Ringberg, July 8, 2005

COSMIC RATE OF SNIa

Laura Greggio

INAF, Padova Astronomical Observatory

Ringberg, July 8, 2005

Chemical evolution of galaxies Chemical evolution of the ICM and IGM Gas flows in Ellipticals The determination of cosmological parameters

SNIa are relevant to the study of:

To study # 1,2 and 3 we need the SNIa rate following a burst of SF

To address # 4 we need to understand the nature of the SNIa progenitor

The cosmic evolution of the SNIa rate helps constraining both

Ringberg, July 8, 2005

Dahlen et al. 2004: SNII trace the recent SF use the rate of type II to trace the cosmic SFR

SNIa come from longer lived progenitors:At a cosmic epoch t the SNIa rate is

t

IaIaIa

i

dftkAtn

)()()(

•τ is the delay time (interval between the birth of the stellar system and its explosion)•fIa is the distribution function of the delay

times •AIa is the realization probability of the SNIa event out of one stellar generation•kα is the number of stars per unit Mass of one stellar generation

Ringberg, July 8, 2005

Close Binary Evolution

(1984)

SD

DD

provides two main cathegories ofSNIa precursors:

Single Degenerate Systemsa CO WD accretes from a living companion

Double Degenerate Systemsthe companion is another WD

Explosion may occur when

• the WD mass reaches the Chandrasekhar limit (Ch-exploders)

•a Helium layer of ≈0.1 MO, accumulated on top of the WD, detonates (Sub-Ch exploders)

Ringberg, July 8, 2005

Pros and Cons

Single Degenerates:

Candidate precursors observed (SSXRS, Symbiotic, CV)

Fine tuning of accretion rate is needed to avoid nova and/or CE (small volume in the phase space)

Absence of H in the spectra

Double Degenerates:

Absence of H in the spectra

Theoretical likelyhood accounts for current rate in the MW

Theoretical explosion leads to neutron star

Observed DDs are not massive enough

CHANDRA exploders : uniform light curves and better spectra BUT few of them

SUB-CHANDRA : many of them BUT variety of Ni56 produced and high velocity of ejected Ni

Ringberg, July 8, 2005

Population Synthesis of Binaries

Yungelson and Livio 2000

Monte Carlo simulations of a population of binaries with n(m1), n(q), n(A0),following the evolution of each system through the RLOsand determining the outcome (CVs, RCBor, sdO,all varieties of DD.., sometimes SNIa)

Tutukov & Yungelson , Ruiz-Lapuente,Burket & Canal, Han et al., Nelemans et al.

The results are: (highly) model dependent ( CE, mass loss, criterion for mass transfer stability …)

hard to implement in other computations(for galaxy evolution, cosmic evolution…)

BUT the distribution function of the delay times can becharacterized on general grounds …

Ringberg, July 8, 2005

Single Degenerates:Clock is the nuclear timescale of the secondary

22 )()( dmmndn

22 )()( mmnf SDIa

21 m

+ limits on primary mass:

)(: 22 mm MS

Evolutionary clock andDistribution of the secondaries insystems which give rise to a SNIa

only Chandra

4.1,2 eWD mm

Ringberg, July 8, 2005

Double Degenerates

3

4

wd2wd1wd2wd1

4

gw 6.0)(

15.0

DDM

A

mmmm

A

Clock is the nuclear timescale of the secondary + the gravitational delay

Double CO WDs: m1, m22 then n≤ 1Gyr

The distribution function of the separations of the DD systems is crucial for the distribution of the gravitational delays

Shrinkage at RLO:• Start from: 100 R0 <A0 < 1000 R0

• Go through RLO:standard CE: (A/AO)≈few 10-3

heavier systems have smaller A/AO & shorter gw

Nelemans et al. : large range of (A/AO) no correlation between mass and gw

MDD=2 τgw ranges in 5Myr – 15 Gyr A ranges from 0.5 to 3.8 Ro

A small dispersion in DD masses and/or final separations yield a wide distributionof delay times

CLOSE DDs

WIDE DDs

Ringberg, July 8, 2005

The distribution function of the delay times for DDs

mainly controlled by:

maximum nuclear delay(minimum m2 of a successful system)

whether evolution leads to WIDE or CLOSE DD

distribution function of the separations of the DDwhether favouring larger or smaller A

Ringberg, July 8, 2005

The distribution function of the delay times

All models normalized at 12 Gyr : Main Parameters :

SD: minimum mass of the primary for a successful SNIa (distribution of mass ratios)

DD: 1) minimum mass of the secondary (fix maximum nuclear delay)

2) distribution function of the separations after II RLO 3) whether WIDE or CLOSE

Different models have:

• different

•different Fe production12

)12(

Ia

Ia

f

f

Ringberg, July 8, 2005

The Cosmic SNIa rate

t

IaIaIa

i

dftkAtn

)()()(

Ringberg, July 8, 2005

Results of the convolution:

The results of the convolutionare rather sensitive to theadopted cosmic SFR:

A steep increase from z=0 to 1favors a steep increase of thecosmic SNIa rate

A decrease from z=1 upwardCould explain the low SNIarate at z=1.6

Ringberg, July 8, 2005

SNIa rate in different galaxy typesAnother way to constrain the distribution function of the delay times

0

)()()( 00

t

IaIaIa

i

dftkAtn

•Younger stellar populations sample the peak of the distribution function of the delay times•Younger stellar populations are bluer Bluer galaxies have larger SPECIFIC SNIa rates

Data from Mannucci et al. 2005

Ringberg, July 8, 2005

CONCLUSIONS I illustrated how the SFR and the distribution function of the delay times

compose to determine the SNIa rate in galaxies

The current SNIa rate in Spirals mostly constrains the realization probability of the SNIa scenario; in Ellipticals it scales as the fIa functionThe ratio between the current SNIa rates in Spirals and Ellipticals constrains the shape of the function

I presented analytic expressions, describing the distribution function of the delay times for Single and Double Degenerate progenitors

These expressions are based on general stellar evolution arguments, which result into a fIa function controlled by a few main parameters Representing Es as instantaneous burst of SF, and using their current rate to

calibrate the fIa function, I showed that:

SD models greatly overproduce Fe in Galaxy Clusters and overpredict the current rate in Spiral galaxies

The data are met with either CLOSE DDs with flat n(A) or WIDE DDs with steep n(A)

Ringberg, July 8, 2005

NORMALIZATION

0

)()(t

Ia

IaIa

i

dft

nkA

0

)()()( 00

t

IaIaIa

i

dftkAtn

Horizontal levels derived from rate in galaxiesPoints derived from cosmic rate