MNRAS 470, 1642–1656 (2017) doi:10.1093/mnras/stx1314
Advance Access publication 2017 May 29
Pre-supernova outbursts via wave heating in massive stars – I.
Red supergiants
Jim Fuller
1,2‹
1
TAPIR, Walter Burke Institute for Theoretical Physics, Mailcode 350-17, Caltech, Pasadena, CA 91125, USA
2
Kavli Institute for Theoretical Physics, Kohn Hall, University of California, Santa Barbara, CA 93106, USA
Accepted 2017 May 24. Received 2017 May 16; in original form 2017 March 8
ABSTRACT
Early observations of supernovae (SNe) indicate that enhanced mass-loss and pre-SN outbursts
may occur in progenitors of many types of SNe. We investigate the role of energy transport via
waves driven by vigorous convection during late-stage nuclear burning of otherwise typical
15 M
red supergiant SN progenitors. Using MESA stellar evolution models including 1D
hydrodynamics, we find that waves carry ∼10
7
L
of power from the core to the envelope
during core neon/oxygen burning in the final years before core collapse. The waves damp
via shocks and radiative diffusion at the base of the hydrogen envelope, which heats up fast
enough to launch a pressure wave into the overlying envelope that steepens into a weak shock
near the stellar surface, causing a mild stellar outburst and ejecting a small (1M
) amount
of mass at low speed (50 km s
−1
) roughly one year before the SN. The wave heating inflates
the stellar envelope but does not completely unbind it, producing a non-hydrostatic pre-SN
envelope density structure different from prior expectations. In our models, wave heating is
unlikely to lead to luminous Type IIn SNe, but it may contribute to flash-ionized SNe and
some of the diversity seen in II-P/II-L SNe.
Key words: waves – stars: evolution – stars: massive – stars: mass-loss – supergiants –
supernovae: general.
1 INTRODUCTION
The connection between the diverse population of core-collapse
supernovae (SNe) and their massive star progenitors is of paramount
importance for the fields of both SNe and stellar evolution. Over the
past decade, substantial evidence has emerged for enhanced pre-SN
mass-loss and outbursts in the progenitors of several types of SNe.
The inferred mass-loss rates are typically orders of magnitude larger
than those measured in Local Group massive stars, and the mass-loss
appears to systematically occur in the last centuries, years or weeks
of the stars’ lives. This deepening mystery cannot be explained by
standard stellar evolution/wind theories, and its solution lies at the
heart of the SN massive star connection.
Type IIn SNe provide the most obvious evidence for pre-SN mass-
loss, and it is well known that these SNe are powered by interaction
between the SN ejecta and dense circumstellar material (CSM).
However, Type IIn SNe are very heterogeneous [Smith (2016)clas-
sifies them into 10 subtypes], as some appear to require interaction
with ∼10 M
of CSM ejected in the final years of their progenitor’s
life, while others require mass-loss rates of only ∼10
−4
M
yr
−1
but lasting for centuries before the explosion (Smith et al. 2017).
These mass-loss rates are much larger than predicted by standard
E-mail: jfuller@caltech.edu
mass-loss prescriptions. In some cases, pre-SN outbursts resulting
in mass ejection have been observed directly, famous examples be-
ing SN 2009ip (which did not explode until 2012; Mauerhan et al.
2013;Grahametal.2014; Margutti et al. 2014; Smith, Mauerhan &
Prieto 2014), 2010mc (Ofek et al. 2013), LSQ13zm (Tartaglia et al.
2016) and SN 2015bh (Elias-Rosa et al. 2016;Ofeketal.2016;
Th
¨
one et al. 2017), which show resemblance with luminous blue
variable star outbursts. Pre-SN outbursts now appear to be common
for Type IIn SNe (Ofek et al. 2014).
Enhanced pre-SN mass-loss has also been inferred from observa-
tions of other types of SNe. Type Ibn SNe (e.g. SN 2006jc that had
a pre-SN outburst, Pastorello et al. 2007; and SN 2015U, Shivvers
et al. 2016) show interaction with He-rich material ejected soon
before core collapse. SN 2014C was a Type Ib SN that transitioned
into a Type IIn SN after the ejecta collided with a dense shell of
H-rich CSM ejected by its progenitor in its final decades of life
(Milisavljevic et al. 2015; Margutti et al. 2017). Early spectra of
Type IIb SN 2013cu reveal emission lines from a flash-ionized
wind (Gal-Yam et al. 2014) with inferred mass-loss rates over
10
−3
M
yr
−1
(Groh 2014). Many bright Type II-P/II-L SNe also
show flash-ionized emission lines in early-time spectra indicative
of a thick stellar wind (Khazov et al. 2016), while even relatively
normal II-P SNe sometimes exhibit peaks in their early light curves
that may be produced by shock cooling of an extremely dense stel-
lar wind (Moriya et al. 2011; Morozova, Piro & Valenti 2017).
C
2017 The Author
Published by Oxford University Press on behalf of the Royal Astronomical Society
Pre-supernova outbursts 1643
Figure 1. Cartoon (not to scale) of wave heating in a red supergiant. Gravity
waves are excited by vigorous core convection and propagate through the
outer core. After tunnelling through the evanescent region created by the
convective He-burning shell, they propagate into the H envelope as acoustic
waves. The acoustic waves damp near the base of the envelope and heat a
thin shell.
Recently, Yaron et al. (2017) found that the otherwise normal type
II-P SN2013fs showed emission lines only within the first sev-
eral hours after explosion, indicating that modest mass ejection of
∼10
−3
M
in the final year of the progenitor’s life is common for
Type II-P SNe.
One of the most promising explanations for pre-SN outbursts
and mass-loss was proposed by Quataert & Shiode (2012), who in-
vestigated the impacts of convectively driven hydrodynamic waves
during late-phase nuclear burning. Convectively driven waves are
a generic consequence of convection that are routinely observed
in hydrodynamic simulations. Quataert & Shiode (2012) showed
that the vigorous convection of late burning stages (especially Ne/O
burning) can generate waves carrying in excess of 10
7
L
of power
to the outer layers of the stars, potentially depositing more than
10
47
erg in the envelope of the star over its last months/years of
life. Fig. 1 provides a cartoon picture of the wave heating pro-
cess. Shiode & Quataert (2014) then showed that the wave heating
is generally more intense but shorter-lived in more massive stars,
and could occur in a variety of SN progenitor types. More recently,
Quataert et al. (2016) have examined the effect of super-Eddington
heat deposition (e.g. due to wave energy) near the surface of a star,
showing that the heat can drive a dense wind with a very large
mass-loss rate.
In this paper, we examine wave heating effects in otherwise ‘typ-
ical’ M
ZAMS
= 15 M
red supergiants (RSGs) that may give rise
to Type II-P, II-L or IIn SNe depending on the impact of wave
heating. We quantify how wave heating alters the stellar structure,
luminosity and mass-loss rate using
MESA simulations (Paxton et al.
2011, 2013, 2015) including the effects of wave heating due to
convectively driven waves. After carbon shell burning, we use the
1D hydrodynamic capabilities of
MESA to account for the pressure
waves, shocks and hydrodynamic/super-Eddington mass-loss that
can result from intense wave heating.
Figure 2. Kippenhahn diagram of our M
ZAMS
=15 M
model from carbon
burning through silicon burning. Shading indicates the wave energy lumi-
nosity L
wave
= M
con
L
con
each convective zone is capable of generating,
and zones are labelled by the element they burn. Purple regions are stably
stratified regions where convectively excited gravity waves may propagate.
2 WAVE ENERGY TRANSPORT
2.1 Wave generation
Gravity waves are low-frequency waves that can propagate in ra-
diative regions of stars where their angular frequency ω is smaller
than the Brunt–V
¨
ais
¨
al
¨
a frequency N (see Fig. 3). They are excited at
the interface between convective and radiative zones, carrying en-
ergy and angular momentum into the radiative zone that is sourced
from the kinetic energy of turbulent convection. The energy carried
by gravity waves is a small fraction of the convective luminosity,
scaling roughly as (Goldreich & Kumar 1990)
L
wave
∼ M
con
L
con
, (1)
where L
con
is the luminosity carried by convection and M
con
is
a typical turbulent convective Mach number. In most phases of
stellar evolution, M
con
10
−3
within interior convection zones,
and the energy carried by gravity waves is negligible. Equation (1)
has been approximately verified by multidimensional simulations
(Rogers et al. 2013; Alvan, Brun & Mathis 2014; Alvan et al. 2015;
Rogers 2015).
Fig. 2 shows the quantity L
wave
within the interior of an
M
ZAMS
= 15 M
stellar model from core carbon burning onwards.
Details and parameters of our
MESA models can be found in Ap-
pendix A. Before carbon shell burning, L
wave
is much less than the
surface luminosity of L 10
5
L
, and wave energy transport is neg-
ligible. However, after carbon burning, neutrino cooling becomes
very efficient within the core, which falls out of thermal equilibrium
with the envelope. To maintain thermal pressure support, burning
luminosities increase and become orders of magnitude larger than
the surface luminosity. Convective mach numbers also increase,
and consequently L
wave
during late burning phases can greatly ex-
ceed the surface luminosity, allowing wave energy redistribution to
produce dramatic effects.
To estimate wave luminosities in our 1D models, we proceed as
follows. First, we calculate L
wave
at each radial coordinate as shown
MNRAS 470, 1642–1656 (2017)
1644 J. Fuller
in Fig. 2. Next, we calculate a characteristic convective turnover
frequency at each radial coordinate via
ω
con
= 2π
v
con
2α
MLT
H
, (2)
where
v
con
=
L
con
/(4πρr
2
)
1/3
(3)
is the rms convective luminosity according to mixing length theory
(MLT), α
MLT
is the mixing length parameter and H is a pressure
scaleheight. The turbulent mach number is M
con
= v
con
/c
s
,where
c
s
is the adiabatic sound speed. Remarkably, these estimates of
convective velocities and turnover frequencies typically match those
seen in 3D simulations of a variety of burning phases (e.g. Meakin
&Arnett2007a; Alvan et al. 2014; C ouch & Ott 2015; Lecoanet
et al. 2016; Jones et al. 2017) to within a factor of 2.
In reality, a spectrum of waves with different angular frequencies
ω and angular wavenumbers k
⊥
=
√
l(l + 1)/r are excited by each
convective zone, where l is the spherical harmonic index of the
wave. Rather than model the wave spectrum, we find the maximum
value of ω
con
(usually located a fraction of a scaleheight below the
zone’s outer radius), and assume that all the wave power is put into
waves at this frequency
ω
wave
= ω
con,max
, (4)
and angular wavenumbers l = 1. Simulations show that realistic
wave spectra are peaked around ω = ω
wave
and l = 1, even for fairly
thin shell convection like that in the Sun (see Alvan et al. 2014),
at least for waves not immediately damped, so these approxima-
tions are reasonable. Waves at lower frequencies are typically much
more strongly damped, while waves at higher frequencies contain
much less power. Waves at higher values of l contain comparable
or less power and are more strongly damped, so we ignore their
contribution. At each time-step in our simulations, we find the ra-
dial location of ω
max
within the core (usually located within the
innermost convective burning zone), and then compute v
con
, ω
wave
and L
wave
at that point using equations (1), (2) and (3).
2.2 Wave propagation and dissipation
The next step is to calculate how waves of frequency ω
wave
and
l = 1 will propagate and dissipate within the star. Typical waves at
ω =ω
wave
during late burning phases are gravity waves in the core of
the star, but in the envelope they are acoustic waves (see Fig. 3). In
order to propagate into the envelope, the waves must tunnel through
one or more intervening evanescent zones, the largest of which is
often created by the convective helium burning shell. Apart from
wave evanescence, we ignore wave interactions with convection in
these regions because their convective energy fluxes and turnover
frequencies are generally much smaller than the core convection
that launches the waves, although some interaction may take place.
Before tunnelling out of the core, the waves may reflect multiple
times and can be damped by neutrino emission or by breaking near
the centre of the star, dissipating some of their energy within the
core. In Appendix B, we provide details of how to calculate these
effects in order to determine the fraction of wave energy f
esc
that
is able to escape from the core and propagate into the envelope as
acoustic waves.
The wave energy that heats the envelope is then
L
heat
= ηf
esc
L
wave
. (5)
Figure 3. Propagation diagram for our model during core oxygen burn-
ing, showing the Brunt–V
¨
ais
¨
al
¨
a frequency N and the = 1 Lamb fre-
quency L
1
. Vigorous convection in the core excites waves of frequency
ω
wave
∼ 5 × 10
−3
rad s
−1
that propagate through the core as gravity waves.
The waves must tunnel through one or two evanescent zones before pen-
etrating into the stellar envelope as acoustic waves, where their energy is
dissipated into heat.
Figure 4. Luminosity of our M
ZAMS
= 15 M
stellar model in its final
century before core collapse. The red line shows the observable surface
luminosity, while the black line is the nuclear energy generation rate. A
small fraction of this energy is converted into waves that propagate out
of the core. The value of L
heat
is the wave heating rate at the base of the
hydrogen envelope.
Here, η is an efficiency parameter (with nominal value η = 1 unless
stated otherwise) that we will adjust to explore the dependence of
our results on the somewhat uncertain wave flux. We find typical
values of f
esc
∼ 0.5 during core neon/oxygen burning, and f
esc
∼ 0.1
during shell burning phases because more wave energy is lost by
tunnelling into the core. We do not compute the effect of wave heat-
ing within the core because its binding energy is much larger than
integrated wave heating rates, and because neutrinos can efficiently
remove much of this thermal energy.
Fig. 4 shows the nuclear energy generation rate L
nuc
(not in-
cluding energy carried away by neutrinos) of our stellar model as a
function of time, along with the envelope wave heating rate L
heat
and
MNRAS 470, 1642–1656 (2017)
Pre-supernova outbursts 1645
Figure 5. Integrated wave energy deposited outside of the core (starting
from core carbon burning) as a function of time until core collapse, for
three different heating efficiencies η. The dashed black line shows the total
binding energy of the hydrogen envelope (in a model not including wave
heating). The dotted black line is the binding energy of the outer solar mass
of the envelope (see Fig. 6).
the surface luminosity L
surf
. Important burning phases are labelled.
Although the fraction of nuclear energy converted into waves that
escape the core is generally very small (<10
−3
), the value of L
heat
can greatly exceed L
surf
. In our models, L
surf
remains smaller than
L
heat
during later burning phases because most of the wave heat
remains trapped under the H envelope and is not radiated by the
photosphere, which we discuss more in Section 3. Fig. 5 shows the
integrated wave energy deposited in the envelope as a function of
time.
After determining L
heat
, we must determine where within the en-
velope the wave energy will damp into thermal energy. This calcula-
tion is detailed in Appendix B3, where we calculate wave damping
via thermal diffusion and describe how we add wave heat into our
stellar model. The most important feature of diffusive wave damp-
ing is that it is strongly dependent on density and sound speed,
with a characteristic damping mass M
damp
∝ ρ
3
(equation B25). In
RSGs, the density falls by a factor of ∼10
6
from the helium core
to the base of the hydrogen envelope (see Fig. 6). Hence, acoustic
waves at frequencies of interest are essentially undamped in the
helium core but quickly damp as they propagate into the hydrogen
envelope, and they always thermalize their energy in a narrow shell
of mass at the base of the hydrogen envelope.
In the late stages of preparing this paper, Ro & Matzner (2017)
demonstrated that acoustic waves will generally steepen into shocks
before damping diffusively, causing them to thermalize their energy
deeper in the star. Using their equation 6 and calculating wave
amplitudes from the value of L
heat
, we find that shock formation in
our models occurs at somewhat larger (by a factor of a few) density
than radiative diffusion, but at very similar mass coordinates and
overlying binding energies. The reason is that the density cliff at the
edge of the He core promotes both shock formation and diffusion.
We therefore suspect that wave energy thermalization via shock
formation will only marginally affect our results, but we plan to
account for it in future work.
Our wave heating calculations during shell Ne/O burning and core
Si burning are less reliable due to an inadequate nuclear network
in our models, and increasing wave non-linearity. These burning
Figure 6. Top: binding energy integrated inwards from the surface of our
M
ZAMS
= 15 M
model just after carbon burning, as a function of mass
coordinate. The right axis shows the corresponding density profile just after
carbon burning, and during oxygen burning. Middle: wave heating rate
L
heat
(r), integrated from the centre of the star to the local mass coordinate,
during oxygen burning. Essentially all of the wave heat is deposited at the
base of the hydrogen envelope at mass coordinate m 5.446 M
.The
right axis shows the damping mass M
damp
through which the waves must
propagate to be attenuated (equation B25). M
damp
plummets just outside
the core, causing the waves to damp at that location. Bottom: dynamical,
thermal and wave heating time-scales as defined in Section 3. The long
thermal time-scale above the heating region prevents most wave heat from
diffusing outwards. Wave heating causes these time-scales to be very short
and comparable to one another in the heating region (inset).
phases occur less than an envelope dynamical time before core
collapse, giving waves little time to alter envelope structure. For
these reasons, we do not closely examine these phases in this work,
but large wave luminosities during these phases may affect some
progenitors.
3 EFFECTS ON PRE-SN EVOLUTION
In our models, wave heating is most important during late C-shell
burning, core Ne burning and core O burning. To quantify the effects
of wave heating on the pre-SN state of the stellar progenitor, we
construct
MESA models and evolve them from the main sequence to
core collapse. At each time-step, we add wave heat L
heat
as described
in Section 2 and Appendix B. Just before C burning, we utilize the
1D hydrodynamic capabilities of
MESA (see Appendix A), which
is essential for capturing the non-hydrostatic dynamics that result
from wave heating.
MNRAS 470, 1642–1656 (2017)
1646 J. Fuller
Figure 7. Internal radial velocity profiles of our model at several times
measured from the start of core Ne burning. The moving velocity peak
arises from the pressure wave that propagates towards the stellar surface,
steepening into a weak shock near the photosphere. This weak shock break-
out creates the mild outburst shown in Figs 8 and 9. Surface velocities are
smaller than the escape speed (v
esc
∼ 45 km s
−1
), so the surface expands
but remains bound.
Relative time-scales are important for understanding wave heat-
ing effects. We define a local wave heating time-scale
t
heat
=
c
2
s
heat
, (6)
where
heat
is the wave heat deposited per unit mass and time. This
can be compared with a thermal cooling time-scale
t
therm
=
4πρr
2
Hc
2
s
L
, (7)
where H is the pressure scaleheight and L is the local luminosity.
We also define a local dynamical time-scale
t
dyn
=
H
c
s
. (8)
Finally, all of these should be considered in relation to the time until
core collapse, t
col
.
The first key insight is that wave energy is deposited at the base
of the hydrogen envelope, above which t
therm
is comparable to (but
generally larger than) t
col
(see Fig. 6). Consequently, wave heat
cannot be thermally transported to the stellar surface before core
collapse, and the surface luminosity L
surf
is only modestly affected
(Fig. 4). We therefore do not expect very luminous (L 10
6
L
)
pre-SN outbursts to be driven by wave heating in RSGs.
The second key insight is that wave heating time-scales can be
very short. In the slow heating regime with t
heat
t
therm
t
dyn
,
wave heat can be thermally transported outwards without affecting
the local pressure. In the moderate heating regime with t
therm
t
heat
t
dyn
, wave heat cannot be thermally transported outwards, but the
star can expand nearly hydrostatically to accommodate the increase
in pressure (see discussion in Mcley & Soker 2014). However, we
find that wave heating can be so intense that it lies in the dynamical
regime t
heat
t
therm
, t
dyn
. In this case, wave heat and pressure build
within the wave damping region, exciting a pressure wave that
propagates outwards at the sound speed (Fig. 7). This pressure
wave crosses the stellar envelope on a global dynamical time-scale
t
dyn,glob
∼
R
3
GM
0.5yr (9)
for our stellar model.
In our models, the most important envelope pressure wave arises
from wave heating during core Ne burning and a third C-shell
burning phase (later waves do not reach the surface before core
collapse). As these pressure waves approach the surface where the
density and the sound speed drop, they steepen into a weak shock
(M 3). When the shock wave breaks out of the surface, it pro-
duces a sudden spike in surface temperature and luminosity (see
Figs 8 and 9), akin to SN shock breakout (Dessart et al. 2013)but
Figure 8. HR diagrams of our models during the century before core collapse, for different heating efficiencies η. Stronger wave heating induces stronger
surface shock breakouts, creating more dramatic temperature/luminosity increases.
MNRAS 470, 1642–1656 (2017)
