L’émission gamma de très haute énergie des supernovae extragalactiques 76

Comme pour les novae symbiotiques, la détection d’un rayonnement gamma d’origine ha-dronique pourrait fournir un moyen d’étudier de manière plus directe l’accélération de rayons cosmiques dans les très jeunes rémanents de supernova. Une estimation du flux de photons d’énergie Eγ ∈ [1 − 50 GeV] est donnée pour SN 1993J dans Tatischeff (2009). Nous n’avons considéré dans ce travail que l’émission due à la production de pions neutres dans la région occupée par les rayons cosmiques en aval du choc principal. Le résultat montre que SN 1993J n’aurait pas été détectée par Fermi/LAT. Etant donnée la sensibilité de ce télescope, seule une supernova (semblable à SN 1993J) explosant à moins de ∼1 Mpc de la Terre pourrait être dé-tectée avec Fermi. Mais il n’y a que quatre galaxies à cette distance – les Nuages de Magellan, la galaxie d’Andromède et celle du Triangle – de sorte que la probabilité d’une détection d’une supernova extragalactique avec Fermi est assez faible.

L’accélération de particules dans les supernovae détectées en radio

Contrairement aux novae symbiotiques, les supernovae émettent également dans le do-maine des rayons gamma du TeV, et même peut-être jusqu’à plusieurs milliers de TeV d’après nos calculs. Mais l’émission dans cette gamme d’énergie peut être fortement atténuée dans le champ de rayonnement des éjectas de la supernova par le processus de production de paires γ + γ → e⁺ + e−. Pendant les premiers mois après l’explosion, le rayonnement des éjectas est maximum dans les domaines de l’ultraviolet et de l’optique. L’atténuation du flux gamma culmine alors dans la gamme du TeV (voir Gould et Schréder, 1967). Dans Tatischeff (2009), nous avons estimé que le flux Fγ(Eγ > 1 TeV)de SN 1993J n’avait atteint son maximum que ∼270 jours après l’explosion (voir également Fig. 2.6). Nous avons aussi montré que l’émission au TeV de cette supernova n’aurait pas été détectée par le réseau de télescopes Cherenkov au sol H.E.S.S. (High Energy Stereoscopic System). Mais le calcul de l’atténuation du flux gamma a été effectué dans Tatischeff (2009) en considérant une distribution isotrope des collisions de photons, ce qui est une approximation car l’émission des éjectas provient d’une région plus interne dans le rémanent que celle de production des rayons gamma. La prise en compte de la géométrie exacte du processus de production de paires γ + γ → e++ e−devrait conduire à une diminution sensible du coefficient d’opacité correspondant et donc à une augmentation de la visibilité du flux gamma.

Nous étudions actuellement cet effet dans le cadre d’une collaboration avec Matthieu Re-naud, Alexandre Marcowith et Vikram Dwarkadas. Notre motivation première est de préparer la détection de supernovae extragalactiques avec le Cherenkov Telescope Array (CTA), qui est un projet de construction d’un nouvel observatoire gamma environ 5 – 10 fois plus sensible que H.E.S.S. entre 0,1 et 10 TeV et avec une couverture en énergie étendue en dessous de 100 GeV et atteignant plus de 100 TeV21. Les premiers résultats obtenus montrent que SN 1993J aurait pu être détecté avec CTA. Nous poursuivons maintenant ces calculs pour estimer la distance de détectabilité et prévoir le taux de détection avec CTA pour chaque type de supernova. Nous tirons aussi de cette modélisation le flux de neutrinos produits par désintégration de pions chargés, ce qui peut être comparé aux prédictions de sensibilité du télescope à neutrinos sous-marin KM3NeT22.

21http ://www.cta-observatory.org/ 22http ://www.km3net.org/

L’accélération de particules dans les ondes de choc des explosions stellaires

L101

The Astrophysical Journal, 663: L101–L104, 2007 July 10 

䉷 2007. The American Astronomical Society. All rights reserved. Printed in U.S.A.

EVIDENCE FOR NONLINEAR DIFFUSIVE SHOCK ACCELERATION OF COSMIC RAYS IN THE 2006 OUTBURST OF THE RECURRENT NOVA RS OPHIUCHI

V. Tatischeff1and M. Hernanz

Institut de Cie`ncies de l’Espai (CSIC-IEEC), Campus UAB, Facultat de Cie`ncies, 08193 Bellaterra, Barcelona, Spain; tatische@csnsm.in2p3.fr, hernanz@ieec.uab.es

Received 2007 May 4; accepted 2007 May 22; published 2007 June 26

ABSTRACT

Spectroscopic observations of the 2006 outburst of the recurrent nova RS Ophiuchi at both infrared (IR) and X-ray wavelengths have shown that the blast wave has decelerated at a higher rate than predicted by the standard test-particle adiabatic shock wave model. Here we show that the observed evolution of the nova remnant can be explained by the diffusive shock acceleration of particles at the blast wave and the subsequent escape of the highest energy ions from the shock region. Nonlinear particle acceleration can also account for the difference of shock velocities deduced from the IR and X-ray data. The maximum energy that accelerated electrons and protons can have achieved in few days after outburst is found to be as high as a few TeV. Using the semianalytic model of nonlinear diffusive shock acceleration developed by Berezhko & Ellison, we show that the postshock tem-perature of the shocked gas measured with RXTE PCA and Swift XRT imply a relatively moderate acceleration efficiency characterized by a proton injection rateh_{injⲏ 10}⫺4.

Subject headings: acceleration of particles — cosmic rays — novae, cataclysmic variables — shock waves —

stars: individual (RS Ophiuchi)

Online material: color figures

1.INTRODUCTION

RS Ophiuchi is a symbiotic recurrent nova, with various recorded eruptions in the last century (the last one in 1985), that erupted again recently, on 2006 February 12 (Narumi 2006). RS Oph’s binary system consists of a white dwarf with mass near the Chandrasekhar limit and a red giant (RG) com-panion star. High white dwarf mass and large accretion rate lead to a much shorter recurrence period of outbursts than in classical novae (where the donor is a main-sequence star). In addition, the presence of the RG wind in the RS Oph system leads to the generation of an X-ray–emitting blast wave that runs into a relatively dense circumstellar medium.

The latest outburst of RS Oph has been observed at various wavelengths, e.g., in radio (O’Brien et al. 2006), IR (Monnier et al. 2006; Das et al. 2006; Evans et al. 2007), and X-rays (Sokoloski et al. 2006; Bode et al. 2006). The X-ray data have made it possible to clearly identify the forward shock wave expanding into the RG wind and to estimate the time evolution of its velocity,v, through the well-known relation for a

test-s

particle strong shock:

0.5

16 kTs

v_sp

(

3 mm_H

)

, (1)

where k is the Boltzmann constant,T_sis the measured postshock temperature, andmm_H is the mean particle mass. The X-ray emission has revealed that after an ejecta-dominated, free ex-pansion stage (phase I) lasting ∼6 days, the remnant rapidly evolved to display behavior characteristic of a shock experi-encing significant radiative cooling (phase III; see Sokoloski et al. 2006; Bode et al. 2006). At day 6 after outburst, however, the shocked material was so hot,T ∼ 10_s 8K, that its cooling by radiative losses was probably not important for the dynamics

1Permanent address: CSNSM, IN2P3-CNRS and Universite´ Paris-Sud, F-91405 Orsay Cedex, France.

of the shock. Thus, the lack or the very short duration of an adiabatic, Sedov-Taylor phase (phase II) differs from the rem-nant evolution model developed by Bode & Kahn (1985), O’Brien & Kahn (1987), and O’Brien et al. (1992) after the 1985 outburst of RS Oph.

The time dependence of shock velocity has also been mea-sured by IR spectroscopy, using the observed narrowing of strong emission lines (Das et al. 2006; Evans et al. 2007). Although the general behavior of the shock evolution was found to be consistent with that deduced from the X-ray emis-sion, the shock velocities determined from the IR data are significantly greater than those obtained using equation (1) to-gether with the X-ray measurements ofTs(see Fig. 1).

In this Letter, we show that production of nonthermal particles at the forward shock through the first-order Fermi acceleration process can be deduced from these observational data. Several observations in the solar system and beyond show that diffusive acceleration of particles can be efficient in collisionless shocks and the backpressure from the energetic ions can strongly modify the shock structure (e.g., Jones & Ellison 1991). In particular, equation (1) is known to underestimate shock velocities when particle acceleration is efficient, because the postshock temper-ature can be much lower than the test-particle value (Decour-chelle et al. 2000; Ellison et al. 2007). We start in § 2 with a simple description of the dynamical evolution of the blast wave based on IR and X-ray observations; we then calculate in § 3 the maximum possible energy of particles accelerated in the nova remnant and determine in § 4 the properties of the cosmic-ray modified shock including the energy carried off by particles escaping the shock region. Our conclusions follow in § 5.

2.SHOCK WAVE EVOLUTION

The full width at zero intensity (FWZI) of IR emission lines provide a good measurement of the shock velocity (Das et al. 2006; Evans et al. 2007). Radio imaging (O’Brien et al. 2006) and IR interferometric observations (Monnier et al. 2006) of the RS Oph remnant have shown departures from spherical

L102 TATISCHEFF & HERNANZ Vol. 663

Fig.1.—Time dependence of forward shock velocity as deduced from the FWZI of IR emission lines (filled squares and circles: Das et al. 2006; filled

triangles: Evans et al. 2007) and X-ray measurements of the postshock

tem-perature (open triangles: Sokoloski et al. 2006; open squares: Bode et al. 2006). The lines are simple fits to the data (see text). [See the electronic edition

of the Journal for a color version of this figure.]

symmetry. But given the intermediate angle between the sym-metry axis of the observed bipolar structure and the line of sight,v ∼ 50⬚–60⬚(O’Brien et al. 2006), the largest blueshifted and redshifted velocities measured in the FWZI should be close to the mean expansion speed of the blast wave. The IR data can be modeled at first approximation by (Fig. 1, dashed line) , where t is the time after outburst,

av ⫺1

v_s(t) p 4300t km s

with days, and (⫺0.5) for (

t p t/t₁ t p 6₁ a p 0_v t ≤ t₁ t1

). The decay of as ⫺0.5for can be expected from a

t₁ v_s t t1t₁

well-cooled shock. We see that the velocities deduced from the X-ray data are consistent with such a decay (Fig. 1, dotted

line), although they are ∼1.7 times lower than the velocities

determined from the IR lines.

The radius of the shock front, which for simplicity we assume to be spherical, is easily obtained by integration of v_s(t): . We do not

con-14 a ⫹1v

r (t) p 2.23 # 10 [(1 ⫺ 2a )ts v ⫹ 2a ] cmv

sider the earliest phase of the outburst, when the shock wave traversed the binary system. Given the binary separation of

∼1.5 AU (Fekel et al. 2000), the free expansion of the ejecta into the unperturbed RG wind started att ∼ t p 10 day. The outer radius of the RG wind is routp uRGDt, with uRG_艑

km s⫺1the terminal speed of the RG wind and

10–20 Dt p

yr the elapsed time between the 1985 and 2006 outbursts. 21.04

The outer radius was reached by the forward shock at t 艑2

days after the 2006 outburst. 24–72

The density of the RG wind as a function of radius is given byr (r) p M /4pr u_W ˙_RG 2 _RG, whereM˙_RGis the RG mass-loss rate. It can be estimated from the X-ray photoelectric absorption mea-sured with the Swift X-Ray Telescope (XRT; Bode et al. 2006). We use equation (4) of Bode et al. (2006) to fit the measured absorbing column density. We do not take into account in this fit the data taken at t p 3.17 days, because the early X-ray emission could partially originate from the reverse shock running into the ejecta. We obtain_M˙RG_/uRG_≈4 # 1013g cm⫺1, which is ∼5 times higher than the value estimated by O’Brien et al. (1992) for the 1985 outburst. Part of the difference is due to the larger ejecta velocity considered here.

A relatively large magnetic field of stellar origin is expected to preexist in the RG wind. Assuming that turbulent motions in the wind amplify the magnetic fieldB_Wup to the equipartition

value (Bode & Kahn 1985), we have 0.5,

B p (8pr kT /mm )W W W H

whereT_Wis the wind temperature, which we assume to be uni-form throughout the wind and equal to 104K. In the vicinity of the shock front, further magnetic field amplification is expected to occur due to various interactions between accelerated particles and plasma waves (e.g., Lucek & Bell 2000). Assuming a time-independent amplification factoraB(expected to be of the order of a few), the magnetic field just ahead of the shock, B p0

, can be evaluated using the above relations for the RG

a BB W

wind density and shock radius:

a ⫹1v ⫺1

B (t) p 0.047a [(1 ⫺ 2a )t_{0 B} v ⫹ 2a ]v G. (2) Given these estimates ofv_s,r r p r (r )_s, _{0 W s} , and B₀, we can now study the effects of particle acceleration at the blast wave.

3.ACCELERATION RATE AND MAXIMUM PARTICLE ENERGY

The rate of momentum gain of nonthermal particles diffusing in the vicinity of a shock wave is given by (e.g., Lagage & Cesarsky 1983)

⫺1

d p p(u ⫺ u ) k ( p)_{0 2 0} k ( p)₂

p ⫹ , (3)

( )

dt _acc 3

[

u₀ u₂

]

whereu₀( ) is the upstream (downstream) component of flowu₂

speed normal to the shock in its rest frame andk₀( ) is thek₂

upstream (downstream) spatial diffusion coefficient in the di-rection normal to the shock. Here and elsewhere, the subscript “0” (“2”) implies quantities determined far upstream2 (down-stream) from the shock front, as in Berezhko & Ellison (1999). To estimate the spatial diffusion coefficient,k p lv/3, we as-sume the scattering mean free path l of all particles of speed to be (Baring et al. 1999; Ellison et al. 2000),

v l p hmfp gr

wherehmfpis a constant andr p pc/QeBg is the particle gy-roradius, c being the speed of light, Q the charge number, and

⫺e the electronic charge. The minimum valueh_{mfpp 1} cor-responds to the Bo¨hm limit.

Because the wind magnetic field should be largely azimuthal, the acceleration efficiency could be significantly reduced as compared with that in a quasi-parallel shock (shock normal parallel to the field direction). A full treatment of this question is beyond the scope of this Letter (see, e.g., Kirk et al. 1996). For simplicity, we consider the shock to be quasi-parallel and allow for large values ofhmfpto account for the possible re-duction of the acceleration efficiency.

Given the expected field compression B p r B2 tot 0, where is the total compression ratio of the shock, we have

r p u /utot 0 2

. The rate of energy gain for ultrarelativistic

k ( p) p k ( p)/r2 0 tot

particles (vp c) can then be written from equation (3) as

2 dE r ⫺ 1 Q v tot s ⫺1 p 50.0 B₀

( )

MeV s ,

( )

dt _acc r_tot h_mfp 10 km s3 ⫺1 (4) whereB0is in units of gauss. Acceleration can only occur for particles whose acceleration rate is lower than their energy-loss rate. Concentrating here on nucleons, we can safely neglect the collision energy losses. Adiabatic losses, however, can limit the maximum energyEmaxthat particles can acquire during the

2By far upstream, we mean ahead of the upstream shock precursor induced by the backpressure of energetic particles.

No. 2, 2007 COSMIC-RAY ACCELERATION IN RS OPH L103

Fig.2.—Estimated maximum proton energy as a function of time after outburst;EmaxageandEmaxsizeare the maximum energies caused by the finite shock age and size, respectively (see text). The solid curve shows the minimum of these two quantities.

Fig.3.—(a) Calculated postshock temperature compared to the RXTE and

Swift data (same symbols as in Fig. 1). Dashed curve:h p 10inj ⫺5. Solid and

dotted curves:h p 1.4 # 10inj ⫺4with and without Alfve´n wave heating of the shock precursor, respectively. All calculations assumea p 2 hB , mfpp 20, and . (b) Nonthermal energy fraction (thin curves) and escape energy

f_{escp 0.25}

fractioneesc(thick curves) for the same parameters as in (a). Forh p 10inj ⫺5, is!10⫺2. (c) Subshock and total compression ratios (dashed curves, left

eesc

axis) and normalized postshock pressures (right axis) in thermal (Pth) and nonthermal (PCR) particles (P p P ⫹ Ptot th CR) forh p 1.4 # 10inj ⫺4and Alfve´n wave heating. [See the electronic edition of the Journal for a color version

of this figure.]

shock lifetime. The rate of momentum loss due to adiabatic deceleration of the nonthermal particles in the expanding flow can be written as(d p/dt)adp pvs(r ⫺ 1)/3r rtot s tot(e.g., Vo¨lk & Biermann 1988), which gives for the energy-loss rate of ul-trarelativistic particles accelerated in the nova remnant

dE r ⫺ 1tot _⫺av_{⫺1 ⫺1}

p 0.64 ETeV[(1 ⫺ 2a )t ⫹ 2a tv v ] MeV s ,

( )

dt _ad r_tot

(5) whereE_TeVis the particle kinetic energy in TeV. By equating the adiabatic loss rate to the acceleration rate (eq. [4]), one obtains an upper limit on the nonthermal particle energy:

Q _av

E ≤ Emaxp 68 a tB TeV. (6)

h_mfp

It is likely, however, that high-energy particles can escape the acceleration process before reaching the maximum energy given above. Following Baring et al. (1999), we assume the existence of an upstream free escape boundary (FEB) ahead of the shock, located at some constant fractionfescof the shock radius:d_{FEBp fesc s}r. The maximum energy that particles can acquire before reaching the FEB is obtained by equating to the upstream diffusion length . Using the

pa-d l ∼ k /v

FEB 0 0 s

rameters derived in § 2, one finds for ultrarelativistic particles

Q

size av

Emaxp 136fesc a tB TeV. (7)

hmfp

We see that forfesc!0.5this size limitation of the acceleration region gives a more restrictive constraint on the maximum par-ticle energy than that obtained from the adiabatic losses (eq. [6]). Calculated maximum proton energies are shown in Figure 2 forf_escp 0.25(Baring et al. 1999) anda /h_{B mfpp 0.1}. The quan-tityE_maxage is the maximum proton energy caused by the finite age of the shock and has been obtained by time integration of from to t, adopting (this value of is (dE/dt)_acc t₀ r p 6.5_tot r_tot

close to what we obtain fort1t₁; see Fig. 3c). We have slightly

underestimated age for the initial nonrelativistic phase by

as-Emax

sumingvp c, but the error is negligible given the very short duration of this phase. The production of proton energies above 1 TeV is a consequence of the high values ofB₀(eq. [2]) implied by the assumption of equipartition. In Figure 2, the time for whichE_maxage _{p Emax}size, i.e., the beginning of particle escape from the shock region, istescp 5.95days. This time only depends on f_esc but not on a /h_{B mfp}, which is a scale factor for both and . It is remarkable that for , is very

age size

E_max E_max f_{escp 0.25 tesc}

close to the observed transition time , which could explain thet₁

apparent lack of an adiabatic phase in the remnant evolution.

4.PROPERTIES OF THE COSMIC-RAY MODIFIED SHOCK

Berezhko & Ellison (1999) have developed a relatively sim-ple model of nonlinear diffusive shock acceleration, which al-lows us to quantify the modification of the shock structure induced by the back-reaction of energetic ions. Although the model strictly applies to plane-parallel, steady state shocks, it has been successfully used by Ellison et al. (2000) for evolving supernova remnants. Given the upstream sonic and Alfve´n

L104 TATISCHEFF & HERNANZ Vol. 663 Mach numbers of the shock, which can be readily calculated

from the parameters derived in § 2, and the maximum particle energies evaluated in § 3, both the thermodynamic properties of the shocked gas and the energy spectrum of the accelerated protons (other particle species can be neglected for evaluating the shock modification) are determined by an arbitrary injection parameterhinj, which is the fraction of total shocked protons in protons with momentump ≥ p_injinjected from the thermal pool into the diffusive shock acceleration process. We used the work of Blasi et al. (2005) to accurately relate the injection momentump_injtoh_inj.

Calculated temperatures of the postshock gas are shown in Figure 3a. We see that the temperatures measured with the Rossi

X-Ray Timing Explorer (RXTE) Proportional Counter Array and Swift XRT can be well reproduced withh_{injp 1.4 # 10}⫺4and Alfve´n wave heating of the shock precursor. The latter process is thought to be an important ingredient of cosmic-ray acceler-ation (McKenzie & Vo¨lk 1982) and appears to be required in this case as well to limit the shock compression ratio and ac-celeration efficiency. Forh_{injp 10}⫺5, the test-particle approxi-mation applies and the standard relation between v_s and T_s

(eq. [1]) overestimates the temperature.

The solution shown in Figure 3a is not unique. For example, an equally good description of theTsmeasurements can be ob-tained withh_{mfpp 100}andh_{injp 1.9 # 10}⫺4. However, all the solutions providing good fits to the data give about the same compression ratio and acceleration efficiency. The latter is shown in Figure 3b for the same input parameters as in Figure 3a. The two quantities plotted in this figure are the fraction of total energy flux,F0, going into nonthermal particles (thin curves) and the fractione_escofF₀escaping the shock system via diffusion of the highest energy particles across the FEB3(thick curves). Here

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