Chemical Evolution of the Galaxy Based on the Oscillatory Star Formation History

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Accepted to ApJ CHEMICAL EVOLUTION OF THE GALAXY BASED ON THE OSCILLATORY STAR FORMATION HISTORY Hiroyuki Hirashita 1Department of Astronomy,Faculty of Science,Kyoto University,Sakyo-ku,Kyoto 606-8502,Japan hirasita@kusastro.kyoto-u.ac.jp Andreas Burkert Max-Planck-Institut f¨u r Astronomie,K¨o nigstuhl 17,D-69117Heidelberg,Germany burkert@mpia-hd.mpg.de and Tsutomu T.Takeuchi Division of Particle and Astrophysical Sciences,Nagoya University,Chikusa-ku,Nagoya 464-8602,Japan takeuchi@u.phys.nagoya-u.ac.jp ABSTRACT We model the star formation history (SFH)and the chemical evolution of the Galac-

tic disk by combining an infall model and a limit-cycle model of the interstellar medium (ISM).Recent observations have shown that the SFH of the Galactic disk violently vari-ates or oscillates.We model the oscillatory SFH based on the limit-cycle behavior of the fractional masses of three components of the ISM.The observed period of the oscillation (～1Gyr)is reproduced within the natural parameter range.This means that we can interpret the oscillatory SFH as the limit-cycle behavior of the ISM.We then test the chemical evolution of stars and gas in the framework of the limit-cycle model,since the oscillatory behavior of the SFH may cause an oscillatory evolution of the metallicity.We ?nd however that the oscillatory behavior of metallicity is not prominent because the metallicity re?ects the past integrated SFH.This indicates that the metallicity cannot be used to distinguish an oscillatory SFH from one without oscillations.

Subject headings:galaxies:ISM—Galaxy:evolution—Galaxy:stellar content—

stars:abundances—stars:formation

1.INTRODUCTION

Revealing the star formation histories(SFHs)of galaxies is essential in understanding the galaxy formation and evolution.The SFH of the Galaxy(Milky Way)is worth studying,since a large number of stars are observed individually and the SFH is inferred directly from the age distribution of the stars.The SFH is closely related to the chemical evolution of the Galaxy.For example,the age–metallicity relation(e.g.,Pagel1997)of Galactic stars is generally believed to originate from the chemical enrichment of the Galaxy as a result of star formation.

Eggen,Lynden-Bell,&Sandage(1962)have pioneered the modeling of the Galactic SFH and its chemical evolution.From the correlation between the ultraviolet excess and orbital eccentricity of stars,they have concluded that the Galaxy formed by collapse on a free-fall timescale from a single protogalactic cloud.An alternative picture of halo formation has been proposed by Searle &Zinn(1978).They have argued that the Galactic system formed from the capture of fragments such as dwarf galaxies over a longer timescale than that proposed by Eggen et al.In any case, determining the timescale of the infall of matter and the chemical enrichment is an important issue to resolve the formation history of the Galaxy.

A number of papers have investigated the formation(e.g.,Burkert,Truran,&Hensler1992) and chemical evolution(e.g.,Matteucci&Fran?c ois1989)of the Galaxy and other spiral galaxies (e.g.,Lynden-Bell1975;Sommer-Larsen1996).Many models of the SFH of the Galaxy have treated the formation of the Galactic disk through gas infall from the halo.This scenario(the so-called infall model)can be consistent with the age–metallicity relation of the disk stars(e.g.,Twarog 1980),if a reasonable SFH is used.Moreover,the infall model provides a physically reasonable way of solving the G-dwarf problem(e.g.,Pagel1997,p.236),contrary to the closed-box model which tends to overpredict the number of the low-metallicity stars.

Since stars are formed from interstellar medium(ISM),one of the factors that determine the star formation rate(SFR)is the gas content of galaxies.Indeed,the SFR and the gas density is closely related(Kennicutt1998).The most commonly used relation is called the Schmidt law (Schmidt1959).It assumes that SFR∝ρn,whereρis the gas density and n=1–2.As long as such a law is assumed and the infall of gas occurs continuously as a smooth function of time,the predicted SFH is also a smooth function of time.

Though the“classical”(i.e.,smooth)infall model is widely accepted,there are observational data that suggest intermittent or oscillatory star formation activities in spiral galaxies.This means that the SFH is not a smooth function of time.Kennicutt,Tamblyn,&Congdon(1994)have shown that the ratio of present-to-past SFR in spiral sample has a signi?cant scatter.More recently, Tomita,Tomita&Saitˉo(1996)have analyzed the far-infrared to B-band?ux ratio f FIR/f B of

1681spiral galaxies(see also Devereux&Hameed1997).The indicator f FIR/f B represents the ratio between the present SFR and the averaged SFR over the recent Gyr.They have shown order-of-magnitude spread of f FIR/f B and suggested a violent temporal variation of the SFR.

The intermittence of the SFH in the Galactic disk is recently suggested by Rocha-Pinto et al.(2000a,hereafter R00).They have provided the SFH of the Galaxy inferred from the stellar age of the solar neighborhood,using552late-type stars.The age of each star has been estimated from the chromospheric emission in the Ca ii H and K lines(Soderblom,Duncan,&Johnson1991). After metallicity-dependent age correction,completeness correction,and scale-height correction2, they have derived the age distribution of the stars.Then,after correcting for evolved stars,they have derived the SFH.They have also asserted that their SFH derived from the stars in the solar neighborhood is representative of the SFH in the whole disk,since the di?usion timescale of stars is much shorter than the Galactic age.The discussion in this paper is based on Figure2of R00.Based on their data,R00have suggested that the star formation activity of the disk is intermittent or variates violently.Their suggestion has been statistically con?rmed by Takeuchi&Hirashita(2000, hereafter TH00),who have also shown that the typical timescale of the variation is2Gyr.We note that Hernandez,Valls-Gabaud,&Gilmore(2000)have also found an oscillatory component of the SFH in the solar neighborhood.

Theoretically,the intermittent or oscillatory SFH is easily reproduced if we treat the ISM as a nonlinear open system(Ikeuchi1988).Ikeuchi&Tomita(1983,hereafter IT83)have considered the ISM composed of three phases(cold,warm,and hot)as suggested by McKee&Ostriker(1977) and modeled the time evolution of the fractional masses of the three components(see also Habe, Ikeuchi,&Tanaka1981).Since the mass exchange among the three components is a nonlinear process,the limit-cycle evolution of the fractional masses can emerge(see also Scalo&Struck-Marcell1986;Korchagin,Ryabstev,&Vorobyov1994).The limit-cycle behavior is supported by Kamaya&Takeuchi(1997),who have interpreted the various levels of the star formation activities in spiral galaxies shown observationally by Tomita et al.(1996)in the framework of the nonlinear open system model.Their interpretation is based on the galaxy-wide limit-cycle behavior of the ISM.

Another interesting topic is the chemical evolution in such a limit-cycle ISM.If the oscillatory SFH is considered,we may?nd an oscillation in a chemical enrichment process.For example,the age–metallicity relation of the stars in the Galactic disk may scatter because of the oscillation.We will examine quantitatively such a scatter caused by the limit-cycle evolution.

In this paper,we model the oscillatory SFH in the Galactic disk proposed by R00by combining the infall model and the limit-cycle model.The chemical evolution in the oscillatory SFH is also investigated.This paper is organized as follows.First,in§2we model the chemical evolution of the Galactic disk by using the infall model.Then,in§3we review the limit-cycle model of ISM.

Some results derived from the equations are described in§4.Finally,we discuss the SFH and the chemical evolution in the limit-cycle ISM in§5.

2.CHEMICAL EVOLUTION MODEL

The chemical evolution model of the Galactic disk is constructed here.The model is based on the infall model,which is characterized by the gradual gas infall from the halo.We adopt a one-zone model for simplicity.In other words,the phenomena of the ISM are averaged in space.This simple treatment is advantageous because the response of the chemical evolution on the parameters is easy to examine.When we compare the result with the observational data,however,we should be careful whether the data are averaged or not.We comment on the one-zone approximation in §3.4.

2.1.Gas and Metal

The changing rates of the gas mass(M g)and metal mass(M i,where i denotes the species of the metal;i=Fe,O,etc.)in the Galactic disk are described by a set of di?erential equations

dM g

=?X iψ+E i+F X f i,(2)

dt

whereψis the SFR,E is the total injection rate of gas from stars,F is the rate of gas infall from halo,X i is the abundance of i(i.e.,X i≡M i/M g),E i is the injection rate of element i from stars, and X f i is the abundance of i in the infall material(see e.g.,Tinsley1980for the basic treatment of chemical evolution of galaxies).Introducing X f i enables us to treat the infall of pre-enriched gas. An early enrichment in the halo may be important for the initial phase of the disk formation(e.g., Ikuta&Arimoto1999).

In this paper,we choose two tracers for the metallicity,O and Fe.Almost all the oxygen is produced by high-mass stars,while the iron is produced mainly by Type Ia supernovae(SNe)as well as by high-mass stars.Thus,we include the contribution from Type Ia SNe in our formulation.We adopt the combination of the instantaneous recycling approximation and the delayed production approximation as formulated by Pagel&Tautvaiˇs ien˙e(1995).The evolution of Fe abundance based on a model of Type Ia SN has been considered in Kobayashi et al.(1998).With these approximations,E and E i at t are expressed by using the SFR as a function of time,ψ(t): E=R insψ(t)+R delψ(t?τ),(3)

E i=[R ins X i(t)+Y i,ins]ψ(t)+[R del X i(t?τ)+Y i,del]ψ(t?τ),(4) where R and Y i are the returned fraction of gas from stars and the fractional mass of the newly formed element i,respectively,and the subscripts“ins”and“del”denote the instantaneous recycling

and delayed production parts,respectively.The delay timeτis set to1.3Gyr,according to§3of Pagel&Tautvaiˇs ien˙e(1995).

We assume that the disk begins to form at t=0.Its age is assumed to be15Gyr.When t?τ<0,all the functions whose arguments depend on(t?τ)are set to zero;for example,ψ(t?τ)=0when t<τ.The initial condition is summarized in§3.5.

With the above expressions(eqs.[3]and[4]),equation(1)becomes

dM g

dt

=Y i,insψ(t)+Y i,delψ(t?τ)+R delψ(t?τ)[X i(t?τ)?X i(t)]

?F(t)[X i(t)?X f i].(6)

2.2.Infall Rate of Gas

For the infall rate F,we follow TH00.They assumed an exponential form for the infall rate

F(t)=

M0

dt =?(1?R ins)?ψ(t)+R del?ψ(t?τ)+

1

M0

and?ψ≡

ψ

dt

=Y i,ins?ψ(t)+Y i,del?ψ(t?τ)+R del?ψ(t?τ)[X i(t?τ)?X i(t)]?X i(t)?X f i

2.3.Star Formation Law

In order to include the three-phase model of the ISM composed of cold,warm and hot com-ponents,we modify the Schmidt law with the index n=1(Schmidt1959)as

ψ=M g X cold/t?,(12) where X cold is the mass ratio of the cold component to the total gas mass(M g)and t?is the timescale of the cold-gas consumption to form stars.In other words,we consider that stars are formed from cold clouds on a gas consumption timescale of t?.The time evolution of X cold will be modeled based on IT83,which treated the ISM as a nonlinear open system,in§3.Equation(12) is equivalent to

?ψ=f

g X cold/t?.(13)

2.4.Choice of the Parameters of the Chemical Evolution

According to Pagel&Tautvaiˇs ien˙e(1995),we choose the fractional masses of newly formed elements(see eq.[4])as follows:Y O,ins/X O⊙=0.70,Y O,del/X O⊙=0.0,Y Fe,ins/X Fe⊙=0.28,and Y Fe,del/X Fe⊙=0.42,where the subscript⊙indicates the solar value.They explained the observed metallicity of Galactic stars along with an infall model.For the abundances in the in?ow gas,we examine two cases:one is the primordial case,(X f Fe/X Fe⊙,X f O/X O⊙)=(0,0);the other is the pre-enriched case,(X f Fe/X Fe⊙,X f O/X O⊙)=(0.1,0.25)3.The parameter in the delayed production approximation,τ,is set asτ=1.3Gyr.The returned fractions of gas,R ins and R del,are determined as follows:R ins=0.16,and R del=0.13.The details about these values are described in Appendix A.We will determine t?and t in in§3.2.

3.LIMIT-CYCLE MODEL OF THE ISM

We model the oscillatory behavior of the Galactic SFH proposed by R00.IT83have shown that an oscillatory behavior of the fractional masses of three components(cold,warm,and hot) emerges if one considers the ISM to be a nonlinear open system.An introduction and details concerning nonlinear open systems are found in Nicolis&Prigogine(1977).We adopt the model by IT83to explain the oscillatory SFH by R00.

As long as the infall timescale(t in)is much longer than the oscillatory timescale,the e?ect of the infall on the limit-cycle evolution is not signi?cant.Indeed,as shown in Table1,for the present

case the case where t in≥9Gyr,which is much longer than the period of oscillation proposed by R00(～1Gyr;see also Takeuchi&Hirashita2000).Thus,we can apply the original model by IT83,which did not include the e?ect of infall.

Table1:Examined Parameters.

Model t sf(Gyr)t?(Gyr)t in(Gyr)

3.1.Model Equations

We review the model by IT83.This model is used to calculate the time evolution of the mass fraction of the three ISM phases(see also§1).The result is used to calculate the SFR through equation(13).

The ISM is assumed to consist of three components(McKee&Ostriker1977);the hot rare?ed gas(T～106K,n～10?3cm?3),the warm gas(T～104K,n～10?1cm?3),and cold clouds (T～102K,n～10cm?3).The fractional masses of the three components are X hot,X warm,and X cold,respectively.A trivial relation holds:

X hot+X warm+X cold=1.(14) The following three processes are considered(see IT83and Ikeuchi1988for the details):[1]the sweeping of a warm gas into a cold component at the rate of aX warm(a～5×10?8yr?1);[2]the evaporation of cold clouds embedded in a hot gas at the rate of bX cold X2hot(b～10?7–10?8yr?1);

[3]the radiative cooling of a hot gas through collisions with a warm gas at the rate of cX warm X hot (c～10?6–10?7yr?1).Writing down the rate equations and using equation(14),we obtain

dX cold

=?X hot(1?X cold?X hot)+BX cold X2hot,(16)

dτ

whereτ≡ct,A≡a/c,and B≡b/c.

The solutions of equations(15)and(16)are classi?ed into the following three types,according to the values of A and B(IT83):

1.A>1;all the orbits in the(X cold,X hot)-plane reduce to the node(0,1),

2.A<1and B>B cr;all the orbits reduce to a stable focus[(1?A)/(AB+1),A],

3.A<1and B

where B cr≡(1?2A)/A2.Apparently,case3is important in the interpretation of the oscillatory SFH shown in R00.Thus,we choose the parameters that satisfy case3as will be described in the next subsection.

3.2.Choice of Parameters of the Limit-Cycle Model

Since the timescale of the variation of SFR derived by R00is～1Gyr(see also TH00),we?rst investigate whether the period of the limit-cycle can be the order of1Gyr.Indeed,a Gyr-timescale cycle is possible in the natural parameter range.According to Figure3of IT83,the period can be ～102/c when we choose A=0.3and A=0.5.Since1/c is of the order of～106–107yr,102/c～1 Gyr is possible.Thus,we choose A=0.3or A=0.5and1/c=107yr to demonstrate the Gyr-scale oscillation of the Galactic SFH.The subsequent discussions are unchanged if we adopt another set of the parameters that satis?es the oscillation period of～1Gyr.

Here we con?rm that the adopted parameters are within the reasonable range of the physical properties of the ISM in the Galactic disk.First,Ikeuchi&Tomita(1983)estimated a from the SN rate and the maximum radius of an SN remnant(SNR)and obtained a?5×10?8yr?1.Next,we estimate b as the reciprocal of the evaporation timescale of a cold cloud.The evaporation timescale estimated in Hirashita(2000a)may be applicable in the present case and we obtain b?10?7yr?1. Finally,c is estimated from the collision rate of a cold cloud with SNRs.The collision rate t col is estimated as t col?(πR2SNR n SNR v)?1,where R SNR is the typical size of a SNR,n SNR is the number density of SNRs in the interstellar space,and v is the typical relative velocity between a SNR and a cloud.If we put R SNR=50pc,n SNR=10?6pc?3,4and v=100km s?1,we obtain t col?107 yr.This means that c?t?1col?10?7yr?1.A=0.3and B=0.5are easily satis?ed if we assume for example a=6×10?8yr,b=10?7yr,and c=2×10?7yr,all of which are consistent with the above order-of-magnitude estimates.

TH00adopted a star formation law?ψ=f g/t sf and did not consider the e?ect of a multi-component medium with phase changes.In order to use their choices of the parameter values A and1/c we must relate their t sf(the timescale in the classical smooth infall model)to our t?(the one in the oscillatory infall model).This is achieved by averaging the gas consumption rate de?ned as?ψ/f g=X cold/t?(eq.[12])over the whole galactic age where the oscillatory part of the e?ciency is smoothed out and becomes1/t sf.In other words,

?ψ/f g = X cold /t?=1/t sf,(17) where · indicates the time average of the quantity over the Galactic history(0

the three sets of(t sf,t in)as summarized in Table1.They determined the parameters by?tting their infall model to the observed SFH proposed by R00.All the three models provide an almost identical SFH and reproduce the smoothed trend of the SFH(T00).Thus,it is meaningful to examine all the three cases.However,Model A gives an infall timescale much larger than that in e.g.,Matteucci&Fran?c ois(1989),although they assumed the same time dependence of infall as that in this paper.This long timescale indicates that the infall rate is almost constant over the history of the Galactic disk.We note that Model A predicts the highest metallicity of the three models(§4).

3.3.Treatment of the Delayed Production

Here we should comment on the delayed production approximation.It assumes that all the delayed production at t is determined by the SFR at t?τ.In reality,τdi?ers among Type Ia SNe.Thus,the delayed production is determined by the averaged SFR around t?τ. Expecting that the lifetimes of Type Ia progenitors are comparable to,or longer than,1Gyr (～the period of the SFR oscillation in the Galaxy)the averaged SFR around t?τis described as M g(t?τ) X cold /t?=M g(t?τ)/t sf,where M g(t?τ)is the gas mass at t?τand equation(17)is used.Thus,we hereafter assume that

?ψ(t?τ)=f g(t?τ)

t cyc～1Gyr,we obtain c s,e?t cyc=10kpc.Thus,the information of the limit-cycle behavior can propagate over the whole disk.Thus,the assumption of the limit-cycle behavior over the whole disk may be good.In this paper,as a?rst step,we treat the model galaxy as being a one-zone object.Here we should note that the gas transport in the radial direction is di?cult if we consider the angular momentum conservation.This di?culty may be a cause of the radial gradient of the metallicity and the gas-to-star fraction in spiral galaxies.

The above discussions are not a satisfactory“proof”for the limit-cycle oscillation on the scale of the whole Galactic disk.(But it is important that it is not rejected.)At present,thus,the cyclic star formation over the whole disk is an assumption that easily explains the variation of the star formation activity observed in the solar neighborhood by R00.We note that it also explains the variety of the star formation activity of spiral galaxies(Kamaya&Takeuchi1997).Hence,in this paper,we base our discussion on the limit-cycle behavior on a whole-disk scale.

When we compare our result with the observational data,we should carefully consider to what extent the data is averaged.The range of Galactocentric radii that enter in the average depends on the age.Considering that the di?usion of stellar orbits on a scale of1kpc occurs in0.2Gyr (Wielen1977),it is reasonable to assume that the observational quantities are averaged on a scale of more than1kpc.Thus,as a?rst step,we adopt the one-zone treatment for the Galactic disk to see the chemical evolution in an oscillatory SFH.We should extend our model to multi-zone treatment as Chiappini,Matteucci,&Gratton(1997)(see also Romano et al.2000for a recent work)in the future.Observationally,the formalism in Meusinger(1991)may be useful in order to link the global observed SFH with the SFH in di?erent Galactocentric annuli.

3.5.Initial Conditions

The initial condition is set as follows:X O(t=0)=0,X Fe(t=0)=0,f g(t=0)=0, X cold(t=0)=0.1,and X hot(t=0)=0.7.The convergence to the limit-cycle occurs on the timescale of a few periods.The results are however not strongly dependent on the choice of the initial conditions for X cold and X hot.

4.RESULTS

In this section,the results calculated from the equations above are presented.They are com-pared with the observational data.Before displaying the results,we review the solving processes of the equations.First,the mass fraction of the cold gas,X cold,is calculated by equations(15) and(16).X cold is used to determine the SFR at t through equation(13).As for the delayed contribution expressed in?ψ(t?τ),we take into account the scatter of the lifetimes of progenitors of Type Ia SNe(§3.3)and assume equation(18).The SFH and the chemical evolution are modeled by the infall model.The evolution of the gas mass normalized by the total available gas mass M0is

calculated by equations(9).For t sf and t in,we examine three cases listed in Table1.These three cases are also examined in TH00.The chemical evolution is calculated by equation(11).

4.1.Star Formation History

The SFH calculated by our model is presented in Figure1a.Since the three models predict almost the same SFH as indicated by TH00,we present only the result of Model A in Table1.We also show the SFH observationally determined by R00in Figure1b in order to demonstrate the qualitative similarity between the model prediction and the observation.

Fig. 1.—(a)Simulated star formation history based on our model.The star formation rate(ψ) as a function of look-back time[(15?t)Gyr]is normalized with the time-averaged value ofψ( ψ ).Since the three models shown in Table1result in almost an identical star formation history, only Model A is shown.(b)Star formation history derived observationally by Rocha-Pinto et al. (2000a).

4.2.Metallicity Evolution

We test the model with the metallicity data of Galactic stars.Age–metallicity relation,G-dwarf metallicity distribution,and[Fe/O]–[Fe/H]relation are examined.First of all,we should note that the yields may be uncertain because of the treatment of convection,nuclear reaction rates, mass loss in the asymptotic giant branch phase,etc.If the yields are systematically larger/smaller than assumed in this paper,the metallicities predicted by our model should be systematically larger/smaller.Thus,quantitative agreement by?ne tuning of the parameters might be meaning-less.However,the qualitative behavior of the metallicity evolution in the limit-cycle ISM is not altered even if the yield changes.

4.2.1.Age–metallicity relation

The age–metallicity relation of stars in the Galactic disk provides us with information on its chemical enrichment history.Thus,our model is worth testing by using the age–metallicity relation of the stars in the solar neighborhood.The sample is provided by Rocha-Pinto et al.(2000b),which used the same sample as R00.

First,we examine the case where the infall gas is of primordial abundance[i.e.,(X f Fe/X Fe⊙, X f O/X O⊙)=(0,0)].The age–metallicity relation predicted by our model is shown in Figure2a.The solid,dotted,and dashed lines represent the results in Models A,B,and C,respectively.We also present the observational data of the age–metallicity relation by Rocha-Pinto et al.(2000b)(see their Table3).Model A predicts the highest present metallicity,since its short gas consumption timescale leads to the most e?cient chemical enrichment.Even in Model A,however,the discrepancy between the model prediction and data is signi?cant in the low-metallicity range.Rocha-Pinto et al.(2000b) noted the high initial metallicity of the disk and attributed it to the pre-enrichment of the gas before the formation of the?rst stars in the disk.They also have shown that the age–metallicity relation determined from the chromospheric age can deviate upward(i.e.,metallicity is overestimated)for larger ages from the real relation because of the uncertainty in the age estimation.Thus,we also examine the case where the infalling gas in enriched with metal[(X f Fe/X Fe⊙,X f O/X O⊙)= (0.1,0.25)].The result is shown in Figure2b.We see that the discrepancy between the model prediction and the observational data is reduced.From the viewpoint of modeling,the yield is also uncertain.Thus,we do not try any?ne-tuning the age–metallicity relation.

Fig. 2.—Age–metallicity relation of the stars in the solar neighborhood.[Fe/H]is used as an indicator for the metallicity.The solid,dotted,and dashed lines represent the results in Models A, B,and C,respectively.The squares with error bars indicate the observational data point by Rocha-Pinto et al.(2000b).(a)Abundance in the infalling gas is assumed as(a)(X f Fe/X Fe⊙,X f O/X O⊙)= (0,0)and(b)(X f Fe/X Fe⊙,X f O/X O⊙)=(0.1,0.25).

In spite of such uncertainty,we can discuss the qualitative behavior of the age–metallicity relation.The amplitude of the oscillation of metallicity is smaller than the typical scatter of the

observed data points(～0.3dex).The small amplitude is natural,because metallicity is determined by all the past history of star formation,and thus the present oscillatory star formation does not signi?cantly contribute to the metallicity.

Rocha-Pinto et al.’s data shown in Figure2seem to show a recent increase in[Fe/H].The pre-enriched infall cannot solve this increase,since the infalling gas has too low a metallicity.However, we should carefully examine whether the most recent data point in Figure2represents the SFH of the whole Galactic disk,because if the recent chemical enrichment rate in the solar neighborhood is signi?cantly higher than that in the whole Galaxy,the most recent data point would naturally show a systematically higher metallicity.Moreover,data sets shown by other authors do not necessarily show such an increase in the recent metallicity(e.g.,Twarog1980).It is necessary to analyze the observational data further before we construct a theoretical model for the recent[15?t 1(Gyr)] increase in metallicity.

We can expect that the oscillation behavior is more prominent for oxygen than for iron,because all the oxygen is produced from the“instantaneous”part(i.e.,Y O,ins?Y O,del).We present the result for the case of pre-enriched infall[i.e.,(X f Fe/X Fe⊙,X f O/X O⊙)=(0.1,0.25)]in Figure3. Indeed,the amplitude of the oscillation is larger than Figure2b.However,the oscillation would not explain the scatter of the oxygen abundance of the stars in the Galactic disk.

Fig. 3.—Age–metallicity relation of the stars in the solar neighborhood.[O/H]is used as an indicator for the metallicity.The solid,dotted,and dashed lines represent the results in Models A, B,and C,respectively.For the initial enrichment,(X f Fe/X Fe⊙,X f O/X O⊙)=(0.1,0.25)is assumed.

4.2.2.Metallicity distribution

The G-dwarf metallicity distribution is also tested along with our model,since the primary motivation for the infall model is to solve the G-dwarf problem(e.g.,Pagel1997).The probability distribution function P(log X i)of the metallicity is calculated from our model as

P(log X i)d log X i=C?ψdt,(19) where the constant C is the normalization so that

C 15Gyr0?ψdt=1.(20) From equation(19),we obtain the following analytical expression for P:

P(log X i)=C(ln10)?ψ(t)X i(t) dX i

√2σ2 du,(22)

where we adoptσ=0.1to compare with Rocha-Pinto&Maciel(1996).We adopt these data because we would like to use a sample of G-dwarfs,whose lifetimes are comparable to the age of the universe.In Figure4,we show P conv as a function of[Fe/H].The solid,dotted,and dashed lines represent the result in Models A,B,and C,respectively.The histogram shows the data by Rocha-Pinto&Maciel(1996).The two?gures(a)and(b)correspond to(X f Fe/X Fe⊙,X f O/X O⊙)=(0,0) and(X f Fe/X Fe⊙,X f O/X O⊙)=(0.1,0.25),respectively(same as Fig.2a and b,respectively).We see that Model A in Figure4b seems to be the best of all the models.However,considering the uncertainty in the yields,we do not try any?ne tuning.The excess of the observed number of stars around[Fe/H]～0.0is consistent with the data by Rocha-Pinto et al.(2000b).As stated in §4.2.1,this may be due to the recent signi?cant enrichment in the solar neighborhood.

4.2.3.Evolution of[Fe/O]

In order to test the e?ect of the limit-cycle behavior on the[Fe/O]ratio,we examine the relation between[Fe/O]and[Fe/H].Since the oxygen is mainly produced by stars with short lifetimes,the e?ect of the limit-cycle ISM is re?ected by the time evolution of the oxygen abundance.On the other hand,the iron is also produced by stars with long lifetimes and the information of the oscillation of ISM phase is lost in the iron abundance.Thus,we expect that[Fe/O]oscillates as the limit-cycle evolution of ISM.

In Figure5,we show[Fe/O]–[Fe/H]relation.The solid,dotted,and dashed lines repre-sent the results in Models A,B,and C,respectively.The two?gures(a)and(b)correspond to(X f Fe/X Fe⊙,X f O/X O⊙)=(0,0)and(X f Fe/X Fe⊙,X f O/X O⊙)=(0.1,0.25),respectively(same as Fig.2a and b,respectively).Indeed,we see that[Fe/O]oscillates.However,the amplitude of the oscillation is not large.This is consistent with the age–metallicity relation(Fig.2).As mentioned in§4.2.1,the amount of metallicity re?ects the past-integrated SFR;thus,as long as the mass of newly formed stars is not dominated in the total stellar mass,the present oscillation has little in?uence on the metallicity evolution.

5.DISCUSSIONS

In this paper,we have modeled the oscillatory SFH proposed observationally by R00.Our model is a combination of an infall model developed in the?eld of chemical evolution and the limit-cycle model proposed by Ikeuchi(1988)and his collaborators.We discuss our result in the following two subsections.

5.1.Limit-Cycle Star Formation History

The oscillatory behavior of the Galactic SFH proposed by R00is modeled by using the limit-cycle model of SFH.The limit-cycle behavior of the three-phase ISM is suggested by Ikeuchi(1988) and his collaborators.Since the period of a limit-cycle orbit can be～1Gyr within the framework of Ikeuchi(1988),the Galactic SFH is explained by the limit-cycle model of the ISM.

Recently,Hirashita&Kamaya(2000)have explained the observed scatter of star formation activity of a sample of spiral galaxies by using the limit-cycle model.They provided a consistent modeling that explains the variation in the scatter of star formation activity among the morpho-logical types(Sa–Sc)as shown in Kennicutt et al.(1994).Since the Galaxy is a spiral galaxy,an oscillatory SFH is consistent with the variation of star formation activity seen in other spirals.

Kennicutt et al.(1994)have also presented the ratio of the present SFR to the past averaged SFR(indicated as b there).From Figure2of R00,we see that b(denoted as SFR/ SFR in R00) can be as large as2–3for the Galactic SFH.Since the morphological type of the Galaxy is Sbc(e.g., Binney&Merri?eld1998,p.171),b=2–3is within the range of the Sbc/Sc sample in Kennicutt et al.(1994,their Fig.6).This consistency implies that the oscillatory SFH may be a common nature for all the spiral galaxies.

Fig.4.—Distribution of the G-dwarf metallicity.The histogram shows the data by Rocha-Pinto &Maciel(1996).The solid,dotted,and dashed lines represent the results in Models A,B,and C, respectively.All the distributions are normalized to unity when they are integrated in the whole range of[Fe/H].(a)Abundance in the infalling gas is assumed as(a)(X f Fe/X Fe⊙,X f O/X O⊙)=(0,0) and(b)(X f Fe/X Fe⊙,X f O/X O⊙)=(0.1,0.25).

Fig.5.—Change in[O/Fe]against[Fe/H].The solid,dotted,and dashed lines represent the results in Models A,B,and C,respectively.The dot-dashed line represents the observational data as summarized in Fig.3of Kobayashi et al.(1998).(a)Abundance in the infalling gas is assumed as (a)(X f Fe/X Fe⊙,X f O/X O⊙)=(0,0)and(b)(X f Fe/X Fe⊙,X f O/X O⊙)=(0.1,0.25).

5.2.Chemical Evolution in Limit-Cycle ISM

The chemical evolution of the Galaxy has been investigated in the framework of the limit-cycle ISM model.We have found that the amplitude of the oscillatory behavior of the metallicity is smaller than the observed scatter(Figs.2and5).This indicates that the observed scatter is not attributed to the limit-cycle behavior.The scatter might be explained by chemical inhomogeneity in the Galactic disk.

The oscillatory behavior of the metallicity is not prominent because the metallicity re?ects all the past SFH.The integrated contribution from all the past SFH smoothes out the oscillatory behavior of SFR.Thus,from the viewpoint of chemical evolution we conclude that we cannot distinguish between the“smooth”infall model without an oscillatory behavior and the oscillatory infall model proposed in this paper.

Contrary to the metallicity,the dust-to-gas ratio can show a oscillatory behavior(Hirashita 2000b).This is because the e?ciency of the dust formation changes according to phase changes in the gas.Moreover,dust is e?ciently destroyed when the mass fraction of the cold gas is small.This oscillation of dust amount may be important for the evolution of infrared luminosity of galaxies.

5.3.Another Possible Mechanism for the Variation of SFR

Rocha-Pinto et al.(2000c)gave some indication that the Magellanic Clouds could play a role in the SFH of the Galaxy.It is meaningful to explore their idea.Since our discussion is based on the limit-cycle behavior inherent in the ISM as stated in§1,we do not include the external force into our formulation.Fortunately,Ikeuchi&Tomita(1983)have investigated the behavior of the ISM in the presence of such an external force.Thus,we discuss the in?uence of the Magellanic Clouds based on the discussion in Ikeuchi&Tomita(1983).

If a perturbation of the external force to the limit-cycle ISM exists,both the period and the amplitude of the oscillation are a?ected.Thus,it is not necessary that the period proper to the ISM is about1Gyr.Even in the stable-focus case(§3.1),an oscillation emerges.Furthermore,the qualitative behavior can be changed:the system can show a chaotic orbit.Since the observational data do not reject such a chaotic orbit a?ected by the perturbation of the Magellanic Clouds,the strongly variable SFH of the Galaxy might be due to the interaction with the Magellanic Clouds. However,we note that the large scatter of the star formation activity of the spiral sample(e.g., Tomita et al.1996)implies a general oscillatory behavior of ISM in spiral galaxies.This is naturally explained if such an oscillatory behavior is caused by the limit-cycle evolution inherent in the ISM.

Finally,we would like to note that Chiappini et al.(1997)have also considered SFR variation due to a di?erent mechanism.Their rapidly variable SFR is caused by a density threshold for star formation:They assumed that star formation occurs only if the surface density of the gas exceeds a critical value,while we have assumed no threshold.However,the timescale of the SFR variation

in Chiappini et al.is much shorter than1Gyr.Although Chiappini et al.’s mechanism may indeed present on a timescale much shorter than1Gyr,it is necessary to introduce a mechanism di?erent from Chiappini et al.in order to explain the SFR variability presented by R00.Thus,we have proposed a limit-cycle scenario for the SFR in the Galactic disk.

We thank H.Rocha-Pinto,the referee,for invaluable comments and suggestions that improved this paper very much.We are grateful to S.Mineshige and H.Shibai for continuous encouragement, H.Kamaya and A.Ibukiyama for useful comments,and K.Yoshikawa for an excellent computa-tional environment.H.H.was supported by the Research Fellowship of the Japan Society for the Promotion of Science for Young Scientists. A.B.acknowledges the hospitality of the depart-ment of astronomy at Kyoto University where this project was started and?nancial support from the Japan Society for the Promotion of Science.We fully utilized the NASA’s Astrophysics Data System Abstract Service(ADS).

Fig.B1.—Time evolution of the cold gas fraction X cold(solid line).The dotted line represents the time-averaged value of X cold.

A. A.DETERMINATION OF R ins AND R del

R ins and R del are described as

R ins= m u m l,ins(m?w m)φ(m)dm,(A1)

R del= m l,ins m l,del(m?w m)φ(m)dm,(A2) whereφ(m)is the initial mass function(IMF),which is normalized so that the integral of mφ(m) in the full range of the stellar mass(0.1–100M⊙in this paper)becomes unity;m u is the upper

mass cut-o?of the stellar mass,and we here adopt m u=100M⊙;m l,ins and m l,del are set as5M⊙and1M⊙,corresponding to the stellar lifetime ofτ(the parameter for the delayed production)and the age of galaxies.If we adopt the Salpeter’s IMF(φ(m)∝m?2.35),we obtain R ins=0.16and R del=0.13.

B. B.DETERMINATION OF X cold

The cold gas mass fraction averaged over the Galactic lifetime, X cold ,is used in§3.2.It is estimated as follows.First,the time evolution of the cold gas is calculated based on the limit-cycle model in§3by adopting the parameters as A=0.3,B=0.5,and1/c=107yr.The time evolution of X cold is shown in Figure B1.Next,we estimate X cold by averaging X cold(t)over the Galactic age(T G)as

X cold =1

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联想乐Pad A1刷机详细图文教程 联想乐Pad A1刷机教程，教你如何刷机此帖是一个较为粗略的教程，不过分三种方法，这里是针对第一种方法进行详细说明。 针对一些不太懂刷机的朋友，我这里针对上面帖子里的第一种方法写一篇更为详细的教程，对联想乐Phone刷机不太清楚的机油可以看看。 首先，要下载一个刷机包A107W0_A234_001_008_2375_SC.zip点击下载。值得说明的是，在最早的2035教程中提到的“压缩包中6个文件 Update.zip,Recovery.img,MLO,uImage,u-boot,make_boot_sdcard. zip均拷贝到TF卡根目录下”的步骤，在2493这个版本时，这个步骤中完全可以只拷贝一个Update.zip文件即可，因为其他几个文件在Update.zip中已有，文件完全一样，作用也一样，没有必要再次全部拷贝了。 第二步是把下载完的固件文件改名为update.zip（注意：不是update.zip.zip，部分网友的电脑默认设置是看不到后缀名，所以不要以为就没有后缀名） 第三步，把改名后的update.zip拷贝到TF卡上，TF卡格式化为FAT32，

且确定能在A1系统中被识别。 刷机前必须关机。把联想A1关机（长按电源键10秒可强行关机，请确定保持A1在关机状态）

同时按住“电源键”和“音量小键”，A1会震动一次，这时A1 开机，持续按住两个按键不松手，当第一次出现Lenovo字样的logo 时，松开两个按键。（提醒一下急性子的人，出现logo时候挺一秒，再松手吧。我觉得0.05秒时候是最好）

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（图3） 1：解析刷机包 打开线刷宝客户端——点击“一键刷机”—点击“选择本地ROM”，打开您刚刚下载的线刷包，线刷宝会自动开始解析（如图4）。 （图4）

第三步：安装驱动 1、线刷宝在解包完成后，会自动跳转到刷机端口检测页面，在刷机端口检测页面（图5）点击“点击安装刷机驱动”， 2、在弹出的提示框中选择“全自动安装驱动”（图6），然后按照提示一步步安装即可。 （图5）

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4、确定全部勾已经勾选，然后点击Ferware-upgade，然后插上你的联想A820(装电池的)，然后进度条会走，四五分钟之后，刷成功，会弹出一个小小的窗口，表示成功刷入中文rec overy。如图： 5.弹出下面的绿色圈圈窗口之后，表示成功刷入中文recovery，拔掉数据线，按住电源键2秒左右，再同时按音量加、减键(此时3个键一起)，一直到进入中文recovery模式。或者借助刷机精灵、卓大师等软件重启到recovery模式!

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AMIDEDOS.EXE /ss "111111" IF errorlevel 1 goto end :end AFUdos4（错误）修改：AFU417 00020003000400050006000700080009修改成你的UUID号。

联想a60刷机步骤

近来有朋友问怎么刷联想A60于是写了个傻瓜操作流程，希望对需要的人有帮助，共享出来。 本文的内容与软件均来自移动叔叔论坛与网络，本人只是整理了一下，下载链接在金山快盘中，不保证永久有效。 By fjnpcch at 2011.10.14 分成三个步骤： 一、root手机。 1、首先把“联想A60固件USB刷机驱动forXP.rar"解压缩。 下载地址：https://www.doczj.com/doc/8d7085223.html,/index.php?ac=file&oid=9015011800255251。 2、把手机关机，连上usb线，这时会找到设备，安装驱动。驱动在第1步中的目录中找。 3、下载Lenovo_A60_Flash_Tool_m44.rar，下载地址： https://www.doczj.com/doc/8d7085223.html,/index.php?ac=file&oid=9015011800255250，将其解压缩。 运行刚解压出来目录中的：Lenovo_A60_Flash_Tool_m44\Lenovo_A60_Flash_Tool_m44.exe 4、选择第二个框后面的，如图中1处红色的。 5、会让你找文件，找到: Lenovo_A60_Flash_Tool_m44\rom\ MT6573_Android_scatter.txt (在第3步中解压出来的目录中)

6、把手机usb线拔下来，记得一定机先拔下来。 7、按软件中的下载，如上图中2处。 8、这里会出现倒计时：如图 9、把手机usb 线插上。 10、出现如下图的黄色条和绿色圈就已经root成功了。 二、刷入第三方recovery。（recover是卡刷系统的前提） 11、下载：下载地址：https://www.doczj.com/doc/8d7085223.html,/index.php?ac=file&oid=9015011800255250， 解压m44-20110812-a60-2[1].3-recovery.rar，得到m44-20110812-a60-2.3-recovery.img文件。 12、下载https://www.doczj.com/doc/8d7085223.html,/index.php?ac=file&oid=9015011800255289，得到m44tools.apk 文件。 13、手机开机，把上面两个文件拷贝到手机卡的根目录中。 14、在手机上安装m44tools.apk文件，出现“移动叔叔工具箱”软件。

刷新网卡激活win7-用带有BootRom功能的网卡为系统添加SLIC2

前言： A. 撰写本文的目的是为了学习和交流计算机技术及操作技巧，并不是鼓励大家使用盗版软件或盗版系统，由此引起的一切直接的、间接的责任和损失本人概不负责。请勿引用本文的内容或使用本文中涉及的技术、手段用于商业盈利目的。 B. 文章中的PCI模块程序来自dkpnop大侠，网卡换SLIC工具由zhaoliang大侠开发，驱动程序以及相应工具来自Intel网站或者驱动之家，下文中另外提到的“超级急救盘光盘版”由DOS之家提供。 C. 在此声明，本文内容仅供参考。引用、借鉴、利用本文中提及的技术、软件、方法而引起的一切直接的、间接的责任和损失本人概不负责！！ D. 其实关于使用网卡激活Win7的文章论坛上已经有不少了，然后就有朋友就问我为什么还要发表类似的文章？我的回答其实很简单：论坛上曾经发表的文章要么就是太简单，要么就是说的太玄乎让人不敢尝试，正因为这样，在本文中不但有比较详细的操作步骤，同时也对一些会碰到的问题进行了简单的讲解，让大家看了后基本都可以明白，也可以放心大胆的按照步骤操作。当然，这样一来，文章的整体字数就上去了，但对于需要的人来说，具体点总是不错的…… ―――――――――――――――――――――――――――――――――――――――――― ―――――――――――――――――――――――――――――――――――――――――― 需要的硬件及软件工具： ――――――――――――――――――――――――――――――――――――――――――

1. intel 82559或者550ey等带bootrom的网卡，启动芯片为eeprom可带电擦除。 2. intel网卡驱动12.0版或更高版本，包含intel proset工具包。 3. ProBoot工具。 4. PCI模块。 5. 网卡换SLIC工具。 6. 超级急救盘光盘版（DOS之家有最新版下载，请自行刻录成光盘） ――――――――――――――――――――――――――――――――――――――――――

酷派手机怎么双清

酷派手机怎么双清 酷派是一个比较知名的手机品牌了，前几年，酷派和中兴、华为、联想并称“中华酷联”，是中国四家手机品牌。酷派的手机一般是运营商运营商定制销售，前几年是市场份额很高，这两年已经下降了很多，不过市面上的酷派手机还是很多的。那么，酷派的手机要如何双清呢？ 什么是双清？ 双清就是指清掉手机的数据，包括用户数据和缓存数据。也叫双wipe。wipe的中文翻译就是"擦，拭，擦去，涂上”。所以双wipe，和双清实际上是一个意思。 为什么要双清呢? 1、刷机之前一般要双清，避免之前的数据和新刷机的系统产生冲突； 2、当许多应用都有问题（比如闪退），但是又无法确定问题的原因时，可以使用双清，基本就能解决问题； 3、觉得自己手机内软件垃圾太多了，而无所适从时，可以使用双清，还原一个崭新的系统。

那么再来看看酷派手机要怎么双清呢？ 手机双清，需要先进入recovery模式，那么酷派的手机怎么进入recovery模式呢？ 一、将手机彻底关机。 二、在关机状态下同时按住：电源按键+音量下，进入Recovery。 三、在recovery模式下使用音量键选择，电源键确认。就可以双清手机了： 1、进入到Recovery模式后，通过“音量-”键选中“wipe data/factory reset”，按“音量+”键确认（进入下一个界面）。 2、通过“音量-”键选中“Yes – delete all user data”，通过“音量+”键确认执行清掉DATA分区数据操作。 3、进入到Recovery模式后，通过“音量-”键选中“Wipe cache partition”，按“音量+”键确认执行清掉CACHE分区数据操作。 4、完成后重启手机。 双清完成，接下来就可以刷机了。 酷派手机线刷工具： https://www.doczj.com/doc/8d7085223.html,/ashx/downloadTransfer.ashx 酷派手机刷机包下载：https://www.doczj.com/doc/8d7085223.html,/rom/coolpad/ 酷派手机刷机教程：https://www.doczj.com/doc/8d7085223.html,/guide?brandId=1666

华为g610-t11刷机步骤

第二步，安装华为G610-T11必需的刷机驱动 打开从第一步解压后的文件夹，找到“MTK智能机USB驱动-刷机必备驱动大全by移动叔叔.rar”，解压后，进入“刷机驱动自动安装版”文件夹，点击“点击安装by移动叔叔.exe”进行驱动安装。如果电脑是64位的，请点击“installdrv64.exe”。 PS:WIN7 64位系统的请更换32位系统来刷机！ 识别刷机驱动步骤：安装完驱动，将手机拔掉电池，直接裸机不带电池的和电脑联机，即可弹出发现硬件。 PS:不成功的，请更换USB端口、更换电脑系统为XP。 如华为G610-T11安装驱动过程出错，提示“inf中的段落无效”之类，请下载缺失文件放到windows目录下相关文件夹中。 inf补丁：https://www.doczj.com/doc/8d7085223.html,/c0tk60b8hc 将mdmcpq.inf 复制到c:/windowsinf 将usbser.sys 复制到c:/windows/system32/drivers 另外考虑到自动安装版驱动未必100%凑效，这里有手动安装版的操作教程，请前往https://www.doczj.com/doc/8d7085223.html,/thread-291645-1-1.html -------------------------------------------------------------------------------- 第三步，具体图解华为G610-T11刷机教程如下： 刷机的时候需要扣掉电池的刷，简单说明下过程： 数据线接电脑一端，手机关机扣电池出来，刷机软件点download（下载），数据线另一端接手机，这样就会开刷。 PS:供电不足情况下，需要在加装电池的刷！就是手机扣完电池后再装回去才点download，操作类似。 还有，必须将DA DL ALL With Check Sum前面的框框勾上勾勾！ 1、单刷recovery教程如下图

联想A68E刷机教程

使用1月23日版集成软件楼主自用版：https://www.doczj.com/doc/8d7085223.html,/viewthread.php?tid=3196249&page=1&extra=#pid73215718 2月3日版，下载地址：https://www.doczj.com/doc/8d7085223.html,/thread-3195039-1-1.html 1月23日版，下载地址：https://www.doczj.com/doc/8d7085223.html,/viewthread.php?tid=3175932&page=1&extra=#pid72305386 增加电池容量的方法实测，待机时间有明显增长：https://www.doczj.com/doc/8d7085223.html,/thread-3180482-1-1.html 官方S019原版，只修改刷机脚本为recovery刷入其它没有任何改变，为刷机上瘾机油和不满意精简ROM的机油预备。下载地址https://www.doczj.com/doc/8d7085223.html,/file/c2mvdhxv#A68E_S019_update.zip 我的所有ROM基于官方原版修改，请参考，官网论坛地址 https://www.doczj.com/doc/8d7085223.html,/forum.php?mod=viewthread&tid=23401&extra=page%3D1 @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@ @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@ @@@@@@@@@@@@@@@@@@@@@@@@@ ......下面是刷机教程……… @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@ @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@ @@@@@@@@@@@@@@@@@@@@@@@@@ 失败原因排名：1、驱动没有装好88.88888%，2、杀毒或者安全软件阻扰11.111%, 3、 其他原因0.000000001% 步骤一、首先安装手机驱动（这步很简单，但后面的更简单。很多机油不成功就是这步都没有搞好) 装驱动方法一、电脑装91助手，并运行，手机usb调试打勾，电脑运行基带升级程序“updatetool”。但是什 么都不要做。切忌手痒去按那个“start”。等会91助手就识别出a68e。哈哈！驱动就已经装好了，这个也是很多机油说不能连接91助手的简单解决方法！！（updatetool在步骤三那里下） 装驱动方法二、把手机和电脑连起。手机：设置—应用程序—开发—USB调试—打勾。电脑会自动安装驱动， 如果没有自动安，双击我的电脑。再点击多出来的盘或者光驱。等一会电脑端就安好了三个东西：1、天翼宽带。 2、天翼网盘。 3、手机驱动（前面两个跟Root 和刷机无关，3才是最重要的。它安1和2， 3自然就有了） 装驱动方法三、单独安装电脑端驱动，下载：https://www.doczj.com/doc/8d7085223.html,/file/c2bq17q8# 如果驱动都装不起那就别刷机了，去大街上找手机维修点刷吧，呵呵！我敢说他们也刷不好

诺基亚手机无法开机后,强刷修复系统的方法

诺基亚手机无法开机后，强刷修复系统的方法 ?最近更新： 2011-07-21 23:41 ?浏览次数： 7840 次 ? 2011年我的手机我做主，手机要玩就要这么玩！！ ---idea_wj 以下内容适用于诺基亚BB5型手机，其他机型还不太确定，你可以上网看看你的诺基亚手机是否是BB5型的，一般非智能的都适用，该教程以6303C为例，vista32位操作系统下进行，软件是凤凰刷机软件，资料包（刷机包）code 0583415。为了让本教程大众化，更通俗易懂，先说一些必要内容，刷机和强刷是有一些区别的，刷机是一些港行货使用不便或必须在客服才允许升级的手机，水货等诺基亚官方不提供升级，只能通过杂牌软件刷机才能是自己手机正常使用，刷机是有很大风险的，且失败几率很大，失败后手机将会彻底不能使用，也就是变成人们所说的废铁或板砖；而强刷是指手机成为板砖不能开机，而客服又不提供合理的解决办法，自己只好通过一些别的软件强行修复这已关机的手机，使成为板砖的手机能正常使用，而前提是，这手机成板砖时，按开机键后，usb在电脑上有反应（中间有个重要步骤，待会儿会解释）！ 如果你是因为刷机或自己在电脑上ovi套件升级手机失败或一些别的什么原因，致使手机无法开机而成为板砖，不要急着找客服或修手机的，他们九成会说：“无法修复，只能换主板”，拜托，换主板的钱够买台新机子了，更何况，即使他会刷机，会给你强刷，没有100到200块钱，他绝对不给你修，对于你，你会损失几百块，对于他，只是动动鼠标，你心里会平衡吗？学会以下内容，将会为你带来极大的方便，随时随地，你都可以修复你的宝机！ 强刷有个优势就是，你可以多次去刷，失败了继续重来，不用担心手机问题，反正已经有问题了。以下内容是通过自己亲自试验后写出的步骤，其中有很多重要步骤，我可以明说，在网上是很难找到的，而每个细节都应该注意，否则你会走很多弯路的，由于兼容问题，vista上安装软件太麻烦，软件光安装就安装了好几次才成功。 工具/原料 ?你得准备这些东西，凤凰软件（可以在凤凰网上找到，我选的是2010年汉语版）、相应的刷机包code(在班塞网上有，我6303c，选的是rm-443 code:0583415。补充：强烈注意：找到的code刷机包的版本必须比手机 成板砖前的版本高，否则刷机会失败，要是实在不清楚自己是哪个版本就 下载个最新的版本) 还有诺基亚官方网站和你手机相应的ovi套件（这是我多次连接失败后，发现的，必须有这个东西，否则你usb连不倒凤凰软件，更别谈强刷），这三样东西是必需的。【除了code外，这些软件我 都库存了，跟前需要的朋友可以直接来取，可以省下不少下载的麻烦】 （注意：你的code是在手机放电话卡旁边的一串数字，7位数基本都是 05开头，找到后再到网上找相应的刷机包）

A820T刷机教程

联想A820T获取ROOT权限教程： （说明：网上好多教程都没用，我试过蘑菇云刷机大师、百度刷机、腾讯一键root···都是显示root成功，但还是不能卸载系统软件，相信多数朋友有相同的苦恼。本人也是走了很多弯路，希望我的经验能帮到你，相信我一定能够成功！） 1、先刷入联想家园网发布的第三方中文recovery卡刷模块 2、将你的A820T手机进入中文recovery模式，进入方法比较多： a、比如用刷机精灵、或者卓大师等自动进入，有重启（进入）到recovery的功能； b、当然，你也可以手动进入中文recovery，进入方法：关机状态下，安装电源键2秒左右，再按住音量加、减两个键（此时3键一起），一直到进入中文recovery模式。 3、进入中文recovery模式之后，选择倒数第二个选项“获取ROOT 权限”-电源键确定，1秒之后提示成功。 4、只要几秒时间，即可成功，完成之后，返回立即重启，你的联想A820t手机就获取ROOT权限了； 具体的步骤： 1、先刷入联想家园网发布的第三方中文recovery卡刷模块（有点麻烦，请耐心看完，也是关键的一步）

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