a basic course on supernova remnants

Rino Bandiera, Arcetri Obs., Firenze, Italy A Basic Course on SNRs

A Basic Course onSupernova Remnants

• Lecture #1– How do they look and how are observed?– Hydrodynamic evolution on shell-type SNRs

• Lecture #2– Microphysics in SNRs - shock acceleration– Non-thermal emission from SNRs


Order-of-magnitude estimates• SN explosion

– Mechanical energy:

– Ejected mass:

• VELOCITY:

• Ambient medium– Density: Mej~Mswept when:

• SIZE:

• AGE:

erg1051SN E

Sun34

ej 5g10 MM

118ejSNej skm000,3scm103/ MEV

3ISM cm3.0 n

pc5cm105.14/3 193/1ISMejSNR nMR

yr1500105/ 10ejSNRSNR sVRt


“Classical” Radio SNRs• Spectacular shell-like morphologies

– compared to optical– spectral index

– polarization

BUT• Poor diagnostics on the physics

– featureless spectra (synchrotron emission)– acceleration efficiencies ?

Tycho – SN 1572

5.0;)( F


90cm Survey 4.5 < l < 22.0 deg (35 new SNRs found; Brogan et al. 2006)

Blue: VLA 90cm Green: Bonn 11cm Red: MSX 8 m

• Radio traces both thermal and non-thermal emission

• Mid-infrared traces primarily warm thermal dust emission

A view of Galactic Plane


Cassiopeia A

SNRs in the X-ray window• Probably the “best”

spectral range to observe

– Thermal:• measurement of

ambient density

– Non-Thermal:• Synchrotron

emission from electrons close to maximum energy (synchrotron cutoff)

keV12ejee VmkT

dVnnEM eH


X-ray spectral analysis• Lower resolution data

– Either fit with a thermal model• Temperature• Density• Possible deviations from ionization eq.• Possible lines

– Or a non-thermal one(power-law)

• Plus estimate of thephotoel. Absorption SNR N132D with BeppoSAX


• Higher resolution data– Abundances of elements– Line-ratio spectroscopy

N132D as seen with

XMM-Newton(Behar et al. 2001)

– Plus mapping in individual lines


Thermal vs. Non-Thermal

Cas A, with Chandra

SN 1006, with Chandra


Shell-type SNR evolutiona “classical” (and incorrect) scenario

Isotropic explosion and further evolutionHomogeneous ambient mediumThree phases:• Linear expansion• Adiabatic expansion• Radiative expansionGoal: simple description of these phases

IsotropicHomogeneous

Linear

AdiabaticRadiative

(but CSM)


Den

sity

Radius

Forward shock

Reverse shock

Forward and reverse shocks

• Forward Shock: into the CSM/ISM (fast)• Reverse Shock: into the Ejecta (slow)


Basic concepts of shocks• Hydrodynamic (MHD)

discontinuities• Quantities conserved

across the shock– Mass– Momentum– Energy– Entropy

• Jump conditions(Rankine-Hugoniot)

• Independent of the detailed physics

12

1122

22 pVpV 1

21112

2222 2/2/ wVVwVV

1122 VV

12 ss

shock111 V,,p222 V,,p

V

4/3;4/;4 21121212 VpVV

If 3/5

2111 Vp Strong shock

21121212 1

2;

1

1;

1

1VpVV


Dimensional analysisand Self-similar models

• Dimensionality of a quantity:• Dimensional constants of a problem

– If only two, such that M can be eliminated, THEN expansion law follows immediately!

• Reduced, dimensionless diff. equations– Partial differential equations (in r and t)

then transform into total differential equations (in a self-similar coordinate).

rqp TLMA

)()()),((),( 21 tffttRftrf


Early evolution

• Linear expansion only if ejecta behave as a “piston”

• Ejecta with and(Valid for the outerpart of the ejecta)

• Ambient mediumwith and

(s=0 for ISM; s=2 for wind material)

trV / ntrth )/(3ej

0Vsqr amb

Log(r)

Log(ρ)

CORE

ENVELO

PE

(n > 5)

(s < 3)


• Dimensional parameters

and

• Expansion law:

)3()3( nn TMLh )3( sMLq

)/()3()/(1/ snnsnc tqhR

n=7 n=12

s=0 0.57 0.75

s=2 0.80 0.90


Evidence of deceleration in SNe

• VLBI mapping (SN 1993J)

• Decelerated shock

• For an r -2 ambient profileejecta profile is derived


Self-similar models

• Radial profiles– Ambient medium– Forward shock– Contact

discontinuity– Reverse shock– Expanding ejecta

(Chevalier 1982)


Instabilities• Approximation: pressure ~ equilibration

Pressure increases outwards (deceleration)• Conservation of entropy

• Stability criterion (against convection)P and S gradients must be opposite

ns < 9 -> SFS, SRS decrease with timeand viceversafor ns < 9

Always unstable region

22)/()3( /;; tRPPRtR FSFSs

FSFSsnn

FS

)/(3/)9(223/22223/2 /// snnssFSFSFSFSFSFS ttRtRPS

FSRS

P P

SS

STABLEUNSTAB

factor ~ 3


(Chevalier et al. 1992)

(Blondin & Ellison 2001)

1-D results, inspherical symmetry are not adequate

n=12, s=0

n=7, s=2

Linear analysis of the instabilities+ numerical simulations


The case of SN 1006• Thermal + non-thermal

emission in X-rays

(Cassam-Chenai et al. 2008)

FS from Ha + Non-thermal X-raysCD from 0.5-0.8 keV Oxygen band(thermal emission from the ejecta)

(Miceli et al. 2009)


• Why is it so important?– RFS/RCD ratios in the range 1.05-1.12

– Models instead require RFS/RCD > 1.16

– ARGUMENT TAKEN AS A PROOF FOR EFFICIENT PARTICLE ACCELERATION

(Decouchelle et al. 2000; Ellison et al. 2004)

• Alternatively, effectdue to mixing triggeredby strong instabilities

(Although Miceli et al. 3-Dsimulation seems still tofind such discrepancy)


Acceleration as an energy sink

• Analysis of all the effects of efficient particle acceleration is a complex task

• Approximate modelsshow that distancebetween RS, CD, FSbecome significantlylower (Decourchelle et al. 2000)

• Large compressionfactor - Low effectiveLorentz factor


End of the self-similar phase• Reverse shock has reached the core

region of the ejecta (constant density)• Reverse shock moves faster inwards

and finally reachesthe center.

See Truelove & McKee1999 for a semi-analytictreatment of this phase

RS

FSDeceleration factor

1-D HD simulation by Blondin


The Sedov-Taylor solution• After the reverse shock has reached

the center• Middle-age SNRs

– swept-up mass >> mass of ejecta– radiative losses are still negligible

• Dimensional parameters of the problem

• Evolution:• Self-similar, analytic solution (Sedov,1959)

3ISMISM : ML 22

SNSN : TMLEE

5/25/1ISMSNSNR )/()( tEtR


The Sedov profiles

• Most of the mass is confined in a “thin” shell• Kinetic energy is also confined in that shell• Most of the internal energy in the “cavity”

Shocked ISM ISM

Blast wave


Thin-layer approximation• Layer thickness

• Total energy

• Dynamics

1233

44

2

11

32

2 RRrRrR

2c13

22c3 ;

3

4;

213

4ppRM

uM

pRE

223c

22 3

14 RRRR

dt

dpRMu

dt

d

2

1

5

2;

3

14

q

q

qtR q

2

5

15

22

13 1

1

2

)1)(1(

2

5

2

2

1

3

4

t

R

t

RRE

12.1

3

5

Correct value: 1.15 !!!


What can be measured (X-rays)

pc5.12 5/24

5/10

5/151Sed tnER

dVnnEM eH shockx 28.1 TT

from spectral fits

d

t

n

E

VkT

dR

dEM

x

0

2

/

/

… if in the Sedov phase


SN 1006 Dec.Par. = 0.34Tycho SNR (SN 1572) Dec.Par. = 0.47

Testing the Sedov expansion

Required:• RSNR/D (angular size)

• t (reliable only for historical SNRs)

• Vexp/D (expansion rate, measurable only in young SNRs)

5/2/ SNRexp RtV

Deceleration parameter


Other ways to “measure”the shock speed

• Radial velocities from high-res spectra(in optical, but now feasible also in X-rays)

• Electron temperature, from modeling the (thermal) X-ray spectrum

• Modeling the Balmer line profile in non-radiative shocks


End of the Sedov phase

• Sedov in numbers:

• When forward shock becomes radiative: with

• Numerically:

117/20

17/15117/7

017/5

51tr

17/90

17/451

4tr skm260

pc19

yr109.2

nEV

nER

nEt

0coolagetr

1:

nttt

pc5.12 5/24

5/10

5/151Sed tnER

13116 scmerg10)( TT


Beyond the Sedov phase• When t > ttr, energy no longer conserved.

What is left?• “Momentum-conserving

snowplow” (Oort 1951)

• WRONG !! Rarefied gas in the inner regions

• “Pressure-driven snowplow” (McKee & Ostriker 1977)

4/13

tRconst

constVR

ISM

ISM

Kinetic energy

Internal energy)33/(2

2ISM

3kin

3inninn

3int

/

/

tR

VRE

RPRE

3/5for7/2 tR


Numerical results

ttr

Blondin et al 1998

2/5 0.33

2/7=0.29

1/4=0.25

(Blondin et al 1998)


An analytic model• Thin shell approximation

• Analytic solution

R

Rp

td

pdRp

td

RMdRR

td

Md

cc2

c2

0 3;4)(

;4

13

2

)2(33

KRRRR

632 HRRKR

H either positive (fast branch)limit case: Oort

or negative (slow branch)limit case: McKee & Ostriker

H, K from initial conditionsBandiera & Petruk 2004


Inhomogenous ambient medium

• Circumstellar bubble (ρ ~ r -2)– evacuated region around the star– SNR may look older than it really is

• Large-scale inhomogeneities– ISM density gradients

• Small-scale inhomogeneities– Quasi-stationary clumps (in optical) in

young SNRs (engulfed by secondary shocks)

– Thermal filled-center SNRs as possibly due to the presence of a clumpy medium


THE END

a basic course on supernova remnants

Documents

thermal nonthermal emission

expansion law

ha nonthermal xrays

s gradients

ambient profile ejecta

ambient mediumdensity

jdecelerated shock

selfsimilar coordinate