Cosmic Ray (Stochastic) Acceleration from a. Background Plasma

Transcription

1 Cosmic Ray (Stochastic) Acceleration rom a V. A. Dogiel Background Plasma P.N.Lebedev Institute o Physics,Moscow, Russia Thanks to my collaborators: D. O. Chernyshov (LPI), K. S. Cheng (HKU), A. D. Erlykin (LPI), C.-M. Ko (NCU) and A. W. Wolendale (DU)

2 Fermi I vs Fermi II acceleration

3 Shock wave and stochas/c accelera/o stochas/c accelera/on at SNR enveloes Plasma instabilities, in articular Rayleigh-Taylor and Kelvin- Helmholtz instabilities generate turbulence at shocks o SNR enveloes (rom Yang and Liu, 2013)

4 Gamma-Ray lux rom the OB-association Cyg OB2 From Ackermann et al. 2011

5 OB-Association as CR Sources The Fermi-LAT observations reorted by Ackermann et al. 2011, together with measurements o cosmic-ray elemental and isotoic comosition, suggest that OB associations and their suerbubbles are likely the source o a substantial raction o galactic cosmic rays. OB associations are considered as CR accelerators rom the collective action o multile shocks rom suernovae and the winds o massive stars. Multi-shock acceleration in OB associations by a suersonic turbulencee (combination o Fermi I + Fermi II acceleration, see Bykov and Totygin, 1993)

6 FERMI bubbles Dobler et al., Su et al., 2010

7 Black Hole at the center o Milky Way Mass ~ 4x10 6 solar masses! Stellar Cature. Energy Release Stage Illustration: NASA/CXC/M.Weiss

8 Letonic model o star /dal disru/on and shock wave accelera/on (Cheng et al. 2011)

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10 Velocity o the shocks in the exonen/al atmoshere (calculated with the solu/on o Baumgartner and Breitschwerdt, 2013)

11 Shock ragmenta/on due to the Rayleigh-Taylor instability on the ront Shock accelera/on as a unc/on o al/tude y Al/tude o shock ragmenta/on as a unc/on o energy release W

12 Letonic model o stochas/c accelera/on in the Bubbles (Mertsch & Sarkar, 2011) From the ROSAT data o Snowden te al. (1997) there is a shock ront at the bubble edge moving with the velocity ~1000 km/s. The total energy release estimated rom arameters o hot lasma in the Bubbles is about erg and the age o the bubble is 10 7 yr. Plasma instabilities may be generated behind the shock. These instabilities are convected into the bubble interior by the downstream lasma low and accelerate CRs there (Fermi II acceleration).

13 Region o turbulent magne/c ields in the halo behind a shock ront

14 Equa/ons or the Fermi II (shock accelera/on) and Fermi I (stochas/c accelera/on by a turbulence) ( ) 0 ) ( ) ( = + + == + esc D dt d t dx du x D x u x t τ

15 Number o Accelerated Par/cles?

16 Sectrum o CRs accelerated by a shock rom a background lasma (Vladimirov et al. 2006) The number o accelerated articles is about 10 4 o background

17 21/9/16 SAN-VITO,COSMIC RAY ORIGIN

18 ParCcle injeccon The thermal sectrum o arccle is ormed by Coulomb collisions which determine ionizacon losses o arccles and their momentum diusion (Landau and Livshitz, KineCcs) 1 2 = F 2 i + D or Coulomb collisions t kt D = Fi and in the equilibrium state we have the equilibrium Maxwell distribution v E = ex kt F i = = ν 0 E 21/9/16 SAN-VITO,COSMIC RAY ORIGIN

19 Einj DeiniCon I we have an acceleracon de/dt=αe we can induce the energy o injeccon, E inj which can be derived rom the equality Einj ~ ν 0 α /9/16 SAN-VITO,COSMIC RAY ORIGIN

20 The ques/on is how correctly es/mate the number o ar/cles accelerated rom background lasma

21 Is it correct?!!! N() inj = m T ν ν ( ) 0 ) ( = + dt d t loss α Thermal Nonthermal No se uede mostrar la imagen. Puede que su equio no tenga suiciente memoria ara abrir la imagen o que ésta esté dañada. Reinicie el equio y, a continuación, abra el archivo de nuevo. Si sigue aareciendo la x roja, uede que tenga que borrar la imagen e insertarla de nuevo. 0 1 ex 2 N acc α = 21/9/16 SAN-VITO,COSMIC RAY ORIGIN

22 Eect o AcceleraCon on Equilibrium (Maxwellian) DistribuCon o Background ParCcles 21/9/16 SAN-VITO,COSMIC RAY ORIGIN

23 Run-away ar/cles (Gurevich 1960) We inves/gate the kine/c equa/on or energies E>kT The rate o ioniza/on losses is α( u) = α u The dimensionless equa/on or ar/cle is 0 α( ) D 0 η η u = u = α0u ν 0

24 Sectrum o ar/cles in the case o accelera/on rom a background lasma (Gurevich 1960) N() T=const Region o Coulomb collisions Collisionless region o ar/cle accelera/on M α( u) ~1/ α = α 1/ u inj ~1/ α 1/3 0

25 In the general case 1 Au ( ) + B( u) = 0 2 τ u u u u 2 B( u) ( u, τ) = N( τ)ex du π Au ( ) u 0 v B() t ex dt dv At () 0 v Av ( ) dv B () t ex dt Av ( ) At ( ) 0 0 S N dt v 2 dv B ( t ) = () τ ex π Av ( ) At ( ) 0 0 From VD et al.2007 T=const!!? 21/9/16 SAN-VITO,COSMIC RAY ORIGIN

26 Wole & Melia (2006) and Petrosian & East (2008): The energy gained by the articles is distributed to the whole lasma on a timescale much shorter than that o the acceleration rocess itsel. Because o the relatively ineiciency o bremsstrahlung or cooling the accelerated electrons, this tail is quickly dumed into the thermal body o the background lasma (lasma overheating without a rominent tail o accelerated articles). Fermi Accelera/on Plasma Plasma Chernyshov, VD & Ko (2012): For a high value o the acceleration momentum cut-o 0 the run-away lux o thermal articles cools the lasma down rom the very beginning. In site o energy suly by external sources the lasma temerature dros down (analogue to Maxwell demon). Acceleration with a rominent tail o accelerated articles. D ( ) = D ς θ( ) The regime o acceleration deends strongly on 0 Fermi Accelera/on o 0 Ioniza/on Losses Nonthermal ar/cles Nonthermal ar/cles

27 Solu/ons o the system o nonlinear equa/ons with back reac/on o accelerated ar/cles o the lasma density and temerature (see Chernyshov, VD & Ko, 2012): ) ( ),, ( 1 ),, ( ex 4 1) )( ( ),, ( 3. ) ( ), ( 2. 0 )] ( ),, ( [ ),, ( D T n dt d T T n D T E T E T E er n A T n dt d T T n n D t n D T n dt d t F F = + = + = = = = + + θ α π ς

28 (rom Chernyshov,VD & Ko 2012) Plasma overhea/ng No accelera/on Plasma Cooling Stochas/c accelera/on

29 Maxwell demon

30 N() Thermal No se uede mostrar la imagen. Puede que su equio no tenga suiciente memoria ara abrir la imagen o que ésta esté dañada. Reinicie el equio y, a continuación, abra el archivo de nuevo. Si sigue aareciendo la x roja, uede que tenga que borrar la imagen e insertarla de nuevo. Nonthermal 0 >> inj Is it correct?!!!

31 Wave Absor/on by CRs Cheng,Chernyshov, VD, Ko 2014 The momentum diusion coeicient

32 Shock Wave Accelera/on (Bulanov and Dogiel, 1979) ( ) ( ) dx du m T mkt x D x u x ) ( = = ν u - u +

33 Regions o Dierent Analytical Solutions: Thermal Maxwellian Sectrum; Quasi-Thermal Sectrum Nonthermal Power-Law Sectrum

34 Sectrum o Par/cles Accelerated by Shocks Accelera/on rom background lasma - the ar/cle sectrum diers rom a simle sum o thermal + nonthermal

35 The Number o accelerated ar/cles? (Bulanov and Dogiel,1979)

36 CR Gradient in the Galactic Disk as an Eect o Background Plasma Temerature

37 The roblem o dierence between the gradients o CRs and sources is live one. From Recchia et al.2015

38 VD & Uryson 1988; Strong et al., 1988, Bloemen, et al., Huge CR Halo (global CR gradient) + arameters o CR roagation in the Galaxy (GALPROP + talks o Blasi, Morlino, Evoli) Strong et al unseen SNR at the erihery o the Galactic disk Breitschwerdt, VD & Voelk 2002 eect o the Galactic wind (see also similar but more develoed model o Recchia et al. 2016) From Ackermann et al.2011 Chandra image

39 Density o SNRs (Green 2012) and the temerature o background electrons (Quiresa 2006) as unctions o the Galactocentric radius. Distribution o CR density in the Disk (summary observations)

40 In some models o article injection into SN shocks the temerature o the ambient ISM has relevance (Berezhko et al.,1996; Kang et al., 2002). Thereore Erlykin, Wolendale and VD (2016) suggested an alternative model - the eect is due to dierent ractions o CRs accelerated rom a background lasmadeending on the background temerature in the Disk E inj = 2.5 ev gives a reasonable coincidence with the Galactic CR gradient but there are a number o uncertainties and a more detailed analysis is required

41 Thank you or your attention! Grazie!