Strong lensing by subhalos in the dwarf-galaxy mass range I Image separations
a r X i v :0806.2149v 1 [a s t r o -p h ] 12 J u n 2008
Draft version June 12,2008
Preprint typeset using L A T E X style emulateapj v.2/19/04
STRONG LENSING BY SUBHALOS IN THE DWARF-GALAXY MASS RANGE I:IMAGE SEPARATIONS
E.Zackrisson 1,2,3?,T.Riehm 2,O.M ¨o
ller 4,K.Wiik 1,&P.Nurmi 1Draft version June 12,2008
ABSTRACT
The cold dark matter scenario predicts that a large number of dark subhalos should be located within the halo of each Milky-way sized galaxy.One tell-tale signature of such dark subhalos could be additional milliarcsecond-scale image splitting of quasars previously known to be multiply-imaged on arcsecond scales.Here,we estimate the image separations for the subhalo density pro?les favoured by recent N-body simulations,and compare these to the angular resolution of both existing and upcoming observational facilities.We ?nd,that the image separations produced are very sensitive to the exact subhalo density pro?le assumed,but in all cases considerably smaller than previous estimates based on the premise that subhalos can be approximated by singular isothermal spheres.Only the most optimistic subhalo models produce image separations that would be detectable with current technology,and many models produce image separations that will remain unresolved with all telescopes expected to become available in the foreseeable future.Detections of dark subhalos through image-splitting e?ects will therefore be far more challenging than currently believed,albeit not necessarily impossible.
Subject headings:Dark matter –galaxies:halos –galaxies:dwarf –gravitational lensing –quasars:
general
1.INTRODUCTION
While the cold dark matter (CDM)scenario has been very successful in explaining the formation of large-scale structures in the Universe (see e.g.Primack 2003,for a re-view),its predictions on the scales of individual galaxies have not yet been con?rmed in any convincing way.One particularly interesting feature of the CDM model is the high level of halo substructure generated.According to current simulations,each galaxy-mass CDM halo should contain large numbers of subhalos (typically accounting for ≈5–10%of its total mass;e.g.Nurmi et al.2006;Diemand et al.2007a)in the dwarf-galaxy mass range.However,these subhalos do not appear to correspond to luminous structures,as the dark halo of the Milky Way would then contain a factor of 10–100more satellite galaxies than observed,provided that each subhalo cor-responds to a luminous dwarf galaxy (e.g.Klypin et al.1999).A similar lack of dwarf galaxies compared to the number of dark halos predicted is also evident on scales of galaxy groups (Tully et al.2002).One way out of this problem is to assume that most of these low-mass halos correspond to so-called dark galaxies (Verde et al.2002),i.e.objects of dwarf-galaxy mass which either do not con-tain baryons or in which the baryons have not formed many stars.While a number of very faint satellite galax-ies have recently been detected (e.g.Zucker et al.2006;Simon et al.2006),it is still far from clear that these exist in su?cent numbers to account for the subhalos predicted by CDM (Simon &Geha 2007).
Gravitational lensing may in principle o?er a route
*E-mail:ez@astro.uu.se
1
Tuorla Observatory,University of Turku,V¨a is¨a l¨a ntie 20,FI-21500Piikki¨o ,Finland
2Stockholm Observatory,AlbaNova University Center,10691Stockholm,Sweden
3Department of Astronomy and Space Physics,Box 515,75120Uppsala,Sweden
4Schloss-Wolfsbrunnenweg 66,69118Heidelberg,Germany
to detecting completely dark galaxies,and the mag-ni?cation associated with dark halo substructures has long been suspected to be the cause of the ?ux ratio anomalies observed in multiply-imaged quasars (e.g.Mao &Schneider 1998;Kochanek &Dalal 2004).However,the subhalos predicted by current CDM simulations appear too few to explain the ?ux ra-tios of many of these systems (e.g.Mao et al.2004;Metcalf 2005a;Macci`o &Miranda 2006).This in-dicates that other mechanisms,like lensing by low-mass ?eld halos outside the main lens (Metcalf 2005b;Miranda &Macci′o 2007),stellar microlensing in the lens galaxy (Schechter &Wambsganss 2002)and absorption or scintillation in the interstellar medium (Mittal et al.2007)may also be at work.
A similar but more direct way of putting the CDM subhalo predictions to the test could be to search for small-scale image separations produced by strong lens-ing from subhalos.Yonehara et al.(2003)argue that by targeting quasars that are already known to be multiply-imaged on arcsecond scales,there should be a signi?cant probability of detecting image splitting by subhalos at scales of milliarcseconds (so-called millilensing or some-times mesolensing).If the sources are extended and can be resolved at scales smaller than the Einstein radii of the subhalos,then not only the number densities of the subhalos but also their internal density pro?les can be constrained (Inoue &Chiba 2005b).It has been argued that this technique may become observationally feasi-ble with ALMA (Inoue &Chiba 2005a)or future space-VLBI missions like VSOP-2(Inoue &Chiba 2005c).If correct,this would constitute a major step forward in the study of dark halo substructures.
These proposals do however rely on the assumption that the image separations (or Einstein radii)of subhalo lenses are similar to those produced by singular isother-mal spheres.This is an assumption that is di?cult to justify,since neither simulations,theoretical arguments
2Zackrisson et al.
nor observations favour a density pro?le of this form for dark matter halos in the relevant mass range.
N-body simulations based on the CDM paradigm typi-cally predict dark matter halos to have inner density pro-?les of the form ρ(r )∝r ?αwith central density slopes α≈1(e.g.Navarro,Frenk,&White 1996,hereafter NFW),whereas the singular isothermal sphere (SIS)as-sumes α=2.While the SIS has proved
to be
a successful model for observed galaxy-mass lenses (e.g.Rusin et al.2003;Koopmans el al.2006),this is believed to be due to the luminous baryons residing in the inner regions of these objects.This component contributes substantially to the overall mass density in the centre,and its forma-tion over cosmological time scales may also have caused the CDM halo itself to contract,thereby steepening the inner slope of its density pro?le (e.g.Gnedin et al.2004;Macci`o et al.2006;Gustafsson et al.2006;Kampakoglou 2006).
Dwarf galaxies are well-known to be more dark mat-ter dominated than their more massive counterparts,and some of the mechanisms proposed for keeping the miss-ing satellites of the Local Group dark assume that most of their baryons have been lost early in the history of the Universe,or are prevented from collapsing into their central regions (e.g.Barkana &Loeb 1999;Read et al.2006).Hence,it seems reasonable that the inner slope αof their density pro?les should be shallower than that of an SIS.Indeed,Ma (2003)?nds that to explain the distribution of angular separations among strong lenses,the lens population must shift from an SIS-type pro?le (α=2)to something more resembling the NFW pro?le (α≈1)at halo masses of 1012M ⊙.Observational con-straints on the slope of the innermost density pro?le of both ?eld and satellite galaxies in the dwarf galaxy mass-range typically favour a slope even shallower than this (α≈0–1;e.g.de Blok &Bosma 2002;Spekkens et al.2005;Zackrisson et al.2006;Gilmore et al.2007).This is potentially bad news for the detectability of low-mass subhalos through millilensing e?ects,since the image sep-aration expected from strong lensing by a halo of ?xed virial mass is extremely sensitive to the slope of its inner density pro?le.In fact,as pointed out by Trentham et al.(2001),the image separation expected from strong lens-ing by dark galaxies would be unobservably small if their density pro?les are of NFW type.An inner slope of the density pro?le even shallower than this would just make the problem worse.
As low-mass halos in the ?eld fall into the potential wells of larger halos,tidal interactions with their host halos and with other subhalos will cause these objects to lose mass.Since this mass loss preferentially takes place in the outer regions of the subhalos,their den-sity pro?les change over time (e.g.Hayashi et al.2003;Kazantzidis et al.2004),thereby altering their lensing properties compared to more isolated ?eld halos of the same mass.Here,we take a critical look at the prospects for strong-lensing detections of dark subhalos in the dwarf-galaxy mass range,by deriving the image sepa-rations expected for subhalo density pro?les favoured by current simulations.
2.DARK HALO DENSITY PROFILES
When deriving the subhalo density pro?les and the corresponding image separations,we assume a ΛCDM
cosmology with ?Λ=0.7,?M =0.3and h =0.7(H 0=100h km s ?1Mpc ?1).As we are mainly inter-ested in image-splitting of the individual macroimages of multiply-imaged quasars,we compute all density pro?les at a typical lens redshift of z l =0.5and adopt a source redshift of z s =2.0.The impact of of other choices for z l and z s on our results are discussed in section 3.We moreover assume that halos contain no material beyond their virial radius r vir (z l ),de?ned as the radius at which the mean enclosed density equals ?vir times the criti-cal density of the Universe at redshift z l .Here,?vir is calculated using approximations from Bryan &Norman (1998).
The majority of papers on the density pro?les of CDM halos have so far focused on relatively isolated halos.When such objects are accreted by more massive halos and become subhalos,substantial mass loss occurs,pref-erentially from their outer regions.Because of this,some sort of modi?cation of these density pro?les is in order when applying them to the study of subhalos.However,since some authors have previously modelled the lensing properties of subhalos using the original,unstripped pro-?les,we will here consider such models as well,so that the the importance of the stripping on the resulting image separations becomes clear.It is moreover possible that the original pro?les may be reasonable approximations for recently accreted objects or low-mass halos which are spatially correlated with the parent halo but formally located outside its virial radius (e.g.Nurmi et al.2006;Diemand et al.2007b).Even though the latter objects are located far away from the central regions of their host halos,they are predicted to exist in great numbers and may end up projected close to the images of strongly-lensed quasars.
2.1.Unstripped pro?les
The original NFW density pro?le,relevant for rela-tively isolated CDM halos,is given by:
ρNFW (r )=
ρi
(r/r S ,M99)1.5[1+(r/r S ,M99)1.5]
.(2)
Navarro et al.(2004,hereafter N04)themselves do how-ever advocate yet another pro?le,
ρN04(r )=ρS,N 04exp(?2/β (r/r S,N 04)β?1
),(3)
with the property of asymptotically approaching a ?nite central density.Here,ρS,N 04is the density at r S ,N04,i.e.ρi /4,and β≈0.17for halos in the dwarf-galaxy mass range.
To derive the R S parameters of the NFW,M99and N04pro?les,we compute these in units of the radius
Strong lensing by subhalos3 r?2at which the power-law slope of the density pro?le
obeys d lnρ/d ln r=?2.This quantity is linked to the
virial radius r vir through the concentration parameter
c=r vir/r?2,with a median value of(Bullock et a.2001):
c=9
1.5×1013M⊙
?0.13
.(4)
Contrary to many other c(M,z)models,this one has been demonstrated to extend into the dwarf-galaxy mass range(Col′?n et al.2004).Once the r S parameters are de-termined,ρi,ρS andρ0can then be derived by requiring that the correct mass is contained within r vir.
In contrast to these CDM-motivated halo models,the commonly used SIS model has a density pro?le of the form:
ρSIS=
σ2v
1+(r/r te)3
ρNFW(r),(6)
where f t,the central density reduction factor,and r te, the e?ective tidal radius of the subhalo(in units of the progenitor scale radius r S),are both related to the mass fraction of the subhalo that remains bound,m bnd, through relations given in H03.For simplicity,we calcu-late the properties of the subhalo progenitor pro?le by assigning it an approximate mass M prog=M sub/m bnd. Based on similar simulations at higher resolution, Kazantzidis et al.(2004,hereafter K04)et al.instead ?nd a density pro?le of the form:
ρK04(r)=kr?γexp(?r
1+(r/r te)3
ρM99/N04(r).(8)
Lacking a better prescription,we adopt the f t(m bnd)and
r te(m bnd)relations presented in H03,although these will
in practice depend on the details of the progenitor halo
model assumed.
When considering the impact of stripping and/or trun-
cation on lensing properties,we have chosen to compare
halos of?xed mass,which is de?ned as the virial mass
for unstripped halos,and as the total subhalo mass after
stripping for the subhalos.This choice–which re?ects
the tradition in the?eld of subhalo simulations,where
one usually present the mass function of the subhalos
themselves and not their progenitors–has important
consequences.For instance,a sharply truncated halo of
a certain mass has a much smaller spatial extent than an
untruncated halo of the same mass.Consequently,the
density in the inner regions of the truncated halo is nec-
essarily higher than that in the untruncated halo of the
same mass,and therefore,the truncated halo will have a
larger Einstein radius.However,a more gradual density
decrease in the outskirts can in principle drive the Ein-
stein radius in either direction,depending on the details
of the stripping process.As it turns out,the stripping
procedure adopted here(equations(6)and(8))tends to
produce Einstein radii that are smaller than those of the
unstripped pro?les.
3.STRONG-LENSING IMAGE SEPARATION VERSUS
OBSERVATIONAL ANGULAR RESOLUTION
To?rst order,the image separation produced by an ex-
tended object with a density that decreases as a function
of distance from the centre is given by
?θ≈2R E/D ol,(9)
where D ol represents the angular-size distance between
observer and lens,and R E represents the linear Einstein
radius.The latter is de?ned as the radius inside which
the mean surface mass densityˉΣof the lens equals the
critical surface mass density
ˉΣ( E )=Σc= c2D os 4 Fig.1.—a)Mean surface mass densityˉΣ( bnd M⊙(with m bnd=0.03),abruptly terminated at a radius enclosing a mass of1010M⊙.The stripped versions of the N04and M99pro?les have been constructed using(8). and K04subhalo models,which should be far more realis-tic than any sharp truncation,do however predictˉΣ(R) smaller than that of an undisturbed NFW halo of the same mass.The N04pro?le(in both its original,stripped and truncated form)also ends up below the threshold, due to its?nite-density core.The e?ects of truncation versus gradual stripping are qualitatively similar for the NFW,N04and M99halos–a sharp truncation increases the Einstein radius whereas a gradual stripping decreases it relative to the Einstein radius produced by the original pro?le.This indicates that previous investigations based on sharp outer truncations are likely to have substantially overestimated the image separations. In Fig.2,we plot the image separations predicted for 104–1011M⊙subhalos against the angular resolution of a number of planned or existing observational facil-ities,operating at a wide range of wavelengths.These include the proposed MAXIM path?nder in X-rays6; VLTI with the proposed VSI instrument(Malbet et al. 2006),the planned GAIA7and SIM PlanetQuest8satel-lites in the optical/near-infrared;the currently avail-able EVN9,HSA10,VLBA11arrays plus the planned ALMA12,EVLA13,SKA14arrays,and also space-VLBI with the planned VSOP-215satellite at radio wave-lengths.Please note that here we consider only the best resolution limits attainable with these telescopes, whereas the resolution at the wavelengths that maximize the number of observable high-redshift sources may be considerably worse. It is immediately evident from Fig.2that there are large di?erences between the image separation https://www.wendangku.net/doc/f03262941.html,/path?nder.html 7www.rssd.esa.int/index.php?project=GAIA https://www.wendangku.net/doc/f03262941.html,/SIM/ https://www.wendangku.net/doc/f03262941.html, https://www.wendangku.net/doc/f03262941.html,/HSA/ https://www.wendangku.net/doc/f03262941.html, https://www.wendangku.net/doc/f03262941.html, https://www.wendangku.net/doc/f03262941.html,/evla/ https://www.wendangku.net/doc/f03262941.html, 15www.vsop.isas.ac.jp/vsop2/tions of the various halo models.As the discrepancy between the number densities of luminous galaxies and dark matter halos does not start to become severe until the halo mass drops below 1010M⊙(e.g.Verde et al. 2002;van den Bosch et al.2003),subhalos at masses be-low this limit need to produce measurable image sepa-rations(θ 4×10?5arcsec for VSOP-2,which has the best theoretical resolution among the telescopes included in Fig.2)in order for dark galaxies to be detectable through image-splitting e?ects.Out of the halo models tested,only two actually meet this criterion without ad-hering to sharp truncations:the SIS and the M99halos. The H03and K04pro?les both give image separations smaller than10?6arcsec for all the halo masses con-sidered and are therefore completely outside the plotted region.Even in the optimistic case of an M99halo(in either its original or stripped form,whereas the sharp truncation,as discussed previously,is not considered re-alistic),the image separations are a factor of≈3–7 smaller than those predicted for a SIS(and≈30–60 times smaller than those of a truncated SIS),render-ing only the few most massive subhalos(～1010M⊙or slightly higher)detectable at～0.01′′resolution(GAIA, SIM and ALMA).At milliarcsecond resolution(VLTI and SKA),dark galaxies with masses 109M⊙may become detectable.To probe further down the sub-halo mass function,submilliarcsecond-resolution facili-ties(MAXIM path?nder,HSA,EVN,VLBA or VSOP-2) will be required. These image separations have been computed for?du-cial lens and source redshifts of z l=0.5and z s=2.0,but the overall picture does not change substantially for other realistic choices of these parameters.A higher z s implies a lower critical surface mass densityΣc for certain z l, which for a?xed subhalo density pro?le will increase the Einstein radius and boost the image separation?θ.This boost becomes more pronounced for objects with?at in-nerˉΣ( Fig.2.—Subhalo mass versus image separation?θfor those density pro?les from Fig1that give rise to image separations on scales larger than microarcseconds.The angular resolution of a number of existing and planned observational facilities have been indicated by horizontal dashed lines,marked with labels(see main text for details).a)The di?erent diagonal lines represent SIS(thin solid),truncated SIS(thick solid),M99(medium dashed),stripped M99(thin dashed)and truncated M99(thick dashed)subhalo models.b)The di?erent diagonal lines represent NFW(thin dash-dotted),truncated NFW(thick dash-dotted)and truncated N04(solid with circles)subhalo models. lution of the virial radius and the concentration param-eter,this has a minor e?ect on?θ,compared to impact of theΣc(z l,z s)dependence.We?nd,that by allowing source redshifts as high as z s=5.0,the image separation of a1010M⊙NFW-type subhalo can be increased by a factor of up to≈30.Even though this boost factor may seem large,the resulting image separation is still only ?θ～10?6arcseconds,and hence far below the observ-able range.For an M99pro?le,the corresponding boost is only≈30%.Hence,subhalos need to have steep in-ner density pro?les(of approximately the M99type)to become observable,even if a sample of multiply-imaged quasars with lens and source redshifts chosen to maxi-mize the subhalo image separations would become avail-able. 4.EXTERNAL CONVERGENCE AND SHEAR The?θestimates presented in the previous section are based on the assumption that the subhalos can be treated as isolated objects.The e?ects of external convergence κand shearγdue to the galaxy(and halo)hosting these subhalos have thereby been neglected.Yonehara et al. (2003)explored the consequeces of non-zeroκandγin the case of SIS subhalos and found the external poten-tial to have a non-negligible impact on the strong lensing properties of such objects.However,their study sug-gests that the resulting image separations?θκ,γare typ-ically within a factor of≈3from those derived in the case ofκ=γ=0.If applied to the predictions plot-ted in Fig.2,a boost factor of this magnitude would be insu?cient to challenge our main results,namely that only subhalos with inner density pro?les as steep as those of M99(or SIS)models produce image sep-arations that can be resolved with current or planned telescopes.The question remains whether the boost fac-tor f boost=?θκ,γ/?θκ=0,γ=0can become considerably larger for some of the more realistic density pro?les con-sidered here. To investigate this,we use ray-tracing simulations to numerically assess the distribution of f boost.For the macrolens(i.e.the halo and galaxy hosting the subhalo) we adopt an SIS density pro?le withσv=150km s?1. At z l=0.5and z s=2.0,the corresponds to a linear(an-gular)Einstein radius of2.5kpc(0.4arcsec).Subhalos are then distributed within this structure,assuming an NFW pro?le with c=10for the subhalo component of the CDM in the macrolens.Since the optical depth for image splitting by subhalos is low(Yonehara et al.2003), the f boost distribution is not very sensitive to the exact spatial distribution of the subhalos within the host halo. For simplicity,we assume all subhalos to have the same mass in each simulation,but repeat the simulations for di?erent subhalo masses to explore the dependence of f boost on the subhalo mass.The sources are assumed to be point-like and are distributed on a regular grid in the source plane.To assess the e?ects of magni?cation bias,two di?erent cases are considered:one in which no magni?cation threshold is imposed,and one in which only source positions which produce total magni?cations μ≥10are analyzed.Source positions for which multiple images are not produced are always rejected. The vast majority of the resulting macroimages turn out to be una?ected by the subhalos due to the low op-tical depth,and are therefore discarded.The proper-ties of the Einstein ring of the subhalo is calculated for the remaining macroimages,and the image separation ?θκ,γestimated from its angular diameter.In the case ofγ=0,the Einstein ring becomes an ellipse,and?θκ,γis then estimated along the major axis.This leads to a systematic overestimate of?θκ,γ,which ensures that the resulting boost factors are conservative upper limits. In the case of no magni?cation threshold,the resulting distribution of f boost is shown in Fig.3for an M99sub-halo(solid line)and an H03subhalo(dashed),both with M sub=1010M⊙.As discussed in Section3,these sub-halo models span the range from e?ectively undetectable (H03)to favourable for detection(M99).In both cases, the tail of the f boost distribution extends up to very high values,which means that it is in principle possible to ?nd macroimages for which subhalos of masses much 6 et al. Fig. 3.—The cumulative probability distribution P (>f boost )of image separation boost factors f boost due to the external poten-tial in the case of M99(solid)and H03(dashed)subhalo density pro?les.In both cases,the mass of the subhalo is 1010M ⊙. lower than indicated by Fig.2can be detected through image-splitting e?ects.However,such macroimages are exceedingly rare.The probability of having f boost ≥100is ～10?3in the case of M99and ≈0.03in the case of H03.The expectation value for the boost factor is f boost ≈2.3for the M99subhalo and f boost ≈14for the H03subhalo.This is enough to shift the ?θprediction for the M99subhalos fairly close to that of an untruncated SIS in Fig.2,but insu?cient to move the H03prediction (?θκ=0,γ=0～10?15arcsec at this mass)into the detectable range.In the case of M99subhalos,we have also explored the mass dependence of f boost ,?nding f boost ≈3.1for M sub =108M ⊙and f boost ≈3.6for M sub =106M ⊙.This trend with in-creasing f boost for decreasing subhalo mass translates into a slight change in slope for the ?θ(M sub )predic-tion in Fig.2,but has no dramatic e?ects on our overall conclusions. Flux-limited observations are a?ected by a magni?-cation bias,since ?ux threshold of the survey tends to favour highly magni?ed quasars from the vast popula-tion of intrinsically faint objects over modestly magni?ed (or even demagni?ed)quasars from the relatively small population of intrinsically bright objects.The exact im-pact of this e?ect depends on the ?ux threshold and the quasar luminosity function (which,in turn,depends on the wavelength at which the quasars are observed),and is outside the scope of this paper.Here,we instead make a crude assessment of the likely impact of magni?cation bias by rejecting all systems which do not ful?ll the cri-terion μ≥10.As expected,this increases the boost of the image separation produced by the subhalos.In the case of M sub =1010M ⊙subhalos,the boost reaches f boost ≈6.7for an M99pro?le and f boost ≈85for an H03pro?le,i.e.an increase by a factor of ≈3(M99)and ≈6(H03)compared to the case without magni?cation bias.While this brightens the prospects of detecting sub-halos with M99pro?les,H03subhalos still produce image separations that are too small to be resolved with any of the telescopes considered in Fig.2. 5.DISCUSSION Our results indicate that detection of subhalos through gravitational image-splitting is likely to be considerably more challenging than suggested in previous studies,due to the smaller image separations predicted for subhalo density pro?les more realistic than the SIS models often adopted.In fact,no currently planned telescope will be able to resolve the image separations produced by subhalos with density pro?les of the type suggested by the most realistic simulations currently available (H03&K04).We stress,however,that these simulations do not necessarily represent the ?nal word on this issue.NFW density pro?les were adopted for the subhalo progenitors in both the H03and K04simulations,which means that the slope of the central density pro?le prior to stripping was assumed rather than derived from the simulations themselves.If the subhalos would have steeper central density slopes (e.g.of M99type),these would give rise to image separations that could be resolved even with existing telescopes. Despite the somewhat bleak detection prospects pre-sented here,there are at least two e?ects that can po-tentially improve the detectability of image splitting by subhalos:baryon cooling and the presence of intermedi-ate mass black holes. Baryon cooling would cause the subhalo (or its progenitor halo)to contract (e.g.Gnedin et al.2004;Macci`o et al.2006;Gustafsson et al.2006;Kampakoglou 2006),thereby increasing the central density and boost-ing the image separation.It is,however,not clear how strong this e?ect is likely to be,since this depends on the details of the mechanism that prevents the dark sub-halo from forming stars.Baryon cooling is usually as-sumed to be associated with star formation,and most attempts to explain the lack of bright subhalos there-fore propose that the baryons have either been lost early in the history of the Universe,or are prevented from cooling by the ultraviolet background provided by reion-ization (e.g.Barkana &Loeb 1999;Read et al.2006).Neither mechanism is likely to result in any signi?cant halo contraction.Nonetheless,claims of dark baryons in the form of cold gas in galactic disks have been made (Bournaud et al.2007),implying that there may be some route for gas to cool without forming stars or being de-tected by the usual H 2tracers (e.g.Pfenniger et al.1994;Pfenniger &Combes 1994).One may therefore speculate that there could be alternative solutions to the missing-satellite problem,in which subhalos are kept dark even though baryon cooling has taken place. Intermediate mass black holes (IMBHs,see e.g.van der Marel 2004;Zhao &Silk 2005;Noyola et al.2008)with masses of ～102–104M ⊙would also boost the image separations,if present in the centres of dark subhalos.This could for instance be the case if the empir-ical relations between the mass of a supermassive black hole and its dark matter halo (Ferrarese 2002)would ex-tend into the dwarf-galaxy mass range.Even in the case of κ=γ=0,an IMBH of mass 104M ⊙,would give an image separation of ≈4×10?4arcsec for z l =0.5and z s =2.0.This is su?cient to allow VSOP-2to re-solve the image splitting,regardless of the density pro?le of the subhalo hosting the IMBH.Of course,even if the Ferrarese relations would hold for luminous dwarf galax-ies,the do not necessarily do so for dark ones,since this depends on the formation details of IMBHs.Moreover, Strong lensing by subhalos7 a population of halo IMBHs not associated with subha-los could form an undesired background of millilensing events that would obfuscate attempts to study subhalos through image-splitting e?ects. Finally,there is an important issue related to the limi-tation of current CDM halo simulations.Current N-body simulations only resolve scales down to R～0.001r vir, whereas for the steeper density pro?les–i.e.those producing detectable image separations for dwarf-galaxy masses–a non-negligible fraction ofˉΣ( EZ acknowledges research grants from the Swedish Re-search Council,the Royal Swedish Academy of Sciences and the Academy of Finland.The anonymous referee is thanked for insightful comments which helped improve the quality of the manuscript. REFERENCES Barkana,R.,&Loeb,A.1999,ApJ,523,54 Bournaud,F.et al.2007,Science,316,1166 Bryan,G.,&Norman,M.1998,ApJ,495,80 Bullock,J.S.,Kolatt,T.S.,Sigad,y.,Somerville,R.S.,Kravtsov, A.V.,Klypin,A.A.,Primack,J.R.,&Dekel,A.,2001,MNRAS, 321,559 Col′?n,P.,Klypin,A.,Valenzuela,O.,Gottl¨o ber,S.2004,ApJ,612, 50 de Blok,W.J.G.,&Bosma,A.2002,A&A,385,816 Diemand,J.,Kuhlen,M.,&Madau,P.2007,ApJ657,262 Diemand,J.,Kuhlen,M.,&Madau,P.2007,ApJ667,859 Ferrarese,L.2002,ApJ,578,90 Gilmore,G.,Wilkinson,M.I.,Wyse,R.F.G.,Kleyna,J.T.,Koch, A.,Evans,N.W.,2007,astro-ph/0703308 Gnedin,O.Y.,Kravtsov,A.V.,Klypin,A.A.,Nagai,D.2004, ApJ,616,16 Gustafsson,M.,Fairbairn,M.,&Sommer-Larsen,J.2006,Phys. Rev.D,74l3522 Hansen,S.H.,Stadel,J.2006,JCAP,5,14 Hayashi,E.,Navarro,J.F.,Taylor,J.E.,Stadel,J.,&Quinn,T. 2003,ApJ,584,541(H03) Inoue,K.T.,&Chiba,M.2005a,ApJ,633,23 Inoue,K.T.,&Chiba,M.2005b,ApJ,634,77 Inoue,K.T.,&Chiba,M.2005c,astro-ph/0512648 Kampakoglou,M.2006,MNRAS,369,1988 Kazantzidis,S.,Mayer,L.,Mastropietro,C.,Diemand,J.,Stadel, J.,&Moore,B.2004,ApJ,608,663(K04) Klypin,A.,Kravtsov,A.V.,Valenzuela,O.,&Prada,F.,1999, ApJ,522,82 Kochanek,C.S.,&Dalal,N.2004,ApJ610,69 Kochanek,C.S.,&Dalal,N.2004,ApJ610,69 Koopmans,L.V.E.;Treu,T.,Bolton,A.S.,Burles,S.Moustakas, L.A.2006,ApJ,649,599 Ma,C.-P.2003,ApJ,584L1 Macci`o,A.V.,&Miranda,M.2006,MNRAS,368,599 Macci`o,A.V.,Moore,B.,Stadel,J.,Diemand,J.2006,MNRAS, 366,1529 Malbet, F.,et al.2006,in SPIE6268,Advances in Stellar Interferometry,ed.J.D.Monnier,M.Sch¨o ller,&W.C.Danchi, p.62680Y Mao,S.,&Schneider,P.1998,MNRAS295,587 Mao,S.,Jing,Y.,Ostriker,J.P.,&Weller,J.2004,ApJ,604,L5Metcalf,R.B.2005a,ApJ,622,72 Metcalf,R.B.,2005b,ApJ,629,673 Miranda,M,&Macci′o,A.V.2007,MNRAS,382,1225 Mittal,R.,Porcas,R.,Wucknitz,O.2007,A&A,465,405 Moore,B.,Quinn,T.,Governato,F.,Stadel,J.,&Lake,G.1999, MNRAS,310,1147(M99) Navarro,J.F.,Frenk,C.S.,&White,S.D.M.1996,ApJ,462, 563(NFW) Navarro,J.F.,et al.2004,MNRAS,349,1039(N04) Noyola,E.,Gebhardt,K.,Bergmann,M.2008,ApJ,676,1008 Nurmi,P.,Hein¨a m¨a ki,P.,Saar,E.,Einasto,M.,Holopainen,J., Mart′?nez,&Einasto,J.2006,astro-ph/0611941 Pfenniger,D.,Combes,F.,&Martinet,L.1994,A&A285,79 Pfenniger,D.,Combes,F.1994,A&A285,94 Primack,J.R.2003,Nuclear Physics B Proceedings Supplements, 124,3 Read,J.I.,Pontzen,A.P.,&Viel,M.2006,MNRAS,371,885 Rusin,D.,Kochanek,C.S.,&Keeton,C.R.2003,ApJ,595,29 Schechter,P.L.,&Wambsganss,J.2002,ApJ,580,685 Simon,J.D.,Blitz,L.,Cole,A.A.,Weinberg,M.D.,&Cohen,M. 2006,ApJ,640,270 Simon,J.D.,&Geha,M.2007,arXiv:0706.0516 Spekkens,K.,Giovanelli,R.,Haynes,M.P.2005,AJ,129,2119 Trentham,N.,M¨o ller,O.,&Ramirez-Ruiz,E.2001,MNRAS,322, 658 Tully,R.B.,Somerville,R.S.,Trentham,N.,&Verheijen,M.A. W.2002,ApJ,569,573 van den Bosch,F.C.,Yang,X.,&Mo,H.J.2003,MNRAS,340, 771 van den Bosch,F.C.,Tormen,G.,&Giocoli,C.2005,MNRAS, 359,1029 van der Marel,R.P.2004,in Coevolution of Black Holes and Galaxies,ed.L. C.Ho,Cambridge University Press,p.37 (astro-ph/0302101) Verde,L.,Oh,S.P.,Jimenez,R.2002,MNRAS,336,541 Yonehara,A.,Umemura,M.,&Susa,H.2003,PASJ,55,1059 Zackrisson,E.,Bergvall,N.,Marquart,T.,&¨Ostlin,G.2006,A&A, 452,857 Zhao,H.,&Silk,J.2005,Physical Review Letters,95,011301 Zucker,D.B.,et al.2006,ApJ,650,L41 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 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 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... “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. 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 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. way 的用法 【语境展示】 1. Now I’ll show you how to do the experiment in a different way. 下面我来演示如何用一种不同的方法做这个实验。 2. The teacher had a strange way to make his classes lively and interesting. 这位老师有种奇怪的办法让他的课生动有趣。 3. Can you tell me the best way of working out this problem? 你能告诉我算出这道题的最好方法吗？ 4. I don’t know the way (that / in which) he helped her out. 我不知道他用什么方法帮助她摆脱困境的。 5. The way (that / which) he talked about to solve the problem was difficult to understand. 他所谈到的解决这个问题的方法难以理解。 6. I don’t like the way that / which is being widely used for saving water. 我不喜欢这种正在被广泛使用的节水方法。 7. They did not do it the way we do now. 他们以前的做法和我们现在不一样。 【归纳总结】 ●way作“方法，方式”讲时，如表示“以……方式”，前面常加介词in。如例1； ●way作“方法，方式”讲时，其后可接不定式to do sth.，也可接of doing sth. 作定语，表示做某事的方法。如例2，例3； t h e-w a y-的用法 The way 的用法 "the way+从句"结构在英语教科书中出现的频率较高, the way 是先行词, 其后是定语从句.它有三种表达形式:1) the way+that 2)the way+ in which 3)the way + 从句(省略了that或in which),在通常情况下, 用in which 引导的定语从句最为正式,用that的次之,而省略了关系代词that 或 in which 的, 反而显得更自然,最为常用.如下面三句话所示,其意义相同. I like the way in which he talks. I like the way that he talks. I like the way he talks. 一.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全句. the way=as 1)I'm talking to you just the way I'd talk to a boy of my own. 我和你说话就象和自己孩子说话一样. 2)He did not do it the way his friend did. 他没有象他朋友那样去做此事. 3)Most fruits are naturally sweet and we can eat them just the way they are ----all we have to do is clean or peel them . 大部分水果天然甜润,可以直接食用,我们只需要把他们清洗一下或去皮. way的用法总结大全 way的用法你知道多少，今天给大家带来way的用法，希望能够帮助到大家，下面就和大家分享，来欣赏一下吧。 way的用法总结大全 way的意思 n. 道路,方法,方向,某方面 adv. 远远地，大大地 way用法 way可以用作名词 way的基本意思是“路,道,街,径”,一般用来指具体的“路,道路”,也可指通向某地的“方向”“路线”或做某事所采用的手段,即“方式,方法”。way还可指“习俗,作风”“距离”“附近,周围”“某方面”等。 way作“方法,方式,手段”解时,前面常加介词in。如果way前有this, that等限定词,介词可省略,但如果放在句首,介词则不可省略。 way作“方式,方法”解时,其后可接of v -ing或to- v 作定语,也可接定语从句,引导从句的关系代词或关系副词常可省略。 way用作名词的用法例句 I am on my way to the grocery store.我正在去杂货店的路上。 We lost the way in the dark.我们在黑夜中迷路了。 He asked me the way to London.他问我去伦敦的路。 way可以用作副词 way用作副词时意思是“远远地,大大地”,通常指在程度或距离上有一定的差距。 way back表示“很久以前”。 way用作副词的用法例句 It seems like Im always way too busy with work.我工作总是太忙了。 His ideas were way ahead of his time.他的思想远远超越了他那个时代。 She finished the race way ahead of the other runners.她第一个跑到终点,远远领先于其他选手。 way用法例句 t h e_w a y的用法大全 The way 在the way+从句中, the way 是先行词, 其后是定语从句.它有三种表达形式:1) the way+that 2)the way+ in which 3)the way + 从句(省略了that或in which),在通常情况下, 用in which 引导的定语从句最为正式,用that的次之,而省略了关系代词that 或 in which 的, 反而显得更自然,最为常用.如下面三句话所示,其意义相同. I like the way in which he talks. I like the way that he talks. I like the way he talks. 如果怕弄混淆，下面的可以不看了 另外，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全句. the way=as 1)I'm talking to you just the way I'd talk to a boy of my own. 我和你说话就象和自己孩子说话一样. 2)He did not do it the way his friend did. 他没有象他朋友那样去做此事. 3)Most fruits are naturally sweet and we can eat them just the way they are ----all we have to do is clean or peel them . 大部分水果天然甜润,可以直接食用,我们只需要把他们清洗一下或去皮. the way=according to the way/judging from the way 4)The way you answer the qquestions, you must be an excellent student. 从你回答就知道,你是一个优秀的学生. 5)The way most people look at you, you'd think a trashman was a monster. 从大多数人看你的目光中,你就知道垃圾工在他们眼里是怪物. the way=how/how much 6)I know where you are from by the way you pronounce my name. 从你叫我名字的音调中,我知道你哪里人. 7)No one can imaine the way he misses her. 人们很想想象他是多么想念她. the way=because 8) No wonder that girls looks down upon me, the way you encourage her. 难怪那姑娘看不起我, 原来是你怂恿的 The way 的用法 "the way+从句"结构在英语教科书中出现的频率较高, the way 是先行词, 其后是定语从句.它有三种表达形式:1) the way+that 2)the way+ in which 3)the way + 从句(省略了that或in which),在通常情况下, 用in which 引导的定语从句最为正式,用that的次之,而省略了关系代词that 或in which 的, 反而显得更自然,最为常用.如下面三句话所示,其意义相同. I like the way in which he talks. I like the way that he talks. I like the way he talks. 一.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全句. the way=as 1)I'm talking to you just the way I'd talk to a boy of my own. 我和你说话就象和自己孩子说话一样. 2)He did not do it the way his friend did. 他没有象他朋友那样去做此事. 3)Most fruits are naturally sweet and we can eat them just the way they are ----all we have to do is clean or peel them . 大部分水果天然甜润,可以直接食用,我们只需要把他们清洗一下或去皮. the way=according to the way/judging from the way 4)The way you answer the qquestions, you must be an excellent student. 从你回答就知道,你是一个优秀的学生. 5)The way most people look at you, you'd think a trashman was a monster. 从大多数人看你的目光中,你就知道垃圾工在他们眼里是怪物. the way=how/how much 6)I know where you are from by the way you pronounce my name. 从你叫我名字的音调中,我知道你哪里人. 7)No one can imaine the way he misses her. 人们很想想象他是多么想念她. the way=because 8) No wonder that girls looks down upon me, the way you encourage her. 难怪那姑娘看不起我, 原来是你怂恿的 the way =while/when(表示对比) 9)From that day on, they walked into the classroom carrying defeat on their shoulders the way other students carried textbooks under their arms. 从那天起,其他同学是夹着书本来上课,而他们却带着"失败"的思想负担来上课. The way的用法及其含义（三） 三、the way的语义 1. the way=as（像） Please do it the way I’ve told you.请按照我告诉你的那样做。 I'm talking to you just the way I'd talk to a boy of my own.我和你说话就像和自己孩子说话一样。 Plant need water the way they need sun light. 植物需要水就像它们需要阳光一样。 2. the way=how（怎样，多么） No one can imagine the way he misses her.没人能够想象出他是多么想念她！ I want to find out the way a volcano has formed.我想弄清楚火山是怎样形成的。 He was filled with anger at the way he had been treated.他因遭受如此待遇而怒火满腔。That’s the way she speaks.她就是那样讲话的。 3. the way=according as （根据） The way you answer the questions, you must be an excellent student.从你回答问题来看，你一定是名优秀的学生。 The way most people look at you, you'd think a trash man was a monster.从大多数人看你的目光中,你就知道垃圾工在他们眼里是怪物。 The way I look at it, it’s not what you do that matters so much.依我看，重要的并不是你做什么。 I might have been his son the way he talked.根据他说话的样子，好像我是他的儿子一样。One would think these men owned the earth the way they behave.他们这样行动，人家竟会以为他们是地球的主人。 一．Way：“方式”、“方法” 1.表示用某种方法或按某种方式 Do it (in) your own way. Please do not talk (in) that way. 2.表示做某事的方式或方法 It’s the best way of studying [to study] English.。 There are different ways to do [of doing] it. 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 正：I don’t like the way he spoke. I don’t like the way that he spoke. I don’t like the way in which he spoke.误：I don’t like the way how he spoke. 4. the way 的从句 That’s the way (=how) he spoke. I know where you are from by the way you pronounce my name. That was the way minority nationalities were treated in old China. Nobody else loves you the way(=as) I do. He did not do it the way his friend did. 二．固定搭配 1. In a/one way：In a way he was right. 2. In the way /get in one’s way I'm afraid your car is in the way， If you are not going to help，at least don't get in the way. You'll have to move－you're in my way. 3. in no way Theory can in no way be separated from practice. 4. On the way (to……) Let’s wait a few moments. He is on the way Spring is on the way. Radio forecasts said a sixth-grade wind was on the way. She has two children with another one on the way. 5. By the way By the way，do you know where Mary lives? 6. By way of Learn English by way of watching US TV series. 8. under way 1. Elbow one’s way He elbowed his way to the front of the queue. 2. shoulder one’s way 3. feel one‘s way 摸索着向前走；We couldn’t see anything in the cave, so we had to feel our way out 4. fight/force one’s way 突破。。。而前进The surrounded soldiers fought their way out. 5.. push/thrust one‘s way（在人群中）挤出一条路He pushed his way through the crowd. 6. wind one’s way 蜿蜒前进 7. lead the way 带路，领路；示范 8. lose one‘s way 迷失方向 9. clear the way 排除障碍，开路迷路 10. make one’s way 前进，行进The team slowly made their way through the jungle. 在the way+从句中, the way 是先行词, 其后是定语从句.它有三种表达形式:1) the way+that 2)the way+ in which 3)the way + 从句(省略了that或in which),在通常情况下, 用in which 引导的定语从句最为正式,用that的次之,而省略了关系代词that 或in which 的, 反而显得更自然,最为常用.如下面三句话所示,其意义相同. I like the way in which he talks. I like the way that he talks. I like the way he talks. 如果怕弄混淆，下面的可以不看了 另外，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全句. the way=as 1)I'm talking to you just the way I'd talk to a boy of my own. 我和你说话就象和自己孩子说话一样. 2)He did not do it the way his friend did. 他没有象他朋友那样去做此事. 3)Most fruits are naturally sweet and we can eat them just the way they are ----all we have to do is clean or peel them . 大部分水果天然甜润,可以直接食用,我们只需要把他们清洗一下或去皮. the way=according to the way/judging from the way 4)The way you answer the qquestions, you must be an excellent student. 从你回答就知道,你是一个优秀的学生. 5)The way most people look at you, you'd think a trashman was a monster. 从大多数人看你的目光中,你就知道垃圾工在他们眼里是怪物. the way=how/how much 6)I know where you are from by the way you pronounce my name. 从你叫我名字的音调中,我知道你哪里人. 7)No one can imaine the way he misses her. 人们很想想象他是多么想念她. the way=because 8) No wonder that girls looks down upon me, the way you encourage her. 难怪那姑娘看不起我, 原来是你怂恿的 the way =while/when(表示对比) 9)From that day on, they walked into the classroom carrying defeat on their shoulders the way other students carried textbooks under their arms. “the way+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 following passage and talk about it with your classmates. Try to tell what you think of Tom and of the way the children treated 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 the way how it happened. 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the way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) these comrades look at problems is wrong.这些同志看问题的方法不对。 The way(that ,in which)you’re doing it is completely crazy.你这么个干法，简直发疯。 We admired him for the way in which he faces difficulties. Wallace and Darwin greed on the way in which 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) he did it. I liked the way (that) she organized the meeting. 3.the way(that)有时可以与how(作“如何”解)通用。例如： That’s the way (that) she spoke. = That’s how she spoke. I should like to know the way/how you learned to master the fundamental technique within so short a time. 4．the way的其它用法：以上我们讲的都是用作先行词的the way，下面我们将叙述它的一些用法。 定冠词the的12种用法 定冠词the 的12 种用法，全知道?快来一起学习吧。下面就和大家分享，来欣赏一下吧。 定冠词the 的12 种用法，全知道? 定冠词the用在各种名词前面，目的是对这个名词做个记号，表示它的特指属性。所以在词汇表中，定冠词the 的词义是“这个，那个，这些，那些”，可见，the 即可以放在可数名词前，也可以修饰不可数名词，the 后面的名词可以是单数，也可以是复数。 定冠词的基本用法： (1) 表示对某人、某物进行特指，所谓的特指就是“不是别的，就是那个!”如： The girl with a red cap is Susan. 戴了个红帽子的女孩是苏珊。 (2) 一旦用到the，表示谈话的俩人都知道说的谁、说的啥。如： The dog is sick. 狗狗病了。(双方都知道是哪一只狗) (3) 前面提到过的，后文又提到。如： There is a cat in the tree.Thecat is black. 树上有一只猫，猫是黑色的。 (4) 表示世界上唯一的事物。如： The Great Wall is a wonder.万里长城是个奇迹。(5) 方位名词前。如： thenorth of the Yangtze River 长江以北地区 (6) 在序数词和形容词最高级的前面。如： Who is the first?谁第一个? Sam is the tallest.山姆最高。 但是不能认为，最高级前必须加the，如： My best friend. 我最好的朋友。 (7) 在乐器前。如： play the flute 吹笛子 Way用法 A:I think you should phone Jenny and say sorry to her. B:_______. It was her fault. A. No way B. Not possible C. No chance D. Not at all 说明：正确答案是A. No way，意思是“别想！没门！决不！” 我认为你应该打电话给珍妮并向她道歉。 没门！这是她的错。 再看两个关于no way的例句： （1）Give up our tea break? NO way! 让我们放弃喝茶的休息时间？没门儿！ （2）No way will I go on working for that boss. 我决不再给那个老板干了。 way一词含义丰富，由它构成的短语用法也很灵活。为了便于同学们掌握和用好它，现结合实例将其用法归纳如下： 一、way的含义 1. 路线 He asked me the way to London. 他问我去伦敦的路。 We had to pick our way along the muddy track. 我们不得不在泥泞的小道上择路而行。 2. （沿某）方向 Look this way, please. 请往这边看。 Kindly step this way, ladies and gentlemen. 女士们、先生们，请这边走。 Look both ways before crossing the road. 过马路前向两边看一看。 Make sure that the sign is right way up. 一定要把符号的上下弄对。 3. 道、路、街，常用以构成复合词 a highway（公路），a waterway（水路），a railway（铁路），wayside（路边） way/time的特殊用法 1、当先行词是way意思为”方式.方法”的时候,引导定语从句的关系词有下列3种形式： Way在从句中做宾语 The way that / which he explained to us is quite simple. Way在从句中做状语 The way t hat /in which he explained the sentence to us is quite simple. 2、当先行词是time时,若time表示次数时,应用关系代词that引导定语从句,that可以省略; 若time表示”一段时间”讲时,应用关系副词when或介词at/during + which引导定语从句 1.Is this factory _______ we visited last year? 2.Is this the factory-------we visited last year? A. where B in which C the one D which 3. This is the last time _________ I shall give you a lesson. A. when B that C which D in which 4.I don’t like the way ________ you laugh at her. A . that B on which C which D as 5.He didn’t understand the wa y ________ I worked out the problem. A which B in which C where D what 6.I could hardly remember how many times----I’ve failed. A that B which C in which D when 7.This is the second time--------the president has visited the country. A which B where C that D in which 8.This was at a time------there were no televisions, no computers or radios. A what B when C which D thatThe way常见用法
The way的用法及其含义(二)
(完整版)the的用法
“the way+从句”结构的意义及用法
way 用法
The way的用法及其含义(一)
way 的用法
the-way-的用法讲解学习
way的用法总结大全
the_way的用法大全教案资料
the way 的用法
The way的用法及其含义(三)
way的用法
the way的用法大全
“the-way+从句”结构的意义及用法知识讲解
定冠词the的12种用法
Way的用法
way与time的特殊用法