A further 'degree of freedom' in the rotational evolution of stars
a r X i v :a s t r o -p h /0508643v 1 30 A u g 2005
Astronomy &Astrophysics manuscript no.repa February 5,2008
(DOI:will be inserted by hand later)
A further ‘degree of freedom’in the rotational evolution of stars
V Holzwarth and M Jardine
School of Physics and Astronomy,University of St Andrews,North Haugh,St Andrews,Fife KY169SS,Scotland
Received ;accepted
Abstract.Observational and theoretical investigations provide evidence for non-uniform spot and magnetic ?ux distributions
on rapidly rotating stars,which have a signi?cant impact on their angular momentum loss rate through magnetised winds.Supplementing the formalism of MacGregor &Brenner (1991)with a latitude-dependent magnetised wind model,we analyse the e ?ect of analytically prescribed surface distributions of open magnetic ?ux with di ?erent shapes and degrees of non-uniformity on the rotational evolution of a solar-like star.The angular momentum redistribution inside the star is treated in a qualitative way,assuming an angular momentum transfer between the rigidly-rotating radiative and convective zones on a constant coupling timescale of 15Myr;for the sake of simplicity we disregard interactions with circumstellar disks.We ?nd that non-uniform ?ux distributions entail rotational histories which di ?er signi?cantly from those of classical approaches,with di ?erences cumulating up to 200%during the main sequence phase.Their impact is able to mimic deviations of the dynamo e ?ciency from linearity of up to 40%and nominal dynamo saturation limits at about 35times the solar rotation rate.Concentrations of open magnetic ?ux at high latitudes thus assist in the formation of very rapidly rotating stars in young open clusters,and ease the necessity for a dynamo saturation at small rotation rates.However,since our results show that even minor amounts of open ?ux at intermediate latitudes,as observed with Zeeman-Doppler imaging techniques,are su ?cient to moderate this reduction of the AM loss rate,we suggest that non-uniform ?ux distributions are a complementary rather than an alternative explanation for very rapid stellar rotation.
Key words.Stars:rotation –Stars:winds,out?ows –Stars:magnetic ?elds –Stars:mass-loss –Stars:evolution –MHD
1.Introduction
In the presence of open magnetic ?elds the angular momen-tum (AM)loss of a star through winds and out?ows is signi?-cantly enhanced since the tension of bent ?eld lines e ?ectively prolongs the lever arm of the associated torque (Schatzman 1962).Whereas during the pre-main sequence (PMS)phase the rotational evolution of a star is dominated by its chang-ing stellar structure and magnetic interaction with a circum-stellar accretion disk,its rotation during the main sequence (MS)phase is mainly determined through braking by mag-netised winds (Belcher &MacGregor 1976).Theoretical stud-ies of magnetised winds go back to classical approaches of Weber &Davis (1967,hereafter WD)and Mestel (1968).At high rotation rates the magnetic ?eld adds considerably to the acceleration of the out?ow through magneto-centrifugal driving (Michel 1969),which makes magnetised winds in-trinsically latitude-dependent.The total AM loss rate is con-sequently susceptible to variations of the surface magnetic ?eld (Solanki et al.1997;Holzwarth 2005)and atmospheric ?eld topology (Mestel &Spruit 1987;Kawaler 1988).More recently,multi-dimensional MHD-simulations have been ac-complished to study structural and temporal wind properties like coronal mass ejections in more detail (e.g.,Sakurai
1985;
2V Holzwarth and M Jardine:A further‘degree of freedom’in the rotational evolution of stars
any mechanism which moderates the AM loss rate at higher ro-tation rates.Respective studies therefore frequently presume a saturation of the AM loss beyond a limiting rotation rate,whose value is very susceptible to model assumptions like the internal AM redistribution;whereas some investigations require low( 20?⊙)saturation limits(Keppens et al.1995;Barnes&So?a 1996;Bouvier et al.1997;Krishnamurthi et al.1997),others argue for higher( 40?⊙)values(Soderblom et al.1993; Collier Cameron&Jianke1994).
The saturation of the total AM loss rate is often ascribed to the underlying dynamo mechanisms in the convective en-velope,because current dynamo theories anticipate a moder-ation and eventually saturation of the ampli?cation process (n de→0)when the back-reaction of strong magnetic?elds suppresses plasma motions and inhibits its further increase (e.g.,R¨u diger&Kichatinov1993).However,the various theo-retical models are as yet unable to provide consistent or explicit values for the critical rotation rate or?eld strength at which this occurs.
The concept of a saturation of magnetic activity is strength-ened by empirical activity-rotation relationships,which reveal (for rotation periods longer than a few days)close correla-tions between the rotation rate and the strength of activity proxies like magnetically induced chromospheric and coronal emission(Noyes et al.1984;Vilhu1984;Mathioudakis et al. 1995;Stau?er et al.1997;Pizzolato et al.2003).In rapidly ro-tating stars several activity signatures are found to saturate:the chromospheric UV emission below rotation periods P～3d (Vilhu1984),and the EUV and(soft)X-ray emission for P 2d(Stau?er et al.1997).However,the variation of pho-tometric light curves,associated with the presence of dark spots in the stellar photosphere,is found to increase for even shorter rotation periods,down to P～0.35?0.5d,for which the chromospheric and coronal emission are already saturated (O’Dell et al.1995;Messina et al.2001);for an antithetical point of view see Krishnamurthi et al.(1998).
The saturation of activity signatures is not unambigu-ously indicative of a saturation of the dynamo mechanisms in the convective envelope,since emission processes are li-able to further rotation-dependent e?ects like a reduction of the X-ray emitting volume through the centrifugal stripping of hot coronal loops,or the shift of coronal loop tempera-tures into di?erent emission regimes as the e?ective gravi-tation and pressure scale hight change with the rotation rate (Unruh&Jardine1997;Jardine&Unruh1999).The conjec-ture that changes of the atmospheric emission are not necessar-ily correlated with the(sub-)photospheric magnetic activity is supported,for example,by observations of the ultra-fast rota-tor VXR45a(V370Vel,P=0.223d),whose X-ray emission is below the typical level of X-ray saturated stars(Marino et al. 2003),whereas its brightness surface maps are still very simi-lar to those of more slowly rotating stars(Marsden et al.2004; Vrielmann&Hussain2005).
The large range of rotation rates(～10?70?⊙)in which ob-served activity signatures are found to saturate raises the ques-tion whether these phenomena re?ect the actual behaviour of the underlying dynamo processes,in particular beyond which critical rotation rate their e?ciency breaks down.Since the range of observed saturation limits practically covers the one of suggested AM loss limits,a de?nite justi?cation of the latter in terms of a dynamo saturation is rather precarious.
1.2.Surface magnetic?ux distributions
Doppler imaging(DI)observations of rapidly rotating stars yield non-uniform surface brightness distributions,where,in contrast to the case of the Sun,dark spots are not only located in equatorial regions,but also at intermediate and polar latitudes (Strassmeier2002,and references therein).Theoretical mod-els considering the formation of magnetic features at higher latitudes involve the pre-eruptive poleward de?ection of mag-netic?ux inside the convection zone by the Coriolis force (Sch¨u ssler&Solanki1992),and/or its post-eruptive pole-ward transport through meridional motions(Schrijver&Title 2001).Backed by these observational and theoretical results, Solanki et al.(1997)investigated the in?uence of a bi-modal magnetic?eld distribution on the rotational evolution of cool stars.They found that a concentration of magnetic?ux at very high latitudes reduces the total AM loss rate as e?ciently as a dynamo saturation limit at～20?⊙.Based on their?ndings, they question the concept of a dynamo saturation at low rota-tion rates and argue instead for a saturation above50?⊙;a sim-ilar though more qualitative argument has also been discussed by Buzasi(1997).
The work of Solanki et al.was focused on?ux concentra-tions around the pole,assuming that the observed brightness distributions indicate likely locations of open?eld lines along which a stellar wind can escape.But the bare existence of starspots does not a priori imply information about the associ-ated magnetic?eld topology,that is neither about the existence nor about the amount of open magnetic?ux.Zeeman-Doppler imaging(ZDI)observations in contrast directly con?rm the magnetic origin of the dark features and enable a determination of the magnetic?eld at the stellar surface(Donati et al.1997). Such?eld distributions serve as boundary conditions for?eld extrapolation techniques(Altschuler&Newkirk1969),which reveal large-scale magnetic?eld topologies and consequently the distribution of closed and open magnetic?eld lines(e.g., Jardine et al.2002a,b).In the case of the rapidly rotating star LQ Hya(P=1.6d)the latitudinal distributions of open?ux show that large amounts are located at intermediate and high latitudes(McIvor et al.2004).A similar result is found in the case of AB Dor(P=0.51d)for observations between1995 and2003(Donati&Collier Cameron1997;Donati et al.1999, 2003):Figure1shows the(normalised)cumulated open mag-netic?ux,integrated from the equator to a co-latitudeθ.The curves indicate that50%of the total open magnetic?ux of a hemisphere is on average located below/above～45?,with vari-ations of±15?depending on the observational epoch.These results show that the distribution of open magnetic?ux can be distinctively di?erent from spot distributions determined from surface brightness maps alone.
The present work extends the study of Solanki et al.(1997) and investigates the impact of latitude-dependent?ux distri-butions on the rotational evolution of solar-type stars in more
V Holzwarth and M Jardine:A further ‘degree of freedom’in the rotational evolution of stars
3
80
60
40
20
θ [o ]
0.0
0.20.40.60.81.0Φθ/Φ0
Fig.1.Cumulative open magnetic ?ux distributions,Φθ/Φ0
(cf.Sect.2.2),on the visible
hemisphere of AB
Dor
(
P
=0.51d),based on ZDI observations secured between 1995–2003(Donati &Collier Cameron 1997;Donati et al.1999,2003).Thin curves:1995(θ50%=54?,solid );1996(47?,long dashed );1997(37?,short dashed );1998(49?,dashed dotted );1999(60?,dotted ).Thick curves:2000(29?,solid );2001(53?,long dashed );2002(56?,short dashed );2003(63?,dashed dot-ted ).
https://www.360docs.net/doc/f316121922.html,ing the magnetic wind model described in Holzwarth (2005),we quantify the in?uence of prescribed ?ux distribu-tions with di ?erent degrees of non-uniformity on the rotational evolution of stars,and verify their importance by comparing their impact with the in?uence of other magnetic ?eld-related model parameters.
2.Model setup
The stellar structure of the low-mass star considered here con-sists of an outer convective envelope and an inner radiative core,each taken to be in solid-body rotation with possibly dif-ferent rotation rates.With J =I ?being the AM,I the moment of inertia,and ?the rotation rate,the rotational evolution of the star is determined by the set of coupled di ?erential equations d lg ?e
d lg t +t d lg t =?
d lg I c
J c
˙J c ,˙M +˙J
c ,RI
,(2)
which comprise changing moments of inertia and the AM
transfer across appropriate boundaries;indices ‘e’and ‘c’de-note quantities of the envelope and of the core,respectively.
2.1.Internal angular momentum redistribution
The stellar structure is taken to be spherically symmetric.The temporal change of the moments of inertia is determined by an evolutionary sequence of stellar models of a 1M ⊙star,which was generated with an updated version of the stellar evolution code of Kippenhahn et al.(1967).Figure 2shows the evolution of the (outer)radii,masses,and moments of inertia of both the convective envelope and the radiative core.
As the core-envelope interface recedes outward,the dy-namical stability properties at the base of the convection zone
0.00.51.01.52.02.5r [R O ? ]
a
0.010.10
1.00M [M O ? ]
b
10
6
10
7
108
10
9
1010
t [yr]
0.11.010.0100.0I [1053 g c m 2]
c
Fig.2.Evolution of the outer radii,r e /c (Panel a ),masses,M e /c (Panel b ),and moments of inertia,I e /c (Panel c )of the convec-tive envelope (solid )and radiative core (dashed )of a 1M ⊙star.For t 1.5Myr the star is fully convective.Its MS phase starts at t ?40Myr;the vertical dashed line marks the age of the Sun.
change and originally unstable mass settles down on the radia-tive core.This mass transfer is accompanied by an AM transfer,˙J e ,˙M =?
21
in the equatorial plane and in the absence of viscosity
4V Holzwarth and M Jardine:A further‘degree of freedom’in the rotational evolution of stars bility condition is violated at the core-envelope interface and a
rotational instability sets in,transferring AM,
˙J e,RI =
?J
I e+I c
=
I e I c
r0(t)
2 B<+?B(?e)·f(θ) ,(6)
given at a reference level,r0,close to the stellar surface.The time-dependent radius ratio is to ensure that the total magnetic ?ux,
Φ0(?e)=
2π
π
B r,0r20sinθdθdφ=4πr20(t0)ˉB r,0(t0,?e),(7)
only depends on the rotation rate of the star
(Saar1991),and an arbitrary reference time,t0.The e?ciency of the underlying dynamo mechanism is expected to increase with the rotation rate of the convection zone.The?eld strength variation,?B,is therefore determined in a way that the surface averaged?eld strength,
ˉB r,0(t0,?e)=
π/2
B r,0sinθdθ,(8)
obeys the functional behaviour shown in Fig.3.The non-uniform?ux distributions,superposed on a constant‘back-ground’?eld,B<,are characterised by an enhancement of mag-netic?ux at non-equatorial latitudes(Fig.4):
10-710-610-510-4
?e [s-1]
1
10
100
1000
B r
,
(
t
)
[
G
]
∝?
Fig.3.Dependence of the surface averaged radial magnetic ?eld strength,ˉB r,0(t0),on the rotation rate,?e,of the convec-tive envelope.For large rotation rates the dependencies fol-low approximately linear(solid),sub-linear(long dashed),or super-linear(short dashed)power laws,∝ ?e/?e,⊙ n?,with n?=1,0.75,and1.25,respectively.The deviation from the power law at small rotation rates is due to the constant back-ground?eld strength.
B
<
B
>
CH
θ0
B
<
B
>
LB
θ0
https://www.360docs.net/doc/f316121922.html,titude-dependent magnetic?eld distributions,f(θ), close to the stellar surface.The non-uniformity of the Coronal Hole(CH)and Latitudinal Belt(LB)model is parametrised through the co-latitudeθ0.Dashed lines show the lower,B<, and upper,B>=B<+?B,?eld strengths of each?eld distribu-tion.
–Coronal Hole(CH)model
f(θ)= 1for0≤θ≤θ0
0forθ0<θ<90?
(9)–Latitudinal Belt(LB)model
f(θ)=cos16(θ?θ0)(10) Whereas the Latitudinal Belt model closely resembles what is found from?eld extrapolations based on ZDI images (McIvor et al.2004),the Coronal Hole model is motivated by numerous DI surface brightness maps(e.g.,Strassmeier 2002).Di?erent degrees of high-latitude?ux concentrations are realised by changing the co-latitudeθ0of the analyti-cally prescribed functions f(Fig.5).We classify non-uniform ?ux distributions by the location of their50%-open?ux level,θ50%,where the cumulated open magnetic?ux,Φθ= 4π θπ/2B r,0r20sinθ′dθ′,reaches half of the total value,Φ0.
V Holzwarth and M Jardine:A further ‘degree of freedom’in the rotational evolution of stars
5
80
60
40
20
θ [o ]
0.0
0.20.40.60.81.0Φθ/Φ0
Fig.5.Cumulative open magnetic ?ux,Φθ/Φ0,of the Coronal Hole (solid ,for θ0=45?)and Latitudinal Belt (dotted ,for θ0=50?)model.Respective curves for a constant (long dashed )and dipolar (short dashed )?eld distribution are show for compari-son;see also Fig.1for observational results.The total,surface integrated AM loss rate,˙J
W =˙J WD 3
ˉr A
4 ρA
ˉv r ,A
sin 3θd θ,
(11)
is expressed in terms of the plasma density,ρA ,and radial ?ow velocity,v r ,A ,at the Alfv′e nic point,r A ,where the ?ow velocity of the wind equals the Alfv′e n velocity (cf.Holzwarth 2005).Whereas ρA ,v r ,A ,and r A are functions of the co-latitude,θ,and subject to the latitude-dependent ?eld distributions,Eq.(6),the respective quantities,ˉρA ,ˉv r ,A ,and ˉr A ,are determined in the equatorial plane (θ=π/2)using the surface averaged ?eld strength,Eq.(8).The latter quantities determine the AM loss rate following the approach of Weber &Davis (1967),˙J
WD =8πτc [Myr]
1510152050100??/?c [%]0.3 1.3 2.6 4.1 5.616.435.7
6V Holzwarth and M Jardine:A further ‘degree of freedom’in the rotational evolution of stars
?0=6?10-5s -1
106
107
1081091010t [yr]
0.01
0.10
1.00
|(?e -?r e f )/?r e f |
75
o
60o
45o
30
o
θ50%=15o
?0= 2?10-5s -1
107
1081091010t [yr]
75
o
60o
45o
30o θ50%=15o
?0= 5?10-6s -1
107
1081091010t [yr]
75o
60o 45o
30o
θ50%=15
o
?0=6?10-5s -1
106
107
1081091010t [yr]
0.01
0.101.00
|(?e -?r e f )/?r e f |
59o 45o 30o
θ50%=15o
?0= 2?10-5s -1
107
1081091010t [yr]
59o
45o 30o
θ50%=15o
?0= 5?10-6s -1
107
1081091010t [yr]
59o
45o
30o
θ50%=15o
Fig.7.Relative deviations of the envelope rotation rate for the Latitudinal Belt (left )and Coronal Hole (right )?ux distributions.For 50%-open ?ux levels at low latitudes (i.e.,large co-latitudes θ50%,labels )the deviations are negative (dashed ),and for high latitudes positive (solid ).
10
6
10
7
10
8
10
9
10
10
t [yr]
10-5
10-4
10-3
?r e f [s -1]
1
10
100
?r e f /?O ?
Fig.6.Rotational evolution of the convective (thick )and radia-tive (thin )zone of stars subject to an AM loss rate according to Weber &Davis (1967).The dashed line indicates the break-up rotation rate,for which the co-rotation radius equals the actual stellar radius,?bu =
V Holzwarth and M Jardine:A further ‘degree of freedom’in the rotational evolution of stars
7
?0=6?10-5s -1
106
107
1081091010t [yr]
0.01
0.101.00|(?e -?r e f )/?r e f |
-0.25
-0.5
-1
?0= 2?10-5s -1
107
1081091010t [yr]
-0.25
-0.5
-1
?0= 5?10-6s -1
107
1081091010t [yr]
-0.25
-0.5
-1
Fig.9.Relative deviations (dashed lines indicate negative val-ues)in the case of rotation-dependent 50%-open ?ux levels θ50%=90?(?/?⊙)n rd ,with n rd =?0.25,?0.5,and ?1(labels ).Its value is constrained to the range 15?≤θ50%≤60?.Latitudinal Belt and the bi-modal Coronal Hole model yield rotational evolutions which are within a tolerance of 15%con-sistent.In the special case of a dipolar ?eld distribution (with f (θ)=cos θand θ50%=45?,Fig.5),the correspondency is found to be good within about 10%.
Observations show that surface distributions of starspots depend on the stellar rotation rate,with spots being prefer-entially located at higher latitudes the faster the star rotates.We investigate this aspect by assuming a rotation-dependent latitude of the 50%-?ux level,which follows the power law θ50%=90?(?/?⊙)n rd ,with n rd =?0.25,?0.5,and ?1;this simple relationship is only used to examine the basic e ?ects and not meant to reproduce any complex observed or theoret-ically derived relations.To avoid unrealistic high ?ux concen-trations in the vicinity of the poles or the equator,the 50%-?ux latitudes are constrained to the range 15?≤θ50%≤60?(cf.Solanki et al.1997).Figure 9shows the relative deviations of the rotation rates from the reference values in the case of a rotation-dependent LB distribution;for the CH model the re-sults are very similar.The major consequence of the rotation-dependence is the enhanced stellar spin-up and spin-down dur-ing the PMS and the late MS phase,respectively.The evolu-tionary stage at which the rotational history is altered by the shifting of magnetic ?ux to lower latitudes depends however on the actual functional dependence of θ50%(?).
https://www.360docs.net/doc/f316121922.html,parison with dynamo ef?ciency and
saturation
To examine whether the impact of non-uniform ?ux distri-butions is signi?cant with respect to other magnetic ?eld-related model assumptions,we compare the deviations de-scribed above with those obtained by successively changing the functional dependence of the magnetic ?eld strength on the stellar rotation rate in the framework of the reference cases (i.e.,with uniform ?ux distributions).
A linear dynamo e ?ciency is an acceptable approximation in the case of slowly rotating stars,but it is found to fail for fast rotators.We analyse the sensitivity of the rotational evolu-tion on changes of the dynamo e ?ciency by re-calculating the
?0=6?10-5s -1
106
107
1081091010t [yr]
0.01
0.101.00|(?e ,W D -?r e f )/?r e f |
?0= 2?10-5s -1
107
1081091010t [yr]
?0= 5?10-6s -1
107
1081091010t [yr]
Fig.10.Relative deviations in the case of non-linear dynamo e ?ciencies,?B ∝?n de .For n de =0.7,0.8,and 0.9(solid,top down )the deviations are positive,and for n de =1.3,1.2,and 1.1(dashed,top down )negative.
reference cases,but now subject to non-linear magnetic ?eld-rotation relations,?B ∝?n de
e ,with n de 1(cf.Fig.3).During the MS phase,the resulting relative deviations cover a large range between ?50%and 150%(Fig.10).Sub-linear (super-linear)dynamo e ?ciencies imply a weaker (stronger)increase o
f the magnetic ?eld strength with rotation rate and conse-quently a moderation (enhancement)of the magnetic braking.Their in?uence is therefore qualitatively similar to rotation-dependent concentrations of magnetic ?ux at high and low lat-itude,respectively.To determine explicit relations between the dynamo e ?ciency and the location of the 50%-open ?ux level,we generate grids of rotational histories with di ?erent n de -and θ50%-values,and associate correspondin
g values by comparing the relative derivations of the rotation rate from the reference case 2.Figure 11shows quadratic ?ts of the resulting grid-based relations for the LB and CH ?ux distribution.The relationships show that non-uniform ?ux distributions can imitate a large range (here:between ?45%and 15%)of dynamo e ?ciencies and,consequently,if not taken properly into account,conceal them from an observational determination.
The limiting ?eld strength beyond which dynamo satura-tion occurs is referred to in terms of a critical rotation rate,?sat ,that is ?B (?e >?sat )=?B (?sat ).We repeat our calculations of the reference cases under the assumption of saturation rotation rates in the range of ?sat =2?80?⊙(see Fig.12for exam-ples).The saturated magnetic braking causes an enhanced spin-up during the PMS phase,higher rotation rates on the ZAMS,and a weaker spin-down during the MS phase until the rota-tion rate descends into the regime of the non-saturated dynamo.We compare the rotational histories resulting from a saturated magnetic braking with those resulting from non-uniform ?ux distributions to associate 50%-open ?ux level with correspond-ing dynamo saturation rates (Fig.13).For given initial stellar rotation rates and ?ux distributions,the curves 3describe nomi-nal dynamo saturations which cause similar rotational histories
8
V Holzwarth and M Jardine:A further ‘degree of freedom’in the rotational evolution of stars
0.600.700.800.901.001.101.20n d e
LB
80
7060
50
40
30
20
10
θ50% [o ]
0.6
0.70.80.91.0n d e
CH
Fig.11.Relationships between the dynamo e ?ciency,n de ,and the latitude,θ50%,of the 50%-open ?ux level in the case of the Latitudinal Belt (LB,top )and Coronal Hole (CH,bottom )distributions.The initial stellar rotation rates are ?0=6·10?5(solid,crosses ),2·10?5(long dashed,triangles ),and 5·10?6s ?1(short dashed,rhombs ).
?0=6?10-5s -1
107
1081091010t [yr]
0.01
0.101.00(?e -?r e f )/?r e f
?0= 2?10-5s -1
107
1081091010t [yr]
?0= 5?10-6s -1
107
1081091010t [yr]
Fig.12.Relative deviations of the envelope rotation rate in the case of a dynamo saturation beyond ?sat =10(solid ),20(long dashed ),30(short dashed ),40(dashed-dotted ),and 50?⊙(dotted ).
like a non-uniform ?ux distribution with a 50%-open ?ux level at the respective co-latitude.If the actual dynamo saturation rate is larger than then nominal one,the rotational evolution is likely to be dominated by the impact of the non-uniform ?ux distribution.If,in contrast,the actual dynamo saturation rate is smaller than the nominal one,then the behaviour of the magnetic dynamo is expected to dominate the evolution.A concentration of magnetic ?ux at high latitudes of rapidly rotating stars can therefore imitate a rotational evolution like a dynamo saturation limit of about 30?40?⊙.In case a con-siderable amount of open ?ux is located at intermediate or low latitudes,as indicated by recent ?eld reconstructions based on ZDI observations,the nominal saturation level would be rather high ( 60?⊙)and therefore probably beyond the actual dy-
V Holzwarth and M Jardine:A further‘degree of freedom’in the rotational evolution of stars9
are usually limited to particular and illustrative cases.Another approach to include a non-uniform magnetic?eld topology is the stellar wind model of Mestel&Spruit(1987),which incor-porates in the vicinity of the stellar surface polar‘wind’and equatorial‘dead zones’,the latter preventing plasma escaping from the star and thus reducing both the mass and AM loss rate.Whereas in this model the extent of the dead zone depends on the rotation rate of the star,the magnetic?eld distribution at the surface is prescribed to be dipolar.Based on the for-malism of Mestel(1968)and Mestel&Spruit(1987),Kawaler (1988)derived a parametrised description of stellar AM loss rates through stellar winds,which also comprises qualitative variations of the magnetic?eld topology;a de?nite association of non-uniform magnetic?ux distributions with the respective model parameter is however missing.Although it remains to be investigated how more complex?ux distributions alter the magnetic?eld topology of stellar winds including e?ects like collimation or dead zones,we deem these aspects to be less crucial since our analyses are based on relative deviations be-tween two rotational histories.However,more detailed studies concerning this hypothesis are required.
The surface averaged magnetic?eld strengths,cover-ing here roughly two orders of magnitude over the range of relevant rotation rates,are consistent with observations both in the case of the Sun and rapidly rotating stars(e.g., Donati&Collier Cameron1997).The localised peak?eld strengths are,depending on the location of the50%-open?ux level and the non-uniformity of the?ux distribution,even larger (up to the order of kilo-Gauss),which is also in agreement with observations.
The even?ux distribution of the Coronal Hole model and the peaked distribution of the Latitudinal Belt model simu-late complementary non-uniformities and allow us to assess the sensitivity of the results beyond our50%-open?ux classi?ca-tion.Whereas both cases are consistent within 15%,we ex-pect this tolerance level to be larger for more complex?ux dis-tributions.But in view of the current observational and model limitations a more sophisticated classi?cation scheme appears yet to be inappropriate.
The thermal wind properties are described by solar-like val-ues,which are taken to be independent of the rotation rate,the stellar latitude,and the evolutionary stage of the star.Although there are indications for a rotation-dependence of the coro-nal temperature and density(e.g.,Jordan&Montesinos1991; Ivanova&Taam2003),it is di?cult to derive accurate wind parameters,since observational wind signatures are veiled by the outshining coronal emission.The polytropic index ofΓ= 1.15implies an e?cient heating and thermal driving of the stel-lar wind;its value lies well in between those of similar studies (e.g.,Sakurai1985;Keppens&Goedbloed2000).It has been chosen to ensure stationary wind solutions at all latitudes even for small rotation rates,when the magneto-centrifugal driving is inherently small.This implies that the contribution of the latitude-in dependent thermal driving is relatively large com-pared with the latitude-dependent magneto-centrifugal driving. In case of a weaker thermal driving,either because of cooler coronae or a smaller energy?ux in the wind,the impact of non-uniform?ux distributions is expected to be even stronger than described above.If,in turn,magnetised winds turn out to be hotter,latitude-dependent e?ects may be diminished(given that the thermal wind properties themselves are not latitude-dependent).
The rapidly rotating stellar core represents an AM reservoir which is tapped by the envelope during the MS evolution.The e?ciency of the internal coupling,quanti?ed through a char-acteristic timescale(here determined to beτc=15Myr),is under debate,with previous studies investigating values over a very large range,from very short(solid-body rotation;e.g., Bouvier et al.1997)to very long(essentially decoupled di?er-ential rotation;Jianke&Collier Cameron1993;Allain1998) timescales.The results are typically not fully consistent with all observational constraints given by the rotational distribu-tions of stars in young open clusters of di?erent age,which may point out possible de?ciencies of previous models.In this respect the non-uniformity of surface magnetic?elds presents an additional and so far rather ignored‘degree of freedom’, which may help to match theoretical and observed rotational histories of stars.
4.2.Relevance to dynamo ef?ciency and saturation Our comparison of the impact of non-uniform?ux distributions with the in?uence of other magnetic model parameters under-lines its importance.The dynamo e?ciency,that is the depen-dence of the(here,open)?ux generation on stellar rotation,is generally accepted to increase with the rotation rate.Analytical relations based on the theory ofα?-dynamos(e.g.,between the dynamo number and the Rossby number;Noyes et al. 1984;Montesinos et al.2001)as well as empirical relation-ships between the rotation rate and magnetic activity signatures like the coronal EUV and X-ray emission(Mathioudakis et al. 1995;Hempelmann et al.1995;Pizzolato et al.2003)imply power law-dependencies over a large range of rotation rates. Skumanich(1972)found the evolution of chromospheric ac-tivity to decrease with time following?∝t?1/2.This rela-tion implies a linear increase of the characteristic stellar mag-netic?eld strength with rotation rate;an example for the com-monly agreed concept that the decrease of magnetic activity with age re?ects the evolution of the stellar AM and rota-tion rate.According to Saar(1991),it is however more the magnetic?ux which increases linearly,instead of the?eld strength.The linear dynamo e?ciency is widely used in stud-ies about the rotational evolution of stars(e.g.,Keppens et al. 1995;Krishnamurthi et al.1997).Here,for deviations from the linearity between±30%the rotation rates on the early MS are found to di?er between150%and?50%.Our analysis has shown that non-uniform?ux distributions can easily produce similar deviations.A large fraction of open?ux in the vicinity of the stellar poles can therefore compensate the in?uence of a super-linear dynamo e?ciency,feigning a less e?cient(e.g., linear)dependence on the rotation rate.
A concentration of magnetic?ux at high latitudes has qual-itatively a similar in?uence on the rotational history as a dy-namo saturation.Since both e?ects entail a reduction of the AM loss rate,their synergistic action is expected to enable even
10V Holzwarth and M Jardine:A further‘degree of freedom’in the rotational evolution of stars
higher rotation rates.Figure13allows for estimates(based on the comparison of exclusive e?ects)of the principal con-tribution to the overall reduction of the AM loss.If the sat-uration limit of the chromospheric and/or coronal emission (P sat,UV/X～3...1.5d)is representative of dynamo saturation, then we expect non-uniform?ux distributions to contribute only marginally to the reduction of the AM loss.If,however, the photometric saturation limit(P sat,phot 12h)re?ects the saturation of the dynamo mechanism,then the rotational evo-lution of most stars is dominated by the actual non-uniformity of the surface?ux distribution.But the saturation of indirect activity signatures does not a priori indicate a saturation of the underlying dynamo processes in the convective envelope,since the former also depend on,for example,atmospheric proper-ties and radiation processes which follow di?erent functional behaviours(e.g.,Unruh&Jardine1997).
Solanki et al.(1997)applied a bi-modal?ux distribution, characterised through polar?ux concentrations,to the rota-tional evolution of stars.For somewhat di?erent model param-eters than ours they found a resemblance between the rotational histories subject to their coronal hole model and a dynamo satu-ration limit of20?⊙,respectively.Since this saturation limit is of the order required to explain the presence of rapidly rotating stars(～10?20?⊙),they question the necessity of a dynamo saturation at low rotation rates and argue in favour for values 50?⊙.Whereas our investigation con?rms their results in principle,we?nd that reductions of the AM loss rate resulting from high-latitude?ux concentrations are smaller;according to our model a?ux distribution with,for example,θ50%≈15?is equivalent to a dynamo saturation limit of about40?⊙.The di?erence with respect to the Solanki et al.value(～20?⊙) may be due to di?erent model assumptions and parameters. Since our value is still below their supposed dynamo saturation limit of～50?⊙,a strict concentration of magnetic?ux around the poles would be able to dominate the rotational evolution of stars.Observations indicate,however,that the50%-open ?ux level is likely located at somewhat lower latitudes.Surface brightness maps occasionally show and dark elongated features reaching down to intermediate latitudes(Strassmeier2002,and references therein),which shift the mean50%-?ux level(av-eraged over longitude and evolutionary timescales)equator-wards.But the presence of magnetic?ux in the form of dark spots is a priori not equivalent with the presence of open mag-netic?eld lines.A more striking constraint arises from ZDI ob-servations,which in combination with?eld extrapolation tech-niques allow for the reconstruction of the magnetic?eld topol-ogy and the determination of the actual surface and latitudinal distribution of open magnetic?elds.Although the number of detailed observations is yet rather small,?rst results show that the principal part of(detectable)open?ux is apparently located at intermediate latitudes(McIvor et al.2004),which motivated our Latitudinal Belt model.The cumulated?ux distributions of AB Dor(cf.Fig.1)show that the average50%-?ux level is in-deed located between30? θ50% 60?.In this range of values our equivalent saturation limit for rapid rotators is 60?⊙and the impact of the non-uniform?ux distribution consequently smaller than the in?uence of the dynamo saturation at～50?⊙supposed by Solanki et al.(1997).In this sense,we consider the e?ect of non-uniform?ux distributions more as a comple-mentary rather than an alternative mechanism for the formation of rapid rotators,which is however based on observationally veri?able principles.
4.3.Observational constraints
Compared to the large number of observed surface brightness distributions of rapidly rotating stars(Strassmeier2002),ZDI observations of actual magnetic?ux distributions are yet rather sparse.A larger database in this?eld is required to put tighter constraints on possible open?ux distributions,that is the quali-tative and quantitative description of its non-uniformity and de-pendence on the stellar rotation rate and the evolutionary phase of the star(including its dependence on stellar mass).Whereas, for example,brightness distributions indicate a clear poleward displacement of starspots with increasing rotation rate,for open ?ux a similar relationship is yet not available.ZDI observa-tions are handicapped through insu?cient signal levels from dark surface regions,so that an unambiguous determination of the?ux topology inside dark polar caps(i.e.,whether it is mainly unipolar and open or more multi-polar and closed)is yet hardly possible(Donati&Brown1997;McIvor et al.2003).If the?eld reconstructions in the case of AB Dor and LQ Hya prove to be representative and characteristic for rapid rotators, then we consider the contributions from high-latitude regions to the total AM loss rate to be of minor importance for the ro-tational evolution of rapid rotators.
Owing to their qualitatively similar behaviour it is question-able whether the impact of non-uniform?ux distributions can be observationally separated from the in?uence of a dynamo saturation.This potentially limits the usefulness of rotation rate distributions as tests of dynamo theories,unless they are sup-plemented by more detailed information about the structure of stellar magnetic?elds.A larger observational database is re-quired to re?ne the rotation rate beyond which the location of the50%-open?ux level is high enough to cause a discernible impact on rotational distributions of cluster stars.Supposed that the limiting rotation rates for high-latitude50%-?ux levels and dynamo saturation are su?ciently low and high,respectively, it may be possible to distinguish characteristic signatures of non-uniform?ux distributions in the(di?erential)distribution of intermediate rotators with rotation rates in the domain con-strained by the two limiting values.
An important role may fall to theoretical models concern-ing the pre-eruptive evolution and post-eruptive transport of magnetic?ux to high latitudes in rapidly rotating young stars (e.g.,Granzer et al.2000;Mackay et al.2004),since they allow for a veri?cation of our insight into stellar magnetic proper-ties by means of activity proxies like(the rotational modulation of)coronal X-ray and chromospheric UV emission(Vilhu et al. 1993).Observations in the UV/EUV spectral range may also be used to re?ne our assumptions about the thermal wind proper-ties,comprising its latitudinal and rotational dependence,be-cause the total AM strongly relies on the stellar mass loss rate and on the acceleration of the wind through thermal driving.
V Holzwarth and M Jardine:A further‘degree of freedom’in the rotational evolution of stars11
5.Conclusion
Non-uniform magnetic?ux distributions have a signi?cant im-pact on the rotational evolution of stars,mimicking the e?ect of a large range of dynamo e?ciencies and saturation lim-its.They present an additional degree of freedom in the mod-elling of stellar rotational histories,which can generate dif-ferences cumulating up to200%.Neglecting their e?ect im-plies considerable uncertainties in other magnetic?eld-related model parameters such as the dynamo e?ciency of up to about 40%.Although our results are,in principle,in agreement with those of Solanki et al.(1997),we?nd the e?ect of non-uniform ?ux distributions to be less e?cient than in their investigation; whereas they?nd that a concentration of magnetic?ux at polar latitudes imitates a nominal dynamo saturation limit at20?⊙, we?nd values of about35?⊙.
Non-uniformities in the form of strong?ux concentrations at high latitudes e?ciently reduce the AM loss through magne-tised winds,entailing high stellar rotation rates.Since magnetic ?eld distributions reconstructed on the basis of ZDI observa-tions however indicate a considerable amount of open?ux at intermediate latitudes,the anticipated reduction of the AM loss is expected to be smaller than implied by frequent DI observa-tions of high-latitude starspots and polar caps.The in?uence of non-uniform?ux distributions alone thus appears to be insuf-?cient to explain the existence of very rapid rotators,but their signi?cant moderation of the AM loss rate makes the require-ments for a dynamo saturation less stringent,enabling satura-tion limits 40?⊙.
Acknowledgements.The authors are grateful for the referee’s sugges-tions,which improved the clarity of the paper.VH acknowledges?-nancial support for this research through a PPARC standard grand (PPA/G/S/2001/00144).
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英语中的比较级与最高级 详解
比较级与最高级 1.as...as 与(not) as(so)...as as...as...句型中，as的词性 第一个as是副词，用在形容词和副词的原级前，常译为“同样地”。第二个as是连词，连接与前面句子结构相同的一个句子(相同部分常省略)，可译为“同..... He is as tall as his brother is (tall) . (后面的as 为连词) 只有在否定句中，第一个as才可换为so 改错: He is so tall as his brother.（X） 2.在比较状语从句中，主句和从句的句式结构一般是相同的 与as...as 句式中第二个as一样，than 也是连词。as和than这两个连词后面的从句的结构与前面的句子大部分情况下结构是相同的，相同部分可以省略。 He picked more apples than she did. 完整的表达为: He picked more apples than she picked apples. 后而的picked apples和前面相同，用did 替代。 He walked as slowly as she did.完整表达为: He walked as slowly as she walked slowly. she后面walked slowly与前面相同，用did替代。
3.谓语的替代 在as和than 引导的比较状语从句中，由于句式同前面 主句相同，为避免重复，常把主句中出现而从句中又出现的动词用do的适当形式来代替。 John speaks German as fluently as Mary does. 4.前后的比较对象应一致 不管后面连词是than 还是as,前后的比较对象应一致。The weather of Beijing is colder than Guangzhou. x than前面比较对象是“天气”，than 后面比较对象是“广州”，不能相比较。应改为: The weather of Bejing is colder than that of Guangzhou. 再如: His handwriting is as good as me. 应改为: His handwriting is as good as mine. 5.可以修饰比较级的词 常用来修饰比较级的词或短语有: Much,even,far,a little,a lot,a bit,by far,rather,any,still,a great deal等。 by far的用法: 用于强调，意为“...得多”“最最...”“显然”等，可修饰形容词或副词的比较级和最高级，通常置于其后，但是若比较级或最高级前有冠词，则可置于其前或其后。
硬件类常用英语词汇
硬件类常用英语词汇 下面是小编整理的硬件类常用英语词汇，希望对大家有帮助。 计算机英语词汇大全 常见硬件篇 CPU：Central Processing Unit，中央处理单元，又叫中央处理器或微处理器，被喻为电脑的心脏。 LD：Laser Disk，镭射光盘，又称激光视盘。 CD：Compact Disc，压缩光盘，又称激光唱盘。 CD-ROM：Compact Disc-Read Only Memory，压缩光盘-只读记忆(存储)，又叫“只读光盘”。 VCD：Video Compact Disc，视频压缩光盘，即人们通常所说的“小影碟”。 RAM：Random Access Memory，随机存储器，即人们常说的“内存”。 ROM：Read-Only Memory，只读存储器。 Seagate：美国希捷硬盘生产商。Seagate英文意思为“通往海洋的门户”，常指通海的运河等。 Quantum：英文含意为“定量，总量”。著名硬盘商标，美国昆腾硬盘生产商(Quantum Corporation)。
Maxtor：“水晶”，美国Maxtor硬盘公司。 PCI：Peripheral Component Interconnection，局部总线(总线是计算机用于把信息从一个设备传送到另一个设备的高速通道)。PCI总线是目前较为先进的一种总线结构，其功能比其他总线有很大的提高，可支持突发读写操作，最高传输率可达132Mbps，是数据传输最快的总线之一，可同时支持多组外围设备。PCI不受制于 CPU处理器，并能兼容现有的各种总线，其主板插槽体积小，因此成本低，利于推广。 EDO：Extended Data Output，扩充数据输出。当CPU的处 理速度不断提高时，也相应地要求不断提高DRAM传送数据速度， 一般来说，FPM(Fast Page Model)DRAM传送数据速度在60-70ns，而EDO DRAM比FPM快3倍，达20ns。目前最快的是SDRAM(Synchronous DRAM，同步动态存储器)，其存取速度高 达10ns。 SDRAM：Synchronous Dynamic Random Access Memory，同步动态随机存储器，又称同步DRAM，为新一代动态 存储器。它可以与CPU总线使用同一个时钟，因此，SDRAM存储 器较EDO存储器能使计算机的性能大大提高。 Cache：英文含义为“(勘探人员等贮藏粮食、器材等的)地窖; 藏物处”。电脑中为高速缓冲存储器，是位于CPU和主存储器 DRAM(Dynamic Randon Access Memory)之间，规模较小，但 速度很高的存储器，通常由SRAM(Static Random Access
必须懂的53个电脑英文缩写
·PC：个人计算机Personal Computer ·CPU：中央处理器Central Processing Unit ·CPU Fan：中央处理器的“散热器”(Fan) ·MB：主机板MotherBoard ·RAM：内存Random Access Memory，以PC-代号划分规格，如PC-133，PC-1066，PC-2700 ·HDD：硬盘Hard Disk Drive ·FDD：软盘Floopy Disk Drive ·CD-ROM：光驱Compact Disk Read Only Memory ·DVD-ROM：DVD光驱Digital Versatile Disk Read Only Memory ·CD-RW：刻录机Compact Disk ReWriter ·VGA：显示卡(显示卡正式用语应为Display Card) ·AUD：声卡(声卡正式用语应为Sound Card) ·LAN：网卡(网卡正式用语应为Network Card) ·MODM：数据卡或调制解调器Modem ·HUB：集线器
·WebCam：网络摄影机 ·Capture：影音采集卡 ·Case：机箱 ·Power：电源 ·Moniter：屏幕，CRT为显像管屏幕，LCD为液晶屏幕 ·USB：通用串行总线Universal Serial Bus，用来连接外围装置·IEEE1394：新的高速序列总线规格Institute of Electrical and Electronic Engineers ·Mouse：鼠标，常见接口规格为PS/2与USB ·KB：键盘，常见接口规格为PS/2与USB ·Speaker：喇叭 ·Printer：打印机 ·Scanner：扫描仪 ·UPS：不断电系统 ·IDE：指IDE接口规格Integrated Device Electronics，IDE接口装置泛指采用IDE接口的各种设备
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
英语中的比较级和最高级
大多数形容词有三种形式,原级,比较级和最高级, 以表示形容词说明的性质在程度上的不同。 形容词的原级: 形容词的原级形式就是词典中出现的形容词的原形。例如: poor tall great glad bad 形容词的比较级和最高级: 形容词的比较级和最高级形式是在形容词的原级形式的基础上变化的。分为规则变化和不规则变化。 规则变化如下: 1) 单音节形容词的比较级和最高级形式是在词尾加 -er 和 -est 构成。 great (原级) (比较级) (最高级) 2) 以 -e 结尾的单音节形容词的比较级和最高级是在词尾加 -r 和 -st 构成。wide (原级) (比较级) (最高级) 3)少数以-y, -er, -ow, -ble结尾的双音节形容词的比较级和最高级是在词尾加 -er 和 -est 构成。 clever(原级) (比较级) (最高级) 4) 以 -y 结尾,但 -y 前是辅音字母的形容词的比较级和最高级是把 -y 去掉,加上 -ier 和-est 构成. happy (原形) (比较级) (最高级) 5) 以一个辅音字母结尾其前面的元音字母发短元音的形容词的比较级和最高级是双写该辅音字母然后再加 -er和-est。 big (原级) (比较级) (最高级) 6) 双音节和多音节形容词的比较级和最高级需用more 和 most 加在形容词前面来构成。 beautiful (原级) (比较级) (比较级) difficult (原级) (最高级) (最高级) 常用的不规则变化的形容词的比较级和最高级: 原级------比较级------最高级 good------better------best many------more------most much------more------most bad------worse------worst far------farther, further------farthest, furthest 形容词前如加 less 和 least 则表示"较不"和"最不 形容词比较级的用法: 形容词的比较级用于两个人或事物的比较,其结构形式如下: 主语+谓语(系动词)+ 形容词比较级+than+ 对比成分。也就是, 含有形容词比较级的主句+than+从句。注意从句常常省去意义上和主句相同的部分, 而只剩下对比的成分。
计算机英语-常见硬件
计算机英语-常见硬件 CPU：Central Processing Unit，中央处理单元，又叫中央处理器或微处理器，被喻为电脑的心脏。 RAM：Random Access Memory，随机存储器，即人们常说的"内存"。 ROM：Read－Only Memory，只读存储器。 EDO：Extended Data Output，扩充数据输出。当CPU的处理速度不断提高时，也相应地要求不断提高DRAM传送数据速度，一般来说，FPM（Fast Page Model）DRAM传送数据速度在60－70ns，而EDO DRAM比FPM快3倍，达20ns.目前最快的是SDRAM（Synchronous DRAM，同步动态存储器），其存取速度高达10ns. SDRAM：Synchronous Dynamic Random Access Memory，同步动态随机存储器，又称同步DRAM，为新一代动态存储器。它可以与CPU总线使用同一个时钟，因此，SDRAM存储器较EDO存储器能使计算机的性能大大提高。 Cache：英文含义为"（勘探人员等贮藏粮食、器材等的）地窖；藏物处"。电脑中为高速缓冲存储器，是位于CPU和主存储器DRAM（Dynamic Randon Access Memory）之间，规模较小，但速度很高的存储器，通常由SRAM（Static Random Access Memory静态存储器）组成。 CMOS：是Complementary Metal Oxide Semiconductor的缩写，含义为互补金属氧化物半导体（指互补金属氧化物半导体存储器）。CMOS是目前绝大多数电脑中都使用的一种用电池供电的存储器（RAM）。它是确定系统的硬件配置，优化微机整体性能，进行系统维护的重要工具。它保存一些有关系统硬件设置等方面的信息，在关机以后，这些信息也继续存在（这一点与RAM完全不同）。开机时，电脑需要用这些信息来启动系统。如果不慎或发生意外而弄乱了CMOS中保留的信息，电脑系统将不能正常启动。 PCI：Peripheral Component Interconnection，局部总线（总线是计算机用于把信息从一个设备传送到另一个设备的高速通道）。PCI总线是目前较为先进的一种总线结构，其功能比其他总线有很大的提高，可支持突发读写操作，传输率可达132Mbps，是数据传输最快的总线之一，可同时支持多组外围设备。PCI不受制于CPU处理器，并能兼容现有的各种总线，其主板插槽体积小，因此成本低，利于推广。
The way的用法及其含义(二)
The way的用法及其含义（二） 二、the way在句中的语法作用 the way在句中可以作主语、宾语或表语： 1.作主语 The way you are doing it is completely crazy.你这个干法简直发疯。 The way she puts on that accent really irritates me. 她故意操那种口音的样子实在令我恼火。The way she behaved towards him was utterly ruthless. 她对待他真是无情至极。 Words are important, but the way a person stands, folds his or her arms or moves his or her hands can also give us information about his or her feelings. 言语固然重要,但人的站姿,抱臂的方式和手势也回告诉我们他(她)的情感。 2.作宾语 I hate the way she stared at me.我讨厌她盯我看的样子。 We like the way that her hair hangs down.我们喜欢她的头发笔直地垂下来。 You could tell she was foreign by the way she was dressed. 从她的穿著就可以看出她是外国人。 She could not hide her amusement at the way he was dancing. 她见他跳舞的姿势，忍俊不禁。 3.作表语 This is the way the accident happened.这就是事故如何发生的。 Believe it or not, that's the way it is. 信不信由你, 反正事情就是这样。 That's the way I look at it, too. 我也是这么想。 That was the way minority nationalities were treated in old China. 那就是少数民族在旧中
英语比较级和最高级的用法归纳
英语比较级和最高级的用法归纳 在学习英语过程中，会遇到很多的语法问题，比如比较级和最高级的用法，对于 这些语法你能够掌握吗？下面是小编整理的英语比较级和最高级的用法，欢迎阅读！ 英语比较级和最高级的用法 一、形容词、副词的比较级和最高级的构成规则 1.一般单音节词和少数以-er，-ow结尾的双音节词，比较级在后面加-er，最高级 在后面加-est; (1)单音节词 如：small→smaller→smallest short→shorter→shortest tall→taller→tallest great→greater→greatest (2)双音节词 如：clever→cleverer→cleverest narrow→narrower→narrowest 2.以不发音e结尾的单音节词，比较在原级后加-r，最高级在原级后加-st; 如：large→larger→largest nice→nicer→nicest able→abler→ablest 3.在重读闭音节(即：辅音+元音+辅音)中，先双写末尾的辅音字母，比较级加-er，最高级加-est; 如：big→bigger→biggest hot→hotter→hottest fat→fatter→fattest 4.以“辅音字母+y”结尾的双音节词，把y改为i，比较级加-er，最高级加-est; 如：easy→easier→easiest heavy→heavier→heaviest busy→busier→busiest happy→happier→happiest 5.其他双音节词和多音节词，比较级在前面加more，最高级在前面加most; 如：bea utiful→more beautiful→most beautiful different→more different→most different easily→more easily→most easily 注意：(1)形容词最高级前通常必须用定冠词 the，副词最高级前可不用。 例句： The Sahara is the biggest desert in the world. (2) 形容词most前面没有the，不表示最高级的含义，只表示"非常"。 It is a most important problem. =It is a very important problem.
电子类常用缩写(英文翻译)
电子类常用缩写(英文翻译) AC(alternating current) 交流(电) A／D(analog to digital) 模拟／数字转换 ADC(analog to digital convertor) 模拟／数字转换器 ADM(adaptive delta modulation) 自适应增量调制 ADPCM(adaptive differential pulse code modulation) 自适应差分脉冲编码调制 ALU(arithmetic logic unit) 算术逻辑单元 ASCII(American standard code for information interchange) 美国信息交换标准码 AV(audio visual) 声视，视听 BCD(binary coded decimal) 二进制编码的十进制数 BCR(bi-directional controlled rectifier)双向晶闸管 BCR(buffer courtier reset) 缓冲计数器 BZ(buzzer) 蜂鸣器，蜂音器 C(capacitance，capacitor) 电容量，电容器 CATV(cable television) 电缆电视 CCD(charge-coupled device) 电荷耦合器件 CCTV(closed-circuit television) 闭路电视 CMOS(complementary) 互补MOS CPU(central processing unit)中央处理单元 CS(control signal) 控制信号 D(diode) 二极管 DAST(direct analog store technology) 直接模拟存储技术 DC(direct current) 直流 DIP(dual in-line package) 双列直插封装 DP(dial pulse) 拨号脉冲 DRAM(dynamic random access memory) 动态随机存储器 DTL(diode-transistor logic) 二极管晶体管逻辑 DUT(device under test) 被测器件 DVM(digital voltmeter) 数字电压表 ECG(electrocardiograph) 心电图 ECL(emitter coupled logic) 射极耦合逻辑 EDI(electronic data interchange) 电子数据交换 EIA(Electronic Industries Association) 电子工业联合会 EOC(end of conversion) 转换结束 EPROM(erasable programmable read only memory) 可擦可编程只读存储器 EEPROM(electrically EPROM) 电可擦可编程只读存储器 ESD(electro-static discharge) 静电放电 FET(field-effect transistor) 场效应晶体管 FS(full scale) 满量程 F／V(frequency to voltage convertor) 频率／电压转换 FM(frequency modulation) 调频
(完整版)the的用法
定冠词the的用法： 定冠词the与指示代词this ,that同源,有“那(这)个”的意思,但较弱,可以和一个名词连用,来表示某个或某些特定的人或东西. (1)特指双方都明白的人或物 Take the medicine.把药吃了. (2)上文提到过的人或事 He bought a house.他买了幢房子. I've been to the house.我去过那幢房子. (3)指世界上独一无二的事物 the sun ,the sky ,the moon, the earth (4)单数名词连用表示一类事物 the dollar 美元 the fox 狐狸 或与形容词或分词连用,表示一类人 the rich 富人 the living 生者 (5)用在序数词和形容词最高级,及形容词等前面 Where do you live?你住在哪? I live on the second floor.我住在二楼. That's the very thing I've been looking for.那正是我要找的东西. (6)与复数名词连用,指整个群体 They are the teachers of this school.(指全体教师) They are teachers of this school.(指部分教师) (7)表示所有,相当于物主代词,用在表示身体部位的名词前 She caught me by the arm.她抓住了我的手臂. (8)用在某些有普通名词构成的国家名称,机关团体,阶级等专有名词前 the People's Republic of China 中华人民共和国 the United States 美国 (9)用在表示乐器的名词前 She plays the piano.她会弹钢琴. (10)用在姓氏的复数名词之前,表示一家人 the Greens 格林一家人(或格林夫妇) (11)用在惯用语中 in the day, in the morning... the day before yesterday, the next morning... in the sky... in the dark... in the end... on the whole, by the way...
英语比较级和最高级的用法
More than的用法 A. “More than+名词”表示“不仅仅是” 1)Modern science is more than a large amount of information. 2)Jason is more than a lecturer; he is a writer, too. 3) We need more than material wealth to build our country.建设我们国家，不仅仅需要物质财富. B. “More than+数词”含“以上”或“不止”之意，如： 4)I have known David for more than 20 years. 5)Let's carry out the test with more than the sample copy. 6) More than one person has made this suggestion. 不止一人提过这个建议. C. “More than+形容词”等于“很”或“非常”的意思，如： 7)In doing scientific experiments, one must be more than careful with the instruments. 8)I assure you I am more than glad to help you. D. more than + (that)从句，其基本意义是“超过（=over）”，但可译成“简直不”“远非”.难以，完全不能（其后通常连用情态动词can） 9) That is more than I can understand . 那非我所能懂的. 10) That is more than I can tell. 那事我实在不明白。 11) The heat there was more than he could stand. 那儿的炎热程度是他所不能忍受的 此外，“more than”也在一些惯用语中出现，如： more...than 的用法 1. 比……多，比……更 He has more books than me. 他的书比我多。 He is more careful than the others. 他比其他人更仔细。 2. 与其……不如 He is more lucky than clever. 与其说他聪明，不如说他幸运。 He is more （a）scholar than （a）teacher. 与其说他是位教师，不如说他是位学者。 注：该句型主要用于同一个人或物在两个不同性质或特征等方面的比较，其中的比较级必须用加more 的形式，不能用加词尾-er 的形式。 No more than/not more than 1. no more than 的意思是“仅仅”“只有”“最多不超过”，强调少。如： --This test takes no more than thirty minutes. 这个测验只要30分钟。 --The pub was no more than half full. 该酒吧的上座率最多不超过五成。-For thirty years，he had done no more than he （had）needed to. 30年来，他只干了他需要干的工作。 2. not more than 为more than （多于）的否定式，其意为“不多于”“不超过”。如：Not more than 10 guests came to her birthday party. 来参加她的生日宴会的客人不超过十人。 比较： She has no more than three hats. 她只有3顶帽子。（太少了） She has not more than three hats. 她至多有3顶帽子。（也许不到3顶帽子） I have no more than five yuan in my pocket. 我口袋里的钱最多不过5元。（言其少） I have not more than five yuan in my pocket. 我口袋里的钱不多于5元。（也许不到5元） more than, less than 的用法 1. （指数量）不到，不足 It’s less than half an hour’s drive from here. 开车到那里不到半个钟头。 In less than an hour he finished the work. 没要上一个小时，他就完成了工作。 2. 比……（小）少 She eats less than she should. 她吃得比她应该吃的少。 Half the group felt they spent less than average. 半数人觉得他们的花费低于平均水平。 more…than,/no more than/not more than (1)Mr．Li is ________ a professor; he is also a famous scientist． (2)As I had ________ five dollars with me, I couldn’t afford the new jacket then． (3)He had to work at the age of ________ twelve． (4)There were ________ ten chairs in the room．However, the number of the children is twelve． (5)If you tel l your father what you’ve done, he’ll be ________ angry． (6)－What did you think of this novel? －I was disappointed to find it ________ interesting ________ that one． 倍数表达法 1. “倍数+形容词（或副词）的比较级+than+从句”表示“A比B大（长、高、宽等）多少倍” This rope is twice longer than that one.这根绳是那根绳的三倍（比那根绳长两倍）。The car runs twice faster than that truck.这辆小车的速度比那辆卡车快两倍（是那辆卡车的三倍）。 2. “倍数+as+形容词或副词的原级+as+从句”表示“A正好是B的多少倍”。
硬件常用的英文缩写
南桥芯片（South Bridge） 北桥芯片（North Bridge） Memory Controller Hub (MCH)－内存控制中心，Intel 8xx（例如820或840）芯片组中用于控制AGP、CPU、内存（RDRAM）等组件工作的芯片。 ICH（Input/Output Controller Hub，输入/输出控制中心） Front Buffer，前置缓冲 FSAA（Full Scene Anti－aliasing，全景抗锯齿） FSB: Front Side Bus，前置总线，即外部总线 FSE（Frequency Shifter Effect，频率转换效果） FSUB（Floationg Point Subtraction，浮点减） FTP（File Transfer Protocol，文件传输协议） FWH（Firmware Hub，固件中心） GART（Graphic Address Remappng Table，图形地址重绘表） GDI（Graphics Device Interface，图形设备接口） Ghost:（General Hardware Oriented System Transfer，全面硬件导向系统转移） Gigabyte GMCH（Graphics & Memory Controller Hub，图形和内存控制中心） GMR（giant magnetoresistive，巨型磁阻） Gouraud Shading，高洛德描影，也称为内插法均匀涂色 GPF（General protect fault，一般保护性错误） GPIs（General Purpose Inputs，普通操作输入） GPS（Global Positioning System，全球定位系统） GPU（Graphics Processing Unit，图形处理器） GTF（Generalized Timing Formula，一般程序时间，定义了产生画面所需要的时间，包括了诸如画面刷新率等） GUI（Graphics User Interface，图形用户界面） GVPP（Generic Visual Perception Processor，常规视觉处理器） HAL（Hardware Abstraction Layer，硬件抽像化层） hardware motion compensation（硬件运动补偿） HCI: Host Controller Interface，主机控制接口 HCT：Hardware Compatibility Test，硬件兼容性测试 HDA（head disk assembly，磁头集合） HDSL: High bit rate DSL，高比特率数字订阅线路 HDTV（high definition television，高清晰度电视） HEL: Hardware Emulation Layer（硬件模拟层） HiFD（high-capacity floppy disk，高容量软盘） high triangle count（复杂三角形计数）
学电脑必懂的53个英文单词和缩写
学电脑必懂的53个英文单词和缩写（我不信你都认识） 潜龙飞天发表于2010年06月28日 09:36 阅读(1) 评论(0) 分类：个人日记 举报 PC：个人计算机Personal Computer ·CPU：中央处理器Central Processing Unit ·CPU Fan：中央处理器的“散热器”(Fan) ·MB：主机板MotherBoard ·RAM：内存Random Access Memory，以PC-代号划分规格，如PC-133，PC-1066，PC-2700 ·HDD：硬盘Hard Disk Drive ·FDD：软盘Floopy Disk Drive ·CD-ROM：光驱Compact Disk Read Only Memory ·DVD-ROM：DVD光驱Digital Versatile Disk Read Only Memory ·CD-RW：刻录机Compact Disk ReWriter ·VGA：显示卡(显示卡正式用语应为Display Card) ·AUD：声卡(声卡正式用语应为Sound Card) ·LAN：网卡(网卡正式用语应为Network Card) ·MODM：数据卡或调制解调器Modem ·HUB：集线器
·WebCam：网络摄影机 ·Capture：影音采集卡 ·Case：机箱 ·Power：电源 ·Moniter：屏幕，CRT为显像管屏幕，LCD为液晶屏幕 ·USB：通用串行总线Universal Serial Bus，用来连接外围装置 ·IEEE1394：新的高速序列总线规格Institute of Electrical Ａnd Electronic Engineers ·Mouse：鼠标，常见接口规格为PS/2与USB ·KB：键盘，常见接口规格为PS/2与USB ·Speaker：喇叭 ·Printer：打印机 ·Scanner：扫描仪 ·UPS：不断电系统 ·IDE：指IDE接口规格Integrated Device Electronics，IDE接口装置泛指采用IDE接口的各种设备 ·SCSI：指SCSI接口规格Small Computer System Interface，SCSI 接口装置泛指采用SCSI接口的各种设备 ·GHz：(中央处理器运算速度达)Gega赫兹/每秒 ·FSB：指“前端总线(Front Side Bus)”频率，以MHz为单位 ·ATA：指硬盘传输速率ATAttachment，ATA-133表示传输速率为133MB/sec
“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.
计算机硬件英文缩写
计算机硬件英汉对照表 VDD、VCC 电源 5VSB = 5V StandBy 待机5V电源 Acer--> 宏基公司?]@8 A/D--> 模拟/数据(@= Address bus--> 地址总线-=:!g ALT=Alternate--> 转换键/更改/更动=. ALT=Alteration Switch--> 转换开关rP AMD=Advanced Micro Devices Inc. --> 高级微设备公司G^(WN AMI=American Megatrends Inc. --> 美国米格特雷德公司%@lu~ AGP=Accelerated Graphics Port --> 图形加速端口} API=Application Program Interface --> 应用程序接口Z6#e9- APM=Advanced Power Driver --> 高级动力驱动器"^p!"_ ASCII=American Standard Code for Information Interchange 美国信息交换用标准码t2L BIN --> 收集器/二进制+ZTo-u BIOS=Basic Input/Output System --> 基本输入输出系统V%iI` Bit --> 位=RQ Block --> 模块d BS=Backspace --> 退格键^l[?7 Cache --> 高速缓存X9
使用电脑必懂的53个英文单词和缩写
使用电脑必懂的53个英文单词和缩写
使用电脑必懂的53个英文单词和缩写 ·PC：个人计算机Personal Computer ·CPU：中央处理器Central Processing Unit ·CPU Fan：中央处理器的“散热器”(Fan) ·MB：主机板MotherBoard ·RAM：内存Random Access Memory，以PC-代号划分规格，如PC-133，PC-1066，PC-2700 ·HDD：硬盘Hard Disk Drive ·FDD：软盘Floopy Disk Drive ·CD-ROM：光驱Compact Disk Read Only Memory ·DVD-ROM：DVD光驱Digital Versatile Disk Read Only Memory ·CD-RW：刻录机Compact Disk ReWriter ·VGA：显示卡(显示卡正式用语应为Display Card) ·AUD：声卡(声卡正式用语应为Sound Card) ·LAN：网卡(网卡正式用语应为Network Card) ·MODM：数据卡或调制解调器Modem ·HUB：集线器 ·WebCam：网络摄影机 ·Capture：影音采集卡 ·Case：机箱 ·Power：电源
·Moniter：屏幕，CRT为显像管屏幕，LCD为液晶屏幕 ·USB：通用串行总线Universal Serial Bus，用来连接外围装置·IEEE1394：新的高速序列总线规格Institute of Electrical Ａnd Electronic Engineers ·Mouse：鼠标，常见接口规格为PS/2与USB ·KB：键盘，常见接口规格为PS/2与USB ·Speaker：喇叭 ·Printer：打印机 ·Scanner：扫描仪 ·UPS：不断电系统 ·IDE：指IDE接口规格Integrated Device Electronics，IDE接口装置泛指采用IDE接口的各种设备 ·SCSI：指SCSI接口规格Small Computer System Interface，SCSI接口装置泛指采用SCSI接口的各种设备 ·GHz：(中央处理器运算速度达)Gega赫兹/每秒 ·FSB：指“前端总线(Front Side Bus)”频率，以MHz为单位·ATA：指硬盘传输速率AT Attachment，ATA-133表示传输速率为133MB/sec ·AGP：显示总线Accelerated Graphics Port，以2X，4X，8X表示传输频宽模式 ·PCI：外围装置连接端口Peripheral Component Interconnect ·ATX：指目前电源供应器的规格，也指主机板标准大小尺寸·BIOS：硬件(输入/输出)基本设置程序Basic Input Output System