The Effects on Supernova Shock Breakout and Swift Light Curves Due to the Mass of the Hydrogen-Rich Envelope

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by  Amanda J. Bayless

Draftversion March25,2015
PreprinttypesetusingLATEXstyleemulateapjv.12/16/11
THE EFFECTS ON SUPERNOVA SHOCK BREAKOUT AND SWIFT LIGHT CURVES DUE TO THE MASS
OF THE HYDROGEN-RICH ENVELOPE
Amanda J. Bayless1,2, Wesley Even3, Lucille H. Frey3, Chris L. Fryer3,4,5, Peter W. A. Roming1,2,6, Patrick
A. Young7
Draft versionMarch 25, 2015
ABSTRACT
5
1 Mass loss remains one of the primary uncertainties in stellar evolution. In the most massive stars,
0 mass loss dictates the circumstellar medium and can significantly alter the fate of the star. Mass
2 loss is caused by a variety of wind mechanisms and also through binary interactions. Supernovae
are excellent probes of this mass loss, both the circumstellar material and the reduced mass of the
r
a hydrogen-richenvelope. Inthispaper,wefocusonthe effectsofreducingthe hydrogen-envelopemass
M on the supernova light curve, studying both the shock breakout and peak light curve emission for a
widevarietyofmasslossscenarios. Eventhoughthetrendsofthismasslosswillbemaskedsomewhat

4 byvariationscausedbydifferentprogenitors,explosionenergies,andcircumstellarmedia,thesetrends
2 have significant effects on the supernova light-curves that should be seen in supernova surveys. We
conclude with a comparison of our results to a few key observations.

]
E Subject headings: supernovae: general
H
. 1. INTRODUCTION drogen ionization zone (Fryer et al. 2006; Paxton et al.
h
2013), or shellburning instabilities producing pulsations
p Core-collapse supernovae are classified by the evolu-
(Heger et al. 2003; Arnett & Meakin 2011). These in-
- tion of their emission and their spectral features (for a
o stabilities can significantly alter both the stellar radius
review, see Filippenko 2005). These features have been
r and mass loss. Stellar radii in massive stars are noto-
t attributedtocharacteristicsoftheprogenitorstar,where
s type Ib, Ic, and all type II supernovae are believed to riously difficult to observe. For massive stars, the mass
a lossfromwindscansetthephotospherebeyondthenom-
arise from massive stars. The collapse of the stellar core
[ inal edge of the star, making it difficult to use massive
inthesestarsreleasestheenergytopowerthesupernova.
starobservationstoobservethestellarradius. Supernova
2 The different types of supernovae: IIP, IIL, IIn, IIb, Ib,
v Ic supernovae are believed to represent stars with differ- observations suffer from some of these same limitations,
9 ent radiiand mass loss (Arnett 1996; Heger et al. 2003). but they have the potential to provide an independent
4 In this basic theoretical picture, a type IIP supernova is determination of stellar radii.
4 believed to arise from the explosion of a massive giant Similarly, supernovae may help us probe the nature of
4 mass loss in massive stars. The simple picture of line-
star, the extended envelope providing a plateau phase
. driven winds for massive star mass loss has gradually
1 in the emission as the photosphere sweeps through the
givenwaytoamorechaoticpicturewhereoutburstsfrom
0 extended giant envelope. As this envelope is removed,
thegiantenvelopeplayadominantroleinthetotalmass
4 the star becomes more compact and the plateau phase
lost from systems. In addition, evidence continues to
1 disappears. As the hydrogen-rich envelope is removed,
grow showing that most massive stars are in binaries, a
: the star exhibits helium-like features, producing a type
v sizablefractionininteractingbinariesthatwillshedmass
IIb. If the hydrogen-rich envelope is entirely removed,
i due to binary interactions (Kobulnicky & Fryer 2007;
X the supernova becomes a pure Ib supernova.
Kochanek et al. 2012). Indeed, the leading models for
Thefoundationofthissimpletheoreticalpictureofsu-
r
well-studied nearby supernovae SN 1987a and SN1993J
a pernova classification is based on our understanding of
and supernova remnants, such as Cas A, both invoke
the evolution of stellar radii and mass loss in massive
binary interactions and mass loss (Podsiadlowski 1993;
stars. As massive stars evolve into a giant phase, the
Young et al. 2006). One of the standard mass-loss sce-
star is susceptible to a wide range of instabilities: e.g.
opacity driven instabilities (κ−mechanism) in the hy- narios from binary interactions occurs when the star ex-
pands in a giant phase. If it envelops its companion,
1SouthwestResearchInstitute,DepartmentofSpaceScience, tidal forces and friction will eject the hydrogenenvelope
6220CulebraRd,SanAntonio,TX78238,USA by tapping orbital energy (see Ivanova et al. 2013 for a
2UniversityofTexasatSanAntonio,SanAntonio,TX78249, review). This “common envelope” phase persists until
USA either the entire hydrogen-richenvelope is ejected or the
3Los Alamos National Laboratory, Los Alamos, NM 87545,
companionmergeswiththeheliumcoreoftheexpanding
USA
4Physics Department, University of Arizona, Tucson, AZ star.
85721, USA Whether the mass-lossis caused by steady winds, vio-
5Physics and Astronomy Department, University of New lent outbursts, or binary interactions, we expect nature
Mexico,Albuquerque,NM87131, USA
6DepartmentofAstronomy&Astrophysics,PennStateUni- to produce, for every individual progenitor star, a range
versity,525DaveyLab,UniversityPark,PA16802,USA ofenvelopemassesandradii. This projectisdesignedas
7School of Earth andSpace Exploration, ArizonaState Uni- a first step in studying the role of mass loss and stellar
versity,411NCentralAve,Phoenix,AZ85004,USA
2
radii in supernova light curves. Here we study a single inclusionoftheseprocesses,whichapproximatetheinte-
supernova progenitor and explosion energy, varying the gratedeffect of dynamic stability criteria for convection,
hydrogenmassandstellarradiustodeterminetheireffect entrainment at convective boundaries, and wave-driven
on the observed supernova light curve. In this manner, mixing, results in significantly larger extents of regions
weisolatetheeffectsofradiusandmasstopredicttrends. processed by nuclear burning stages.
These trends can be used to tie supernova observations This new mixing algorithm can significantly alter the
to uncertainties in stellar mass loss and radii. heliumshell. Figure1showsthedistribution(massfrac-
For this paper, we discuss the effects of removing hy- tions) of key elements in the post-explosion star. Notice
drogenfromthe outer layersofthe star onthe evolution the peculiar helium shell abundances. The mixing al-
of SNe events. We remove the hydrogen in two ways: gorithmin TYCHO produced extensive helium burning,
1) by removing mass in bulk from the outer shell, which converting most of the helium in this shell to oxygen.
alsochangesthe radius,and2)byalteringthe densityof When the hydrogen-rich envelope is removed exposing
theoutershells. Thissimulatessomeofthe manywasin the He-shell, this object will look much more like a type
which a star can lose mass, e.g. winds, binary interac- Ic supernova (Frey et al. 2013b).
tions, etc. As a star loses hydrogen, it is expected that
the SN would transitionfroma Type II/IIP to Type IIb 2.2. Supernova Explosion
and eventually to a Ib/c. In this paper, we study the
The core collapse itself was done with a one-
changes in light curves as this transition takes place.
dimensionalLagrangiancode developedby Herant et al.
2. SUPERNOVAMODELS (1994). This code includes three-flavor neutrino trans-
portusing a flux-limited diffusion calculationanda cou-
Supernova light curves depend upon a wide range of
pled set of equations of state and nuclear networks to
physical effects and stellar characteristics including the
model the wide range of densities in the collapse phase
structure of the stellar core, the circumstellar medium,
(seeHerant et al.1994;Fryer et al.1999fordetails). Af-
the explosion energy and the asymmetry of the super-
ter collapse and bounce, the proto-neutron star is re-
nova. In this project, we focus on the effects of mass
moved (and replaced with a hard boundary). We con-
loss from the hydrogen-rich envelope on the supernova
tinue the evolution by injecting energy at the surface of
light curve. As such, our study will use a single pro-
the proto-neutron star to drive an explosion. The du-
genitor with a standard r−2 wind profile for the circum-
ration and power of this energy injection can be modi-
stellar medium. This study will use a single, spherically
fied to mimic rapid and delayed explosions (Fryer et al.
symmetric explosion. Before we discuss our light curve
2012). For this paper, we produced a rapid explosion
results, we will review our progenitor and supernova ex-
with a higher than average energy, E = 5×1051 erg, in
plosion model.
a spherical explosion.
2.1. Progenitor We follow this explosion until the shock is at 2.9 ×
The light curve models in this paper use a 23 M⊙ 1m0u1c0hcomf.thAesinwneeremxpaetcetriafolrismnaontygsivtaernseanboouvgeh2e0neMrg⊙y
progenitor produced by the TYCHO (Young & Arnett
toescapethegravitationalpulloftheproto-neutronstar
2005) stellar evolution code. This model takes ad-
and it falls back onto the neutron star. We model the
vantage of the newly revised mixing algorithm in
fallback by allowing it to pile up on the proto-neutron
the TYCHO code. TYCHO uses OPAL opacities
star surface and cool via neutrino emission. When the
(Iglesias & Rogers 1996; Alexander & Ferguson 1994; fallbackmaterialdensityexceeds109 gcm−3,weassume
Rogers et al. 1996), a combined OPAL and Timmes
neutrino emission is able to cool the material quickly
equation of state (HELMHOLTZ; Timmes & Arnett
(on the timescale of our hydrodynamics timestep) and
1999; Rogers & Nayfonov 2002), gravitational settling,
assimilate it into the proto-neutron star.
diffusion (Thoul et al. 1994), general relativistic grav-
The explosion code includes a small 17-isotope net-
ity, automatic rezoning, and an adaptable nuclear re-
work. But we post-process all the ejected material with
action network with a sparse solver. A 177 element
the 489-isotope TORCH8 code. Note in Figure 1 that
neveotwluotriokn.termTinhaetinngetwaotrk74GuesesistuhseedlatthesrtouRghEoAuCtLtIhBe there is 7.3×10−3 M⊙ of 56Ni in the core because most
of the inner material fell back and was accreted onto
rates(Rauscher & Thielemann2000;Angulo et al.1999;
the proto-neutron star. The low 56Ni yield alters the
Iliadis et al. 2001; Wiescher et al. 2006), weak rates
light-curve,especially pastpeak and must be considered
from Langanke & Mart´ınez-Pinedo (2000), and screen-
when comparing our light-curve calculations to observa-
ing from Graboske et al. (1973). Neutrino cooling from
tions. To demonstrate the importance of the 56Ni yield,
plasma processes and the Urca process is included.
we include two models with enhanced 56Ni in Section 5.
Mass loss uses updated versions of the prescriptions of
Kudritzki et al.(1989)forOBmassloss,Bloecker(1995)
2.3. Hydrogen-Rich envelope and Mass Loss
forredsupergiantmassloss,andLamers & Nugis(2002)
for WR phases. It incorporates a description of tur- The 23 M⊙ solar metallicity star is evolved up to
bulent convection (Meakin & Arnett 2007; Arnett et al. the onset of core collapse in TYCHO. The single, non-
2009, 2010; Arnett & Meakin 2011) which is based on rotating23M⊙starevolvesnormallyasaredsupergiant.
three dimensional, well-resolved simulations of convec- This final star mass is 18.9 M⊙, with a 11.9 M⊙ H-rich
tion sandwiched between stable layers, which were ana- envelope, containing 6.2 M⊙ of hydrogen and 5.6 M⊙ of
lyzedindetailusingaReynoldsdecompositionintoaver- helium. This progenitor has an unusually high helium
age and fluctuating quantities. It has no free convective
parameters to adjust, unlike mixing-length theory. The 8 http://cococubed.asu.edu
3
1.0
H Mass
He Mass
O Mass
0.8
Si Mass
S Mass
n
actio0.6 Ni Mass
s fr
s
a
m
nt
e0.4
m
e
el
0.2
0.0
0 5 10 15
mass enclosed [M_sun]
Fig.1.—Materialmassfractions as afunction ofmassforour 23M⊙ progenitor, post-explosion. Thedashed vertical linescorresponds
totheouterlayerofthestaraftershellmassremovalforthemodelsdescribedinTable1
10-2 10-2
23M12.12s 23M10d
10-4 2233MM1111..97s5s 10-3 2233MM86dd
23M11s 23M4d
10-6 23M10s 10-4 23M2d
23M8s 23M0
^3] 10-8 2233MM64ss ^3] 10-5
m 23M2s m
Density [g/c111000---111420 23M0 Density [g/c 1100--76
10-16 10-8
10-18 10-9
10-20 10-10
1012 1013 1014 1015 1012 1013 1014 1015
Radius [cm] Radius [cm]
Fig.2.— The initial density profiles for the simulations presented in this paper. The figure on the left displays the simulations where
the mass was removed byremoving layers fromthe star (shell models) and the figureon the rightdisplays simulations wherethe density
intheouterlayerwasdecreasedtoremoveadditionalmassafteraninitialshellwasremoved(densitymodels).
composition containing 52% hydrogen and 47% helium. of the trends from mass loss. Table 1 shows the range
Mass loss remains one of the primary uncertainties in of models used in this study and Figure 2 displays the
our understanding of the hydrogen envelope. The focus initial density profiles for all models.
of this paper is to study the effects of enhanced mass
loss. 2.4. Light Curve Code
For this study, we use the exploded TYCHO simula-
Before the shock has reached the helium shell, the ex-
tion as a base and then remove mass using two differ-
plosionis mappedinto RAGE (Radiative Adaptive Grid
ent procedures: 1) a shell mass removal where the outer
Eulerian;Gittings et al.2008)tomodelthe couplingbe-
layers of the star are removed from our model, reduc-
tweenmatterandradiationastheshockbreaksoutofthe
ing both the H shell mass and the stellar radius, and
starandinteractswiththeinterstellarmedium. Theden-
2) a density-decrease mass removalwhere we reduce the
sity structure and abundance of the interstellar medium
density of the H shell, reducing the mass, but not the
can greatly affect the resulting simulated light curves,
radius of the star. Mass loss occurs through a variety of
even for low masses of interstellar material. In order to
mechanisms: winds, stellar instabilities, binary interac-
minimizetheimpactofthecircumstellarmaterialonthe
tions. Although one can imagine scenarios where mass
light curves a low density wind resulting from a mass
is removedand the star shrinks or expands significantly,
these two procedures span a relatively wide range of the loss rate of 10−7 M⊙/yr and velocity of 108 cm/s was
implemented in all models. Even at this extremely low
possible outcomes frommass loss,providinga basic idea
mass loss rate the wind will still alter the light curves at
4
TABLE 1
Summaryof Explosion Models 1044
23M0
Modelc Radius ShellMass Removal 23M2s
Name (cm) Removed[M⊙] Mechanism 23M4s
23M0 1.01×1014 0.0 Baseline 2233MM68ss
23M2s 9.45×1013 2.0 Shella 23M10s
222333MMM468sss 876...675488×××111000111333 468...000 SSShhheeellllllaaa y [erg/s]1043 22223333MMMM11111112s...7915s2ss
23M10s 4.63×1013 10.0 Shella osit
23M11s 2.93×1013 11.0 Shella min
23M11.75s 5.56×1012 11.75 Shella Lu
23M11.9s 1.61×1011 11.9 Shella
23M12.12s 5.59×1011 12.12 Shella
23M10.42d 4.49×1013 10.42 Densityb
23M10.72d 4.49×1013 10.72 Densityb 1042
23M11.01d 4.49×1013 11.01 Densityb
23M11.31d 4.49×1013 11.31 Densityb 10-2 10-1 100
23M11.60d 4.49×1013 11.6 Densityb Time [days]
aForourShellModels,weremovemassstartingfromouterlayers Fig.3.—Bolometriclightcurvesfortheshellremovalmodelsat
ofthestar,bothremovingmassandshrinkingthestellarradius. shockbreakout.
bFor our density models, we lower the density in the hydrogen
shell,removingH-shellmass,butretainingthestellarradius. released in the hard UV, X-rays, and gamma rays. In
cAll Models use a 23 M⊙ star with 5×1051 erg explosion and starswithdensecircumstellarmaterialthephotonbreak-
0.0073Nimass. outcanbe delayedsignificantlyfromthe shockbreakout
at the surface of the star (Colgate 1974; Dopita et al.
breakout, but this allows for a nearly single parameter
1987;Ensman & Burrows1992;Tan et al.2001). Figure
numericalstudy overthe time frameofwhichSwift data
3 shows bolometric light curves for shock breakoutof all
is present. Balberg & Loeb (2011) demonstrate that the
10 shell removal models. The breakout peaks last from
radiation energy in the shock at breakout is approxi- <10−2sfor23M12.12sto∼1dayfor23M0. Whilebrief,
mately equal to the mass loss rate to the 16 power.
21 the peak bolometric luminosity reached during shock
Therefore, increasing the mass loss rate to 10−5 M⊙/yr breakoutcanbeoveranorderofmagnitudegreaterthan
would result in a ∼ 40 times brighter breakout in mod- what is typically labeled as peak in a standard SN light
els where the breakout occurs in the wind, which would curve. Theearlytimelowamplitudemodulationsinthis
mask some of the differences we are studying here. figure and in the following figures are created by multi-
Although the RAGE code is capable of simulating the ple small shocks. These are likely an artifact of the 1D
explosion in 1-, 2-, and 3-dimensions with multi-group simulations and in multi-dimensions turbulence within
flux-limiteddiffusion,forthesecalculationswemodelthe the ejecta will cause dissipation in these shocks. The
explosion in 1-dimension using a gray opacity scheme. decrease in breakout time with increasing mass removal
These calculations include the shock heating effects on results mainly from the decrease in radius, although the
the temperature and the radiation effects on the hy- relationisnotlineardue tothe decelerationofthe shock
drodynamics that are critical in modeling shock break- as it sweeps up mass while propagating through outer
out and the peak supernova light-curve for most core- layers. Figure 4 shows the transition as mass is removed
collapse supernovae. To produce the detailed spectra from the shell.
needed to produce light-curves in different bands, we Shock breakout luminosity is commonly estimated by
post-process these radiation-hydrodynamics calculation applying the Stefan-Boltzmann equation at the point
using the opacities from the SESAME database. The when the shock first reaches the τ = 1 radius, result-
post-process technique, developed by Fryer (2009, 2010) ing in luminosity being a simple function of radius and
is described in detail in Frey et al. (2013). shock temperature (Svirski et al. 2012). This simple
back of the envelope calculation can deviate from the
3. SHOCKBREAKOUT actual breakout luminosity by orders of magnitude be-
The supernova explosion launches a shock from the cause there is no single radius where radiation breakout
core that travels outward through the star. When this occurs. Insteadeachphotonenergyhasauniqueopacity
shock reaches the surface it rapidly accelerates and in- resulting in a potentially wide range in τν =1 radii and
creases in temperature as it traverses the steep density temperatures.
gradient between the star and the surrounding circum- ThisisillustratedinFigure5,whereweshowtheτ =1
stellar material (see Figure 2). Prior to shock break- surface calculated at two different wavelengths for each
out the radiation is trapped within the hydrodynamic modelatthe time ofpeak breakoutluminosity. Figure5
shockbecause thediffusiontime forthe photonsismuch also shows that temperature varies by a factor of a few
greater than the hydrodynamic time scales. If there withintheemittingregion,withthetemperatureincreas-
is little circumstellar material, at shock breakout the ing with smaller radii. This gradient in temperature is
photon diffusion timescale decreases below the hydro- also a factor in creating a large emitting region as more
dynamic timescale and results in a short but powerful luminosity is created in the higher temperature region
(& 1044erg/s) burst of photons escaping from the outer and therefore can contribute to the observed luminosity
edge of the shock. The majority of this energy will be even though it is at a higher τ. The spectra in Fig-
5
ure 5 reflect the higher breakout temperature with the an expansion that is homologous (v ∝ r), the radiation
most compact explosion peaking in the X-ray, while the energy dominates the energy equation (the total energy
more extended stars have spectral energy distribution E = aT4V where a is the radiation constant, T is the
that peak in the UV. temperature, and V is the volume), single-group gray
opacity, and the diffusion equation is adequate model
In Table 2 we compare the single radius black-body
the light-curves. This approach(Arnett 1980, 1982) has
approximation to the simulated results shown in Figure
beenusedsuccessfullytobuildintuitionandmakeafirst
5. A luminosity-weighted averaged radius and temper-
passatthelightcurvesfromexplosions. Our“test”code
ature are calculated from the models in Figure 5. The
numericallyevaluatesthelight-curvewiththesesameas-
analytic luminosity is constructed by extracting the ra-
sumptions: we assume homologous expansion of the su-
diusandtemperatureatthelocationoftheτ =1surface
pernova after the shock breaks out of the star, we in-
at 20˚A from the simulation. This radius and tempera- clude energy deposition from the decay of 56Ni (high
turepairareusedtocalculatetheluminosityforanideal 56Ni model), and diffusion scheme using a constant gray
black-body sphere. The difference between the analytic
opacity to transport energy. The initial conditions are
and the simulated bolometric luminosities are the most
set by approximating the initial conditions in our full
extreme for the more compact stars, where the discrep-
calculations: we assume a constant density profile and a
ancy is over two orders of magnitude. The 23M12.12s
constant temperature of 30eV. Early emission and adi-
and 23M11s are emitting light from an average depth
abatic cooling quickly deplete this initial energy during
such that there is ∼ 2×101 of column density that the
shock breakout and the late-time light-curve is entirely
photonsmusttravelthroughto escape. Onlyphotonen-
poweredbythedecayof56Nianditsdaughterproducts.
ergies with opacities . 0.1 g/cm2 will be able to escape
This code matches the analytic approximations,but can
from this regioncausing non-blackbody emission, as can
easily be modified to include additional physics to com-
be seen in the spectra in the bottom right panel of Fig-
pare to our more detailed light-curve code.
ure 5. In contrast, the more massive models only have
These light-curve calculations are plotted in Figure 7.
a column density of ∼10−3 g/cm2 from the emitting re-
The gray opacity and the assumption of a single photo-
gionresultinginmuchlessextinctionandamorereliable
sphereproducesaverysharpbreakoutsignalthatisboth
black-body fit.
higher and shorter in duration than our simulations. A
The wavelength dependence of the opacity is also re-
major assumption in these analytic calculations (and in
sponsibleforthetransitionfromthesinglepeakedbreak-
many radiation-transportonly calculations) is that 56Ni
out light curve for the most stripped stars to the double
is the dominant energy source for the light curve. How-
peaked breakout in the more massive stars. The dou-
ever, shock heating can dominate the energy source in
ble peak results from higher energy photons with lower
many core-collapse explosions. Once we launch our ex-
opacity escaping from deeper within the surface of the
plosion,weassumenofurthershockheating(eitherfrom
star than the lower energy photons that can only begin
windorreverse-shockinteractions). Comparingwithour
to free stream closer to the surface.
full simulations,we see that shock heating playsa domi-
The left panel ofFigure 6 comparesthe breakoutlight
nantrolein the lightcurve,especially atlate times. Ad-
curves for the mass and shell removal models. In simu-
ditionally, the light curves from a full simulation tend
lations, the density altered models, which have a larger
to be better fits with a simple model that had less mass
radii, are dimmer than the corresponding shell removal
stripped than its direct comparison model.
modelsatpeak brightness,buthaveaslowerdecay. The
Our simulations are also shown in the Swift
differenceinincreasedpeakbrightnessislargestformod-
(Gehrels et al. 2004) UVOT (Roming et al. 2000, 2004,
els with the least amount of mass removed, which have
2005) band passes. Figure 8 shows the shell model light
the most material for the shock to interact with as it
curves and Figure 9 shows the altered density models.
breaks out of the surface of the star.
The central wavelengths for the Swift filters are uvw2
4. LIGHT CURVES (λc = 1928 ˚A), uvm2 (λc = 2246 ˚A), uvw1 (λc = 2600
We present multiple simulated light curves from the ˚A), u (λc =3465˚A), b(λc =4392˚A), andv (λc =5468
models described above. Bolometric light curves are ˚A; Breeveld et al. 2010). We note that the Swift u-band
shown in Figure 3. The models with 0 to 4 M⊙ re- is not a traditional U-band, but has a bluer response
movedareverysimilarforthefirst20daysandtheearly than the atmospheric cut-off. The models with < 4 M⊙
time light curves do not start to deviate until 6 M⊙ of removedshowaverysimilarriseandfallintheUVanda
material is removed. Since all models have an identical gradualrise and fall in the optical, as typical for a Type
explosion, the differences observed in the light curve are IIP SNe (Brown et al. 2009). As more mass is removed,
solelyaresultofinteractionswiththe outerlayersofthe the slope of the post-peak fall off becomes steeper and
star, which for 23M0 to 23M4s are not dramatic with beginstoresembleTypeIIbandTypeIb/cSNe. Forthe
only a 14% change in radius and 21% change in mass case of 12 solar masses removed in Figure 8, the entire
between the 3 models. However, when ≥ 6 M⊙ is re- hydrogen shell has been removed. The time of peak lu-
moved the slope of the fall-off changes dramatically and minosity and the slope of the post-peak decline for the
when&11M⊙ thepeakalsobeginstorapidlydropwith baselinemodelandmodels23M6sand2311.01daresum-
mass removal. To better understand the importance of marized in Table 3. These models are shown because
shock heating, we have developed a simplified model of they are representative of the slope changes as mass is
the light-curve evolution based on the work of (Arnett lost.
1980, 1982). An analytic method can be developed by Figure 10 shows how the model’s radius,temperature,
making a number of simplifying assumptions including density, and velocity change with time. The upper left
6
TABLE 2
BreakoutParameters
model Rbo [cm] Tbo [eV] Lan [erg/s] Lsim [erg/s] ρcolumn [g/cm2]
23M12.12s 2.96×1012 36.7 3.7×1044 8.3×1042 1.7×101
23M11s 6.16×1013 13.3 1.6×1045 9.4×1043 1.4×10−2
23M8s 1.42×1014 3.89 6.0×1043 5.4×1043 8.6×10−3
23M4s 1.88×1014 5.11 3.1×1044 3.9×1043 5.5×10−4
1044
23M0
23M2s
23M4s
23M6s
1043 23M8s
23M10s
23M11s
g/s] 23M11.75s
er 23M11.9s
sity [1042 23M12.12s
o
n
mi
u
L
1041
1040
20 40 60 80 100
Time [days]
Fig.4.—Bolometriclightcurvesfortheshellremovedmodelsshowingthetransitionasmoremassisremoved.
panel of Figure 10 displays the position of the τ = 1 particularly in the UV and required adjustment to be
surface at 3 different Swift wavelengths (uvm2, u, and comparable to the Swift observations. This adjustment
v) for the 23M8s, 23M10s, and 23M12.12s models. The wasto artificiallyaddreddening byincreasingE(B−V)
upper right, lower left, and lower right panels present until the v and b-bands were close to fitting and then to
the density, temperature, and velocity in the simulation add an additional constant magnitude term to the UV
correspondingtotheτ =1surface. From0to10daysthe and u-bands. This needed to be done because the mod-
τ =1 surface is expanding and rapidly cooling resulting els produced 5 foe of energy, much more than an typical
inarapiddeclineinthelightcurve. At∼10daystheτ = explosion. Futuremodelswillhavelowerenergiesandbe
1 surface drops deeper into the ejecta and revealshigher more realistic for the comparison to observations.
temperaturematerialcausingariseinthelightcurve. In The top left panel shows the baseline model with the
the uvw2-band there is a similar, but less dramatic rise SwiftlightcurvesfortheTypeIIPSN2010F(Maza et al.
in the light curve and a correspondingly smaller rise in 2010). SN 2010F does not have well constrained param-
the temperature at the τ = 1 surface. It is also noted eters allowing some adjustment in reddening and time
that the τ =1 surface for the UV bands and the optical of explosion. The discovery of SN 2010F was on JD
bands represent very different velocities and will create 2455209.8 with an earliest possible date of explosion on
differentDopplershiftsforlinesacrossthesewavelengths. 2455189.5. The galactic reddening is 0.095,but the host
reddening is unknown (Maza et al. 2010). We are able
4.1. Comparisons to Normal Supernovae
to come close to fitting the post-peak slope until about
Figure 11 shows a sample comparison to Swift obser- day 40, but this required shifting the explosion date to
vations (see Pritchard et al. 2013). The error bars on an unrealistic 14.7 days after discovery,to JD2455224.5.
the observations are approximately the size of the data We also needed an additional reddening of 0.3 and re-
points. Note that these models are not intended to fit quired an additional constant added to the UV and u-
these specific light curves, but are shown only to illus- band models of 1.3 mag and 1.0 mag respectively. The
trate that we do match observed trends. The Swift data top right panel shows the same baseline model with the
hasbeengalaxysubtractedandareddeninglawhasbeen Type IIP SN2012aw (Bayless et al. 2013). SN 2012aw
appliedtothemodelsbasedonCardelli et al.(1989)with was some what unique observationally in that its close
Rv = 3.1. In general, the baseline model can be fit to a proximity(10Mpc,inM95)allowedlengthyUVobserva-
Type IIP and the model where hydrogenis removedcan tions. TheseextendedUVobservationsshowedaflatten-
be fit to Type IIb and Type Ib. However, there are still ingatlatetimes, >30dayspastexplosion. Thebaseline
a few issues that require further modeling. The overall model is matching the general late time slope observed
modellightcurvesarestilltooluminousafterreddening,
7
103
10-4 23M12.12s
23M11s
10-6 2233MM84ss
102
10-8
3] V]
^ e
nsity [g/cm1100--1120 mperature [ 101
De10-14 Te
10-16 100
10-18
10-20 10-1
1012 1013 1014 1015 1012 1013 1014 1015
Radius [cm] Radius [cm]
1013
1012 1043
1011 1042
3]1010
m^ 109 m]1041
minosity Density [erg/s/c 111111100000002345678 Luminosity [erg/s/angstro11111000003333467890
Lu 101 1035
100
10-1 1034
10-2 1033
1012 1013 1014 1015 101 102 103 104
Radius [cm] Wavelength [angstrom]
Fig.5.—Thedensity(top left),temperature(top right),luminositydensity(bottom left),andspectra(bottom right)forfourdifferent
simulations atthe timethat corresponds to peak breakout luminosity. The vertical dashed lines inthe top plots enclose the volume that
isthesourceof 99% oftheluminosity. Thevertical dashed linesinthe bottom leftplotrepresent τ =1surfacesattwo wavelengths near
thepeakofthespectraforthatmodel(10˚A&20˚Afor23M12.12s,20˚A&40˚Afor23M11s,100˚A &1000˚Afor23M8s&23M4s).
1044 1044
23M10s
23M11s
23M11.75s
23M10.42sd
23M10.72sd
s] s]1043 23M11.01sd
erg/ erg/ 23M11.31sd
sity [1043 sity [ 23M11.60sd
o o
n n
mi mi
Lu Lu1042
1042 1041
0.2 0.4 0.6 0.8 1.0 0 5 10 15 20 25 30
Time [days] Time [days]
Fig.6.—Comparisonofbolometriclightcurvesbetweentheshellremovedanddensityalteredmodels.
8
44.0
23M10s Simulation
23M10s Simulation
43.5 23M2s Simulation
23M12.12s Simulation
23M0 Analytic
nosity [erg/s])4432..05 222222333333MMMMMM11246801ssssss AAAA AAnnnnnnaaaaaallllyyyyllyyttttttiiiicccciicc
mi42.0 23M11.75s Analytic
g (Lu 2233MM1112..91s2 sA Ananlayltyitcic
Lo41.5
41.0
40.5
5 10 15 20 25 30 35 40
Time [days]
Fig.7.—Acomparisonoflightcurvesgeneratedfromragesimulations(dotted)withasimplehomologousexpansionplusdiffusionmodel
TABLE 3
Peak&Slope ofSelected LightCurve Models
MassRemoved= 0M⊙ 6M⊙,shell 11.01M⊙,density
BandPass Peaka Slope1b Slope2c Peak Slope1 Slope2 Peak Slope1 Slope2
uvw2 12 0.11 0.08 9 0.24 0.11 6 0.21 0.07
uvm2 14 0.09 0.09 10 0.26 0.11 7 0.17 0.10
uvw1 16 0.07 0.10 14 0.21 0.08 3 0.17 0.08
u 21 0.04 0.12 16 0.14 0.05 5 0.19 0.08
b 22 0.02 0.12 17 0.11 0.00 5 0.21 0.04
v 26 0.02 0.14 20 0.10 0.00 5 0.20 0.02
aPeakisnumberofdayspastexplosion.
bSlope1istheaveragedeclinebetweenthepeakandabout40dayspastexplosioninmag/day.
cSlope2istheaveragedeclineafterabout40dayspastexplosioninmag/day.
9
Fig. 8.—ThelightcurvesforthemodelsinTable1. Thesixband Fig.9.—ThelightcurvesforthealtereddensitymodelsinTable
passes are the UVOT filters. The general trend has the UV light 1 inthe same UVOT filters as inFigure 8. These show the same
curves of the larger star (less removed) peaking later and having generaltrend,buthaveaslowerfalloffpost-peak.
a faster fade out. The optical light curves in all the models are
similarwithinthefirstmonth. agation, meaning the outer layers were ignorant of the
and the time of the peaks in all band passes is close to interior of the star. The star at this time is 18.9 M⊙,
matching, even if not the same magnitude. In this case with a 11.9 M⊙ shell comprised of 6.2 M⊙ of hydrogen
the galactic reddening is 0.024 and additional E(B-V) and 5.6 M⊙ of helium, having lost mass from the ini-
of 0.4 was added. A constant of 3.0 mag and 2.0 mag tial23 M⊙. The amountofbulk mass removedfrom the
were added to the UV and u-band light curves. The shell varied from nothing removed (baseline model) up
bottom left panel shows the 4 M⊙ shell removed model to 12.12 M⊙. In the altered density models, 2-10 M⊙ of
with the Type IIb SN2008ax (Roming et al. 2009). The material were removed.
uvm2 observations are only an upper limit indicated by The evolution of the 2 M⊙ and 4 M⊙ shell removed
the arrows. The peak is well fit in the optical and only models appearverysimilar to the baselinemodel for the
a few days early in the UV. This model required an ad- first month, after which differences begin to develop. As
ditional reddening of 0.4 and UV and u-band constants more and more hydrogenis removed,we would expect a
of 2.0 and 1.0 mag respectively. The bottom right panel transition from Type IIP’s to Type IIb’s and eventually
shows the 6 M⊙ shell removed model with the Type Ib producing Type Ib/c’s. It is interesting that in the shell
SN 2007Y (Joubert et al. 2007; Stritzinger et al. 2009). modelsthereisnotasignificantchangeinthefirstmonth
Thepostpeakgeneralslopetrendmatches,butthepeak until 6 M⊙ is removed (Figure 3), highlighting the need
in the model is too early. This model also required an for late time observations. Models with thicker shells
added reddening of 0.55 and UV and u-band constants all have similar early time light curves. As more mass
of 2.0 and 1.0 mag respectively. is removed, there is a transition to where the luminosity
fallsoffearlierasmoremassisremoved,whichresembles
5. SUMMARY&CONCLUSIONS the Type IIb and Ib/c light curves. The altered density
In this paper we have tested the effects of the amount models follow a similar trend as the shell models, but
of mass in the hydrogen-rich envelope and the density thepost-peakdeclineismuchshallower. Thepeakinthe
structure and consequently stellar radius on the appear- lightcurveinallthemodelsisearliestinthebluestfilters
anceofSNelightcurvesandontheevolutionoftheshock as would be expected for thermal cooling. The most
waveasitpropagatesthoughthe layersofthe star. This massive star shows the latest light curves peaks, with
test wasdone in twoways: 1) to removethe outer layers the least massive star’s light curves peaking the earliest.
of the shell, which also alters the radius, and 2) adjust TheeffectofthemasslossismostpronouncedintheUV
the hydrogen density in the outer shells, lowering the band passes.
amount of hydrogen, but maintaining the same radius. Itisclearthatlightcurvemodelscoveringalargerange
The shell removal and density changes were done just of peak luminosity and durations can be created with a
after the launch of the shock, prior to the shock prop- single progenitor model. The amount and method used
10
1016
23M8s 10-10
23M10s
23M12.12s
10-11
1015 3]
^
m] m10-12
Radius [c nsity [g/c10-13
e
1014 D
10-14
10-15
1013
0 10 20 30 40 50 0 10 20 30 40 50
Time [d] Time [d]
101 1010
Temperature [eV] 100 Velocity [cm/s] 109
108
10-1
0 10 20 30 40 50 0 10 20 30 40 50
Time [d] Time [d]
Fig. 10.— Time-Series evolution of the radius, density, temperature, and velocity. The time series evolution of the position, density,
temperature, and velocity of the τ = 1 surface for 3 different Swift bands for 3 different models. The dotted lines correspond to the
uvm2-band,thesolidlinestotheu-band,andthedashedlinestothev-band.
to cause mass loss has a significant impact on the light With the advent of time-sensitive surveys (e.g. PTF),
curve. These models can ultimately be constrained by we are now discovering more rapid transients as well as
observations. The Swift SNe database (Pritchard et al. rapidly varying features in traditional supernovae. For
2013) is an excellent source for optical and UV light example, shock breakout, which occurs in the first few
curves of more than 50 CCSNe, including complete UV days of a supernova explosion has a rise/fall timescale
light curves for many CCSNe. If the removal of hydro- ranging from <10 minutes to ∼1 day. These timescales
geninthemodelsrepresentsachangefromtheTypeIIP are extremely sensitive to the stellar radius and shock
to Type Ib/c, we should see this trend reflected in the breakout making this time domain an ideal probe of
data. This general trend is demonstrated in Figure 11, the radial variations caused by mass loss. Another ex-
but more modeling is needed to adjust the peak times ample arises from the discovery of new, short duration
and the luminosity. Additionally, we tested 2 models (<10days)transients,whichcanbemodeledwithafully
with a higher Ni mass. These were the same as 23M8s, stripped star that lacks a strong wind. These outbursts
23M10s, and 23M12.12s, but with less fall back giving are ideally suited to probe extreme mass loss in stars.
a Ni mass of 0.37 M⊙. Figure 12 shows the bolomet- We haveshownfromfirstprinciplesthatremovinghy-
ric light curves for these models and the low Ni mass drogenfromthe outershelldoesconvertaTypeIIPtoa
counterparts. The light curve is identical until about IIb/Ib. Changingthemasslossdoesnotchangetheover-
day10. Then, asexpected, the lightcurveremainsmore allluminosityandthemodelsmustbefainterandredder
luminous. The model with 12.12 M⊙ removed shows a to match SN 2010F, SN 2012aw, 2008ax, and 2007Y as
doublepeakwithasuddenbrighteningofseveralmagni- wellassimilarSNeprobablybecauseourmodelsweretoo
tudes. Further modeling along this avenue would allow energetic for these specific SNe. However, the change in
for a better fit to observed SNe light curves in the post- mass loss does show the correcttrend to transition from
peak decline and to determine the cause of the extreme TypeIIPtoTypeIb/c. Infuture modeling,wewillneed
mass loss double peak. to consider other progenitor stars and parameters, but