Detection of Strong Evolution in the Population of Early-Type Galaxies

a r X i v :a s t r o -p h /9605136v 2 15 O c t 1996Detection of Strong Evolution in the Population of

Early-Type Galaxies

Guinevere Kau?mann 1,St′e phane Charlot 2&Simon D.M.White 11Max-Planck Institut f¨u r Astrophysik,D-85740Garching,Germany 2Institut d’Astrophysique du CNRS,98bis Boulevard Arago,F-75014Paris,France Abstract The standard picture holds that giant elliptical galaxies formed in a single burst at high redshift.Aging of their stellar populations subsequently caused them to fade and become redder.The Canada-France Redshift Survey provides a sample of about 125galaxies with the luminosities and colours of passively evolving giant ellipticals and with 0.1

models suggest that both merging and recent star formation play a role in the strong evolution we have detected.

Keywords:galaxies:formation,evolution;galaxies:elliptical and lenticular;galaxies:stellar content

1Introduction

In the standard model of elliptical galaxy formation?rst proposed by Tinsley&Gunn(1976), all stars in the galaxy form in an initial burst at high redshift and the galaxy’s luminosity subsequently evolves passively as the more massive stars evolve o?the main sequence.This leads to luminosity evolution with cosmic time that can be parametrized as

L(t)=L(t0)[(t?t f)/(t0?t f)]?1+θx,(1) where t f is the time of formation,x is the slope of the initial mass function(x=1.35for a Salpeter mass function),andθ?0.26is the slope of the mass-main sequence lifetime relation (see Phillipps1993).Spectral synthesis techniques show that simple passive evolution models provide good?ts to the colours and spectral properties of a class of galaxies conventionally called early-type,which include the ellipticals and the S0s.

With the superior imaging capability of the Hubble Space Telescope,it has recently be-come possible to identify early-type galaxies at high redshift purely on the the basis of their morphologies(see for example Driver et al1995,Abraham et al1996).There is an emerging consensus that the colours and luminosities of early-type galaxies in rich clusters are consistent with simple passive evolution models and with a standard value of the IMF slope(Aragon-Salamanca et al1993,Dickinson1995,Bender,Ziegler&Bruzual1996,Van Dokkum&Franx 1996,Schade et al1996,Pahre,Djorgovski&de Carvalho1996,Ellis et al1996).It appears that the luminosity evolution long predicted as a consequence of stellar aging has?nally been detected.These studies do not prove,however,that the early-type galaxy population as a whole formed at high redshift and evolved passively.A test of this hypothesis requires a large redshift survey of early-type galaxies that is complete to faint limiting magnitudes.

Morphological classi?cation of early-type galaxies has been carried out to limiting mag-nitudes of I=21and I=25in the Medium Deep and the Hubble Deep Field surveys respectively,but redshifts for a complete sample of these galaxies are lacking at present.The Canada France Redshift Survey(CFRS)is one of the deepest large redshift surveys carried out to date(Lilly et al1995a,Le F`e vre et al1995,Hammer et al1995,Crampton et al 1995,Lilly et al1995b).As we will show,it provides a sample of about125I-band selected galaxies with the luminosities and colours of passively evolving giant ellipticals and with red-shifts lying in the range0.1to1.Morphological classi?cations for these objects are not yet available.The Hawaii Deep Fields Spectroscopic Survey(Cowie et al1996)provides us with an independent K-band selected sample of28early-type galaxies.The great advantage of working with magnitude-limited redshift surveys is that a given evolutionary hypothesis may be tested directly in a way which is independent of the galaxy luminosity function.This was ?rst illustrated in a seminal paper by Schmidt(1968),who introduced the so-called V/V max test and used a?ux-limited sample of only33QSOs to show that the population has evolved strongly with redshift.The test is particularly powerful in the present context because it avoids the need to assume anything about the highly uncertain local luminosity function of early-type galaxies(compare the very di?erent results of Loveday et al(1992)and Marzke et al(1994)).

In this Letter,we apply the Schmidt V/V max test to early-type galaxies selected by colour from the CFRS and Hawaii surveys.We show that these samples are both inconsistent with the simple passive evolution picture with better than99.7%con?dence.

2Selecting Early-type Galaxies in the CFRS

Ellipticals and S0s are the reddest objects in the local Universe.To de?ne a colour threshold for separating early from late-type galaxies,we make use of new population synthesis models by Bruzual&Charlot(1996),which include the e?ects of metallicity(see also Charlot1996). For our standard model,we assume that all early-type galaxies form in a single burst of duration0.1Gyr at z=5and have a Salpeter IMF with upper and lower cuto?s at100M⊙and0.1M⊙.

Ideally,our adopted colour boundary should be blue enough to include all elliptical and S0galaxies,yet red enough to exclude spiral galaxies of type Sa or later.In practice galaxies of given type show a substantial spread in colour,so no perfect boundary exists.We adopt a colour threshold corresponding to a passively evolving model with50%solar metallicity. We have chosen this model because it gives the best separation between early and late-type galaxies in local photometric surveys.We?nd that under this criterion,88%of the galaxies in the Bower,Lucey&Ellis(1992)sample of66ellipticals and S0s in the Coma and Virgo clusters would be included in our sample,while84%of the galaxies in the Visvanathan(1992) survey of177luminous Sa-Sc spirals towards the Great Attractor region would be rejected.

Figure1shows the resulting(V?I)AB redshift relation superposed on the CFRS data. We identify98early-type galaxies down to a limiting magnitude of I=22.5,17%of the total sample of591galaxies with secure redshifts.In the Hawaii Survey,galaxies are selected according to B?K colour.We identify23early-type galaxies to K=19.5,again about one?fth of the total sample.Note that these fractions agree rather well with the20?25% of galaxies brighter than I=22.5in the HST Medium Deep Survey which have early-type morphology according to Driver et al(1995)and Abraham et al(1996).

In addition to information about colours,magnitudes and redshifts,the CFRS catalogue contains a list of the main features seen in the spectrum of each galaxy.Evidence for ongoing star formation is provided by the detection of O[II]emission at3727?A.Such emission is almost never seen in nearby E/S0galaxies.If we exclude galaxies with detected O[II],our sample is reduced to72galaxies.In?gure2,we plot redshift and absolute magnitude histograms for these samples.Note that the absolute magnitudes are present-day values,assuming that each galaxy evolves passively from the time of detection until the present day.Galaxies with detectable O[II]emission tend to lie at at higher redshift and to be intrinsically fainter than those with no such emission.However,almost all objects in the sample have absolute magnitudes typical of giant ellipticals.

It is important to realise that the CFRS survey is only just over80%complete.The Hawaii Survey is87%complete to K=19.5.Omission of the galaxies without secure redshifts would introduce signi?cant bias into our analysis,since many of them are red and lie close to the magnitude limit of the survey.It is thus important that we correct for incompleteness as well as possible and investigate the uncertainties which this correction introduces.

Our“standard”correction procedure is as follows and is similar to one described by Lilly et al(1995b).We assume that each galaxy without a measured redshift has the same distribution in z as galaxies of the same apparent magnitude and colour which do have secure redshifts.In practice,we de?ne intervals in I and V?I(or K and B?K)centred on the galaxy and adjust them so that they contain20galaxies with redshifts.We randomly select one of these galaxies and assign its redshift to our candidate.If the galaxy then falls above the colour threshold

Figure1:The division of the CFRS galaxies into early and late-types according to the colour-redshift criterion discussed in the text.Solid circles represent the ellipticals and S0s

and stars represent the spirals and irregulars.

shown in?gure1,it is classi?ed as early-type.As shown in?gure2for the CFRS data,this procedure adds about28objects to the sample,about20%of all the galaxies without secure redshifts.Most lie close to I=22.5and are redder than the majority of galaxies of the same apparent magnitude which do have secure redshifts.Their redshift and absolute magnitude distributions are thus biased towards higher values of z and somewhat fainter luminosities. 3The Schmidt Test

The ratio V/V max is a measure of the position of a source within the total volume V max where it could have been included in the sample.To determine V max,one must know the intrinsic luminosity of the source,and hence the distance at which it would fall below the limiting magnitude of the survey,assuming that it evolves in luminosity according to the passive evolution model described in section2.When applied to the CFRS data,one must also take account of the fact that no galaxies brighter than I=17.5are included in the survey.If passive evolution is the correct model,V/V max should be uniformly distributed between0and 1and V/V max should scatter around0.5,with a variance only dependent on sample size.In this Letter,we calculate all magnitudes and volumes assuming that q0=0.5and H0=50km s?1Mpc?1.We have checked that changing q0has almost no e?ect on our results.

In?gure3,we show the V/V max distribution for early-type galaxies selected by colour from the CFRS catalogue.The solid histogram shows the result obtained if galaxies with O[II]emission are excluded from the sample,while the hatched area shows the contribution from galaxies with such O[II]emission.Finally,the un?lled area shows the V/V max distribution of the galaxies included by the incompleteness correction of section2.

The V/V max distribution is clearly skewed to values less than0.5.We obtain V/V max = 0.398when objects with detected star formation are excluded and V/V max =0.410when they are included.For a uniform distribution,the expected standard deviations in V/V max for samples of these sizes are0.029and0.026respectively.The observational data are thus inconsistent with the standard model of passive evolution with better than99.9%con?dence. It seems that with increasing redshift,a larger and larger fraction of the nearby elliptical/S0 population must drop out of the sample,either because the galaxies are no longer single units or because star formation alters their colours.We can parametrize the evolution of the remaining fraction as F=(1+z)?γand determine the value ofγrequired for the V/V max distribution to come out uniform.We?nd thatγ=1.7±0.4for the sample without O[II] emission and thatγ=1.5±0.4for the full sample(see the lower panel of?gure3).This density evolution is quite dramatic!It implies that at z=1only about one third of nearby bright E and S0galaxies were already assembled and had the colours of old,passively evolving stellar systems.

For the23early-type galaxies identi?ed in the Hawaii data,we obtain V/V max =0.317 The expected variance for this sample is0.060.Thus even though this sample is much smaller, the deviation of V/V max from0.5is almost as signi?cant as in the CFRS data.The smaller value of V/V max re?ects the fact that passively evolving galaxies could in principle be de-tected to higher redshift at K,but are not in fact found.This sample givesγ=2.0±0.7, quite consistent with the values from the CFRS.

It should be noted that a very similar calculation was carried out by Lilly et al(1995b).

Figure2:Redshift and absolute magnitude histograms for early-type galaxies selected from the CFRS catalogue.The solid area is for galaxies with no detected O[II]emission and the hatched area for galaxies with O[II]emission.The un?lled area represents galaxies included by the incompleteness correction described in section2.

They found that V/V max for colour-selected ellipticals was not signi?cantly below0.5,but for a non-evolving model.As mentioned previously,however,passive evolution has now been observationally established for cluster ellipticals,so a non-evolving model does not represent a viable physical picture.

4Sensitivity of the Results to Stellar Models,Sample Selection,Incompleteness and Photometric Error

In this section,we describe a series of tests carried out to explore the sensitivity of our results to the various modelling and sample selection procedures that we have adopted.

?Stellar Population Models.The standard model of passive evolution adopted in this paper is a single star formation burst of duration0.1Gyr at redshift z f=5with a Salpeter IMF(x=1.35in equation1).Higher formation redshifts or a longer duration (up to1Gyr)of the initial starburst lead to nearly identical predictions.If a more recent formation epoch is assumed,the passive evolution model is even more strongly ruled out since galaxies then fade more rapidly between z=1and z=0(this more than compensates for the fact that high z galaxies are also somewhat bluer in such a model).

The results are also only weakly sensitive to changes in the IMF slope.Increasing x leads to slower luminosity evolution because low-mass stars evolve less rapidly than high-mass stars(see equation1).However,even for an extreme slope of x=2.5,we?nd that V/V max only increases by1.6%to0.417.Finally,we note that using alternative population synthesis models by Worthey(1994)or Tantalo et al.(1996)would lead to results similar to those presented here.

?The Colour Threshold.The50%solar model is our canonical boundary for separating early from late-type galaxies.For comparison,Table1shows how our results are a?ected if redder or bluer boundaries are adopted.Although changing the colour threshold alters the relative fractions of elliptical/S0s and spirals included in the sample quite substantially,the derived values of V/V max vary very little.

?Field-to-Field https://www.doczj.com/doc/025903751.html,rge-scale structures such as voids or great walls can cause signi?cant?uctuations in the number of galaxies in certain redshift bins.This might cause us to underestimate the sampling variance of V/V max .To test for this e?ect, we analyze separately each of the5?elds that make up the CFRS survey.These?elds are well enough separated so that structure should not correlate between them.The ?eld-to-?eld?uctuations in V/V max scatter about the mean withχ2=6.54for four degrees of freedom,showing that any e?ect is small.

?Incompleteness.So far we have quoted results for samples corrected for incompleteness as described in section2.We have also experimented with an alternative procedure that takes into account the possibility that the surveys may be systematically biased against including early-type galaxies at redshifts close to1,simply because at z>0.7?0.8 it becomes substantially more di?cult to determine redshifts in the absence of strong emission lines.Since V and I-band photometry are available for all galaxies,even

Figure3:upper panel:The V/V max distribution for early-type galaxies selected from the CFRS catalogue.Explanations of the histogram shadings are as in?gure2.lower panel:The resulting V/V max distribution when density evolution of the form F=(1+z)?1.5is applied to the full(incompleteness corrected)sample of150early-type galaxies.

those without redshifts,one can evaluate the maximum redshift z max for which each “unidenti?ed”galaxy would still lie above our colour threshold and be classi?ed as early-type.If z max>0.7,we assign z max to be the redshift of the unidenti?ed galaxy.

If z max<0.7,we assign a redshift as before.In practice,what this means is that all unidenti?ed galaxies that could be early-type galaxies at redshifts greater than0.7are assigned their maximum possible value of V/V max.Even this extreme procedure only raises V/V max to0.451for the full CFRS sample,implyingγ=1.0±0.3and a factor2 decrease in the number density of early-type galaxies by redshift1,rather than a factor 3.

?V/V max for early-type galaxies limited at I=21.5.As a further check,we repeat our analysis for the subsample of early-type galaxies limited at I=21.5.There are then 76galaxies with redshifts and the incompleteness correction adds only4extra objects.

This sample givesγ=1.2±0.6,in good agreement with the results for the fainter sample.

?The E?ect of Photometric Errors.We model the e?ect of photometric errors on our results by introducing a random error in the V and I magnitudes that increases for galaxies with fainter apparent magnitudes.If the maximum errors are less than0.4 mag,there is no signi?cant change in the results.If the photometric errors are bigger than this, V/V max rises above its true value.This is because of the number of blue galaxies increases at fainter apparent magnitudes,so photometric errors have the net e?ect of scattering more faint galaxies into the early-type colour window than out of it.

The low values of V/V max which we obtain for the CFRS and Hawaii data are thus overestimates of the true values if photometric errors are signi?cant.

5Conclusions

We conclude that uncertainties in the stellar population models,sample selection and incom-pleteness corrections are insu?cient to reconcile the observations with the standard picture. Early-type galaxies selected from the Canada France Redshift Survey according to V?I colour have a luminosity and redshift distribution that is inconsistent with the hypothesis that they have all been evolving passively since a redshift of1.It appears that by z=1,two thirds of nearby early-type galaxies have dropped out of the sample,either because they are star-forming and no longer have colours consistent with an old stellar population,or because they have broken up into several pieces too faint to be included in the sample.This evolution may apply exclusively to the elliptical galaxy population,exclusively to the S0galaxy popu-lation,or to both populations equally.We cannot use colour alone to separate ellipticals from S0s.

In recent hierarchical models of galaxy formation(Kau?mann,White&Guiderdoni1993, Baugh et al1996),galaxy disks form as gas cools and condenses at the centres of dark matter halos,while elliptical galaxies form when two disk galaxies merge.If no further gas cools onto the elliptical,its stellar population will fade and it will evolve passively until the present day.In such models,ellipticals form by mergers at all redshifts.The typical formation redshift of an elliptical is higher in a rich cluster than in the?eld,simply because galaxy-

sized perturbations collapse earlier in dense environments.The typical formation redshift of ellipticals also depends sensitively on the cosmological parameters,in particular on the density parameter?and the normalization parameterσ8(sometimes referred to as b≡1/σ8).Studies of the evolution of elliptical galaxies can thus provide important constraints on these models.

In recent work,Kau?mann(1996)has shown that a“standard”CDM model with?=1 andσ8=0.7can explain the observed spread in the colours of elliptical galaxies in clusters at redshifts between0and0.6,as well as the apparent passive evolution of the colours of cluster ellipticals.It is interesting that this model predicts that the global number density of bright ellipticals should decrease by a factor2-3by redshift1,in rather good agreement with our results from the CFRS.By contrast,if a lower normalization ofσ8=0.4is adopted,as would be appropriate for a COBE-normalized CDM model with a“shape”-parameterΓ=0.2,one obtains much more rapid evolution,with the number density of ellipticals decreasing by a factor25by redshift1.

There is also considerable spectroscopic evidence that many elliptical galaxies have under-gone recent episodes of star formation.Charlot&Silk(1994)attempt to quantify this using signatures of intermediate-age stars in the spectra of ellipticals in clusters at redshifts between 0and0.4.They?nd that the Balmer absorption line strengths increase with redshift and they interpret this in terms of an increasing contribution of younger stars to the total light(see also Barger et al1996).It is not possible,however,to determine from the spectra the star formation history of the elliptical prior to its last burst,or to assess what physical mechanism was responsible for triggering the star formation.In future,morphological information will be available to complement the colours and redshifts from the Canada-France survey.The combination of morphologies,colours and redshifts will help decide whether merging,star for-mation,or both,are responsible for loss of early-type galaxies at high redshift.Hierarchical formation models suggest that the answer will be both.

Acknowledgments

We thank Olivier le F`e vre and Len Cowie for making the CFRS and Hawaii data available to us in electronic form and Fran?c ois Hammer and the referee,Richard Ellis,for helpful advice and discussions.This work was carried out under the auspices of EARA,a European Association for Research in Astronomy,and the TMR Network on Galaxy Formation and Evolution funded by the European Commission.

Table1:Variation in V/V max for the CFRS and Hawaii surveys as the colour threshold

is changed.

Model%E/S0included%Sp rejected%E/S0 V/V max %E/S0 V/V max (Bower et al)(Visvanathan)(CFRS)(CFRS)(Hawaii)(Hawaii)

0.3Z⊙9865210.413±.023340.343±.045

0.4Z⊙9778190.408±.025260.356±.052

0.5Z⊙8884170.410±.026190.317±.060

0.6Z⊙7992140.409±.028130.326±.075

0.7Z⊙6594120.434±.031110.274±.080

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Figure Captions

Figure1:The division of the CFRS galaxies into early and late-types according to the colour-redshift criterion discussed in the text.Solid circles represent the ellipticals and S0s and stars represent the spirals and irregulars.

Figure2:Redshift and absolute magnitude histograms for early-type galaxies selected from the CFRS catalogue.The solid area is for galaxies with no detected O[II]emission and the hatched area for galaxies with O[II]emission.The un?lled area represents galaxies included by the incompleteness correction described in section2.

Figure3:upper panel:The V/V max distribution for early-type galaxies selected from the CFRS catalogue.Explanations of the histogram shadings are as in?gure2.lower panel:The resulting V/V max distribution when density evolution of the form F=(1+z)?1.5is applied to the full(incompleteness corrected)sample of150early-type galaxies.

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英语中的比较级与最高级 详解

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常见用法

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

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.

英语中的比较级和最高级

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)

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

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.

(完整版)the的用法

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...

英语比较级和最高级的用法

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”。

“the way+从句”结构的意义及用法

“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

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）

way 用法

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

英语比较级和最高级

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：

青岛恒源热电

注意：以下内容请进一步总结！ 青岛恒源热电有限公司 目标公司主要从事蒸汽、热水的生产及供应、蒸汽余热发电业务，同时提供供热管道及设施维修、安装业务。据介绍，目标公司开发了循环水供热工程项目，该项目是青岛市获批的第一个清洁发展机制(CDM)项目；前处该项目处于施工建设阶段，预计将于2009年上半年内正式投产。据介绍，目标公司主要负责临港工业区辖区内的蒸汽供应及热网管理，发电业务，对居民的用热服务。 公司成立于2001年，主要从事蒸汽、热水的生产及供应、蒸汽余热发电业务。 青岛恒源热电有限公司位于开发区B区供热范围，拥有12MW的抽凝式汽轮发电机组1台及12MW的背压机组1台，75t/h循环流化床锅炉3台和150t/h锅炉1台，最大供热能力是355t/h，担负着B区的生产、民用供热负荷，主要满足热电厂东部居民小区供热和山东科技大学供热。 青岛恒源热电有限公司位于青岛经济技术开发区临港工业区的中北部，海尔大道与渭河路交界处东北角，渭河路777号。厂区所在地东侧隔宽约100m绿化地为鑫龙物流公司，该公司东侧、距离本项目最近300m处为澳柯玛人才公寓；厂区南侧隔渭河路、绿化带100m处为东小庄村（原村庄平房已搬迁，现建有多座两层复式楼房），该村庄南侧、距离本项目约420m处为山孚日水食品有限公司；项目隔渭河路东南方向约200m处为澳柯玛工业园；西及西南方向隔海尔大道、渭河路均为浦项制铁有限公司；北侧与开发区消防大队以及正友砼业相邻。 企业所在地厂址东南距市中心约8km，东面距前湾港区约4.5km。 现有工程内容：青岛恒源热电有限公司主要服务于黄岛供热分区B 区（齐长城路以北、疏港高速以南、镰湾河以西、柳花泊和珠山以东片区（包括柳花泊），总占地面积约60平方公里）。企业现有锅炉规模为3×75t/h+1×130t/h 循环流化床蒸汽锅炉，总计约355t/h锅炉容量；发电机组规模为1×12MW C12-34.9/0.98（抽凝）+1×12MW B12-4.9/0.98（背压），总计发电装机容量24 MW。 近几年，恒源热电强化能源管理，合理调整运行方式，加强节能技术改造，企业能源管理工作上了一个新台阶，先后通过了“企业能源审计”、“热电联产机组认定”等审核认证工作，被评为“青岛市清洁生产企业”，2007年度“山东省节能先进企业”。 为进一步加强企业能源管理，完善优化企业节能减排工作，公司在本年度开始推行循环经济试点工作。目前，作为试点工作重点项目之一的企业冷渣机改造项目已基本完成，初步具备投运条件，预计本年度六月份正式投入运行。该项目是将循环流化床锅炉的人工排渣（温度一般在900℃），通过加装冷渣机把炉渣余热加热除盐水，将锅炉效率提高1-3%，同时解决人工放渣存在安全隐患、能源浪费以及不环保等问题，项目投资为85万元，年可节标煤700吨。

高中英语的比较级和最高级用法总结

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