Mostly on supernova remnants: Shock heating & particle acceleration

by Astrophysical shocks

Jacco Vink University of Amsterdam

Galactic Cosmic Rays

2

●Galactic cosmic rays:●cosmic rays up to the “knee” @ 3x1015Z eV

●Are supernovae (energy)/supernova remnants (sites of acceleration) responsible?●Required:

●5-10% of SN explosion energy into cosmic rays●SNRs must be able to accelerate to 3x1015Z eV

Supernova remnant example: Cassiopeia A

3

●Bell, Gull, Kenderdine, 1975●Later: expansion study

Importance Cas A

4

●Brightest radio source: relativistic electrons cannot come from crushing pre-existing particles

●Minimum energy argument: ~1049 erg (e.g. Rosenberg 1970)●Cas A: high magnetic field: ~0.5 mG●Gull 1975: B-field amplification in convective zone -> account for Cas A

●B-field high interior of shell, not near shock

Can SNRs accelerate up to the knee?

5

1983A&A...125..249L

Important observational advances

6

SN1006 RX J1713

●X-ray imaging spectroscopy (CCDs)●Koyama et al. 1995 (ASCA):

●SN 1006 displays X-ray synchrotron emission from >10 TeV electrons

●Imaging Cherenkov Telescopes● > TeV gamma-rays from SNRs●> 10 TeV particles●Electrons or protons?

X-ray synchrotron from young SNRs

7

Cas A SN1604/Kepler SN1572/Tycho

SN185/RCW86SN1006 RX J1713

(Loss-limited) Synchrotron cut-off

8

⌧acc ⇡ 1.83D2V 2s

3�2

�� 1 = 124⌘B�1�4

⇣ Vs5000 km s�1

⌘�2⇣ E100 TeV

⌘ �24�4 � 14

yr,

⌧syn =E

dE/dt= 12.5

⇣ E100 TeV

⌘�1⇣ Be↵100µG

⌘�2yr.

h⌫cut�o↵ = 1.4⌘�1

⇣�4

� 14

�24

⌘⇣ Vs5000 km s�1

⌘2

keV

●Synchrotron loss-time

●Diffusive acceleration time (depends on diffusion coeff. D, compression X)

●Equating gives expected cut-off for loss-limited case, plugging in hν=7.4E2B keV:

Implications

9

●Young SNRs are X-ray synchrotron emitters: acceleration close to Bohm-diffusion limit!

●The higher the B-field -> faster acceleration, but for electrons: Emax lower!●For B=10-100 μG: presence of 1013-1014 eV electrons●Loss times are:

X-ray synchrotron emission tells us that- electrons can be accelerated fast- acceleration is still ongoing (loss times ~10-100 yr)- particles can be accelerated at least up to 1014 eV

�syn =E

dE/dt= 12.5

⇣ E100 TeV

⌘�1⇣ Be�100µG

⌘�2yr.

1 . ⌘ . 10

Narrow X-ray synchrotron filaments

10

SN1572

Chandra●In many cases X-ray synchrotron filaments appear very narrow (1-4”)

●Including deprojections implies l≈1017cm

Vink & Laming 03

Explanation narrow synchrotron rims

11

●Combining diffusion and advection:

●Cas A/Tycho/Kepler: ~100-500 μG (e.g. Vink&Laming ‘03, Völk et al. 03, Bamba+ ’04, Warren+ ’05, Parizot+ ’06)

●High B ⇒fast acceleration ⇒ protons beyond 1015eV?

•High B-field likely induced by cosmic rays (e.g. Bell ‘04)•High B-fields are a signature of efficient acceleration

Vink&Laming ‘03

B2 ⇡ 26⇣ ladv

1.0⇥ 1018cm

⌘�2/3⌘1/3

⇣�4 �

14

⌘�1/3µG

Magnetic Field Amplification

12

●There is a clear correlation between ρ, V and B, in rough agreement with theoretical predictions by Bell 2004 (B2∝ρVs3)

●Dynamical range in V low (~3000-6000 km/s)●Relation may even extend to supernovae (B2∝ρVs3 ?)(Völk et al. ’05, Vink ‘08)

A possible history for Cas A

13

Maximum energy for Fe

•Acceleration most efficient early on in supernovae in red supergiant winds (Type II/Type IIb) (e.g. Cas A, SN1993J)

•Highest energy CRs may escape first (Ptuskin & Zirakashvili ’05)•Highest energy particles from earliest (radio supernova) phases (Bell & Lucek ’01)

Acceleration @ Cas A reverse shock

14

●Spectral index: 2 regions of hard emission: X-ray synchrotron emission●Deprojection: Most X-ray synchrotron from reverse shock!●Prominence of West: No expansion ⇒ ejecta shocked with V>6000 km/s●Reverse shock: metal-rich -> more electrons -> bright radio

Deprojection

Γ= -3.2

B-field amplification is not very sensitive to initial B-field!

Helder&Vink ‘08

4-6keV

H.E.S.S. Observations of RX 1713.7-3946:The escape of cosmic rays

15

H.E.S.S. Collaboration: Observations of RX J1713.7�3946

Fig. 2: Gamma-ray excess map and radial profiles. Top left: the H.E.S.S. gamma-ray count map (E > 250 GeV) is shown withXMM-Newton X-ray contours (1–10 keV, smoothed with the H.E.S.S. PSF) overlaid. The five regions used to compare the gamma-ray and X-ray data are indicated along with concentric circles (dashed grey lines) with radii of 0.2� to 0.8� and centred at R.A.:17h13m25.2s, Dec.: �39d46m15.6s. The Galactic plane is also drawn. The other five panels show the radial profiles from theseregions. The profiles are extracted from the H.E.S.S. maps (black crosses) and from an XMM-Newton map convolved with theH.E.S.S. PSF (red line). The relative normalisation between the H.E.S.S. and XMM-Newton profiles is chosen such that for regions1, 2, 4 the integral in [0.3�, 0.7�] is the same, for regions 3, 5 in [0.2�, 0.7�]. The grey shaded area shows the combined statisticaland systematic uncertainty band of the radial gamma-ray extension, determined as described in the main text. The vertical dashedred line is the radial X-ray extension. For the X-ray data, the statistical uncertainties are well below 1% and are not shown.

4

H.E.S.S. Collaboration: Observations of RX J1713.7�3946

Fig. 2: Gamma-ray excess map and radial profiles. Top left: the H.E.S.S. gamma-ray count map (E > 250 GeV) is shown withXMM-Newton X-ray contours (1–10 keV, smoothed with the H.E.S.S. PSF) overlaid. The five regions used to compare the gamma-ray and X-ray data are indicated along with concentric circles (dashed grey lines) with radii of 0.2� to 0.8� and centred at R.A.:17h13m25.2s, Dec.: �39d46m15.6s. The Galactic plane is also drawn. The other five panels show the radial profiles from theseregions. The profiles are extracted from the H.E.S.S. maps (black crosses) and from an XMM-Newton map convolved with theH.E.S.S. PSF (red line). The relative normalisation between the H.E.S.S. and XMM-Newton profiles is chosen such that for regions1, 2, 4 the integral in [0.3�, 0.7�] is the same, for regions 3, 5 in [0.2�, 0.7�]. The grey shaded area shows the combined statisticaland systematic uncertainty band of the radial gamma-ray extension, determined as described in the main text. The vertical dashedred line is the radial X-ray extension. For the X-ray data, the statistical uncertainties are well below 1% and are not shown.

4

H.E.S.S. Collaboration: Observations of RX J1713.7�3946

Fig. 7: Spatial distribution of physical best-fit parameters across the SNR, overlaid on the H.E.S.S. gamma-ray significance contoursat 3, 5, 7, and 9� in black, red, orange, and green. For the leptonic model, colour codes are shown for the magnetic field strength (topleft), exponential cut-o↵ energies (top right), and particle indices (bottom left). For the hadronic models, only the particle indices(bottom right) are relevant and shown here. The 29 subregions labelled with grey numbers are boxes of side lengths 0.18� or 10.8arcminutes. To judge whether the di↵erences region to region are significant, the statistical uncertainties listed in Table 6 and 7 haveto be taken into account, and ultimately the H.E.S.S. systematic measurement uncertainties discussed above as well. When doingthis, the spectral indices show no variation across the SNR in either scenario.

Explaining this spectral shape is thus a challenge for the leptonicscenario, which is discussed further in Sect. 6.1. Figure 7 (bot-tom left) shows that the spatial distribution of the electron indexis not entirely uniform, even when taking the statistical uncer-tainties given in Table 6 into account the indices in the brighterwestern part of the shell tend to be larger. Such a trend is alsoseen in the distribution of the high-energy exponential cut-o↵ en-ergy (in the range 50–200 TeV) and the average magnetic fieldstrength (in the range 8–20 µG) shown in the same figure. Thewestern half of the remnant shows higher values of the mag-netic field strength and lower values of the cut-o↵ with the op-posite behaviour seen in the eastern half (see top left and rightof Fig. 7). In a synchrotron-loss-limited acceleration scenario,the maximum energy achievable at a given shock is proportional

to B�1/2, so that the anti-correlation between cut-o↵ energy andmagnetic field strength is to be expected.

In a hadronic scenario we only consider radiation from pri-mary protons without considering secondary X-ray emissionfrom charged pions produced in interactions of protons with am-bient matter (Aharonian 2013a). Using only the H.E.S.S. spec-tra, we find that the proton cut-o↵ energy is not constrained formany of the regions. We therefore fix the cut-o↵ energy when fit-ting the subregions spectrum to the value found for the full SNRspectrum: Ec = 93 TeV. Under this assumption, all the regionsare well fit by a neutral pion decay spectrum with the parametersshown in Table 7. The proton particle indices for all the regionscover a range between 1.60 and 2.14 as shown in Fig. 7 (bot-tom right) and listed in Table 7. As already found above for thegamma-ray spectral fits (Sect. 4.2), the maximum di↵erence be-

14

• Very deep TeV gamma-ray observation of bright SNR RX J1713 (164 hours)• Allows for imaging spectroscopy• Assumption of leptonic (IC) emission: B-field map (≈14 μG)• Surprise: gamma-ray extends beyond X-ray emission

• X-ray boundary->shock• extent in region 3: Δr=0.87d1 pc = 13% of the radius!!

arXiv:1609.08671v2

Extended gamma-rays: diffusion implications

16

H.E.S.S. Collaboration: Observations of RX J1713.7�3946

ment, which is clearly beyond our scope here. We therefore re-strict the discussion to some general considerations. We also em-phasise here that the extent of gamma-ray emission from aroundRX J1713.7�3946 varies considerably, which likely reflects dif-ferent particle acceleration conditions around the shell.

The observations reveal the presence of gamma rays fromparsec scale regions of size �r upstream of the shock. If theVHE gamma rays are from IC scattering of electrons, the spatialdistribution of the gamma-ray emission simply traces the distri-bution of electrons (the target photon field density is not likelyto vary on such small scales). If the emission is due to neutralpion decay, its morphology results from the convolution of thespatial distributions of CR protons and interstellar medium gas.In both cases, a rough estimate of the maximal extension of theTeV emission outside of the SNR can be obtained by computingthe di↵usion length of multi-TeV particles ahead of the shock.

To do this, we use �r1/e listed in Tab. 2 as the typical extentof the particle distribution upstream of the shock. In theoreticalassessments the di↵usion length scale is usually taken to be thedistance from the shock at which the particle density has droppedto 1/e. Even though the physical di↵usion length scale is in ad-dition subject to projection e↵ects, for our purpose of an orderof magnitude assessment we assume that the di↵erence in �r1/ebetween X-rays and gamma rays is equivalent to the di↵usionlength scale. From Tab. 2, this angular di↵erence in regions 2, 3,and 4 is �r ⌘ (�rgamma rays1/e � �r

X�rays1/e ), and we therefore obtain

a maximum of �r = 0.05� for region 3, which corresponds to0.87 d1 pc, where d1 is the distance to the SNR in units of 1 kpc.In the precursor scenario, the di↵usion length scale is given by

`p ⇡D(E)ushock

. (4)

For the escape scenario the typical length scale over which theparticles di↵use is given by the di↵usion length scale

`e ⇡p

2 D(E)�t . (5)

Here, ushock is the shock velocity, and �t is the escape time. D(E)is the energy dependent di↵usion coe�cient, which we parame-terise as

D(E) = ⌘(E)13

cEeB. (6)

⌘ is the ratio between the mean free path of the particles andtheir gyroradius. In general, ⌘ is an energy dependent parameterthat expresses the deviation from Bohm di↵usion, which itselfis thus defined as ⌘ = 1. Its value in regions associated with theSNR should in any case be close to ⌘ = 1 for particle energies of10-100 TeV in order to explain the fact that RX J1713.7�3946is a source of X-synchrotron emission (see Aharonian & Atoyan1999).

Assuming that the di↵usion length scale in both cases isequal to the measured parameter �r we arrive at

B⌘⇡ 0.36

✓ E10 TeV

◆ ushock3000 km s�1

!�1 �rpc

!�1µG (7)

for the precursor scenario. For the escape scenario we shouldtake into account that the shock itself will also have displacedduring a time �t. So we have �r = `e � ushock�t. However, forescape it holds that `e > ushock�t, since escape implies that dif-fusion is more important than advection, and even more so since

during the time �t the shock slows down and hence ushock de-creases. Dropping terms with u2shock�t

2/�r2 we find that

B⌘⇡ 1.1

✓ E10 TeV

◆ �t

500 yr

! �rpc

!�2 "1 +

ushock�t�r

#�1µG, (8)

with B the magnetic field upstream of the shock and ⌘again the mean free path of the particles in units of thegyroradius. The factor in square brackets is . 1.5. Forthe shock velocity of RX J1713.7�3946, an upper limit of4500 km s�1 has been derived from Chandra data (Uchiyamaet al. 2007) and from Suzaku data the velocity is estimated tobe 3300⌘1/2 km s�1 (Tanaka et al. 2008). For particles in theshock or shock precursor region, RX J1713.7�3946 thereforeoperates at or close to the Bohm regime since the synchrotronX-ray data require ⌘ = 1 � 1.8 for shock velocities of 3300–4500 km s�1. Taking this into account, for ⌘ = 2, we obtain forregion 3: B = 0.8 µG in the precursor scenario. In the escapescenario where the particles have left the shock region, ⌘ is notconstrained by the X-ray emission any more and in particularit can be larger (⌘ > 1). We therefore derive in more generalterms B . ⌘ 2.8 µG in the escape scenario. In the standard DSAparadigm, and in the absence of further magnetic field amplifi-cation through turbulences (discussed for example in Giacalone& Jokipii 2007), the expected magnetic field compression at theshock would result in downstream magnetic fields a factor ofRB = 3� 4 higher than those upstream, that is, up to B = 3.2 µGand B = ⌘ 11.2 µG for region 3 in the precursor and escape sce-nario, respectively.

Whilst the escape scenario is compatible with our broadbandleptonic fits, in the precursor scenario the downstream magneticfield value is lower than the values obtained with these fits (seeFig. 7 and Tab. 6). In particular, B = 3.2 µG downstream is some-what lower than expected in the DSA paradigm, unless we in-voke a recent sudden increase of ⌘ to values well above 2 or adecrease of ushock to well below 3300 km s�1 to recover higherdownstream magnetic field values. Such sudden changes mustoccur on timescales smaller than the synchrotron radiation losstime of the downstream electrons, since ⌘ . 5 is needed to ex-plain X-ray synchrotron radiation from the shell in these regions(Tanaka et al. 2008). We therefore require that the timescalefor substantial changes in the upstream di↵usion properties, �t,must satisfy

⌧loss =634B2E

s > �t, (9)

with ⌧loss = |E/(dE/dt)| (Ginzburg & Syrovatskii 1965). Thetypical X-ray synchrotron photon energy is given by ✏ =7.4E2B keV (Ginzburg & Syrovatskii 1965), so that the condi-tion for the presence of X-ray emission from the shell at 1 keVfor a given timescale �t is

B . 23 �t

500 yr

!�2/3µG. (10)

This condition is fully consistent with the leptonic emission sce-nario, but requires for the hadronic emission scenario timescalesshorter than �t = 500 yr.

To summarise, the significant extension of the gamma-rayemission beyond the X-ray defined shock in some regions ofRX J1713.7�3946 requires either low magnetic fields or di↵u-sion length scales much larger than for Bohm di↵usion, irrespec-tive of whether the gamma rays are from particles originating inthe shock precursor or escaping the remnant di↵usively. In bothcases, the length scales are in fact governed by di↵usion.

17

H.E.S.S. Collaboration: Observations of RX J1713.7�3946

ment, which is clearly beyond our scope here. We therefore re-strict the discussion to some general considerations. We also em-phasise here that the extent of gamma-ray emission from aroundRX J1713.7�3946 varies considerably, which likely reflects dif-ferent particle acceleration conditions around the shell.

The observations reveal the presence of gamma rays fromparsec scale regions of size �r upstream of the shock. If theVHE gamma rays are from IC scattering of electrons, the spatialdistribution of the gamma-ray emission simply traces the distri-bution of electrons (the target photon field density is not likelyto vary on such small scales). If the emission is due to neutralpion decay, its morphology results from the convolution of thespatial distributions of CR protons and interstellar medium gas.In both cases, a rough estimate of the maximal extension of theTeV emission outside of the SNR can be obtained by computingthe di↵usion length of multi-TeV particles ahead of the shock.

To do this, we use �r1/e listed in Tab. 2 as the typical extentof the particle distribution upstream of the shock. In theoreticalassessments the di↵usion length scale is usually taken to be thedistance from the shock at which the particle density has droppedto 1/e. Even though the physical di↵usion length scale is in ad-dition subject to projection e↵ects, for our purpose of an orderof magnitude assessment we assume that the di↵erence in �r1/ebetween X-rays and gamma rays is equivalent to the di↵usionlength scale. From Tab. 2, this angular di↵erence in regions 2, 3,and 4 is �r ⌘ (�rgamma rays1/e � �r

X�rays1/e ), and we therefore obtain

a maximum of �r = 0.05� for region 3, which corresponds to0.87 d1 pc, where d1 is the distance to the SNR in units of 1 kpc.In the precursor scenario, the di↵usion length scale is given by

`p ⇡D(E)ushock

. (4)

For the escape scenario the typical length scale over which theparticles di↵use is given by the di↵usion length scale

`e ⇡p

2 D(E)�t . (5)

Here, ushock is the shock velocity, and �t is the escape time. D(E)is the energy dependent di↵usion coe�cient, which we parame-terise as

D(E) = ⌘(E)13

cEeB. (6)

⌘ is the ratio between the mean free path of the particles andtheir gyroradius. In general, ⌘ is an energy dependent parameterthat expresses the deviation from Bohm di↵usion, which itselfis thus defined as ⌘ = 1. Its value in regions associated with theSNR should in any case be close to ⌘ = 1 for particle energies of10-100 TeV in order to explain the fact that RX J1713.7�3946is a source of X-synchrotron emission (see Aharonian & Atoyan1999).

Assuming that the di↵usion length scale in both cases isequal to the measured parameter �r we arrive at

B⌘⇡ 0.36

✓ E10 TeV

◆ ushock3000 km s�1

!�1 �rpc

!�1µG (7)

for the precursor scenario. For the escape scenario we shouldtake into account that the shock itself will also have displacedduring a time �t. So we have �r = `e � ushock�t. However, forescape it holds that `e > ushock�t, since escape implies that dif-fusion is more important than advection, and even more so since

during the time �t the shock slows down and hence ushock de-creases. Dropping terms with u2shock�t

2/�r2 we find that

B⌘⇡ 1.1

✓ E10 TeV

◆ �t

500 yr

! �rpc

!�2 "1 +

ushock�t�r

#�1µG, (8)

with B the magnetic field upstream of the shock and ⌘again the mean free path of the particles in units of thegyroradius. The factor in square brackets is . 1.5. Forthe shock velocity of RX J1713.7�3946, an upper limit of4500 km s�1 has been derived from Chandra data (Uchiyamaet al. 2007) and from Suzaku data the velocity is estimated tobe 3300⌘1/2 km s�1 (Tanaka et al. 2008). For particles in theshock or shock precursor region, RX J1713.7�3946 thereforeoperates at or close to the Bohm regime since the synchrotronX-ray data require ⌘ = 1 � 1.8 for shock velocities of 3300–4500 km s�1. Taking this into account, for ⌘ = 2, we obtain forregion 3: B = 0.8 µG in the precursor scenario. In the escapescenario where the particles have left the shock region, ⌘ is notconstrained by the X-ray emission any more and in particularit can be larger (⌘ > 1). We therefore derive in more generalterms B . ⌘ 2.8 µG in the escape scenario. In the standard DSAparadigm, and in the absence of further magnetic field amplifi-cation through turbulences (discussed for example in Giacalone& Jokipii 2007), the expected magnetic field compression at theshock would result in downstream magnetic fields a factor ofRB = 3� 4 higher than those upstream, that is, up to B = 3.2 µGand B = ⌘ 11.2 µG for region 3 in the precursor and escape sce-nario, respectively.

Whilst the escape scenario is compatible with our broadbandleptonic fits, in the precursor scenario the downstream magneticfield value is lower than the values obtained with these fits (seeFig. 7 and Tab. 6). In particular, B = 3.2 µG downstream is some-what lower than expected in the DSA paradigm, unless we in-voke a recent sudden increase of ⌘ to values well above 2 or adecrease of ushock to well below 3300 km s�1 to recover higherdownstream magnetic field values. Such sudden changes mustoccur on timescales smaller than the synchrotron radiation losstime of the downstream electrons, since ⌘ . 5 is needed to ex-plain X-ray synchrotron radiation from the shell in these regions(Tanaka et al. 2008). We therefore require that the timescalefor substantial changes in the upstream di↵usion properties, �t,must satisfy

⌧loss =634B2E

s > �t, (9)

with ⌧loss = |E/(dE/dt)| (Ginzburg & Syrovatskii 1965). Thetypical X-ray synchrotron photon energy is given by ✏ =7.4E2B keV (Ginzburg & Syrovatskii 1965), so that the condi-tion for the presence of X-ray emission from the shell at 1 keVfor a given timescale �t is

B . 23 �t

500 yr

!�2/3µG. (10)

This condition is fully consistent with the leptonic emission sce-nario, but requires for the hadronic emission scenario timescalesshorter than �t = 500 yr.

To summarise, the significant extension of the gamma-rayemission beyond the X-ray defined shock in some regions ofRX J1713.7�3946 requires either low magnetic fields or di↵u-sion length scales much larger than for Bohm di↵usion, irrespec-tive of whether the gamma rays are from particles originating inthe shock precursor or escaping the remnant di↵usively. In bothcases, the length scales are in fact governed by di↵usion.

17

●Two possible reasons, both governed by diffusion:●We observe the cosmic-ray precursor ●We observe particles escaping

●Diffusion length scale → corresponds to B-field/turbulence level

●Requires low B-field/or small turbulence●For leptonic model: upstream B≈4 µG ⇒η≈5-10

H.E.S.S. Collaboration: Observations of RX J1713.7�3946

ment, which is clearly beyond our scope here. We therefore re-strict the discussion to some general considerations. We also em-phasise here that the extent of gamma-ray emission from aroundRX J1713.7�3946 varies considerably, which likely reflects dif-ferent particle acceleration conditions around the shell.

The observations reveal the presence of gamma rays fromparsec scale regions of size �r upstream of the shock. If theVHE gamma rays are from IC scattering of electrons, the spatialdistribution of the gamma-ray emission simply traces the distri-bution of electrons (the target photon field density is not likelyto vary on such small scales). If the emission is due to neutralpion decay, its morphology results from the convolution of thespatial distributions of CR protons and interstellar medium gas.In both cases, a rough estimate of the maximal extension of theTeV emission outside of the SNR can be obtained by computingthe di↵usion length of multi-TeV particles ahead of the shock.

To do this, we use �r1/e listed in Tab. 2 as the typical extentof the particle distribution upstream of the shock. In theoreticalassessments the di↵usion length scale is usually taken to be thedistance from the shock at which the particle density has droppedto 1/e. Even though the physical di↵usion length scale is in ad-dition subject to projection e↵ects, for our purpose of an orderof magnitude assessment we assume that the di↵erence in �r1/ebetween X-rays and gamma rays is equivalent to the di↵usionlength scale. From Tab. 2, this angular di↵erence in regions 2, 3,and 4 is �r ⌘ (�rgamma rays1/e � �r

X�rays1/e ), and we therefore obtain

a maximum of �r = 0.05� for region 3, which corresponds to0.87 d1 pc, where d1 is the distance to the SNR in units of 1 kpc.In the precursor scenario, the di↵usion length scale is given by

`p ⇡D(E)ushock

. (4)

For the escape scenario the typical length scale over which theparticles di↵use is given by the di↵usion length scale

`e ⇡p

2 D(E)�t . (5)

Here, ushock is the shock velocity, and �t is the escape time. D(E)is the energy dependent di↵usion coe�cient, which we parame-terise as

D(E) = ⌘(E)13

cEeB. (6)

⌘ is the ratio between the mean free path of the particles andtheir gyroradius. In general, ⌘ is an energy dependent parameterthat expresses the deviation from Bohm di↵usion, which itselfis thus defined as ⌘ = 1. Its value in regions associated with theSNR should in any case be close to ⌘ = 1 for particle energies of10-100 TeV in order to explain the fact that RX J1713.7�3946is a source of X-synchrotron emission (see Aharonian & Atoyan1999).

Assuming that the di↵usion length scale in both cases isequal to the measured parameter �r we arrive at

B⌘⇡ 0.36

✓ E10 TeV

◆ ushock3000 km s�1

!�1 �rpc

!�1µG (7)

for the precursor scenario. For the escape scenario we shouldtake into account that the shock itself will also have displacedduring a time �t. So we have �r = `e � ushock�t. However, forescape it holds that `e > ushock�t, since escape implies that dif-fusion is more important than advection, and even more so since

during the time �t the shock slows down and hence ushock de-creases. Dropping terms with u2shock�t

2/�r2 we find that

B⌘⇡ 1.1

✓ E10 TeV

◆ �t

500 yr

! �rpc

!�2 "1 +

ushock�t�r

#�1µG, (8)

with B the magnetic field upstream of the shock and ⌘again the mean free path of the particles in units of thegyroradius. The factor in square brackets is . 1.5. Forthe shock velocity of RX J1713.7�3946, an upper limit of4500 km s�1 has been derived from Chandra data (Uchiyamaet al. 2007) and from Suzaku data the velocity is estimated tobe 3300⌘1/2 km s�1 (Tanaka et al. 2008). For particles in theshock or shock precursor region, RX J1713.7�3946 thereforeoperates at or close to the Bohm regime since the synchrotronX-ray data require ⌘ = 1 � 1.8 for shock velocities of 3300–4500 km s�1. Taking this into account, for ⌘ = 2, we obtain forregion 3: B = 0.8 µG in the precursor scenario. In the escapescenario where the particles have left the shock region, ⌘ is notconstrained by the X-ray emission any more and in particularit can be larger (⌘ > 1). We therefore derive in more generalterms B . ⌘ 2.8 µG in the escape scenario. In the standard DSAparadigm, and in the absence of further magnetic field amplifi-cation through turbulences (discussed for example in Giacalone& Jokipii 2007), the expected magnetic field compression at theshock would result in downstream magnetic fields a factor ofRB = 3� 4 higher than those upstream, that is, up to B = 3.2 µGand B = ⌘ 11.2 µG for region 3 in the precursor and escape sce-nario, respectively.

Whilst the escape scenario is compatible with our broadbandleptonic fits, in the precursor scenario the downstream magneticfield value is lower than the values obtained with these fits (seeFig. 7 and Tab. 6). In particular, B = 3.2 µG downstream is some-what lower than expected in the DSA paradigm, unless we in-voke a recent sudden increase of ⌘ to values well above 2 or adecrease of ushock to well below 3300 km s�1 to recover higherdownstream magnetic field values. Such sudden changes mustoccur on timescales smaller than the synchrotron radiation losstime of the downstream electrons, since ⌘ . 5 is needed to ex-plain X-ray synchrotron radiation from the shell in these regions(Tanaka et al. 2008). We therefore require that the timescalefor substantial changes in the upstream di↵usion properties, �t,must satisfy

⌧loss =634B2E

s > �t, (9)

with ⌧loss = |E/(dE/dt)| (Ginzburg & Syrovatskii 1965). Thetypical X-ray synchrotron photon energy is given by ✏ =7.4E2B keV (Ginzburg & Syrovatskii 1965), so that the condi-tion for the presence of X-ray emission from the shell at 1 keVfor a given timescale �t is

B . 23 �t

500 yr

!�2/3µG. (10)

This condition is fully consistent with the leptonic emission sce-nario, but requires for the hadronic emission scenario timescalesshorter than �t = 500 yr.

To summarise, the significant extension of the gamma-rayemission beyond the X-ray defined shock in some regions ofRX J1713.7�3946 requires either low magnetic fields or di↵u-sion length scales much larger than for Bohm di↵usion, irrespec-tive of whether the gamma rays are from particles originating inthe shock precursor or escaping the remnant di↵usively. In bothcases, the length scales are in fact governed by di↵usion.

17

H.E.S.S. Collaboration: Observations of RX J1713.7�3946

ment, which is clearly beyond our scope here. We therefore re-strict the discussion to some general considerations. We also em-phasise here that the extent of gamma-ray emission from aroundRX J1713.7�3946 varies considerably, which likely reflects dif-ferent particle acceleration conditions around the shell.

The observations reveal the presence of gamma rays fromparsec scale regions of size �r upstream of the shock. If theVHE gamma rays are from IC scattering of electrons, the spatialdistribution of the gamma-ray emission simply traces the distri-bution of electrons (the target photon field density is not likelyto vary on such small scales). If the emission is due to neutralpion decay, its morphology results from the convolution of thespatial distributions of CR protons and interstellar medium gas.In both cases, a rough estimate of the maximal extension of theTeV emission outside of the SNR can be obtained by computingthe di↵usion length of multi-TeV particles ahead of the shock.

To do this, we use �r1/e listed in Tab. 2 as the typical extentof the particle distribution upstream of the shock. In theoreticalassessments the di↵usion length scale is usually taken to be thedistance from the shock at which the particle density has droppedto 1/e. Even though the physical di↵usion length scale is in ad-dition subject to projection e↵ects, for our purpose of an orderof magnitude assessment we assume that the di↵erence in �r1/ebetween X-rays and gamma rays is equivalent to the di↵usionlength scale. From Tab. 2, this angular di↵erence in regions 2, 3,and 4 is �r ⌘ (�rgamma rays1/e � �r

X�rays1/e ), and we therefore obtain

a maximum of �r = 0.05� for region 3, which corresponds to0.87 d1 pc, where d1 is the distance to the SNR in units of 1 kpc.In the precursor scenario, the di↵usion length scale is given by

`p ⇡D(E)ushock

. (4)

For the escape scenario the typical length scale over which theparticles di↵use is given by the di↵usion length scale

`e ⇡p

2 D(E)�t . (5)

Here, ushock is the shock velocity, and �t is the escape time. D(E)is the energy dependent di↵usion coe�cient, which we parame-terise as

D(E) = ⌘(E)13

cEeB. (6)

⌘ is the ratio between the mean free path of the particles andtheir gyroradius. In general, ⌘ is an energy dependent parameterthat expresses the deviation from Bohm di↵usion, which itselfis thus defined as ⌘ = 1. Its value in regions associated with theSNR should in any case be close to ⌘ = 1 for particle energies of10-100 TeV in order to explain the fact that RX J1713.7�3946is a source of X-synchrotron emission (see Aharonian & Atoyan1999).

Assuming that the di↵usion length scale in both cases isequal to the measured parameter �r we arrive at

B⌘⇡ 0.36

✓ E10 TeV

◆ ushock3000 km s�1

!�1 �rpc

!�1µG (7)

for the precursor scenario. For the escape scenario we shouldtake into account that the shock itself will also have displacedduring a time �t. So we have �r = `e � ushock�t. However, forescape it holds that `e > ushock�t, since escape implies that dif-fusion is more important than advection, and even more so since

during the time �t the shock slows down and hence ushock de-creases. Dropping terms with u2shock�t

2/�r2 we find that

B⌘⇡ 1.1

✓ E10 TeV

◆ �t

500 yr

! �rpc

!�2 "1 +

ushock�t�r

#�1µG, (8)

with B the magnetic field upstream of the shock and ⌘again the mean free path of the particles in units of thegyroradius. The factor in square brackets is . 1.5. Forthe shock velocity of RX J1713.7�3946, an upper limit of4500 km s�1 has been derived from Chandra data (Uchiyamaet al. 2007) and from Suzaku data the velocity is estimated tobe 3300⌘1/2 km s�1 (Tanaka et al. 2008). For particles in theshock or shock precursor region, RX J1713.7�3946 thereforeoperates at or close to the Bohm regime since the synchrotronX-ray data require ⌘ = 1 � 1.8 for shock velocities of 3300–4500 km s�1. Taking this into account, for ⌘ = 2, we obtain forregion 3: B = 0.8 µG in the precursor scenario. In the escapescenario where the particles have left the shock region, ⌘ is notconstrained by the X-ray emission any more and in particularit can be larger (⌘ > 1). We therefore derive in more generalterms B . ⌘ 2.8 µG in the escape scenario. In the standard DSAparadigm, and in the absence of further magnetic field amplifi-cation through turbulences (discussed for example in Giacalone& Jokipii 2007), the expected magnetic field compression at theshock would result in downstream magnetic fields a factor ofRB = 3� 4 higher than those upstream, that is, up to B = 3.2 µGand B = ⌘ 11.2 µG for region 3 in the precursor and escape sce-nario, respectively.

Whilst the escape scenario is compatible with our broadbandleptonic fits, in the precursor scenario the downstream magneticfield value is lower than the values obtained with these fits (seeFig. 7 and Tab. 6). In particular, B = 3.2 µG downstream is some-what lower than expected in the DSA paradigm, unless we in-voke a recent sudden increase of ⌘ to values well above 2 or adecrease of ushock to well below 3300 km s�1 to recover higherdownstream magnetic field values. Such sudden changes mustoccur on timescales smaller than the synchrotron radiation losstime of the downstream electrons, since ⌘ . 5 is needed to ex-plain X-ray synchrotron radiation from the shell in these regions(Tanaka et al. 2008). We therefore require that the timescalefor substantial changes in the upstream di↵usion properties, �t,must satisfy

⌧loss =634B2E

s > �t, (9)

with ⌧loss = |E/(dE/dt)| (Ginzburg & Syrovatskii 1965). Thetypical X-ray synchrotron photon energy is given by ✏ =7.4E2B keV (Ginzburg & Syrovatskii 1965), so that the condi-tion for the presence of X-ray emission from the shell at 1 keVfor a given timescale �t is

B . 23 �t

500 yr

!�2/3µG. (10)

This condition is fully consistent with the leptonic emission sce-nario, but requires for the hadronic emission scenario timescalesshorter than �t = 500 yr.

To summarise, the significant extension of the gamma-rayemission beyond the X-ray defined shock in some regions ofRX J1713.7�3946 requires either low magnetic fields or di↵u-sion length scales much larger than for Bohm di↵usion, irrespec-tive of whether the gamma rays are from particles originating inthe shock precursor or escaping the remnant di↵usively. In bothcases, the length scales are in fact governed by di↵usion.

17

H.E.S.S. Collaboration: Observations of RX J1713.7�3946

Fig. 2: Gamma-ray excess map and radial profiles. Top left: the H.E.S.S. gamma-ray count map (E > 250 GeV) is shown withXMM-Newton X-ray contours (1–10 keV, smoothed with the H.E.S.S. PSF) overlaid. The five regions used to compare the gamma-ray and X-ray data are indicated along with concentric circles (dashed grey lines) with radii of 0.2� to 0.8� and centred at R.A.:17h13m25.2s, Dec.: �39d46m15.6s. The Galactic plane is also drawn. The other five panels show the radial profiles from theseregions. The profiles are extracted from the H.E.S.S. maps (black crosses) and from an XMM-Newton map convolved with theH.E.S.S. PSF (red line). The relative normalisation between the H.E.S.S. and XMM-Newton profiles is chosen such that for regions1, 2, 4 the integral in [0.3�, 0.7�] is the same, for regions 3, 5 in [0.2�, 0.7�]. The grey shaded area shows the combined statisticaland systematic uncertainty band of the radial gamma-ray extension, determined as described in the main text. The vertical dashedred line is the radial X-ray extension. For the X-ray data, the statistical uncertainties are well below 1% and are not shown.

4

Extended gamma-rays: precursor or escape?

17

●What is the maximum size of the precursor?●Acceleration time (k=8 to 20):

●Precursor length:

●Shock for SNR (m=0.4-0.8):●Hence:

H.E.S.S. Collaboration: Observations of RX J1713.7�3946

The relative length scale of the gamma-ray emission mea-sured beyond the shock is rather large, �r/rSNR ⇡ 13%, for aprecursor scenario. One can estimate the typical relative lengthscale of a shock precursor by starting from Eq. 3.39 of Drury(1983) for the particle acceleration time ⌧acc:

⌧acc =3

u1 � u2

D1u1+

D2u2

!, (11)

with the subscript 1 and 2 referring to the di↵usion coe�cientsand velocities of the upstream and downstream regions, respec-tively. We note that ushock = u1. With the compression ratio atthe shock R = u1/u2, we obtain

⌧acc =3u21

RR � 1 D1

1 +

D2D1R!. (12)

Assuming Bohm di↵usion for D1 and D2, their ratio is D2/D1 =1 for a parallel shock and D2/D1 = 1/R for a perpendicularshock. With this, and a compression ratio of R = 4, we get

⌧acc = D1u21, (13)

with = 8 for a perpendicular and = 20 for a parallel shock.The following relation connects the shock velocity of SNRswith their radius over long stretches of time (Chevalier 1982;Truelove & McKee 1999):

r / tmage ) ushock = mr

tage, (14)

where m = 0.4 for the Sedov-Taylor phase and m = 0.5 � 0.7for younger remnants like RX J1713.7�3946. Since the age ofthe SNR tage corresponds to the maximum possible accelerationtime of particles, and hence ⌧acc < tage, the maximum precursorlength scale can now be calculated as

`p =D1(E)ushock

=⌧accushock

<tageushock

=m

r = 0.0875 r, (15)

with m = 0.7 and = 8 for a perpendicular shock. This estimateof the maximum precursor size of about 10% of the SNR radiusis conservatively large as most particles have not been acceler-ated from the date of the explosion, but considerably later, andthus ⌧acc < tage. We therefore conclude that the measured lengthscale of 13% is of the order of the maximum possible scale ex-pected for a shock precursor. More precise measurements andmodelling of the precursor or di↵usion region, including line ofsight e↵ects, are needed to assess whether the extended emis-sion we measure is from the shock precursor or from particlesescaping the shock region.

This discussion only pertains to certain regions ofRX J1713.7�3946; there are other regions where the gamma-ray size does not exceed the X-ray size. Keeping in mind thatRX J1713.7�3946 is argued to be a supernova remnant evolv-ing in a cavity (Zirakashvili & Aharonian 2010), the shock wavecould be starting to interact with a positive density gradient as-sociated with the edges of the cavity in those regions where thegamma-ray emission extends farther out. As a result of the den-sity gradient, the shock wave velocity and/or the magnetic fieldturbulence are decreasing and the VHE particles start di↵usingout farther ahead of the shock, close to, or already beyond theescape limit.

The above analysis is somewhat simplified, and we are leftwith one surprising observational fact: within the current uncer-tainties, the gamma-ray emission beyond the shell is energy in-dependent (Sect. 3.3), whereas one would expect that the dif-fusion length scale is larger for more energetic particles. Thisis true for both the precursor and the escape scenario. The en-ergy dependence is therefore either too small to be measurablewith H.E.S.S.; for instance, only for pure Bohm di↵usion wouldone expect that D / E. More generically, one expects D = E�,so perhaps � < 1 in the regions with extended emission. Orelse the energy dependence of the di↵usion coe�cient could besuppressed as recently argued in Malkov et al. (2013), where amodel is developed for older SNRs interacting with molecularclouds. Elements of this model may also be relevant for the in-teraction of RX J1713.7�3946 with the cavity wall. Given thepotential evidence for escape and the surprising lack of any en-ergy dependence of the gamma-ray emission and therefore thedi↵usion coe�cient, RX J1713.7�3946 will remain a key prior-ity target for the future Cherenkov Telescope Array (CTA) ob-servatory (Acharya et al. 2013; Nakamori et al. 2015).

7. Summary

The new H.E.S.S. measurement of RX J1713.7�3946 reachesunprecedented precision and sensitivity for this source. With anangular resolution of 0.048� (2.9 arcminutes) above gamma-rayenergies of 250 GeV, and 0.036� (2.2 arcminutes) above energiesof 2 TeV, the new H.E.S.S. map is the most precise image of anycosmic gamma-ray source at these energies. The energy spec-trum of the entire SNR confirms our previous measurements atbetter statistical precision and is most compatible with a powerlaw with an exponential cut-o↵, both a linear power-law modelat gamma-ray energies of 12.9 TeV and a quadratic model at16.5 TeV.

A spatially resolved spectral analysis is performed in a regu-lar grid of 29 small rectangular boxes of 0.18� (10.8 arcminutes)side lengths, confirming our previous finding of the lack of spec-tral shape variation across the SNR.

The broadband emission spectra of RX J1713.7�3946 fromvarious regions are fit with present age parent particle spectrain both a hadronic and leptonic scenario, using Suzaku X-rayand H.E.S.S. gamma-ray data. From the resolved spectra in the29 small boxes in the leptonic scenario, we derive magneticfield, energy cut-o↵, and particle index maps of the SNR. Forthe latter parameter, we do the same for the hadronic scenario.The leptonic and hadronic parent particle spectra of the entireremnant are also derived without further detailed assumptionsabout the acceleration process. These particle spectra reveal thatthe Fermi-LAT and H.E.S.S. gamma-ray data require a two-component power-law with a break at 1-3 TeV, challenging ourstandard ideas about di↵usive particle acceleration in shocks. Ineither leptonic or hadronic scenarios, approaches more involvedthan one or two zone models are needed to explain such a spec-tral shape. Neither of the two scenarios (leptonic or hadronic),or a mix of both, can currently be concluded to explain the dataunambiguously. Either better gamma-ray measurements with thefuture CTA, with much improved angular resolution and muchhigher energy coverage, or high sensitivity VHE neutrino mea-surements will eventually settle this case for RX J1713.7�3946.

Comparing the gamma-ray to the XMM-Newton X-ray imageof RX J1713.7�3946, we find significant di↵erences betweenthese two energy regimes. As concluded before by Tanaka et al.(2008), the bright X-ray hotspots in the western part of the shellappear relatively brighter than the H.E.S.S. gamma-ray data. The

18

H.E.S.S. Collaboration: Observations of RX J1713.7�3946

The relative length scale of the gamma-ray emission mea-sured beyond the shock is rather large, �r/rSNR ⇡ 13%, for aprecursor scenario. One can estimate the typical relative lengthscale of a shock precursor by starting from Eq. 3.39 of Drury(1983) for the particle acceleration time ⌧acc:

⌧acc =3

u1 � u2

D1u1+

D2u2

!, (11)

with the subscript 1 and 2 referring to the di↵usion coe�cientsand velocities of the upstream and downstream regions, respec-tively. We note that ushock = u1. With the compression ratio atthe shock R = u1/u2, we obtain

⌧acc =3u21

RR � 1 D1

1 +

D2D1R!. (12)

Assuming Bohm di↵usion for D1 and D2, their ratio is D2/D1 =1 for a parallel shock and D2/D1 = 1/R for a perpendicularshock. With this, and a compression ratio of R = 4, we get

⌧acc = D1u21, (13)

with = 8 for a perpendicular and = 20 for a parallel shock.The following relation connects the shock velocity of SNRswith their radius over long stretches of time (Chevalier 1982;Truelove & McKee 1999):

r / tmage ) ushock = mr

tage, (14)

where m = 0.4 for the Sedov-Taylor phase and m = 0.5 � 0.7for younger remnants like RX J1713.7�3946. Since the age ofthe SNR tage corresponds to the maximum possible accelerationtime of particles, and hence ⌧acc < tage, the maximum precursorlength scale can now be calculated as

`p =D1(E)ushock

=⌧accushock

<tageushock

=m

r = 0.0875 r, (15)

with m = 0.7 and = 8 for a perpendicular shock. This estimateof the maximum precursor size of about 10% of the SNR radiusis conservatively large as most particles have not been acceler-ated from the date of the explosion, but considerably later, andthus ⌧acc < tage. We therefore conclude that the measured lengthscale of 13% is of the order of the maximum possible scale ex-pected for a shock precursor. More precise measurements andmodelling of the precursor or di↵usion region, including line ofsight e↵ects, are needed to assess whether the extended emis-sion we measure is from the shock precursor or from particlesescaping the shock region.

This discussion only pertains to certain regions ofRX J1713.7�3946; there are other regions where the gamma-ray size does not exceed the X-ray size. Keeping in mind thatRX J1713.7�3946 is argued to be a supernova remnant evolv-ing in a cavity (Zirakashvili & Aharonian 2010), the shock wavecould be starting to interact with a positive density gradient as-sociated with the edges of the cavity in those regions where thegamma-ray emission extends farther out. As a result of the den-sity gradient, the shock wave velocity and/or the magnetic fieldturbulence are decreasing and the VHE particles start di↵usingout farther ahead of the shock, close to, or already beyond theescape limit.

The above analysis is somewhat simplified, and we are leftwith one surprising observational fact: within the current uncer-tainties, the gamma-ray emission beyond the shell is energy in-dependent (Sect. 3.3), whereas one would expect that the dif-fusion length scale is larger for more energetic particles. Thisis true for both the precursor and the escape scenario. The en-ergy dependence is therefore either too small to be measurablewith H.E.S.S.; for instance, only for pure Bohm di↵usion wouldone expect that D / E. More generically, one expects D = E�,so perhaps � < 1 in the regions with extended emission. Orelse the energy dependence of the di↵usion coe�cient could besuppressed as recently argued in Malkov et al. (2013), where amodel is developed for older SNRs interacting with molecularclouds. Elements of this model may also be relevant for the in-teraction of RX J1713.7�3946 with the cavity wall. Given thepotential evidence for escape and the surprising lack of any en-ergy dependence of the gamma-ray emission and therefore thedi↵usion coe�cient, RX J1713.7�3946 will remain a key prior-ity target for the future Cherenkov Telescope Array (CTA) ob-servatory (Acharya et al. 2013; Nakamori et al. 2015).

7. Summary

The new H.E.S.S. measurement of RX J1713.7�3946 reachesunprecedented precision and sensitivity for this source. With anangular resolution of 0.048� (2.9 arcminutes) above gamma-rayenergies of 250 GeV, and 0.036� (2.2 arcminutes) above energiesof 2 TeV, the new H.E.S.S. map is the most precise image of anycosmic gamma-ray source at these energies. The energy spec-trum of the entire SNR confirms our previous measurements atbetter statistical precision and is most compatible with a powerlaw with an exponential cut-o↵, both a linear power-law modelat gamma-ray energies of 12.9 TeV and a quadratic model at16.5 TeV.

A spatially resolved spectral analysis is performed in a regu-lar grid of 29 small rectangular boxes of 0.18� (10.8 arcminutes)side lengths, confirming our previous finding of the lack of spec-tral shape variation across the SNR.

The broadband emission spectra of RX J1713.7�3946 fromvarious regions are fit with present age parent particle spectrain both a hadronic and leptonic scenario, using Suzaku X-rayand H.E.S.S. gamma-ray data. From the resolved spectra in the29 small boxes in the leptonic scenario, we derive magneticfield, energy cut-o↵, and particle index maps of the SNR. Forthe latter parameter, we do the same for the hadronic scenario.The leptonic and hadronic parent particle spectra of the entireremnant are also derived without further detailed assumptionsabout the acceleration process. These particle spectra reveal thatthe Fermi-LAT and H.E.S.S. gamma-ray data require a two-component power-law with a break at 1-3 TeV, challenging ourstandard ideas about di↵usive particle acceleration in shocks. Ineither leptonic or hadronic scenarios, approaches more involvedthan one or two zone models are needed to explain such a spec-tral shape. Neither of the two scenarios (leptonic or hadronic),or a mix of both, can currently be concluded to explain the dataunambiguously. Either better gamma-ray measurements with thefuture CTA, with much improved angular resolution and muchhigher energy coverage, or high sensitivity VHE neutrino mea-surements will eventually settle this case for RX J1713.7�3946.

Comparing the gamma-ray to the XMM-Newton X-ray imageof RX J1713.7�3946, we find significant di↵erences betweenthese two energy regimes. As concluded before by Tanaka et al.(2008), the bright X-ray hotspots in the western part of the shellappear relatively brighter than the H.E.S.S. gamma-ray data. The

18

●On face value: 13% > 8.8% → particles appear unbound to shock●More scrutiny needed for firm conclusion (e.g. no ene●What could be cause escape:

●Sudden drop in shock velocity●Drop in magnetic field turbulence

lp =D1u1

u1

= mrshock

tage

Optical spectroscopy: Measuring acceleration efficiency using plasma temperatures

18

(Fig. 1). The only other remnant in which Haemission is seen all along the shell, includingregions with x-ray synchrotron emission, is theSN 1006 SNR (22).

The right panel in Fig. 1 shows both the Haand the x-ray emission of the northeast rim ofRCW 86. The Ha emission marks the onset ofthe x-ray synchrotron radiation, which indicatesthat they are from the same physical system.

To measure the proton temperature, we usedlong-slit spectra obtainedwith the visual and nearultraviolet Focal Reducer and low-dispersion Spec-trograph (FORS2) instrument on the Very LargeTelescope (VLT) (23). We first imaged the north-east side of RCW 86, where the x-ray spectrumis dominated by synchrotron emission. Usingthis image as a guide, we pointed the slit at alocation where the Ha emission is bright (Fig.1 and table S1).

The spectrum’s (Fig. 2) measured full widthat half maximum is 1100 T 63 km/s [see sup-porting online material (SOM) for further details],corresponding to a sv = 467 T 27 km/s and im-plying a postshock temperature of 2.3 T 0.3 keV.

To measure the shock velocity of the north-east rim of RCW 86, we observed it with theChandra X-Ray Observatory in June 2007 andmatched it with an observation taken in June2004 (18). To make both observations as simi-lar as possible, we used the same observationparameters as in 2004 (table S2). We measuredthe proper motion of the shock at the location ofthe slit of the Ha spectrum by comparing thepositions of the shock in the two images (seeSOM for further details). A solid estimate of theproper motion is 1.5 T 0.5′′ in 3 years’ time (Fig. 3and fig. S1), implying a shock velocity of (6.0 T

2.0) × 103 km/s at a distance of 2.5 kpc (24, 25).The statistical error on the measured expansion ison the order of 0.2′′. However, when calculatingthe proper motions, we found that small details,such as slightly changing the angle in which wemade the profile, tended to give a different propermotion, with a difference larger than the 0.2′′statistical error that we measured. However, innone of the measurements did we find a propermotion below 1.0′′. Because the proper motion ishigher than expected (18), we verified that it isconsistent with data taken in 1993 with the Posi-tion Sensitive Proportional Counter (PSPC) onboard the Roentgen Satellite (ROSAT) comparedwith the 2007 observation (Fig. 3 and fig. S1).Although the proper motion, using the nominalpointing of the ROSAT PSPC, is statisticallyhighly significant, the large pointing error ofROSAT (~4′′) results in a detection of the propermotion at the 2s level.

Compared to other remnants of a similar age,the shock velocity is surprisingly high. Recentmodels (26) predict vs ~ 5000 km/s after 2000years for SNRs evolving in a wind-blown bubble(27). This fits with the scenario in which RCW86 is evolving in a cavity and the southwest cor-ner, which has a slower shock velocity (28, 29)and a mostly thermal (3) x-ray spectrum, hasalready hit the cavity shell. Shock accelerationtheory suggests that only shocks with velocitiesexceeding 2000 km/s emit x-ray synchrotron emis-sion (18, 30), which is also consistent with ob-servations (31).

An additional uncertainty in the shock veloc-ity is in the distance to RCW 86, which is basedon converging but indirect lines of evidence.RCW86was found to be in the same direction as

an OB association, at a distance of 2.5 kpc (32).Because high-mass stars are often found in suchassociations, the progenitor of RCW86may wellhave formed in this one, provided that RCW86 isthe remnant of an exploded massive star. Otherstudies (24, 25) found a distance of 2.3 and 2.8kpc, respectively, based on the line-of-sight ve-locity of ISM swept up by the remnant, combinedwith an observationally determined rotation curveof the Galaxy (33). The third argument supportinga distance of 2.5 kpc is the molecular supershellseen in CO emission in the direction of RCW 86,whose line-of-sight velocity agrees with that ofRCW86 (34). In further calculations, we take thedistance toward RCW 86 to be 2.5 T 0.5 kpc,leading to a shock velocity of 6000 T 2800 km/s.

The relation between shock velocity and mea-sured postshock proton temperature has been ex-tensively studied (20, 29, 35–37), including thecross sections for excitation and charge exchangeas function of vs. Although recent studies showthat there can be a substantial effect of cosmicrays on the postshock proton spectrum (38), untilnow, there was no need to include cosmic-rayacceleration in the interpretation of the postshocktemperature, possibly because most of the Haspectra are taken from the brightest rims of SNRs.Because Ha emission and efficient cosmic-rayacceleration are likely to anticorrelate (21), theserims probably have low cosmic-ray accelerationefficiency. A possible exception is “knot g” in theTycho SNR, where indications for cosmic-rayacceleration in the form of a precursor have beenfound (39–41). Additionally, for some SNRs(22, 42), the distance has been determined byusing the postshock proton temperature in com-bination with the proper motion, using theoreticalmodels that do not take into account energy lossesand cosmic-ray pressure. This procedure leads toan underestimate of the distance if cosmic-rayacceleration is present. Thus, unless the distanceis accurately determined in an independent way,there will be no discrepancy between the pre-dicted vs, based on kT and Eq. 1, and the actualshock velocity.

The shock velocity of the x-ray synchrotronrim implies a postshock temperature of 70 keV(assuming no thermal equilibrium) or 42 keV(assuming equilibrium), whereas the measuredpostshock temperature is 2.3 keV. This measure-ment is at least a factor 18 less than the postshocktemperature estimated from the shock velocity,which can now be used to constrain current theo-retical shock-heating models (12, 13). Additionally,this proton temperature is close to the electrontemperature at the same location (18), implyingfast thermal equilibration between both species,breaking the trend between the shock velocityand the measure of thermal equilibrium seen inprevious observations (36, 37).

To translate this discrepancy into the energyand pressure in cosmic rays, we followed the ap-proach of (11), which is based on standard shockequations for plane-parallel, steady-state shocks,modified by additional pressure and loss terms [see

Fig. 2. The Ha spectrum, with broad and narrow components (dotted lines). The best-fitting spectrum isoverplotted. The lower panel shows the residuals divided by the errors.

7 AUGUST 2009 VOL 325 SCIENCE www.sciencemag.org720

REPORTS

on

Augu

st 1

1, 2

009

ww

w.s

cien

cem

ag.o

rgD

ownl

oade

d fro

m

• Currently best way to measure post-shock plasma temperature: Hα spectra• Requires neutrals entering shock• Neutrals can get excited, charged exchange with hot protons, ionise• Direct excitation → probe pre-shock temperature → narrow Hα• Charge exchange → probe shock heated protons → broad Hα

• Measure broad Hα → post shock temperature → acceleration efficiency?

Non-linear acceleration: simplify the problem by extending the Rankine-Hugoniot relations

• Assume two “fluids”: 1. plasma with γg=5/3, 2. cosmic rays with 4/3

The extended Rankine-Hugoniot relations (Vink, Yamazaki, Helder, Schure, 2010)

w2

⌘ Pcr,2P

tot,2=

(1� ��gprec

) + �g

M2g,0

⇣1� 1�

prec

⌘

1 + �g

M2g,0

⇣1� 1�

tot

⌘

✏ = 1 +2

�g

M2g,0

"G

0

� G2�

tot

#� 2G2

�tot

+1

�2tot

(2G2

� 1)

G2 ⌘ w2�cr

�cr � 1+ (1� w2)

�g�g � 1

• One running parameter: precursor compression Xprec• Assume only adiabatic heating in precursor• Assume value of γcr ϵ [4/3 - 5/3]• Total compression ratio:

• Expression for fractional cosmic-ray pressure:

• Expression for energy escape:

20

�tot

= �prec

�sub

=(�

g

+ 1)M2g,0�

��gprec

(�g

� 1)M2g,0�

�(�g+1)prec

+ 2

Mg,1 = Mg,0��(�g+1)/2prec

Predicted compression ratios and escape flux as a function of cosmic-ray pressure

Total and shock compression ratio Cosmic-ray (energy) escape

21

w2=Pcr/Ptot w2=Pcr/Ptot

ϵ

Com

pres

sion

fact

ors

Vink et al., 2010, ApJ 722, 1727

Higher cosmic-ray pressure

●NB some level of escape needed to drive Bell’s instability!

By measuring the post-shock temperature the cosmic-ray efficiency can be measured

22

correction w.r.t. standard Rankine Hugoniot result

kT =316

mV 2s

• Post-shock temperature expression follows from pressure equilibrium

Pg,2 = (1� w)

P

0

+✓

1� 1�

tot

◆⇢0

V 2sh

�

Pg,2 + Pcr,2 + ⇢2v22 = P0 + ⇢0v20

A caveat: do collisionless shocks equilibrate electrons and ions?

23

A&A proofs: manuscript no. ms_v2

Fig. 1. The electron-ion temperature ratio expected for minimum electron-heating (solid black line, Eq. 13), for the case of adiabatic heating of theelectrons (dashed black line, Eq. 21), and for magnetised plasmas with � = 0.01, 0.1, 1 (blue dashed line, Eq 29). In addition the expected ratio isshown if on top of various thermodynamic e↵ects there is energy exchange between the electrons and ions at the level of 5% (magenta dashed line,Eq. B.7). For the calculation here it is assumed that the plasma consists of electrons, protons, and fully ionised helium, and the ion temperatureis the average temperature of abundance weighted temperature of the protons and helium ions. The data points are from the compilation byGhavamian et al. (2013), and represent measured values of the electron-ion temperature ratio behind the Earth bowshock (green circles,originaldata from Schwartz et al. 1988), Saturn’s bowshock as measured by the Cassini spacecraft (X-shaped symbols, Masters et al. 2013) and supernovaremnants (red, solid squares van Adelsberg et al. 2008). Note that for the supernova remnants the Mach numbers are not measured, but instead theestimated shock velocity has been divided by assumed interstellar sound speed of 11 km s�1 (Ghavamian et al. 2013).

2.4. How much non-adiabatic heat exchange is there between ions and electrons?

In the preceding subsections we have approached the expected electron-ion temperature ratio from the point of view of the availableenthalpy of the electron and ion components separately, but allowing for adiabatic heating of the electrons (Sect. 2.2) and the factthat for magnetised plasma’s work has to be done by mostly the ions to compress the magetic field (Sect. 2.3).

However, collisionless shock heating is complex process, and the microphysics of the heating process of both the ions andelectrons is not well understood. In the Appendix (Sect. B) we show how one can quantify the additional thermal energy that theelectrons pick-up from ions. This is done by introducing an electron-ion heat exhange parameter ⇠. A value of ⇠ = 50% correspondsto a fully equilibrated plasma, whereas ⇠ = 0 gives the same result as Eq. 29.

Fig. 1 shows the electron/ion temperature ratio for ⇠ = 5%, which seems to approximately describe the leveling o↵ of theelectron-ion temperature ratio seen in the Earth bow shock for magnetosonic Mach numbers above ⇠ 20. However, more data areneeded to see whether this is a general trend, as not that much data points above Ms = 10 exist. The supernova remnant shocks havegenerally higher Mach numbers, but for them the actually Mach numbers are poorly constraint as we discuss below.

3. Discussion

The relation that we derived for the electron-ion temperature ratio is simple and based on the assumption that all particle speciesobserve the same density jump, but that the electron and ion enthalpy fluxes are preserved separately. In addition, we introducedenthalpy-flow exchange between ions and electrons using a dimensionless variable ⇠, with (realistically) 0% ⇠ 50%, with ⇠ = 0corresponding to full non-equilibration.

Comparing our relations with observations (Fig. 1) shows that Eq 21 seems to describe the data points best for Mach numbersbetween 1 and ⇠ 10, whereas the the pure elastic scattering case (Eq. 13) appears to form a firm lower limit to the measuredtemperature ratios. However, adiabatic heating of the electrons for magnetised plasma with � = 1 also seems to provide a lowerlimit to the measured electron-ion temperature ratio. For Mach numbers Mms & 10 the temperature ratio appears to asymptoticallyreach a value that is far above the relations as predicted by thermodynamic processes alone.

There are a few data points obtained from solar system shocks for which the electrons appear hotter than the ions. These pointscannot be explained by our simple model, and they are counter intuitive, as it implies that heat is flowing from the cooler componentto the hotter component. It may hint at possible heating of the electrons upstream of the sub-shock, perhaps caused by ions reflectedfrom the subshock (Cargill & Papadopoulos 1988). But it is not quite clear from the literature whether the measured temperatureratios are not consistent with our relations given the unknown measurement errors.

The measured SNR temperature ratios seem to behave somewhat di↵erently than the solar-system temperature ratios. But, asalready noted by Ghavamian et al. (2013), for supernova remnants the actual Mach number is not directly measured, but at best only

Article number, page 6 of 12page.12

Data: Ghavamian+ 14Models: Vink+ 15

●Low Mach number: ●adiabatic compression electrons●all temperature partially due to compression●post-shock ratio kinetic to thermal is different for electron protons

●High Mach number (> √(mp/me)≈43, Vink+ ‘15):●ratio minimally Te/Tp=me/mp●evidence for 5-10% energy exchange

●SNRs do not fit, unless upstream plasma is hotter (lower Mach nr)

H-ɑ from fastest known SNR shock: 0509-675 (LMC)

24

●Distance known (LMC, 50 kpc)●Shock velocity: Vs ≈6500 km/s (Hovey+ ’15)●One of the fastest shocks measured for a SNR!●H-alpha broad line widths: 2680 ± 70 km/s (SW), 3900 ± 800 km/s

Helder, Kosenko, Vink ‘10

SNR 0509-675 (LMC)

A measurement of the cosmic-ray efficiency in a fast supernova remnant shock 0509-675

2525

• Hα broad line widths: 2680 ± 70 km/s (SW), 3900 ± 800 km/s• kT=16 keV• Discrepancy in kT: kTmeasured/kTexp≤0.7

Helder, Kosenko, Vink ‘10

• Hence: cosmic-ray efficiency w≥25%• Caveat: local shock velocity wrt global shock velocity

esca

pe

Consequence of extended Rankine Hugoniot model: For Mach numbers M

There are always solutions with conserved energy-flux: correspond to Drury&Völk model

Non-relativistic particle population Relativistic particle population

• For non-relativistic cosmic rays for given M: one CR solution with ϵ=0• For relativistic dominated particles: two CR solutions with ϵ=0• Since acceleration starts non-relativistically: M=√5 is a real lower limit

contours/colors: escape flux

27

M=√5 M=5.88

Theory vs observations: coronal mass ejections

• Coronal mass ejections induced interplanetary shocks:• Not always accelerated particles• All shock X>2.5 (M>√5) show SEPs! (Giaccalone ‘12)• Low Mach shocks: depends on recent past CME (Gopalswamy+ ’04)

➞ larger fraction of pre-existing cosmic rays?➞qualitative agreement with extended Rankine-Hugoniot relations➞NB relations show acceleration is possible, it does not require acceleration

ACE (Giaccalone ’12)

28

Radio-loud vs Radio-Quiet CMEs (Gopalswamy+ ’10)

Investigation of efficiency CME shocks with ACE

29

Figure 10: A plot of acceleration e�ciency against sonic Mach number. The red data pointsrepresent calculations based on CME-driven shocks. The solid black curve is the maximume�ciency as a function of Mach number, while the dashed black line is the e�ciency forwhich the escaping energy flux is maximal.

Shock Date Mach Number Acceleration E�ciency(yyyy, dd) (M

S

[±]) (! [±])2003, 308 8.75 [1.49] 0.19 [0.03]2002, 138 3.06 [0.55] 0.20 [0.04]2002, 113 4.54 [0.53] 0.07 [0.01]2000, 160 2.93 [0.29] 0.17 [0.02]2000, 97 4.73 [0.85] 0.16 [0.02]1999, 49 3.23 [0.59] 0.10 [0.02]1998, 238 2.60 [0.41] 0.33 [0.05]

The figure above shows the e�ciency of solar system shocks, as well as the limitationsimposed by Vink & Yamazaki. The red data points are the Mach number and acceleratione�ciency for a number of CME-driven shocks, calculated as discussed in the previous section.

31

• Efficiency defined as w=Pacc/Ptot• Preliminary conclusion (based on MSc thesis Michiel Bustraan)

• Typical acceleration efficiency 10-20%• No clear trend with Mach number• NB: Mach number not always clearly defined

MSc Thesis Michiel Bustraan (2015)

A CME shock with M

Summary

31

●Last 20 years: observational progress in defining acceleration in SNRs●X-ray synchrotron emission

● Fast acceleration → B-field turbulence high)● High B-fields needed → Bell mechanism● B2∝ρV3

●Gamma-ray observations (Hinton talk)● protons and/or electrons?● >10 TeV particles present● observing escape of cosmic rays

●Optical: measure heating ● cosmic-ray heating deficiency?● electron vs ions temperatures● requires neutrals → dampen Halpha waves

●Also discussed:●Is there a minimum Mach number for acceleration?

● Yes: M=√5 (up to 6 for fully relativistic particles)● Relies on steady state arguments

32

The models agrees with the kinetic non-linear acceleration model of Blasi et al. (2005)

• Crosses: Blasi model for different Emax• Blasi model: one solution (depends on acceleration details)• Extended Rankine-Hugoniot: range of possibilities (curve)

33

The critical Mach number as function of γcr

34

• Critical Mach number depends on adiabatic index of accelerated particles

X-ray synchrotron profiles

35

Helder, JV, et al. 2012

●Model: sudden increase at shock + exponential fall off (projected)●Models do generally not fit very (exception Vela jr)

36

Observational Signatures of Particle Acceleration in Supernova Remnants 385

Table 2 Observed widths of synchrotron filaments and downstream inferred magnetic field strength

SNR Age(yr)

Dist(kpc)

Radius(pc)

Rw(′′)

ladv(1017 cm)

B2(µG)

Eel(TeV)

τsyn(yr)

G1.9+0.3 (SW) 110 8.5 1.8 3.1 2.8 67 33 86

Cas A (NE) 334 3.4 2.5 1.1 0.4 246 17 12

Kepler (SE) 401 6.0 3.7 1.8 1.1 122 24 35

Tycho (W) 433 3.0 3.7 1.6 0.5 207 19 16

SN1006 (E) 999 2.2 9.1 9.1 2.1 81 30 64

RX J1713.7-3946 (SW) 1612 1.0 7.8 63.5 6.7 37 44 206

RCW 86 (NE) 1820 2.5 16.0 28.6 7.6 35 46 232

RX J0852.0-4622 (N) 2203 1.0 16.3 28.4 3.0 64 34 92

Notes: The ages are calculated for the time of proper motion estimation and are either based on the historicalsupernova events (Tycho—SN 1572, Kepler—SN 1604, and RX J1713.7-3946, possibly SN 393, Stephensonand Green 2002; Wang et al. 1997), or on kinematic estimates, assuming a deceleration parameter of 0.55 forRX J0852.0-4622 (Katsuda et al. 2008) and 0.7 for G1.9+0.3 (Carlton et al. 2011). Distance estimates are:G1.9+0.3 (Carlton et al. 2011); Cas A (Reed et al. 1995); Kepler (Vink 2008c); Tycho’s distance somewherebetween 2–3 kpc, here we adopt the large scale for kinematic reasons (Furuzawa et al. 2009); SN1006 (Win-kler et al. 2003); RCW 86 (Westerlund 1969; Rosado et al. 1994); RX J1713 (Fukui et al. 2003); RX J0852(Katsuda et al. 2008). The value for ladv was calculated from the measured, deprojected rim width Rw, usingthe distance listed and an additional factor 0.7 to take into account that the rim width is a combination ofdiffusion and advection (see text)

et al. 2007), with the possible exception of one filament in the northeast of Tycho’s su-pernova remnant (Reynolds et al. 2011). Nevertheless, some form of decay may occur ingeneral, and would affect the geometry of the X-ray synchrotron rims.

Another assumption is that the spectral cut-off frequency is determined by radiativelosses, i.e. we assume a loss-limited spectrum. These broader rims imply smaller magneticfields (Eq. (26)) and, therefore, longer synchrotron loss times. During these synchrotronloss times the shock properties may have changed, i.e. the shock velocity was likely higherin the past, and the densities may have been different in the past. Another case where thisassumption may not be valid is for the very young SNR G1.9+0.3.

We note here that a projected uniform thin shell emissivity fits in many cases the ob-served profiles as well, or even better than an exponential emissivity model. A thin shell hasa peak that lies more inward of the shock radius. Indeed, the exponential model tends tounderpredict the emission around the peak. A clear exception is Vela Jr (RX J0852.0-4622),where an exponential model gives a much better fit than a uniform, projected shell. The bestfit shell width of the uniform model is typically a factor two larger than the best fit charac-teristic width of the exponential model. Magnetic field estimates based on a uniform shellmodel are, therefore, 40 % smaller.

Table 2 lists magnetic field estimates of synchrotron rims in several supernova remnants,based on Eq. (20) and the profiles shown in Fig. 4. In order to assess whether the spectraare loss-limited or age-limited we also list a rough estimate of the synchrotron loss times,assuming a typical photon energy of 1 keV. It shows that only for G1.9+0.3 (Reynolds 2008;Borkowski et al. 2010; Carlton et al. 2011) it seems likely that the spectrum is age- ratherthan loss limited. For this reason, one should treat the magnetic field estimates as upperlimits. For the RCW 86, RX J1713.7-3946, RX J0852.0-3622 and possibly SN 1006 oneshould still be concerned about the steady-state assumption, as the synchrotron loss timesare such that the shock velocity, magnetic fields may have changed during a time ∼ tloss.

Helder, JV, et al. 2012