The hidden harmony is better than the obvious one.

Heraclitus

On Variations in the Peak Luminosityof Type Ia Supernovae

Frank TimmesThermonuclear Applications Group X-2

Los Alamos National Laboratory

LA-UR-04-5097 www.cococubed.com

KITP - Accretion and Explosion: the Astrophysics of Degenerate Stars

20Feb2007

• A few observations

• Why the intrinsic scatter?

• Tracking the proton/neutron ratio

• Some new results

An outline of this talk on thermonuclear supernovae

Filippenko, 1997

The spectra and light curves near peak light are similar.

Barbon et al 1973Doggett et al 1985

13

14

15

16

174000 6000 8000 10000

Rest Wavelength (Angstrom)

-2.5

log

f ! +

Con

stan

t

SNIa

t ~ 1 week

90N

87N

87D

Fe IICo II

Si IICa II

Fe IIIFe II

Ee IIFe IIISi II

S II

Si IIO I

Ca II 0

1

2

3

4

5

6

7

0 50 100 150 200 250 300

Days After Maximum Light

mB B

elow

Max

imum

Lig

ht

Type Ia Supernovae

Blue Light Curves

38 Events

• The Phillips relation compensates for the variation in peak luminosity to give a standard candle.

• This makes the peak luminosity a function of a single parameter: e.g., the width of the light curve or the mass of 56Ni ejected.

Kim et al. 1997

Brighter light curves are broader.

-20 0 20 40 60

-17

-18

-19

-20

-20 0 20 40 60

-17

-18

-19

-20

as measured

light-curve timescale

“stretch-factor”corrected

days

MV

- 5

log(h

/65)

days

MV

- 5

log(h

/65)

Calan/Tololo SNe Ia

Riess et al. 1998

Dimmer than the template is interpreted as evidence an accelerating universe.

Supernova Cosmology Project

34

36

38

40

42

44

WM=0.3, WL=0.7

WM=0.3, WL=0.0

WM=1.0, WL=0.0

m-M

(m

ag

)

High-Z SN Search Team

0.01 0.10 1.00z

-1.0

-0.5

0.0

0.5

1.0

!(m

-M)

(ma

g)

Accelerating

Low Density

High Density

Accelerating

Low Density

High Density

For nearby supernovae, the intrinsic variation in peak magnitude is ~0.5 in the B and V bands.

For more distant events, there are several sub-luminous events which broaden the variation to about 1 magnitude in B.

-19.8

-19.6

-19.4

-19.2

-19

Peak A

bsolu

te M

agnitude B

-band

SN

19

90

NN

GC

46

39

SN

19

81

BN

GC

45

36

SN

19

89

BN

GC

36

27

SN

19

98

bu

NG

C 3

36

8

SN

19

72

EN

GC

52

53

SN

19

37

CIC

41

82

SN

19

60

FN

GC

44

96

A

Type Ia SN with Cepheid-based distances

Gibson et al. 2000

-19.8

-19.6

-19.4

-19.2

-19

-18.8

-18.6

-18.4

-18.2

Pe

ak

Ab

so

lute

M

ag

nitu

de

B

-ba

nd

90

O9

0T

90

Y9

0a

f9

1S

91

U9

1a

g9

2J

92

K9

2P

92

ae

92

ag

92

al

92

aq

92

au

92

bc

92

bg

92

bh

92

bk

92

bl

92

bo

92

bp

92

br

92

bs

93

B9

3H

93

O9

3a

g9

3a

h

Distant Type Ia SN

Hamuy et al. 1996

School of Athens1510Raffaello Sanzio

Let’s re-explore the idea that variations in the peak luminosity originate in part from a scatter in the metallicity of the main-sequence stars that become white dwarfs.

Most of a main-sequence star's initial metallicity comes from the CNO and 56Fe nuclei inherited from its ambient interstellar medium.

The slowest step in the hydrogen burning CNO cycle is 14N(p,γ).All the CNO piles up at 14N when hydrogen burning is done.

12C

13N

13C 14N

15O

15N

Cycle 1

(p,!)

(p,!)

(p,!)(,e+")

(,e+")

(p,#)

17O

17F

16O

18F

18O 19F

Cycle 2 Cycle 3

Cycle 4

(p,!)

(p,!)

(p,!)

(p,!)

(,e+")

(,e+")

(p,#)

(p,#)(p,#)5.0-

0

5.0

1

5.1

2

5.2

3

5.3

4

5.4

5.345.45

log

L/L s

un

Tgol ffe

Central Stars of Planetary Nebulae

WhiteDwarfs

AGB

RGB

post-AGB

main-sequence

ZAHB

9.1

8.3 7.7

6.4

2.73.7

shown: 6.8(9.7 to Teff=4200K)

Herwig, ARAA, 20052 Msun, Z=Zsun

During helium burning all of the 14N is converted into 22Ne by 14N(α,γ)18F (β+,νe)18O (α,γ)22Ne.

Mass and charge conservation set the white dwarf’s 22Ne mass fraction and neutron enrichment

X(22Ne) = 22!X(12C)

12+

X(14N)14

+X(16O)

16

"

Ye =1022

X(22Ne) +2656

X(56Fe) +12

!1!X(22Ne)!X(56Fe)

"

n!

i=1

Xi = 1 Ye =n!

i=1

Zi

AiXi

Assuming the 22Ne and 56Fe are uniformly distributed.

Carbon-Oxygen White Dwarf

Type Ia Supernova Neutron Star

Accrete He Accrete H or He Accrete C+ODouble degenerate merger

Near Central IgnitionDetonate He at base

Supersoft x-ray sources?

Carbon doesn't detonate

Carbon detonatesSub-Chandra model

Fast, dim SNIawith remnant

Light C at edge

O+Ne+Mg WD

> 8x109 g/cc

~ 2x109 g/cc

Mchandra

Standard Model

He S

hell Grows

C+O Nova

M < 4x10-8 Msun/yr

M > 3x10-6 Msun/yr

M < 10-8 Msun/yr

We’ll assume the standard model of a Type Ia supernova.

W7, Nomoto et al. 1984

Nearly all such 1D models produce most of their 56Ni in a nuclear statistical equilibrium environment between ~ 0.2 and 0.8 Msun.

In this region, weak reactions occur on time-scales longer than the time-scale for disruption of the white dwarf.

Höflich et al., 1998

While many 1D models have sophisticated flame treatments, we want to elucidate physics that are robust to any complicated hydrodynamics.

Iwamoto et al., 1999

Consider the case when 56Ni and 58Ni are the only two species in nuclear statistical equilibrium. Mass and charge conservation

imply a linear relationship between the mass fraction of 56Ni and Ye:

n!

i=1

Xi = 1 Ye =n!

i=1

Zi

AiXi

X(56Ni) = 1!X(58Ni) = 58Ye ! 28

We can set this final Ye equal to the initial Ye of the white dwarf since weak interactions don’t dominant where most of the 56Ni is made.

X(56Ni) = 1! 0.057Z

Z!

The average peak B and V magnitudes of nearby Type Ia events imply ~0.6 Msun of 56Ni is produced. Using this fiducial mass gives

M(56Ni) =!

X(56Ni)dm ! 0.6"1" 0.057

Z

Z!

#M!

If a third isotope is present, say 54Fe, then Saha-like equations must be solved for the NSE distribution. The net result is a slightly shallower slope

M(56Ni) ! 0.6!1" 0.054

Z

Z!

"M!

As long as the region that reaches NSE does so on a timescale over which Ye is nearly constant, then the mass of 56Ni produced is largely independent of the details of flame front propagation.

This result is robust.

“For every complex natural phenomenon there is a simple, elegant, compelling, wrong explanation.” - Tommy Gold

10-1

100

101

.2

.4

.6

Mass o

f 56N

i eje

cte

d (

Msun)

Metallicity of Progenitor (Z/Zsun

)

Dominguez et al.

Analytical result

W7 models

Factor of 3 variation

in the CNO + Fe abundances

~25% variation

in56

Ni

Post-processing thermodynamic trajectories of 1D simulations reproduces the analytical result to within 5%.

A factor of 3 scatter in the initial metallicity leads to a variation of about 25% (0.13 Msun, ΔMV ~ 0.3 mag) in the mass of 56Ni ejected, accounting for most, but not all, of the observed variation.

Feltzing et al 2001

0 1 2 3 40

.1

.2

.3

.4

.5

Ma

ss o

f 56N

i e

jecte

d (

Msun)

Metallicity of Progenitor (Z/Zsun

)

Roepke et al. 2005

Travaglio et al. 2004

Brown et al. 2004

Timmes et al. 2003M(56Ni) = M(56Ni)Z=0

!1! 0.057

Z

Z!

"M!

From 3D simulations the Max Planck group find 56Ni variations of 2% from the C/O ratio, 7% from the central density, 20% from metallicity.

Röpke et al. 2005

0.5

1

1.5

2

2.5

8.4 8.6 8.8 9 9.2 9.4

m1

5(B

)

Log(O/H) + 12

E/S0 Galaxies

Spiral Galaxies

H00 Spiral Galaxies

H00 E/S0 Galaxies

Model Prediction

Gallagher et al 2005

From ~60 host galaxies, Ivanov et al (2000) and Gallagher et al (2005) suggest age rather than metallicity better expresses the observed trends.

Ivanov et al 2000

Podsiadlowski et al 2006 showed that electron captures on 22Ne during the simmering phase could magnify the effect of metallicity

Podsiadlowski et al 2006

15M = 0.8

M = 1.815

!cfirst parameter ( ?)

faint

brightseco

nd

par

amet

er (

Z?)

high!z sample

local sample

faint bright

"

"

X(56Ni) = 1!

0.1650.1110.058

Z

Z!

and examined the effects of metallicity on the determination of cosmological parameters.

Dursi & Timmes 2007

1e+09

2e+09

3e+09

4e+09

5e+09

6e+09

7e+09

8e+09

9e+09

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045

Tem

p(K

)

Time (s)

Ignition Delay Time

Metallicity reduces the ignition time; even modest amounts of 22Ne can reduce the ignition time of CO mixtures 20-30% +

Ignition occurs at rare peaks in the tails of PDFs; 22Ne can greatly increase probability of points igniting.

Different state at ignition time for metal-rich WD?If so, may introduce a metallicity-central density entanglement.

7.0 7.5 8.0 8.5 9.0 9.5 10.0Log10 density

8.6

8.8

9.0

9.2

9.4

9.6

9.8

10.0

Log10 tem

pera

ture

never ignites million sec1000 sec

1 sec

1 sec 1 millisec

1 microsec

1 nanosec

1 picosec

7.0 7.5 8.0 8.5 9.0 9.5 10.0Log 10 dens

8.6

8.8

9.0

9.2

9.4

9.6

9.8

10.0

Lo

g 1

0 t

em

p

+2%

-2%

-2%-2%

-5%

-5%

-5% -5%

-10%

-10%-10%

-10% -10%

-20%

-20%

-20%

-30%

0.0 0.2 0.4 0.6 0.8 1.0

1-[Y12/max(Y12)]

0.000

0.002

0.004

0.006

0.008

0.010

Y

4He

22Ne

1H

28Si

20Ne

X 22 = 0.06

X 22 = 0.00

108 109

density (g cm-3)

0.1

1.0

10.0

100.0

1000.0

flam

e sp

eed (

km

s-1

)

TW92

130 nuclide

430 nuclide

Fit

Chamulak, Brown, & Timmes 2007

Metallicity increases the laminar flame speed; being roughly linear with 22Ne and ~ 30% for X(22Ne)=0.06.

These results pertain to the initial burning front near the center, and at late times where the flame may make a transition to distributed burning.

Dlam =!23.26!9 + 37.34!1.1

9 ! 1.288""

#1 + 0.3

$X22

0.06

%&"

'0.3883

$X12

0.5

%+ 0.09773

$X12

0.5

%3(

kms!1

0.000 0.001 0.002 0.003

dY(12C)

0.0000

0.0002

0.0004

0.0006

0.0008

dYe

Can 22Ne be produced in-situ?

Yes, during the helium shell flashes in an AGB star. Falk Herwig and I are calculating some numbers.

Chamulak, Brown, & Timmes, in preparation,2007

Yes, during laissez-faire carbon burning during the simmering phase!

5.0-

0

5.0

1

5.1

2

5.2

3

5.3

4

5.4

5.345.45

log L

/L sun

Tgol ffe

Central Stars of Planetary Nebulae

WhiteDwarfs

AGB

RGB

post-AGB

main-sequence

ZAHB

9.1

8.3 7.7

6.4

2.73.7

shown: 6.8(9.7 to Teff=4200K)

Self-heating calculations suggest 12C(12C,p)23Na(e-,ν)23Ne and 12C(p,ϒ)13N(e-,ν)13C operate with enough vigor to make a Ye floor.

1/3 slope from 2 electron captures every 6 C12 consumed

burning timescale faster than weak timescale

HeraclitusSchool of Athens1510Raffaello Sanzio