this paper,we illustrate how di?erences in clustering evolution between galaxies of
di?ering luminosity,colour,morphological type and star formation rate may help constrain galaxy formation models,and perhaps even cosmological parameters.
One interesting diagnostic that we highlight is the“dip”in correlation amplitude observed
between z=0and z=1.We show that this dip occurs naturally in aΛCDM model, where structure forms early and halos with masses in the range1011?1012M⊙,which contain galaxies of intermediate luminosities,are unbiased tracers of the mass over this redshift range. In theτCDM model,bias evolves rapidly,and the clustering amplitude of L?galaxies remains constant from z=0to z=1.Although it might be possible to“force”a dip in clustering in
theτCDM model by requiring that L?galaxies form in less massive halos,it would be di?cult to come up with a physically-motivated scheme for doing this that would not simultaneously
produce too many bright galaxies.
We also show that the strength of the dip in theΛCDM model is sensitive to sample selec-tion.If galaxies are selected according to star formation rate rather than B-band luminosity,
objects in low mass halos contribute more to the clustering signal at high redshifts and the dip is stronger.If galaxies are selected in the red rather than the blue,the dip is reduced. Very luminous galaxies and massive early-type galaxies exhibit no dip in clustering between
z=0and z=1because they occur in high mass halos(1013?1014M⊙)that are already biased at z=0and become substantially more biased at high redshift.
The predictions presented in this paper should be viewed as illustrative rather than quan-titative.As discussed in Paper I,the precise relation between the mass of a halo and the properties of the galaxies that form within it depends strongly on the adopted recipes for star formation and feedback;these are very uncertain.The exciting prospect is that future observations of galaxy clustering at high redshift will place strong empirical constraints on these processes.
Acknowledgments
The simulations in this paper were carried out at the Computer Center of the Max-Planck Society in Garching and at the EPPC in Edinburgh.Codes were kindly made available by the Virgo Consortium.We especially thank Adrian Jenkins and Frazer Pearce for help in carrying them out.We are also grateful to John Peacock for useful discussions. A.D.is a
Marie Curie Fellow and holds grant ERBFMBICT-960695of the Training and Mobility of Researchers program?nanced by the EC.
比较级与最高级 1.as...as 与(not) as(so)...as as...as...句型中，as的词性 第一个as是副词，用在形容词和副词的原级前，常译为“同样地”。第二个as是连词，连接与前面句子结构相同的一个句子(相同部分常省略)，可译为“同..... He is as tall as his brother is (tall) . (后面的as 为连词) 只有在否定句中，第一个as才可换为so 改错: He is so tall as his brother.（X） 2.在比较状语从句中，主句和从句的句式结构一般是相同的 与as...as 句式中第二个as一样，than 也是连词。as和than这两个连词后面的从句的结构与前面的句子大部分情况下结构是相同的，相同部分可以省略。 He picked more apples than she did. 完整的表达为: He picked more apples than she picked apples. 后而的picked apples和前面相同，用did 替代。 He walked as slowly as she did.完整表达为: He walked as slowly as she walked slowly. she后面walked slowly与前面相同，用did替代。
3.谓语的替代 在as和than 引导的比较状语从句中，由于句式同前面 主句相同，为避免重复，常把主句中出现而从句中又出现的动词用do的适当形式来代替。 John speaks German as fluently as Mary does. 4.前后的比较对象应一致 不管后面连词是than 还是as,前后的比较对象应一致。The weather of Beijing is colder than Guangzhou. x than前面比较对象是“天气”，than 后面比较对象是“广州”，不能相比较。应改为: The weather of Bejing is colder than that of Guangzhou. 再如: His handwriting is as good as me. 应改为: His handwriting is as good as mine. 5.可以修饰比较级的词 常用来修饰比较级的词或短语有: Much,even,far,a little,a lot,a bit,by far,rather,any,still,a great deal等。 by far的用法: 用于强调，意为“...得多”“最最...”“显然”等，可修饰形容词或副词的比较级和最高级，通常置于其后，但是若比较级或最高级前有冠词，则可置于其前或其后。
The way 的用法 Ⅰ常见用法： 1)the way+ that 2)the way + in which（最为正式的用法） 3)the way + 省略（最为自然的用法） 举例：I like the way in which he talks. I like the way that he talks. I like the way he talks. Ⅱ习惯用法： 在当代美国英语中，the way用作为副词的对格，“the way+ 从句”实际上相当于一个状语从句来修饰整个句子。 1)The way =as I am talking to you just the way I’d talk to my own child. He did not do it the way his friends did. Most fruits are naturally sweet and we can eat them just the way they are—all we have to do is to clean and peel them. 2）The way= according to the way/ judging from the way The way you answer the question, you are an excellent student. The way most people look at you, you’d think trash man is a monster. 3）The way =how/ how much No one can imagine the way he missed her. 4）The way =because
人教版（新目标）初中英语形容词与副词的比较级与最高级 （一）规则变化： 1．绝大多数的单音节和少数双音节词，加词尾-er ，-est tall—taller—tallest 2．以不发音的e结尾的单音节词和少数以-le结尾的双音节词只加-r，-st nice—nicer—nicest , able—abler—ablest 3．以一个辅音字母结尾的重读闭音节词或少数双音节词，双写结尾的辅音字母，再加-er，-est big—bigger—biggest 4．以辅音字母加y结尾的双音节词，改y为i再加-er，-est easy—easier—easiest 5．少数以-er，-ow结尾的双音节词末尾加-er，-est clever—cleverer—cleverest, narrow—narrower—narrowest 6．其他双音节词和多音节词，在前面加more，most来构成比较级和最高级 easily—more easily—most easily （二）不规则变化 常见的有： good / well—better—best ; bad (ly)/ ill—worse—worst ; old—older/elder—oldest/eldest many / much—more—most ; little—less—least ; far—farther/further—farthest/furthest
用法： 1．原级比较：as + adj./adv. +as（否定为not so/as + adj./adv. +as）当as… as中间有名字时，采用as + adj. + a + n.或as + many / much + n. This is as good an example as the other is . I can carry as much paper as you can. 表示倍数的词或其他程度副词做修饰语时放在as的前面 This room is twice as big as that one. 倍数+as+adj.+as = 倍数+the +n.+of Your room is twice as larger as mine. = Your room is twice the size of mine. 2．比较级+ than 比较级前可加程度状语much, still, even, far, a lot, a little, three years. five times,20%等 He is three years older than I (am). 表示“（两个中）较……的那个”时，比较级前常加the（后面有名字时前面才能加冠词） He is the taller of the two brothers. / He is taller than his two brothers. Which is larger, Canada or Australia? / Which is the larger country, Canada or Australia? 可用比较级形式表示最高级概念，关键是要用或或否定词等把一事物（或人）与其他同类事物（或人）相分离 He is taller than any other boy / anybody else.
大多数形容词有三种形式,原级,比较级和最高级, 以表示形容词说明的性质在程度上的不同。 形容词的原级: 形容词的原级形式就是词典中出现的形容词的原形。例如: poor tall great glad bad 形容词的比较级和最高级: 形容词的比较级和最高级形式是在形容词的原级形式的基础上变化的。分为规则变化和不规则变化。 规则变化如下: 1) 单音节形容词的比较级和最高级形式是在词尾加 -er 和 -est 构成。 great (原级) (比较级) (最高级) 2) 以 -e 结尾的单音节形容词的比较级和最高级是在词尾加 -r 和 -st 构成。wide (原级) (比较级) (最高级) 3)少数以-y, -er, -ow, -ble结尾的双音节形容词的比较级和最高级是在词尾加 -er 和 -est 构成。 clever(原级) (比较级) (最高级) 4) 以 -y 结尾,但 -y 前是辅音字母的形容词的比较级和最高级是把 -y 去掉,加上 -ier 和-est 构成. happy (原形) (比较级) (最高级) 5) 以一个辅音字母结尾其前面的元音字母发短元音的形容词的比较级和最高级是双写该辅音字母然后再加 -er和-est。 big (原级) (比较级) (最高级) 6) 双音节和多音节形容词的比较级和最高级需用more 和 most 加在形容词前面来构成。 beautiful (原级) (比较级) (比较级) difficult (原级) (最高级) (最高级) 常用的不规则变化的形容词的比较级和最高级: 原级------比较级------最高级 good------better------best many------more------most much------more------most bad------worse------worst far------farther, further------farthest, furthest 形容词前如加 less 和 least 则表示"较不"和"最不 形容词比较级的用法: 形容词的比较级用于两个人或事物的比较,其结构形式如下: 主语+谓语(系动词)+ 形容词比较级+than+ 对比成分。也就是, 含有形容词比较级的主句+than+从句。注意从句常常省去意义上和主句相同的部分, 而只剩下对比的成分。
The way的用法及其含义（二） 二、the way在句中的语法作用 the way在句中可以作主语、宾语或表语： 1.作主语 The way you are doing it is completely crazy.你这个干法简直发疯。 The way she puts on that accent really irritates me. 她故意操那种口音的样子实在令我恼火。The way she behaved towards him was utterly ruthless. 她对待他真是无情至极。 Words are important, but the way a person stands, folds his or her arms or moves his or her hands can also give us information about his or her feelings. 言语固然重要,但人的站姿,抱臂的方式和手势也回告诉我们他(她)的情感。 2.作宾语 I hate the way she stared at me.我讨厌她盯我看的样子。 We like the way that her hair hangs down.我们喜欢她的头发笔直地垂下来。 You could tell she was foreign by the way she was dressed. 从她的穿著就可以看出她是外国人。 She could not hide her amusement at the way he was dancing. 她见他跳舞的姿势，忍俊不禁。 3.作表语 This is the way the accident happened.这就是事故如何发生的。 Believe it or not, that's the way it is. 信不信由你, 反正事情就是这样。 That's the way I look at it, too. 我也是这么想。 That was the way minority nationalities were treated in old China. 那就是少数民族在旧中
英语比较级和最高级的用法归纳 在学习英语过程中，会遇到很多的语法问题，比如比较级和最高级的用法，对于 这些语法你能够掌握吗？下面是小编整理的英语比较级和最高级的用法，欢迎阅读！ 英语比较级和最高级的用法 一、形容词、副词的比较级和最高级的构成规则 1.一般单音节词和少数以-er，-ow结尾的双音节词，比较级在后面加-er，最高级 在后面加-est; (1)单音节词 如：small→smaller→smallest short→shorter→shortest tall→taller→tallest great→greater→greatest (2)双音节词 如：clever→cleverer→cleverest narrow→narrower→narrowest 2.以不发音e结尾的单音节词，比较在原级后加-r，最高级在原级后加-st; 如：large→larger→largest nice→nicer→nicest able→abler→ablest 3.在重读闭音节(即：辅音+元音+辅音)中，先双写末尾的辅音字母，比较级加-er，最高级加-est; 如：big→bigger→biggest hot→hotter→hottest fat→fatter→fattest 4.以“辅音字母+y”结尾的双音节词，把y改为i，比较级加-er，最高级加-est; 如：easy→easier→easiest heavy→heavier→heaviest busy→busier→busiest happy→happier→happiest 5.其他双音节词和多音节词，比较级在前面加more，最高级在前面加most; 如：bea utiful→more beautiful→most beautiful different→more different→most different easily→more easily→most easily 注意：(1)形容词最高级前通常必须用定冠词 the，副词最高级前可不用。 例句： The Sahara is the biggest desert in the world. (2) 形容词most前面没有the，不表示最高级的含义，只表示"非常"。 It is a most important problem. =It is a very important problem.
定冠词the的用法： 定冠词the与指示代词this ,that同源,有“那(这)个”的意思,但较弱,可以和一个名词连用,来表示某个或某些特定的人或东西. (1)特指双方都明白的人或物 Take the medicine.把药吃了. (2)上文提到过的人或事 He bought a house.他买了幢房子. I've been to the house.我去过那幢房子. (3)指世界上独一无二的事物 the sun ,the sky ,the moon, the earth (4)单数名词连用表示一类事物 the dollar 美元 the fox 狐狸 或与形容词或分词连用,表示一类人 the rich 富人 the living 生者 (5)用在序数词和形容词最高级,及形容词等前面 Where do you live?你住在哪? I live on the second floor.我住在二楼. That's the very thing I've been looking for.那正是我要找的东西. (6)与复数名词连用,指整个群体 They are the teachers of this school.(指全体教师) They are teachers of this school.(指部分教师) (7)表示所有,相当于物主代词,用在表示身体部位的名词前 She caught me by the arm.她抓住了我的手臂. (8)用在某些有普通名词构成的国家名称,机关团体,阶级等专有名词前 the People's Republic of China 中华人民共和国 the United States 美国 (9)用在表示乐器的名词前 She plays the piano.她会弹钢琴. (10)用在姓氏的复数名词之前,表示一家人 the Greens 格林一家人(或格林夫妇) (11)用在惯用语中 in the day, in the morning... the day before yesterday, the next morning... in the sky... in the dark... in the end... on the whole, by the way...
More than的用法 A. “More than+名词”表示“不仅仅是” 1)Modern science is more than a large amount of information. 2)Jason is more than a lecturer; he is a writer, too. 3) We need more than material wealth to build our country.建设我们国家，不仅仅需要物质财富. B. “More than+数词”含“以上”或“不止”之意，如： 4)I have known David for more than 20 years. 5)Let's carry out the test with more than the sample copy. 6) More than one person has made this suggestion. 不止一人提过这个建议. C. “More than+形容词”等于“很”或“非常”的意思，如： 7)In doing scientific experiments, one must be more than careful with the instruments. 8)I assure you I am more than glad to help you. D. more than + (that)从句，其基本意义是“超过（=over）”，但可译成“简直不”“远非”.难以，完全不能（其后通常连用情态动词can） 9) That is more than I can understand . 那非我所能懂的. 10) That is more than I can tell. 那事我实在不明白。 11) The heat there was more than he could stand. 那儿的炎热程度是他所不能忍受的 此外，“more than”也在一些惯用语中出现，如： more...than 的用法 1. 比……多，比……更 He has more books than me. 他的书比我多。 He is more careful than the others. 他比其他人更仔细。 2. 与其……不如 He is more lucky than clever. 与其说他聪明，不如说他幸运。 He is more （a）scholar than （a）teacher. 与其说他是位教师，不如说他是位学者。 注：该句型主要用于同一个人或物在两个不同性质或特征等方面的比较，其中的比较级必须用加more 的形式，不能用加词尾-er 的形式。 No more than/not more than 1. no more than 的意思是“仅仅”“只有”“最多不超过”，强调少。如： --This test takes no more than thirty minutes. 这个测验只要30分钟。 --The pub was no more than half full. 该酒吧的上座率最多不超过五成。-For thirty years，he had done no more than he （had）needed to. 30年来，他只干了他需要干的工作。 2. not more than 为more than （多于）的否定式，其意为“不多于”“不超过”。如：Not more than 10 guests came to her birthday party. 来参加她的生日宴会的客人不超过十人。 比较： She has no more than three hats. 她只有3顶帽子。（太少了） She has not more than three hats. 她至多有3顶帽子。（也许不到3顶帽子） I have no more than five yuan in my pocket. 我口袋里的钱最多不过5元。（言其少） I have not more than five yuan in my pocket. 我口袋里的钱不多于5元。（也许不到5元） more than, less than 的用法 1. （指数量）不到，不足 It’s less than half an hour’s drive from here. 开车到那里不到半个钟头。 In less than an hour he finished the work. 没要上一个小时，他就完成了工作。 2. 比……（小）少 She eats less than she should. 她吃得比她应该吃的少。 Half the group felt they spent less than average. 半数人觉得他们的花费低于平均水平。 more…than,/no more than/not more than (1)Mr．Li is ________ a professor; he is also a famous scientist． (2)As I had ________ five dollars with me, I couldn’t afford the new jacket then． (3)He had to work at the age of ________ twelve． (4)There were ________ ten chairs in the room．However, the number of the children is twelve． (5)If you tel l your father what you’ve done, he’ll be ________ angry． (6)－What did you think of this novel? －I was disappointed to find it ________ interesting ________ that one． 倍数表达法 1. “倍数+形容词（或副词）的比较级+than+从句”表示“A比B大（长、高、宽等）多少倍” This rope is twice longer than that one.这根绳是那根绳的三倍（比那根绳长两倍）。The car runs twice faster than that truck.这辆小车的速度比那辆卡车快两倍（是那辆卡车的三倍）。 2. “倍数+as+形容词或副词的原级+as+从句”表示“A正好是B的多少倍”。
“tｈｅwａｙ+从句”结构的意义及用法 首先让我们来看下面这个句子: Ｒead the foｌloｗｉnｇpassagｅａnd talkａbout ｉt wi ｔh your classmaｔes．Try tｏｔeｌl whaｔyｏu thiｎk ｏf Tom aｎd ｏｆｔhe ｗay the chiｌｄrenｔrｅated ｈim. 在这个句子中，ｔhe waｙ是先行词,后面是省略了关系副词that或in whｉch的定语从句。 下面我们将叙述“the ｗaｙ+从句”结构的用法。 1.tｈe wａy之后，引导定语从句的关系词是tｈat而不是hoｗ,因此，<<现代英语惯用法词典＞＞中所给出的下面两个句子是错误的：Ｔhｉs is ｔｈeｗayｈowｉtｈａppened. This is the way how he ａlwａｙs treats me. 2．在正式语体中,thaｔ可被in which所代替;在非正式语体中，ｔhat则往往省略。由此我们得到theｗay后接定语从句时的三种模式：1) tｈe ｗaｙ＋ｔhａt-从句２）the way +ｉn whiｃh－从句3) the ｗay +从句 例如：Ｔｈe way(in whiｃh ，thａt) ｔhｅｓｅｃomｒade ｓloｏｋａｔｐrobｌems is wrong．这些同志看问题的方法
不对。 Ｔｈｅｗａy(that ,ｉn ｗhiｃh)yoｕ’ｒe doinｇit is comple ｔeｌy crａzy.你这么个干法,简直发疯。 Wｅａdmiｒｅd him for thｅｗay ｉｎｗhｉch he fａｃeｓdiｆficultieｓ． Waｌlａｃe ａｎd Ｄarwiｎｇreed ｏn the way ｉｎwhi ｃh ｄｉfｆｅrｅnt forms ｏf life had ｂegｕn.华莱士和达尔文对不同类型的生物是如何起源的持相同的观点。 Thｉs is ｔｈe ｗaｙ（tｈａｔ) hｅdｉd it. I lｉkeｄｔhe waｙ(ｔhat) ｓｈeｏｒganized ｔhe ｍeetｉng． 3.theｗay(tｈat)有时可以与hｏw(作“如何”解）通用。例如： That’s tｈe ｗaｙ(tｈaｔ) shｅspoke. = Tｈat’s how shｅspoke.
初中英语比较级和最高级讲解与练习 形容词比较级和最高级 一．绝大多数形容词有三种形式,原级,比较级和最高级, 以表示形容词说明的性质在程度上的不同。 1. 形容词的原级: 形容词的原级形式就是词典中出现的形容词的原形。例如: poor tall great glad bad 2. 形容词的比较级和最高级: 形容词的比较级和最高级形式是在形容词的原级形式的基 础上变化的。分为规则变化和不规则变化。 二．形容词比较级和最高级规则变化如下: 1) 单音节形容词的比较级和最高级形式是在词尾加-er 和-est 构成。 great (原级) greater(比较级) greatest(最高级) 2) 以-e 结尾的单音节形容词的比较级和最高级是在词尾加-r 和-st 构成。 wide (原级) wider (比较级) widest (最高级) 3) 少数以-y, -er, -ow, -ble结尾的双音节形容词的比较级和最高级是在词尾加 -er 和-est构成。 clever(原级) cleverer(比较级) cleverest(最高级)， slow(原级) slower(比较级) slowest (最高级) 4) 以-y 结尾,但-y 前是辅音字母的形容词的比较级和最高级是把-y 去掉,加上-ier 和-est 构成. happy (原形) happier (比较级) happiest (最高级) 5) 以一个辅音字母结尾其前面的元音字母发短元音的形容词的比较级和最高级是双写该 辅音字母然后再加-er和-est。 原形比较级最高级原形比较级最高级 big bigger biggest hot hotter hottest red redder reddest thin thinner thinnest 6) 双音节和多音节形容词的比较级和最高级需用more 和most 加在形容词前面来构 成。 原形比较级最高级 careful careful more careful most careful difficult more difficult most difficult delicious more delicious most delicious 7)常用的不规则变化的形容词的比较级和最高级: 原级比较级最高级 good better best 好的 well better best 身体好的 bad worse worst 坏的 ill worse worst 病的 many more most 许多 much more most 许多 few less least 少数几个 little less least 少数一点儿 （little littler littlest 小的） far further furthest 远（指更进一步，深度。亦可指更远） far farther farthest 远（指更远，路程）
表示“方式”、“方法”，注意以下用法： 1.表示用某种方法或按某种方式，通常用介词in(此介词有时可省略)。如： Do it (in) your own way. 按你自己的方法做吧。 Please do not talk (in) that way. 请不要那样说。 2.表示做某事的方式或方法，其后可接不定式或of doing sth。 如： It’s the best way of studying [to study] English. 这是学习英语的最好方法。 There are different ways to do [of doing] it. 做这事有不同的办法。 3.其后通常可直接跟一个定语从句(不用任何引导词)，也可跟由that 或in which 引导的定语从句，但是其后的从句不能由how 来引导。如： 我不喜欢他说话的态度。 正：I don’t like the way he spoke. 正：I don’t like the way that he spoke. 正：I don’t like the way in which he spoke. 误：I don’t like the way how he spoke. 4.注意以下各句the way 的用法： That’s the way (=how) he spoke. 那就是他说话的方式。 Nobody else loves you the way(=as) I do. 没有人像我这样爱你。 The way (=According as) you are studying now, you won’tmake much progress. 根据你现在学习情况来看，你不会有多大的进步。 2007年陕西省高考英语中有这样一道单项填空题： ——I think he is taking an active part insocial work. ——I agree with you_____. A、in a way B、on the way C、by the way D、in the way 此题答案选A。要想弄清为什么选A，而不选其他几项，则要弄清选项中含way的四个短语的不同意义和用法，下面我们就对此作一归纳和小结。 一、in a way的用法 表示：在一定程度上，从某方面说。如： In a way he was right.在某种程度上他是对的。注：in a way也可说成in one way。 二、on the way的用法 1、表示：即将来(去)，就要来(去)。如： Spring is on the way.春天快到了。 I'd better be on my way soon.我最好还是快点儿走。 Radio forecasts said a sixth-grade wind was on the way.无线电预报说将有六级大风。 2、表示：在路上，在行进中。如： He stopped for breakfast on the way.他中途停下吃早点。 We had some good laughs on the way.我们在路上好好笑了一阵子。 3、表示：(婴儿)尚未出生。如： She has two children with another one on the way.她有两个孩子，现在还怀着一个。 She's got five children，and another one is on the way.她已经有5个孩子了，另一个又快生了。 三、by the way的用法
形容词比较级和最高级的形式 一、形容词比较级和最高级的构成 形容词的比较级和最高级变化形式规则如下 构成法原级比较级最高级 ①一般单音节词末尾加 er 和 est strong stronger strongest ②单音节词如果以 e结尾，只加 r 和 st strange stranger strangest ③闭音节单音节词如末尾只有一个辅音字母， 须先双写这个辅音字母，再加 er和 est sad big hot sadder bigger hotter saddest biggest hottest ④少数以 y, er(或 ure), ow, ble结尾的双音节词， 末尾加 er和 est(以 y结尾的词，如 y前是辅音字母， 把y变成i，再加 er和 est，以 e结尾的词仍 只加 r和 st) angry Clever Narrow Noble angrier Cleverer narrower nobler angriest cleverest narrowest noblest ⑤其他双音节和多音节词都在前面加单词more和most different more different most different 1) The most high 〔A〕mountain in 〔B〕the world is Mount Everest，which is situated 〔C〕in Nepal and is twenty nine thousand one hundred and fourty one feet high 〔D〕 . 2) This house is spaciouser 〔A〕than that 〔B〕white 〔C〕one I bought in Rapid City，South Dakota 〔D〕last year. 3) Research in the social 〔A〕sciences often proves difficulter 〔B〕than similar 〔C〕work in the physical 〔D〕sciences. 二、形容词比较级或最高级的特殊形式：
比较级和最高级 1.在形容词词尾加上―er‖ ―est‖ 构成比较级、最高级： bright（明亮的）—brighter—brightest broad（广阔的）—broader—broadest cheap（便宜的）—cheaper—cheapest clean（干净的）—cleaner—cleanest clever（聪明的）—cleverer—cleverest cold（寒冷的）—colder—coldest cool（凉的）—cooler—coolest dark（黑暗的）—darker—darkest dear（贵的）—dearer—dearest deep（深的）—deeper—deepest fast（迅速的）—faster—fastest few（少的）—fewer—fewest great（伟大的）—greater—greatest hard（困难的,硬的）—harder—hardest high（高的）—higher—highest kind（善良的）—kinder—kindest light（轻的）—lighter—lightest long（长的）—longer—longest loud（响亮的）—louder—loudest low（低的）—lower—lowest near（近的）—nearer—nearest new（新的）—newer—newest poor（穷的）—poorer—poorest quick（快的）—quicker—quickest quiet（安静的）—quieter—quietest rich（富裕的）—richer—richest short（短的）—shorter—shortest slow（慢的）—slower—slowest small（小的）—smaller—smallest smart（聪明的）—smarter—smartest soft（柔软的）—softer—softest strong（强壮的）—stronger—strongest sweet（甜的）—sweeter—sweetest tall（高的）-taller-tallest thick（厚的）—thicker—thickest warm（温暖的）—warmer—warmest weak（弱的）—weaker—weakest young（年轻的）—younger—youngest 2.双写最后一个字母,再加上―er‖ ―est‖构成比较级、最高级： big（大的）—bigger—biggest fat（胖的）—fatter—fattest hot（热的）—hotter—hottest red（红的）—redder—reddest sad（伤心的）—sadder—saddest thin（瘦的）—thinner—thinnest wet（湿的）—wetter—wettest mad（疯的）—madder—maddest 3.以不发音的字母e结尾的形容词,加上―r‖ ―st‖ 构成比较级、最高级：able（能干的）—abler—ablest brave（勇敢的）—braver—bravest close（接近的）—closer—closest fine（好的,完美的）—finer—finest large（巨大的）—larger—largest late（迟的）—later—latest nice（好的）—nicer—nicest ripe（成熟的）—riper—ripest
The way的用法及其含义（一） 有这样一个句子：In 1770 the room was completed the way she wanted. 1770年，这间琥珀屋按照她的要求完成了。 the way在句中的语法作用是什么？其意义如何？在阅读时，学生经常会碰到一些含有the way 的句子，如：No one knows the way he invented the machine. He did not do the experiment the way his teacher told him.等等。他们对the way 的用法和含义比较模糊。在这几个句子中，the way之后的部分都是定语从句。第一句的意思是，“没人知道他是怎样发明这台机器的。”the way的意思相当于how；第二句的意思是，“他没有按照老师说的那样做实验。”the way 的意思相当于as。在In 1770 the room was completed the way she wanted.这句话中，the way也是as的含义。随着现代英语的发展，the way的用法已越来越普遍了。下面，我们从the way的语法作用和意义等方面做一考查和分析： 一、the way作先行词，后接定语从句 以下3种表达都是正确的。例如：“我喜欢她笑的样子。” 1. the way+ in which +从句 I like the way in which she smiles. 2. the way+ that +从句 I like the way that she smiles. 3. the way + 从句(省略了in which或that) I like the way she smiles. 又如：“火灾如何发生的，有好几种说法。” 1. There were several theories about the way in which the fire started. 2. There were several theories about the way that the fire started.
英语语法---比较级和最高级的用法 在英语中通常用下列方式表示的词:在形容词或副词前加more(如 more natural,more clearly )或加后缀 -er(newer,sooner )。典型的是指形容词或副词所表示的质、量或关系的增加。英语句子中，将比较两个主体的方法叫做“比较句型”。其中，像“A比B更……”的表达方式称为比较级；而“A最……”的表达方式则称为最高级。组成句子的方式是将形容词或副词变化成比较级或最高级的形态。 一、形容词、副词的比较级和最高级的构成规则 1．一般单音节词和少数以-er，-ow结尾的双音节词，比较级在后面加-er，最高级在后面加-est； （1）单音节词 如：small→smaller→smallest short→shorter→shortest tall→taller→tallest great→greater→greatest （2）双音节词 如：clever→cleverer→cleverest narrow→narrower→narrowest 2．以不发音e结尾的单音节词，比较在原级后加-r，最高级在原级后加-st； 如：large→larger→largest nice→nicer→nicest able→abler→ablest 3．在重读闭音节（即：辅音＋元音＋辅音）中，先双写末尾的辅音字母，比较级加-er，最高级加-est； 如：big→bigger→biggest hot→hotter→hottest fat→fatter→fattest 4．以“辅音字母＋y”结尾的双音节词，把y改为i，比较级加-er，最高级加-est； 如：easy→easier→easiest heavy→heavier→heaviest busy→busier→busiest happy→happier→happiest 5．其他双音节词和多音节词，比较级在前面加more，最高级在前面加most； 如：beautiful→more beautiful→most beautiful different→more different→most different easily→more easily→most easily