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Long Type I X-ray Bursts and Neutron Star Interior Physics

a r X i v :a s t r o -p h /0508432v 1 22 A u g 2005

D RAFT VERSION F EBRUARY 5,2008

Preprint typeset using L A T E X style emulateapj v.6/22/04

LONG TYPE I X-RAY BURSTS AND NEUTRON STAR INTERIOR PHYSICS

A NDREW C UMMING 1,J ARED M ACBETH 2,J.J.M.

IN ’T

Z AND 3,AND D ANY P AGE 4

Draft version February 5,2008

ABSTRACT

Superbursts are very energetic Type I X-ray bursts discovered in recent years by long term monitoring of X-ray bursters,believed to be due to unstable ignition of carbon in the deep ocean of the neutron star.A number of intermediate duration bursts have also been observed,probably associated with ignition of a thick helium layer.We investigate the sensitivity of these long X-ray bursts to the thermal pro?le of the neutron star crust and core.We ?rst compare cooling models of superburst lightcurves with observations,and derive constraints on the ignition mass and energy release.Despite the large uncertainties associated with the distance to each source,these parameters are quite well constrained in our ?ts.For the observed superbursts,we ?nd ignition column depths in the range 0.5–3×1012g cm ?2,and energy release ≈2×1017erg g ?1.This energy release implies carbon fractions of X C >10%,constraining models of rp-process hydrogen burning.We then calculate ignition models for superbursts and pure helium bursts,and compare to observations.We show that achieving unstable ignition of carbon at accretion rates less than 0.3of the Eddington rate requires X C 0.2,consistent with our lightcurve ?ts.Most importantly,we ?nd that when Cooper pairing neutrino emission in the crust is included,the crust temperature is too low to support unstable carbon ignition at column depths of ～1012g cm ?2.Some additional heating mechanism is required in the accumulating fuel layer to explain the observed properties of superbursts.If Cooper pair emission is less ef?cient than currently thought,the observed ignition depths for superbursts imply that the crust is a poor conductor,and the core neutrino emission is not more ef?cient than modi?ed URCA.The observed properties of helium bursts support these conclusions,requiring inef?cient crust conductivity and core neutrino emission.

Subject headings:accretion,accretion disks-X-rays:bursts-stars:neutron

1.INTRODUCTION

In the past few years a new regime of nuclear burning on the surfaces of accreting neutron stars has been revealed by the discovery of X-ray superbursts (Cornelisse et al.2000;Strohmayer &Brown 2002;Kuulkers 2003).These are rare (recurrence times ≈1year),extremely energetic (energies ≈1042ergs)and long duration (4–14hours)Type I X-ray bursts that have been discovered with long term monitor-ing campaigns by BeppoSAX and RXTE.Whereas normal Type I X-ray bursts involve unstable thermonuclear ignition of hydrogen and helium (see Lewin,van Paradijs,&Taam 1993,1995;Strohmayer &Bildsten 2003for reviews),su-perbursts are thought to involve ignition of carbon in a much thicker layer (Cumming &Bildsten 2001,hereafter CB01;Strohmayer &Brown 2002).

Theoretical studies of superbursts initially focused on their potential as probes of nuclear physics.The fuel for su-perbursts is thought to be produced by hydrogen and he-lium burning at lower densities by the rp-process (Wallace &Woosley 1981),a series of proton captures and beta-decays on heavy nuclei close to the proton drip line.This pro-cess naturally explains the ≈100s extended tails observed in some X-ray bursts (e.g.from the regular burster GS 1826-24;Galloway et al.2004).The amount of carbon remaining after H/He burning depends on the details of the rp-process (Schatz et al.2003b),which involves unstable heavy nuclei

Physics Department,McGill University,3600rue University,Montreal,QC,H3A 2T8,Canada

2Department of Astronomy and Astrophysics,University of California,Santa Cruz,CA 95064,USA

3SRON National Institute for Space Research,Sorbonnelaan 2,NL-3584CA Utrecht,The Netherlands

4Instituto de Astronomía,Universidad Nacional Autónoma de México,04510Mexico D.F.,Mexico

whose properties are not well known experimentally (Schatz et al.1998).

CB01argued that the heavy elements made by the rp-process will make the accumulating layer less conductive to heat,increasing the temperature gradient within it,and lead-ing to earlier ignition than pure carbon models (as had been considered earlier by Woosley &Taam 1976,Taam &Pick-lum 1978,Lamb &Lamb 1978,and Brown &Bildsten 1998),in better agreement with observed superburst energies.In fact,Brown (2004)and Cooper &Narayan (2005)showed that the ignition conditions are much more sensitive to the thermal properties of the neutron star interior,speci?cally the neutrino emissivity of the neutron star core and composition of the crust.This is exciting because it offers a new way to probe the neutron star interior,complementary to observations of transiently-accreting neutron stars in quiescence (Brown et al.1998,Colpi et al.2001,Rutledge et al.2002;Wijnands et al.2002;Yakovlev et al.2004),or cooling isolated neutron stars (see Yakovlev &Pethick 2004and Page et al.2005for recent reviews).

Several other long duration X-ray bursts have been ob-served that are intermediate in duration and energy between normal Type I X-ray bursts and superbursts (e.g.Figure 1of Kuulkers 2003).These intermediate bursts have durations of ≈30mins and energies ≈1041ergs,and sources include SLX 1737-282(in ’t Zand et al.2002),1RXS J171824.2-402934(Kaptein et al.2000),and 2S 0918-549(in ’t Zand et al.2005).Long duration bursts are expected from accre-tion of hydrogen and helium at low rates ≈0.01˙M

Edd (Fu-jimoto,Hanawa,&Miyaji 1981;Bildsten 1998;Narayan &Heyl 2003;Cumming 2003b).For accretion of solar com-position material at these accretion rates,a massive layer of pure helium accumulates and ignites beneath a steady hydro-gen burning shell.Whereas the hydrogen shell is heated by

hot CNO hydrogen burning,the helium shell is heated mainly by the heat?ux emerging from the crust.Therefore,just like superbursts,these bursts are potentially sensitive to the crust composition and core temperature.The case of pure helium accretion is particularly interesting because heating by hydro-gen burning then plays no role,making the ignition conditions directly sensitive to interior physics.

It is therefore important to constrain the ignition depth,re-currence times,and energy released during superbursts and other long X-ray bursts.Our knowledge of superburst recur-rence times is limited because they are rare events.Three superbursts were seen from4U1636-54separated by in-tervals of2.9and1.8years(Wijnands2001;Kuulkers et al.2004).Dividing the total duration of observations of X-ray bursters with the BeppoSAX/WFC by the number of su-perbursts observed gives a recurrence time estimate of0.4–2 years(in’t Zand et al.2003).Brown(2004)and Cooper& Narayan(2005)emphasized that to achieve ignition of carbon on≈1year timescales at accretion rates˙M≈0.1˙M Edd re-quires the accumulating layer to be suf?ciently hot.An en-hanced core neutrino emissivity(as would be produced if, for example,the direct URCA process operated in the core, e.g.Yakovlev&Pethick2004,Page et al.2005)together with a large crust conductivity gives very long(?10yr)superburst recurrence times,inconsistent with observations.Recently, in’t Zand et al.(2005)showed that the intermediate dura-tion X-ray burst from2S0918-549is well explained by ac-cretion of pure helium at the observed rate of˙M≈0.01˙M Edd, assuming that most of the heat released in the crust by pyc-nonuclear reactions and electron captures(Haensel&Zdunik 1990,2003)?ows outwards and heats the accumulating he-lium layer.However,they did not explore the sensitivity of this assumption to the interior physics.

In this paper,we investigate the constraints on interior physics coming from superbursts and pure helium bursts.We ?rst derive independent constraints on the ignition depth and energetics of superbursts by?tting the observed lightcurves to theoretical cooling models as calculated by Cumming&Mac-beth(2004,hereafter CM04).We then calculate ignition con-ditions for both superbursts and pure

helium bursts,and com-pare with observed properties.We start in§2by summarizing the properties of our cooling models for superbursts,present the?ts to the observed lightcurves,and discuss the constraints on the ignition depth and energy release.In§3,we calculate ignition conditions for superbursts and discuss the implica-tions for the thermal structure of the interior.We show that the best?t is obtained for inef?cient neutrino emission in the neu-tron star crust and core.Next,in§4,we apply these ignition models to pure helium bursts,and show that their properties imply the same conclusion:inef?cient neutrino emission.We conclude in§5.In Appendix A,we discuss a simple model of the early phase of the superburst lightcurve which reproduces the time-dependent results,and in Appendix B give approxi-mate analytic solutions for the crust temperature pro?le.

2.COOLING MODELS FOR SUPERBURSTS AND

COMPARISON TO OBSERV ATIONS

2.1.Cooling models

CM04computed lightcurves for superbursts by assuming that the fuel is burned locally and instantly at each depth,and then following the thermal evolution and surface luminosity as the burning layers cool.They showed that the lightcurve of the cooling tail of the superburst is a broken power law,

F IG.1.—Energy radiated from the surface after3hours(dotted curves),6 hours(solid curves),and12hours(dashed curves)for E17=1,1.5,2,2.5and 3,as a function of the column depth.We assume a neutron star radius R=10 km(E rad,∞∝R2).

with time of the break proportional to the cooling time of the entire layer.The early phase of cooling depends mostly on the energy released in the?ash;the late phase of cooling de-pends mostly on the thickness of the layer.We now apply these models to the observations,and discuss the constraints on superburst ignition conditions.

We refer the reader to CM04for full details of the cooling models,including approximate analytic expressions for the ?ux as a function of time.The parameters of the models are the ignition column depth(y121012g cm?2),and the energy release per gram(E171017erg g?1)which is assumed to be independent of depth.The thermal evolution is followed nu-merically by the method of lines,which involves?nite differ-encing on a spatial grid,and then integrating the resulting set of coupled ordinary differential equations for the temperature at each grid point forward in time.It is important to note that the rise of the superburst is not resolved,since the entire fuel layer is assumed to burn instantly.The models assume a neu-tron star mass and radius of M=1.4M⊙and R=10km,giving the surface gravity g=(GM/R2)(1+z)=2.45×1014cm s?2 and redshift1+z=1.31.We include the equation of state,ra-diative and conductive opacities,heat capacity,and neutrino emissivities as described by Schatz et al.(2003a).At the tem-peratures and densities appropriate for a superburst,the neu-trino emission is mostly due to pair annhilation(CM04).

We?rst summarize some of the properties of the models. CM04already noted that the power law decay gives a long tail to the superburst lightcurves,which is similar to the long tails observed in superbursts(Kuulkers et al.2002;Cornelisse et al.2002).Figure1shows the amount of energy radiated from the surface in the?rst3,6,and12hours as a function of column depth for different choices of E17.The insensitivity of radiated energy to column depth for y 1012g cm?2in Figure 1shows that the total emitted energy is not a good indicator of the ignition column depth.There are two reasons for the

F I

G .2.—The “thermostats”of neutrino emission and inwards conduction of heat.Upper panel:ratio of energy released as neutrinos to energy radiated from the surface,both in the ?rst 24hours.Neutrinos dominate the energy release for large y and E 17.Lower panel:Fraction of the total nuclear energy released that escapes in the ?rst 24hours,either as neutrinos or from the surface.For large y ,a signi?cant fraction of the energy released is conducted inwards and released on a longer timescale.

characteristic radiated energy of ≈1042ergs (Strohmayer &Brown 2002).First,neutrino emission takes away most of the energy for large columns,and secondly heat ?ows inwards to be released on longer timescales.These effects are quanti?ed as a function of y 12and E 17in Figure 2.The ?rst panel shows the ratio of energy lost as neutrinos to the energy lost through the surface.For example,for y ≈1013g cm ?2and E 17≈3,neutrinos take away an order of magnitude more energy than is lost from the surface.This is in rough agreement with the one-zone model of Strohmayer &Brown (2002).The second panel shows the fraction of energy that is lost in the ?rst 24hours,either as neutrinos,or from the surface.The remaining energy,which is released on longer timescales,can be a sig-ni?cant fraction of the total for column depths ≈1013g cm ?2

and E 17≈1.

Even without detailed ?ts to observed lightcurves,these results give some indication of the values of E 17needed to match the observed properties of superbursts.Figure 1shows that an energy release E 17>1is required for the ob-served burst energy to reach 3×1041ergs during the ?rst few hours.On the other hand,for large values of E 17,the initial ?ux exceeds the Eddington ?ux F Edd =cg /κ=2.2×1025erg cm ?2s ?1(g 14/2.45)(1.7/(1+X )),in which case the superburst would be expected to show photospheric radius ex-pansion.In Figure 3,we plot the time for which the ?ux ex-ceeds F Edd for different E 17values.This time is not very sen-sitive to the ignition column,since the early evolution of the burst is independent of the layer thickness.For E 17 2,the ?ux is super-Eddington for timescales of minutes or longer.The superburst from 4U 1820-30showed an extended period of photospheric radius expansion lasting for ～1000s (SB02).This is in good agreement with the expectation that this source had a signi?cant energy release due to large amounts of car-bon produced by stable burning of pure helium (SB02;Cum-ming 2003a).Figure 3implies that E 17>5is required to get such a long period of super-Eddington luminosity with pure helium.However,there is no strong evidence for pho-tospheric radius expansion in any other superburst 5.Taken together,these two constraints imply that E 17≈2for most superbursts.

2.2.Fits to superburst lightcurves

We have ?tted the superburst lightcurves to the cooling models.The parameters of the models are E 17and y 12.How-ever,there are two additional parameters in our ?ts.The rise of most superbursts is not observed because of data gaps,making the start time of the burst uncertain,and so we in-clude the start time as an extra parameter.Most importantly,the distance to the source is not well constrained in most cases.This dominates the uncertainty in the ?tted parame-ters,and so we have ?tted the models by holding distance ?xed at different trial values,and searching over the remain-ing parameters to ?nd the best ?tting model at each distance.We include BeppoSAX/WFC data for the superbursts from 4U 1254-690(in ’t Zand et al.2003),KS 1731-260(Kuulk-ers et al.2002),4U 1735-444(Cornelisse et al.2000),Ser X-1(Cornelisse et al.2002),GX 17+2(in’t Zand et al.2004),and the RXTE/PCA lightcurve of 4U 1636-54(Strohmayer &Markwardt 2002;Kuulkers et al.2004).For GX 17+2,we use burst 2from Figure 7of in ’t Zand et al.(2004).This is one of the best candidates for a superburst,and has the most complete lightcurve.

We have extended the CM04models to a large grid in E 17and y 12for comparison to the observations.For a given source distance,we calculate the ?ux at the surface of the star F ?which corresponds to the observed peak ?ux f peak ,i.e.4πR 2F ?=4πd 2f peak .We will refer to F ?in units of 1024erg cm ?2s ?1as F 24.This quantity sets the normaliza-tion scale for comparison with the theoretical models,and is

Precursors were seen with BeppoSAX/WFC from KS 1731-260,4U 1254-69,and GX 17+2.In GX 17+2,the spectral data are of insuf?cient quality to see radius expansion during the precursor or the minutes thereafter (because of the high persistent emission);in KS 1731-260,no radius expan-sion was seen (Kuulkers et al.2002);in 4U 1254-69there are no indications.In all cases the peak ?ux of the precursor is smaller by a factor of 1.5–2than the brightest of the ordinary bursts.

F IG.3.—Time for which the?ux exceeds the Eddington?ux as a function of energy release E17.The curves are for y=1011(long-dashed),3×1011 (short-dashed),1012(dotted),and1013g cm?2(solid).We show two sets of curves for solar composition(F Edd=2.2×1025erg cm?2s?1)and pure helium(F Edd=3.7×1025erg cm?2s?1).

TABLE1

F ITS TO SUPERBURST LIGHTCURVES

Source f peak a d/R b E17c y12c

4U1254-6900.2213 1.5 2.7

4U1735-444 1.58 2.6 1.3

KS1731-260 2.4 4.5 1.9 1.0

GX17+2burst20.88 1.80.64 Ser X-1 1.96 2.30.55

4U1636-54 2.4 5.9 2.60.48

a Observed peak?ux in units of10?8erg cm?2s?1.

b Adopted distance in units of kpc/10km.

c The?tte

d parameters scal

e roughly as E17∝(d/R)8/7and y12∝(d/R)10/7 (see text).For a50%distance uncertainty,the uncertainties in E17and y12 are60%and70%respectively(see also Fig.4).

given by

F24=9.5 f peak10kpc/10km 2.(1)

We then search for the minimum value ofχ2over the grid of theoretical models,with E17ranging from0.5to3in steps of 0.125,and y12ranging from1011to3×1013g cm?2in steps of1/16in log10y(i.e.factors of15%between successive y values).For each model,we vary the start time of the super-burst between the limits allowed by the observations to?nd the best?t.Before comparing the model to the data,we red-shift the time and?ux assuming a gravitational redshift factor of1+z=1.31,appropriate for a10km,1.4M⊙neutron star. Our results are not very sensitive to variations in the redshift factor within the expected range(roughly1.2–1.5).

Figure4shows the best?tting E17,y,and the reducedχ2 of the?t for each source,as a function of both F24and the distance to radius ratio d/R.A larger?ux normalization for the observed lightcurve results in larger values of E17and y12,which increase in such a way as to maintain the over-all shape of the cooling curve.The scalings are straightfor-ward to understand from the analytic expressions for the?ux given by CM04(see eq.[4]of that paper).At early times,

the?ux is F∝t?0.2E7/4

(independent of column depth).In Appendix A,we discuss the physics underlying these https://www.wendangku.net/doc/e015515848.html,paring with the?tted values to set the constant,we

?nd E17≈0.8F4/7

,which is in good agreement with the ob-served relation between the?tted E17value and F24.There is a similar scaling for the best?t column depth,which can also be understood from the analytic?t,but now at late times,

where F∝yE1/2

,giving y∝F5/7.For a given?t,the frac-tional uncertainties in E17and y can therefore be estimated as ≈(4/7)(δF/F)and(5/7)(δF/F)assuming that the distance uncertainty dominates.

For speci?c choices of distance to each source,we show the best?tting models in Figures5to10,and list the parameters in Table1.The?tted values can be rescaled to a different dis-tance using the analytic scalings,or by referring to Figure4. We adopt distance estimates from the literature for4U1254-690(in’t Zand et al.2003)and4U1636-54(Augustein et al.1998).For GX17+2and4U1735-444we adopt a?ducial value of8kpc.For Ser X-1and KS1731-260,we take a lower distance then the upper limits or estimates in the literature,be-cause this signi?cantly improves the?t of our models.For ex-ample,Muno et al.(2000)place a distance limit of d<7kpc for KS1731-260using radius expansion X-ray bursts,assum-ing that the peak luminosity is the Eddington luminosity for pure helium.We?nd that for d/R 5kpc/10km the super-burst lightcurve is not well?t by our models,withχ2rapidly increasing for larger d/R.If the distance is7kpc,the required neutron star radius is 13km.Alternatively,the source could be closer.For example,using the Eddington luminosity for a solar composition rather than pure helium gives a closer dis-tance by a factor of(1.7)1/2or1.3.We choose a distance d/R=4.5kpc/10km for the?t shown in Figure5.

The most detailed lightcurve is for4U1636-54.This source has shown three superbursts(Wijnands2001;Strohmayer& Markwardt2002;Kuulkers et al.2004),but we show here the superburst observed by RXTE/PCA(Strohmayer&Mark-wardt2002).Figure6shows the Standard1mode lightcurve, which has a time resolution of1second,but has been binned to10second resolution for clarity.The best?t model agrees well with the observed decay.However,there are differences at the≈10%level between the model and the shape of the ob-served lightcurve.The BeppoSAX data for the other sources have a much lower time resolution,but still allow a good constraint on the ignition depth.The?tted column depth is not very sensitive to the assumed start time of the super-burst.Most important is how quickly the luminosity decays away from the peak value.For example,the count rate for 4U1254-690takes several hours to fall to30%of the peak value,whereas for4U1636-54the count rate reaches30%of the peak after less than2hours.We?t only to data points that have count rates more than10%of the peak value.At low luminosities,the lightcurve is sensitive to how well the accre-tion luminosity has been subtracted,however,this uncertainty has only a small effect on the?tted column depth.

The best-?tting models have E17in the range1.5to2.6. As we argued in§2.1,lower values of E17give a luminos-ity at early times that is smaller than observed.At the upper end of this range,Figure3shows that the?ux should exceed the Eddington?ux for several minutes,inconsistent with the lack of observed photospheric radius expansion.This may

F IG.4.—Left panel:best?tting E17and y,and the associated reducedχ2,as a function of assumed peak?ux F24.The?tted values approximately follow the scalings E17≈0.8F4/7

and y∝F5/7

.We show results for4U1254-690(short-dashed),KS1731-260(long dashed-short dashed),4U1735-444(solid),Ser X-1 (long-dashed),GX17+2(burst2dot-dashed,burst3long-dot-dashed),and4U1636-54(dotted).Right panel:same as left panel,but now using the observed peak?ux to plot everything in terms of the distance to the source.Theχ2for4U1636-54(dotted curves)is off scale in the lower

panel.

F IG.5.—Fitted lightcurve for KS1731-260,assuming the distance given

in Table1.Solid data points are included in the?t,open data points(with

?uxes less than0.1of the peak?ux)are not included.

indicate that the burning does not extend all the way to the

surface,which our models assume,but instead stalls at a loca-

tion where the thermal time to the surface is of order minutes.

More generally,our models are not valid for times less than

the superburst rise time.Also,we have not?tted our mod-

els to the superburst from4U1820-30,which was

observed

F IG.6.—Fitted lightcurve for4U1636-54.

by RXTE/PCA(Strohmayer&Brown2002).This superburst

had a complex lightcurve,with an extended period of photo-

spheric radius expansion,lasting about1000seconds,indicat-

ing a large energy release.More detailed1D models which

can follow the superburst rise are needed to address both of

these issues.

The best-?tting column depths are in the range0.5–3×

F I

G .7.—Fitted lightcurve for 4U

1254-690.F IG .8.—Fitted lightcurve for 4U 1735-444.

1012g cm ?https://www.wendangku.net/doc/e015515848.html,rger column depths closer to 1013g cm ?2are not consistent with

the observed lightcurves.We have ranked the sources in Table 1in order of decreasing column depths.This ordering approximately reproduces the ordering of su-perbursts by their observed durations in Figure 7of in ’t Zand et al.(2004).As pointed out in that paper,the superbursts from the rapidly accreting source GX 17+2have low column depths,but not signi?cantly lower than other superbursts.We ?nd that the GX 17+2burst has a similar ignition depth to the superbursts seen from 4U 1636-54and Ser X-1.

CM04derived constraints on the ignition column depth from the observed “quenching”of normal Type I bursting behavior for weeks following a superburst (e.g.Kuulkers et al.2002).The layer continues to cool well after the superburst luminosity falls below the accretion luminosity.This residual heat ?ux quenches the instability of H/He burning (CB01).

F I

G .9.—Fitted lightcurve for Ser X-1.

F I

G .10.—Fitted lightcurve for GX 17+2(burst 2from in ’t Zand et al.2004).

CM04showed that the observed limits on the quenching timescale,although not very constraining,were at least con-sistent with ignition at column depths of ≈1012–1013g cm ?2.Our ?tted values of y 12are consistent with Figure 4of CM04,except for KS 1731-260.The quenching timescale implies y 12 3for this source,whereas our ?t gives y 12≈1.Apart from the uncertainties associated with distance,one possibil-ity is that the ?ux required to stabilize H/He burning is a factor of 3lower than the crude estimate of CM04(their eq.[5]).

3.IGNITION MODELS FOR SUPERBURSTS

The ?ts to the superburst lightcurves imply ignition column depths ≈(0.5–3)×1012g cm ?2,which is accumulated in 2–10years at 0.1˙m Edd ,or 0.6–3years at 0.3˙m Edd ,roughly consis-tent with the observational constraints on recurrence times.In this section,we compare our ?ts to ignition models for su-

7 perbursts,and use the cooling models to predict superburst

properties as a function of accretion rate.In particular,we

emphasize the constraints on the thermal pro?le of the crust

and temperature of the core.

3.1.Details of the ignition calculations and physics input

Our ignition models follow those of Brown(2004),and are

extensions of the CB01carbon ignition models.However,

we now integrate down to the crust/core interface,solving the

thermal structure of the crust directly,rather than taking the

outwards?ux from the crust as a free parameter.Following

the simpli?cations of Yakovlev&Haensel(2003)and Brown

(2004),we do not integrate the full structure of the star,but

adopt a plane-parallel approximation,and take the gravity g

and gravitational redshift factor1+z to be constant across the

crust.Our independent variable is then the column depth y,

where hydrostatic balance gives the relation y=P/g(units

of mass per unit area).We integrate the heat equation and

entropy equation

dy =

5 4

Z56 4/3,(4)

where T8=T/108K.For the core,we adopt the sim-pli?ed equation of stateρ(r)=ρc(1?(r/R)2),where M= (8π/15)(ρc R3)(Yakovlev&Haensel2003).This givesρc= 1.7×1015g cm?3(M/1.4M⊙)(R/10km)?3.For a density at the crust/core interface of1.6×1014g cm?3(Lorentz et al.1993),the core radius is≈0.95R.In fact,in our mod-

els,the depth of the core/crust interface from the surface is ≈1km≈0.1R.We expect this difference to have only a small effect on our results.

We integrate the temperature pro?le inwards,changing the composition from“fuel”to“ash”at a depth y ign.We set the outer boundary at y=108g cm?2,and take the temperature there to be2×108K.We have checked that the ignition depth is not very sensitive to this choice of outer temperature6.We iterate to?nd the choice of?ux at the surface that results in the?ux at the base matching the core neutrino luminosity, F c+Lν(T c)/4πR2=0.We write the core luminosity as roughly Lν≈(4π/3)R3Qν,where Qνis the emissivity per unit vol-ume,giving the inner boundary condition F c=?RQν(T c)/3. We calculate the ignition criterion for carbon according to a one-zone approximation(Fujimoto,Hanawa,&Miyaji1981; Fushiki&Lamb1987b;Cumming&Bildsten2000),compar-ing the temperature sensitivity of the heating rate at the base of the layer to the that of a local approximation to the cool-ing rate.Note that we calculate the temperature sensitivity of the heating rate numerically rather than assume a particular value(Brown2004assumed that d ln?CC/d ln T=26).Al-though approximate,this ignition criterion agrees well with more detailed linear stability(Narayan&Heyl2003)and time-dependent calculations(Woosley et al.2004)for H/He burning,and we expect it to be accurate here also(Cooper& Narayan2005).The carbon burning rate is given by Caughlan &Fowler(1988)with screening from Ogata et al.(1993)7.In addition,at the ignition point we check whether the timescale for carbon depletion is longer than the accumulation time.As shown by CB01,carbon burns stably during accumulation for low accretion rates,so that the thermal instability is avoided. We show only results for which the depletion time is longer than the recurrence time.Our results compare well with those of Brown(2004).Typically,the recurrence times we?nd are a factor of 50%larger than those in Brown(2004),after correcting those results for gravitational redshifting.

3.2.Neutrino cooling and crust composition and

conductivity

The main parameters in our models are the crust neutrino emissivity,the core neutrino emissivity,and the crust compo-sition and conductivity.In the crust,we include cooling due to neutrino Bremsstrahlung according to Haensel,Kaminker, &Yakovlev(1996)in the liquid phase,and Kaminker et al.(1999)in the solid phase.The?tting formula given by Kaminker et al.(1999)is for an equilibrium crust compo-sition.To account for an accreted composition,we multi-ply the emissivity by a factor R where log10R=?0.2for ρ<1011g cm?3,?0.3for1011g cm?3<ρ<1013g cm?3, and?0.4forρ>1013g cm?3.This closely reproduces the results for accreted matter shown in Figure7of Kaminker et al.(1999),and agrees to a factor of3with the formula of Haensel et al.(1996)for densitiesρ>1012g cm?3.

Most importantly,we include the possibility that the neu-trons in the crust are super?uid.In this case,there is an addi-tional neutrino cooling mechanism involving the continuous formation and breaking of Cooper pairs(Flowers,Ruderman, &Sutherland1976;V oskresensky&Senatorov1987).We use the emissivity

calculated by Yakovlev,Kaminker,&Lev-en?sh(1999)(see eq[C5]),and we take the neutron1S0crit-ical temperature T c as a function of density as given by the calculation of Schwenk,Friman,&Brown(2003).We have also used the results of Ainsworth,Wambach,&Pines(1989) (case2from their Fig.3),which has a slightly different pro?le 6The most sensitive case is for fast cooling in the core,and Q=100in the crust,for which changing the outer temperature by a factor of2increases the outwards?ux by a factor of2,and increases the ignition depth by5%.

7The screening calculations of Ogata et al.(1993)are not appropriate for the pycnonuclear regime(e.g.Kitamura2000;Gasques et al.2005).How-ever,for the temperatures T8>2that we consider in this paper,carbon burn-ing is safely thermonuclear.

TABLE2

C ORE NEUTRINO EMISSION

Label Type a Prefactor b Comment

(erg cm?3s?1)

a fast1026fast cooling

b slow3×1021enhanced

c slow1020mURCA

d slow1019nn Bremsstrahlung

e slow1017suppressed

a Fast and slow cooling laws are of the form Qν=Q f(T c/109K)6and Qν= Q s(T c/109K)8respectively.

b Either Q s or Q f for slow or fast cooling,

respectively.

F IG.11.—The effect of core neutrino emissivity on superburst ignition

conditions at˙m=0.3˙m Edd.We assume a disordered lattice in the crust,

and do not include Cooper pairing.The accreted composition is20%12C

(X C=0.2)and80%56Fe by mass.From top to bottom,the temperature

pro?les are for increasing core neutrino emissivity;the letters refer to Table

2.The long-dashed line shows the carbon ignition curve for X C=0.2,and the

vertical dotted line indicates a column depth of1012g cm?2.

and a larger maximum temperature,but the results are simi-

lar and so we do not show them here.Cooper pair emission

was not considered by Brown(2004)and Cooper&Narayan

(2005);however we show here that it has a dramatic effect on

the crust temperature pro?le.

For the core neutrino emissivity,we consider the“fast”

and“slow”cooling laws Qν=Q f(T c/109K)6and Qν=

Q s(T c/109K)8(e.g.Yakovlev&Haensel2003;Yakovlev&

Pethick2004,Page et al.2005).The“standard”slow cool-

ing by modi?ed URCA processes has Q s～1020erg cm?3s?1.

However,if either the core protons or neutrons are super-

?uid,with very high values of T c(?109K),then this pro-

cess is totally suppressed,leading to cooling by nucleon-

nucleon Bremsstrahlung(involving the non-super?uid com-

ponent).This process is roughly a factor of ten slower than

modi?ed URCA,and so we take Q s～1019erg cm?3s?1in

this case.If both protons and neutrons are strongly super-

?uid in the core,the neutrino emission will be supressed

further.To model this case,we assume that the core neu-

trino emission is suppressed by a further factor of100,giving

Q s～1017erg cm?3s?1.However,in the more reasonable case

F IG.12.—The effect of crust composition and conductivity on superburst

ignition conditions.Temperature pro?les for superburst ignition models at

˙m=0.3˙m Edd.We show two cases of core neutrino emissivity:slow cooling

with Q s=1019erg cm?3s?1and fast cooling with Q f=1026erg cm?3s?1.

Solid lines are for a composition of56Fe and a disordered lattice.Short-

dashed lines have a heavier composition(A=106,Z=46),and dot-dashed

lines are for a larger thermal conductivity(Q=100).The long-dashed line

shows the carbon ignition curve for X C=0.2,and the vertical dotted line

indicates a column depth of1012g cm?2.

that the neutron and/or proton T c in the core are of the order

of109K there is intense neutrino emission from the Cooper

pair formation,resulting in an enhanced slow cooling rate

which we model by considering Q s～3×1021erg cm?3s?1

(see,e.g.,Figures20and21in Page et al.2004).Finally,we

also consider a fast cooling rate with Q f～1026erg cm?3s?1

corresponding,e.g.,to the direct Urca process.These mod-

els are summarized in Table2.The core temperature T c

can be estimated in each case.For slow cooling,we?nd

T c≈4.9×108K(f1/8

/Q1/8s,20) ˙m/˙m Edd 1/8and fast cooling

T c≈5.0×107K(f1/6

/Q1/6f,26) ˙m/˙m Edd 1/6where f in is the

fraction of heat released in the crust that is conducted into the

core.

For the composition of the crust,we use the composition

calculated by either Haensel&Zdunik(1990)or Haensel&

Zdunik(2003).The difference between these two calcula-

tions is the nucleus assumed to be present at low densities,ei-

ther56Fe(Haensel&Zdunik1990),or a heavy nucleus106Pd

(Z=46)(Haensel&Zdunik2003),as would be appropriate

if rp-process hydrogen burning is able to run to its endpoint

(Schatz et al.2001).We calculate results for these two cases

to illustrate the variation expected from changes in composi-

tion.For the conductivity,we consider two cases.The?rst

is a“disordered”crust,for which we take the conductivity

to be that of a liquid phase,in the second case,we calculate

the contributions from phonons(Baiko&Yakovlev1996)and

electron-impurity scattering(Itoh&Kohyama1993),taking

the impurity parameter Q=100(see Itoh&Kohyama1993for

a de?nition of the impurity parameter,written as (?Z)2 in

their notation).Note that a crust with Q=100is very impure.

However,we do not consider smaller values of the impurity

parameter because as we will show they would not agree with

observed X-ray burst properties.

F IG.13.—The effect of neutrino cooling by Cooper pairs on superburst

ignition conditions.For two different core neutrino emissivities,we show

temperature pro?les with(solid)and without(dot-dashed)neutrino cooling

by Cooper pairs.These models are for˙m=0.3˙m Edd and have X C=0.2.

The long-dashed line shows the carbon ignition curve for X C=0.2,and the

vertical dotted line indicates a column depth of1012g cm?2.

3.3.Ignition conditions at a?xed accretion rate

We?rst calculate ignition conditions for carbon at˙m=

0.3˙m Edd,for different values of neutrino emission and crust

properties.In order to illustrate the effects of different param-

eters,we start by assuming that the neutrons in the crust are

normal(no

cooling due to Cooper pair neutrinos).For this

case,Figure11shows the effect on the temperature pro?le

of varying the core neutrino emissivity.Less ef?cient neu-

trino emission leads to a higher core temperature and a greater

fraction of the energy released in the crust is emitted through

the surface,heating the carbon layer.At this accretion rate,

standard slow cooling in the core results in recurrence times

>3years,longer than inferred from observations.Some sup-

pression of the modi?ed URCA rate is necessary to bring the

predicted and observed recurrence times into agreement.

Figure12illustrates the effect of the crust composition and

conductivity on the temperature pro?le for fast and slow cool-

ing in the core.At˙m=0.3˙m Edd,the model with Q=100and

fast core neutrino emission gives superburst recurrence times

that are much longer than observed.In general,the change

in ignition depth with composition is much smaller than the

change in ignition depth with other model parameters.This is

because a heavier composition decreases the thermal conduc-

tivity,but also results in less outwards?ux from the crust,as

pointed out by Brown(2004)and Cooper&Narayan(2005).

In Appendix B we give a simple analytic argument to under-

stand this.

We now include neutron super?uidity in the crust.Figure

13shows the dramatic effect of the extra cooling from Cooper

pair neutrino emission.We show pro?les for either fast cool-

ing in the core,or highly suppressed core cooling,with and

without Cooper pair cooling in the crust.When Cooper pair-

ing of neutrons is included,the temperature is limited by neu-

trino losses to a value T 5×108K.This is true even for

highly suppressed neutrino cooling in the core;in this case,

most of the energy release in the crust leaves as neutrino emis-

sion from within the crust itself.In Appendix B,we show

F IG.14.—The critical temperature for neutron super?uidity in the crust,

according to Schwenk et al.2003,and an example of the neutrino emis-

sivity as a function of depth from Cooper pairing(solid lines)and electron

bremsstrahlung(dotted line),for model“e”with Cooper pairing shown in

Figure13.The low density peak in the Cooper pair emissivity corresponds

to column depths in the range1016–1017g cm?2,the peak at higher densities

corresponds to column depths≈3×1018g cm?2near the base of the crust.

how to understand this limiting temperature analytically by

balancing the heating and cooling rates.

Figure13shows that if Cooper pairing is important in

the crust,the superburst recurrence times should be long

≈10years,and insensitive to core neutrino emissivity.In

Figure14,we show the critical temperature for the neutron

super?uid,and the neutrino emissivity from Cooper pairing

and electron Bremsstrahlung for comparison.The Cooper

pair emission is concentrated in two regions where T～T c,as

discussed by Yakovlev et al.(1999),and is therefore sensitive

to the behavior of T c close to the super?uid threshold,which

is uncertain.We address these uncertainties in Appendix C.

However,we?nd that as long as the critical temperature in-

creases from zero to large values,crossing the crust temper-

ature,the process is important.For example,we have tried

modelling the T c pro?le as log-Gaussian in density,and vary-

ing the central density and width,but have not been able to

signi?cantly reduce the Cooper pair neutrino emission.The

peak in emission at lower densities has the largest effect,since

this extra cooling occurs at the location of the energy release

in the crust(close to neutron drip).The peak in emissivity

near the core boundary has a smaller effect,equivalent to an

extra core neutrino emission.

3.4.Variation with accretion rate and comparison to

observations

CB01showed that the ignition conditions are very sensi-

tive to accretion rate,and so a natural question is how much

the results of§3.3depend on the assumed accretion rate.We

explore this dependence here.The accretion rate in the super-

F I

G .15.—Flux from the crust heating the fuel layer and ignition column depth as a function of accretion rate.The solid curves show results for a dis-ordered crust,and a composition of

X C =0.2and 56Fe,for the four different core neutrino emissivities of Figure 11.More ef?cient core neutrino emis-sion gives a lower ?ux from the crust Q b ,and a larger ignition column depth.Other curves show variations on the “d”model.The short-dashed curve is for a heavier composition (A =106,Z =46);the dot-dashed curve is a higher crust conductivity (Q =100);the dotted curve includes Cooper pairing in the crust (labelled ”SF”).The results with Cooper pairing are not very sensitive to the core neutrino emissivity.At low accretion rates,the curves are termi-nated at the accretion rate where the carbon begins to burn stably (de?ned as the point where depletion time for carbon equals the recurrence time).

burst sources is believed to lie in the narrow range 0.1–0.3Ed-dington,but there is some uncertainty in these estimates due to for example uncertainty in the relation between accretion rate and X-ray luminosity,and distance uncertainties.Figure 15shows the ignition column depth and the energy per gram released in the crust that ?ows outwards Q b as a function of accretion rate for different models.

For normal crust neutrons,the constraint on core neu-trino emission can be relaxed if the accretion rate is in fact larger than inferred from the observed X-ray luminos-ity.For example at ˙m ≈0.5˙m Edd ,standard slow cooling from modi?ed URCA reactions explains the observed igni-tion columns.However,with Cooper pair cooling in the crust (dotted curve in Fig.15),the ignition columns remain well above 1012g cm ?2even at accretion rates ≈˙m Edd .This im-plies that some extra heating of the carbon layer must occur that is not included in our model.

Another important point is that with X C =0.2,unstable ig-nition requires ˙m 0.3˙m Edd ,because at lower rates the car-bon burns stably (the curves in Figure 15terminate on the left where the carbon begins to burn stably).A carbon fraction X C 0.2is consistent with the results of our lightcurve ?ts,which gave E 17 2in most cases.

Predictions for the observable quantities recurrence time and superburst energy are shown in Figure 16.We indi-

F I

G .16.—For the models shown in Figure 15,we plot the energy released from the surface in the ?rst 6hours following ignition (as calculated using the cooling models of §2),and the recurrence time.The errorbars indicate the estimated recurrence times and accretion rates for most superburst sources and for the near-Eddington accretor GX 17+2.

cate the observed constraints on recurrence time for super-burst sources,and separately for the rapidly accreting source GX 17+2.Only the models with low neutrino emissivity in the crust and core come close to the observed values at the estimated accretion rates.The accretion rate for GX 17+2is quite uncertain;we adopt a value of ˙m Edd for this source.For a given ignition depth and carbon fraction,we use our cooling models to predict the superburst energy,which we take to be the energy released in the surface in the ?rst 6hours.Note that the energies are close to 1042ergs in Figure 16because we take X C =0.2in these models,the energy would be sig-ni?cantly smaller if X C =0.1.The behavior of the superburst energy with accretion rate is in general not constraining.For long recurrence times 1year,the superburst energy satu-rates at ≈1042erg because of the effects of neutrino cooling and inwards conduction of heat,as discussed in §2.

The overall conclusion is that to achieve ignition at column depths implied by our ?ts requires inef?cient neutrino cooling from the core and the crust,and accretion rates larger than in-ferred from the X-ray luminosity.Even with normal neutrons and core neutrino emission that is less ef?cient than modi?ed URCA,it is dif?cult to reproduce the observed superburst re-currence times and column depths at accretion rates as low as 0.1˙m Edd .Neutrino cooling from the crust due to Cooper pair formation results in ignition depths that are too large even for accretion rates near Eddington.When this process is in-cluded,our models cannot reproduce the observed superburst recurrence times.In addition,carbon fractions of 0.2are required to avoid stable burning of the carbon and achieve un-stable ignition at accretion rates of 0.3˙m Edd .

F I

G .17.—Temperature pro?les for pure helium ignition models at ˙m =0.01˙m Edd ,with a disordered lattice.We show ?ve examples of core neutrino emissivity,a to e from Table 2.The dot-dashed curve is model e including Cooper pair emission from the crust.The long-dashed curve is the triple alpha ignition curve.The dotted line marks a column depth of 1010g cm ?2,as inferred for the long burst from 2S 0918-549observed by in ’t Zand et al.(2005).

4.IGNITION MODELS FOR PURE HELIUM BURSTS

We now consider the constraints that come from pure he-lium accretors.Pure helium bursts are interesting because they can occur at a wide range of accretion rates.Two sources in particular are thought to be accreting pure helium (per-haps with a small amount of hydrogen;Podsiadlowski,Rap-paport,&Pfahl 2002),with accretion rates different by an order of magnitude.The ultracompact binary 4U 1820-30has an orbital period of only 11.4minutes (Stella,Priedhorsky,&White 1987),implying a hydrogen-poor companion.This source shows frequent and regular Type I X-ray bursts whose properties are consistent with accretion of pure helium at rates

close to ˙M

≈0.1–0.2˙M Edd as inferred from the X-ray lumi-nosity at the time when bursts are seen (Bildsten 1995;Cum-ming 2003a).The persistent X-ray source 2S 0918-549is suspected also to be an ultracompact binary because of its low optical to X-ray ?ux ratio,and lack of hydrogen lines in its optical spectrum (Juett et al.2001;Nelemans et al.2004).Recently,a long duration X-ray burst was observed from this source whose properties can be explained by accretion of pure

helium at the observed rate of ˙M

≈0.01˙M Edd (in ’t Zand et al.2005).

We have calculated ignition conditions for pure helium bursts as a function of accretion rate,crust composition,and core neutrino emissivity.The calculations follow those for superburst ignition in §3,except that the accumulated fuel is pure helium,and the nuclear burning rate is given by the triple alpha rate from Fushiki &Lamb (1987a).We start integrat-ing at a column depth of 103g cm ?3,and set the temperature

there proportional to F 1/4

b ,although the solutions are not very sensitive to the outer temperature in most cases.We ?rst consider accretion at a rate ˙m =0.01˙m Edd appro-priate for 2S 0918-549.

Temperature pro?les for this accre-tion rate are shown in Figure 17.We show pro?les for the

F I

G .18.—The outwards heat ?ux Q b ,ignition column depth y ign ,and

predicted energy and recurrence times for pure helium ?ashes,for the same models as Figure 17.In addition,we show a model with Q =100in the crust for core emission “c”(dot-dashed curve),and a model with Cooper pairs included for core emission ”e”(dashed line).

?ve different core neutrino emissivities in Table 2,and for core emissivity “e”but including Cooper pair emission.At ˙m ≈0.01˙m Edd ,Cooper pair emission limits the crust tem-perature to T ≈2.3×108K (see eq.[B6]in Appendix B for an analytic estimate).The long burst from 2S 0918-549(in ’t Zand et al.2005)had an energy of ≈1041ergs,implying an ignition column depth of y ≈1010g cm ?2for an energy release of ≈1018erg g ?1appropriate for helium burning to heavy elements.This column depth is also consistent with the burst lightcurve,which is well-?tted by a cooling model based on this column depth (in ’t Zand et al.2005).Figure 17shows that ignition at y ≈1010g cm ?2requires that the core neutrino emissivity not be more ef?cient than modi?ed URCA.En-hanced slow cooling (model b),e.g.by Cooper pairing in the core,or fast core cooling (model a)lead to ignition at columns of 1011g cm ?2.

F I

G .19.—Predicted burst energy against recurrence time for pure helium ?ashes.For comparison,we show observed burst properties for 4U 1820-30,and 2S 0918-549.The solid curves are for a disordered crust with different core neutrino emissivities,the dot-dashed curve is for standard slow cooling with Q =100in the crust;the dashed curve is for Cooper pairing in the crust and core emission ”e”.

This conclusion is sensitive to the assumed accretion rate.However,models d and e require substantial increases in the accretion rate to obtain burst energies ≈1041ergs,by factors

of 5–10above the inferred rate of 0.01˙M

Edd .Figure 18shows the variation in the heat ?ux from the crust Q b ,ignition depth,and burst energy and recurrence time with accretion rate.The ignition conditions at low accretion rates are not very sensitive to the crust composition,and depend mostly on core neutrino emission.For comparison with the disordered crust models,a crust with Q =100and standard modi?ed URCA slow cooling in the core is shown as the dashed curve in Figure 18.

4U 1820-30accretes at a rate comparable to the super-burst sources,˙m ≈0.2˙m Edd .The burst properties observed in 4U 1820-30are shown in Figure 18.This source under-goes periodic variations in accretion rate,with bursts being seen in the low state when the accretion rate is a factor of two or more below the time-averaged rate.Because the crust tem-perature pro?le is set by the time-averaged rate,we correct for this by plotting the burst properties at the time-averaged rate,and decreasing the recurrence time by a factor of two.The recurrence time is again better explained if the neutrino emis-sion is inef?cient in the core and crust.Whereas Cooper pair neutrino emission does not signi?cantly affect the recurrence times at low accretion rates,it does make a difference at the higher accretion rates appropriate for 4U 1820-30because of the larger crust temperatures.Our results are consistent with the previous analysis of Cumming (2003a),who noted that to achieve ignition for pure helium at the observed rates required a ?ux from the crust of Q b ≈0.4MeV per nucleon.An es-timate of the residual heat released between bursts was not enough to account for this extra ?ux;inef?cient core neutrino emission offers a new explanation.Another complication for this source is that the accreted material may contain a small amount of hydrogen,which can signi?cantly heat the accu-mulating layer and shorten the recurrence time (Cumming 2003a).

An accurate measurement of recurrence time for the long helium burst would impose further constraints.In Figure 19we plot burst energy against recurrence time for the different models.This plot shows clearly that the long duration bursts at low accretion rates are most sensitive to core neutrino emis-sion,whereas short bursts at higher accretion rates are most sensitive to crust composition.The two systems 4U 1820-30and 2S 0918-549therefore offer complementary constraints on the interior model.Unfortunately,the recurrence time for the 2S 0918-549burst is not well constrained (in’t Zand et al.2005).In Figure 19,we show the observed lower limit of 1.1days.

To summarize,the conclusions for pure helium bursts are the same as for superbursts.Enhanced core neutrino emission relative to modi?ed URCA leads to larger ignition columns,energies,and recurrence times than observed for 2S 0918-549.Cooper pairing in the crust leads to much larger recur-rence times and energies than observed for 4U 1820-30.The constraints again depend on the assumed accretion rate,and can be relaxed if the accretion rate is larger than inferred from the X-ray luminosity by factors of 2.

5.SUMMARY AND DISCUSSION

In this paper,we have compared models of carbon and he-lium ignition on accreting neutron stars to observations of long duration X-ray bursts.In particular,we have investi-gated the effect of the thermal pro?le of the crust and core on the ignition conditions,and how well the ignition conditions reproduce the observed burst properties.We have improved on the earlier work of Brown (2004)and Cooper &Narayan (2005)by (i)using cooling models of superbursts to predict observational properties,and then using these lightcurves to provide an independent constraint on ignition depth and ener-getics,(ii)including neutrino cooling in the inner crust due to Cooper pairing of neutrons,and (iii)considering pure helium accretion in addition to carbon.

5.1.Superbursts

We applied the cooling models for superbursts calculated by Cumming &Macbeth (2004)to observed superburst lightcurves.Despite the large uncertainties in distance,we ?nd that the energy release and ignition column depths are quite well constrained,with the best ?tting models giving E 17≈2and y 12=0.5–3.Lower values of E 17give a lumi-nosity at early times that is lower than observed,or equiv-alently,total superburst energies much smaller than the ob-served energies of ≈1042ergs.An upper limit on E 17comes from the lack of photospheric radius expansion observed in most https://www.wendangku.net/doc/e015515848.html,rge values of E 17 2lead to extended periods of super-Eddington luminosities (durations of min-utes and longer),inconsistent with observations.The column depth is determined by the rate at which the luminosity falls in the tail of the superburst.For example,the range of ?t-ted values y 12=0.5–3goes from 4U 1636-54at one end to 4U 1254-690at the other.The superburst from 4U 1254-690is the longest observed,taking 7hours to fall to a luminosity 30%of the peak value,whereas the superburst from 4U 1636-54had a much shorter duration,falling to 30%of the peak luminosity after roughly 1.5hours.In our models,large ig-nition column depths of ≈1013g cm ?2lead to much slower decays than observed.

The ?tted column depths are roughly consistent with obser-vational constraints on recurrence times.At the moment,only 4U 1636-54and GX 17+2have shown multiple superbursts.

F I

G .20.—Ignition column depth for carbon as a function of the ?ux from below heating the accumulating fuel layer.We write the ?ux as the equivalent energy per nucleon at 0.1of the Eddington accretion rate.The solid curve are models with iron as the heavy element,the dashed curve is for a heavy composition A =104,Z =44.The ignition column is not very sensitive to carbon abundance;for this Figure we assume X C =0.2.

For 4U 1636-54we derived a column depth of y 12≈0.5by ?tting the superburst lightcurve.The time between the pre-vious superburst and the superburst observed by RXTE/PCA was 1.75years (Kuulkers et al.2004).Taking this to be the recurrence time and combining with the ?tted ignition col-umn gives an accretion rate ˙m =0.10˙m Edd ,exactly as in-ferred from the persistent X-ray luminosity.For GX 17+2,the mean recurrence time is 30days (in ’t Zand et al.2004),giving an accreted column depth of 2×1011g cm ?2for ac-cretion at ˙m =˙m Edd .The ?tted column depth for burst 2from this source is 6×1011g cm ?2,a factor of 3larger.The gen-eral constraints on superburst recurrence times are 0.4–2years (in’t Zand et al.2003),which gives column depths y ≈1–5×1011g cm ?2(˙m /0.1˙m Edd ).

How do the ?tted column depths compare to carbon igni-tion models for superbursts?The most striking result is that to achieve ignition at the inferred column depths for accre-tion rates thought to be appropriate for these sources,0.1–

0.3˙M

Edd ,requires adjusting each parameter to maximize

the ?ux emerging from the crust.To illustrate this,Figure 20shows the ignition column depth as a function of the base ?ux.We ?nd that the ?ux required for ignition 8at y =1012g cm ?2is Q b ≈0.25(˙m /0.3˙m Edd )?1.Figure 15shows that this value of ?ux requires that (i)crust cooling by Cooper pairs is not active,(ii)the core neutrino emission is signi?cantly reduced below modi?ed URCA,and (iii)the crust conductivity should be “disordered”so that it has a low thermal conductivity.We now discuss the likelihood of satsifying each of these require-ments.

Most important is the effect of Cooper pairs in the crust.

We give the result here for a heavy element of 56Fe.The argument for a heavier composition is similar because as Brown (2004)pointed out,the ?ux emerging from the crust is smaller,compensating for the fact that a smaller ?ux is needed for ignition at a particular column depth.Nonetheless,a heav-ier composition does give a smaller ignition column depth,but the crust and core properties are more important parameters.

F I

G .21.—Maximum outwards ?ux and minimum column depth for un-stable carbon ignition for different carbon fractions.At a given accretion rate,a larger ?ux than indicated in the upper panel results in stable rather than unstable burning of carbon.This translates into the minimum possible column depth for unstable carbon ignition shown in the lower panel.The dotted lines indicate the range of accretion rates for most superburst sources,0.1–0.3˙m Edd .

The emissivity due to this process is large wherever the tem-perature of the crust is close to the critical temperature for super?uidity T c ,because this allows the ef?cient formation and breaking of Cooper pairs (Yakovlev et al.1999).This happens near the base of the crust,but most importantly close to neutron drip where most of the nuclear energy release in the crust occurs.The effect is to limit the temperature of the crust to be 4.4×108K (˙m /˙m Edd )1/7(eq.[B6]).In Ap-pendix C,we discuss the uncertainties in this cooling mecha-nism.The emissivity depends on the T c pro?le with density,however all models that we have tried give substantial cool-ing rates from this process,resulting in ignition columns for superbursts 4×1012g cm ?2for accretion rates less than the Eddington rate.Some extra heating of the accumulating car-bon layer is needed to explain observed superburst properties if Cooper pair cooling is active.

Suppression of the core neutrino emissivity below the mod-

F I

G .22.—Ignition column depth for pure helium as a function of the ?ux from below heating the accumulating fuel layer.We write the ?ux as the equivalent energy per nucleon at 0.1of the Eddington accretion rate.

i?ed URCA rate will occur if either the protons or neutrons are super?uid in the core.However layers whose tempera-ture T ≤T c will copiously emit neutrinos through the Cooper pair process and hence reduction of the core neutrino luminos-ity requires critical temperatures for neutrons and/or protons wich satisfy either T c

Finally,the crust conductivity is expected to be low in ac-creting neutron stars,because hydrogen and helium burning produces a complex mixture of heavy elements (Schatz et al.1999).Our results suggest a completely disordered crust with a thermal conductivity essentially equivalent to that of the liquid state.Even a very impure crust with impurity pa-rameter Q =100does not ?t the data as well as a completely disordered crust.Interestingly,recent work by Jones (2001,2004a,2004b)concludes that the same is likely to be true for the original crust before accretion starts.

It is very important to stress that conclusions about the in-terior thermal properties are sensitive to the choice of local accretion rate.The constraints on core emissivity can be re-laxed by an increase in accretion rate by factors of 2or 3.This is a possibility since the relation between X-ray luminosity and accretion rate is uncertain,and the accreted material may cover only part of the stellar surface (Bildsten 2000).How-ever,we stress that if Cooper pair cooling operates,we cannot reproduce observed superburst properties even for accretion rates near the Eddington rate.

The carbon ignition models also show that a large carbon fraction X C 0.2is needed if conditions for the thermal in-stability are to be achieved before the carbon stably burns away.This is illustrated in Figure 21,which shows the max-imum value of Q b that allows stable burning as a function of ˙m and X C .For larger base ?uxes,the carbon burns sta-bly.This limit on base ?ux translates into a lower limit to the ignition column depth at particular accretion rate,shown in the lower panel of Figure 21.Ignition at column depths near 1012g cm ?2at the observed accretion rates for superburst sources requires X C >0.2.This conclusion is consistent with the lightcurve ?ts,which imply E 17≈2,if carbon burning releases ≈1018X C erg g ?1as expected for carbon burning to iron group.There is no need for additional energy release,for example from photodisintegration of heavy elements (Schatz,Bildsten,&Cumming 2003a).The large inferred carbon frac-tion is an important constraint on models of rp-process hydro-gen and helium burning.Current models suggest that stable burning of hydrogen and helium most likely plays a role in producing the fuel (in ’t Zand et al.2003;Schatz et al.2003b),although further work is needed.

5.2.Pure helium bursts

Pure helium bursts are interesting because they probe lower ignition masses and densities than superbursts,and can occur at a wider range of accretion rates.The likely ultracompact bi-nary 2S 0918-549is a persistent source as far as is known,and

accretes at a rate ≈0.01˙M

Edd .By considering the energetics and by ?tting the burst lightcurve with the cooling models of CM04extended to low column depths,in ’t Zand et al.(2005)showed that this burst is consistent with pure helium ignition at y ≈1010g cm ?2.They also showed that pure helium accre-tion at ≈0.01˙M

Edd gives ignition at 1010g cm ?2if most of the heat released in the crust ?ows outwards.Figure 22shows the ignition column depth for pure helium accretion as a function of base ?ux.At 0.01˙m Edd ,Q b ≈1MeV per nucleon is re-quired for ignition at y ≈1010g cm ?2.Our ignition models in this paper show that this requires that the core neutrino emis-sivity not be enhanced over modi?ed URCA.Either a slow cooling rate enhanced by a factor of 30,or fast cooling in the core give ignition column depths >1011g cm ?2at this accre-tion rate.An increase in accretion rate of factors of >5over the assumed value is required to bring the enhanced cooling models into agreement.At low accretion rates,the ignition depth is most sensitive to core temperature,and is not very sensitive to crust properties.In particular,the crust neutrino emission plays a smaller role than for superbursts because of the lower crust temperatures.

Pure helium bursts are also observed at a similar accre-tion rate to superburst sources,from the ultracompact binary 4U 1820-30.In this case,we showed that the observed burst properties are again best ?t by models which maximize the outwards ?ux from the crust.Models with Cooper pair emis-sion from the crust give ignition depths,recurrence times and

energies that are too large by a factor of5.This is consistent with the previous conclusions of Bildsten(1995)and Cum-ming(2003),who did not consider the crust or core physics, but noted that the helium layer must be quite hot to achieve ig-nition at the depth inferred from observations.If the accretion rate is larger by a factor of 2than inferred from the X-ray luminosity,these constraints are relaxed.The uncertainty as-sociated with the accretion rate can be bypassed by studying the burst energy as a function of recurrence time,as shown in Figure19,however,current constraints are limited.Unlike at low accretion rates,the ignition conditions mainly depend on crust properties at high rates,giving a complementary view of the interior.

5.3.Conclusions and Future Work

The observational progress on long Type I X-ray bursts has opened up a new probe of accreting neutron star in-teriors,complementary to studies of isolated neutron stars (e.g.Yakovlev&Pethick2004,Page et al.2005)and accret-ing neutron stars in quiescence(Brown,Bildsten,&Rutledge 1998;Colpi et al.2001;Rutledge et al.2002;Wijnands et al.2002;Yakovlev et al.2004).We?nd in this paper that the long Type I burst from2S0918-549,a pure helium accretor at 0.01˙M Edd,is best?t by models with core neutrino emissivity equivalent to modi?ed URCA or smaller.For superbursts,and pure helium bursts from4U1820-30,which occur at higher accretion rates 0.1˙M Edd,the ignition models limit both core and crust neutrino emission.In particular,neutrino cooling by Cooper pairing of neutrons in the crust leads to superburst ig-nition column depths that are too large.Either the Cooper pairing emissivity is much less than current calculations sug-gest9(see Appendix C for an assessment of the uncertainties in this process),or an additional heating source not included in current superburst ignition models is required in the accu-mulating fuel layer.

Our models can be improved in several respects.First, our ignition models use the one-zone criterion of Fujimoto, Hanawa,&Miyaji(1981)and Bildsten(1998)to estimate the ignition column depth.Although this technique compares well with numerical simulations and normal mode analyses (e.g.Woosley et al.2003;Cooper&Narayan2005),time-dependent calculations of ignition should be carried out to cal-culate ignition conditions.These calculations are in progress (Halpin&Cumming2005,in preparation).Our cooling mod-els for burst lightcurves assume instantaneous burning of the fuel,and cannot address the physics of the rise.Further stud-ies of the superburst rise are needed.An additional motiva-tion for this is to understand the observed precursors to super-bursts,possibly due to triggering of an overlying H/He layer by the carbon runaway.

The thermal models of the interior used here assume steady state accretion.In fact,superbursts have been observed from transient systems,in which case the core temperature will be lower than assumed in our models.Observations of quiescent cooling in KS1731-260(Rutledge et al.2002;Wijnands et al.2002),interpreted as cooling of the crust,imply a cold core and high crust conductivity,exactly opposite to the conclu-sions from superburst ignition calculations,as emphasized by Brown(2004).The time-dependent calculations of Rutledge et al.(2002)for this source indicate that the crust tempera-ture reaches a maximum value of≈2.5×108K,lower than the temperature in our steady-state models.Cooper pair cool-ing in the crust was not included in the models of Rutledge et al.(2002),but is probably not important at these low tem-peratures.The lower crust temperatures may make achieving ignition at the inferred column depth for KS1731-260dif?-cult,implying that an extra heating mechanism is required in superburst models.On the other hand,this may be related to the larger ignition column depth for KS1731-260compared to sources such as4U1636-54for example.Further work on the time-dependent thermal pro?le in transiently accret-ing sources and the consequences for superburst ignition is needed.

We thank L.Bildsten,E.Brown,and R.Rutledge for help-ful comments,and T.Strohmayer and R.Cornelisse for kindly supplying RXTE/PCA and BeppoSAX/WFC lightcurves.We thank Achim Schwenk and Dima Yakovlev for discussions about the content of Appendix C.AC acknowledges support from McGill University startup funds,an NSERC Discovery Grant,Le Fonds Québécois de la Recherche sur la Nature et les Technologies,and the Canadian Institute for Advanced Research.We thank S.Woosley for making possible support for JM at the University of California,Santa Cruz through DOE grant No.DE-FC02-01ER41176to the Supernova Sci-ence Center/UCSC.DP aknowledges partial support from a UNAM-DGAPA grant#IN112502.

9An alternative explanation is that these sources are not neutron stars but rather“strange stars”(e.g.Alcock,Farhi,&Olinto1986).Strange stars do not have an inner crust which would naturally explain the lack of emission due to Cooper pairing of neutrons.This scenario is explored in Page&Cum-ming2005).

APPENDIX

A.THE EARLY PHASE OF THE SUPERBURST LIGHTCURVE

When?tting our time-dependent cooling models to observed superburst lightcurves,the inferred value of E17depends on the early part of the cooling curve,for times shorter than the thermal time of the fuel layer.Therefore it is important to understand the physics of this phase of the lightcurve.In this Appendix,we describe a simple steady-state model of the early cooling which highlights the physics,and gives us con?dence in our numerical results.

CM04showed that after the fuel burns,the early phase of the superburst lightcurve is set by a cooling wave which propagates inwards from the surface.At column depth y,there is a characteristic thermal timescale t therm(y)≈H2/D,where H is the pressure scale height,and D the thermal diffusivity.The thermal timescale grows with depth.After time t,the cooling wave has penetrated to a depth y b at which t≈t therm(y b).At lower column depths yy b,the temperature pro?le has not evolved signi?cantly from its initial state.

This picture suggests a simple model of the early phase of the lightcurve.We?rst make an analytic estimate for constant opacity in the layer,and then present numerical calculations integrating the true opacity pro?le.For constant opacity,the temperature

pro?le in the constant?ux region is given by integrating F=(4acT3/3κ)(dT/dy)from the surface.The radiative zero solution is

T=4.0×109K F1/4

24y1/4 12 κ

0.02cm2g?1 ?1 g14

K =

3c Pκy2

E17 κ2.45 ?1/4.(A4) Now setting t=t therm and rewriting equation(A2)in terms of t therm using equation(A4)speci?es the?ux evolution with time.We ?nd

F24≈2.2 t0.02cm2g?1 ?2/3 g14

F I

G .A23.—Flux as a function of time for E 17=1(lower curves)and E 17=2(upper curves).The solid curves show the simple steady-state model described here;the dotted curves are the results of time-dependent simulations (with y 12=

1).

F I

G .A24.—Opacity (continuous line)as a function of depth immediately after burning for E 17=2.We also show the separate contributions to radiative opacity from electron scattering (es;dotted curve)and free-free absorption (ff;short-dashed curve),and the contribution from electron conduction (cond;long-dashed curve).At low densities,electron scattering dominates the opacity;at high densities,free-free absorption blocks radiative transport of heat,and electron conduction takes over.

the energy enters the core.In this case,the peak temperature in the crust is whatever it needs to be to conduct the heat into the core,given the thermal conductivity.If electron-ion collisions set the conductivity,as for a disordered crust,then

K =

π2k 2

B T n e

4e 4m ?Z (B1)(e.g.Yakovlev &Urpin 1980),where we assume a single species of ions with charge Z ,m ?=E F /c 2is the electron effective mass,and the second term is the inverse of the electron-ion collision frequency.We have set the Coulomb logarithm to unity,a reasonable approximation for our purposes.

We now solve F =ρKdT /dy in the inner crust to ?nd the temperature pro?le.In the inner crust,the pressure is mostly from degenerate non-relativistic neutrons,giving P ∝(Y n ρ)5/https://www.wendangku.net/doc/e015515848.html,ing this to integrate,we ?nd

T 8≈16f 1/2

˙m 2×1014g cm ?3

1/6,(B2)where we write the fraction of the energy released in the crust that ?ows inwards as f in .To write this expression,we have assumed that the core temperature is much smaller than the maximum crust temperature,and that the density at the crust/core boundary

is much greater than the density at the location of the temperature maximum(these approximations are good enough for our purposes).We have also taken Y n=0.8,Y e=0.05,and Z=22in the inner crust.The accretion rate enters this formula because the inwards?ux is F=f in Q nuc˙m.

Similarly,we can integrate into the crust from low densities.In the outer crust,degenerate relativistic electrons set the pressure. In this case,the temperature pro?le is given by

T8≈7.9 f out12 1/2 ˙m20 1/2(B3) (see also CB01),where P0is the outer pressure at which we start the integration,and we have assumed that the temperature there is small.

Now matching the outer and inner temperatures,and assuming that f out+f in=1and f out?1,we?nd

Q b≈Q nuc f out≈0.3MeV per nucleon Z2/A

˙m Edd <0.10MeV per nucleon ˙m12 ?1 ln(P1/P0)

˙m Edd <0.043MeV per nucleon

˙m12 ?1 ln(P1/P0)

C.NEUTRON1S0PAIRING AND NEUTRINO EMISSION BY THE FORMATION OF COOPER PAIRS

Neutron1S0pairing

Given the importance of the neutrino energy losses due to the Cooper pair formation process found in this work,we describe in this Appendix in some detail the nature of the underlying physics and robustness of the ingredients needed for our models. First of all,the existence of a neutron drip regime is beyond doubt and results from the?nite depth(～50MeV)and?nite width (～nucleus diameter)of the nuclear potential,i.e.,this potential can only accomodate a?nite,and small,number of bound states. With increasing density,the enormous Fermi energy of the electrons leads to neutronization and the resulting large number of neutrons cannot be accomodated within the bound levels,i.e.,neutrons have to drip at high enough density12.These dripped neutrons form a degenerate Fermi liquid and,according to the Cooper theorem(Cooper1956),they will unavoidably pair and become a super?uid if there is any attractive interaction between them(immediately afer the development of the BCS theory it was proposed that nucleons in nuclei must pair due to this mechanism;Bohr,Mottelson,&Pine1958).The important,and delicate,issue is the value of the pairing critical temperature T c which depends very sensitively on the strength of the pairing interaction.At the density range relevant for a neutron star crust the dominant attractive interaction between the dripped neutrons is in the spin-angular momentum channel1S0,which,fortunately is very well understood in vacuum.

In a medium,many-body effects alter the interaction and much effort has been dedicated to studying them(see,e.g.,Lombardo &Schulze2001for a review).At the densities corresponding to neutron star cores,there are still very large uncertainties in the size and density extent of the gaps,but in the low density regime of the crust the situation is much better.Many-body techniques used to calculate the size of the neutron1S0gap have increased in sophistication with time and results obtained in the last?fteen years show a clear convergence.The most important effect turns out to be the polarization of the medium which,in some sense, screens the interaction between neutrons and results in a reduction of the gap.We plot in Figure C25results of the most reliable calculations(as well as one example of a calculation which explicitly did not include the effects of medium polarization for illustration of the importance of this effect).Numerical values are listed in Table C3as well as reference to the relevant works. Both the table and the?gure illustrate the present uncertainties on T c.A good indication of the convergence of the models is that the most recent calculations of Schwenk,Friman,&Brown(2003)incorporated signi?cant new improvements and obtained values for T c very close to previous calculations.Given the range of temperatures in accreting neutron star crusts,1?8×108K, and considering that the Cooper pair neutrino process becomes negligible when T<0.2T c(see below),the important region is at neutron Fermi momenta smaller than0.5fm?1,i.e.,densities below1013g/cm3(Fig C25)where all T c curves we show are very close to each other.At higher densities the differences become signi?cant but,fortunately,they do not seriously affect our results. For very low neutron densities one can use the following analytical solution(Schwenk2004),which incorporates the medium polarization effect to calculate the zero temperature energy gap(see next paragraph),

?(0)=(2/e)7/3?F exp(π/2k F a nn)(C1) where a nn=?18.5fm is the neutron-neutron scattering length and?F≡k2F/2m n.The above formula is formally valid only when |k F a nn|?1but gives reasonable results even at k F～0.1fm?1.At all densities it is customary to calculate the critical temperature T c using the BCS result

?(0)=1.76T c.(C2) Even though this is not necessarily correct for calculations beyond the BCS approximation,it gives a credible value for T c.

Neutrino emission by Cooper pair formation

The essence of pairing is the formation of a condensate of Cooper pairs,with the result that the energy of single-particle excitation changes from

?(k)=ˉh2k2

2M n

=v Fˉh(k?k F)with v F≡

dk k=k F(C3)

in absence of pairing to

?P(k)=

M n c T79?F(T/T c)erg cm?3s?1.(C5) The control function13?F is plotted in Figure C26.The shape of?F re?ects the fact that when T～T c only a small fraction of neutrons are in the paired state and the gap is small,resulting in a diminished emission of neutrinos with little energy,while when 12The only exception to this can occur in a“strange star”made of self-bound strange quark matter,in which normal baryonic matter can exist only below the neutron drip density in the form of a thin outer crust(Alcock,Farhi,&Olinto1986).

13Our normalized function?F is related to the F of Yakovlev et al.(1999)by?F=F/F max with F max=4.313.

TABLE C3

C RITICAL TEMPERATURE T c,VS NEUTRON F ERMI MOMENTUM k F,FOR FIVE RELIABLE CALCULATIONS

AWP II&AWP III:Ainsworth,Wambach,&Pines(1989),WAP:Wambach,Ainsworth,&Pines(1993),CCDK:Chen et al.(1993),SFB:Schwenk,Friman,& Brown(2003).

?For values of k F this small,T c cannot be found from the above references,except in the“SFB”case:using

Eq.C1one obtains T c=1.9×108K(Schwenk 2004).

F IG.C25.—Modern results for the neutron1S0pairing critical temperature T c as a function of the neutron Fermi momentum k F,from Table C3.The curve labelled“CCKS”from an older calculation(Chen et al.1986),in contradistinction to the other ones does not include medium polarization effects and is shown for illustration.The upper scale shows the corresponding densities for a crust chemical composition as used in the present work

T?T c it becomes impossible to break pairs and hence pair formation does not occur anymore,resulting in a strong suppression of the emissivity approximately by a Boltzmann-like factor exp??(0)/k B T.

This neutrino emission process is extremely ef?cient but not“exotic”in any way and has to be considered in any cooling neutron star model,even minimal(Page et al.2004).Finally,we mention that a similar process occurs in the laboratory when free electrons are injected into a superconductor,although the energy released is emitted predominantly in phonons(Schrieffer& Ginsberg1962)instead of neutrinos(!),leading to a pair formation rate in agreement with experiments(see,e.g.,Carr et al.2000

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术，检测周期长、效率低下。“十二五”期间，将有更多的油气管道建设工程相继启动，如何将一种可靠的、快速的、“绿色”的射线数字检测技术应用于工程建设中，以替代传统射线胶片检测技术已成为目前管道焊缝射线检测领域亟需解决的问题。 2 国内外管道焊缝数字化检测的现状 2.1 几种主要的射线数字检测技术 1）CCD型射线成像（影像增强器） 2）光激励磷光体型射线成像（CR） 3）线阵探测器（LDA）成像系统 4）平板探测器（FPD）成像系统几种技术各有特点，目前适用于管道工程检测的是CR 和FPD，但CR不能实时出具检测结果，且操作环节较繁琐、成本较高，因此平板探测器成像系统成为射线数字检测的主要发展方向。 2.2 国内研发情况国内目前从事管道焊缝射线数字化检测系统研发的机构主要有几家射线仪器公司，但其产品主要用于钢管生产厂的螺旋焊缝检测。通过实践应用比较，研究应用电子学研究所研发的基于平板探测器的管道焊接射线数字化检测与评估系统已能够满足管道工程检测需要，并通过了科技成果鉴

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K层电子被逐出后,其空穴可以被外层中任一电子所填充，从而可产生一系列的谱线，称为K系谱线：由L层跃迁到K层辐射的X射线叫Kα射线,由M层跃迁到K层辐射的X射线叫Kβ射线……。同样,L层电子被逐出可以产生L系辐射(见图1-2)。

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全固态薄膜锂离子二次电池的研究进展

论著8 全固态薄膜锂离子二次电池的研究进展耿利群任岳*朱仁江陈涛（重庆师范大学物理与电子工程学院，重庆 400047）摘要：本文综述了全固态薄膜锂离子二次电池的研究进展，主要阐述了薄膜锂电池的结构设计以及正极、负极和固体电解质材料研究现状，并对其今后的发展趋势及研发热点进行了展望。关键词：全固态薄膜锂离子二次电池；固体电解质；电池结构 DOI：10.3969/j.issn.1671-6396.2013.01.004 1 引言随着电子信息工业和微型加工技术快速发展，对其所需的微型能源则提出了特殊微型化的要求。其中全固态薄膜锂离子二次电池因其高的能量密度、强的安全性、长的循环寿命、宽的工作电压和重量轻等优点，成为微电池系统需求的最佳选择[1]。本文主要介绍了全固态薄膜锂离子二次电池的关键性薄膜材料及电池结构的研究现状，并对其的开发应用及研究前景作了分析。 2 全固态薄膜锂离子二次电池结构的研究薄膜电池结构的设计，对整个电池性能将产生直接的影响；同样对提高电池的能量密度、循环寿命和锂离子的传输速率也起到至关重要的作用。所以优化薄膜电池结构的设计，则是对构造高性能薄膜锂离子电池做到了强有力的支撑。 1993年美国橡树岭国家实验室（ORNL）Bates等[2]研制出了一种经典的薄膜锂离子电池叠层结构（见图1）。在衬底上先沉积两层阴阳极电流收集极薄膜，而后依次沉积阴极、固体电解质和阳极薄膜，最后在薄膜电池外表面上涂一层保护层，以此来防止阳极上金属锂和空气中的一些物质发生化学反应。图1 薄膜锂离子电池结构剖面示意图 Baba等[3]研发出另一种典型的薄膜锂离子电池结构（见图2）。其较图1薄膜锂电池结构设计更为简单，制作更为容易。在不锈钢衬底上依次沉积各层薄膜电池材料，而在图示中有两个引线端子则是为了便于薄膜电池的连接使用。这种结构设计很好地提高了整个电池的有效面积，进而也极大地改善了薄膜电池的性能。 Nakazawa等[4]利用直流溅射和射频溅射的方法，研制出一种“直立型”全固态薄膜锂离子电池结构（见图3）。该研究小组利用该薄膜电池结构设计，成功制备出有效面积更大的全固态薄膜锂离子电池，这样也使得薄膜电池的能量密度和循环寿命等电化学性能得到大幅度提升。图2 全固态薄膜锂离子电池结构剖面示意图图3 “直立型”全固态薄膜锂离子电池剖面示意图 Hart等[5]设计了柱状电极交替排列的微型锂电池结构（见图4）。并对几种不同的正极、负极排列方式进行了相关的研究计算，得出了此薄膜电池的结构能够大大提升薄膜电池本身的能量密度。然而Eftekhari[6]则研制出了一种3-D微型锂电池结构的LiMn2O4电极，与以往微型锂电池结构的LiMn2O4电极在电池容量方面得到了提升。图4 3-D微电池柱状结构示意图 [正极（灰色）、负极（白色）交替排列分布]

晶体X射线衍射实验报告全解

中南大学 X射线衍射实验报告材料科学与工程学院材料学专业1305班班级姓名学号0603130500 同组者无黄继武实验日期2015 年12 月05 日指导教师评分分评阅人评阅日期一、实验目的 1)掌握X射线衍射仪的工作原理、操作方法； 2)掌握X射线衍射实验的样品制备方法； 3)学会X射线衍射实验方法、实验参数设置，独立完成一个衍射实验测试； 4)学会MDI Jade 6的基本操作方法； 5)学会物相定性分析的原理和利用Jade进行物相鉴定的方法； 6)学会物相定量分析的原理和利用Jade进行物相定量的方法。本实验由衍射仪操作、物相定性分析、物相定量分析三个独立的实验组成，实验报告包含以上三个实验内容。二、实验原理

1 衍射仪的工作原理特征X射线是一种波长很短(约为20～0.06nm)的电磁波，能穿透一定厚度的物质，并能使荧光物质发光、照相乳胶感光、气体电离。在用电子束轰击金属“靶”产生的X射线中，包含与靶中各种元素对应的具有特定波长的X射线，称为特征（或标识）X射线。考虑到X射线的波长和晶体内部原子间的距离相近，1912年德国物理学家劳厄(M.von Laue)提出一个重要的科学预见：晶体可以作为X射线的空间衍射光，即当一束X射线通过晶体时将发生衍射，衍射波叠加的结果使射线的强度在某些方向上加强，在其他方向上减弱。分析在照相底片上得到的衍射花样，便可确定晶体结构。这一预见随即为实验所验证。1913年英国物理学家布拉格父子(W. H. Bragg, W. L Bragg)在劳厄发现的基础上，不仅成功地测定了NaCl、KCl等的晶体结构，并提出了作为晶体衍射基础的著名公式──布拉格定律： 2dsinθ=nλ 式中λ为X射线的波长，n为任何正整数。当X射线以掠角θ（入射角的余角，又称为布拉格角）入射到某一点阵晶格间距为d的晶面面上时，在符合上式的条件下，将在反射方向上得到因叠加而加强的衍射线。 2 物相定性分析原理 1) 每一物相具有其特有的特征衍射谱，没有任何两种物相的衍射谱是完全相同的 2) 记录已知物相的衍射谱，并保存为PDF文件 3) 从PDF文件中检索出与样品衍射谱完全相同的物相 4) 多相样品的衍射谱是其中各相的衍射谱的简单叠加，互不干扰，检索程序能从PDF文件中检索出全部物相 3 物相定量分析原理 X射线定量相分析的理论基础是物质参与衍射的体积活重量与其所产生的衍射强度成正比。当不存在消光及微吸收时，均匀、无织构、无限厚、晶粒足够小的单相时，多晶物质所产生的均匀衍射环上单位长度的积分强度为：式中R为衍射仪圆半径，V o为单胞体积，F为结构因子，P为多重性因子，M为温度因子，μ为线吸收系数。三、仪器与材料 1)仪器：18KW转靶X射线衍射仪 2)数据处理软件：数据采集与处理终端与数据分析软件MDI Jade 6 3)实验材料：CaCO3+CaSO4、Fe2O3+Fe3O4

射线数字成像检测技术

射线数字成像检测技术韩焱 (华北工学院现代元损检测技术工程中心，太原030051) 摘要：介绍多种射线数字成像(DR)系统的组成及成像机理，分析其性能指标、优缺点及应用领域。光子放大的DR系统(如图像增强器DR系统)实时性好，但适应的射线能量低，检测灵敏度相对较低；其它系统的检测灵敏度较高但成像时间较长。DR系统成像方式的主要区别在于射线探测器，除射线转换方式外，影响系统检测灵敏度的主要因素是散射噪声和量子噪声；可采用加准直器和光量子积分降噪的方法提高检测灵敏度。关键词：射线检验；数字成像系统；综述中图分类号：TGll5.28 文献标识码：A 文章编号：1000-6656(2003109-0468-04 DIGITAL RADIOGRAPHIC TECHNOLOGY HAN Yan （Center of Modern NDT ＆E, North China Institute of Technology, Taiyuan 030051, China) Abstract: The structure and imaging principle of digital radiographic （DR） systems are introduced. And thecharacteristics, performances, advantages, disadvantages and applications of the systems are analyzed. The DR sys-tern with photon amplification such as the DR system with intensifier can get real-time imaging, but it fits for lowerenergy and its inspection sensitivity is lower. The systems working with high energy can obtain higher sensitivity,while is time-eonsurning. The imaging way of a DR system depends on the detector used, and the factors influencinginspection sensitivity are the quantum noise from ray source and scatter noise besides the transform way of rays.Quantum integration noise reducer and collimator can be used to improve the inspection sensitivity of the system. Keywords:Radiography; Digital imaging system; Survey 射线检测技术作为产品质量检测的重要手段，经过百年的历史，已由简单的胶片和荧屏射线照相发展到了数字成像检测。随着信息技术、计算机技术和光电技术等的发展，射线数字成像检测技术也得到了飞速的发展，新的射线数字成像方法不断涌现，给射线探伤赋予了更广泛的内涵，同时也使利用先进网络技术进行远程评片和诊断成为可能。目前工业中使用的射线数字成像检测技术主要包括射线数字直接成像检测技术(Digital Radio—graphy，简称DR)和射线数字重建成像检测技术，如工业CT(Industry Computed Tomography，简称ICT)。以下将在介绍DR检测系统组成的基础上，重点分析系统的成像原理、特点、特性及应用场合。 1 DR检测系统简介 DR检测系统组成见图1。按照图像的成像方式分为线扫描成像和面扫描成像；根据成像过程可分为直接和间接式DR系统。以下重点介绍直接DR系统。图1 DR检测系统组成框图 1.1 直接式DR系统直接DR成像系统主要分为图像增强器成像系统、平板型成像系统和线阵扫描成像系统等。图2为图像增强器式DR系统，主要通过射线视频系统与数字图像处理系统集成实现。系统采用射线--可见光--电子--电子放大--可见光的光放大技术，是将射线光子由转换效率较高的主射线转换屏转换为可见光图像，可见光光子经光电转换变为电子，而后对电子进行放大，放大后的电子聚集在小屏上再次

薄膜锂电池

能源材料课程业 ——薄膜锂电池的研究进展院系：材料科学与工程学院专业：金属材料与成型加工班级：2012级金属材成1班学号：20120800828 姓名：吴贵军

薄膜锂电池的研究进展摘要：微电子机械系统(MEMS)和超大规模集成电路(VLSI)技术的发展对能源的微型化、集成化提出了越来越高的要求.全固态薄膜锂电池因其良好的集成兼容性和电化学性能成为MEMS和VLSI能源微型化、集成化的最佳选择.简单介绍了薄膜锂电池的构造,举例说明了薄膜锂电池的工作原理.从阴极膜、固体电解质膜、阳极膜三个方面概述了近年来薄膜锂电池关键材料的研究进展.阴极膜方面LiCoO2依旧是研究的热点,此外对LiNiO2、LiMn2O4、LiNixCo1-xO2、V2O5也有较多的研究;固体电解质膜方面以对LiPON膜的研究为主;阳极膜方面以对锂金属替代物的研究为主,比如锡的氮化物、氧化物以及非晶硅膜,研究多集中在循环效能的提高.在薄膜锂电池结构方面,三维结构将是今后研究的一个重要方向.。关键词：薄膜锂电池；微系统；薄膜：微电子机械系统随着电子集成技术的飞速发展，SO C (System on chi p) 成为现实，电子产品在不断地小型化、微型化。以整合集成电路及机械系统，如各种传感器于同一块晶片上的技术，即微机电技术，受到了普遍重视。微小型飞行器、微小型机器人和微小型航天器等都在源源不断地出现和进一步地改进。这些微型系统的功能强大，必然对其能源系统提出了微型化的

要求。当电池系统被微型化，电池底面积小于10 m m2、功率在微瓦级以下时，被称为微电池。微电池的制备通常是将传统的电池微型化、薄膜化。目前，用于微电池的体系有：锌镍电池、锂电池、太阳能电池、燃料电池、温差电池和核电池。锂电池是目前具有较高比能量的实用电池体系，因此人们对薄膜化的锂电池投入了大量的研究。优点：（1）成本低，根据Photon 的预测，预计到2012 年下降到2.08 美元/w；预计薄膜电池的平均价格能够从2.65 美元/w 降至1.11 美元/w，与晶体硅相比优势明显；而相关薄膜电池制造商的预测更加乐观，EPV 估计到2011 年，薄膜组件的成本将大大低于1 美元/w；Oerlikon 更估计2011 年GW 级别的电站其组件成本将降低于0.7 美元/w，这主要是由转化率提高和规模化带来的。（2）弱光性好（3）适合与建筑结合的光伏发电组件(BIPV)，不锈钢和聚合物衬底的柔性薄膜太阳能电池适用于建筑屋顶等，根据需要制作成不同的透光率，代替玻璃幕墙。缺点：（1）效率低，单晶硅太阳能电池，单体效率为14%-17%(AMO)，而柔性基体非晶硅太阳电池组件（约1000平方厘米）的效率为 10-12%，还存在一定差距。

X射线数字成像检测系统郑金泉.doc

实用标准文档 X射线数字成像检测系统

目录一、目的意义 (3) 二、系统介绍 (3) 2.1 CR 技术与 DR技术的共同点 (4) 2.2 CR 技术与 DR技术的不同点 (4) 2.3 对比分析 (5) 2.4 系统组成 (5) 2.5 X 射线数字平板探测器 (6) 2.6 X 射线源 (7) 2.7 图像处理系统 (8) 2.8 成像板扫描仪 (9) 2.9IP 成像板 (9) 三、 DR检测案例 (10) 3.1 广西 220kV 振林变 (10) 3.2 广西 220kV 水南变 (11) 3.3 温州 220kV 白沙变 (13) 3.4 广西 110kV 城东变 (15) 3.5 广西乐滩水电站 (16) 四、 CR检测案例 (18) 4.1 百色茗雅 220kV变电站 (18)

一、目的意义气体绝缘全封闭组合电器（GIS）设备结构复杂，由断路器、隔离开关、接地开关、互感器、避雷器、母线、连接件和出线终端等组成，内部充有SF6绝缘气体，给解体检修工作带来很大的困难，且检修工作技术含量高，耗时长，停电所造成的损失大。通过对 GIS 设备事故的分析发现，大部分严重事故，未能通过现有的检测手段在缺陷发展初期被发现，导致击穿、烧损等严重事故的发生。通过 GIS 设备局放监测，结合专家数据库和现场经验，可大致判断 GIS 设备局放类型，进行大致的定位，但无法明确GIS 设备内部的具体故障。结合X 射线数字成像检测系统，对 GIS 设备进行多方位透视成像，配合专用的图像处理与判读技术，实现其内部结构的“可视化”与质量状态快速诊断，极大地提高 GIS 设备故障定位与判别的准确性，提高故障诊断效率，为整个设备的运行安全与质量监控提供一种全新的检测手段。对 GIS 设备局放可能造成的危害及其影响范围和程度，提出相应策略，采取相应的措施，对电网的安全、稳定、经济运行具有重要意义。二、系统介绍按照读出方式（即X 射线曝光到图像显示过程）不同，可分为：数字射线成像（ DR-Digital Radiography）计算机射线成像（ CR-Computed Radiography）图 1-1 检测原理图

X射线数字成像检测系统

X射线数字成像检测系统X射线数字成像检测系统

(XYG-3205/2型) 一、设备基本说明 X射线数字成像系统主要是由高频移动式(固定式)X射线探伤机、数字平板成像系统、计算机图像处理系统、机械电气系统、射线防护系统等几部分组成的高科技产品。它主要是依靠X射线可以穿透物体，并可以储存影像的特性，进而对物体内部进行无损评价，是进行产品研究、失效分析、高可靠筛选、质量评价、改进工艺等工作的有效手段。探伤机中高压部分采用高频高压发生器，主机频率40KHz为国际先进的技术指标。连续工作的高可靠性，透照清晰度高，穿透能力强，寿命长，故障率低等特点。X光机通过恒功率控制持续输出稳定的X射线，波动小，保证了优质的图像质量。高频技术缩短了开关机时间，有助于缩短检测周期，提高工作效率。数字平板成像采用美国VEREX公司生产的Paxscan2530 HE型平板探测器，成像效果清晰。该产品已经在我公司生产的多套实时成像产品中使用，性能稳定可靠。计算机图像处理系统是我公司独立自主研制开发的、是迄今为止国内同行业技术水平最高的同类产品。主要特点是可以根据不同行业用户的需求，编程不同的应用界面及图像处理程序，利用高性能的编程技术，使操作界面简单易懂，最大限度的减少操作步骤，最快速度的达到操作人员的最终需求。机械传动采用电动控制、无极变速，电气控制采用国际上流行的钢琴式多功能操作台，将本系统中的X射线机控制、工业电视监视、机械操作等集中到一起，操作简单、方便。该系统的自动化程度高, 检测速度快，极大地提高了射线探伤的效率，降低了检验成本，检测数据易于保存和查询等优点，其实时动态效果更是传统拍片法所无法实现的，多年来该系统已成功应用于航空航天、军事工业、兵器工业、石油化工、压力容器、汽车工业、造船工业、锅炉制造、制管行业、耐火材料、低压铸造、陶瓷行业、环氧树脂材料等诸多行业的无损检测中。

射线数字成像技术发展

射线数字成像技术发展摘要：射线数字成像是一种先进辐射成像技术，是辐射成像技术的重要发展方向，该技术利用射线观察物体内部的技术。这种技术可以在不破坏物体的情况下获得物体内部的结构和密度等信息，并且通过计算机进行图像处理和判定。目前已经广泛应用于医疗卫生、国民经济、科学究等领域。关键词：辐射成像射线数字成像 1引言自德国物理学家伦琴1895年发现X射线以来，射线无损探伤作为一种常规的无损检测方法在工业领域应用已有近百年的历史，人们一直使用胶片记录X（γ）射线穿过被检物件后的影像，其中60多年来，则一直使用增感屏配合胶片来获取高品质的影像，曝光过后的胶片经过化学处理，产生可视的影像后，在观片灯上显示出来以供读取、分析及判断。胶片-增感屏系统可使射线检测人员实现对影像的采集、显示和存储。这种方法操作简单，产生的图像质量优异，功能效用全面，因此该技术在包括核工业在内的工业、医疗领域一直被广泛使用。胶片照相法的不足在于检测周期长，因为需要暗室处理，检测周期在3～20个小时不等；大量底片造成保存上的困难，查阅不便；胶片成本高；曝光时间长；在大量的检测工作面前，需要大量人力资源；底片难以共享，某些焊缝底片在需要专家共同研讨评定时，该弊端特别明显；不利于环境保护等。无法满足目前工业化生产和竞争日益激烈的需要。随着科学技术和设备制造能力的进步，例如电子技术、光电子技术、数字图像处理技术的发展；高亮度高分辨率显示器的诞生；高性能计算机/工作站的广泛应用；计算机海量存储、宽带互联网的发展，使得数字成像技术挑战传统胶片成像方式在技术上形成可能。以射线DR、CR和CT为代表的数字射线成像技术，结合远程评定技术将是无损检测技术领域的一次革命。数字射线照相技术具有检测速度快，图像保存方便，容易实现远程分析和判断，是未来射线检测发展的方向[1]。

X射线数字成像检测系统(郑金泉)

X射线数字成像检测系统

目录一、目的意义 (3) 二、系统介绍 (3) 2.1 CR技术与DR技术的共同点 (4) 2.2 CR技术与DR技术的不同点 (4) 2.3对比分析 (5) 2.4 系统组成 (5) 2.5 X射线数字平板探测器 (6) 2.6 X射线源 (7) 2.7 图像处理系统 (8) 2.8成像板扫描仪 (9) 2.9IP成像板 (9) 三、DR检测案例 (10) 3.1 广西220kV振林变 (10) 3.2 广西220kV水南变 (11) 3.3 温州220kV白沙变 (13) 3.4 广西110kV城东变 (15) 3.5 广西乐滩水电站 (16) 四、CR检测案例 (18) 4.1百色茗雅220kV变电站 (18)

一、目的意义气体绝缘全封闭组合电器（GIS）设备结构复杂，由断路器、隔离开关、接地开关、互感器、避雷器、母线、连接件和出线终端等组成，内部充有SF6绝缘气体，给解体检修工作带来很大的困难，且检修工作技术含量高，耗时长，停电所造成的损失大。通过对GIS设备事故的分析发现，大部分严重事故，未能通过现有的检测手段在缺陷发展初期被发现，导致击穿、烧损等严重事故的发生。通过GIS设备局放监测，结合专家数据库和现场经验，可大致判断GIS设备局放类型，进行大致的定位，但无法明确GIS设备内部的具体故障。结合X射线数字成像检测系统，对GIS设备进行多方位透视成像，配合专用的图像处理与判读技术，实现其内部结构的“可视化”与质量状态快速诊断，极大地提高GIS 设备故障定位与判别的准确性，提高故障诊断效率，为整个设备的运行安全与质量监控提供一种全新的检测手段。对GIS设备局放可能造成的危害及其影响范围和程度，提出相应策略，采取相应的措施，对电网的安全、稳定、经济运行具有重要意义。二、系统介绍按照读出方式（即X射线曝光到图像显示过程）不同，可分为： ◆数字射线成像（DR-Digital Radiography ） ◆计算机射线成像（CR-Computed Radiography）图1-1检测原理图

X射线荧光光谱分析的基础知识

《X射线荧光光谱分析的基础知识》讲义廖义兵 X射线是一种电磁辐射，其波长介于紫外线和γ射线之间。它的波长没有一个严格的界限，一般来说是指波长为0.001-50nm的电磁辐射。对分析化学家来说，最感兴趣的波段是0.01-24nm，0.01nm左右是超铀元素的K系谱线，24nm则是最轻元素Li 的K系谱线。1923年赫维西(Hevesy, G. Von)提出了应用X射线荧光光谱进行定量分析，但由于受到当时探测技术水平的限制，该法并未得到实际应用，直到20世纪40年代后期，随着X射线管、分光技术和半导体探测器技术的改进，X荧光分析才开始进入蓬勃发展的时期，成为一种极为重要分析手段。一、X射线荧光光谱分析的基本原理元素的原子受到高能辐射激发而引起内层电子的跃迁，同时发射出具有一定特殊性波长的X射线，根据莫斯莱定律，荧光X射线的波长λ与元素的原子序数Z有关，其数学关系如下： λ=K(Z? s) ?2 式中K和S是常数。而根据量子理论，X射线可以看成由一种量子或光子组成的粒子流，每个光具有的能量为： E=hν=h C/λ 式中，E为X射线光子的能量，单位为keV；h为普朗克常数；ν为光波的频率；C为光速。因此,只要测出荧光X射线的波长或者能量,就可以知道元素的种类，这就是荧光X射线定性分析的基础。此外,荧光X射线的强度与相应元素的含量有一定的关系，据此，可以进行元素定量分析。图1为以准直器与平面单晶相组合的波长色散型X射线荧光光谱仪光路示意图。图1 平面晶体分光计光路示意图 A—X射线管；B—试料；C—准直器；D—分光晶体；E—探测器由X射线管（A）发射出的X射线（称为激发X射线或一次X射线）照射到试料（B），试料（B）中的元素被激发而产生特征辐射（称为荧光X射线或二次X

X射线荧光光谱仪结构和原理

X射线荧光光谱仪结构和原理第一章 X荧光光谱仪可分为同步辐射X射线荧光光谱、质子X射线荧光光谱、全反射X射线荧光光谱、波长色散X射线荧光光谱和能量色散X射线荧光光谱等。波长色散X射线荧光光谱可分为顺序（扫描型）、多元素同时分析型（多道）谱仪和固定道与顺序型相结合的谱仪三大类。顺序型适用于科研及多用途的工作，多道谱仪则适用于相对固定组成和批量试样分析，固定道与顺序式相结合则结合了两者的优点。 X射线荧光光谱在结构上基本由激发样品的光源、色散、探测、谱仪控制和数据处理等几部分组成。 §1.1 激发源激发样品的光源主要包括具有各种功率的X射线管、放射性核素源、质子和同步辐射光源。波长色散X射线荧光光谱仪所用的激发源是不同功率的X射线管，功率可达4~4.5kW，类型有侧窗、端窗、透射靶和复合靶。能量色散X射线荧光光谱仪用的激发源有小功率的X射线管，功率从4~1600W，靶型有侧窗和端窗。靶材主要有Rh、Cr、W、Au、Mo、Cu、Ag等，并广泛使用二次靶。现场和便携式谱仪则主要用放射性核素源。激发元素产生特征X射线的机理是必须使原子内层电子轨道产生电子空位。可使内层轨道电子形式空穴的激发方式主要有以下几种：带电粒子激发、电磁辐射激发、内转换现象和核衰变等。商用的X射线荧光光谱仪中，目前最常用的激发源是电磁辐射激发。电磁辐射激发源主要用X射线管产生的原级X射线谱、诱发性核素衰变时产生的γ射线、电子俘获和内转换所产生X射线和同步辐射光源。 §1.1.1 X射线管 1、X射线管的基本结构目前在波长色散谱仪中，高功率X射线管一般用端窗靶，功率3~4KW，其结构示意图如下：