Wave-driven outbursts inmassive stars
Can they explain interacting supernovae?

Samantha Wu | MIAPbP Interacting Supernovae | 02/07/2023
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Artist’s impression of a red supergiant: Astrophysical Journal/Northwestern

Observations of interacting supernovae
fast-rising, more luminous lightcurves
blue/featureless early spectra, narrow flash-ionized emission lines
Type IIb/IIn
SN 2011ht
SN 2013cu
PTF09uj
SN2013fs
SN 2016bkv
SN 2018zd

Type Ib/c (n)SN 2006jc
SN 2015G
SN 2015U
LSQ 13abf
LSQ 13ddu
SN 2019dge

also superluminous SNe
SN 2006gy, ultraluminous Ics(Quimby et al. 2011)

Progenitor Outbursts Observed
SN 2006jc
SN 2010mc
SN 2009ip
LSQ13zm
SN 2015bhand many more…

2Motivation

Wave energy escape from core

Wave damping in envelope

Wave-heating: basic idea
waves excited by convection in core propagate to envelope
Quataert & Shiode (2012), Shiode & Quataert (2014)

Late burning stages inmassive stars exhibit
extremely highnuclear luminosities

Infer CSM within
Convection

IGW∼ 100 AU ofprogenitor: intense
mass loss close tocore collapse

Acousticwaves
3Motivation

Wave energy escape from core

Wave damping in envelope

How much wave energy
escapes the core?

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Excitation of waves by core convection
OOM estimates are promising
Waves excited with power

Convective Mach number(typical for C/Ne/O fusion)

Lwave ∼ ℳconLcon
7vcon−3ℳcon =∼ 10 -0.03
cs10Lcon ∼ 10 -10 L⊙
convective luminosity
for C to O/Ne burning

Shiode & Quataert (2014)

Convection

IGW

5Motivation

Wave energy escape from core

Wave damping in envelope

Excitation of waves by core convection
OOM estimates are promising
Waves excited with power
9Lwave ∼ ℳconLcon ≲ 10 L⊙
Spatial scale set by convective
eddies ∼ scale height H:

Characteristic frequency ω ≃ ωconvcon−4 −1ωcon ≃∼ 10 s
HC burning

Convection

Wave angular wavenumberℓ ∼ ℓcon = r/H−3 −1∼ few × 10s

O/Ne burning

IGW

Shiode & Quataert (2014)

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Motivation

Wave energy escape from core

Wave damping in envelope

Gravity wave propagation in radiative zones
Internal gravity waves (IGW) either tunnel to envelope or get trapped in core

Convection

IGW

7Motivation

Wave energy escape from core

Wave damping in envelope

Gravity wave propagation in radiative zones
Internal gravity waves (IGW) either tunnel to envelope or get trapped in core
Propagation diagram

Wave dispersion relation:

2kr =Understand wave behavior bycomparing wave frequency to N, Lℓ(N 2 − ω 2)(Lℓ2 − ω 2)
ω 2cs2

Brunt-Väisälä frequency:

Lamb frequency:
2Lℓ =IGW

Radiative
Zone

2

ConvectiveZone

1 d ln P d ln ρN =g−( γ drdr )Convectionℓ(ℓ + 1)cs2
r2
8Motivation

Wave energy escape from core

Wave damping in envelope

Fraction of wave energy that can escape core:
2Tmin)

fν: fraction attenuated fromneutrino and radiative losses
2Tmin: fraction transmitted throughthickest evanescent zone

2 ℓ(ℓ + 1)

RadiativeZone(1+ConvectiveZone

fesc,ℓ =fν − 1−1ri≈( ro )

Power that escapes to heat the envelope:·Lheat,ℓ = fesc,ℓEℓ

Initial wave
power

simplest assumption: ℓ = 1·
then Eℓ = Lwave

Need reasonable fraction of IGW power in low ℓ modes with ω ≳ ωcon
9Motivation

Wave energy escape from core

Wave damping in envelopeLater developments: wave excitation
Spectrum over angular wavenumber reduces power in low ℓ modes

proportion of wave power·per ℓ value isOOM Assumptions

EℓLwave

Waves excited with power

Lwave ∼ ℳconLconfrequency ω ≃ ωconConvection

angular wavenumber

IGWℓ ∼ ℓcon = r/H ≲ 2*prior work assumed ℓ = 1
carried all of Lwaveℓcon = r/ min(Δrshell, H)
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Motivation

Wave energy escape from core

Wave damping in envelope

Including power spectrum reduces wave power• ℓcon ∼ 2 − 4: high-ℓ waves carry most of the power• But fesc,ℓ is several OOM larger for low-ℓ waves

11 M⊙

11Motivation

Wave energy escape from core

Wu and Fuller (2021)
Wave damping in envelope

Later developments: IGW damping
Estimates of non-linear damping curtail power from low ω or high Lheat

If |krξr|>1, thenamplitude is non-linear
Compare amplitude ξr and wavenumber kr

Expect waves to break
Convection| krξr | ∝IGW

Lheat,ℓ2 ω4 )( Tmin1/2[ℓ(ℓ + 1)]

3/4

12Motivation

Wave energy escape from core

Wave damping in envelope

Fraction of wave energy that can escape core:(1+2Tmin)

ConvectiveZone

fν: fraction attenuated fromneutrino and radiative losses
2Tmin: fraction transmitted throughthickest evanescent zone

2 ℓ(ℓ + 1)

Radiative
Zone

fesc,ℓ =fν − 1−1ri≈( ro )

Power that escapes to heat the envelope:·Lheat,ℓ = fesc,ℓEℓ

Nonlinearity criterion: If max

Consider ℓ = 1-10 waves:·10
Generate Lheat = ∑ℓ=1 fesc,ℓEℓ

Initial wave
power

krξr > 1 for any ℓ: reduce Lheat by krξr

213Motivation

Wave energy escape from core

Wave damping in envelopeSome stars may have outbursts
But wave heating is not likely to drive outbursts in most stars• Calculations of wave heating rates in a suite of MESA stellar evolution models ofMZAMS = 11-50 M⊙ supergiants- followed methods of previous studies,

11 M⊙: semi-degenerate

added wave spectrum over ℓ andnonlinear wave breaking

Ne ignition- compare to, e.g. Fuller (2017):
48

deposit 10 erg,
Total energy deposited byeject ≲ 1 M⊙
−2
10 yr before core collapse
at low speed−2tdelay ∼ 10Myr( 10M⊙ )−0.5R( 100R⊙ )1.5and E ∼ 1047 erg to unbind significant supergiant envelope

Motivation

not enough energy before
core collapse

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Time before core collapse for47
Wu and Fuller (2021)
wave energy ≥ 10 erg

Wave energy escape from core

Wave damping in envelope

Wave excitation+propagation is not solved…
• Wave spectrum remains uncertain (ours: Goldreich & Kumar 1990; Shiode et al. 2013)• Mixing induced by non-linear breaking of IGW: may affect core structure, burning

Meakin & Arnett (2007)
15Motivation

Wave energy escape from core

Wave damping in envelope

Where in the envelope does
wave energy dissipate?

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Acoustic wave damping in stellar envelope
Sound waves dissipate well before reaching stellar surface, and envelope responds

Convection

Radiative diffusion
damping of sound waves

IGW
Acousticwaves
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Motivation

Wave energy escape from core

Wave damping in envelope

Initial calculations match some observations
e.g. from Quataert & Shiode (2012), Shiode & Quataert (2014):·−3−2• M ∼ 10 -10 M⊙ /yr ⇒Type IIn Sne (Kiewe et al. 2012)·• M ∼ 0.1-1 M⊙ /yr ⇒most luminous SNe like SN 2006gy (Smith et al. 2007)- or shock breakout in dense CSM (Ofek et al. 2010)• timescales of months (high-mass)-years (low-mass) before core collapse- Compared to observed pre-SN outbursts:‣ SN 2010mc: energetically ✅, timescale (40 days) ✅
‣ Type Ibn SN 2006jc: energetically ✅, timescale (2 yr) ❌

18Motivation

Wave energy escape from core

Wave damping in envelope

Later developments: envelope damping
Including shock dissipation and 1d hydrodynamics moderates envelope response

escaping Lheat is ∼ OOM
lower than prev. estimates

Convection

IGW
With MESA 1d hydro, add
wave heat as wave damps

Radiative diffusion
damping of sound waves
Weak shock damping
from Fuller & Ro (2018) onward

Acousticwaves
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Motivation

Wave energy escape from core

Wave damping in envelope

Observations matched by MESA hydro runs
focusing on lower-mass progenitors (semi-degenerate Ne ignition in 11 M⊙)• timescales of ~years before core collapse- With updates: surface variation, no mass loss

H-poorWu and Fuller (2022a)
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Motivation

Wave energy escape from core

Wave damping in envelope

High-mass hydrogen-poor progenitors
Energy scale ∼ 10 erg, outlier below ∼ 10 erg
4647

MHe ≈ 6 M⊙
MZAMS = 20 M⊙, Z = 0.007

Leung, Wu, and Fuller (2021)
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Motivation

Wave energy escape from core

Wave damping in envelopePre-SN variation, no mass loss
MESA 1d hydrodynamical response of H-rich and H-poor stars to wave heating
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MZAMS = 11 M⊙ H-poor model: Ewave ∼ 10 erg• Wave energy deposited wherebinding energy is high• No mass loss drivenhydrodynamically from waveheating• Star expands quasi-hydrostaticallyin response to tdyn < theat < ttherm

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Motivation

Wave energy escape from core

Wu and Fuller (2022a)
Wave damping in envelopePre-SN variation, no mass loss
• Significant changes in Teff, R for H-poor stars
approximately consistent with Type Ib SNe
iPTF13bvn, SN 2019 yvr

where does CSM come from?

maybe degenerate Si ignition (Woosley & Heger 2015)
maybe expansion initiates mass transfer w/binary companion
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Motivation

Wave energy escape from core

Wu and Fuller (2022a)
Wave damping in envelope

Binary evolution can explain SNe Ibn/USSNe
Progenitors are stripped He stars surrounded by nearby He-rich CSM
Large mass loss →low precollapse mass → low Mej

fiducial modeledstages
from De et al. 201824

Motivation

Wave energy escape from core

Wave damping in envelope

Most progenitor models don’t explain nearby CSM
But also omit promising evolution during off-center O/Ne burning!

single helium stars with2.5 M⊙ ≲ MHe ≲ 3 M⊙ expand again

C burning O/Ne burning(104−5 years) (≲ decades)

during O/Ne burning

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Motivation

Wave energy escape from core

Wu and Fuller (2022b)
Wave damping in envelope

Expansion initiates high MT rate
MESA binary models at range of orbital periods
MHe ∼ 2.5-3 M⊙ donors + MNS = 1.4 M⊙ point mass accretor; assume fully non-conservative MT

Dotted lines: If MESA stops·evolving MT (M too high),
we extrapolate assuming·
constant M until Si burn26

Motivation

Wave energy escape from core

Wu and Fuller 2022b

Wave damping in envelope

Late-stage mass transfer in massive binaries
Stripped-star progenitor transferring mass to companion (e.g. NS) during O/Ne burning• Mass transfer is likely super-Eddington
onto companion (so mass is ejectedfrom system)

Initial Porb 1, 10, 100 day• May be stable or unstable (likelyleading to common envelope)- SNe Ibn favor unstable MT →CEE
scenario- USSNe favor stable mass loss
scenario

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Motivation

Wave energy escape from core

Wu and Fuller (2022b)
Wave damping in envelope

3d effects may provide channel for wave heating
May depend sensitively on deposition radius

Rdep ∼ 240 R⊙

tdep ∼ 20 day
tdyn = 2.7 day

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Motivation

Wave energy escape from core

Tsang et al. (2022)
Wave damping in envelope

Summaryupdated wave heating models so far produce no direct mass loss
• Including the wave power spectrum and estimating non-linear effects reduces theescaping wave energy by ∼ OOM.
• Including weak-shock dissipation causes acoustic modes to damp just outside the star’s
core where the binding energy is high.
• Further exploration of multi-dimensional effects will clarify uncertainties such as nonlinear mixing in the core and energy deposition in convective envelopes. The initialwave spectrum is also subject to debate.

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