a r X i v :a s t r o -p h /0401074v 2 8 J a n 2004
THE DETECTION OF COLD DUST IN CAS A:EVIDENCE FOR THE
FORMATION OF METALLIC NEEDLES IN THE EJECTA
Eli Dwek
Laboratory for Astronomy and Solar Physics
NASA Goddard Space Flight Center,Greenbelt,MD 20771,
e-mail:eli.dwek@https://www.doczj.com/doc/0b3759209.html,
ABSTRACT
Ejecta from core collapse supernovae contain a few solar masses of refractory el-
ements and can therefore be the most important source of interstellar dust if these elements condense e?ciently into solids.However,infrared observations of young su-pernova remnants,such as Cas A or Kepler,and observations of SN 1987A have detected only ～10?3M ⊙of hot dust in these objects.Recently,Dunne et al.(2003)obtained 450and 850μm SCUBA images of Cas A,and reported the detection of 2–4M ⊙of cold,18K,dust in the remnant.Here we show that their interpretation of the observations faces serious di?culties.Their inferred dust mass ignores the e?ect of grain destruction by sputtering,and is larger than the mass of refractory material in the ejecta of a 10to 30M ⊙star.The cold dust model faces even more di?culties if the 170μm observations of the remnant are included in the analysis,decreasing the cold dust temperature to ～8K,and increasing its mass to 20M ⊙.We o?er here a more plausible interpretation of their observation,in which the cold dust emission is generated by conducting needles in the ejecta.The needle properties are completely determined by the combined sub-millimeter and X-ray observations of the remnant.The needles are collisionally heated by the shocked gas.They are very e?cient emitters at submillimeter wavelengths,and with a resistivity of a few μ?cm can readily attain a temperature of 8K.Taking the destruction of needles into account,a dust mass of only 10?4to 10?3M ⊙is needed to account for the observed SCUBA emission.The needles consist of metallic whiskers with 1%of embedded impurities,that may have condensed out of blobs of material that were expelled at high velocities from the inner metal–rich layers of the star in an asymmetric explosion.Conductive needles may also be the source of the cold dust emission detected by Morgan et al.(2003)in Kepler.Aligned in the magnetic ?eld,needles may give rise to observable polarized emission.The detection of submillimeter polarization will therefore o?er de?nitive proof for a needle origin for the cold dust emission.Supernovae may still be proven to be important sources of interstellar dust,but the evidence is still inconclusive.
Subject headings:ISM:supernova remnants –ISM:individual (Cassiopeia A)–
ISM:interstellar dust –Infrared:general
1.INTRODUCTION
Cas A,the young remnant of a Type II supernova(SN),has been suggested as an ideal observing target for dust that may have formed in the explosive ejecta(Dwek&Werner1981). Initial ground-based searches for dust(Wright et al.1980,Dinerstein et al.1982)yielded negative results.Dust was?rst detected in Cas A in the Infrared Astronomical Satellite(IRAS)all–sky survey(Mezger et al.1986,Dwek et al.1987,Braun1987,Arendt1989,Saken,Fesen,&Shull 1992).However,due to the low spatial resolution of the IRAS images,its origin whether interstellar, circumstellar or supernova,could not be ascertained.Higher resolution infrared images of Cas A, obtained with the Infrared Space Observatory(ISO)satellite,revealed the presence of hot dust in the fast–moving knots of the remnant,thereby unambiguously establishing its SN origin(Lagage et al.1996,Arendt,Dwek,&Moseley1999,Tu?s et al.1999).Dust temperatures were typically ～100–200K,consistent with those expected for shock–heated dust.Dust masses were between 10?7?10?3M⊙,depending on the size of the observed region,signi?cantly below the mass of condensable elements expected to be present in the ejecta of a massive progenitor star(Woosley& Weaver1995).
Supernovae are potentially the most important source of interstellar dust and they play an important role in establishing the elemental depletion pattern in the interstellar medium(Dwek &Scalo1980,Dwek1998,Jones2000).Furthermore,the early rise in the UV-optical opacity of high redshift galaxies suggests copious dust production in these objects(Todini&Ferrara2001). The lack of any observational evidence for the formation of massive amounts of dust in supernovae is therefore quite frustrating.In light of this,the recent detections of emission from cold dust in Cas A(Dunne et al.2003)and Kepler(Morgan et al.2003)are very encouraging,since they may provide the?rst observational con?rmation of the role of supernovae as prominent interstellar dust sources.Their?ndings require therefore careful scrutiny.In our analysis we will concentrate on the cold dust detection from Cas A.
The450and850μm SCUBA images of Cas A(Dunne et al.2003)revealed a new,cold,dust component,primarily concentrated in the southern half of the remnant,and bounded between the forward and reverse shocks,located at angular radii of,respectively,153′′and95′′(Gotthelf et al. 2001).The total IR spectrum from Cas A,comprised of the IRAS(12–100μm)and SCUBA observations,from which the synchrotron component has been subtracted,was?tted by Dunne et
al.(2003)with a hot(112+11
?21K)and a cold(18+2.6
?4.6
K)dust component.The hot dust component
detected by the IRAS has a mass of～10?3M⊙,and consists of supernova dust heated by the interaction of the ejecta with the ambient medium(Arendt,Dwek,&Moseley1999).The cold dust has a mass between～2and12M⊙,depending on its radiative properties(Dunne et al.2003and §2below).
The properties and origin of the cold dust are di?cult to explain even if one adopts the lower mass estimate.The inferred dust mass is too large to be of either circumstellar or interstellar origin. Such origin will suggest the presence of an associated～200M⊙mass of hydrogen,clearly ruling
out the former.An interstellar cloud of that mass interacting with the remnant will give rise to optical and IR emission lines and to dynamical e?ects that are unobserved.Below we argue that the inferred dust mass is also too large to be of supernova origin.Furthermore,the gas associated with the dust,will collisionaly heat the dust to a temperature that is signi?cantly higher than that inferred from the SCUBA observations.Nevertheless,ruling out an interstellar or circumstellar origin,Dunne et al.(2003)adopted the least implausible explanation,and concluded that the dust must be of SN origin.
This interpretation of the SCUBA observations faces several di?culties:
1.The required dust condensation e?ciency in the SN ejecta is too high even for the amorphous
or clumpy dust aggregates.Cas A is believed to be the remnant of the explosion of a10to 30M⊙star(Fesen et al.2001).The total mass of condensible elements(C,Mg,Si,S,Ca,Fe, Ni,and associated O)ejected in the explosion of10and30M⊙stars is about0.3and2M⊙, respectively(Woosley&Weaver1995).So even the lowest estimate of～2M⊙of cold dust requires a very unlikely condensation e?ciency of100%in the supernova ejecta of a30M⊙star.The large dust mass becomes even more embarrassing if,as suggested by the distribution of elemental abundance ratios in the ejecta,the progenitor of Cas A was only a12M⊙star (Willingale et al.2002).Even allowing for a massive progenitor,the required condensation e?ciency is too high considering the fact that important refractory elements(Si,Ca,and Fe) are observed to be in the gas phase of the remnant,and to be more uniformly distributed than required by the Dunne et al.(2003)interpretation of the SCUBA data(Hwang,Holt, &Petre2000;Hughes et al.2000,Willingale et al.2002).Finally,the total mass of dust that must have formed in the ejecta may actually be greater than implied from the SCUBA observations,since a fraction of it may have been destroyed by thermal sputtering.
2.The density of the gas associated with the cold dust is too high to account for the low dust
temperature.Associated with the refractory elements produced in a30M⊙star are about 4M⊙of other abundant metals,primarily oxygen,that are not locked up in dust.We can derive a lower limit to the electron density of the emitting region by assuming that it is smoothly distributed between the forward and reverse shocks,and that it covers about 15%of the sky as seen from the center of the explosion.The volume of the region,for an adopted distance of3.4kpc,is then～2×1056cm?3,giving a minimum electron density of ～3cm?3.Actual electron densities are signi?cantly higher,since oxygen is expected to be multiply ionized in the emitting region.However,even at the low density of3cm?3,typical
0.01μm-sized supernova condensates will be collisionally heated to temperatures of about
50K(Dwek1987).Put di?erently,a density of3cm?3is about100times higher than that required to heat the dust particles to the observed temperature of18K.To achieve this cold dust temperatures at these high electron densities,the radii of the dust particles in the ejecta must be 1μm.However,such radii are much larger than those predicted from nucleation calculations(Kozasa,Hasegawa,&Nomoto1991).
3.Finally,the170μm ISO observations of Cas A are actually a detection,implying an even
larger amount of colder dust.In their analysis,Dunne et al.(2003)regarded the ISO170μm observations of Cas A(Tu?s et al.1999)as a lower limit,predicting a signi?cantly higher ?ux from the remnant than observed at that wavelength.However,it was pointed out by the referee that it is di?cult to explain how the ISOPHOT instrument on board the ISO could have missed most of the emission from that region of the remnant.In fact,the observed 170μm emission is an actual detection(private communications between the referee and R.
J.Tu?s made available to the author),and the170μm?ux can be entirely attributed to the hot dust emission.If the170μm?ux produced by the cold dust is constrained to be less than10Jy,then the SCUBA data can only be?tted with～7to9K dust assuming a λ?2emissivity law.The mass of cold dust is then increased to～24to16M⊙,respectively, even if it has the high submillimeter radiative e?ciency of amorphous or clumpy aggregate material.So regarding the170μm?ux as an upper limit on the emission from the cold dust component simply exacerbates the di?culties listed above.
The problems listed above can be alleviated if the dust responsible for the observed emission consists of conducting needles or whiskers.The high conductivity(low resistivity)of these needles gives rise to a mass absorption e?ciency that is several orders of magnitudes greater than that of interstellar graphite or silicates,and even the amorphous clumpy aggregates considered by Dunne et al.(2003).Su?ciently large needles are e?cient antenna–like radiators out to millimeter wave-length,depending on their length–to–diameter ratio.Their large radiative e?ciency signi?cantly lowers the mass of cold dust required to explain the SCUBA observations.It also increases the density of electrons needed to collisionally heat the dust to the observed temperature.The intro-duction of such e?cient radiators as the source of the observed submillimeter dust emission requires therefore a balance between the need to reduce the mass of the emitting dust without increasing the plasma density beyond the limits that may be imposed from X-ray observations.
Conducting needles have been considered before,in a di?erent context,by Hoyle&Wick-ramasinghe(1999)and Wickramasinghe(1992)as a source of starlight opacity that could have produced a non–cosmological cosmic microwave background(CMB)in a steady state cosmology. They were also considered as a way to thermalize starlight and generate the CMB after the big bang in cold big bang models(Wright1982,Li2003).It should not be too surprising to?nd needles in supernova ejecta.Supernovae condensates may originally be di?erent in morphology or compo-sition from the dust particles commonly found in the di?use interstellar medium(ISM),and are likely to undergo additional chemical and physical processing in the ISM.There is prior evidence that SN condensates may be di?erent from their ISM counterparts.The hot dust emission from Cas A detected by the ISO was interpreted as emission from protosilicate material(Arendt,Dwek, &Mosleley1999),and conducting needles may have been detected in SN1987a(Wickramasinghe &Wickramasinghe1993).
In the model proposed here,the metallic needles were formed in metal-rich ejecta that were expelled at high velocities into the ambient medium.The needles are collisionaly heated by the
reverse shock resulting from the interaction of the ejecta with the ambient medium.In the following section(§2)we examine the di?erent dust component contributing to the observed IR to submil-limeter spectrum of Cas A,showing that conducting needles are a necessary emission component if one wants to?t the170μm ISO observations with a reasonable dust mass.In§3we calculate the properties of the needles and the electron density required to explain the SCUBA observations for various type of conducting material.The results of the paper are summarized and discussed in§4.
2.DUST EMISSION COMPONENTS IN THE SPECTRUM OF CAS A
Figure1depicts the observed infrared(IR)to submillimeter spectrum of Cas A comprising of the12,25,60,and100μm data obtained by the Infrared Astronomical Satellite(IRAS)(Dwek et al.1987),the170μm datum point obtained by the Infrared Satellite Observatory(ISO)satellite (Tu?s et al.1999),and the450and850μm SCUBA data(Dunne et al.2003).An almost identical 850μm?ux was reported by Loinard et al.(2003).Also shown in the?gure is the synchrotron emission spectrum,extrapolated with aν?0.69power law(Mezger et al.1986).Table1summarizes the data used in this paper.
The speci?c?ux at wavelengthλreceived from an ensemble of dust particles with a total mass M d,located at a distance D,and radiating at an equilibrium dust temperature T d,is given by:
Fν(λ)= M d
κ(λ0)λ nλ?3μm exp 14387.7
D2kpc
Fig. 1.—The infrared–submillimeter spectrum of Cas A consisting of the IRAS12,25,60,and 100μm(?lled triangles,Dwek et al.1987),the ISO the170μm(?lled diamond,Tu?s et al.1999), and the SCUBA450and850μm observations(open squares,Dunne et al.2003).Regarding the 170μm?ux as a lower limit,Dunne et al.?tted the data with a hot+cold dust components. Taking the170μm?ux as a detection,the data can be?tted with a hot dust+conductive needles
components.Needles are required to alleviate the excess mass problem.
from the hot dust component(see Figure1).A?t to the SCUBA observations would then lead to a colder dust temperature and therefore to a signi?cantly higher dust mass,even if it consists of amorphous or clumpy aggregates.
The mass of cold dust depends on the mass absorption coe?cient,and can be further reduced if the dust is a more e?cient emitter at far-IR and submillimeter wavelengths than the amorphous clumpy aggregates considered by Dunne et al.(2003).Conducting needles are just such kind of dust.
3.CONDUCTING NEEDLES
3.1.Mass Absorption Coe?cient
Consider a conducting needle–like dust particle represented by a circular cylindrical of radius a,length?(a??),mass densityρm,and mass m d=πa2?ρm.Most of the incident radiant energy is absorbed by ohmic dissipation.The absorption cross section is given byσabs=P/S,where S=(c/8π)E2the time-averaged Poynting vector of the incident radiation,E the amplitude of the incident electric?eld,and P the power absorbed in the grain,are given by(Wright1982):
P=V2
3
(E?)2 3
πa2(E?)2
3
arises from averaging over the angles of incident between the electric?eld and the needle(Wright1982).The absorption cross section isσabs=(4π/3c)πa2?/ρR,and the mass
absorption coe?cient is:
κ0≡σabs
3 1
2
ρR c
(?/a)2
temperature dependent,generally dropping by2to3orders of magnitude from room temperature to20K.For example,the resistivity of pure iron drops from～10?5?cm at293K to a value of ～3×10?8?cm at20K(1?cm=1.139×10?12sec).The contribution of impurities and lattice defects to the resistivity,also referred to as the residual resistivity of the material,is independent of temperature,and can dominate the resistivity at su?ciently low temperatures.For alloys,such as nichrome(80%Ni–20%Cr),the resistivity is virtually constant between temperatures of300and 20K.At very low concentrations,impurities can contribute about4μ?cm per percent of impurity to the resistivity(Kittel1963).SN condensates are likely to have embedded impurities,however, their concentration is unknown.Given the uncertainties in the resistivities of some elements at very low temperatures,we will take the value ofρR as a variable in our calculation.
3.2.Temperature and Long Wavelength Cuto?
For given material properties,the needle emission spectrum is completely determined by its temperature and long-wavelength cuto?.The observational constraints are the Fν(450μm)to Fν(850μm)?ux ratio,which is equal to=3.5±2,and the rapid drop in the spectrum at170μm. Figure2depicts the450-to-850μm(dashed lines)and the450-to-170μm?ux ratios(solid lines) as a function of the cuto?wavelength and needle temperature.The?gure shows that the SCUBA observations are well matched by8.2K needles with a long wavelength cuto?ofλ0=400μm. Figure3depicts the?/a ratio forλ0=400μm as a function of needle resistivity.The?/a ratio varies from～4000to about100over the range of resistivities depicted in the?gure.For nichrome, which has a constant resistivity as a function of temperature,the?/a ratio is about260giving a needle length of～2.6μm for a radius of a=0.01μm.Figure1depicts the?t of the needle spectrum to the SCUBA data.The needle model predicts a signi?cantly lower?ux at wavelengths below～300μm compared to the cold dust model of Dunne et al.(2003).The100to400μm?ux from Cas A is therefore an important discriminator between the cold dust and the needle model.
3.3.Total Mass
The total mass M d,of needles radiating at temperature T d is given by:
D2Sν(λ)
M d=
Fig. 2.—Contour levels of the R1≡Fν(450μm)/Fν(850μm)(dashed lines)and the R2≡Fν(450μm)/Fν(170μm)(solid lines)?ux ratios are plotted versus the cuto?wavelength,λ0,and needle temperature.A good?t to the observational constraints R1=3.5±2and R2>>1require
λ0=400μm,and a needle temperature of8.2K.The needle spectrum is depicted in Figure1.
sputtering in the shock-heated gas.In the following we calculate the density of the gas required to heat the needles to a temperature of ～8K,and the corresponding rate of grain destruction.
3.4.The Heating and Cooling of Needles
The heating rate of a needle due to electronic collisions is given by:
H d (T )=2πa?n e (1?f r ) g (E )v (E )E dep (E )d E
(7)
=2m d n e (1?f r ) g (E )v (E ) E dep (E )g cm ?3 ?1E (eV )1.492(8)
Taking R e =2a =0.02μm as the e?ective pathlength through the cylinder,we get that the maximum energy E ?at which the electrons are stopped in the needle is given by:
E ?(eV )=403 ρm
d x =2.59×109 ρm
eV ?0.492eV cm ?1,(10)
The dust heating rate can be now written as the sum:
H d (T )=2m d n e (1?f r ){
E ?0g (E )v (E ) E ρm
d E
Radiating at temperature T d,the needle cools at a rate given by:
L d=4m d κ(ν0)πBν(ν,T d)dν(12) where
κ(λ)=κ0forλ<λ0(13)
=κ0 λ0
(15)
n(O)
where n(O)is the number density(in cm?3)of the oxygen nuclei in the hot gas.Iron dust has a lower surface binding energy of about4.3eV,compared to the surface binding energy of silicates,which is about6eV(Dwek&Scalo1980).Iron dust will therefore have a shorter lifetime than silicate particles of identical size.To be de?nite,we adopt a value of105for the numerical coe?cient in the expression for the dust lifetime.Assuming that the density of heavy elements is approximately given by the electron density in the two di?erent plasma components,and taking a=0.01μm, we get that the lifetime of iron needles is about60yr in the cool,and about16yr in the hot plasma component.Both times are shorter than the range of ages of these two plasma components
Fig.3.—Plot of the mass of8.2K needles required to?t the SCUBA data(see Figure1),and the needle length-to-radius,?/a,ratio as a function of needle resistivity.Also shown in the?gure are
the room temperature resistivities of iron(Fe),and nichrome(Ni-Cr).
Fig.4.—The electron density required to heat a needle to8.2K is plotted versus needle resistivity for di?erent plasma temperatures.The shaded areas de?ne the parameters of the cool and hot plasma components in Cas A,de?ned by{n e,T e}={61±15cm?3,0.45±0.10keV},and{16±3
cm?3,3.27±0.86keV},respectively.
which are,respectively,about80(20–273)and131(101-182)yr(Willingale et al.2003).The radiating dust mass represents therefore the fraction of the total mass of shocked dust which dust has not yet been destroyed.A rough estimate for the actual mass of needles that must have been condensed in the ejecta in order to produce the observed emission can be obtained by multiplying the masses given in Figure3by the ratio of the age of the plasma to the sputtering lifetime.Typical needle masses need therefore to be2to10times larger than indicated in the?gure if they reside, respectively,in the cool or hot plasma component of the remnant.Adopting average resistivities for the needles in the two plasma components(Figure4),we get that the total mass of needles required to produce the SCUBA observations is～×10?4M⊙if they reside in the cool plasma,and ～×10?3M⊙if they reside in the hot plasma.There may yet be an additional reservoir of colder dust.So even after the e?ects of grain destruction have been taken into account,the total mass of needles required to have formed in the ejecta still represents a very small fraction of the mass of available metals in the ejecta.
4.SUMMARY AND DISCUSSION
Recent SCUBA observations of Cas A(Dunne et al.2003,Loinard et al.2003)have revealed an excess of submillimeter emission above the extrapolated synchrotron emission from the remnant. Dunne et al.(2003)interpreted the excess as emission from about2M⊙of cold,18K,dust that has formed in the SN ejecta.This dust mass requires the implausible scenario that essentially all the condensible elements that formed in ejecta be locked up in the dust.X-ray observations rule out such scenario.Their interpretation faces more di?culties if grain destruction by sputtering is taken into account,and if the170μm observations of the remnant are also included as a detection in the analysis.The cold dust temperature then becomes～8K,increasing the inferred cold dust mass to about20M⊙.
A conductive needle origin for the cold dust emission from Cas A provides a simpler alternative explanation than the one put forward by Dunne et al.(2003),even when the170μm observations are included in the analysis.The results of the paper can be brie?y summarized as follows:
1.the submillimeter spectrum can be?t with8.2K needles having a long wavelength cuto?of
400μm(Figures1and2),
2.adopting a range of10?6to10?3?cm of material resistivities,the mass of needles required
to produce the SCUBA observations falls between2×10?5and0.02M⊙,respectively,and that the needle length-to-radius(?/a)ratio is between4000and100,respectively(Figure3),
3.balancing the radiative cooling rate of the needles at8.2K to the collisional heating rate
for a range of plasma densities and temperatures,the range of needle resistivities that are compatible with observational X-ray constraints can be narrowed to(2–5)×10?6?cm(Figure
4).These values suggest that the needles are made of pure conducting material(iron?)that
includes about0.5to1%of embedded impurities
4.the needles are destroyed by sputtering in the hot gas.The needle lifetime is shorter than
the ionization age of the various X-ray emitting components,suggesting a continuous supply of newly swept-up dust.The mass of needles required to produce the SCUBA observations is therefore increased to～10?4M⊙if they reside in the cool plasma,and～10?3M⊙if they reside in the hot plasma.There may be an additional reservoir of cold dust that has not been shocked yet.
The needle model proposed here is consistent with a scenario in which the metallic needles are formed in bullets of metal–rich ejecta that were expelled at high velocities into the ambient medium.Such scenario is similar to the one observed in SN1987A,in which the increased ionization state of its envelope,the early appearance of X-andγ-rays from the radioactive decay of56Co, and the width of the spectral lines of heavy elements,suggested that metal–rich material from the inner region of the ejecta was macroscopically mixed and expelled at velocities of～3000km s?1 (Graham1988,Arnett et al.1989).The same picture emerges from optical and X–ray studies of the ejecta of Cas A.The spatial distribution of the nucleosynthesis products in the remnant shows that the most Fe–rich material is very clumpy and located at the outer edge of the ejecta(Hughes et al.2000,Willingale et al.2002),suggesting that the stellar layers were macroscopically mixed, spatially inverted,and ejected as bullets into the ambient medium in an asymmetric explosion. The interaction of the ejecta with the ambient medium will drive a reverse shock wave through the ejecta.The shocked plasma will then collisionally heat the dust to the observed temperature. The submillimeter emission detected by the SCUBA from Kepler(Morgan et al.2003)may have a similar origin.
Conductive needles may be e?ciently aligned in a magnetic?eld,so that the cold dust emission may be partially polarized,depending on the geometry of the magnetic?eld.The submillimeter polarization from the dust can dominate that from the synchrotron emission.The detection of polarization at wavelengths 450μm,and a drop in the cold dust spectrum from400to170μm will therefore be de?nitive con?rmations of the proposed model.
The results of our analysis show that the SCUBA observations need not imply the detection of massive amounts of dust in the remnant.Conductive needles o?er a better explanation with only a fraction of the mass inferred by Dunne et al.(2003)and Morgan et al.(2003).Nevertheless, supernovae may yet be important sources of interstellar dust.Here we argue that the evidence put forward sofar is still inconclusive.
Acknowledgements:In the course of this work I have bene?tted from useful discussions with Kazik Borkowski,Eric Gotthelf,Una Hwang,Harvey Moseley,and Ned Wright.Dale Fixsen and David Cottingham steered me to useful sources of resistivity data.I thank Haley Morgan for useful communications,and Rick Arendt for many insightful discussions and comments on the manuscript.
I am especially grateful to the referee,Jean-Philippe Bernard,for suggesting the inclusion of a spectral?t to the data in the manuscript,for pointing out the importance of the170μm datum
point,and for his thorough review and detailed comments that resulted in a signi?cantly improved presentation of the model.ED acknowledges NASA’s Astrophysics Theory Program for support of this work.
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Table1.Observed Infrared and Submillimeter Fluxes From Cas A
Emission component12μm25μm60μm100μm170μm450μm850μm
1Fluxes in units of Jy.IRAS12,25,60,and100μm data are from Dwek et al.(1987),170μm ?ux from Tu?s et al.(1999),and SCUBA450and850μm?uxes are from Dunne et al.(2003).
2Synchrotron?uxes calculated for aν?0.69power law(Mezger et al.1986),normalized to2.0Jy at12μm.
Table2.Summary of Physical Properties of Di?erent Materials1
Pure iron Nichrome Silicon carbide Graphite
(Fe)(Ni-Cr)(SiC)(C)
1Resistivities measured at293K.Data taken from the CRC handbook of Chemistry and Physics,84th Edition, 2003–2004.For unit conversion:1?cm=1.139×10?12s.The value ofκ0was calculated using eq.(4).
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 that