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					 COSMIC RATE OF SNIa




            Laura Greggio
INAF, Padova Astronomical Observatory




               Ringberg, July 8, 2005
  SNIa are relevant to the study of:

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

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
                                 nIa ( t )  AIa k   ( t   ) f Ia ( )d
                                 
                                                    i


                          •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
                                                                          (1984)


Close Binary Evolution
 provides two main cathegories of
 SNIa precursors:

 Single Degenerate Systems
 a CO WD accretes from a living companion

 Double Degenerate Systems
 the companion is another WD


  Explosion may occur when

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

•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:                                Double Degenerates:
Candidate precursors observed                       Absence of H in the spectra
(SSXRS, Symbiotic, CV)
                                                     Theoretical likelyhood accounts
Fine tuning of accretion rate                        for current rate in the MW
is needed to avoid nova and/or CE
(small volume in the phase space)                    Theoretical explosion leads to
                                                     neutron star
Absence of H in the spectra
                                                     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
    Monte Carlo simulations of a population of binaries with n(m1), n(q), n(A0),
    following the evolution of each system through the RLOs
    and determining the outcome
     (CVs, RCBor, sdO,all varieties of DD.., sometimes SNIa)

    Tutukov & Yungelson , Ruiz-Lapuente,Burket & Canal,
                                                                             Yungelson and Livio 2000
    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 be
    characterized on general grounds …
                                                    Ringberg, July 8, 2005
             Single Degenerates:                                            n( )d  n( m2 )dm2
 Clock is the nuclear timescale of the secondary                            m2 :  MS (m2 )  
                                          + limits on primary mass:
Evolutionary clock      and
Distribution of the secondaries in
                                                                          f Ia ( )  n( m2 ) m2
                                                                             SD
                                                                                              
systems which give rise to a SNIa



                                             m1  2




                       mWD  m2,e  1.4
                       Chandra only
                                                 Ringberg, July 8, 2005
                                                   Double Degenerates
   Clock is the nuclear timescale of the secondary                         Double CO WDs: m1, m2  2 then n≤ 1Gyr
     + the gravitational delay
                                                   MDD=2 τgw ranges in 5Myr – 15 Gyr    The distribution function of
                  0.15  A4                  A4           A ranges from 0.5 to 3.8 Ro
   gw                                 0.6 3                                           the separations of the DD
           m1wd m2 wd ( m1wd  m2 wd )      M DD
                                                                                         systems is crucial for the
                                                                                         distribution of the
                                                                                         gravitational delays
                                                     Shrinkage at RLO:
                                                    • Start from:
                                                    100 R0 <A0 < 1000 R0
                                                    • Go through RLO:                                   WIDE DDs
                                                    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                             CLOSE DDs



A small dispersion in DD masses and/or
final separations yield a wide distribution
of delay times                                               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 DD
whether 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:
                                                                f Ia (12)
                                               • different
                                                                   f Ia 12
                                               •different Fe production


                               Ringberg, July 8, 2005
             The Cosmic SNIa rate


                   t
nIa ( t )  AIa k   ( t   ) f Ia ( )d

                   i




                        Ringberg, July 8, 2005
Results of the convolution:



                              The results of the convolution
                              are rather sensitive to the
                              adopted cosmic SFR:

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

                              A decrease from z=1 upward
                              Could explain the low SNIa
                              rate at z=1.6




         Ringberg, July 8, 2005
                                SNIa rate in different galaxy types
             Another way to constrain the distribution function of the delay times

                    t0                              •Younger stellar populations sample the peak of
nIa ( t0 )  AIa k   ( t0   ) f Ia ( )d
                                                      the distribution function of the delay times
                    i                              •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 function
The 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
Horizontal levels derived from rate in galaxies
Points derived from cosmic rate
                                                                             t0

                                                        nIa ( t0 )  AIa k   ( t0   ) f Ia ( )d
                                                        
                                                                             i


                                                                                  
                                                                                  nIa
                                                          AIa  k     t0

                                                                         (t   ) f
                                                                        
                                                                                        Ia   ( )d
                                                                         i




                                         Ringberg, July 8, 2005

				
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