The Reverse Shock of SNR 1987A
Kevin Heng
JILA, University of Colorado, Boulder, CO 80301-0440
Abstract. The reverse shock of supernova remnant (SNR) 1987A emits in Hα and Lyα , and comes
in two flavors: surface and interior. The former is due to direct, impact excitation of hydrogen
atoms crossing the shock, while the latter is the result of charge transfer reactions between these
atoms and slower, post-shock ions. Interior and surface emission are analogous to the broad- and
narrow-line components observed in Balmer-dominated SNRs. I summarize a formalism to derive
line intensities and ratios in these SNRs, as well as a study of the transition zone in supernova
shocks; I include an appendix where I derive in detail the ratio of broad to narrow Hα emission.
Further study of the reverse shock emission from SNR 1987A will allow us to predict when it will
vanish and further investigate the origins of the interior emission.
Keywords: Atomic processes and interactions ; physical processes (kinematics) ; supernova rem-
nants
PACS: 95.30.Dr; 98.38.Am; 98.38.Mz
INTRODUCTION: SNR 1987A
For the past 20 years, supernova remnant (SNR) 1987A has provided a wonderful op-
portunity to study emission mechanisms, radiative transfer and a myriad of physics for
conditions unattainable on Earth. One such sub-field is the study of high Mach num-
ber, collisionless shocks. The impact of the supernova (SN) blast wave upon ambient
medium sets up a double shock structure consisting of a forward and a reverse shock. In
SNR 1987A, the ejecta comprising mostly neutral hydrogen (which exists due to adia-
batic expansion cooling) crosses the reverse shock at ∼ 12,000 km s−1; the excitation
and subsequent radiative decay of the atoms result in Hα and Lyα emission, readily
measured by instruments such as the Space Telescope Imaging Spectrograph (STIS)
onboard the Hubble Space Telescope (see [1] and references therein).
In the most recent study of the reverse shock [1], it was found that both Hα and Lyα
emission exist in two flavors: surface and interior. In a young, pre-Sedov-Taylor remnant
such as SNR 1987A, the freely-streaming debris has a unique velocity for a given radial
distance from the SN core, exactly analogous to Hubble flow in an expanding universe.
The projected velocity of the atoms crossing the reverse shock is proportional to the
line-of-sight depth of the shock surface from the supernova mid-plane. It follows that
upon impact excitation, the wavelength of the emitted photon is uniquely related to this
depth, and the emission streaks in Figure [1] trace out the surface of the reverse shock,
thereby warranting the term “surface emission”. If one believes this interpretation, then
it is apparent from Figure [1] that there is both Hα and Lyα emission emerging from
beneath the surface of the reverse shock, since at any given frequency or wavelength,
flux appears at radial distances smaller than the radius of the shock. On this basis, we
coin the term “interior emission”.
http://arxiv.org/abs/0704.1304v1
+10000 km/s +5000 km/s -10000 km/s0
-5000 km/s
FIGURE 1. STIS data of reverse shock emission from SNR 1987A and accompanying schematic, taken
from [1]. (a) Hα surface emission from the reverse shock isolated by masks. (b) Lyα surface emission
with the same masks applied. (c) Schematic representation of the supernova debris with the boundary
being defined by the reverse shock. For freely-expanding debris, there is a unique correspondence between
velocity and the origin of the emission along the line of sight.
The shock velocity of SNR 1987A is ∼ 8000 km s−1, since it is the velocity of the
atoms in the rest frame of the reverse shock, moving at ∼ 4000 km s−1. Strong shock
jump conditions dictate that the ions are then at a velocity of ∼ 6000 km s−1 in the
observer’s frame. Thus, the fast atoms are being converted into slow ions at the reverse
shock. In addition to impact excitation, atoms may also donate their electrons to ions in
the shocked plasma (i.e., charge transfer), thereby producing a population of slow atoms.
The subsequent excitation (or charge transfer to excited states) of these atoms results in
lower velocity Hα and Lyα emission, creating the illusion that these photons originate
from beneath the reverse shock surface — “interior” emission. Both interior and surface
emission originate from the same location, but the spectral-spatial mapping is no longer
unique.
BALMER-DOMINATED SUPERNOVA REMNANTS
Dick McCray and I puzzled over the origins of the interior emission — he came up
with the charge transfer idea, while I sat down and worked out the mathematical details.
Deep into creating a formalism to compute the line intensities and ratios, I stumbled
upon an old problem, namely the study of Balmer-dominated SNRs ([2], [3] and [4]). (I
call the problem “old” because it was posed in the same year I was born.) These objects
are typically much older than SNR 1987A, and are observationally characterized by
blast wave
reverse 
shock
fast H I
SNR 1987ABalmer-Dominated SNRs
blast wave
Stationary H I
FIGURE 2. Contrasting the physical situations in “normal" Balmer-dominated SNRs and SNR 1987A,
taken from [5].
two-component, Balmer line profiles consisting of a narrow (∼ 10 km s−1) and a broad
(∼ 1000 km s−1) line. The former comes from the direct, impact excitation of stationary
hydrogen atoms by the SN blast wave, while the latter is a result of charge transfer
reactions of these atoms with post-shock ions.
The terms “fast” and “slow” are solely a matter of one’s frame of reference. In the
frame of the observer, the situation of fast atoms and slow ions in SNR 1987A now gets
switched to slow atoms and fast ions in these Balmer-dominated SNRs (Figure [2]). The
interior and surface emission of the former are the broad and narrow components of the
latter. Nevertheless, the physics of the problem remain the same. I suddenly realized
that I now had the mathematical machinery not only to model the emission lines in SNR
1987A, but to treat this broader class of objects as well. We generalized the methods of
[3] — we asked the question: can one exhaustively track the fate of a hydrogen atom as it
engages in charge transfer and excitation, eventually culminating in impact ionization?
It turns out that we can if we make certain fairly accurate approximations, allowing us
to find simple, analytical formulae for the rate coefficients of these reactions, weighted
by how many times the atom undergoes charge transfers; each such event changes the
nature of the atomic velocity distribution [4]. By knowing how to compute these rate
coefficients, we can in turn compute the probability for each reaction occurring, thereby
obtaining the composite velocity distribution. These distributions are intermediate be-
tween a beam and a Maxwellian, and we thus named them “skewed Maxwellians”.
We call atoms in such a skewed Maxwellian “broad neutrals”. The full width at half-
maximum (FWHM) of these velocity distributions is then uniquely related to the shock
velocity, provided one knows the temperatures of the electrons and ions. I have included
an appendix describing in detail the derivation of the broad and narrow Hα rate coef-
ficients (§), since the ratio of broad to narrow Hα emission is extensively studied in
FIGURE 3. Ratio of the broad to narrow Hα emission, Ib/In, versus shock velocity, vs. The theoretical
predictions by [3] (denoted “CKR80”) and [4] (denoted “HM06”) are plotted against several data points
from various SNRs. Models N and F represent calculations for β = 0.25 and 1, respectively, where
β ≡ Te/Tp is the ratio of electron to proton temperatures.
Balmer-dominated SNRs.
We can set theoretical bounds on the ratio of broad to narrow Hα emission, Ib/In, as
shown in Figure [3]. Generally, our predictions agree quite well with observations, but
a glaring discrepancy persists: the theoretical prediction of Ib/In ∼ 0.1 (i.e., interior-to-
surface Hα ratio) in SNR 1987A is lower by an order of magnitude compared to the
observed ratio. This points to two possibilities: there is a mechanism for interior emis-
sion we have not yet modeled (C. Fransson, Aspen talk, 2007); and/or the assumption of
thin shock fronts in these SNRs is a flawed one.
THE SHOCK TRANSITION ZONE
What if these shock fronts that we have been modeling as mathematical discontinuities
all along do indeed have a finite width? We decided to investigate this issue, resolving
the atomic physics while keeping the plasma kinetics unresolved [6]. In a system of
pre-shock atoms and post-shock ions, there must exist a transition zone in which one
population is converted into the other, via charge transfers and ionizations. This “shock
transition zone” has a width on the order of the mean free path of atoms passing through
the ionized gas, lzone ∼ 10
15n−10 cm, where n0 is the pre-shock ionic density (in cm
Velocity
atomic beam
pre-shock
protons
Density
residual atoms
width ~ 1/n(σ
post-shock protonsShock Frame
beginning of
transition zone
end of
transition zone
FIGURE 4. Schematic diagram of the shock transition zone, in the case of a strong shock, taken
from [6]. The width of the zone is on the order of the mean free path of interactions (charge transfer
and ionization). The velocity of the ions goes down to 1/4 of its pre-shock value almost immediately,
according to the Rankine-Hugoniot jump condition. The ionic density first jumps by a factor of 4 to
conserve momentum, then eventually evolves to a value which depends on the pre-shock ionic density.
The results are surprising — for a strong (∼ 1000 km s−1) shock, the ions are shocked
immediately. There is no velocity structure within the shock transition zone (Figure
4), thus validating the thin shock assumptions of [3] and [4]. The ionic velocities are
decelerated to 1/4 of their pre-shock values at the beginning of the zone, while the ionic
densities jump by a factor of 4 to conserve momentum, consistent with the Rankine-
Hugoniot jump conditions. There is, however, structure in both the atomic and ionic
densities, which is relevant to the study of Lyα resonant scattering in young SNRs (pre-
Sedov-Taylor phase). The mean free path for the scattering of Lyα photons is much less
than lzone; photons are produced in the zone but scatter in a distance much less than its
width. There is evidence for Lyα resonant scattering in SNR 1987A [1].
THE FUTURE
As SNR 1987A enters its third decade, many questions regarding its fate abound.
A central one concerning the reverse shock is: when will it disappear? There is a
competition between pre-shock atoms crossing the shock — and ultimately emitting
the Hα and Lyα photons we observe — and post-shock (ultraviolet and X-ray) photons
diffusing upstream. These photons are capable of ionizing the atoms before they have a
chance to undergo impact excitation (or charge transfer). If the flux of ionizing photons
exceeds that of the atoms, the reverse shock emission will vanish. In [7], we predict
this event to occur between about 2012 and 2014; we are currently planning further
observations to finetune this prediction (PI: J. Danziger). These observations may yet
shed light on the origins of the interior emission. One thing is for certain — SNR 1987A
will provide current and future, young generations of astronomers/astrophysicists (such
as myself) with an abundance of rich problems to ponder over.
ACKNOWLEDGMENTS
I am deeply grateful to Richard McCray for being a wonderful advisor, and to the Aspen
Center for Physics for the hospitality of their support staff, and the generosity of both
financial support and the Martin and Beate Block Prize (awarded at the conference). I
thank Roger Chevalier, John Danziger, Eli Dwek, Alak Ray, Dick Manchester, Bryan
Gaensler, Brian Metzger, Claes Fransson, Dieter Hartmann, Peter Lundqvist, Karina
Kjaer, Alicia Soderberg, Lifan Wang, Philipp Podsiaklowski, Shigeyama Nagataki, Avi
Loeb, Bob Kirshner, Saurabh Jha, Jason Pun, Andrew MacFayden, Jeremiah Murphy
and Chris Stockdale for intriguing conversations and/or wonderful company during the
conference. I apologize if I have left out anyone who belongs to the preceding list.
APPENDIX: DERIVING Ib AND In IN HENG & MCCRAY (2007)
In this section, I derive in more detail the Hα broad- and narrow-line rate coefficients,
denoted Ib(Hα) and In(Hα) respectively, and simply stated in [4]. For simplicity, we
refer to them just as Ib and In.
For narrow Hα line emission, atoms are found in a beam and may be excited an
arbitrary number of times until it gets transformed into a broad neutral via charge
transfer or destroyed by ionization. Let the probability of excitation be PE0 , where the
“0” means that the atom has undergone zero charge transfers prior to excitation. Let
the rate coefficient for excitation to the atomic level n be RE0,n. Considering multiple
excitations yield:
RE0,n
1+PE0 +P
+P3E0 + ...
= RE0,n
PiE0 =
RE0,n
1−PE0
, (1)
since 0 < PE0 < 1.
One can consider excitations up to some level m, depending on the atomic data
available. Ignoring collisional de-excitation, the rate coefficient for the narrow Hα line
1−PE0
RE0,nCn3, (2)
where Ci j is the probability that an atomic excited to a state i will transit to a state j < i
via all possible cascade routes; it is thus called the “cascade matrix”.
Let us next derive the rate coefficient for the broad Hα line. We first account for charge
transfer to excited states directly from the atomic beam to the level n, which has a rate
coefficient RT ∗0 ,n. Accounting for multiple excitations before such a charge transfer, we
have RT∗0 /(1−PE0). Next, we need to account for the creation of broad neutrals and the
multiple charge transfers they are capable of undergoing:
1−PE0
+ ...
1−PE0
1−PE0
The 1/(1−PE0) and 1/(1−PE) terms account for repeated excitations prior to engaging
in charge transfer. As in [4], we make the approximation that the rate coefficients and
probabilities are approximately unchanged after the first charge transfer, and thus they
do not possess a subscript (e.g., PE versus PE0). Physically, these are reactions involving
broad neutrals. Charge transfer to excited states and excitation of the broad neutrals are
given by RT∗,n/(1−PE) and RE,n/(1−PE), respectively. Putting everything together and
summing excitations to some level m, we get:
1−PE0
(RE,n +RT ∗,n)+RT ∗0 ,n
Cn3. (4)
REFERENCES
1. K. Heng et al., Astrophysical Journal 644, 959–970 (2006).
2. R. Chevalier, and J. Raymond, Astrophysical Journal 225, L27–L30 (1978).
3. R. Chevalier, R. Kirshner, and J. Raymond, Astrophysical Journal 235, 186–195 (1980).
4. K. Heng, and R. McCray, Astrophysical Journal 654, 923–937 (2007).
5. K. Heng, Celestial Outbursts & their Effects on Ambient Media, Ph.D. thesis, University of Colorado,
Boulder (2007), available soon on astro-ph.
6. K. Heng, M. van Adelsberg, R. McCray, and J. Raymond, in preparation for submission to the
Astrophysical Journal 0, 0–0 (2007).
7. N. Smith, S. Zhekov, K. Heng, R. McCray, J. Morse, and M. Gladders, Astrophysical Journal 635,
L41–L44 (2005).
	Introduction: SNR 1987A
	Balmer-Dominated Supernova Remnants
	The Shock Transition Zone
	The Future
	Appendix: Deriving Ib and In in Heng & McCray (2007)

  The reverse shock of supernova remnant (SNR) 1987A emits in H-alpha and
Ly-alpha, and comes in two flavors: surface and interior. The former is due to
direct, impact excitation of hydrogen atoms crossing the shock, while the
latter is the result of charge transfer reactions between these atoms and
slower, post-shock ions. Interior and surface emission are analogous to the
broad- and narrow-line components observed in Balmer-dominated SNRs. I
summarize a formalism to derive line intensities and ratios in these SNRs, as
well as a study of the transition zone in supernova shocks; I include an
appendix where I derive in detail the ratio of broad to narrow H-alpha
emission. Further study of the reverse shock emission from SNR 1987A will allow
us to predict when it will vanish and further investigate the origins of the
interior emission.

Introduction: SNR 1987A
	Balmer-Dominated Supernova Remnants
	The Shock Transition Zone
	The Future
	Appendix: Deriving Ib and In in Heng & McCray (2007)
