Rotation and activity in the solar-type stars of NGC 2547
a r X i v :a s t r o -p h /0004339v 1 25 A p r 2000
Mon.Not.R.Astron.Soc.000,1–12(0000)Printed 1February 2008
(MN L
a T E X style ?le v1.4)Rotation and activity in the solar-type stars of NGC 2547
R.D.Je?ries 1,E.J.Totten 1,D.J.James 2,3
1Department of Physics,Keele University,Keele,Sta?ordshire,ST55BG,UK
2Department of Physics and Astronomy,University of St Andrews,Fife,KY169SS,UK 3
Observatoire de Gen`e ve,Chemin de Maillettes 51,CH-1290,Sauverny,Switzerland
Received 10February 2000
ABSTRACT
We present high resolution spectroscopy of a sample of 24solar-type stars in the young
(15-40Myr),open cluster,NGC 2547.We use our spectra to con?rm cluster member-ship in 23of these stars,determine projected equatorial velocities and chromospheric activity,and to search for the presence of accretion discs.We have found examples of both fast (v e sin i>50km s ?1)and slow (v e sin i<10km s ?1)rotators,but ?nd no evidence for active accretion in any of the sample.The distribution of projected rotation velocities is indistinguishable from the slightly older IC 2391and IC 2602clus-ters,implying similar initial angular momentum distributions and circumstellar disc lifetimes.The presence of very slow rotators indicates that either long (10-40Myr)disc lifetimes or internal di?erential rotation are needed,or that NGC 2547(and IC 2391/2602)were born with more slowly rotating stars than are presently seen in even younger clusters and associations.The solar-type stars in NGC 2547follow a similar rotation-activity relationship to that seen in older clusters.X-ray activity increases until a saturation level is reached for v e sin i >15?20km s ?1.We are unable to explain why this saturation level,of log(L x /L bol )??3.3,is a factor of two lower than in other clusters,but rule out anomalously slow rotation rates or uncertainties in X-ray ?ux calculations.
Key words:stars:X-rays –stars:late-type –stars:rotation –open clusters and associations:individual:NGC 2547
1INTRODUCTION
Open clusters are obvious laboratories in which to study the evolution of stellar X-ray activity.They contain stars with a variety of masses but a similar age,distance and com-position.A large amount of Einstein ,and ROSAT X-ray observatory time was spent looking at open clusters (see for instance the reviews of Randich 1997and Je?ries 1999)and a major achievement of these missions was to show that solar analogues,and stars of even lower mass,in young open clus-ters,could have X-ray activity orders of magnitude greater than the Sun.This activity correlates with fast rotation and is hypothesized to be due to an internal convective dynamo which generates the magnetic ?elds that both heat and con-?ne hot coronae.The evolution of X-ray activity is thought to obey an age-rotation-activity paradigm (ARAP).Young single stars are rapidly rotating and active,but lose angu-lar momentum and spin-down as they age,resulting in a decrease of their X-ray activity.
The spin-down of cool stars as they age is not as simple as the ?∝t ?1/2law once proposed by Skumanich (1972).It appears that G and K stars stars arrive on the main sequence (for instance in the Pleiades –age ?100Myr)with a spread
in rotation rates from a few times to a hundred times the so-lar rotation rate.Subsequently,this spread almost converges
by the age (600Myr)of the Hyades.In recent times these phenomena have been understood in terms of braking caused by a magnetically coupled,ionized wind,discussed in detail by (for instance)Barnes &So?a (1996)and Krishnamurthi et al.(1997).The spread in rotation rates observed at the ZAMS combined with the magnitude and rather narrow dis-tribution of rotation rates among pre main-sequence (PMS)stars implies that,in order to produce the fastest ZAMS rotators,substantial angular momentum must be lost dur-ing the PMS phase,and the wind braking mechanism must saturate at high rotation rates (Bouvier,Forestini &Allain 1997a).This could be due to a saturation of the dynamo mechanism itself,or perhaps changes in the magnetic ?eld geometry (Barnes &So?a 1996).
It has long been supposed that during the initial stages of PMS rotation evolution,wind braking was negligible com-pared with the moment of inertia decrease as a star con-tracts towards the ZAMS.An alternative angular momen-tum loss mechanism is required and might be provided by magnetic torques transferring angular momentum to a cir-cumstellar disc (K¨o nigl 1991;Shu et al.1994).It can be
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shown that disc-regulated angular momentum loss leads to almost constant angular velocity as a PMS star shrinks.A range of disc lifetimes,perhaps connected to the initial disc mass(Armitage&Clarke1996),then results in stars be-coming decoupled from their discs at varying ages.Spin up from this point to the ZAMS,combined with wind angular momentum loss that saturates above some threshold rota-tion rate,can provide a very wide spread of ZAMS rotation rates.This scenario has been modelled extensively by Kep-pens,MacGregor&Charbonneau(1995),Collier-Cameron, Campbell&Quaintrell(1995),Bouvier et al.(1997a)and Krishnamurthi et al.(1997).
Support for disc-regulated PMS angular momentum loss comes from observations that show a connection be-tween rotation rates in PMS stars and the presence of cir-cumstellar accretion discs.Choi&Herbst(1996and ref-erences therein)claimed that rotation rates in the Orion nebula cluster were bimodal,with periods either shorter or longer than4-5days.They proposed that the slower group of rotators might be those that still maintained a circum-stellar accretion disc.Bouvier et al.(1993)showed that in their sample of Taurus-Auriga PMS stars,the classical T-Tauri stars(CTTS-those stars showing optical signatures of active accretion and circumstellar discs)rotated more slowly on average than the weak T-Tauri stars(WTTS)that showed no sign of circumstellar discs.Furthermore,Edwards et al.(1993)were able to show that a similar situation held when the near-IR signatures of discs were considered for Orion PMS stars.More recently the whole disc-regulated angular momentum loss idea has been challenged by Stas-sun et al.(1999),who?nd little correlation between disc signatures and rotation rates in a larger sample of low mass (0.2-0.6M⊙)Orion PMS stars,as well as a population of extremely rapid rotators(periods<2day)both with and without discs.They claim that an alternative to disc-locking is required,if the Orion rotation rate distribution is to evolve into that seen among the ZAMS stars of the Pleiades cluster.
These new ideas on the evolution of stellar rotation rate have been successfully applied to X-ray observations of young clusters of stars(e.g.IC2391and IC2602,age ?30Myr–Stau?er et al.1997[S97],Alpha Per,age ?60Myr–Randich et al.1996,Pleiades,age?100Myr –Stau?er et al.1994).In every cluster studied so far the ARAP appears to hold,with rotation providing the pa-rameter that determines the level of X-ray emission from a star.This was most clearly demonstrated in the Pleiades by Stau?er et al.(1994).They showed that X-ray activity (measured by L x/L bol)in solar-type stars,increases with v e sin i until a saturation is reached at L x/L bol?10?3 for v e sin i>15?20km s?1,with perhaps a decrease in the v e sin i threshold for lower mass stars with thicker con-vection zones(Krishnamurthi et al.1998).This relation-ship has since been con?rmed in the younger Alpha Per and IC2391/2602clusters,with some hint that the X-ray activity may even decline at ultra-fast rotation rates (v e sin i>100km s?1–Randich et al.1998).
NGC2547is an excellent cluster with which to explore some of these issues.Je?ries&Tolley(1998[JT98])reported X-ray observations of the cluster,detecting a rich popula-tion of PMS stars with an age,deduced from?ts to low mass isochrones,of(14±4)Myr–somewhat younger than IC2391/2602.In order to produce the large numbers(～85%with v e sin i<20km s?1)of slow rotators at the age of the Pleiades,the solid-body rotation models of Bouvier et al. (1997a)predict that at～15Myr about15-20%of solar-type stars should still possess circumstellar discs and that ap-proximately50%of stars should have a projected equatorial velocity(v e sin i)less than20km s?1.Shorter disc lifetimes are allowed if di?erential rotation between the core and con-vective envelope is possible(Keppens et al.1995;Krishna-murthi et al.1997),and would be more in accord with the (few)available measurements in T-Tauri stars,which sug-gest median and maximum disc lifetimes of about1-3Myr and～10Myr respectively(Strom et al.1989;Skrutskie et al.1990;Edwards et al.1993;Kenyon&Hartmann1995).
We would therefore expect(according to the ARAP) that approximately half of the solar-type stars in NGC2547 should show saturated X-ray emission.In fact the distribu-tion of X-ray emission in NGC2547does not meet these expectations.Figure1compares L x/L bol as a function of intrinsic colour for NGC2547with that of IC2391/2602 members(taken from Randich et al.1995;Patten&Simon 1996;S97and Simon&Patten1998).The X-ray activity appears to peak or saturate in NGC2547at a level about a factor of two lower than in IC2391/2602for the late F to early K stars.The same is true when NGC2547is compared with the Alpha Per and Pleiades clusters(see also Fig.6in Randich et al.1995and Fig.13in JT98).JT98argued that this was not a simple scaling error in the conversion from X-ray count rates to X-ray?uxes in NGC2547,because cooler stars((B?V)0>1.3,(V?I)0>1.8)appear to have a saturation level,L x/L bol?10?3,that is consistent with other clusters.They suggested that perhaps all the solar-type stars in NGC2547were rotating slower than a speed of20km s?1,above which,the X-ray emission of solar-type stars in other clusters appears to saturate.This might be the case if the stars in NGC2547had either started life with much less angular momentum than stars in other clus-ters or had somehow retained circumstellar accretion discs for longer than usual.
The possibility that disc lifetimes could exceed10Myr in some circumstances would have important implications for stellar angular momentum loss and the possible forma-tion of planetary systems.In this paper we present the re-sults of high resolution spectroscopy of a sample of solar-type stars in NGC2547.Our aim is to test for the pres-ence of active accretion discs,measure rotation rates and to see whether the ARAP can successfully explain the X-ray emission that is seen in these stars.In section2we outline the sample of stars we have observed,the observations that were made and their analysis.Section3presents the results of these analyses and compares the rotation and activity in NGC2547with that in other young clusters.These results are discussed in section4.
2OBSER V ATIONS
2.1Sample selection
All of our targets were selected as optical counterparts to X-ray sources by JT98.They have B?V and V?I c colours and V magnitudes that are consistent with membership of the NGC2547cluster.For the remainder of this paper we
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Rotation and activity in NGC 2547
3
Figure 1.X-ray activity,expressed as L x /L bol ,in NGC 2547(dots)as a function of intrinsic colour,compared with stars in IC 2391/2602(triangles and crosses).The dotted line indicates the X-ray sensitivity limit for NGC 2547and the dashed line indicates the “saturation level”for X-ray emission reached in all young clusters.The circled NGC 2547points were selected for high resolution optical spectroscopy in this paper.Triangles represent members of IC 2391/2602con?rmed by spectroscopy in S97.Crosses are X-ray selected members of IC 2391/2602so far uncon?rmed by spectroscopy.
assume that the intrinsic distance modulus to the cluster is 8.1±0.1and that the reddening is given by E (B ?V )=0.06or E (V ?I c )=0.077(see JT98).An earlier photoelectric study of early-type members by Clari′a (1982)has estab-lished that any di?erential reddening in the cluster is less than 0.02(rms).JT98?tted isochrones to the X-ray sources in NGC 2547and found an age of 14±4Myr,compared to about 25Myr for IC 2391and IC 2602using the same isochrones and colour-T ef f relationship.There is some evi-dence that these isochronal ages may be underestimates (see section 4.1).
Figure 1shows the distribution of X-ray activity in NGC 2547as a function of intrinsic colour.The approxi-mate sensitivity threshold for detecting X-ray sources in the cluster is shown as a dotted line.This threshold was deter-mined by JT98and is appropriate for cluster members situ-ated near the centre of the ROSAT ?eld of view.For objects nearer the edge of the ROSAT ?eld of view,the detection threshold is approximately 0.3dex higher.The argument used by JT98,which we shall also use here,is that whilst an X-ray selected sample of cluster members would normally be biased towards faster rotators;if the X-ray sensitivity threshold is low enough that there are no cluster members situated at or slightly above this threshold,then it is most likely that the X-ray selected sample is complete.This might not be true if X-ray luminosity functions showed a bimodal
distribution,but this is not the case in the solar-type stars
of the Pleiades and Hyades where complete optical samples have been observed at X-ray wavelengths (Stern et al.1992;Stau?er et al.1994).
If we now consider just the stars in NGC 2547with 0.8<(V ?I c )0<1.40–corresponding roughly to masses 1.0M ⊙>M >0.8M ⊙according to the D’Antona &Mazz-itelli (1997)isochrones used to determine the age,there does seem to be a signi?cant gap between the X-ray sensitivity threshold and the lowest activity levels detected,indicating that the X-ray selected sample of solar-type stars should be almost complete.The same may not be true for hotter and cooler stars,where it is still possible that some slow rota-tors have not been seen in X-rays.The number of X-ray selected solar-type stars found in the cluster is consistent with the number of higher mass stars and canonical initial mass functions (see JT98for details).However,the uncer-tainties in these numbers are too large to place any strong constraints on the sample completeness.
The stars we have observed spectroscopically are indi-cated by the circled points in Fig.1.The colours and mag-nitudes of these stars are listed in Table 1,where we adopt the identi?ers and data from JT98.Some of these stars lie signi?cantly above the single star sequence in the V,B ?V and V,V ?I c colour-magnitude diagrams (CMDs)shown in Fig.2,possibly due to binarity.Where a target is 0.4mag
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Figure 2.Colour magnitude diagrams for the sample of stars chosen for high resolution spectroscopy in NGC 2547.A number of stars referred to in section 2.3are labelled.(a)V vs B ?V .(b)V vs V ?I c .
or more brighter in V than suggested by its intrinsic B ?V and V ?I c ,we have identi?ed it as a possible binary that is unresolved by the CCD photometry in JT98.Note that the presence of an unresolved binary with period greater than a few days is unlikely to a?ect X-ray activity as measured by L x /L bol (although such sources should be easier to detect because of their higher L x ),but that shorter period binary systems may have enhanced X-ray activity over single stars of the same colour because of tidally enforced rapid rotation.
In summary,we believe our sample is unbiased with respect to rotation for (V ?I c )0>0.8,but may be missing some of the slowest rotators in a truly optically selected sample for stars hotter than this.
2.2High resolution spectroscopy
The stars circled in Fig.1and shown in Fig.2were observed on the 6th and 7th of January 1999at high resolution us-ing the UCLES coud′e echelle spectrograph on the 3.9-m Anglo-Australian Telescope.The data were collected using a 79grooves/mm echelle grating and a 4096by 2048pixel MIT/LL CCD device.Each cross-dispersed echellogram cov-ered a wide spectral range (but with gaps between orders)from about 5000?A to 8500?A ,including the H αand O i 6300?A lines.There were several orders with no telluric lines and many neutral metal lines that could be used to measure ra-dial velocities and projected equatorial velocities by cross-correlation with standard stars.The 1.2arcsec slit projected to about 3.5pixels on the CCD leading to a resolving power of around 44000(or a resolution of 0.15?A at H α).A
dekker
Figure 3.Examples of our high resolution spectra:(a)One of the orders used for radial velocity and v e sin i measurements.(b)Spectra around H αfor two of our targets,including the ultra-fast rotator RX35.
was used to separate the orders,but the spatial width of
each order (about 14arcsecs)was su?cient to achieve back-ground subtraction,given the typical 1.3-1.6arcsec seeing that was encountered during the majority of the run.
Targets were observed for between 20minutes and 1hour,resulting in consistent signal to noise levels of about 20-25per CCD pixel.Along with the usual ?ats,bias and arc lamp exposures,we also obtained spectra of several ra-dial velocity standards,a number of slowly rotating spectral type standards with minimal chromospheric activity,and a number of rapidly rotating B-stars to facilitate telluric line correction around the H αand O i 6300?A lines.
Heliocentric radial velocities (RVs)were determined for all our targets by cross-correlation with the spectra of RV standards –HR 4786,HD 4128and HD 126053.Two orders with spectral ranges λλ5157?5282?A and λλ5989?6141were used independently with each standard.The average value is taken from all these cross-correlations and the standard deviation used as an estimate of the likely RV error.This is typically about 1km s ?1,although it is higher for very fast rotators.The internal consistency of the measured standard
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Rotation and activity in NGC25475
RVs suggests our external error is of order1km s?1.The RV results are presented in Table1.
Projected equatorial velocities(v e sin i)were estimated by cross-correlation with slowly rotating stars of similar colour to the targets.The stars used were HD102870(F9V), HD126053(G1V)HD115617(G5V),HD10700(G8V), HD4628(K2V)and HD16160(K3V).The FWHM of the cross-correlation function yields v e sin i when calibrated by broadening the slowly rotating standards with limb-darkened rotational pro?les of increasing v e sin i.At the S/N levels of our target spectra,we?nd that v e sin i be-comes unresolved below6km s?1,has a～1km s?1error up to10km s?1and about a10%error in v e sin i for more rapid rotators.The rotational velocities determined in this way are listed in Table1.Figure3a shows two examples of our spectra for both rapid and slowly rotating stars.
In all but two cases the RV cross-correlation functions were strong and single-peaked.RX55is a probable SB2bi-nary system,with two clearly resolved narrow peaks in the cross-correlation functions.A v e sin i upper limit was deter-mined for each component.RX35seems to be an example of an ultra-fast rotator.No clear peak could be seen in the RV cross-correlation functions and the only feature of note visible in the spectrum is a very broad Hαabsorption line (see Fig.3b).Assuming the width of this line was due to ro-tational broadening,we estimate that v e sin i>160km s?1. The centroid of the Hαline was used to determine the ap-proximate RV listed in Table1.The same technique ap-plied to the next fastest rotator,RX30a,yields a v e sin i of 110km s?1and an RV of9±8km s?1,in reasonable agree-ment with the cross-correlation results.
The equivalent width(EW)of the Hαline was measured by integration under a continuum modelled with a third or-der polynomial.Telluric features were divided out approxi-mately by reference to a rapidly rotating B-star spectrum. The EWs are listed in Table1.For relatively slow rota-tors(v e sin i<30km s?1),the width of the Hαfeature is roughly constant and the EWs are accurate to about0.05?A. For the broader rapid rotators,the errors are more like0.1-0.2?A and0.3?A for RX35.Figure3b shows two examples of our Hαspectra.
2.3Cluster membership
Based on the size of the X-ray error circles and spatial den-sity of possible optical counterparts,JT98estimated that there would only be0.8spurious correlations with X-ray sources for V<15along the NGC2547CMD sequence.As X-ray emitting?eld stars at this level of L x/L bol should be relatively rare,then all but perhaps one of our targets should be NGC2547members.The RV measurements o?er us an opportunity to check membership credentials.In a cluster, one expects the single stars to have a single RV value(for clusters with small angular extent)with a dispersion of no more than1km s?1or so.Binary stars will introduce some scatter.Wide binaries will have RVs close to the mean single star value,close binary members could have RVs radically di?erent from the cluster mean and SB2systems should have two measured RVs,either side of the cluster mean.
Consulting Table1we can see that20/24stars have RVs within2.5σof a weighted mean value of+12.8km s?1,with a standard deviation of0.9km s?1.The error in this mean cluster RV is dominated by the～1km s?1external error in the RV values.Of the other4stars,we classify RX12a as a non-member,because we have two consistent radial ve-locity measurements on two di?erent nights that are very di?erent to the cluster mean.The only way we could be mistaken is if RX12a were a cluster SB1with an orbital pe-riod close to the1day separation of the observations.How-ever,we also note that RX12a actually lies slightly below the single star sequence in Fig.2,casting further doubt on a cluster SB1interpretation.Because RX12a has a v e sin i of 35km s?1though,it must be the counterpart to the X-ray source.Both RX66and RX87are likely to be SB1cluster members in moderately wide binary systems because both lie signi?cantly above the trend of single stars in Fig.2and both have RVs which are only3-6km s?1from the cluster mean.They are also both chromospherically active in the Hαline(see section3and Table1)and therefore almost certainly the counterparts to the X-ray sources.Of course we cannot rule out that they are in fact short period sys-tems with large velocity amplitudes or indeed interloping ?eld stars with very high X-ray emission–these possibili-ties are simply less likely.RX55is obviously an SB2,with roughly equal mass components judging by the nearly equal power in each of the cross-correlation peaks,and by the fact it lies about0.7mag above the cluster sequence in Fig.2. The mean RV of the components is+15.1±1.5,very close to the cluster mean.We conclude that this is a nearly equal mass SB2member of the cluster.If the velocity amplitude is at least32km s?1and the components are1M⊙then the period is less than74sin3i days,where i is the(unknown) orbital inclination.Without further information we cannot say whether the period of RX55is short enough to tidally enforce rotation at the orbital period.The v e sin i upper limits for the two components could be perfectly consistent with rotation periods synchronised to orbital periods of a few days if the system has a low orbital and rotational incli-nation.Finally we note that RX34is also a possible binary system based on its position in Fig.2,but if so,it is proba-bly a moderately wide binary system because its RV agrees with the cluster mean.
In summary,we have strong evidence that20of the 24stars we have observed are single cluster members,2are possible SB1members,1is almost certainly an SB2member and1is probably a very active?eld star behind the cluster. 3RESULTS
The best way to present our results is by comparison with the IC2391and IC2602clusters.These have been studied at X-ray wavelengths by Randich et al.(1995),Patten& Simon(1996)and Simon&Patten(1998)and have been the subject of an extensive optical spectroscopy campaign to establish membership and measure rotational broaden-ing and chromospheric activity by S97.Rotation periods(as opposed to v e sin i)have also been measured in samples of cool stars in IC2391and IC2602by Patten&Simon(1996) and Barnes et al.(1999)respectively.
Our?rst exhibit is Fig.1,which as we have said previ-ously shows that the X-ray activity in all the clusters rises rapidly between(V?I)0?0.5?0.7,but that the coronal activity peaks in IC2391and IC2602at L x/L bol?10?3,
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Table 1.Spectroscopy in NGC 2547.Identi?ers and photometry are from JT98.Columns 5and 6give heliocentric RVs and v e sin i .Column 7gives the EW of the H αline and column 8lists the L x /L bol from JT98.
ID V B ?V V ?I c RV v e sin i
H αEW
Log(L x /L bol )
Notes
(km s ?1)
(?A )RX314.403 1.082 1.330+13.4±0.818.8+0.5-3.30RX1013.9840.897 1.032+13.3±0.720.1-0.2-3.32RX12a 14.4920.888 1.055+29.3±0.535.50.0-3.42
RX12a +27.1±1.135.50.02
RX1612.1990.5110.642+12.8±0.67.7-1.4-4.47RX2413.3070.7260.869+12.4±1.031.2-0.1-3.35RX29a 12.6770.6310.750+13.7±0.727.2-1.0-3.63RX30a 12.3170.5770.692+15.4±3.386.0-1.3-3.43RX3412.6580.7450.850+12.1±0.6 6.1-0.9-4.451RX3513.2780.8010.937+21±10>160-1.6-3.603
RX4212.5220.5990.761+14.2±0.957.3-0.9-3.52RX4913.3350.803 1.022+13.0±1.0<6-0.4-3.40RX5212.5280.5770.709+12.8±0.628.4-1.2-4.01RX5313.5740.8120.930+13.6±1.111.8-0.4-3.50RX55112.4860.6970.834+47.9±1.0<6-1.1-4.381,4
RX552?17.6±1.1<6RX5813.8730.880 1.011+13.3±1.112.0-0.3-3.81RX6412.6180.6040.720+13.9±0.723.8-1.2-4.28RX6613.3500.946 1.161+19.2±1.1 6.0+0.1-3.301
RX6913.1690.7220.826+12.1±1.112.8-0.6-3.78RX72a 12.6230.6170.763+11.2±1.114.5-0.9-3.76RX7912.3520.5670.699+11.8±1.238.5-1.0-3.97RX8713.7280.992 1.132+9.3±1.014.7+0.1-3.391
RX9413.0890.6950.813+11.6±1.129.3-0.2-3.31RX9913.0470.6870.798+11.5±1.110.2-0.8-3.89RX10113.143
0.706
0.883
+11.3±1.156.5
-0.2
-3.42
1Possible photometric binary system.
2Spectra were taken on both 06and 07January 1999for RX12a.3RV and v e sin i values taken from the H αline.
4
SB2system.H αis not quite resolved so only one value is given for the
system.
Figure 4.Projected equatorial velocities (v e sin i )as a function of intrinsic colour for NGC 2547(dots)and IC 2391/2602(trian-gles).
about a factor of two higher than in NGC 2547.The extra information we now have is that all but one of the circled NGC 2547stars are probable cluster members,so any
re-
Figure 5.Histograms of v e sin i for solar-type stars in NGC 2547(top)and IC 2391/2602(bottom)in the colour range 0.6<(V ?I c )0<1.1.
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duced X-ray activity levels cannot be blamed on?eld star interlopers.Exactly the same picture is seen in a compari-son with the cool stars of the older Alpha Per cluster(this is Fig.13in JT98–which we do not reproduce here),but this and Fig.1also clearly show that at late spectral types ((V?I c)0>1.5,(B?V)0>1.3),the peak level of X-ray emission in NGC2547returns to a level that is indistinguish-able from that in the IC2391/2602,Alpha Per or Pleiades (see Stau?er et al.1994)late K and M-stars.
Figure4compares projected equatorial velocities in the clusters as a function of intrinsic colour.We are more com-fortable comparing v e sin i than attempting a comparison with the measured rotation periods in IC2391/2602(Pat-ten&Simon1996;Barnes et al.1999)because(a)we do not have rotation periods for NGC2547and(b)rotation period data can be subject to additional selection biases beyond those we discuss immediately below,because of the need for substantial magnetic spot activity on the stellar surface and possible sampling biases.
Recall that we believe the NGC2547sample is unbiased with respect to rotation for(V?I c)0>0.8,but may lack some of the slowest rotators among the hotter stars.Note that in Fig.4and subsequent?gures,we have not included the non-member RX12a and display the SB2system,RX55, as a single point.S97have used similar arguments to those that we used in section2.1to show that their X-ray selected sample of G-stars in IC2391/2602should be unbiased with respect to rotation,but that hotter and cooler stars may preferentially be the more rapidly rotating cluster members. Figure4suggests that the rotation rate distributions are ex-tremely similar,although perhaps there are one or two more slow rotators in NGC2547than in IC2391/2602where all the solar-type stars have resolved v e sin i≥8km s?1.How-ever,given the uncertainties in inclination angles and sample completeness at low rotation rates we do not think there is strong evidence for di?erences in the slowest rotation rates in NGC2547and IC2391/2602.Figure5shows the v e sin i histograms in NGC2547and IC2391/2602for an intrinsic colour range0.6<(V?I c)0<1.1that encompasses the bulk of the NGC2547sample.As the reader can see,the distributions are very similar.We have performed a formal Kolmogorov-Smirnov double-sided test between the cumula-tive v e sin i distributions which yields a probability of only 28%that the NGC2547and IC2391/2602distributions are drawn from di?ering parent samples.
What is very clear from Figs.4and5,is that NGC2547 does not appear to contain an anomalously slowly rotating population of solar-type stars.There are several late F and G stars with v e sin i≥20km s?1,the threshold for X-ray saturation in these stars de?ned by Stau?er et al.(1994), and4ultra-fast rotators with v e sin i>50km s?1.
Figure6combines the rotation and X-ray data for NGC 2547to show the the rotation-activity correlation compared with that in IC2391and IC2602.We have split the samples according to their colour.There is a weak correlation present for stars with(V?I)0<0.7in NGC2547and very little sign of a correlation in IC2391and IC2602.We think this is because in F stars,the depth of the convection zone,rather than rotation rate is the dominant in?uence on dynamo ac-tivity.If there were enough stars in these clusters,and the photometry was accurate enough,we believe that choosing a very narrow colour range would yield a
rotation-activity Figure6.The X-ray activity-rotation correlations for NGC2547 (top)and IC2391/2602(bottom).The samples have been split into two intrinsic colour bins:Solid symbols are for0.4<(V?I c)0<0.7and open symbols for0.7<(V?I c)0<1.
3.
Figure7.Hαequivalent width versus intrinsic B?V for NGC 2547(dots)and a set of slowly rotating,low activity stars that we used for v e sin i cross-correlation templates(squares). correlation.This is made clearer by Fig.1,where the X-ray activity is seen to rise steeply between0.5<(V?I)0<0.7. Small di?erences in colour and the randomizing e?ect of un-known rotation axis inclination angles can e?ectively destroy the correlation with rotation in this colour interval.
For cooler stars(0.7<(V?I c)0<1.3)it does appear that X-ray activity rises with rotation rate and saturates above a v e sin i of about15-20km s?1.The correlation is not perfect,probably because of random inclination angles. Stars with low v e sin i could have high activity levels but be fast rotators viewed close to pole-on.This may well be the case for RX49and RX66.The key point is that NGC 2547apparently saturates at a lower coronal activity level than IC2391and IC2602,but within the limitations of the few data points we have,the saturation seems to occur at a similar rotation rate.There is also weak evidence,based
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Figure 8.H αequivalent width versus intrinsic V ?I c for NGC 2547(dots)and IC 2391/2602(triangles).The levels of chromo-spheric activity appear very similar in the three clusters.
only on RX35,that as in the IC2391/2602and Alpha Per clusters,there may be a decrease in the saturated level of X-ray emission at very fast rotation rates.
Figures 7and 8show the behaviour of H αas a function of colour in the three clusters,represented by the equiv-alent width (EW)of the H αfeature.In magnetically in-active stars,H αis always seen in absorption,but is chro-mospherically ?lled in and then goes into weak emission (EW ?1?5?A )for cooler stars in young open clusters.Figure 7makes the comparison between the H αEWs in NGC 2547and the inactive standard stars we used for the v e sin i com-parisons.The H αabsorption line is clearly ?lled or even in emission for NGC 2547when compared with inactive stars of the same colour.
The three NGC 2547stars that lie above the trend for the other cluster members in Fig.7are RX24,RX94and RX101.These objects do indeed have the largest v e sin i values in this colour range.However,the correlation with rotation is certainly not perfect.RX42,with a v e sin i of 57km s ?1and a colour only slightly bluer than these three objects lies in the sequence de?ned by the majority of stars.Another peculiarity is that the ultra-fast rotator RX35ap-pears to have anomalously deep H αabsorption for its colour,deeper even than inactive,slowly rotating stars of the same colour.We have no convincing explanation for this strange result at present.We can speculate though,that perhaps RX35is seen almost equator on and is surrounded by the cool,“slingshot prominences”that have been seen around some ultra fast rotating ?eld stars and G stars in the Al-pha Per cluster (Collier-Cameron &Robinson 1989;Collier-Cameron &Woods 1992;Je?ries 1993).These prominences appear to be co-rotating clouds,con?ned by the stellar mag-netic ?eld,which scatter chromospheric H αphotons out of the line of sight –causing absorption features which move from blue to red across the stellar H αpro?le.Our single 30minute observation (see Fig.3b)may have been too long to resolve individual cloud features,or there may be many clouds around the star,because the H αpro?le appears rea-sonably smooth.If this explanation were true then a highly variable H αpro?le might be expected and our v e sin i de-
termination based on the width of the H αabsorption may underestimate the true v e sin i .
Figure 8compares NGC 2547with IC 2391/2602.S97and others have suggested that the colour at which chro-mospheric H αemission rises above the continuum may be an excellent indicator of rotation rates and by implication,age,because it occurs at cooler colours in the older Pleiades and Hyades clusters.Stars with active accretion discs how-ever (the CTTS),show H αemission way above that seen in even the most chromospherically active stars,with emission EWs >10?A .This diagnostic of accretion correlates excel-lently with others such as near infrared excess emission over that expected from a photosphere alone,veiling of the opti-cal spectrum by continuum emission from accretion hotspots or emission from forbidden metallic lines such as O i at 6300?A (Hartigan et al.1990,Hartigan,Edwards &Ghan-dour 1995).Figure 8demonstrates that NGC 2547behaves very similarly to IC 2391and IC 2602.H αemission ?rst appears at (V ?I )0?1.0,which is more or less as expected for a very young cluster containing magnetically active stars.None of the stars show any signs of excess H αthat come even close to the levels expected from CTT accretion phenomena.
We have also checked our optical spectra for veiling or the presence of an O i emission line at 6300?A .Edwards et al.(1993)show that infrared excesses are present in stars with O i 6300?A EWs of between 0.1and 10?A and that such stars also show an excess optical continuum ranging from 10%to >90%of the observed ?ux.In our slowly rotating stars,we can place ?rm upper limits of <0.05?A on the EW of any O i emission and by comparison with the low activity standard stars we ?nd no evidence for any veiling continuum above a level of about 10-20%of the observed ?ux.We do not detect emission lines or veiling in the fast rotators (>20km s ?1)either,but here the limits are relaxed to <0.1?A and 30%respectively.In summary,we can categorically state that none of the stars we have observed show any evidence for active accretion discs.
4DISCUSSION
4.1
The age of NGC 2547
How we interpret the rotation data for NGC 2547depends a great deal on what we assume its age is.JT98obtained 14±4Myr from low mass isochrone ?ts.The same isochrones would yield ages of 25Myr for IC2391/2602,50Myr for Al-pha Per and 90Myr for the Pleiades,in reasonable agree-ment with the traditional nuclear turn-o?ages determined from high mass stars in the Hertzsprung-Russell diagram (Mermilliod 1981).In the last couple of years these ages have been challenged by measurements of the lithium de-pletion boundary (LDB)in very low mass cluster stars.The luminosity at which lithium remains unburned in a fully convective star that is contracting towards the ZAMS can be mapped onto an age with reasonable precision (see Ushomirsky et al.1998).This method has been used to ob-tain ages of 53±5Myr for IC 2391(Barrado y Navascues,Stau?er &Patten 1999),85±10Myr for Alpha Per (Stauf-fer et al.1999)and 125±8Myr for the Pleiades (Stau?er,Schultz &Kirkpatrick 1998).This older age scale implies a modest amount of convective core overshoot to bring the nu-clear turn-o?ages into agreement (Mazzei &Pigatto 1988).
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Je?ries et al.(2000)have attempted to?nd the LDB in NGC2547,but could only establish a lower limit to the age of about23Myr.If the relative positions of the low mass stars in IC2391and NGC2547are accepted as an indica-tion of an age di?erence between the two clusters and we assume that the LDB age for IC2391is correct,then NGC 2547could be as old as35-40Myr.This would make a sub-stantial di?erence in the interpretation of the rotation data because at40Myr,a solar-type star would have completed the vast majority of its contraction(and consequent change in moment of inertia)towards the ZAMS.At15Myr,the surface rotation rate could still increase by about a factor 1.8(neglecting angular momentum loss)due to changes in radius and moment of inertia(from the models of D’Antona &Mazzitelli1997).Also of course,any deductions about the lifetimes of circumstellar discs are crucially dependent upon the assumed ages of the younger clusters.
Without making a judgement on the relative merits of the isochronal and LDB ages,we will need to consider the case of both the younger and older ages scales.i.e.where the ages of NGC2547and IC2391are roughly15Myr and 25Myr and where they are roughly40Myr and55Myr re-spectively.
4.2Rotational evolution of solar-type stars
NGC2547(along with the IC2391/2602clusters)occupies an important age position between the older,well studied Alpha Per and Pleiades clusters and PMS stars in star form-ing regions.Previous attempts to study rotation in this age range(10-40Myr)have concentrated on dispersed popula-tions of X-ray selected objects in and around OB and T associations(e.g.Bouvier et al.1997b).These studies ap-pear to show a lack of the slow rotators that are needed to explain the older Pleiades rotation distribution where50% of solar-type stars have v e sin i<10km s?1(Queloz et al. 1998).The problems with these investigations of scattered PMS populations are that the stellar ages rely on rather un-certain distances and that X-ray selection might be quite severe,so biasing against the presence of slow rotators.In our NGC2547study and in the IC2391/2602study of S97, it seems likely that for solar-type stars at least,this selection e?ect is absent or weak.
The rotation rates we have measured in NGC2547 largely con?rm the results found in IC2391/2602by S97. If the clusters had ages of40Myr and55Myr respectively and assuming the initial angular momentum distributions and circumstellar disc lifetimes were similar,then we would expect to see little di?erence in their rotation rate distri-butions.This is because solar type stars in both clusters would have reached the ZAMS,there would be little mo-ment of inertia change and angular momentum losses over the course of15Myr might be too small to be measured, except perhaps in the few most rapid rotators.However,if the clusters were aged15Myr and25Myr,then assuming solid-body rotation and ignoring angular momentum losses, we might expect to see a rotational spin-up of50%between NGC2547and IC2391/2602.The median v e sin i among the solar-type stars(0.6<(V?I c)0<1.1)in NGC2547 is about20km s?1and very similar in IC2391/2602.These ?gures are based on relatively small numbers but one could view this similarity as a(very)weak argument for the older age scale.
The upper quartile of rotation in the Pleiades solar type stars occurs for v e sin i>15km s?1.In IC2391/2602it is 50km s?1and about40km s?1in NGC2547.The numbers here really are too small to analyse any di?erence between NGC2547and IC2391/2602.If the solar type stars in all three clusters have completed their PMS contraction,then taken together,the results indicate that if they rotate as solid bodies,the fastest rotating stars must lose60-70%of their angular momentum between40-50Myr and～125Myr. If the clusters are younger then the amount of angular mo-mentum loss must be even greater(80-90%)to allow for some contraction and spin up onto the ZAMS.The simi-larity in v e sin i of the rapid rotators of NGC2547and IC 2391/2602argues for similar initial conditions and circum-stellar disc lifetimes.
Overall what we have measured is in very good agree-ment with the models put forward by Bouvier et al.(1997a). These models start with an observed rotation rate in T-Tauri stars and evolve this using wind angular momentum loss(which saturates at fast rotation rates)and early cou-pling to a circumstellar disc which is responsible for the predominance of slow rotators at later times.These solid-body rotation models predict maximum rotational veloc-ities of order150-200km s?1for ages15-40Myr and that roughly half the solar-type stars in NGC2547should have v e sin i<20km s?1,which is what we have measured.This high proportion of slow rotators is achieved by assuming cir-cumstellar disc lifetimes as old as40Myr in some stars and that about15%of stars(the slowly rotating ones)are locked to their discs at15Myr.
We have no evidence that any of the solar-type stars in NGC2547still have discs.This could argue that the cluster has an age of～40Myr,but other interpretations are possible.Cameron&Campbell(1993)and Armitage& Clarke(1996)show that discs with mass accretion rates of only10?10M⊙/yr can still enforce rotational equilibrium, whereas mass accretion rates at least an order of magnitude higher are needed to provoke the optical accretion signatures we have searched for in this paper.Some of our slowest ro-tators may still have remnant discs and it would be worth searching for these in more detail at infrared wavelengths. Another possibility is that the radiative core and convec-tive envelope are not perfectly coupled and that interior dif-ferential rotation is possible.This would allow less angular momentum loss to produce slow rotators and thus requires shorter disc lifetimes.However,the core-envelope coupling timescale must be substantially greater than the10Myr pro-posed by Keppens et al.(1995),who found that short disc lifetimes(～6Myr)could not produce enough slow rotators on the ZAMS in these circumstances.The di?erential ro-tation models put forward by Krishnamurthi et al.(1997) show that su?cient slow rotators can be produced with disc lifetimes of3-10Myr if the core-envelope coupling timescale is of order100Myr.
Alternatively,NGC2547and IC2391/2602may have been born with a population of slower rotators than are typ-ically seen in even younger clusters and star forming regions. Barnes et al.(1999)show that to explain the slow rotators in IC2602requires that20-30%of solar-type stars in IC 2602needed to have initial periods as slow as16days if
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disc lifetimes are to be limited to≤3Myr.However,Choi &Herbst(1996)and Kearns&Herbst(1998)?nd that90% of stars in the3Myr old NGC2264cluster and1Myr Orion Nebula and Trapezium clusters have rotation periods faster than10days.Thus either long disc lifetimes(>10Myr),in-ternal di?erential rotation with long core-envelope coupling timescales(～100Myr),or anomalously small initial angular momenta are required to explain the slow rotators in NGC 2547,IC2391and IC2602.
In any of these scenarios it is at least clear that the NGC2547(and IC2391/2602)data have partially solved the problem of the lack of slow rotators at ages between the PMS stars in Taurus and Orion and the older Alpha Per and Pleiades clusters.The slow rotators are there,it just requires observations of optically selected samples,or at least complete X-ray selected samples which are not bi-ased against slow rotators.We can also say that the com-bination of initial angular momentum distribution and disc lifetimes must be reasonably similar in NGC2547and IC 2391/2602in order to produce similar v e sin i distributions at their current ages.This is an important result because in the disc-regulated angular momentum loss model,even a small variation in disc locking timescales would produce big changes in the v e sin i distribution as solar-type stars reached the ZAMS.
4.3Anomalous X-ray emission in NGC2547
Our main reason for performing high resolution spectroscopy in NGC2547was to explain the anomalously low level of X-ray emission in the most active solar type stars in the cluster. Our working hypothesis was that all of the NGC2547late F and G stars were rotating slower than20km s?1and hence none of them showed the saturated level of X-ray emission seen in other young clusters.Our data conclusively reject this hypothesis.There are several examples of very rapid rotators in NGC2547and the rotation rate distribution is indistinguishable from the IC2391and IC2602clusters.
We had also suggested that slow rotation in NGC2547 might be caused by long lived circumstellar discs or an un-usually small amount of initial angular momentum.Neither of these is now required and we have evidence that none of the solar type stars in NGC2547possess active accretion discs.This latter discovery in itself places an upper limit on the lifetime of such discs(that could be detected with Hα, O i emission or optical veiling)of40Myr and possibly as low as15Myr depending on what is?nally concluded about the age of NGC2547.
NGC2547appears to follow the ARAP discussed in the introduction up to a point.The levels of activity are appropriate for its age and measured rotation rates,except for the case of coronal activity in the fastest rotators.There, the“saturation level”for X-ray emission is a factor of two lower than seen in all other young clusters,but appears to occur at similar rotation rates of15-20km s?1.
The fact that the X-ray saturation occurs at a similar rotation rate and that the chromospheric activity in NGC 2547concurs with that in IC2391and IC2602,leads us to suspect that perhaps the X-ray?uxes in NGC2547have been underestimated by a factor of two.A further piece of evidence in support of this view is that RX12a,which is almost certainly a background?eld star,has v e sin i=35.5km s?1and L x/L bol=10?3.42.The spectral type of this object(determined from the cross-correlations)is about K0V,so it does not appear to su?er from much more red-dening or absorption than the NGC2547stars.If the low X-ray saturation levels in NGC2547are peculiar to that cluster for some reason,then it is di?cult to explain why a similar phenomenon occurs in an unconnected fast rotating ?eld star in the same direction.
A factor of two underestimate of intrinsic X-ray?uxes might be possible if the interstellar absorption towards the cluster is higher than assumed by JT98,or if the assumed stellar X-ray spectrum is incorrect.Another factor to con-sider is that the IC2391,IC2602,Alpha Per and Pleiades ROSAT data we have discussed were obtained with the Po-sition Sensitive Proportional Counter(PSPC),rather than with the High Resolution Imager(HRI)as in the case of NGC2547.However,we do not believe there could be as much as a factor of two error produced here.The assumed interstellar column density for NGC2547of3×1020cm?2 was estimated from the cluster reddening(Bohlin,Savage &Drake1978)and from Lymanαmeasurements of early type stars at similar galactic coordinates(Fruscione et al. 1994).A likely error in these estimates is50%,but the col-umn density would have to be as high as(2-3)×1021cm?2 to double the unabsorbed X-ray?uxes in NGC2547.Such a large column density probably exceeds the column den-sity out of the Galaxy in this direction,as deduced from 21cm maps(Marshall&Clark1984).JT98also assumed a 1keV optically thin plasma,but again,the consequences of this coronal temperature being wrong by as much as50% only changes X-ray?uxes by15%(David et al.1996).We also cannot appeal to a mismatch in the calibrations of the PSPC and HRI.Simon&Patten(1998)have measured X-ray?uxes for stars in IC2391with the HRI and compared them with?uxes measured for the same stars with the PSPC by Patten&Simon(1996).They?nd excellent agreement with essentially no systematic di?erence and little variability in the X-ray?uxes.The HRI count rate to?ux conversion factor used by Simon&Patten(1998)is10%smaller than that used for NGC2547by JT98,but this is consistent with the smaller assumed value of interstellar absorption for IC https://www.wendangku.net/doc/a118747548.html,stly,we can also say that the bolometric corrections used by various authors to calculate L x/L bol are the same to within a few hundredths of a magnitude at all colours,so that none of the discrepancy can be attributed to di?erences in these.
Our other line of argument for claiming that JT98cal-culated the?uxes correctly is more indirect.It seems that the peak levels of X-ray activity in the M stars of NGC2547 are very similar to those in IC2391/2602and other clusters. Fig.1shows that this is the case.Note that we have not tried to compare mean X-ray emission in these cool stars because the samples are incomplete and heavily biased towards the most active stars.A global factor of two increase in all the X-ray?uxes in NGC2547would shift its M dwarfs to activ-ity levels higher than seen in other clusters.The only way of escaping this problem would be if the solar type stars were more absorbed or had radically di?erent coronal spectra to the M dwarfs.Neither of these seem likely but we will be able to rule them out when we have X-ray spectra from the Chandra or XMM satellites.
We have also considered compositional di?erences be-
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tween the clusters as a possible solution.Di?erent metallic-ities could a?ect convection zone depths and dynamo activ-ity or may simply alter the coronal abundances and emission measure distributions.The metallicities of these three young open clusters are not expected to strongly depart from solar values but they remain undetermined at the present time. However,we have interpreted the strong turn-on of X-ray activity at0.5<(V?I)0<0.7as due to the onset and deepening of convection zones in F stars.The fact that this occurs at a very similar intrinsic colours in NGC2547,IC 2391and IC2602argues that any compositional di?erences between the clusters are small and do not greatly in?uence the magnetic dynamo e?ciency.
We are left with a puzzle,perhaps akin to the very di?erent X-ray luminosity functions in the older(600Myr) Hyades and Praesepe clusters(Randich&Schmitt1995; Barrado y Navascues,Stau?er&Randich1998),which also remains unexplained and does not seem likely to result from very di?erent rotational properties.That clusters with sim-ilar ages can have di?erent X-ray properties means we must be careful about using X-ray data and the ARAP to draw conclusions about the age distributions of arbitrary samples of stars,whether in clusters or the?eld.
5SUMMARY
We have obtained high resolution spectroscopy for a sample of solar-type stars in the young open cluster,NGC2547.We have determined projected equatorial velocities,searched for the presence of active accretion discs and measured their chromospheric activity.Our main conclusions can be sum-marised as follows.
?The rotation rate distribution in NGC2547is indistin-guishable from that in the slightly older IC2391and IC2602 clusters.In the current paradigm for the rotational evolution of cool stars,this points to very similar initial conditions and circumstellar disc lifetimes in the three clusters.
?We?nd both examples of ultra-fast rotating stars and stars with v e sin i<10km s?1.If the slow rotating stars evolve from populations with the rotation rate distributions seen in very young PMS clusters,then either very long(～10?40Myr)disc lifetimes or internal di?erential rotation are required.An alternative might be that NGC2547(and IC 2391/2602)were born with a high proportion of anomalously slowly rotating objects.
?We?nd no evidence for active accretion discs in our sample.This sets an upper limit to the lifetime of such discs at15-40Myr,depending on what is assumed for the age of NGC2547.
?The slowly rotating objects in NGC2547(and IC 2391/2602)have no counterparts in the X-ray selected sam-ples of10-40Myr PMS stars that have been studied previ-ously.We ascribe this to biases towards fast rotators caused by strong X-ray selection.We believe this bias is weak or absent in our sample of solar-type stars.
?NGC2547appear to follow the same rotation-activity correlation seen in other young clusters.X-ray activity in-creases up to a saturated peak for v e sin i>15?20km s?1. However,we are unable to explain why the X-ray activity of solar-type stars in NGC2547saturates at log(L x/L bol)=?3.3,a factor of two lower than in other young clusters.We rule out slow rotation,and consider signi?cant uncertainties in calculating the X-ray?uxes unlikely. ACKNOWLEDGEMENTS
This work was based on data collected at the Anglo-Australian Observatory,partly funded by the UK Parti-cle Physics and Astronomy Research Council(PPARC). We thank the sta?of the Anglo-Australian Observatory for assistance during the https://www.wendangku.net/doc/a118747548.html,putational work was performed on the Keele and St Andrews nodes of the PPARC funded Starlink network.
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The way常见用法
The way 的用法 Ⅰ常见用法： 1)the way+ that 2)the way + in which（最为正式的用法） 3)the way + 省略（最为自然的用法） 举例：I like the way in which he talks. I like the way that he talks. I like the way he talks. Ⅱ习惯用法： 在当代美国英语中，the way用作为副词的对格，“the way+ 从句”实际上相当于一个状语从句来修饰整个句子。 1)The way =as I am talking to you just the way I’d talk to my own child. He did not do it the way his friends did. Most fruits are naturally sweet and we can eat them just the way they are—all we have to do is to clean and peel them. 2）The way= according to the way/ judging from the way The way you answer the question, you are an excellent student. The way most people look at you, you’d think trash man is a monster. 3）The way =how/ how much No one can imagine the way he missed her. 4）The way =because
The way的用法及其含义(二)
The way的用法及其含义（二） 二、the way在句中的语法作用 the way在句中可以作主语、宾语或表语： 1.作主语 The way you are doing it is completely crazy.你这个干法简直发疯。 The way she puts on that accent really irritates me. 她故意操那种口音的样子实在令我恼火。The way she behaved towards him was utterly ruthless. 她对待他真是无情至极。 Words are important, but the way a person stands, folds his or her arms or moves his or her hands can also give us information about his or her feelings. 言语固然重要,但人的站姿,抱臂的方式和手势也回告诉我们他(她)的情感。 2.作宾语 I hate the way she stared at me.我讨厌她盯我看的样子。 We like the way that her hair hangs down.我们喜欢她的头发笔直地垂下来。 You could tell she was foreign by the way she was dressed. 从她的穿著就可以看出她是外国人。 She could not hide her amusement at the way he was dancing. 她见他跳舞的姿势，忍俊不禁。 3.作表语 This is the way the accident happened.这就是事故如何发生的。 Believe it or not, that's the way it is. 信不信由你, 反正事情就是这样。 That's the way I look at it, too. 我也是这么想。 That was the way minority nationalities were treated in old China. 那就是少数民族在旧中
(完整版)the的用法
定冠词the的用法： 定冠词the与指示代词this ,that同源,有“那(这)个”的意思,但较弱,可以和一个名词连用,来表示某个或某些特定的人或东西. (1)特指双方都明白的人或物 Take the medicine.把药吃了. (2)上文提到过的人或事 He bought a house.他买了幢房子. I've been to the house.我去过那幢房子. (3)指世界上独一无二的事物 the sun ,the sky ,the moon, the earth (4)单数名词连用表示一类事物 the dollar 美元 the fox 狐狸 或与形容词或分词连用,表示一类人 the rich 富人 the living 生者 (5)用在序数词和形容词最高级,及形容词等前面 Where do you live?你住在哪? I live on the second floor.我住在二楼. That's the very thing I've been looking for.那正是我要找的东西. (6)与复数名词连用,指整个群体 They are the teachers of this school.(指全体教师) They are teachers of this school.(指部分教师) (7)表示所有,相当于物主代词,用在表示身体部位的名词前 She caught me by the arm.她抓住了我的手臂. (8)用在某些有普通名词构成的国家名称,机关团体,阶级等专有名词前 the People's Republic of China 中华人民共和国 the United States 美国 (9)用在表示乐器的名词前 She plays the piano.她会弹钢琴. (10)用在姓氏的复数名词之前,表示一家人 the Greens 格林一家人(或格林夫妇) (11)用在惯用语中 in the day, in the morning... the day before yesterday, the next morning... in the sky... in the dark... in the end... on the whole, by the way...
“the way+从句”结构的意义及用法
“tｈｅwａｙ+从句”结构的意义及用法 首先让我们来看下面这个句子: Ｒead the foｌloｗｉnｇpassagｅａnd talkａbout ｉt wi ｔh your classmaｔes．Try tｏｔeｌl whaｔyｏu thiｎk ｏf Tom aｎd ｏｆｔhe ｗay the chiｌｄrenｔrｅated ｈim. 在这个句子中，ｔhe waｙ是先行词,后面是省略了关系副词that或in whｉch的定语从句。 下面我们将叙述“the ｗaｙ+从句”结构的用法。 1.tｈe wａy之后，引导定语从句的关系词是tｈat而不是hoｗ,因此，<<现代英语惯用法词典＞＞中所给出的下面两个句子是错误的：Ｔhｉs is ｔｈeｗayｈowｉtｈａppened. This is the way how he ａlwａｙs treats me. 2．在正式语体中,thaｔ可被in which所代替;在非正式语体中，ｔhat则往往省略。由此我们得到theｗay后接定语从句时的三种模式：1) tｈe ｗaｙ＋ｔhａt-从句２）the way +ｉn whiｃh－从句3) the ｗay +从句 例如：Ｔｈe way(in whiｃh ，thａt) ｔhｅｓｅｃomｒade ｓloｏｋａｔｐrobｌems is wrong．这些同志看问题的方法
不对。 Ｔｈｅｗａy(that ,ｉn ｗhiｃh)yoｕ’ｒe doinｇit is comple ｔeｌy crａzy.你这么个干法,简直发疯。 Wｅａdmiｒｅd him for thｅｗay ｉｎｗhｉch he fａｃeｓdiｆficultieｓ． Waｌlａｃe ａｎd Ｄarwiｎｇreed ｏn the way ｉｎwhi ｃh ｄｉfｆｅrｅnt forms ｏf life had ｂegｕn.华莱士和达尔文对不同类型的生物是如何起源的持相同的观点。 Thｉs is ｔｈe ｗaｙ（tｈａｔ) hｅdｉd it. I lｉkeｄｔhe waｙ(ｔhat) ｓｈeｏｒganized ｔhe ｍeetｉng． 3.theｗay(tｈat)有时可以与hｏw(作“如何”解）通用。例如： That’s tｈe ｗaｙ(tｈaｔ) shｅspoke. = Tｈat’s how shｅspoke.
way 用法
表示“方式”、“方法”，注意以下用法： 1.表示用某种方法或按某种方式，通常用介词in(此介词有时可省略)。如： Do it (in) your own way. 按你自己的方法做吧。 Please do not talk (in) that way. 请不要那样说。 2.表示做某事的方式或方法，其后可接不定式或of doing sth。 如： It’s the best way of studying [to study] English. 这是学习英语的最好方法。 There are different ways to do [of doing] it. 做这事有不同的办法。 3.其后通常可直接跟一个定语从句(不用任何引导词)，也可跟由that 或in which 引导的定语从句，但是其后的从句不能由how 来引导。如： 我不喜欢他说话的态度。 正：I don’t like the way he spoke. 正：I don’t like the way that he spoke. 正：I don’t like the way in which he spoke. 误：I don’t like the way how he spoke. 4.注意以下各句the way 的用法： That’s the way (=how) he spoke. 那就是他说话的方式。 Nobody else loves you the way(=as) I do. 没有人像我这样爱你。 The way (=According as) you are studying now, you won’tmake much progress. 根据你现在学习情况来看，你不会有多大的进步。 2007年陕西省高考英语中有这样一道单项填空题： ——I think he is taking an active part insocial work. ——I agree with you_____. A、in a way B、on the way C、by the way D、in the way 此题答案选A。要想弄清为什么选A，而不选其他几项，则要弄清选项中含way的四个短语的不同意义和用法，下面我们就对此作一归纳和小结。 一、in a way的用法 表示：在一定程度上，从某方面说。如： In a way he was right.在某种程度上他是对的。注：in a way也可说成in one way。 二、on the way的用法 1、表示：即将来(去)，就要来(去)。如： Spring is on the way.春天快到了。 I'd better be on my way soon.我最好还是快点儿走。 Radio forecasts said a sixth-grade wind was on the way.无线电预报说将有六级大风。 2、表示：在路上，在行进中。如： He stopped for breakfast on the way.他中途停下吃早点。 We had some good laughs on the way.我们在路上好好笑了一阵子。 3、表示：(婴儿)尚未出生。如： She has two children with another one on the way.她有两个孩子，现在还怀着一个。 She's got five children，and another one is on the way.她已经有5个孩子了，另一个又快生了。 三、by the way的用法
The way的用法及其含义(一)
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
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；
the-way-的用法讲解学习
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
the_way的用法大全教案资料
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 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)
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。
way的用法
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.
the way的用法大全
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”结构的意义及用法知识讲解
“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 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的用法
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与time的特殊用法
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