Sec$on6.超新星からの電磁波放射(1)理論

6.1超新星の熱源

6.2超新星の光度曲線

• 2/13(月)2,3,4限(3回)• 全体の概論

• 星の構造と進化

• 2/14(火)2,3限(2回)+談話会• 超新星爆発のメカニズム

• 元素の起源

• 談話会:重力波天体からの電磁波放射

• 2/15(水)2,3,4限(3回)• 超新星からの電磁波放射

• 超新星の観測

• 突発天体探査

予定

成績 • 出席、質問

• レポート資料 h7p://th.nao.ac.jp/MEMBER/tanaka/tohoku2017

•物理学を使って宇宙の爆発天体に挑む•星はなぜ爆発するのかを理解する• 星の構造と星の進化（復習）• 超新星の爆発メカニズム

•超新星爆発の観測量を理解する• 電磁波放射のメカニズム• 観測量から物理を引き出す

•宇宙の元素の起源を理解する•突発天体天文学を味わう

恒星物理学特論II「超新星爆発の理論と観測」

Sec$on6.超新星からの電磁波放射(1)理論

6.1超新星の熱源

6.2超新星の光度曲線

超新星：４つのタイプ

3000 4000 5000 6000 7000 8000

Rel

ativ

e flu

x +

cons

t

Rest wavelength (Å)波長（オングストローム）

ケイ素

水素

ヘリウム

II型

I型

Ia型

Ib型

Ic型

超新星：４つのタイプ水素

ケイ素

ヘリウム

II型

I型 なし あり

あり

Ia型

Ib型 Ic型あり

なし

なし「核爆発型」超新星

「重力崩壊型」超新星

「重力崩壊型」超新星「重力崩壊型」超新星

超新星の光度曲線

-20

-18

-16

-14

-12

-10 0 50 100 150 200 250 300 350

Abso

lute

mag

nitu

de

Days after the explosion

Type IaType Ib and Ic

Type II

I型-ピークがある

-Ia型>Ib,Ic型

II型-平坦な部分

（plateau）がある

1043ergs-1

1042

1041

II型超新星のバラエティ(1)The Astrophysical Journal Letters, 756:L30 (6pp), 2012 September 10 Arcavi et al.

0 20 40 60 80 100 120 140

0

0.5

1

1.5

2

SN2005cs

SN2009krSN2011dhSN1993J

Days Since Explosion (estimated)

Shi

fted

R−B

and

Mag

nitu

de

SN1999em

SN Ib/c Template

0 20 40 60 80 100 120 140

−17.5

−17

−16.5

−16

−15.5

−15

−14.5

SN2005au

SN2005bw

SN2005aa SN2004et

SN2004er

SN2004du

Days Since Explosion (estimated)

Abs

olut

e R

−Ban

d M

agni

tude

SN1999em

SN2005cs

SN2005aySN2004fx

Figure 1. Top panel: R-band light curves of 15 Type II SNe from CCCP (excluding the four events presented in Figure 4), normalized in peak magnitude (SN2004fxdata taken from Hamuy et al. 2006; SN2005ay data taken from Gal-Yam et al. 2008a; SN2005cs data taken from Pastorello et al. 2009). A clear subdivision into threedistinct subtypes is apparent: plateau, slowly declining, and rapidly declining SNe (the latter consisting only of SNe IIb). Reference SNe are shown for comparison(SN1999em from Leonard et al. 2002; SN2009kr from Fraser et al. 2010, found to be a member of the IIL subclass as claimed by Elias-Rosa et al. 2010; SN1993Jfrom Richmond et al. 1994; SN2011dh from Arcavi et al. 2011). We also overplot the SN Ib/c template derived by Drout et al. (2011). The data have been interpolatedwith spline fits (except for SN2005by, where a polynomial fit provided a better trace to the data). The shaded regions denote the average light curve ±2σ of eachsubclass. The maximal 7 day uncertainty in determining the explosion times is illustrated by the interval in the top right corner. Bottom panel: R-band light curves of9 Type IIP SNe from CCCP with respect to their estimated explosion time (except for SN2005au and SN2005bw, marked by dashed lines, for which the explosion dateis not known to good accuracy). The light curve of SN2004fx is taken from Hamuy et al. (2006), that of SN2005ay from Gal-Yam et al. (2008a), and that of SN2005csfrom Pastorello et al. (2009). SN1999em (Leonard et al. 2002) is shown for comparison. A spread in plateau luminosities is apparent while plateau lengths seem toconverge around 100 days. Spline fits were applied to the data.(A color version of this figure is available in the online journal.)

continuum, we find that the light curves group into three distinctsubclasses: plateau, slowly declining (1–2 mag/100 days), andinitially rapidly declining (5–6 mag/100 days) events (see alsoTable 1). We note that the three rapidly declining events areall Type IIb and that they display similar light curve shapesto those of Type Ib/c SNe (Drout et al. 2011). We perform aKolmogorov–Smirnov test and find that the probability that themeasured ∆M15R values for the rapid- and slow-decline groupsare drawn from a single underlying distribution is 2%.

Three events (SN2004ek, SN2005ci, and SN2005dp;Figure 4) display prolonged rising periods in their light curves.They do not show signs of interaction in their spectra andmay be explosions of compact blue supergiant progenitors(Kleiser et al. 2011; Pastorello et al. 2012), as demonstrated

directly in the case of SN 1987A (see Arnett et al. 1989 fora review).

Finally, one event (SN2004em; Figure 4) displays a verypeculiar photometric behavior. For the first few weeks it issimilar to a Type IIP SN, while around day 25 it suddenlychanges behavior to resemble an SN 1987A-like event.

The full photometric data set is available online throughWISeREP15 (Yaron & Gal-Yam 2012).

3.1. Declining SNe

Aside from establishing a different rate of decline for SNeIIb compared to SNe IIL, Figure 1 (top panel) suggests that the

15 http://www.weizmann.ac.il/astrophysics/wiserep

3

プラトー

単調に暗くなるIb,Ic型

IIP型(plateau):平坦な部分がある

IIL型(linear):単調に暗くなる

Arcavi+11

II型超新星のバラエティ(2)

1993ApJ...415L.103F

Ib型

II型 SN1993J-最初はII型

-時間がたつにつれて

Hが弱く、Heが強くなる

=>Ib型に似る

IIb型

Filippenko+93

II型超新星のバラエティ(2)

IIb型

-プラトーはない

-Ibc型に似ている

-最初明るいものも

VanDyk+13

The Astronomical Journal, 147:37 (9pp), 2014 February Van Dyk et al.

Figure 2. BVRIzJH light curves of SN 2013df from KAIT (solid points) andRATIR (open points; with r and i converted to R and I, respectively, followinghttp://www.sdss.org/dr7/algorithms/sdssUBVRITransform.html#Lupton2005).The observed curves have been offset from each other for clarity. Shown forcomparison are the BVRIJH light curves of SN 1993J (Richmond et al. 1994,1996; Matthews et al. 2002; dashed lines) and of SN 2011dh (Arcavi et al.2011; Van Dyk et al. 2013b; Ergon et al. 2013; dot–dashed lines), and thez-band light curve of SN 2008ax (Pastorello et al. 2008, solid line), all adjustedin time and relative brightness. The estimated time t = 0 of the explosion isindicated.(A color version of this figure is available in the online journal.)

each band. Consequently, the photometry presented here shouldbe considered preliminary; however, the SN is far from themain light from the host galaxy, so results including templatesubtraction prior to photometry might not substantially differfrom what we present here.

2.2. Early-time Spectroscopy

We have obtained a number of spectra of the SN at earlytimes, using the Kast spectrograph (Miller & Stone 1993) on theLick Observatory 3 m Shane telescope and the DEep ImagingMulti-Object Spectrograph (DEIMOS; Faber et al. 2003) on theKeck-II 10 m telescope. Ultraviolet (UV) spectroscopy has alsobeen obtained using the Hubble Space Telescope (HST) SpaceTelescope Imaging Spectrograph as part of program GO-13030(PI: A. V. Filippenko). The results of these HST observationswill be presented in a future paper, together with the bulk ofthe ground-based optical spectra. However, here we present andanalyze a representative spectrum obtained on 2013 July 11.2with DEIMOS using the 600 l mm−1 grating.

2.3. HST Imaging

The region of the host galaxy containing the SN site wasobserved with the HST Wide Field Planetary Camera 2 on 1999April 29 by program GO-8400 (PI: K. Noll), as part of theHubble Heritage Project. The bands used were F439W (twoindividual images with 40 s exposure times and two with 1000 s),F555W (four 400 s exposures), F606W (two 60 s exposures),and F814W (two 40 s and four 400 s exposures). The F555W andF814W data were combined with images obtained by programsGO-5397 and GO-5972 at an earlier time for the rest of the

Figure 3. Absolute V light curve for SN 2013df (solid points), compared to thoseat V for SNe 1993J (dashed line; colored red in the online version), 2008ax (solidline; colored green in the online version), and 2011dh (dot–dashed line; coloredblue in the online version) shown in Figure 2. All of the curves are displayedrelative to the day of V maximum; see the text.(A color version of this figure is available in the online journal.)

galaxy, and drizzled into mosaics in each band at the scale0.′′05 pix−1 by Holwerda et al. (2005).

We have also observed the SN on 2013 July 15 with HST usingthe Wide Field Camera 3 (WFC3) UVIS channel in F555W, aspart of our Target of Opportunity program GO-12888 (PI: S.Van Dyk). The observations consisted of 28 exposures of 5 s;the short exposure time was intended to avoid saturation in eachframe by the bright SN.

3. ANALYSIS

3.1. Light Curves

In Figure 2 we display the early-time KAIT and RATIR lightcurves in all bands for SN 2013df. We also include the veryearly V measurement from June 11.202 by Stan Howerton.14

We compare these curves with those at BVRIJH for SN 1993J(Richmond et al. 1994, 1996; Matthews et al. 2002) and forSN 2011dh (Arcavi et al. 2011; Van Dyk et al. 2013b; Ergon et al.2013). We also compare the z-band light curve of SN 2008ax(Pastorello et al. 2008). The curves for the comparison SNe wereadjusted in time and relative brightness to match the curves ofSN 2013df, particularly at the secondary maximum in eachband. Clearly, from its overall photometric similarity with theother SNe, SN 2013df appears to be an SN IIb; see Arcavi et al.(2012) for a general description of SN IIb light-curve shapes.What is most notable from the comparison is that the post-shock-breakout cooling of SN 2013df occurred at a later epoch in allbands, relative to that of SN 1993J. The post-breakout declineof SN 2011dh occurred at an even earlier relative epoch (e.g.,Arcavi et al. 2011; Bersten et al. 2012).

We show in Figure 3 the absolute V-band light curve ofSN 2013df, relative to those of SNe 1993J, 2008ax, and 2011dh.

14 http://www.flickr.com/photos/watchingthesky/9035874997

3

II型超新星のバラエティ(3)

0

1

2

3

4

5

4000 5000 6000 7000 8000 9000

Flux

Wavelength (A)

水素

水素の細い輝線

=>IIn型(narrow)

IIP型

The Astronomical Journal, 144:131 (13pp), 2012 November Zhang et al.

Figure 3. U − B, B − V, V − R, and V − I color curves of SN 2010jl compared with those of Type IIn SNe 1997cy (Germany et al. 2000), 1998S (Fassia et al. 2000),and 2006tf (Smith et al. 2008). All of the comparison SNe have been dereddened for the reddening in the Milky Way. The dotted lines are the least-squares fit to thecolors of SN 2010jl.

Figure 4. Absolute R-band light curve of SN 2010jl compared with other notableType IIn SNe 1997cy (Germany et al. 2000), 1998S (Fassia et al. 2000), 2006gy(Smith et al. 2007), and 2006tf (Smith et al. 2008); Type Ia SN 2005cf (Wanget al. 2009); and Type IIP SN 1999em (Leonard et al. 2002).

3.3. Absolute Magnitudes and Bolometric Light Curves

In Figure 4, we compare the absolute R-band light curves ofSN 2010jl with other SN samples. The pre-maximum data pointsare extrapolated through the V-band light curves published byStoll et al. (2011) and the linear V −R color curve as presentedin Figure 3. Overplotted are the light curves of a typical TypeIa SN 2005cf (Wang et al. 2009) and Type IIP SN 1999em(Leonard et al. 2002). The Hubble constant H0 is taken to be72 km s−1 Mpc−1 (Freedman et al. 2001) in deriving the absolutemagnitudes for these objects. Days of the light curves are givenrelative to the estimated phase of the maximum brightness. Onenotable feature of this plot is the heterogeneous light curves ofthe SNe IIn. Compared with Type Ia and IIP SNe, the SN IInsamples are very luminous and their high luminosity lasts for along time after the peak. A recent study by Kiewe et al. (2012)suggests that the rise time for those luminous core-collapse canbe very long (>20 days). As seen from the plot, SN 2006gycould have a rise time longer than 60 days, which is the mostluminous SNe IIn ever recorded in recent years. Although lessextreme relative to SN 2006gy, SN 2010jl clearly shows a highluminosity with a long duration. It is interesting to note thatthe light curve of SN 2010jl is similar to that of SN 2006tf andSN 1997cy at early times, but remarkable difference betweenthem emerges at late times. By t ∼ 90 days from the maximumlight, the light curve of SN 2010jl becomes almost flat, unlikeSN 1998S or SN 2006tf, which declined in R at a faster paceat a similar phase. By t ! 200 days, SN 2010jl becomes themost luminous SN IIn of our samples due to its remarkablyslow evolution at late times. Such a long-duration emission athigh luminosity demands a large amount of emitting materials.

6

II型超新星のバラエティ(3)

IIn型

-IIP型よりも明るい

ものが多い

-明るい時期が長い

ものも

(ゆっくりと暗くなる)

-多様性が大きい

Zhang+12

IIn型

IIn型

IIP

IaIIn型

様々なタイプの超新星水素

ケイ素

ヘリウム

II型

I型 なし あり

あり

Ia型

Ib型 Ic型あり

なし

なし IIP型IIL型IIb型

IIn型

「重力崩壊型」超新星

細い輝線

光度曲線の形

Ibへ進化

「核爆発型」超新星

様々な質量 => 様々な性質~ チャンドラセカール限界

各タイプの割合(重力崩壊型)

Shivvers+16

20 Shivvers et al.

IIP

IIL

IIn

Ibc-pec

Ic

Ib

IIb

PrevLous

II

II-87A

IInIc-BL

Ic

Ib

IIb

7hLs Work

Figure 21. Relative fractions of core-collapse SN types within a volume-limited sample using the original classifications from L11(left) compared to the updated classifications presented here (right). Subtypes are color-coded along with the other members oftheir major type, and the “peculiar” subtype labels are grouped with the appropriate “normal” events (except for the SN Ibc-pecgroup of L11, which included both SNe Ic-BL and Ca-Rich transients). All fractions are listed in Table 3 and any objects listedin Table 1 with more than one possible classification are given a fractional weight in each class, as described in §5.

Ic-BL with the SNe Ic, which only a↵ects these rates bya small amount). L11 calculate a ratio of SNe Ic/SNe Ib= 54.2± 9.8%/21.2+8.4

�7.7% = 2.6± 1.1, while Smith et al.(2011a, excluding SNe from highly inclined galaxies) cal-culated SNe Ic/Ib = 14.9+4.2

�3.8%/7.1+3.1�2.6% = 2.1±1.1 (in

all cases the errors listed are statistical only, and werederived from Monte Carlo simulations similar to thosedescribed above).We now calculate a ratio of normal SNe Ic to normal

SNe Ib of 0.6±0.3 and, if we include the SNe Ic-BL andother peculiar subtypes with the normal SNe Ib and Ic,we find a (SN Ic+Ic-BL+Ic-pec)/SN Ib ratio of 0.8±0.4.This update to the population fractions is driven by

our reclassifications of seven stripped-envelope events.First, we relabeled four events from a Ic subtype toa Ib or IIb subtype (SNe 2001M, 2001ci, 2004C, and2005lr). In each of these cases, the need for reclassifi-cation is easily understood: three of these events hadspectra severely reddened by host-galaxy dust and wereoriginally classified by eye without the aid of SNID, andone showed only weak He I lines in the spectrum (SN2001M). Second, we created the SN Ib/Ic (unsure) cate-gory, which includes an additional two events that showweak He I lines with some uncertainty on their iden-tification (SNe 2002jz and 2004cc) and one event withonly sparse and noisy observations (SN 2006eg). If weassume that all of the SNe in the latter category deservethe Ic label, our Monte Carlo trials indicate that normalSNe Ib and SNe Ic (excluding peculiar subtypes) occurat similar rates: SNe Ic/Ib = 0.9± 0.5. If we rather as-sume that they are all SNe Ib, we get a ratio of normalSNe Ic/Ib = 0.5± 0.3.

These results have implications for our understand-ing of the progenitors of stripped-envelope SNe, as wediscuss below, and may a↵ect other works that use theLOSS rates as input (e.g., Foley & Mandel 2013).

6. PROGENITOR CONSTRAINTS ONSTRIPPED-ENVELOPE SNE

Wolf-Rayet (WR) stars have long been discussed asGalactic analogues of SN Ib/c progenitors (e.g., Meynet& Maeder 2003; Crowther 2007), though many authorshave argued that binary stars which undergo mass lossvia Roche-lobe overflow before core collapse are likelythe most common SN Ib/c progenitor (e.g., Podsiad-lowski et al. 1992; Smartt 2009; Smith et al. 2011a; El-dridge et al. 2013). Regardless, stellar modeling e↵ortshave found it di�cult to match the SN Ic/Ib fractionspresented by L11 and Smith et al. (2011a), which de-mand more SN Ic progenitors (stars that lose both theirhydrogen envelope and a large fraction of their heliumenvelopes) than Ib progenitors (stars that lose just thehydrogen; e.g., Georgy et al. 2009; Yoon et al. 2010;Yoon 2015), though some success has been achievedby invoking rapid rotation of the progenitors (e.g., Caoet al. 2013; Groh et al. 2013b).To address this putative issue, some authors have pro-

posed that some amount of helium in SNe Ic may be“hidden” and remain neutral if the 56Ni (which providesnonthermal excitations via radioactive decay) is insu�-ciently mixed with the helium-rich ejecta (e.g., Dessartet al. 2011, 2012). Comparisons to observation do notfind evidence for large amounts of hidden helium in SNeIc, however, and it is unclear from the models how muchhelium could truly be hidden in this way (e.g., Hachinger

様々なタイプの超新星

「明るさ」と「時間スケール」は何が決めているのか？

Sec$on6.1Sec$on6.2

レポート課題456Niの放射性崩壊で得られる光度（ニュートリノを除く）が以下のように書けることを示せ

=3

L � (6.5� 1042e�td/8.8 + 1.5� 1042e�td/111)�

M56Ni

0.1M�

�erg s�1

19 94

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No. 2, 1994 PROPERTIES OF Ni ^ Co -> Fe DECAY

The full scheme of Huo et al. ( 1987) gives, per 56Co decay:

529

Total energy emitted via gamma photons: Q7 = 3.61 MeV ,

Total kinetic energy of positrons: = 0.12 MeV ,

Total energy carried away by neutrinos: Qve = 0.84 MeV .

The simplified scheme results in about a 3% lower value, Qy = 3.49 MeV. One could also include in the simplified scheme the transitions from level E2l = 4.298 MeV (4+) (the intensity of56Co decay into this level is equal to (3.7)) to level/ = 1 followed by the emission of 3.45 MeV gammaphotons with intensity (0.9), as well as those to level 8,1.175 MeV (intensity 2.3). In such a case, Qy would be equal to 3.55 MeV, that is, only 1.5% less than the strict value.

The number of positrons, dn+, per unit time emitted with kinetic energy w within an interval [w, w + dw] can be represented as follows:

, AT In 2 dw (3)

4>^(£+ 1)2(2.8552 — e)2G{w) , (4)

where Vq, is the number of 56Co atoms in the system, e = w/0.511, and w is in MeV. The function G( w) was tabulated by Rose et al. ( 1955). Figure 3 shows the positron and neutrino spectra for the ß+ transition to level E2 = 2.085 MeV for which log^ = 8.625. Here t = t+= r1/2/0.181 = 3.681 X 107 s. Since the neutrino energy wv = 1.459 - w, one can describe the neutrino spectrum by equations ( 3 ) and (4) when substituting <£( 1.459 - wj for 4>( w). For the dashed curve in Figure 3, w means the neutrino energy w,, while $( w) stands for $(1.459 - wv).

The total number of positrons emitted per unit time, dN+/dt, is given by

dN+

dt pi.459

Jo dn+ dw

, In 2 . . dw = — NCo(t). (5)

The energies and gamma photon number per 100 decays are compiled in Table 1.

3. THE KINETICS OF Ni ^ Co ^ Fe DECAY The numbers of 56Ni, 56Co, and 56Fe nuclides are controlled by a simple set of differential equations:

dNm _ _ Nm

dt rNi

dNCo _ NNi _ NCo

dt rNi tqq

dNFe _ NCo

dt tCo ’

with the initial conditions

Aní — Anío, Nqo — 0, VFe — 0, at t 0 .

Solving equations (6)-(9), one gets

ANi = ANioe_(//TNi) ,

Nco = Nmo ^ {e~^ - e-*'/�)), TCo rNi

Ap#. — ANin( 1 F rNi ?Co

TCo rNi TCo rNi c>_(i/TCo)

(6)

(7)

(8)

(9)

(10)

(ID

(12)

© American Astronomical Society • Provided by the NASA Astrophysics Data System

(参考)崩壊の式 崩壊当たりのエネルギー

19 94

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. . .9

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528 NADYOZHIN Vol. 92

The total energies released per 56Ni decay, as calculated from the full scheme of Huo et al. ( 1987), are

Total energy emitted via gamma photons: = 1.75 MeV , Total energy carried away by neutrinos: Qve = 0.41 MeV .

The simplified scheme presented in Figure 1 gives Qy = 1.72 MeV, i.e., ~2% less than the exact value.

2. A SIMPLIFIED SCHEME OF 56Co DECAY Radioactive 56Co, the product of 56Ni decay, transforms into a stable isotope 56Fe either by means of electron capture (EC) (81

cases out of 100) or via positron decay (ß+) ( 19 cases out of 100):

Í 56Fe + 7 + ^ (81 cases), 56Co=> I (2) [ 56Fe + e+ + y + ve (19 cases) .

The half-life and lifetime of 56Co are Tx/2 = 77.12 days and tq, = T1/2/ln 2 = 111.3 days, respectively. The scheme shown in Figure 2 presents the transition energies ^ (in MeV), intensities (the number of transitions per 100 56Co

decays), spins, and parities for the eight most efficient levels. Three close levels (/ = 18-20) are represented by the total effective intensity and mean transition energy.

The ß+ decay is a source of positrons, e+, of kinetic energy distributed within the interval 0-1.459 MeV, the mean value being 0.632 MeV. The positrons interact with matter and, having lost all their kinetic energy, annihilate with the electrons, producing a pair of 0.511 MeV gamma photons. In total, 38 annihilation gamma photons are produced per 100 56Co decays.

The electron capture is followed by the emission of monoenergetic neutrions ve, with discrete energies ranging from 0.51-0.45 MeV (for decays into levels i = 18-20) to up to 2.48 MeV for decay into level i = 2. In contrast, ß+ decay produces neutrinos of energies distributed continuously between 0 and 1.459 MeV with mean energy of 0.827 MeV.

(3,4,3)+ E18.20 =4.05,4.10,4.12

37C0 (Tl/3 = 77.12 d)

4+ E0 =4.566 777777^77777777^777

EC o.siifis;

3+ Ei7 =3.856

3+ En =3.445

E8 =3.123

4+ Eo =2.085

0.99 (t.8)

2.03 1.77

(27.9)- (16.7)-

* (21.9)-

(7.8)-

1.36 1.04 (4-3) (14)

-(U)~

\ o.siifis;

i ß+(19) -(0.9)—

-(18.1)—1

3.24 (11.5) 2.6 (¡7) 1.24 (68)

2+ Ej =0.847

0.847 (100)

E„=0 0+ 1

777777777777777777777777777777

S«Fe a6*e

Fig. 2.—Simplified 56Co - ,6Fe decay scheme

© American Astronomical Society • Provided by the NASA Astrophysics Data System

56Ni ガンマ線ニュートリノ

19 94

ApJS

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No. 2, 1994 PROPERTIES OF Ni ^ Co -> Fe DECAY

The full scheme of Huo et al. ( 1987) gives, per 56Co decay:

529

Total energy emitted via gamma photons: Q7 = 3.61 MeV ,

Total kinetic energy of positrons: = 0.12 MeV ,

Total energy carried away by neutrinos: Qve = 0.84 MeV .

The simplified scheme results in about a 3% lower value, Qy = 3.49 MeV. One could also include in the simplified scheme the transitions from level E2l = 4.298 MeV (4+) (the intensity of56Co decay into this level is equal to (3.7)) to level/ = 1 followed by the emission of 3.45 MeV gammaphotons with intensity (0.9), as well as those to level 8,1.175 MeV (intensity 2.3). In such a case, Qy would be equal to 3.55 MeV, that is, only 1.5% less than the strict value.

The number of positrons, dn+, per unit time emitted with kinetic energy w within an interval [w, w + dw] can be represented as follows:

, AT In 2 dw (3)

4>^(£+ 1)2(2.8552 — e)2G{w) , (4)

where Vq, is the number of 56Co atoms in the system, e = w/0.511, and w is in MeV. The function G( w) was tabulated by Rose et al. ( 1955). Figure 3 shows the positron and neutrino spectra for the ß+ transition to level E2 = 2.085 MeV for which log^ = 8.625. Here t = t+= r1/2/0.181 = 3.681 X 107 s. Since the neutrino energy wv = 1.459 - w, one can describe the neutrino spectrum by equations ( 3 ) and (4) when substituting <£( 1.459 - wj for 4>( w). For the dashed curve in Figure 3, w means the neutrino energy w,, while $( w) stands for $(1.459 - wv).

The total number of positrons emitted per unit time, dN+/dt, is given by

dN+

dt pi.459

Jo dn+ dw

, In 2 . . dw = — NCo(t). (5)

The energies and gamma photon number per 100 decays are compiled in Table 1.

3. THE KINETICS OF Ni ^ Co ^ Fe DECAY The numbers of 56Ni, 56Co, and 56Fe nuclides are controlled by a simple set of differential equations:

dNm _ _ Nm

dt rNi

dNCo _ NNi _ NCo

dt rNi tqq

dNFe _ NCo

dt tCo ’

with the initial conditions

Aní — Anío, Nqo — 0, VFe — 0, at t 0 .

Solving equations (6)-(9), one gets

ANi = ANioe_(//TNi) ,

Nco = Nmo ^ {e~^ - e-*'/�)), TCo rNi

Ap#. — ANin( 1 F rNi ?Co

TCo rNi TCo rNi c>_(i/TCo)

(6)

(7)

(8)

(9)

(10)

(ID

(12)

© American Astronomical Society • Provided by the NASA Astrophysics Data System

56Coガンマ線陽電子の運動エネルギーニュートリノ

tdは日単位の時間

1.放射性元素(56Ni)　全タイプで重要　Ia型>重力崩壊型

2.内部エネルギー(衝撃波加熱)　半径が大きいと重要、IIP型,IIL型

3.運動エネルギー=>熱エネルギー　濃い星周物質と衝突、IIn型

超新星の放射メカニズム：まとめ

超新星の光度曲線-20

-18

-16

-14

-12

-10 0 50 100 150 200 250 300 350

Abso

lute

mag

nitu

de

Days after the explosion

Type IaType Ib and Ic

Type II

~20日

~100日

56Ni

内部エネルギー

1043ergs-1

1042ergs-156Ni

II型超新星のバラエティ(1)The Astrophysical Journal Letters, 756:L30 (6pp), 2012 September 10 Arcavi et al.

0 20 40 60 80 100 120 140

0

0.5

1

1.5

2

SN2005cs

SN2009krSN2011dhSN1993J

Days Since Explosion (estimated)

Shi

fted

R−B

and

Mag

nitu

de

SN1999em

SN Ib/c Template

0 20 40 60 80 100 120 140

−17.5

−17

−16.5

−16

−15.5

−15

−14.5

SN2005au

SN2005bw

SN2005aa SN2004et

SN2004er

SN2004du

Days Since Explosion (estimated)

Abs

olut

e R

−Ban

d M

agni

tude

SN1999em

SN2005cs

SN2005aySN2004fx

Figure 1. Top panel: R-band light curves of 15 Type II SNe from CCCP (excluding the four events presented in Figure 4), normalized in peak magnitude (SN2004fxdata taken from Hamuy et al. 2006; SN2005ay data taken from Gal-Yam et al. 2008a; SN2005cs data taken from Pastorello et al. 2009). A clear subdivision into threedistinct subtypes is apparent: plateau, slowly declining, and rapidly declining SNe (the latter consisting only of SNe IIb). Reference SNe are shown for comparison(SN1999em from Leonard et al. 2002; SN2009kr from Fraser et al. 2010, found to be a member of the IIL subclass as claimed by Elias-Rosa et al. 2010; SN1993Jfrom Richmond et al. 1994; SN2011dh from Arcavi et al. 2011). We also overplot the SN Ib/c template derived by Drout et al. (2011). The data have been interpolatedwith spline fits (except for SN2005by, where a polynomial fit provided a better trace to the data). The shaded regions denote the average light curve ±2σ of eachsubclass. The maximal 7 day uncertainty in determining the explosion times is illustrated by the interval in the top right corner. Bottom panel: R-band light curves of9 Type IIP SNe from CCCP with respect to their estimated explosion time (except for SN2005au and SN2005bw, marked by dashed lines, for which the explosion dateis not known to good accuracy). The light curve of SN2004fx is taken from Hamuy et al. (2006), that of SN2005ay from Gal-Yam et al. (2008a), and that of SN2005csfrom Pastorello et al. (2009). SN1999em (Leonard et al. 2002) is shown for comparison. A spread in plateau luminosities is apparent while plateau lengths seem toconverge around 100 days. Spline fits were applied to the data.(A color version of this figure is available in the online journal.)

continuum, we find that the light curves group into three distinctsubclasses: plateau, slowly declining (1–2 mag/100 days), andinitially rapidly declining (5–6 mag/100 days) events (see alsoTable 1). We note that the three rapidly declining events areall Type IIb and that they display similar light curve shapesto those of Type Ib/c SNe (Drout et al. 2011). We perform aKolmogorov–Smirnov test and find that the probability that themeasured ∆M15R values for the rapid- and slow-decline groupsare drawn from a single underlying distribution is 2%.

Three events (SN2004ek, SN2005ci, and SN2005dp;Figure 4) display prolonged rising periods in their light curves.They do not show signs of interaction in their spectra andmay be explosions of compact blue supergiant progenitors(Kleiser et al. 2011; Pastorello et al. 2012), as demonstrated

directly in the case of SN 1987A (see Arnett et al. 1989 fora review).

Finally, one event (SN2004em; Figure 4) displays a verypeculiar photometric behavior. For the first few weeks it issimilar to a Type IIP SN, while around day 25 it suddenlychanges behavior to resemble an SN 1987A-like event.

The full photometric data set is available online throughWISeREP15 (Yaron & Gal-Yam 2012).

3.1. Declining SNe

Aside from establishing a different rate of decline for SNeIIb compared to SNe IIL, Figure 1 (top panel) suggests that the

15 http://www.weizmann.ac.il/astrophysics/wiserep

3

Ib,Ic型

IIP型(plateau):平坦な部分がある

IIL型(linear):単調に暗くなる

Arcavi+11

水素が多い(~10Msun)

水素が少ない(~1Msun)

内部エネルギー

冷却が早い

冷却がより早い

II型超新星のバラエティ(2)

IIb型

-プラトーはない

-Ibc型に似ている

-最初明るいものも

VanDyk+13

The Astronomical Journal, 147:37 (9pp), 2014 February Van Dyk et al.

Figure 2. BVRIzJH light curves of SN 2013df from KAIT (solid points) andRATIR (open points; with r and i converted to R and I, respectively, followinghttp://www.sdss.org/dr7/algorithms/sdssUBVRITransform.html#Lupton2005).The observed curves have been offset from each other for clarity. Shown forcomparison are the BVRIJH light curves of SN 1993J (Richmond et al. 1994,1996; Matthews et al. 2002; dashed lines) and of SN 2011dh (Arcavi et al.2011; Van Dyk et al. 2013b; Ergon et al. 2013; dot–dashed lines), and thez-band light curve of SN 2008ax (Pastorello et al. 2008, solid line), all adjustedin time and relative brightness. The estimated time t = 0 of the explosion isindicated.(A color version of this figure is available in the online journal.)

each band. Consequently, the photometry presented here shouldbe considered preliminary; however, the SN is far from themain light from the host galaxy, so results including templatesubtraction prior to photometry might not substantially differfrom what we present here.

2.2. Early-time Spectroscopy

We have obtained a number of spectra of the SN at earlytimes, using the Kast spectrograph (Miller & Stone 1993) on theLick Observatory 3 m Shane telescope and the DEep ImagingMulti-Object Spectrograph (DEIMOS; Faber et al. 2003) on theKeck-II 10 m telescope. Ultraviolet (UV) spectroscopy has alsobeen obtained using the Hubble Space Telescope (HST) SpaceTelescope Imaging Spectrograph as part of program GO-13030(PI: A. V. Filippenko). The results of these HST observationswill be presented in a future paper, together with the bulk ofthe ground-based optical spectra. However, here we present andanalyze a representative spectrum obtained on 2013 July 11.2with DEIMOS using the 600 l mm−1 grating.

2.3. HST Imaging

The region of the host galaxy containing the SN site wasobserved with the HST Wide Field Planetary Camera 2 on 1999April 29 by program GO-8400 (PI: K. Noll), as part of theHubble Heritage Project. The bands used were F439W (twoindividual images with 40 s exposure times and two with 1000 s),F555W (four 400 s exposures), F606W (two 60 s exposures),and F814W (two 40 s and four 400 s exposures). The F555W andF814W data were combined with images obtained by programsGO-5397 and GO-5972 at an earlier time for the rest of the

Figure 3. Absolute V light curve for SN 2013df (solid points), compared to thoseat V for SNe 1993J (dashed line; colored red in the online version), 2008ax (solidline; colored green in the online version), and 2011dh (dot–dashed line; coloredblue in the online version) shown in Figure 2. All of the curves are displayedrelative to the day of V maximum; see the text.(A color version of this figure is available in the online journal.)

galaxy, and drizzled into mosaics in each band at the scale0.′′05 pix−1 by Holwerda et al. (2005).

We have also observed the SN on 2013 July 15 with HST usingthe Wide Field Camera 3 (WFC3) UVIS channel in F555W, aspart of our Target of Opportunity program GO-12888 (PI: S.Van Dyk). The observations consisted of 28 exposures of 5 s;the short exposure time was intended to avoid saturation in eachframe by the bright SN.

3. ANALYSIS

3.1. Light Curves

In Figure 2 we display the early-time KAIT and RATIR lightcurves in all bands for SN 2013df. We also include the veryearly V measurement from June 11.202 by Stan Howerton.14

We compare these curves with those at BVRIJH for SN 1993J(Richmond et al. 1994, 1996; Matthews et al. 2002) and forSN 2011dh (Arcavi et al. 2011; Van Dyk et al. 2013b; Ergon et al.2013). We also compare the z-band light curve of SN 2008ax(Pastorello et al. 2008). The curves for the comparison SNe wereadjusted in time and relative brightness to match the curves ofSN 2013df, particularly at the secondary maximum in eachband. Clearly, from its overall photometric similarity with theother SNe, SN 2013df appears to be an SN IIb; see Arcavi et al.(2012) for a general description of SN IIb light-curve shapes.What is most notable from the comparison is that the post-shock-breakout cooling of SN 2013df occurred at a later epoch in allbands, relative to that of SN 1993J. The post-breakout declineof SN 2011dh occurred at an even earlier relative epoch (e.g.,Arcavi et al. 2011; Bersten et al. 2012).

We show in Figure 3 the absolute V-band light curve ofSN 2013df, relative to those of SNe 1993J, 2008ax, and 2011dh.

14 http://www.flickr.com/photos/watchingthesky/9035874997

3

水素が少しだけ(~0.1Msun)

内部エネルギー冷却が早い

The Astronomical Journal, 144:131 (13pp), 2012 November Zhang et al.

Figure 3. U − B, B − V, V − R, and V − I color curves of SN 2010jl compared with those of Type IIn SNe 1997cy (Germany et al. 2000), 1998S (Fassia et al. 2000),and 2006tf (Smith et al. 2008). All of the comparison SNe have been dereddened for the reddening in the Milky Way. The dotted lines are the least-squares fit to thecolors of SN 2010jl.

Figure 4. Absolute R-band light curve of SN 2010jl compared with other notableType IIn SNe 1997cy (Germany et al. 2000), 1998S (Fassia et al. 2000), 2006gy(Smith et al. 2007), and 2006tf (Smith et al. 2008); Type Ia SN 2005cf (Wanget al. 2009); and Type IIP SN 1999em (Leonard et al. 2002).

3.3. Absolute Magnitudes and Bolometric Light Curves

In Figure 4, we compare the absolute R-band light curves ofSN 2010jl with other SN samples. The pre-maximum data pointsare extrapolated through the V-band light curves published byStoll et al. (2011) and the linear V −R color curve as presentedin Figure 3. Overplotted are the light curves of a typical TypeIa SN 2005cf (Wang et al. 2009) and Type IIP SN 1999em(Leonard et al. 2002). The Hubble constant H0 is taken to be72 km s−1 Mpc−1 (Freedman et al. 2001) in deriving the absolutemagnitudes for these objects. Days of the light curves are givenrelative to the estimated phase of the maximum brightness. Onenotable feature of this plot is the heterogeneous light curves ofthe SNe IIn. Compared with Type Ia and IIP SNe, the SN IInsamples are very luminous and their high luminosity lasts for along time after the peak. A recent study by Kiewe et al. (2012)suggests that the rise time for those luminous core-collapse canbe very long (>20 days). As seen from the plot, SN 2006gycould have a rise time longer than 60 days, which is the mostluminous SNe IIn ever recorded in recent years. Although lessextreme relative to SN 2006gy, SN 2010jl clearly shows a highluminosity with a long duration. It is interesting to note thatthe light curve of SN 2010jl is similar to that of SN 2006tf andSN 1997cy at early times, but remarkable difference betweenthem emerges at late times. By t ∼ 90 days from the maximumlight, the light curve of SN 2010jl becomes almost flat, unlikeSN 1998S or SN 2006tf, which declined in R at a faster paceat a similar phase. By t ! 200 days, SN 2010jl becomes themost luminous SN IIn of our samples due to its remarkablyslow evolution at late times. Such a long-duration emission athigh luminosity demands a large amount of emitting materials.

6

II型超新星のバラエティ(3)

IIn型

-IIP型よりも明るい

ものが多い

-明るい時期が長い

ものも

(ゆっくりと暗くなる)

-多様性が大きい

Zhang+12

IIn型

IIn型

IIP

IaIIn型

運動エネルギー

星周物質の多様性か？