Jacco Vink- Magnetars in Supernova Remnants & Magnetars Formation
A Basic Course on Supernova Remnants
-
Upload
keaton-davenport -
Category
Documents
-
view
45 -
download
1
description
Transcript of 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
Rino Bandiera, Arcetri Obs., Firenze, Italy A Basic Course on 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
Rino Bandiera, Arcetri Obs., Firenze, Italy A Basic Course on SNRs
“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
Rino Bandiera, Arcetri Obs., Firenze, Italy A Basic Course on SNRs
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
Rino Bandiera, Arcetri Obs., Firenze, Italy A Basic Course on SNRs
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
Rino Bandiera, Arcetri Obs., Firenze, Italy A Basic Course on SNRs
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
Rino Bandiera, Arcetri Obs., Firenze, Italy A Basic Course on SNRs
• Higher resolution data– Abundances of elements– Line-ratio spectroscopy
N132D as seen with
XMM-Newton(Behar et al. 2001)
– Plus mapping in individual lines
Rino Bandiera, Arcetri Obs., Firenze, Italy A Basic Course on SNRs
Thermal vs. Non-Thermal
Cas A, with Chandra
SN 1006, with Chandra
Rino Bandiera, Arcetri Obs., Firenze, Italy A Basic Course on SNRs
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)
Rino Bandiera, Arcetri Obs., Firenze, Italy A Basic Course on SNRs
Den
sity
Radius
Forward shock
Reverse shock
Forward and reverse shocks
• Forward Shock: into the CSM/ISM (fast)• Reverse Shock: into the Ejecta (slow)
Rino Bandiera, Arcetri Obs., Firenze, Italy A Basic Course on SNRs
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
Rino Bandiera, Arcetri Obs., Firenze, Italy A Basic Course on SNRs
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
Rino Bandiera, Arcetri Obs., Firenze, Italy A Basic Course on SNRs
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)
Rino Bandiera, Arcetri Obs., Firenze, Italy A Basic Course on SNRs
• 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
Rino Bandiera, Arcetri Obs., Firenze, Italy A Basic Course on SNRs
Evidence of deceleration in SNe
• VLBI mapping (SN 1993J)
• Decelerated shock
• For an r -2 ambient profileejecta profile is derived
Rino Bandiera, Arcetri Obs., Firenze, Italy A Basic Course on SNRs
Self-similar models
• Radial profiles– Ambient medium– Forward shock– Contact
discontinuity– Reverse shock– Expanding ejecta
(Chevalier 1982)
Rino Bandiera, Arcetri Obs., Firenze, Italy A Basic Course on SNRs
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
Rino Bandiera, Arcetri Obs., Firenze, Italy A Basic Course on SNRs
(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
Rino Bandiera, Arcetri Obs., Firenze, Italy A Basic Course on SNRs
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)
Rino Bandiera, Arcetri Obs., Firenze, Italy A Basic Course on SNRs
• 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)
Rino Bandiera, Arcetri Obs., Firenze, Italy A Basic Course on SNRs
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
Rino Bandiera, Arcetri Obs., Firenze, Italy A Basic Course on SNRs
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
Rino Bandiera, Arcetri Obs., Firenze, Italy A Basic Course on SNRs
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
Rino Bandiera, Arcetri Obs., Firenze, Italy A Basic Course on SNRs
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
Rino Bandiera, Arcetri Obs., Firenze, Italy A Basic Course on SNRs
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 !!!
Rino Bandiera, Arcetri Obs., Firenze, Italy A Basic Course on SNRs
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
Rino Bandiera, Arcetri Obs., Firenze, Italy A Basic Course on SNRs
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
Rino Bandiera, Arcetri Obs., Firenze, Italy A Basic Course on SNRs
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
Rino Bandiera, Arcetri Obs., Firenze, Italy A Basic Course on SNRs
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
Rino Bandiera, Arcetri Obs., Firenze, Italy A Basic Course on SNRs
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
Rino Bandiera, Arcetri Obs., Firenze, Italy A Basic Course on SNRs
Numerical results
ttr
Blondin et al 1998
2/5 0.33
2/7=0.29
1/4=0.25
(Blondin et al 1998)
Rino Bandiera, Arcetri Obs., Firenze, Italy A Basic Course on SNRs
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
Rino Bandiera, Arcetri Obs., Firenze, Italy A Basic Course on SNRs
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