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COSMIC-RAY POSITRONS FROM MILLISECOND PULSARS

COSMIC-RAY POSITRONS FROM MILLISECOND PULSARS
COSMIC-RAY POSITRONS FROM MILLISECOND PULSARS

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COSMIC-RAY POSITRONS FROM MILLISECOND PULSARS C.VENTER 1,A.KOPP 1,?,A.K.HARDING 2,P.L.GONTHIER 3,AND I.B ¨USCHING 1Received

ABSTRACT

Observations by the Fermi Large Area Telescope ofγ-ray millisecond pulsar light curves imply copious pair production in their magnetospheres,and not ex-clusively in those of younger pulsars.Such pair cascades may be a primary source of Galactic electrons and positrons,contributing to the observed enhancement in positron?ux above~10GeV.Fermi has also uncovered many new millisec-ond pulsars,impacting Galactic stellar population models.We investigate the contribution of Galactic millisecond pulsars to the?ux of terrestrial cosmic-ray electrons and positrons.Our population synthesis code predicts the source prop-erties of present-day millisecond pulsars.We simulate their pair spectra invoking an o?set-dipole magnetic?eld.We also consider positrons and electrons that have been further accelerated to energies of several TeV by strong intrabinary shocks in black widow and redback systems.Since millisecond pulsars are not surrounded by pulsar wind nebulae or supernova shells,we assume that the pairs freely escape and undergo losses only in the intergalactic medium.We compute the transported pair spectra at Earth,following their di?usion and energy loss through the Galaxy.The predicted particle?ux increases for non-zero o?sets of the magnetic polar caps.Pair cascades from the magnetospheres of millisecond pulsars are only modest contributors around a few tens of GeV to the lepton ?uxes measured by AMS?02,PAMELA,and Fermi,after which this component cuts o?.The contribution by black widows and redbacks may,however,reach levels of a few tens of percent at tens of TeV,depending on model parameters.

Subject headings:cosmic rays—pulsars:general—stars:neutron

1.Introduction

Recent measurements by PAMELA(Adriani et al.2009,2013),Fermi Large Area Telescope(LAT;Ackermann et al.2012),and the Alpha Magnetic Spectrometer(AMS?02; Aguilar et al.2013,2014;Accardo et al.2014)have provided?rm evidence that the positron fraction(PF)φ(e+)/[φ(e+)+φ(e?)],withφthe?ux,is increasing with energy above ~10GeV.Improved spectral measurements for30months of AMS?02data extended the PF up to500GeV,and indicated a leveling o?of this fraction with energy,as well as the PF being consistent with isotropy.

Secondary positrons are created during inelastic collisions between cosmic-ray nuclei and intergalactic hydrogen,which produce charged pions that in turn decay into positrons, electrons,and neutrinos.The fraction of this secondary component with respect to the total(electron+positron)cosmic-ray spectrum is expected to smoothly decrease with energy within the standard framework of cosmic-ray transport(e.g.,Moskalenko&Strong 1998).1However,the AMS?02electron spectrum is softer than the positron one in the range20?200GeV(Aguilar et al.2014),and the measured PF rises with energy,pointing to nearby sources of primary positrons2.Moreover,the rising PF can be ascribed to a

hardening of the positron spectrum(up to200GeV,after which it softens with energy), and not a softening in electron spectrum above10GeV.

Alternatively,it has been argued that the observed rise in PF with energy may be explained purely by secondary positrons originating in the interstellar medium(ISM), without the need to invoke a primary positron source.Shaviv et al.(2009)demonstrated that an inhomogeneous distribution of supernova remnants(SNRs),such as a strong concentration in the Galactic spiral arms,may explain the PF shape(see also Gaggero et al. 2014,who note that an unrealistically steep index for the primary electron spectrum needs to be invoked when assuming a homogeneous or smoothly varying source distribution; however,they do?nd evidence for an extra/secondary charge-symmetric electron-positron source to explain the data).Moskalenko(2013)pointed out that the concave shape of the primary electron spectrum of Shaviv et al.(2009)introduces an arguably arti?cial rise in the PF.Cowsik&Burch(2010)put forward a model assuming that a signi?cant fraction of the boron below10GeV is generated through spallation of cosmic-ray nuclei in small regions around the sources.In this case,the contribution from spallation in the ISM would have a?at or weak energy dependence,and the GeV positrons would almost exclusively be generated through cosmic-ray interactions in the ISM.Moskalenko(2013)noted that such sources should be observable as very bright GeVγ-ray sources with soft spectra,while the di?use emission would be signi?cantly dimmer than observed.This scenario is also at odds with current estimates of the supernova birth rate.Blum et al.(2013)found an upper bound to the positron?ux by neglecting energy losses,arguing that the?attening of the PF seen by AMS-02around several hundred GeV is consistent with a purely secondary

origin for the positrons.Moskalenko(2013)noted that their arguments imply quite hard injection spectra for primary nuclei,in contradiction toγ-ray observations of SNRs that seem to require rather steep spectra.In addition,a very fast escape time for the positrons is implied,and if this is extrapolated to higher energies,it would lead to a large cosmic-ray anisotropy,which has not been observed.Dado&Dar(2015)furthermore conclude that if the energy losses of positrons in the ISM are included in the transport calculation,the upper limit to the positron?ux is much lower than the limit derived by Blum et al.(2013), requiring a primary source of positrons in this case.

MSPs are the oldest population of rotation-powered pulsars,characterized by low surface magnetic?elds,and are thought to have acquired their very short periods through spin-up by accretion from a binary companion(Alpar et al.1982).For the most part,they have not been considered as an important source of cosmic-ray positrons since the majority lie below the death lines for high-multiplicity pair cascades(assuming dipole magnetic?elds; Harding et al.2002;Zhang&Cheng2003)and were thus considered to be pair-starved (Harding et al.2005).However,this picture changed with the detection of pulsedγ-ray emission from a large number of MSPs by Fermi(Abdo et al.2013).Most of theγ-ray light curves show narrow,double peaks trailing the radio peaks,very similar to those of younger pulsars.Such light curves can only be?t by outer magnetospheric gap models(Venter et al. 2009;Johnson et al.2014).The existence of narrow accelerator gaps requires large numbers of electron-positron pairs(high multiplicity)to screen the electric?eld parallel to the magnetic?eld in the open magnetosphere interior to(at lower colatitudes than)the gaps. It has been suggested that distortions of the surface magnetic?eld may increase pair production for MSPs,either in the form of higher multipoles(e.g.,Zhang&Cheng2003), or o?set polar caps(PCs;Arons1996;Harding&Muslimov2011a,b).Harding&Muslimov (2011a)found that even small o?sets of the PC from the magnetic axis(a small fraction of the stellar radius)can greatly enhance the pair multiplicity.This is due to the increase in

accelerating electric?eld on one side of the PC,which stems from the decrease in curvature radius of the distorted magnetic?eld.Furthermore,MSPs produce pairs with energies around100times higher that those of young pulsars,due to their relatively low magnetic ?elds which require a higher photon energy for magnetic photon pair production to take place.In this case,the pair spectra extend to several TeV(Harding&Muslimov2011b). There has also recently been a substantial increase in the population of known MSPs through discovery of new radio MSPs in Fermi unidenti?ed sources(Abdo et al.2013). Many of these are nearby(within1kpc)and a number are relatively bright,indicating that the existing radio surveys were incomplete(or insensitive to the detection of many MSPs). All of the above factors(more sources characterized by higher pair multiplicities and larger maximal particle energies than previously thought)make the study of MSPs as sources of cosmic-ray electrons and positions quite attractive.

We have previously studied the contribution to the terrestrial electron spectrum

by the nearby MSP PSR J0437?4715assuming a pair-starved potential,but found the contribution of this nearby MSP to be negligible within this model.We also considered the contribution of the much younger Geminga(see also Aharonian et al.1995),and found that it may contribute signi?cantly,depending on model parameters(B¨u sching et al.2008a). B¨u sching et al.(2008b)furthermore noted that both Geminga and PSR B0656+14may be dominant contributors to the terrestrial positron?ux,and may be responsible for an anisotropy of up to a few percent in this?ux component.We have recently made a?rst attempt to carefully assess the contribution of MSPs(excluding those found in globular clusters)to the cosmic-ray lepton spectrum at Earth(Venter et al.2015),where we have considered pairs originating in cascades within the magnetospheres of MSPs.However, since about80%of MSPs have binary companions,in some fraction of these systems shocks may form in the pulsar winds as they interact with the companion wind or atmosphere (Harding&Gaisser1990;Arons&Tavani1993),which could accelerate the pairs to higher

energies.It is possible that such shock acceleration occurs in some black widow(BW) systems,such as PSR B1959+20(Arons&Tavani1993).Due to Fermi observations,the population of BWs and redbacks(RBs)has increased signi?cantly.We therefore now also study the e?ect of pairs that have been reaccelerated in intrabinary shocks of BW and RB systems.We furthermore include Klein-Nisihna(KN)e?ects(Schlickeiser&Ruppel 2010;Blies&Schlickeiser2012)when assessing the inverse Compton(IC)loss rate the particles su?er as they traverse the interstellar radiation?eld(ISRF)of the Galaxy.We describe the assumed source properties of MSPs by?rst discussing the central expectation of roughly equal numbers of electrons and positrons coming from pulsar magnetospheres (Section2.1),after which we describe our population synthesis code used to predict the present-day number of MSPs as well as their location and power(Section2.2).We describe an additional BW/RB source population in Section2.3.Moving to source spectra,we describe our PC pair cascade code that yields realistic pair spectra(Section3.1).We also describe the spectra injected by BW and RB systems(Section3.2),and motivate why we neglect the small contribution due to primaries(Section3.3).We next discuss our assumptions regarding the ISRF(Section4.1)and Galactic magnetic?eld strength (Section4.2),which are necessary inputs to the calculation of energy losses su?ered by the leptons(Section4.3).We use this together with a prescription for particle di?usion when solving a transport equation(Section4.4)to calculate the spectra at Earth(Section5).We discuss our results in Section6,while our conclusions follow in Section7.

https://www.wendangku.net/doc/0d18054281.html,lisecond pulsars as sources of cosmic-ray electrons and positrons

We?rst address the question of pair production in pulsar magnetospheres(Section2.1), speci?cally as this pertains to MSPs,before describing two pulsar populations we consider in the rest of the paper:Galactic MSPs resulting from population synthesis modeling

(Section2.2),and BWs and RBs which may further accelerate particles?owing out of the MSP magnetospheres in their intrabinary shocks.(Section2.3).

2.1.Pair production in pulsar magnetospheres

Production of electron-positron pairs in pulsar magnetospheres,?rst proposed

by Sturrock(1971),is widely considered to be critical for supplying charges to the magnetosphere as well as plasma for the observed coherent radio emission.The pairs can be e?ciently produced in electromagnetic cascades above the PCs(Daugherty&Harding 1982)byγrays that undergo conversion to electron-positron pairs by the strong magnetic ?eld(Erber1966).These cascades are initiated by the acceleration of primary electrons in strong electric?elds above the neutron star surface.Curvature and IC radiation from these particles reaches tens of GeV,creating pairs in excited Landau states.The pairs lose their perpendicular momentum by emitting synchrotron radiation(SR)photons that create more pairs.In young pulsars with magnetic?elds above1012G,the cascades can produce multiplicities of103?104pairs per primary electron(Daugherty&Harding 1982;Harding&Muslimov2011a).The dense pair plasma will screen the accelerating electric?eld above the gap,except in a narrow gap along the last open?eld lines (Muslimov&Harding2004).Screening by pairs may provide nearly force-free conditions (e.g.,Spitkovsky2006)throughout the magnetosphere,maintaining the narrow accelerator and emission gaps necessary to produce the sharp causticγ-ray peaks observed by Fermi. The pair plasma created by pulsars?ows out of the magnetosphere along open magnetic ?eld lines close to the pole and provides the radiating particles for the surrounding PWNe. Models of PWNe require high pair multiplicity to produce the observed SR and IC emission (de Jager et al.1996;Bucciantini et al.2011).

Most MSPs,because of their very low magnetic?elds,have di?culty producing

high-multiplicity pair cascades initiated by curvature radiation if the surface?elds are dipolar.They are able to produce cascades from IC radiation,but these cascades do not have high enough multiplicity to screen the electric?elds(Harding et al.2002).They were thus assumed to have pair-starved magnetospheres(Harding et al.2005)that have particle acceleration on all open?eld lines up to high altitudes.Such magnetospheres would produce broadγ-ray peaks(Venter et al.2009)at earlier phase than the radio peak.However,Fermi detected MSPs with narrow peaks in theirγ-ray light curves arriving at later phase than the radio peak,very similar to those of young pulsars,implying that MSPs are somehow able to produce the high multiplicity pair cascades required to screen most of the open ?eld region.Harding&Muslimov(2011a,b)suggested that MSPs have non-dipolar?elds near their surface that enhance the accelerating electric?elds and enable creation of more pairs.Introducing a generic toroidal component to the dipole?eld that e?ectively caused an o?set of the PC relative to the magnetic pole,Harding&Muslimov(2011a)were able to specify the?eld distortion with two o?set parameters,εandφ0,describing the magnitude and azimuthal direction of the shift.Physically,ε~0.1for MSPs corresponds to the PC o?set caused by the sweepback near the light cylinder of a vacuum retarded dipole

?eld(Deutsch1955;Dyks&Harding2004),ε~0.2to the PC o?set from sweepback of a force-free?eld(Spitkovsky2006),andε>0.2to the PC o?set by multiple?elds near the surface.Harding&Muslimov(2011b)found that for magnetic?elds withε>0.4, requiring moderate surface multipole components,all known MSPs were able the produce pair cascades by curvature radiation.

Aside from the requirement of?eld distortions to produce higher pair multiplicity for theγ-ray pro?les,there is evidence of a non-dipolar surface?eld structure in MSPs from the study of their X-ray emission.The thermal X-ray pulse pro?les of some MSPs show asymmetries that require o?sets from the magnetic axis of the emitting hot spot on the neutron star surface in order to successfully?t the light curves.Since the emission

likely originates from PC heating,it is argued that MSPs such as PSR J0437?4715 (Bogdanov et al.2007;Bogdanov2013)and PSR J0030+0451(Bogdanov&Grindlay2009) have either o?set dipoles or o?set PCs.The shift of the heated PC needed for modeling the light curve of PSR J0437?4715,~2km,corresponds to an o?set parameterε~0.6.(In what follows,we will adopt values ofε=0.0,0.2,and0.6in our modeling.) Below,we discuss two classes of MSPs which we consider to be sources of cosmic-ray electrons and positrons.

2.2.Galactic synthesis model for the present-day MSP population

We implement the results of a new study by Gonthier et al.(2015)of the population synthesis of radio andγ-ray MSPs that lead to the present-day distribution of MSPs.This is assumed to be an equilibrated distribution within the Galaxy whose evolution has been described in Section3of the work of Story et al.(2007,hereafter SGH)where the radial(ρin cylindrical coordinates)distribution was assumed to be that of Paczy′n ski(1990),with a radial scaling of4.5kpc and a scale height of200pc,instead of75pc used in that work.In addition,the supernova kick velocity model that was implemented was that of Hobbs et al. (2005)using a Maxwellian distribution with a width of70km s?1(resulting in an average speed of110km s?1).The Galaxy is seeded with MSPs treated as point particles with ages going back to the past12Gyr assuming a constant birth rate of4.5×10?4MSPs per century as obtained in SGH.The MSPs are evolved in the Galactic potential from their birth location to the present time when an equilibrium distribution has been established.

We assume that MSPs are“born”on the spin-up line with initial period P0dependent on the surface magnetic?eld B s,which we assume does not decay with time.We assume a power-law distribution for the magnetic?elds.As in the case of the study of SGH,the

simulation prefers a power-law distribution of periods P0(B8),with an index ofαB,with a normalized distribution given by the expression

(α+1)BαB8

P0(B8)=

3c3 1+sin2α ,(2) whereμis the magnetic dipole moment,?is the rotational angular velocity,c is the speed of light,andαis the magnetic inclination angle relative to the pulsar’s rotational axis. Considering accelerating?elds and force-free solutions,Li et al.(2012)constructed solutions of magnetospheres?lled with resistive plasma,arriving at a very similar spin-down formula. Contopoulos et al.(2014)considered the ideal force-free magnetosphere everywhere except

within an equatorial current layer,and also arrived at a similar prescription for L sd.These results encourage us to implement such a spin-down model into our population synthesis https://www.wendangku.net/doc/0d18054281.html,ing a dipole moment ofμ=B s R3/2,where R is the stellar radius and B s the surface?eld at the pole,and equating L sd to the rate of rotational energy loss yields the expression

6c3IP˙P

B2s=

3c3I 1+sin2α B2s t.(4) We assume R=12km and MSP mass M MSP=1.6M⊙,where M⊙is the mass of

the Sun.We use the prescription outlined in Section2of Pierbattista et al.(2012)to obtain the moment of inertia,which with these values of R and M MSP yields a value of I=1.7×1045g cm2.While there is growing evidence that the inclination angle becomes aligned with the neutron star’s rotational axis with time in the case of normal pulsars (Johnston et al.2007;Young et al.2010),we do not consider such an alignment model in the case of MSPs.

Figure1indicates histograms of period log10(P),period derivative log10(˙P),surface magnetic?eld log10(B s),and distance d characterizing the simulated present-day Galactic MSP population.Figure2shows several best-?t simulated and observed radio properties (log10(P),log10(˙P),characteristic age log10(τc),and log10(B s))of radio-loud MSPs detected in12radio surveys.The output from this simulation predicts the location as well as P and ˙P of roughly50,000Galactic MSPs,which we use as discrete sources of relativistic electrons and positrons in the calculations that follow.

2.3.MSPs in binary systems–BWs and RBs

The majority of MSPs(about80%)are in binary systems,and a subset of these,the BWs and RBs,may contain strong intrabinary shocks that can further accelerate the pairs. BWs are close binary systems,with orbital periods of hours,containing a rotation-powered MSP and a compact companion having very low mass,~0.01?0.05M⊙.The companion stars in BWs undergo intense heating of their atmospheres by the MSP wind,which drives a stellar wind and rapid mass loss from the star.A shock will form in the pulsar wind at the pressure balance point of the two winds and particle acceleration may occur in these shocks (Harding&Gaisser1990;Arons&Tavani1993).RBs are similar systems,except that the companions have somewhat higher masses,~0.1?0.4M⊙(Roberts2011).The MSPs in both types of system are typically energetic,with L sd~1034?1035erg s?1.Figure3is a schematic view of a shock formed between the colliding pulsar and companion star winds.

Before the launch of Fermi these systems were rare,with only three BWs and one RB known.The large amount of material blown o?from the companion stars absorbs and scatters the radio pulsations from the MSPs,making them di?cult to detect at radio wavelengths.In the last few years,radio searches of Fermi unidenti?edγ-ray point sources(Ray et al.2012)have discovered14new BWs and6new RBs to date,making a present total of24of these systems.In order to assess the contribution of these systems to the Galactic cosmic-ray positrons,we compiled a list of public detections,plus some measured and derived quantities(see Tables1and2).In deriving the spin-down luminosity and surface magnetic?elds for the pulsars in these systems,we used an MSP radius of

R=9.9×105cm and moment of inertia of1.56×1045g cm2,in order to be consistent with our pair cascade model assumptions(Section3.1).

Evolution models and population synthesis of MSP binary systems yield a birthrate for BW systems~1.3×10?7yr?1(Kiel&Taam2013).Taking an age of the Galaxy around12

billion years,there may be a total population of several thousand BW systems.Since only a small fraction of these have been discovered,it is harder to estimate how many undiscovered BW and RB systems are within several kpc of Earth.Conservatively,the known nearby population may be~10%of the total,or around several hundred.By considering only the 24known BWs and RBs,we are obtaining a lower limit to the cosmic-ray?ux contribution by binary MSPs.

3.Models for pair injection spectra

https://www.wendangku.net/doc/0d18054281.html,putation of pair spectra from pulsar polar caps

We calculate the spectra of pairs leaving the MSP magnetosphere using a code that follows the development of a PC electron-positron pair cascade in the pulsar magnetosphere (details of the calculation can be found in Harding&Muslimov2011b).The pair cascade is initiated by curvature radiation of electrons accelerated above the PCs by a parallel electric ?eld,derived assuming space-charge-limited?ow(i.e.,free emission of particles from the neutron star surface;Arons&Scharlemann1979).A fraction of the curvature photons undergo magnetic pair attenuation(Erber1966;Daugherty&Harding1983),producing a?rst-generation pair spectrum which then radiates SR photons that produce further generations of pairs.The total cascade multiplicity M+(average number of pairs spawned by each primary lepton)is a strong function of pulsar period P and surface magnetic?eld strength B s,so that many pulsars with low magnetic?elds and long periods produce either few or no pairs for dipole?eld structure(ε=0),leading to a pair death line in the P˙P diagram.

However,as discussed in Section2.1,the sweepback of magnetic?eld lines near the light cylinder(where the corotation speed equals the speed of light)as well as asymmetric

currents within the neutron star may cause the magnetic PCs to be o?set from the dipole axis.We adopt the distorted magnetic?eld structure introduced by Harding&Muslimov (2011b)that leads to enhanced local electric?elds,boosting pair formation,even for pulsars below the pair death line.Harding&Muslimov(2011b)considered two con?gurations for the dipole o?set in which the magnetic?eld is either symmetric or asymmetric with respect to the dipole axis.Sweepback of the global?eld would produce asymmetric o?sets,while the observed o?set in the MSP J0437?4715is symmetric(Bogdanov2013).We adopt a symmetric?eld structure for calculating the pair spectra of MSPs in this paper.In the symmetric case,the magnetic?eld in spherical polar coordinates(η,θ,φ)is

B≈B s

2

?θ(1+a)sinθ??φεsinθcosθsin(φ?φ

) ,(5)

where B s is the surface magnetic?eld strength at the magnetic pole,η=r/R is the dimensionless radial coordinate in units of neutron star radius R,a=εcos(φ?φ0)is the parameter characterizing the distortion of polar?eld lines,andφ0is the magnetic azimuthal angle de?ning the meridional plane of the o?set https://www.wendangku.net/doc/0d18054281.html,ing this?eld structure, Harding&Muslimov(2011b)derive the component of the electric?eld parallel to the local magnetic?eld,E ,that accelerates electrons.We have used the E of Equation(11)of Harding&Muslimov(2011b)that corresponds to a symmetric o?set and use these?eld structures to accelerate the electrons above the PC to simulate the pair cascades.The pair spectra(Figure4)are characterized by P,˙P(or equivalently,B s via Equation[3]),and o?set parameterε.From our simulations,we?nd that about~1%of L sd is tapped to generate the pairs.

We used a grid in P and B s encompassing P=(1,1.8,2,2.5,3,4,5,7,10,20,50,100)ms, and B8=(1,1.5,2,3,5,8,10,15,20,50).For each source in the present-day MSP population with predicted values of P and˙P(Section2.2),we found its associated pair spectrum

by interpolating spectra on this grid.We used an inclination angle ofα=45?,mass

M MSP=2.15M⊙,radius R=9.9km,and moment of inertia I=1.56×1045g cm2for all MSPs.We adopted an equation of state with larger M MSP here(and associated smaller I)compared to that used in the population code(Section2.2),since some MSPs have measured masses M MSP~2M⊙(Demorest et al.2010),and this enhances pair multiplicity. However,this discrepancy is removed by considering a large range ofε,since the latter simulates a large range of pair multiplicities that would correspond to di?erent equations of state,and thus di?erent values of M MSP.We used dipole o?sets ofε=(0.0,0.2,0.6)and set φ0=π/2(this parameter controls the direction of o?set of the PC).

We use the above spectra as input for the calculation of the positron component from the population-synthesis sources(Sections2.2and5).Since MSPs are not surrounded by nebulae that can trap the pairs and degrade their energy before escape,we can assume that the pair spectra emerging from the MSPs are good representations of the actual source spectra.

3.2.Spectra from particles accelerated in the intrabinary shocks of BWs and

RBs

We assume that the pairs escaping from the pulsar magnetosphere may be further accelerated in the intrabinary shock that originates between the pulsar and companion winds in BW and RB systems.Acceleration of leptons at a large distance outside the pulsar light cylinder is necessary to account for the extended SR emission observed from PWNe.Such acceleration is thought to occur at or near the termination shock in the pulsar wind(Kennel&Coroniti1984)that is con?ned by the sub-relativistic expansion

of the surrounding supernova shell.The acceleration mechanism near the pulsar wind termination shocks is not understood,but is known to be highly e?cient,since the bolometric luminosity of the Crab nebula is about20%of the pulsar spin-down luminosity

and the inferred maximum particle energy,~1016eV,is at least10%

of the available

voltage across open?eld lines(de Jager et al.1996).The pulsar wind termination shock is relativistic and perpendicular,so that the di?usive?rst-order Fermi mechanism becomes problematic unless most of the magnetic energy is converted into particle energy upstream of the shock(Sironi&Spitkovsky2011a).However,either shock-driven reconnection (Sironi&Spitkovsky2011b)or strong electromagnetic waves(Amano&Kirk2013)could cause demagnetization,enabling di?usive acceleration to proceed.

Regardless of the acceleration mechanism,the maximum particle energy will be limited by the universal scaling,E max~vBR s/c(Harding1990),where v is a bulk?ow velocity, B is the magnetic?eld strength,and R s is a scale size of the system.In the case of shock acceleration,the maximum energy comes from a balance between the minimum acceleration timescale,set by the particle di?usion,and the timescale for escape from the shock of radius R s.However,for leptons,the timescale for SR losses is shorter than the escape time and the maximum energy will be set by balancing the acceleration timescale with the SR loss timescale.

We assume that the reaccelerated shock-accelerated spectrum will be an exponentially cut o?power law with spectral index of?2

Q i(E)=Q0,i E?20exp ?E0

ξ(ξ+1) 1/2TeV,(7)

with P ms the pulsar period in milliseconds,a11=a/(1011cm)the binary separation, andξthe shock compression ratio.This is slightly di?erent from Equation(34)in Harding&Gaisser(1990),since they assumed that the shock distance from the pulsar is r s≈a?R?,with R?the companion radius.For BWs and RBs,the shock is close to the companion star,and we assume r s≈a,leading to the modi?ed expression given above.The binary separation may be found as follows(given the extremely small eccentricities of these systems)

a= G(M MSP+M comp)

e =

4π2B s R3

The above is a system of two equations and two unknowns,Q0,i and E min(when?xing ηp,max).We?nd that the spectrum of Equation(6)can only be normalized for some choices of M+,E cut,andηp,max.Figure5shows contour plots of log10(E min/E cut)vs.log10(M+) and log10(E cut)assuming P ms=3,B8=5,R=9.9×105cm,and I=1.56×1045g cm2. Panel(a)is forηp,max=0.1,while panel(b)is forηp,max=0.3.Values near unity(dark red regions,i.e.,the lower left corners)indicate that no solution could be found for the given parameters.Fixingηp,max,one can see that for a?xed value of E cut,some minimum value of M+is required in order to?nd a physical solution E min

With the solutions of source spectra in hand for the population of24BWs and RBs considered(Tables1and2),we may next calculate their transport through the Galaxy (Section4.4).

3.3.Neglecting the primary component from population-synthesis MSPs

We have noted that the secondary component almost always vastly dominates the primary component in the case of the BWs/RBs(Section3.2),i.e.,usually M+?1.This is due to the fact that multiplicities grow very rapidly withε.Even in the case ofε=0.0,

while the primary spectra may dominate the secondary spectra for some low-B s and large-P

pulsars(which would imply M+?1),there will always be pulsars with high enough B s and short P(i.e.,M+~100?1000)so that their secondary spectra will dominate the cumulative?ux contribution from a population of pulsars.This means that the cumulative

spectrum from the BW and RB pulsars will be dominated by secondary,and not by primary

spectra.3

On the other hand,for the MSPs from our population synthesis model,where we

assume no shock acceleration,the primaries may form nearly mono-energetic spectra at

very high Lorentz factorsγ~107?8,depending on?eld-line curvature,i.e.,colatitude,and

also P and B s.Given this small energy range(the spectrum is almost aδ-distribution),one

might think that this component may leave a distinct signature in the total spectrum of

particles leaving the pulsar magnetosphere.However,when combining primary spectra from

several pulsars,and following their transport through the Galaxy to Earth,the cumulative

primary spectrum will have been smeared out due to the di?erent source locations and

properties.The primary spectra should also be at a lower intensity than the secondaries,

given the typical multiplicities encountered for the B s and P values of the closest MSPs.

Furthermore,if there would have been any signature at high energies~10TeV,where the

secondary spectra drop o?in this case,this will be completely masked by the contribution

of the BW/RB.

Given the above arguments,we do not include the primary spectra from the MSP

synthesis population since they should not have an impact on our results.

(完整版)介词for用法归纳

介词for用法归纳 用法1:(表目的)为了。如: They went out for a walk. 他们出去散步了。 What did you do that for? 你干吗这样做? That’s what we’re here for. 这正是我们来的目的。 What’s she gone for this time? 她这次去干什么去了? He was waiting for the bus. 他在等公共汽车。 【用法说明】在通常情况下,英语不用for doing sth 来表示目的。如: 他去那儿看他叔叔。 误:He went there for seeing his uncle. 正:He went there to see his uncle. 但是,若一个动名词已名词化,则可与for 连用表目的。如: He went there for swimming. 他去那儿游泳。(swimming 已名词化) 注意:若不是表目的,而是表原因、用途等,则其后可接动名词。(见下面的有关用法) 用法2:(表利益)为,为了。如: What can I do for you? 你想要我什么? We study hard for our motherland. 我们为祖国努力学习。 Would you please carry this for me? 请你替我提这个东西好吗? Do more exercise for the good of your health. 为了健康你要多运动。 【用法说明】(1) 有些后接双宾语的动词(如buy, choose, cook, fetch, find, get, order, prepare, sing, spare 等),当双宾语易位时,通常用for 来引出间接宾语,表示间接宾语为受益者。如: She made her daughter a dress. / She made a dress for her daughter. 她为她女儿做了件连衣裙。 He cooked us some potatoes. / He cooked some potatoes for us. 他为我们煮了些土豆。 注意,类似下面这样的句子必须用for: He bought a new chair for the office. 他为办公室买了张新办公椅。 (2) 注意不要按汉语字面意思,在一些及物动词后误加介词for: 他们决定在电视上为他们的新产品打广告。 误:They decided to advertise for their new product on TV. 正:They decided to advertise their new product on TV. 注:advertise 可用作及物或不及物动词,但含义不同:advertise sth=为卖出某物而打广告;advertise for sth=为寻找某物而打广告。如:advertise for a job=登广告求职。由于受汉语“为”的影响,而此处误加了介词for。类似地,汉语中的“为人民服务”,说成英语是serve the people,而不是serve for the people,“为某人的死报仇”,说成英语是avenge sb’s death,而不是avenge for sb’s death,等等。用法3:(表用途)用于,用来。如: Knives are used for cutting things. 小刀是用来切东西的。 This knife is for cutting bread. 这把小刀是用于切面包的。 It’s a machine for slicing bread. 这是切面包的机器。 The doctor gave her some medicine for her cold. 医生给了她一些感冒药。 用法4:为得到,为拿到,为取得。如: He went home for his book. 他回家拿书。 He went to his friend for advice. 他去向朋友请教。 She often asked her parents for money. 她经常向父母要钱。

中考英语现在进行时知识点总结

中考英语现在进行时知识点总结 一、初中英语现在进行时 1.—Did you hear someone knocking at the door just now, Tom? —No, I _______ TV with my friend in my bedroom. A. was watching B. watched C. am watching D. watch 【答案】 A 【解析】【分析】句意:——汤姆,你刚才听到有人敲门了吗?——没有,我和我的朋友正在卧室里看电视。A. was watching过去进行时;B. watched一般过去时;C. am watching 现在进行时;D. watch观看,动词原形。根据Did you hear someone knocking at the door just now, Tom?No,可推知刚才有人敲门时我和我的朋友正在卧室里看电视。所以该句强调的是过去某个时间正在进行和发生的动作,确定时态为过去进行时态,其构成为was/were+现在分词,根据主语是I,故助动词用was,watch的现在分词为watching,故填was watching,故选A。 【点评】考查过去进行时。根据语境和上下文的联系确定句子的时态。 2.The sports meeting in our school now. A. being held B. is having C. is holding D. is being held 【答案】 D 【解析】【分析】句意:在我们学校运动会正在被举行。“be+being +动词的过去分词” 是现在进行时态的被动句的结构。所以选D。 【点评】考查现在进行时的被动语态。 3.A woman with two children ________ along the street at the moment. A. is walking B. are walking C. walk D. walks 【答案】 A 【解析】【分析】句意:一个带着两个孩子的女人此刻正走在大街上。with连接的两个名词作主语是,谓语与with前的名词保持一致。即句子的主语是 a woman,谓语动词用单数,结合at the moment (此刻)可知要用现在进行时,故选A。 【点评】考查主谓一致和现在进行时。 4.Lucy practices singing every evening. Listen, she so loudly. A. is singing B. sings C. sang D. singing 【答案】A 【解析】【分析】句意:露西每天练习唱歌。听,她唱得那么大声。根据动词listen,可知这里是此时正在进行的动作,用现在进行时:be+doing,结合句意,故答案为A。 【点评】考查现在进行时。掌握进行时的结构和用法。

螺纹通止规

螺纹通止规 定是:螺纹止规进入螺纹不能超过2.5圈,一般的要实际不得超过2圈,并且用得力度不能大,我们的经验是用拇指和食指轻轻夹持螺纹规以刚好能转动螺纹规的力度为准.力大了就相当于在使用丝锥或牙板了,那样规就用不了几次了. 螺纹通止规 螺纹通止规是适用于标准规定型号的灯头作为灯用附件电光源产品时候的设计和生产、检验的工具设备。 用途 一般用于检验螺纹灯头或灯座的尺寸是否符合标准要求,分别检验螺纹灯头的通规和止规尺寸或灯座的通规或止规尺寸。 工作原理 具体检验要求及介绍详见中国人民国国家标准:GB/T1483.1-2008或 IEC60061-3:2004标准规定容。 操作方法 具体检验要求及介绍详见中国人民国国家标准:GB/T1483.1-2008或 IEC60061-3:2004标准规定容。 通止规

通止规,是量规的一种。作为度量标准,用于大批量的检验产品。 通止规是量具的一种,在实际生产批量的产品若采取用计量量具(如游标卡尺,千分表等有刻度的量具)逐个测量很费事.我们知道合格的产品是有一个度量围的.在这个围的都合格,所以人们便采取通规和止规来测量. 通止规种类 (一)对统一英制螺纹,外螺纹有三种螺纹等级:1A、2A和3A级,螺纹有三种等级:1B、2B和3B级,全部都是间隙配合。等级数字越高,配合越紧。在英制螺纹中,偏差仅规定1A和2A级,3A级的偏差为零,而且1A和2A级的等级偏差是相等的等级数目越大公差越小,如图所示:1B 2B 3B 螺纹基本中径3A 外螺纹2A 1A 1、1A和1B级,非常松的公差等级,其适用于外螺纹的允差配合。 2、2A和2B级,是英制系列机械紧固件规定最通用的螺纹公差等级。 3、3A和3B级,旋合形成最紧的配合,适用于公差紧的紧固件,用于安全性的关键设计。 4、对外螺纹来说,1A和2A级有一个配合公差,3A级没有。1A级公差比2A级公差大50,比3A级大75,对螺纹来说,2B级公差比2A公差大30。1B级比2B级大50,比3B级大75。 (二)公制螺纹,外螺纹有三种螺纹等级:4h、6h和6g,螺纹有三种螺纹等级:5H、6 H、7H。(日标螺纹精度等级分为I、II、III三级,通常状况下为II级)在公制螺纹中,H 和h的基本偏差为零。G的基本偏差为正值,e、f和g的基本偏差为负值。如图所示:公差G H 螺纹偏差基本中径外螺纹f g h e 1、H是螺纹常用的公差带位置,一般不用作表面镀层,或用极薄的磷化层。G位置基本偏差用于特殊场合,如较厚的镀层,一般很少用。 2、g常用来镀6-9um的薄镀层,如产品图纸要6h的螺栓,其镀前螺纹采用6g的公差带。 3、螺纹配合最好组合成H/g、H/h或G/h,对于螺栓、螺母等精制紧固件螺纹,标准推荐采用6H/6g的配合。 (三)螺纹标记M10×1–5g 6g M10×1–6H 顶径公差代号中径和顶径公差代号(相同)中径公差代号。 通止规是两个量具分为通规和止规.举个例子:M6-7h的螺纹通止规一头为通规(T)如果能顺利旋进被测螺纹孔则为合格,反之不合格需返工(也就是孔小了).然后用止规(Z)如果能顺利旋进被测螺纹孔2.5圈或以上则为不合格反之合格.且此时不合格的螺纹孔应报废,不能进行返工了.其中2.5圈为国家标准,若是出口件最多只能进1.5圈(国际标准).总之通规过止规不过为合格,通规止规都不过或通规止规都过则为不合格。

感官动词和使役动词

感官动词和使役动词 默认分类2010-05-28 23:14:26 阅读46 评论0 字号:大中小订阅 使役动词,比如let make have就是3个比较重要的 have sb to do 没有这个用法的 只有have sb doing.听凭某人做某事 have sb do 让某人做某事 have sth done 让某事被完成(就是让别人做) 另外: 使役动词 1.使役动词是表示使、令、让、帮、叫等意义的不完全及物动词,主要有make(使,令), let(让), help(帮助), have(叫)等。 2.使役动词后接受词,再接原形不定词作受词补语。 He made me laugh. 他使我发笑。 I let him go. 我让他走开。 I helped him repair the car. 我帮他修理汽车。 Please have him come here. 请叫他到这里来。 3.使役动词还可以接过去分词作受词补语。 I have my hair cut every month. 我每个月理发。 4.使役动词的被动语态的受词补语用不定词,不用原形不定词。 (主)He made me laugh. 他使我笑了。 (被)I was made to laugh by him. 我被他逗笑了。 使役动词有以下用法: a. have somebody do sth让某人去做某事 ??i had him arrange for a car. b. have somebody doing sth.让某人持续做某事。 ??he had us laughing all through lunch. 注意:用于否定名时,表示“允许” i won't have you running around in the house. 我不允许你在家里到处乱跑。 ******** 小议“使役动词”的用法 1. have sb do 让某人干某事 e.g:What would you have me do? have sb/sth doing 让某人或某事处于某种状态,听任 e.g: I won't have women working in our company. The two cheats had the light burning all night long. have sth done 让别人干某事,遭受到 e.g:you 'd better have your teeth pulled out. He had his pocket picked. notes: "done"这个动作不是主语发出来的。 2.make sb do sth 让某人干某事 e.g:They made me repeat the story. What makes the grass grow?

介词for用法完全归纳

用法1:(表目的)为了。如: They went out for a walk. 他们出去散步了。 What did you do that for? 你干吗这样做? That’s what we’re here for. 这正是我们来的目的。 What’s she gone for this time? 她这次去干什么去了? He was waiting for the bus. 他在等公共汽车。 【用法说明】在通常情况下,英语不用for doing sth 来表示目的。如:他去那儿看他叔叔。 误:He went there for seeing his uncle. 正:He went there to see his uncle. 但是,若一个动名词已名词化,则可与for 连用表目的。如: He went there for swimming. 他去那儿游泳。(swimming 已名词化) 注意:若不是表目的,而是表原因、用途等,则其后可接动名词。(见下面的有关用法) 用法2:(表利益)为,为了。如: What can I do for you? 你想要我什么? We study hard for our motherland. 我们为祖国努力学习。 Would you please carry this for me? 请你替我提这个东西好吗? Do more exercise for the good of your health. 为了健康你要多运动。 【用法说明】(1) 有些后接双宾语的动词(如buy, choose, cook, fetch, find, get, order, prepare, sing, spare 等),当双宾语易位时,通常用for 来引出间接宾语,表示间接宾语为受益者。如:

现在进行时用法

个性化教学辅导教案 姓名周咏杰年级七性别男总课时第6 次课 教学目标1·现在进行时的用法 2·现在进行时还可以表示将来时 难点重点教学重点:掌握现在进行时的基本用法 教学难点:将现在进行时的用法用于实际解题、和写句子当中 课堂教学过程课前 检查作业完成情况:优□良□中□差□建议 过 程 一·知识呈现 现在进行时用法 1、现在(说话的瞬间)正在进行或发生的动作,强调“此时此刻”。一般由look, listen, now, at this moment等时间状语做标志(也就是告诉你该句子要用进行时态)。 E.g. Look,He is reading.看!他在阅读 They are talking now.他们现在在谈话 2、当前一段时间内一直在进行的动作。 E.g. They are working these days. 这些天,他们一直在工作 3·现在进行时与always, often,等连用表示赞扬、厌烦等语气。如: Eg,My father is always losing his car keys. 我爸老丢车钥匙。(不满) 难点⊙4、某些动词的现在进行时,表预定的计划或即将发生的动作(常与一个表示将来的时间状语连用)。 E.g I am coming tomorrow.明天我要来、我将会来。 二·小试牛刀翻译下列句子 She is opening the window now. Who is cleaning the window? She is not closing the door now. I am doing your homework. They are singing under the tree now. They’re having a meeting. I’m studying at an evening school. ‘ They’re having a party next week

螺纹通止规要求螺纹通规通

螺纹通止规要求螺纹通规通,止规止。 但是如果螺纹通规止,说明什么? 螺纹止规通,又说明什么? 我也来说两句查看全部回复 最新回复 ?wpc (2008-11-07 20:11:20) 在牙型正确的前提下螺纹通止规检测螺纹中径 ?lobont (2008-11-08 11:16:32) 对外螺纹而言,螺纹通规是做到中径上偏差,所以能通过就表示产品合格,通不过就表示螺纹做大了,要再修一刀; 螺纹止规做到中径下偏差,所以只能通过2~3牙,如果也通过,就表示外螺纹做小了,产品成为废品 ?qubin8512 (2008-11-18 15:36:05) 螺纹赛规与螺纹环规主要测量螺纹的中径。 ?datafield (2008-11-29 19:12:51) 检具不是万能的,只是方便而已。具体没什么的我有在哪本书上看过,是一本螺纹手册上的。 ?ZYC007 (2009-2-09 20:31:13) 在牙型正确的前提下螺纹通止规检测螺纹中径。 对外螺纹而言,但是如果螺纹通规止,说明螺纹中径大;螺纹止规通,又说明螺纹中径小。 ?WWCCJJ (2009-3-19 09:27:19) 检测的是螺纹的中径,螺纹检测规在检定时,也是检测其中径. ?tanjiren (2009-3-20 22:23:06) 螺纹通止规只能检测螺纹的作用中径,大径和底径等均无法准确测量出来. ?月夜(2009-4-01 21:47:13) 用来测量中径 ?丽萍(2009-4-02 10:11:41)

只能检测工件螺纹的中径 yg196733456 (2009-4-03 09:15:56)原来是测中径的知道了

感官动词的用法

感官动词 1.see, hear, listen to, watch, notice等词,后接宾语,再接省略to的动词不定式或ing形式。前者表全过程,后者表正在进行。句中有频率词时,以上的词也常跟动词原形。 注释:省略to的动词不定式--to do是动词不定式,省略了to,剩下do,其形式和动词原形是一样的,但说法不同。 see sb do sth 看到某人做了某事 see sb doing sth 看到某人在做某事 hear sb do sth 听到某人做了某事 hear sb doing sth 听到某人在做某事 以此类推... I heard someone knocking at the door when I fell asleep. (我入睡时有人正敲门,强调当时正在敲门) I heard someone knock at the door three times. (听到有人敲门的全过程) I often watch my classmates play volleyball after school. (此处有频率词often) (了解)若以上词用于被动语态,须将省略的to还原: see sb do sth----sb be seen to do sth hear sb do sth----sb be seen to do sth 以此类推... We saw him go into the restaurant. → He was seen to go into the restaurant. I hear the boy cry every day. → The boy is heard to cry every day. 2.感官动词look, sound, smell, taste, feel可当系动词,后接形容词。 He looks angry. His explanation sounds reasonable. The cakes smell nice.

for的用法完全归纳

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现在进行时用法归纳

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NPT螺纹以及检测方法详解

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介词for 的常见用法归纳

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感官动词的用法

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int[] array = {1,2,5,8,9}; int total = 0; for (int i = 0; i < array.length; i++) { total += array[i]; } System.out.println(total); } //现在我们只需这样写(和以上写法是等价的): void someFunction () { int[] array = {1,2,5,8,9}; int total = 0; for (int n : array) { total += n; } System.out.println(total); } 这种写法的缺点: 显而易见,for/in(for each)循环自动控制一次遍历数组中的每一个元素,然后将它赋值给一个临时变量(如上述代码中的int n),然后在循环体中可直接对此临时变量进行操作。这种循环的缺点是: 1. 只能顺次遍历所有元素,无法实现较为复杂的循环,如在某些条件下需要后退到之前遍历过的某个元素;

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