Diversity of Luminous Supernovae from Non-Steady Mass Loss

0.3 MB·English

by  Takashi J. Moriya

Draftversion January24,2012
PreprinttypesetusingLATEXstyleemulateapjv.12/01/06
DIVERSITY OF LUMINOUS SUPERNOVAE FROM NON-STEADY MASS LOSS
Takashi J. Moriya1,2,3 and Nozomu Tominaga4,1
Draft version January 24, 2012
ABSTRACT
We show that the diversity in the density slope of the dense wind due to non-steady mass loss can
be one way to explain the spectraldiversity of Type II luminous supernovae (LSNe). The interaction
2
of SN ejecta and wind surrounding it is considered to be a power source to illuminate LSNe because
1
manyLSNeshowthewindsignatureintheirspectra(TypeIInLSNe). However,therealsoexistLSNe
0
without the spectral features caused by the wind (Type IIL LSNe). We show that, even if LSNe are
2
illuminated by the interaction, it is possible that they do not show the narrowspectra from the wind

n if we take into account of non-steady mass loss of their progenitors. When the shock breakout takes
a place in the dense wind with the density structure ρ∝r−w, the ratio ofthe diffusion timescale in the
J
optically thick region of the wind (t ) and the shock propagation timescale of the entire wind after
d
3 the shock breakout (ts) strongly depends on w. For the case w <∼ 1, both timescales are comparable
2 (t /t ≃ 1) and t /t gets smaller as w gets larger. For the case t /t ≃ 1, the shock goes through
d s d s d s
the entire wind just after the light curve (LC) peak and narrow spectral lines from the wind cannot
]
be observed after the LC peak (Type IIL LSNe). If t /t is much smaller, the shock wave continues
E d s
to propagate in the wind after the LC peak and unshocked wind remains (Type IIn LSNe). This
H
difference can be obtained only through a careful treatment of the shock breakout condition in a
h. dense wind. The lack of narrow Lorentzian line profiles in Type IIL LSNe before the LC peak can
p alsobeexplainedbythedifferenceinthedensityslope. Furthermore,weapplyourmodeltoTypeIIn
- LSN 2006gy and Type IIL LSN 2008es and find that our model is consistent with the observations.
o
Subject headings: supernovae: general — supernovae: individual (SN 2006gy, SN 2008es) — stars:
r
t mass-loss — shock waves — radiative transfer
s
a
[
1. INTRODUCTION tered by the wind. Photons emitted from the shock dif-

2 fuse in the wind and the light curve (LC) of the shock
Shockbreakoutis aphenomenonwhichis predictedto
v breakout becomes broader (e.g., Falk & Arnett 1977;
be observed when a shock wave emerges from the sur-
7 Grasberg & Nadezhin 1987; Moriya et al. 2011). If the
face of an exploding star. Before the shock wave ap-
0 wind is much denser, the shock breakout itself can take
proaches the surface of the star, the diffusion timescale
8 placeinthewind. Theshockbreakoutinthedensewind
of photons is much longer than the dynamical timescale
3
is related to astrophysical phenomena, e.g., PTF 09uj
of the shock wave because of the high optical depth of
.
0 the stellar interior and photons cannot go out of the (Ofek et al. 2010), XRO 080109(Balberg & Loeb2011),
1 and production of high energy particles (Murase et al.
shock wave. At the stellar surface, the optical depth
1 2011;Katz et al.2011). Inparticular,Chevalier & Irwin
above the shock wave suddenly becomes low enough for
1 (2011) associate luminous supernovae (LSNe) to the
photons to diffuse out from the shock wave and pho-
: shock breakout in the dense wind.
v tons start to travel away from the star. This sud-
Many LSNe are believed to be brightened by the
i den release of photons is predicted to be observed as
X shock interaction between SN ejecta (or materials re-
a flash of X-rays or ultraviolet (UV) photons (e.g.,
r Ohyama 1963; Colgate 1974; Klein & Chevalier 1978; leased from stellar surface) and the dense circumstellar
a wind (e.g., Smith & McCray 2007; Woosley et al. 2007;
Ensman & Burrows 1992; Blinnikov et al. 1998, 2000;
van Marle et al. 2010; Blinnikov & Sorokina 2010)5.
Matzner & McKee 1999; Calzavara & Matzner 2004;
This is because many LSNe are spectroscopically clas-
Nakar & Sari 2010; Tominaga et al. 2011) and it is ac-
sified as Type IIn SNe which show narrow spectral
tually observed for several times, e.g., XRO 080109/SN
lines from the wind surrounding SN ejecta6 (e.g.,
2008D (e.g., Soderberg et al. 2008) and SNLS-04D2dc
Smith et al. 2010; Drake et al. 2010; Rest et al. 2011;
(Schawinski et al. 2008; Gezari et al. 2009).
Chatzopoulos et al. 2011; Drake et al. 2011). For exam-
If the circumstellar windof the SNprogenitoris dense
ple, SN 2006gy shows Lorentzian H Balmer lines with
and optically thick, the shock breakout signal is al-
thefullwidthathalfmaximumvelocity≃1,000km s−1
1 Institute for the Physics and Mathematics of the Uni- (e.g.,Smith et al.2010)whicharesuggestedtooriginate
verse, Todai Institutes for Advanced Study, University of
Tokyo, Kashiwanoha 5-1-5, Kashiwa, Chiba 277-8583, Japan; 5 There are other suggestions for energy sources to brighten
[email protected] LSNe: e.g., huge amount of 56Ni produced during SN explosions
2 Department of Astronomy, Graduate School of Science, Uni- (e.g.,Gal-Yametal.2009;Youngetal.2010;Moriyaetal.2010),
versityofTokyo,Hongo7-3-1,Bunkyo,Tokyo113-0033,Japan newlyborn magnetars (e.g., Maedaetal. 2007; Kasen&Bildsten
3 Recearch Center for the Early Universe, Graduate School of 2010; Woosley 2010), and optical afterglows of gamma-ray bursts
Science, University of Tokyo, Hongo 7-3-1, Bunkyo, Tokyo 113- (e.g.,Youngetal.2005).
0033,Japan 6 See, for example, Schlegel (1990); Filippenko (1997) for the
4 Department of Physics, Faculty of Science and Engineering, spectralclassificationofTypeIInandotherSNtypes.
KonanUniversity,Okamoto8-9-1,Kobe,Hyogo658-8501,Japan
2 Moriya & Tominaga
from the dense wind (e.g., Chugai 2001; Chugai et al. comparable to the shock propagation timescale of the
2004;Dessart et al.2009). Inaddition,SN2006gyshows entire wind, i.e.,
narrow P-Cygni profiles from a ≃ 100 km s−1 outflow Ro c
whichis alsopresumedto stem fromthe wind surround- κρdr ≃ (2)
Z v
ing the SN ejecta (e.g., Smith et al. 2010). However, xRo s
therecommonlyexistLSNewithoutnarrowspectrallines (see,e.g.,Weaver1976;Nakar & Sari2010,forthedetails
from the circumstellar wind (e.g., Quimby et al. 2007; of the shock breakout condition).
Miller et al. 2009; Gezari et al. 2009; Pastorello et al. However,the wind couldcontaina largeoptically thin
2010; Quimby et al. 2011; Chomiuk et al. 2011). Based regionevenif the entire windis optically thick. Figure1
on the LC shapes of LSNe, Chevalier & Irwin (2011) is a simplified illustration of the effect of w in the dense
show that, if the shock breakout takes place inside the wind. Twodensewindswiththedifferentwbutthesame
dense wind, the SN is observed as SN 2006gy-like Type Ro and xRo are comparedin the figure: (a) a wind with
IIn LSNe and, if it takes place at the surface, the SN is a constant density and (b) a wind with a steep density
observed as SN 2010gx-likenon-Type IIn LSNe. gradient. In both cases, the shock breakout is assumed
Inthepreviousworksontheshockbreakoutinadense to occurin the wind atthe same radiusr =xRo (x<1)
wind, the density slope of the wind has been assumed with the same forward shock velocity vs and thus the
to be ≃ −2 which is a consequence of the steady mass opticaldepthbetweenxRo andRo isexactlythesamein
loss of the progenitor. However, non-steady mass loss both cases (τb). One of the important differences in the
is actually observed in the massive stars which are sug- two winds are in the radius of the last scattering surface
gestedtobepossibleprogenitorsofLSNe,e.g.,η Carinae y1Ro, where τ =1 (see Figure 2 in the following for the
(e.g.,Davidson & Humphreys1997;Gal-Yam & Leonard value of y1). Even if the entire wind is optically thick
2009). In addition, historical X-ray SN observations are in both cases, the region where τ becomes larger than
suggested to indicate that mass loss from progenitors of 1 (r < y1Ro) is more concentrated to the central region
Type IIn SNe is inconsistent with the steady mass loss andthewindcontainslargeropticallythinregionoutside
(Dwarkadas & Gruszko 2012). Here, we investigate the whose size is ∆R=Ro−y1Ro in the case of large w.
influence of non-steady mass loss on the shock breakout Ifthe wind containsanextendedopticallythin region,
in the dense wind and show that the diversity in the Equation (2) is no longer an appropriate condition for
wind density slope caused by the non-steady mass loss the shock breakout because it postulates that the entire
can explain why some Type II LSNe show narrow spec- windatr ≤Roisopticallythickenoughforphotonstobe
tral components from the wind (Type IIn) while others diffusive. Theshockbreakoutconditionshouldbeevalu-
do not (Type IIL) even if both LSNe are illuminated by atedonlyattheopticallythickregionwherephotonsare
the shock interaction. Ourmodelis presentedinSection diffusive. Thus, the shock breakout should occur when
2 and it is applied to LSNe in Section 3. We discuss thediffusiontimescaleoftheopticallythickregionofthe
our results in Section 4. Conclusions are summarized in windiscomparabletotheshockpropagationtimescaleof
Section 5. the region. Hence, the shock breakout condition should
be set as
2. EFFECTOFDENSENON-STEADYWIND y1Ro c
τ ≡ κρdr ≃ , (3)
x
2.1. Wind Configuration ZxRo vs
wherecisthespeedoflightandτ =τ −1. InEquation
We consider a spherically symmetric dense wind ex- x b
(3), wepresumethatphotonsdiffuse inthe regionwhere
tending from r = R to r = R where r is radius. The
i o
density ρ is assumed to follow ρ(r)=Dr−w with a con- the optical depth evaluated from the wind surface ex-
ceeds1forsimplicity. I.e.,photonsareassumedtodiffuse
stant D. The opacity κ of the wind is assumed to be
at R < r < y R and freely stream at y R < r < R .
constant throughout this paper. Although our model is i 1 o 1 o o
In this sense, Equation (3) may also be interpreted as
applicable to any uniform compositions with a constant
Equation (2) combined with a kind of flux limited diffu-
κ, we mainly consider H-rich winds throughout this pa-
sion approximation. For the case of the shock breakout
per. We assume that a SN explosion has occurred in
at the surface of the wind (x ≃ 1), the conditions of
the dense wind and that the shock breakout occurs in
Equations (2) and (3) are similar.
the wind (e.g., Chevalier & Irwin 2011, see Section 1).
Since the observations of Type II LSNe display a con-
The radiusofthe forwardshockatthe time of the shock
stant shock velocity until some time in the declining
breakout is set to r = xR . Note that the entire wind
o
phase of their LCs (e.g., Smith et al. 2010), we assume
abovetheprogenitorstarisopticallythickbecauseofthe
thatv isconstant. Thisassumptioncanbe wrongifthe
assumption that the shock breakout occurs in the dense s
shockedwindmassbecomescomparabletotheSNejecta
wind. Wealsointroducearadiusy R wheretheoptical
τ o
mass. Equations (1) and (3) lead us to
depth evaluated from the wind surface becomes τ, i.e.,
(1−w)(1+c/vs) (w 6=1),
τ = Ro κρdr. (1) D≃κ(1−x1−w)R1o−w (4)
ZyτRo  1+c/vs (w =1).
κ(−lnx)
In addition, usingEquation (4), we can express yτ as
2.2. Shock Breakout Condition in Non-Steady Dense 1
Wind c/vs+τx1−w 1−w (w 6=1),
y ≃(cid:16) c/vs+τ (cid:17) (5)
Shock breakout in a wind had been simply defined to τ 
occur when the diffusion timescale of the entire wind is xc/vτs+τ (w =1).

Shock Breakout in Non-Steady Dense Wind 3
(a1) (b1)
τ = τ
b
τ = τ τ = 1
y b y
t t
si si τ = 1
n n
e e
d d
τ > 1
τ > 1 τ < 1
r r
∆R
xR y R R xR y R R
o 1 o o o 1 o o
e) (a2) e) (b2)
al al
c c
s s
e (log τb e (log τb
c c
a a
urf urf
s s
e e
h h
m t m t
o o
r 1 r 1
h f h f
pt pt
e e
d τ > 1 d
al al τ > 1 τ < 1
c c
pti τ pti r
o o ∆R
xR y R R xR y R R
o 1 o o o 1 o o
Fig. 1.— Illustration of the density and the optical depth distributions for the winds with different density slopes: (a) a flat density
slope and (b) a steep density slope. The corresponding (1) density structures and (2) optical depth distributions are shown. The shock
breakout is assumed to occur at the same r =xRo with x<1 where the opacity τ from Ro becomes τb. All the opacities shown in the
figureisevaluatedfromRo. Largeτ <1regionappearsintheouterpartofthewindin(b). SeeFigure4fortheconcreteexamplesofthe
distribution.
Figure 2 shows a plot of y as a function of x for several 2.3. Timescales of Photon Diffusion and Shock
1
w. Larger w leads to smaller y for a given x, as is Propagation in Dense Wind
1
discussed qualitatively above.
Here,weestimatethetimescaleofphotondiffusion(t )
d
Finally, the wind mass M is defined as
wind whichcharacterizestheLCsofLSNeandthetimescaleof
Mwind =Z Ro4πr2ρdr. (6) ftohretshheocfkorpwraorpdagsahtoiockn(ttos)gwohthicrhouregphretsheentesntthireetwiminedsc.atlde
Ri correspondstothetimescalefortheLCtoreachthepeak
Using Equation (4), we get
4π(1−w)(1+c/vs)(R3o−w−R3i−w) (w 6=1,3),
 κ(3−w)(1−x1−w)R1o−w
Mwind ≃2π(1+κc(/−vsl)n(Rx)2o−R2i) (w =1), (7)
8π(1κ+(xc/−v2s−)1ln)(RR−oo2/Ri) (w =3).
4 Moriya & Tominaga
1 1
y1 0.1 /tds 0.1
t
w=0 w=0
w=1 w=1
w=1.5 w=1.5
w=2 w=2
w=3 w=3
w=4 w=4
w=5 w=5
0.01 0.01
0.001 0.01 0.1 1 0.001 0.01 0.1 1
x x
Fig. 2.— Location of the last scattering surface in the wind. Fig. 3.— Ratio of the diffusion timescale (td) and the shock
The region r >y1Ro is optically thin and photons do not diffuse propagationtimescale(ts)asafunctionofthelocationoftheshock
intheregion. breakout(x).
(e.g., Arnett 1980, 1982). t can be expressed as
d
τ (R −xR −∆R) 2.4. Observational Features and Diversities of
td≃ x o o , (8) Interaction-Powered LSNe
c
τ (y R −xR ) Inthis section,we presentconsequencesfromthe vari-
x 1 o o
= , (9) ation in t /t which results from the variation in w. We
c d s
show that the two kinds of Type II LSNe, i.e., Type IIn
1
Ro c/vs+x1−w 1−w −x (w 6=1), LSNe (e.g., SN 2006gy,Smith et al. 2010) and Type IIL
 vs (cid:20)(cid:16) c/vs+1 (cid:17) (cid:21) LSNe (e.g., SN 2008es, Miller et al. 2009; Gezari et al.
= (10) 2009), are naturally expected from the shock breakout
Ro x1+c1/vs −x (w =1). inthedenseH-richwindwiththedifferentdensityslope.
t isdefinedasvtsh(cid:16)etimerequir(cid:17)edfortheforwardshockto byIfthweeinatsesruamcteiotnhaotftbhoethH-tryipchesdoefnsLeSwNiendaraenidlluSmNienjaetcetda
s
go through the entire wind including the optically thin and that the wind is so dense that the shock breakout
region after the shock breakout, occurs in the wind, the spectral evolution of LSNe is
Ro−xRo determined by td/ts.
ts = v . (11) If td/ts ≃1, the shock wave reaches the surface of the
s dense wind soonafter the LC has reachedthe peak with
Hence, we can derive the ratio of the two timescales: the timescale t . Since the entire wind is shocked just
d
1 aftertheLCpeak,nosignatureinspectrafromthewind
1 c/vs+x1−w 1−w −x (w 6=1), is observable after the LC peak. On the other hand,
ttds ≃11−−1xx(cid:20)(cid:16)x1+cc1//vvss+−1 x(cid:17) (cid:21) (w =1). (12) tpifheetadko/.ptsAtic<satlhl1y,erttehhiernemsrheaogicnikonuwnoasfhveothcckeoenwdtiimnnduaetesevretiaonlspafirntoeprtahtgehaewteiLniCdn
Figure3showst(cid:16)heratioasa(cid:17)functionofxwithseveral evenaftertheLCpeak,weexpecttoseenarrowP-Cygni
profilesfromtheunshockedwindevenaftertheLCpeak.
w, in which v is set to 10,000 km s−1 corresponding to
s To sum up, Type IIL LSNe can come from the dense
the observational value of SN 2008es (see Section 3.2).
wind with t /t ≃ 1 while Type IIn LSNe can result
Every line reaches t /t ≃ c/(v +c) = 0.97 at x ≃ 1. d s
d s s from the dense wind with t /t < 1. The ratio of the
Thiscorrespondstothecaseoftheshockbreakoutatthe d s
two timescales is determined by w.
surface of the wind (e.g., Chevalier & Irwin 2011).
The narrow Lorentzian line profiles which are sug-
When the shock breakout occurs inside the wind (x<
gestedtobecausedbythedensewind(e.g.,Chugai2001;
1),theratiot /t variesdependingonthedensityslopeof
d s Dessart et al. 2009) can appear before the LC peak de-
thewind. Foragivenx, t /t getssmallerasthedensity
d s pendingontheopticaldepthofthewind. Ifweapplythe
slope of the wind gets steeper (i.e., larger w). This is
model of Chugai (2001), the ratio U of the unscattered
because the last scattering surface of the wind locates
Hα line flux to the total Hα line flux of the Lorentzian
farther away from the surface as the density slope gets
profile is
steeper, i.e., y1 gets smaller as w gets larger for a given 1−e−τ
x (see Figure 2 for values of y1). In other words, the U ≃ . (13)
τ
optically thin region in the wind is spatially larger for
thewindwithsteeperdensitygradient. Thisistrueeven Forthecaseofflatdensityslopes,τ remainstoohighun-
ifthewindradiusisthesame. Wenoteagainthat,when tiltheforwardshockreachesthesurface(Figure1)andU
theshockbreakoutoccursinthewind,theforwardshock isexpectedtobeverysmallforalongtimebeforetheLC
reaches the last scattering surface (r = y R ) with the peak. On the other hand, if the density decline is steep,
1 o
diffusion timescale t , i.e., the shock locates at r =y R the optical depth decreases gradually with time and the
d 1 o
at the LC peak. suitable optical depth for the appearance of Lorentzian
Shock Breakout in Non-Steady Dense Wind 5
profiles would be realized for a long while. Therefore, Smith et al.(2010), we adoptthe followingparameters:
Lorentzian lines are expected to be observed well before
v ≃5,200 km s−1, (14)
the LC peak for Type IIn LSNe. s
The LC evolution of Type II LSNe is also consistent td≃70 days. (15)
with our models. In our models for both Type IIn and
v isconstrainedbytheevolutionoftheblackbodyradius
Type IIL LSNe, the forward shock stays in the dense s
andt isobtainedfromthe risingtime ofthe LC.As the
wind until the LC peak. As the wind with τ > 1 is d
narrow Hα P-Cygni profile is detected at 179 days7 and
shocked with the timescale of t , the dense wind adia-
d disappears at 209 days (Smith et al. 2010), we presume
batically cools down after the LC peak. Thus, the LCs
thatthe forwardshockhasgonethroughtheentire wind
ofTypeIILSNearesupposedtofollowtheshell-shocked
between 179 days and 209 days. We simply take the
diffusion model presented by Smith & McCray (2007).
central date (194 days) as the time when the forward
The shell-shocked diffusion model is based on the adia-
shock has gone through the entire wind, i.e., t ≃ 194
batic cooling of the shocked dense wind, which is basi- s
days. With t , t , and v , we can estimate x and R for
cally the same as the LC model suggested for Type II d s s o
a given w from Equations (10) and (11).
SNe by Arnett (1980), and the model had been already
If we adopt the model with w = 2, for example,
shown to be consistent with the declining phase of the
x and R are estimated to be 0.0095 and 8.8 × 1015
LC of SN 2006gy (Smith & McCray 2007). However, it o
cm, respectively. In this case, shock breakout occurs
should be noted that the model is too simplified and
at xR ≃ 3.2 × 1014 cm and the last scattering sur-
manyeffectswhichcannotbetreatedbytheformulation o
face is y R ≃ 3.2×1015 cm. The total wind mass is
of Arnett (1980) are ignoredin the model. For example, 1 o
the model assumes a constant opacity and it ignores the Mwind ≃ 0.81 M⊙ (c.f. Ri ≪ Ro) and is much smaller
thanthevalueestimatedfromtheshell-shockeddiffusion
presence of a recombination wave which is supposed to
be created in the diffusing shocked shell. Thus, we can- LC model (∼ 10 M⊙; Smith & McCray 2007). How-
ever,theshell-shockeddiffusionmodelisatoosimplified
not confirm that our model is consistent with the LCs
model and we cannot exclude this model just because of
of Type II LSNe just by the comparison with the shell-
the inconsistencywithit, asisnotedinthe previoussec-
shocked diffusion model and numerical LC modeling is
tion. Alternatively,ifweadoptasteeperdensitygradient
requiredto see if our models are consistentwith Type II
w=5,xandR areestimatedtobe0.17and1.05×1016
LSN LCs. o
cm, respectively, and thus xR ≃ 1.8 × 1015 cm and
o
3. COMPARISONWITHOBSERVATIONS y1Ro ≃4.9×1015 cm. y1Ro is consistentwiththe black-
body radius at the LC peak estimated from the obser-
In the previous section, we have shown that, if the
vations (6×1015 cm). If we assume that R ≃ 1015 cm,
shock breakout occurs inside a dense wind (x < 1), the i
the mass contained in the optically thick region (R <
ratio of the timescale of the photon diffusion to that of i
the shock propagation in the wind depends on the wind r < y1Ro) is 22 M⊙ in our w = 5 model. In this case,
density slope and thus the different density slope can the mass of the entire wind becomes Mwind ≃ 23 M⊙.
The left panel of Figure 4 is the optical depth and the
result in two kinds of Type II LSNe, i.e., Type IIn and
enclosed mass distributions. The existence of the un-
Type IIL LSNe. As an example, we apply our model
shocked wind may also account for the weakness of the
to two LSNe: Type IIn SN 2006gy and Type IIL SN
X-ray emissionof SN 2006gy(e.g., Woosley et al. 2007).
2008es. If we look into Type IIn LSN 2006gy and Type
The spectral evolution of SN 2006gy is also consis-
IILLSN2008es,oneimportantdifferenceistheexistence
tent with our model. Lorentzian H Balmer lines seen in
of narrow P-Cygni profiles in the spectra of SN 2006gy
the spectra of SN 2006gy are presumed to be caused by
after the LC peak. Based on the observational feature,
theopticallythickwind(e.g.,Chugai2001;Dessart et al.
we can guess that Type IIL LSN 2008es came from the
2009). For example, for the case w = 5, τ become ≃ 10
dense wind with t /t ≃ 1 while Type IIn LSN 2006gy
d s at around 3 × 1015 cm (Figure 4). This is consistent
resulted from the dense wind with t /t < 1. We apply
d s with τ ≃ 15 at 36 days which is estimated from the ob-
those models to the two LSNe. In this section, κ is set
to 0.34 cm2 g−1. served ratio U derived from Hα (Smith et al. 2010). In
our model, the Lorentzian line profiles are expected to
3.1. Type IIn LSNe (SN 2006gy) be observedbefore the forwardshock wavegoes through
the opticallythick regionofthe wind, i.e.,before t ,and
SN 2006gy is extensively studied by, e.g., Ofek et al. d
thus, the Lorentzian spectra should disappear after the
(2007); Smith et al. (2007); Smith & McCray
LC peak. This is also consistent with the spectra of SN
(2007); Woosley et al. (2007); Smith et al. (2008);
2006gy (Smith et al. 2010).
Agnoletto et al. (2009); Kawabata et al. (2009);
Narrow Hα P-Cygni profiles can be created at the op-
Smith et al. (2010); Miller et al. (2010). It is clas-
tically thin wind above the last scattering surface of the
sified as Type IIn and the luminosity reaches ∼ −22
continuum photons (y R < r < R ) because of the
mag in the R band (Smith et al. 2007). The detailed 1 o o
larger line opacities. Whether the narrow Hα P-Cygni
spectral evolution is summarized in Smith et al. (2010).
profiles can be formed or not depends also on the ion-
The narrow P-Cygni Hα lines with the absorption
ization level of the wind and thus the spectral modeling
minimum of ≃ 100 km s−1 are considered to come from
must be performed to see whether the narrow Hα pro-
the wind surrounding the progenitor of SN 2006gy. As
files are actually synthesized in the unshocked wind in
SN 2006gy shows narrow P-Cygni profiles after the
our model.
maximum luminosity, an unshocked wind is supposed to
remainafterthemaximum. Thus,modelswithtd/ts <1 7 Days since the explosion. The explosion date is set to be the
and y1 < 1 are preferred. Based on the observations of sameasinSmithetal.(2010).
6 Moriya & Tominaga
1000 1000
w=2 optical depth w=0 optical depth
Msun) 100 w=ee5nn occpllootissceeaddl dmmeaapssthss Msun) 100 w=ee1nn occpllootissceeaddl dmmeaapssthss
s ( s (
s s
a 10 a 10
m m
d d
e e
s s
o 1 o 1
cl cl
n n
e e
pth, 0.1 pth, 0.1
e e
d d
al al
ptic 0.01 ptic 0.01
o o
0.001 0.001
0 2 4 6 8 10 0 0.5 1 1.5 2
radius (1015 cm) radius (1015 cm)
Fig. 4.— Left: Optical depth andenclosed massdistributionofthe models w=2andw=5appliedforLSN 2006gy. Right: Sameas
theleftpanelbutforthemodelsofLSN2008es (w=0,1).
3.2. Type IIL LSNe (SN 2008es) the actual spectral evolution expected from the density
profile of our model.
Here, we apply our model to SN 2008es which is one
of the best observed Type IIL LSNe (Miller et al. 2009;
Gezari et al. 2009). Although SN 2008es does not show 4. DISCUSSION
any features of the wind in the spectra, we assume that We have shown that the difference in density slopes of
it is also illuminated by the interaction based on their dense winds can make a variety of LSNe after the shock
brightness, rapid decline of the LC, and blue spectra. breakoutin the dense wind. Flatdensity slopes resultin
In our model, the lack of the wind features after the LC Type IIL LSNe and steep density slopes result in Type
peakcanbeexplainedbythesmalldifferenceintd andts IInLSNe. Amodelwiththeshockbreakoutinthedense
because the entire wind is shockedby the forwardshock wind is recently applied to LSNe by Chevalier & Irwin
just after the LC peak. In other words, y1 should be (2011). Their idea for SN 2006gy is basically the same
close to 1. This can be achieved by the wind slope with as our suggestion for Type IIn LSNe: the shock break-
w <∼1 for the case of x<1 (Figure 2). out inside the dense wind (x < 1). However, as they
The following parameters are estimated from the ob- onlyconsiderthe casew=2,non-TypeIInLSNe arere-
servations: latedto the shock breakoutat the surface (x≃1) of the
v ≃10,000 km s−1, (16) densewind. Inthispaper,weshowthattheshockbreak-
s
out does not necessarily occur at the surface to explain
t ≃t ≃23 days. (17)
d s non-TypeIInLSNe,especiallyTypeIILLSNe,ifthepro-
If we adopt the model of w = 0, y is close to 1 and genitorstarexperiencesnon-steadymassloss. Currently,
1
R ≃ v t ≃ y R ≃ 2×1015 cm. y R is consistent both models can explain Type IIL LSNe. For the case
o s s 1 o 1 o
with the blackbody radius at the LC peak estimated ofthe shock breakoutinside the dense wind (x<1), the
from the observations (3×1015 cm). Assuming x = 0.1 Lorentzian spectral lines might be able to be observed
and Ri ≪ Ro, the wind mass is Mwind ≃ 0.85 M⊙. just before the LC peak when a suitable opticaldepth is
M does not vary so much on x unless it is close realized. The detailed spectralobservations near the LC
wind
to 1. The model with w = 1 also gives y ≃ 1 with peak can distinguish the two scenarios. Note that we do
1
Mwind ≃0.50M⊙. TherightpanelofFigure4showsthe not exclude the possiblity that steep density slopes can
opticaldepthandmassdistributions. Miller et al.(2009) become Type IIL LSNe. If the density is high enough
estimateMwind ≃5M⊙ basedontheshell-shockeddiffu- up to the surface, steep dense winds can end up with
sion LC model of Smith & McCray (2007). Gezari et al. Type IIL LSNe, i.e., y becomes close to 1 at x = 1 no
1
(2009) obtained Mwind ≃ 0.2 M⊙ based on the peak lu- matter what the density decline is. This configuration
minosity. M of both w = 0 and w = 1 models are correspondstothe shockbreakoutatthe surfaceandex-
wind
almost consistent with those estimates. actlythesameaswhatissuggestedbyChevalier & Irwin
Lack of the Lorentzian H Balmer lines before the LC (2011).
peak is another important difference between Type IIL An important difference between our treatment of the
LSN 2008es and Type IIn LSN 2006gy. For the case of shockbreakoutinadensewindfromthoseoftheprevious
the flat density slope, the wind optical depth remains to worksisthatweadoptEquation(3)fortheshockbreak-
be very large until the forward shock reaches the wind outconditioninsteadofEquation(2). IfweuseEquation
surface (Figure 4). Hence, narrow H lines, even if they (2), the differencescausedbythe differentdensityslopes
are emitted from the dense region of the wind, are scat- are missed. For example, with Equation (2), we do not
tered by the dense wind with a large optical depth for a expect to see narrow spectral lines from the dense wind
long while. Then, U will be very small until the forward after the LC peak of all LSNe with shock breakout in
shockreachesthewindsurfaceandtheLorentzianHlines the dense wind and they are all expected to be observed
will be very weak. Thus, it is likely that the Lorentzian as Type IIL SNe. This is because the forward shock is
H lines are missed. Detailed modeling is required to see regarded to go through the entire wind at the LC peak
Shock Breakout in Non-Steady Dense Wind 7
in Equation (2). in this paper, the understanding of other Type IIL
The different density slope in the dense wind is nat- SNe, i.e., less-luminous Type IIL SNe, is also lacking.
urally expected to be caused by the non-steady mass Currently, there are many models for Type IIn SNe
lossof the progenitorjust before the explosion8. IfType but only a few models exist for Type IIL SNe (e.g.,
IIL LSNe are actually caused by the shock breakout in Blinnikov & Bartunov 1993; Swartz et al. 1991). Al-
the wind with t /t ≃ 1, it indicates that non-steady thoughthediversityinthewindconditionmayberelated
d s
mass loss producing the flat dense wind (w <∼ 1) may tootherTypeIILSNe,therecanbeotherimportant,but
take place just before the explosions of some massive currently ignored, ingredients for the full understanding
stars. In addition, our model for Type IIn LSN 2006gy of Type IIL SNe.
prefers w 6= 2 because M of the w = 2 model may
wind
be too small to account for the LC of SN 2006gy af-
5. CONCLUSIONS
ter the peak. This also supports the existence of the
non-steady mass loss at the pre-SN stage of the massive Weinvestigatetheeffectofthenon-steadymasslosson
stars. Dwarkadas & Gruszko (2012) show that the den- the shock breakout in the dense wind. The non-steady
sityslopeofthe windestimatedfromX-rayobservations mass loss varies the density slope of the wind (ρ∝r−w)
ofTypeIInSNeisinconsistentwithρ∝r−2. Theyshow and the density slope alters the ratio of the diffusion
that Type IIn SNe do not usually come from the steady timescale in the optically thick wind (td) and the shock
wind with ρ ∝ r−2. X-ray luminous Type IIn SNe are propagation timescale of the entire wind (ts) after the
presumed to be originated from relatively dense winds shockbreakoutinthe wind. Bothtimescales are compa-
with high mass-loss rates. Although the wind densities rable(td/ts ≃1)forw <∼ 1andtd/ts becomes smalleras
oftheseSNearenothighenoughtobeLSNe,itishighly w gets larger. This is because the last scattering surface
possiblethatthedensewindsfromhighermass-lossrates of the dense wind locates farther inside from the wind
also result in flat or steep density slopes. The presence surface for the wind with the steeper density gradient
of the two kinds of slopes can end up with two different (Figure 2). The difference can only be obtained by the
kinds of Type II LSNe. careful treatment of the shock breakoutcondition in the
So far, we just consider a single slope for the dense dense wind (Section 2; Equation (3)).
wind. One essential difference between Type IIn and If the two timescales are comparable (td/ts ≃ 1), the
Type IIL LSNe is the existence of the spatially-large forwardshockgoesthroughtheentirewindjustafterthe
optically-thinregioninthewindofTypeIInLSNewhich LC reaches the peak with the timescale td. In this case,
can make narrow P-Cygni profiles. Although we show no signature on the spectra from the wind is expected
that large w can make such spatially-large optically- to be observed especially after the LC peak because the
thin region with the optically thick region inside, the entirewindisalreadyshockedaftertheLCpeak. Onthe
similar condition can also be achieved by assuming the otherhand,ifthetwotimescalesaredifferent(td/ts <1),
twocomponents inthe wind, i.e., optically thick(inside) the shock continues to propagate in the wind after the
and thin (outside) regions with any density slopes. The LC peak and the unshocked wind remains after the LC
two-componentwind configurationis suggestedfor, e.g., peak. Thus, narrow P-Cygni profiles from the wind are
Type IIn SN 1998S (Chugai 2001). Both models can expected to be observed even after the LC peak. The
explainType IIn LSNe. In either case, the P-Cygnipro- formercasecorrespondstoTypeIILLSNeandthelatter
files can be observed not only after but also before the to Type IIn LSNe. The difference in the density slope
LC peak. Currently, there are no spectral observations can also account for the lack of the Lorentzian emission
of Type IIn LSNe before the LC peak with resolutions profiles in Type IIL LSNe.
sufficient to resolve the narrow P-Cygni profile and the Our results imply that the luminosity of Type IIL
highresolutionspectroscopicobservationsbefore the LC LSNe can be explained in the context of the shock in-
peakareimportanttorevealthewindsurroundingLSNe. teraction between SN ejecta and the dense wind even if
Our model cannot be simply extended to the spec- theydonotshowthesignatureofthewindintheirspec-
tral evolution of other kinds of LSNe without H lines. tra. We propose that the difference between Type IIn
Especially, Type Ic LSNe with fast LC decline show, and Type IIL LSNe can stem from the density slope of
e.g., Si and O lines which are not seen in Types II the dense wind which results from the non-steady mass
LSNe (e.g., Quimby et al. 2011; Pastorello et al. 2010; loss of their progenitors.
Chomiuk et al. 2011). Although it is possible that the
shock breakout in a dense wind also occurs in Type Ic
LSNe as is suggested by Chevalier & Irwin (2011), it We thank Sergei I. Blinnikov for the comments on the
seems to be difficult to attribute the difference between manuscript and the continuous discussion regarding to
Type Ic LSNe and Type II LSNe only to the density radiation hydrodynamics. We also thank Keiichi Maeda
slope of the dense wind. For example, the composition for discussion. T.J.M. is supported by the Japan So-
of the wind is presumed to be quite different between ciety for the Promotion of Science Research Fellowship
Type Ic and Type II LSNe. If the shock breakout in the for Young Scientists. This research is also supported by
dense wind is alsotaking place in Type Ic LSNe, narrow World Premier International Research Center Initiative,
spectral lines from the materials other than H may be MEXT,JapanandbytheGrant-in-AidforScientificRe-
observed. searchofthe JapanSocietyforthe PromotionofScience
While we focus on the origin of Type IIL LSNe (23740157,23224004).
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