当前位置:文档之家› The bulk Lorentz factor crisis of TeV blazars evidence for an inhomogeneous pileup energy

The bulk Lorentz factor crisis of TeV blazars evidence for an inhomogeneous pileup energy

The bulk Lorentz factor crisis of TeV blazars  evidence for an inhomogeneous pileup energy
The bulk Lorentz factor crisis of TeV blazars  evidence for an inhomogeneous pileup energy

a r X i v :a s t r o -p h /0511610v 1 21 N o v 2005Accepted for publication in the Astrophysical Journal

The bulk Lorentz factor crisis of TeV blazars :

evidence for an inhomogeneous pileup energy distribution ?

Gilles Henri Laboratoire d’Astrophysique de Grenoble,Universit′e Joseph-Fourier,BP 53,F-38041Grenoble,France and Ludovic Saug′e Institut de Physique Nucl′e aire de Lyon,UCBL/IN2P3-CNRS ,4,rue Enrico Fermi,F-69622,Villeurbanne cedex,France Gilles.Henri@obs.ujf-grenoble.fr,l.sauge@ipnl.in2p3.fr ABSTRACT There is growing evidence that the estimations of the beaming Doppler factor in TeV BL Lac object based on the Self Synchrotron Compton (SSC)models are in strong disagreement with those deduced from the uni?cation models between blazars and radio galaxies.When corrected from extragalactic absorption by the di?use infrared background (DIrB),the SSC one-zone models require very high Lorentz factor (around 50)to avoid strong γ?γabsorption.However,the statis-tics on beamed vs.unbeamed objects,as well as the luminosity contrast,favors

much lower Lorentz factor of the order of 3.In this paper,we show that for the special case of Markarian 501,the need for very high Lorentz factor is unavoid-able for all one-zone models where all photons are assumed to be produced at the same location at the same time.Models assuming a double structure with two di?erent beaming patterns can partially solve the problem of luminosity contrast,but we point out that they are inconsistent with the statistics on the number of detected TeV sources.The only way to solve the issue is to consider inhomoge-neous models,where low energy and high energy photons are not produced at the same place,allowing for much smaller Lorentz factors.It implies that the jet is strati?ed,but also that the particle energy distribution is close to a monoen-ergetic one,and that pair production is likely to be signi?cant.The implications on relativistic jet physics and particle acceleration mechanism are discussed.

Subject headings:radiation mechanisms:non-thermal—gamma rays:theory—

galaxies:active—galaxies:BL Lacertae objects:general—galaxies:jets

1.Introduction

It is now admitted that the blazar phenomenon is due to relativistic Doppler beaming

of the non-thermal jet emission taking place in radio-loud Active Galactic Nuclei(AGN)

where the jet axis is closely aligned with the observer’s line of sight.They exhibit an

important level of optical polarization,a?at radio spectrum,a strong variability in all

frequency bands and a very broad spectral energy distribution(SED)ranging from the radio

to the extreme gamma ray band.The SED consists typically in two broad components.

In the so-called Synchrotron-Self-Compton process(SSC)model,the lowest energy hump is

attributed to the synchrotron emission from relativistic electrons and/or positrons,and the

highest one is attributed to the Inverse Compton(IC)process of the same charged particles

onto the synchrotron photons and/or external photons.The blazar class of objects includes

both the Flat Spectrum Radio Quasars(FSRQ)and the BL Lac sources(or Lacertids),

depending respectively on the existence or the lack of detectable emission lines in their

spectra.Following Chiaberge et al.(2000),one can de?ne two classes of BL Lac objects

(which are most probably two extreme cases in a continuous distribution):the LBL or

”red”BL Lac,for which the synchrotron component peaks in far IR to optical,and the IC

component peaks in the MeV-GeV range,and the HBL or”blue”BL Lac,for which the

synchrotron component peaks in the UV-X range,and the IC component peaks above10

GeV.The most extreme objects up to now are those whose non thermal emission extends

up to the TeV range,the so-called TeV blazars.The two main prototypes are Mrk421

(Punch et al.1992)and Mrk501(Quinn et al.1996),two radio-loud AGN relatively close

to us and roughly at the same distance,z s≈0.031and z s≈0.034respectively.Five other TeV detections have been repeatedly detected(1ES1959+650,PKS2155-304(Aharonian et

al.2005a),1ES1426+428and PKS2005-489(Aharonian et al.2005b),and1ES2344+514

(Aharonian et al.2004)).All of them are Lacertids,although it is not clear up to now

whether only BL Lac objects do emit TeV radiation or if this is due to a selection e?ect.As

a matter of fact,BL Lac objects appear to be much more numerous than quasars and the

closest blazars all belong to this class.A high sensitivity threshold would strongly bias the

detection toward the closest sources.Furthermore it is well-known that TeV photons are

absorbed by the Di?use Infra Red Background(DIrB)to create electron-positron pairs,and

it is not obvious whether even the closest quasar,3C273(z s≈0.158)could be detected in the TeV range.

One-zone SSC models assume that highly relativistic particles are injected in a spherical zone,where they cool by emitting synchrotron radiation and by Inverse Compton process. The models require specifying the source radius,the magnetic?eld,as well as the density and the energy distribution of the emitting relativistic particles.The latter is most often assumed to be a power law or a broken power law(e.g.Marscher1983;Tavecchio et al. 1998).It turns out however that the computation of emitted radiation is not compatible with the hypothesis of a static source,because in most cases the photon density would be so high that all TeV photons should be absorbed to form electron-positron pairs.Furthermore the time variability is so short(down to15minutes in some cases,Gaidos et al.(1996))that it is incompatible with a spherical static source through the causality argument.This leads to assume that the source is moving with a relativistic bulk velocity v=βc.The e?ect of relativistic bulk motion is entirely described by the Doppler beaming factorδ=1/Γ(1?βμ), whereΓ=(1?β2)?1/2is the usual Lorentz factor andμ=cosθis the cosine angle of the jet according to the observer’s line of sight.The Doppler e?ect shifts all frequencies by a factor δand all speci?c intensities by a factorδ3.So the actual photon density in the jet frame is much lower than what would be deduced for a static source.The relativistic motion has been invoked for a long time(Rees1966)to solve a similar issue for radio emission of quasars. Namely the brightness temperature is so high that,for a static sources,the relativistic lep-tons emitting synchrotron radiation should have cooled immediately through the so-called ”Inverse Compton catastrophe”(Rees&Simon1968).Again the relativistic motion can?x this issue,because the actual photon density in the jet frame is much lower when taking into account the Doppler ampli?cation.This beautiful theoretical explanation has been later con?rmed by the discovery of superluminal motion,which requires Lorentz factors at least as great as the observed apparent reduced velocityβapp=v app/c(for a review,see Zensus 1997).

Forμ β,corresponding toθ 1/Γ,one has1 δ 2Γ,whereasδ~1/Γoutside this interval.It means that for a few beamed Doppler sample of boosted sources,one expects a lot of unbeamed and not ampli?ed counterparts.It is natural to think that the unbeamed counterparts of bright quasars are the weaker radio galaxies,whose jet is thought to make a larger angle with the line of sight.Particularly it has been proposed that the unbeamed counterparts of BL Lac object could be a sub class of radio galaxies,the so-called Fanaro?-Riley I(FRI)radio galaxies(Urry&Padovani1995).These are characterized by a rather faint,weakly beamed,and core-brightened radio jet.Statistical studies of radio and X-ray AGN samples have con?rmed the possibility of such an association.The inferred beaming factors seem to imply a rather modest value of the bulk Lorentz factor,of about3.However, the modeling of SSC radiation by one zone models requires much higher values:following the authors,they range from10to50(Tavecchio et al.1998;Konopelko et al.2003;Saug′e &Henri2004).The highest value seems to be needed when one takes properly into account

the extragalactic absorption.The problem is further complicated by the absence of clear superluminal motion in TeV blazars,together with a rather modest brightness temperature, which implies also a low Lorentz/Doppler factor(Edwards&Piner2002;Piner&Edwards 2004).All these contradictory facts lead to what we call here the”Bulk Lorentz factor crisis of TeV blazars”.

The aim of this paper is?rst to ascertain this crisis.We will?rst show that all one-zone SSC models imply high Lorentz factors,only with the argument ofγ?γabsorption and discarding any variability argument.Then we will recall the arguments for low Lorentz fac-tor,based on general geometric properties of the Doppler boosting.We will show that the explanations based on two di?erent structures,with a possible deceleration of a fast spine responsible for TeV emission,are not satisfactory concerning the statistics of TeV blazars. We argue that the best solution is to admit the low Lorentz factor constraint,abandoning the one-zone assumption.We will show that this conclusion has important consequences regarding the jet physics and the particle acceleration mechanism.

2.The case for high Lorentz factor

In the following,we will develop the need for high Lorentz factors for one-zone models, with the fewest theoretical assumptions and relying only on observational data.We will only assume that the SSC process is at work,with the usual assumptions of one-zone models:the relativistic particles are assumed to be injected in a spherical homogeneous”blob”of radius R,moving at a relativistic velocity characterized by the Lorentz factorΓand a corresponding Doppler factorδ.The blob is?lled with a tangled magnetic?eld of constant strengh B.We will refer to all quantities expressed in source rest frame by a star and quantities in observer’s frame are not labeled.All energies are expressed in reduced unit of m e c2.Throughout this paper,we express the Hubble parameter by H0=100h km s?1Mpc?1and assuming h to be equal to h=0.65.

2.1.The synchrotron and IC di?erential Luminosity

Inspection of the TeV blazars spectra shows that the IC spectra reaches their maximum luminosity at some peak energyεc,which is of the order of106for TeV photons.This energy corresponds to an energyε?c=εcδ?1in the blob frame.We will consider only the particles

emitting this typical energy via the IC process,which have a typical individual Lorentz factor (in the blob frame)γc,which must be greater thanε?c.

We then de?ne another typical energyεs,that is emitted by synchrotron process by the same particles.It can be expressed in the blob frame asε?s=(B/B0)γ2c where B0=3B c/2and B c=2πm2e c3/eh≈4.41×1013G is the usual“QED critical magnetic?eld strength”.One has thenεs=δ(B/B0)γ2c.Synchrotron spectra of TeV blazars are typically peaking in the 1-100keV range so thatεs~10?2?10?1.

Synchrotron photons are up-scattered at high-energy via Inverse Compton process.It has been stressed by various authors that,giving the observed energies of IC and synchrotron photons,the collisions between the most energetic particles and the peak synchrotron photons take place in the Klein-Nishina regime,that isε?sγc 1.In this condition,the particle (electron or positron)gives all of his energy in a single interaction.It follows thatγc~ε?c. This gives an estimate of the magnetic?eld strength,

B=B0ε?s

ε2c

(1)

which is only valid in the Klein-Nishina scattering regime.

The di?erential synchrotron luminosity Lε,s per unit reduced energy emitted by a pop-ulation of particles of energyγat the energyεs with di?erential energy number of particles

d N/dγreads

Lε,s(εs)=d L s

dε?

(ε?s)=δ3

d L?s

3

cσTh W B

ε3c

(3)

where W B=B2/8πis the usual magnetic energy https://www.doczj.com/doc/cf17744113.html,bining with equation(1),we

can write:

Lε,s(εs)=δ31

εc

d N

Photons of this energy will also be the main contributors for absorbing photons of energyεc to create electron/positron pairs.If we neglect the Klein-Nishina contribution aboveεt,the total power lost per particle of energyγwrites d L?c/d N=(4/3)cσThγ2W e??

ph

,where

W e??

ph =

L e??

s

4πR2c ε?tε?min dε?d L s

4πR2c

δ?2

3πR2

εc Lε,s(εt)

d N

2πm2e c7/2εc

βεs Lε,s(εt)Lε,s(εs)

d z

τγγ(ε?)=αγγσThε?t n(ε?t),

where?γγ(ε?)is the free mean path of the photon and n(ε?)the di?erential photon density per unit of reduced photon energyε?.In the framework of one-zone model,the typical interaction scale is of the order of the size of source R.It follows that the typicalγ?γoptical depth writes,

τγγ(ε?)≈

R

The functionαγγ(Svensson1987;Coppi&Blandford1990)depends on the indexβof the power-law of the spectral soft photon density expressed inνFν∝νβform.A commonly used value ofαγγ(β)is0.2or0.25.More precisely we have(Svensson1987)

αγγ(β)=41?β6×Γ2(2?β)

(4?β)(3?β)

.(9)

The di?erential energy density number of particle is given as a function of the di?erential luminosity by

n(ε?t)=

L?ε,s(ε?t)

4πm e c3R =δ?3αγγ(β)

σTh Lε,s(εt)

6eh

(12)

×√

εc Lε,s(εt)Lε,IC(εc)β.Values of?αγγandαγγ

for someβare tabulated in table2.

2.3.Constraints on the local synchrotron spectral shape

Equation(2)shows that if we are able to measure the position in frequency and?ux of both the synchrotron and the IC peak,then we can evaluate the optical depth toγ?γabsorption at the IC peak as a function of the assumed Doppler factor value.This optical depth is controlled by the synchrotron luminosity at the frequencyεt=δ2/εc.We can use this relation either by assuming some Doppler factor and evaluate the optical depth, or constrain the value ofδby limiting the value ofτγγ.We can de?ne r max,the Compton dominance parameter,as the ratio of IC luminosity’s peak to the synchrotron one,

r max=[νc F c(νc)]

max

εs Lε,s(εs)

.(13)

We can rewrite equation(12)to express the luminosity atεt=δ2/εc as a function of the optical depth and the r max parameter.We?nally obtain,

εt Lε,s(εt)=δ4

?αγγ(β)

6eh

εmax

s

2

.(14)

Equations(5)and(14)can be considered as a system of two parametric equations of the curve givingεt Lε,s(εt)as a function ofεt.Eliminatingδbetween the two previsously cited equation,one gets the following expression:

εt Lε,s(εt)=ε2tε2c

?αγγ(β)

6eh

εmax

s

2

.(15)

For nearby sources,the luminosity distance writes d?(z)≈cz/H0and previous expression can expressed in term on?ux F instead luminosity L using the well known relation F=L/4πd2?, νs d F s zτγγ(εmax c)νmax s 2r?1max(16) For an observed SED and a given value of the opacity parameterτγγ,the only remaining unknown quantity in the previous equation is the beaming Doppler factorδ.Each value ofδgives a point in the log10ν?log10(νFν)plane lying on straight line of slope2,the level of the curve depending only on the value ofτγγ.Intersection of the synchrotron spectrum with the straight line directly constrains the minimum valueδmin(τγγ)of the beaming Doppler factor required to avoid theγ?γabsorption with an opacity value ofτγγof the Inverse Compton bump(at the peak frequency).

2.4.Application to Markarian501

We apply this calculation to the case of the Mrk501object during the period of the 1997April16where the Beppo-SAX satellite(Pian et al.1998)and the CAT imaging At-mosphericˇCerenkov Telescope(Djannati-Ata¨?et al.1999;Barrau et al.1998)have recorded simultaneous data(see?gure2).All observational parameters we need in the equation(16) are reported Table1.We consider the two cases where we take into account,or not,the attenuation of the high energy component by cosmic di?use infrared background(DIrB). This e?ect consists in the interaction of emitted gamma rays during their travel through the Universe with the photon?eld of the di?use infrared background(DIrB)to create pairs (Gould&Schr′e der1967a,b;Stecker,de Jager,&Salamon1992;Vassiliev2000).The tail of the high energy spectra is then de-reddened using the method described in Saug′e&Henri (2004).This situation changes the position of Inverse Compton peak and the Compton dominance parameter r max.In this case,forτγγ=1,we obtain both in the reddened and the de-reddened caseδmin(1)≈50(see?gure3).

Given equation16,the position of the line constrainingδdepends on the value of (?max

c

)4/Lε,IC.It turns out that,also the IR un-folding of the spectrum changes both quan-tities,the previous ratio depends only slightly on the level of assumed absorption.The

value ofδmin(1)are thus quite similar in the two cases because when we correct the Inverse Compton bump,position of the maximum moves both in luminosity and in frequency.This e?ect could be clearly seen on?gure3,where the di?erence between the two panels is hardly perceptible.

Note that in fact the level of the curve depends implicitly also on the value of modi?ed power-law index of the spectrumβ(see eq.[16]).In our case,we choose a valueβ=0.5 directly measured on the SED.

2.5.Constraint from the variability timescale

Another constraint can be derived from the observation of short variability timescale. The classical argument is that a spherical static source cannot be variable on a timescale smaller than R/δc.So one gets an upper bound of radius of the source R R var,min=δct var. Combining previous inequality to the equation(8)and expressing all the quantities in their ?ducial units,we?nally get a constraint similar to the one obtained in the previous section for the local synchrotron shape(see eq.[16]):

νs d F s zνmax s

For a component moving along the jet axis at a reduced speedβ=v/c and making an angle θfrom the line of sight,the apparent transverse velocity measured by the observer is:

βsinθ

βapp=

2/2andθis such that sin2θ>(Γ2?1)?1,the motion will appear to be superluminal i.e.βapp>1.Expressed in degrees the latter condition writesθ>θcrit= 0.28(Γ/10)?2deg.

As a matter of fact,VLBI/VLBA campaigns have not clearly succeeded in?nding su-perluminal motion at the parsec scale for any TeV blazars(Edwards&Piner2002;Piner& Edwards2004).Observed radio components seem to be stationary or subluminal,requiring low or moderate values of the Lorentz factor(Γ≈2?4).

The absence of superluminal motion could be explained by a very close alignment of the jet with the line of sight.Indeed,following the previous expressions,ifθ 1/2Γ2the apparent velocity is always smaller than c,and object appears to be subluminal despite the large value ofΓ.But it this case,a simple statistical argument based on the density number of unbeamed counterparts rule out this possibility as we will see in the next section.

Moreover,derived value of the brightness temperature of the VLBI core is in the order of1010?11K and lie well below the usual Inverse Compton limit of≈1011?12K necessary to avoid the”Inverse Compton catastrophe”,i.e.situation where ultra-relativistic particles su?er from dramatically Compton cooling in a very short time.Piner&Edwards(2004)have concluded that the jet should be only mildly relativistic at parsec scale.They propose that the TeV emitting inner jet is strongly decelerated before reaching the parsec scale.However we will see in the following that the existence of the highly relativistic motion is challenged by other observational facts concerning the statistics of beamed vs.unbeamed sources.

3.2.Number of beamed sources

in the BL Lac/FR-I uni?cation paradigm

As we said in the introduction,the blazar phenomenon arises from a close alignment of jet axis with the observer’s line of sight.Following this scheme,one expects the existence of sources sharing the same physical properties(i.e.intrinsically the same objects),but viewed at larger angle.It has been proposed that Fanaro?-Riley radio galaxies can be the unbeamed parent population of blazars and particularly,FR-I galaxies can be the counterparts of Lacertids(Urry&Padovani1995).

The uni?cation hypothesis can be tested on samples of objects both by their luminosity ratio and by their spatial density.Doppler beaming e?ect enhances the intrinsic bolometric luminosity by a factorδ4.The Doppler factor itself varies fromδmax=2Γfor a jet pointing exactly toward the observer,toδmin=1/Γfor jets lying close to the sky plane.Although the exact de?nition of what is a beamed object can be somewhat subtle,one can estimate an order of magnitude of the number of such objects.It is easy to see that the solid angle for which the Doppler factor is larger than some given valueδ0(where of courseΓ?1<δ0<2Γ

is

?=2π(1?μ0)?2π

δ0?

1

Γ 12Γ ,(20)

if we assume always two symmetrical jets.

So any”beaming criterion”imposing a Doppler factor larger than some sizable fraction of Γwill give a fraction of beamed sources of the order ofΓ?2.For one beamed source,one expects thus aroundΓ2unbeamed sources.It turns out that careful statistical studies do indeed con?rm the association of BL Lac objects with FR-I galaxies,but they converge toward a much lower Lorentz factor than what is expected from the gamma-ray emission. For X-ray selected BL Lacs,which comprise all known TeV blazars,the inferred density ratio is1:7,corresponding to a bulk Lorentz factor around3.5(Urry&Padovani1995).

In the same way,we can examine the hypothesis that the lack of detection of super-luminal motion would be due to a close alignment of the jet with the line of sight.As we note in the previous section,a beamed source withθ 1/2Γ2can not appear superluminal. The cone substained by this angle corresponds to the solid angle?≈π/4Γ4.The ratio f′between the density of unbeamed sources and subluminal beamed sources one is thus given by

f′=

n FR?I

in the BL Lac/FR-I uni?cation paradigm

Another constraint can be derived from the luminosity ratio between the Lacertids sources and the FR-I ones.Supposing the same assumption as above (see previous section

3.2),ie Lacertids and FR-I are on average the same intrinsic objects but viewed at di?erent angles,the bolometric luminosity contrast between the two parents population (Lacertids and FR-I radio galaxies)is given by,

?=L Lac δFRI

4.(22)In the case of Lacertids,relativistic beaming requires 0 θ 1/Γor equivalently 2Γ δLac Γ.On the other hand,we suppose that o?-axis counterparts verify δ≈2/Γ(corre-sponding to an average angle value of θ≈60deg for Γ>1).Then,equation (22)rewrites

Γ8 ? Γ8

First detection was reported by the HEGRA collaboration with an integral?ux above250 GeV at about3.3%of the?ux of the Crab Nebula(with a signi?cance of4.7σ)during an high state(Aharonian et al.2003;Beilicke et al.2004).Such TeV events are con?rmed by recent measurements of High Energy Stereoscopic System(HESS)(Beilicke et al.2005).The powerful radio jet of M87has been well studied in various wavelengthes from radio to X-rays, showing that the jet axis makes an angle between30and40deg with the line of sight.This angle is clearly large enough to ensure that the emission is unbeamed.Previous works based on the study of the proper motion of the VLBI knots(Biretta et al.1995)or on the detailed analysis of HST and VLA observations(Lobanov et al.2003)converge toward value forΓof 3–5at the kiloparsec scale.The jet di?erential?ux of a source expressed in the observer’s frame can be written as function of the intrinsic di?erential luminosity as

Fν(ν;θ,z)≈(1+z)δ3L?ν(ν?)

νthr dν[F bν(ν)/hν]= z b1+z u α?2 δu

δb 2+α,(25)

where the index u(resp.b)refers to the observed unbeamed(resp.beamed)quantities,and where we suppose that the high energy spectrum can be expressed as a simple power-law with a photon indexα.

For beamed sources,the Doppler factor can be written asδb≈2Γwhile for the unbeamed case one hasδu=1/Γ(1?βcosθ)<Γwithβ≈1?1/2Γ2.Finally we can express the bulk Lorentz factor as a function ofθand the observational parameters only

Γ(θ)= [k(z b,z u;α)R?1]1/(2+α)?cosθ

θ k(z b,z u;α)

In1997April?aring period,the TeV blazar Mrk501(z s≈0.034)became roughly8 times as bright as the Crab Nebula as reported by the French collaboration CAT(Djannati-Ata¨?et al.1999).Assuming M87is an unbeamed counterpart of Mrk501with an angle 30deg θM87 40deg we obtain4 Γ 5.3.Again we?nd that the luminosity ratio is compatible with modest values of the Lorentz factor.Due to the increasing sensitivity of the present and the next generation of the Imaging AtmosphericˇCerenkov Telescope Arrays,the detections of more and more TeV radio galaxies should help us to constrain the dynamics of the emitting plasma at the subparsec scale in a more reliable statistical way.

3.5.Summary

All the above considerations show that observational data are compatible with the beaming model only if the bulk Lorentz factor for the X-ray and TeV emitting part of the object is relatively low,between3and5.This value reproduces correctly the luminosity ratio and the statistical number of sources(which are a priori independant factors).Conversely, a value ofΓ=12.5which is the minimum typical value derived from the one-zone modeling approach,would lead to a luminosity contrast of?≈107.6–109.This latter estimation is clearly not compatible with the previous observations,ascertaining the”Bulk Lorentz factor crisis of TeV blazars”.In the following,we will examine some suggestions made by various authors to solve the crisis.

4.How to solve the crisis

4.1.Two pattern model

Chiaberge et al.(2000)and Trussoni et al.(2003)argue that a jet velocity structure can solve the problem of the BL Lac/FR-I uni?cation scheme.They consider a(med-)relativistic external layer and a fast internal spine which dominates the emission in the case of a favorable alignment along the observer’s line of sight,i.e.in the blazar case.Although similar in appearance to the two-?ow model of Pelletier(1985)(see below for details),it di?ers by the fact that both?ows are relativistic,one with a”low”Lorentz factor(around 3)and one with a high Lorentz factor(at least10).In the following,we consider the same approach considering a two-components modeling of the velocity structure,where a fast inner structure is supposed to be surrounded by a slow one.Each of these components is respectively characterized by a bulk Lorentz factorΓf andΓs.As we saw,the radiative emission of the moving source with a bulk Lorentz factorΓis beamed in a cone sustained

by a solid angleδ?=π/Γ2along the motion.Therefore the emitted radiation appears to

be Doppler boosted when the jet lies intoδ?around the observer’s line of sight.In this

case,the luminosity contrast between the two parents population(Lacertids and FR-I radio

galaxies)writes,

Γ8s ? (ΓsΓf)4,(28) where right and left bound correspond to the case where fast velocity component respectively

dominates or not the emission.Uni?cation models are sensitive to the slow component only,

so(Γs=3?5)(Hardcastle et al.2003;Trussoni et al.2003;Chiaberge et al.2000;Urry&

Padovani1991).Therefore,assumingΓs≈4we obtain104.81 ? 108ifΓf=25and 104.81 ? 106.4ifΓf=10.

The results give a possible solution to the luminosity ratio problem,being more compatible

with observations.But in the next section we will examine the consequences of such a

velocity structure on the detection probability of TeV emitters among BL Lac objects.

4.1.1.Statistics of detected sources

Suppose a populationΣof sources randomly oriented per unit volume n0.Then the

density number of sources oriented with an angleθ=cos?1μaccording to the observer’s line

of sight is d n/dμ=n0/2.We de?ne BL Lac sources as those seen into theδ?s=π/Γ2s cone

and therefore the TeV emitters as the part of Lacertids lying into theδ?f=π/Γ2f.Therefore

the probability of detecting a BL Lac object inΣwrites

P Lac=P(μ μ0)=1dμ=1

Γf 2.(30) The probability of detecting n TeV emitters among a population of N Lacertids is given by the usual binomial probability law,

P(n/N)=N!

which writes,

P(N n0 n)=k=N

k=n P(k/N).(32)

4.1.2.Applications

For a given value of(n,N),requiring that P(N n0 n)is larger than an a pri-ori probability P0constrains the space parameters(Γs,Γf).The latter inequality leads to eliminate parameter’s region lying above a straight line which corresponds equivalently to a constant value of P0or of the ratioΓs/Γf(see eq.[32],[31]and[30]).Further restric-tion come from theγ?rays transparency argument and FR-I/Lacertids uni?cation models as developed above.

1.Firstly,theγ?rays transparency argument developed in the?rst part of this work

directly constrains the value of the fast component as it requires a minimum value of the Doppler factorδmin,and thereforeΓf δmin/2.We have shown thatδmin≈50 exclude all part of the(Γs,Γf)lying aboveΓf=25.

2.Secondly,basic statistics argument based on the number FR-I radio galaxies regarding

the Lacertid one and the comparison of luminosity distribution of the previous popu-lations constrain the value of the slow component to reasonable values less thanΓs≈7 (Urry&Padovani1995;Chiaberge et al.2000).

We test this result on the catalog of BL Lac objects from Padovani&Giommi(1995).At z s 0.13they report29Lacertids with known redshift.Setting(n=7,N=29),P0=1% and recalling thatΓs,max=7andΓf,min=25,the intersection of all listed previous constraints reduces to null region(see?gure5).Even with the hypothesis of a structured?ow,a large value of the Lorentz factor recquired by one-zone homogeneous models is clearly untenable (excluded with a con?dence level of99%).

We demonstrate that even if the two-components velocity structure can give a satis-factory answer to the luminosity problem of the Lacertids even with large value of Doppler factor required by high energy emission models,it fails to explain the detection statistics of the TeV emitters among the BL Lac object population supposed to be o?-axis FR-I sources.

5.Discussion

5.1.Inhomogeneous models

Altogether,the previous considerations lead to a serious paradox,where a high Lorentz

factor larger than20seems mandatory to avoid strongγ?γabsorption,whereas all other

facts tend to favour modest values around3.The only way to solve the discrepancy seems

to give up the implicit assumption of all one zone model,i.e.the fact that all photons are

produced co-spatially and simultaneously in some characteristic region of size R.Alterna-

tive to one-zone models have already been discussed in the literature.For instance,in the

”blob-in-jet”model(Katarzy′n ski et al.2001,2003),low energy photons are produced in a

continuous jet and only the high energy ones are produced in a spherical blob.This allow to

?t the overall spectrum with a smaller Doppler factor of around15.Another possibility is to

take explicitly the variability and use a time-dependant model to reproduce the data.Again,

the constraints arising fromγ?γopacity can be somewhat released because soft photons

are emitted at a later stage than high energy ones.As has been remarked by Ghisellini et

al.(1985),time-dependant model will produce e?ects comparable to inhomogeneous ones.If

the evolving source is moving at relativistic velocity,and that many?ares are contributing

to the emission,the overall system will be in fact an strati?ed jet composed with many

”one-zone”regions in a di?erent evolutionary stage.However,none of these models do use

bulk Lorentz factors as low as3.

We are led thus to consider models where photons are distributed along a jet in a

continuous structure,instead of?lling a spherical source.In this case,the luminosity is

proportional to the photon density times the lateral surface of the jet,which is2πR j h j=

2πAR2j,where R j and h j are the typical jet radius and length at the emission region,and

A=h j/R j is an aspect ratio of the source.For a self similar jet for which all quantities

(radius,magnetic?eld,particle density etc...)are described by power law as a function of

the distance z,one expects h j~z j,where z j is the distance of the emitting region from the center.It follows that A~z j/R j~θ?1j,whereθj is the typical opening angle of the jet.One can see that for a given synchrotron luminosity and photon density(implying the same IC

luminosity),one must conserve the quantity AR2j,so the typical radius of the jet,and hence

theγ?γoptical depth will be reduced by a factor A1/2with respect to a spherical source.

This simple geometrical modi?cation helps thus to increase luminosity without increasing

optical depth.Furthermore,the particle distribution needs not to be the same all along the

jet.Rather one expects a gradual cooling of the particles,the overall spectrum being the

envelope of all slices of the jet.The local photon spectrum can thus be di?erent from the

observed one,and particularly the local soft photon density can be much lower,helping again

to reduce theγ?γoptical depth.As we shall see,all these factors can o?er a clue to the Bulk Lorentz factor crisis,but imply strong constraints on the physical picture of relativistic jets.

5.2.Theoretical implications

5.2.1.Local photon density

Considering the above constraints,we will take the opposite attitude,considering that the value of the bulk Lorentz factor is constrained by the uni?cation models and the detec-tion of unbeamed sources to be around3.The typical high energy emission zone as de?ned above is equivalent to the superposition of A spherical sources with individual luminosities Lν/A~θj Lν.Therefore,all previous equations in section2are still valid provided we re-place the observed luminosity Lνbyθj Lν.Using equation(12),we conclude that all opacity

τγγ,which is of constraints remain unchanged if we replace the optical depthτγγbyθ?1/2

j

course in accordance with the estimate made in the previous paragraph.So we can use the ?gure3with slightly di?erent values ofτγγ.The typical angleθj must be of the order of 10?2?10?1,so the optical depth will be reduced by a factor between3and10.In the following,we will still use the same lineθ?1/2

τγγ≈1to constrain the optical depth,meaning

j

thatτγγ 0.1to0.3.

5.2.2.Local photon spectrum

We can thus put an upper limit on the soft photon luminosity corresponding to this value and a Doppler factor of3,which constrains the soft photon luminosity at an energy εt=δ2/εc~10eV.As the spectrum is by de?nition approximately the same in all the char-acteristic emission region,we can thus estimate the local photon spectrum by interpolating between the peak synchrotron luminosity and the above upper limit.Inspection of?gure 3shows that the spectral index between10eV and100keV is very close to1/3,which is characteristic of a quasi monoenergetic distribution;an example of such distribution is pro-vided by the quasi-maxwellian or”pileup”distribution(Henri&Pelletier1991;Schlickeiser 1985;Saug′e&Henri2004),which is a natural outcome of some acceleration processes like second order Fermi acceleration or magnetic reconnexion.This distribution is not the usual power law often claimed to exist in AGN,and which is naturally produced in MHD shocks. Rather than localized shocks,the assumption of low Lorentz factor leads to a picture of a

continuous jet?lled by relativistic particles,continuously reheated by a di?use acceleration mechanism.

5.2.3.Pair production

The local synchrotron spectrum can not be harder than the monoenergetic one;so?gure 3proves that this implies a lower limit to the quantityθ?1/2

τγγ 1.Thus the limit onγ?γ

j

optical depth can not be very low,unless we have an extremely well collimated jet that is not supported by the general FR-I morphology.Modest collimation factors imply that τγγ 0.1.This supports the formation of an electron-positron pair plasma in the acceleration site.If the acceleration is not localized,which is suggested by the picture of a continuous jet ?lled by a pile-up distribution,the pairs created byγ?γinteraction can not avoid being reaccelerated and will trigger a pair cascade(Henri&Pelletier1991).These constraints are thus suggestive of a inner continuous pair dominated,jet-like emission zone,maintained at a relativistic temperature.

https://www.doczj.com/doc/cf17744113.html,patibility with the two-?ow model

All the previous considerations?nd a natural explanation in the context of the two-?ow model,which was proposed to account for the formation of relativistic jets in AGN:in this model,extragalactic jets are in fact the results of a double structure:a?rst jet,not highly but only mildly relativistic(v≈0.5c),is emitted by a MHD mechanism by a large scale magnetic?eld anchored in an accretion disk(Blandford&Payne1982;Ferreira&Pelletier 1993a,b,1995);this powerful,but weekly dissipative jet,can sustain a MHD turbulence able to accelerate non thermal particles.These particles will produce synchrotron and gamma-rays photons,and if the optical depth becomes large enough,these photons will trigger an intense pair cascade leading to a dense pair plasma in the empty”throat”of the jet.We have shown in previous works that this pair plasma will be spontaneously accelerated to relativistic velocities even if the surrounding jet is not highly relativistic by itself,by the so called”Compton Rocket e?ect”,which is a recoil e?ect associated with anisotropic IC pro-cess originally introduced by Odell(1981).The Compton Rocket e?ect has been shown to be ine?cient to accelerate an isolated relativistic plasma because the cooling time is always shorter than the bulk acceleration time(Phinney1982).In the two-?ow model however,the heating by the surrounding jets compensates for the cooling and the pair plasma remains relativistic over large distances(Marcowith,Henri,&Pelletier1995).

Detailed calculations of the Compton Rocket e?ect in this con?guration(Renaud&

Henri1998)show that the pair plasma accelerates gradually in the vicinity of an accretion

disk,being maintained to a quasi equilibrium Lorentz factorΓbeq≈(z/r i)1/4,where r i is the inner radius of the accretion disk(3gravitational radii for a Schwarschild black hole).

The equilibrium Lorentz factor is de?ned by the fact that the photon?eld of the accretion

disk,seen in the comoving frame,appears to be nearly isotropic due to relativistic aberra-

tion.It grows slowly with the distance,because the?eld becomes more and more anisotropic.

The acceleration continues until the photon density becomes to low to e?ciently accelerate

the plasma.Then the plasma decouples from the ambient radiation?eld and ends up with

an asymptotic balistic motion at constantΓb→Γb∞,which depends on the disk lumi-nosity and the particle energy distribution.For a relativistic energy distribution function n(γ)∝γ2exp(?γ/ˉγ),the asymptotic bulk Lorentz factor is approximatelyΓb∞≈(?sˉγ)1/7, where?s=L sσTh/4πm e c3r i is the soft photon disk compactness andˉγis the characteristic energy of the pileup depending on the details of the acceleration/cooling processes(Renaud &Henri1998).

The?rst interesting feature in this model is that it predicts naturally a gradual accel-eration from the core.The value ofΓb≈3is naturally obtained at≈100r g,which is a typical distance where gamma-ray emission seems to occur,based on variability arguments. Thus low Lorentz factor are not surprising in this model,but are explained naturally.As a matter of fact,very high values of20near the core would be di?cult to explain in this frame!

The second one is that the asymptotic bulk Lorentz factor is controlled by the density of the photon?eld emitted by the accretion disk.For BL Lac objects and FR-I galaxies,the disk luminosity is known to be much lower than luminous FSRQ and FR-II galaxies,by a factor around10?3.One would expect thus a lower asymptotic Lorentz factor for BL Lac object in average,which would help to understand the absence of superluminal motion in TeV blazars.As a matter of fact,numerical estimates show that the expected asymptotic Lorentz factors are between10and20for near-Eddington accreting supermassive black holes, whereas they are rather between5and10for low luminosity AGN.We note that bulk Lorentz factors around5are indeed observed in M87,which would mean that the decoupling occurs at some thousands Schwarzschild radii from the core.Uni?cation models are compatible with slowly accelerating jets,the inner(X-ray emitting)jets having bulk Lorentz factors around3and the outer radio jet having a larger Lorentz factor around7(Urry&Padovani (1995)).Again this is perfectly compatible with the predictions of the two-?ow model,with an inner jet emitting X-ray and TeV radiation with a modest bulk Lorentz factor,and an outer jet responsible for radio emission with a higher one.Also we note that there is no

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2008年浙师大《外国文学名著鉴赏》期末考试答案

(一)文学常识 一、古希腊罗马 1.(1)宙斯(罗马神话称为朱庇特),希腊神话中最高的天神,掌管雷电云雨,是人和神的主宰。 (2)阿波罗,希腊神话中宙斯的儿子,主管光明、青春、音乐、诗歌等,常以手持弓箭的少年形象出现。 (3)雅典那,希腊神话中的智慧女神,雅典城邦的保护神。 (4)潘多拉,希腊神话中的第一个女人,貌美性诈。私自打开了宙斯送她的一只盒子,里面装的疾病、疯狂、罪恶、嫉妒等祸患,一齐飞出,只有希望留在盒底,人间因此充满灾难。“潘多拉的盒子”成为“祸灾的来源”的同义语。 (5)普罗米修斯,希腊神话中造福人间的神。盗取天火带到人间,并传授给人类多种手艺,触怒宙斯,被锁在高加索山崖,受神鹰啄食,是一个反抗强暴、不惜为人类牺牲一切的英雄。 (6)斯芬克司,希腊神话中的狮身女怪。常叫过路行人猜谜,猜不出即将行人杀害;后因谜底被俄底浦斯道破,即自杀。后常喻“谜”一样的人物。与埃及狮身人面像同名。 2.荷马,古希腊盲诗人。主要作品有《伊利亚特》和《奥德赛》,被称为荷马史诗。《伊利亚特》叙述十年特洛伊战争。《奥德赛》写特洛伊战争结束后,希腊英雄奥德赛历险回乡的故事。马克思称赞它“显示出永久的魅力”。 3.埃斯库罗斯,古希腊悲剧之父,代表作《被缚的普罗米修斯》。6.阿里斯托芬,古希腊“喜剧之父”代表作《阿卡奈人》。 4.索福克勒斯,古希腊重要悲剧作家,代表作《俄狄浦斯王》。5.欧里庇得斯,古希腊重要悲剧作家,代表作《美狄亚》。 二、中世纪文学 但丁,意大利人,伟大诗人,文艺复兴的先驱。恩格斯称他是“中世纪的最后一位诗人,同时又是新时代的最初一位诗人”。主要作品有叙事长诗《神曲》,由地狱、炼狱、天堂三部分组成。《神曲》以幻想形式,写但丁迷路,被人导引神游三界。在地狱中见到贪官污吏等受着惩罚,在净界中见到贪色贪财等较轻罪人,在天堂里见到殉道者等高贵的灵魂。 三、文艺复兴时期 1.薄迦丘意大利人短篇小说家,著有《十日谈》拉伯雷,法国人,著《巨人传》塞万提斯,西班牙人,著《堂?吉诃德》。 2.莎士比亚,16-17世纪文艺复兴时期英国伟大的剧作家和诗人,主要作品有四大悲剧——《哈姆雷特》、《奥赛罗》《麦克白》、《李尔王》,另有悲剧《罗密欧与朱丽叶》等,喜剧有《威尼斯商人》《第十二夜》《皆大欢喜》等,历史剧有《理查二世》、《亨利四世》等。马克思称之为“人类最伟大的戏剧天才”。 四、17世纪古典主义 9.笛福,17-18世纪英国著名小说家,被誉为“英国和欧洲小说之父”,主要作品《鲁滨逊漂流记》,是英国第一部现实主义长篇小说。10.弥尔顿,17世纪英国诗人,代表作:长诗《失乐园》,《失乐园》,表现了资产阶级清教徒的革命理想和英雄气概。 25.拉伯雷,16世纪法国作家,代表作:长篇小说《巨人传》。 26.莫里哀,法国17世纪古典主义文学最重要的作家,法国古典主义喜剧的创建者,主要作品为《伪君子》《悭吝人》(主人公叫阿巴公)等喜剧。 五、18世纪启蒙运动 1)歌德,德国文学最高成就的代表者。主要作品有书信体小说《少年维特之烦恼》,诗剧《浮士德》。 11.斯威夫特,18世纪英国作家,代表作:《格列佛游记》,以荒诞的情节讽刺了英国现实。 12.亨利·菲尔丁,18世纪英国作家,代表作:《汤姆·琼斯》。 六、19世纪浪漫主义 (1拜伦, 19世纪初期英国伟大的浪漫主义诗人,代表作为诗体小说《唐璜》通过青年贵族唐璜的种种经历,抨击欧洲反动的封建势力。《恰尔德。哈洛尔游记》 (2雨果,伟大作家,欧洲19世纪浪漫主义文学最卓越的代表。主要作品有长篇小说《巴黎圣母院》、《悲惨世界》、《笑面人》、《九三年》等。《悲惨世界》写的是失业短工冉阿让因偷吃一片面包被抓进监狱,后改名换姓,当上企业主和市长,但终不能摆脱迫害的故事。《巴黎圣母院》 弃儿伽西莫多,在一个偶然的场合被副主教克洛德.孚罗洛收养为义子,长大后有让他当上了巴黎圣母院的敲钟人。他虽然十分丑陋而且有多种残疾,心灵却异常高尚纯洁。 长年流浪街头的波希米亚姑娘拉.爱斯梅拉达,能歌善舞,天真貌美而心地淳厚。青年贫诗人尔比埃尔.甘果瓦偶然同她相遇,并在一个更偶然的场合成了她名义上的丈夫。很有名望的副教主本来一向专心于"圣职",忽然有一天欣赏到波希米亚姑娘的歌舞,忧千方百计要把她据为己有,对她进行了种种威胁甚至陷害,同时还为此不惜玩弄卑鄙手段,去欺骗利用他的义子伽西莫多和学生甘果瓦。眼看无论如何也实现不了占有爱斯梅拉达的罪恶企图,最后竟亲手把那可爱的少女送上了绞刑架。 另一方面,伽西莫多私下也爱慕着波希米亚姑娘。她遭到陷害,被伽西莫多巧计救出,在圣母院一间密室里避难,敲钟人用十分纯朴和真诚的感情去安慰她,保护她。当她再次处于危急中时,敲钟人为了援助她,表现出非凡的英勇和机智。而当他无意中发现自己的"义父"和"恩人"远望着高挂在绞刑架上的波希米亚姑娘而发出恶魔般的狞笑时,伽西莫多立即对那个伪善者下了最后的判决,亲手把克洛德.孚罗洛从高耸入云的钟塔上推下,使他摔的粉身碎骨。 (3司汤达,批判现实主义作家。代表作《红与黑》,写的是不满封建制度的平民青年于连,千方百计向上爬,最终被送上断头台的故事。“红”是将军服色,指“入军界”的道路;“黑”是主教服色,指当神父、主教的道路。 14.雪莱,19世纪积极浪漫主义诗人,欧洲文学史上最早歌颂空想社会主义的诗人之一,主要作品为诗剧《解放了的普罗米修斯》,抒情诗《西风颂》等。 15.托马斯·哈代,19世纪英国作家,代表作:长篇小说《德伯家的苔丝》。 16.萨克雷,19世纪英国作家,代表作:《名利场》 17.盖斯凯尔夫人,19世纪英国作家,代表作:《玛丽·巴顿》。 18.夏洛蒂?勃朗特,19世纪英国女作家,代表作:长篇小说《简?爱》19艾米丽?勃朗特,19世纪英国女作家,夏洛蒂?勃朗特之妹,代表作:长篇小说《呼啸山庄》。 20.狄更斯,19世纪英国批判现实主义文学的重要代表,主要作品为长篇小说《大卫?科波菲尔》、《艰难时世》《双城记》《雾都孤儿》。21.柯南道尔,19世纪英国著名侦探小说家,代表作品侦探小说集《福尔摩斯探案》是世界上最著名的侦探小说。 七、19世纪现实主义 1、巴尔扎克,19世纪上半叶法国和欧洲批判现实主义文学的杰出代表。主要作品有《人间喜剧》,包括《高老头》、《欧也妮·葛朗台》、《贝姨》、《邦斯舅舅》等。《人间喜剧》是世界文学中规模最宏伟的创作之一,也是人类思维劳动最辉煌的成果之一。马克思称其“提供了一部法国社会特别是巴黎上流社会的卓越的现实主义历史”。

2019-2020年高一音乐 甜美纯净的女声独唱教案

2019-2020年高一音乐甜美纯净的女声独唱教案 一、教学目标 1、认知目标:初步了解民族唱法、美声唱法、通俗唱法三种唱法的风格。 2、能力目标:通过欣赏部分女声独唱作品,学生能归纳总结出她们的演唱 风格和特点,并同时用三种不同风格演唱同一首歌曲。 3、情感目标:通过欣赏比较,对独唱舞台有更多元化的审美意识。 二、教学重点:学生能用三种不同风格演唱形式演唱同一首歌。 三、教学难点:通过欣赏部分女声独唱作品,学生能归纳总结出她们的演唱 风格和特点。 四、教学过程: (一)导入 1、播放第十三界全国青年歌手大奖赛预告片 (师)问:同学们对预告片中的歌手认识吗 (生)答: (师)问:在预告片中提出了几种唱法? (生)答:有民族、美声、通俗以及原生态四种唱法,今天以女声独唱歌曲重点欣赏民族、美声、通俗唱法,希望通过欣赏同学们能总结出三种唱法的风格和特点。 (二)、音乐欣赏

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