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Lecture 9:Supernova Rates
Star-Formation Efficiency, Yield
How many supernovae per year for each galaxy type ?
Use power-law IMF, Salpeter slope -7/3 = -2.33
N(M)!M"7/3 0.1M
20M
.
.
Limits of validity,
not well known
20 M!
logN(M)
0.1 M!
8 M!
slope = -7/3 = -2.33
logM
Supernova limit
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Universal IMF (Kroupa 2002)
N(M
)!M
!
log(M/ M!)
!
MW MC
GC local
log(M/ M!
)
M42 M35Pleiades local
!~ - 7/3 M> 1 M!
- 4/3 0.1 - 1 M!
- 1/3 M< 0.1 M!
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Number of stars :
Fraction of stars withM > 8 M
( forB = -7/3 )
500 stars --> 1 supernova!
fN!number of SNe
number of stars=
MB
dM8
20
"M
BdM
0.1
20
"
fN =
A
B+1M
B+1
8
20
A
B+1M
B+1
0.1
20
=
M!4/3
8
20
M!4/3
0.1
20
=
0.018! 0.063
0.018!21.544
Most stars at
low-mass end!
fN =0.2%!
N= N(M) dM" = A MB dM" =A
B +1M
B +1 ( if B # $1)
Integrating a Power-Law IMF
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Supernovae are rare, but each is very massive.
What fraction of the massgoes into SNe?
fM =M!M"7/3 dM
8
20
#M!M"7/3 dM
0.1
20
#
=
M!1/3
8
20
M
!1/3
0.1
20 =
0.37-0.50
0.37! 2.15Most of mass is in
low-mass stars.
%2.7=Mf!
SN Mass Fraction
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Median mass:
Mean mass:
1
2=
M! M"7/3 dM8
MSN
#M! M"7/3 dM
8
20
#=
MSN
"1/3 " 0.50
0.37" 0.50
M2.12=SNM .!
M =M! M"7/3 dM
8
20
#
M"7/3
dM8
20
#
=
1
"1/3M
"1/3
8
20
1"4/3
M"4/38
20
=4! (20"1/3 "8"1/3)
20"4/3 "8"4/3
=4! (0.37" 0.50)
0.018" 0.062=12M
Typical SN Mass
.
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Spiral Galaxy: SFR: ~ 8 M!yr
-1. 7.2% haveM> 8 M! .
(8 M!
yr-1) x 0.072 ~ 0.6 M!
yr-1go into SNe
SN rate:
(fewer seen due to dust)
Irregular Galaxy: ~10x this rate during bursts (1 SN per 2 yr)!
No SNe between bursts.
0.6 M yr -1
12.2 M ~1
20 yr-1.
.
!
SN Rates vs Galaxy Type
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SN Rates: Ellipticalst*= 1 Gyr e-folding time
t= 10 Gyr age!
= 0.95 efficiency
M0= 1011M
! total mass = initial gas mass
Gas consumption:
Star formation:
SN rate:
3 SN per 105yr. Negligible!
MG(t) = M0 e
" t/ t#= M0 "$MS(t)
dMS
dt" M
S=
M0
#
e$t/ t
%
t%
=
1011M( ) e$10
(0.95) (109 yr)= 5&10$3 M yr -1.
MS(t) = M0
"
1# e#t/ t
$( )
.
0.072( ) 5 "10-3M yr -1( )12.2 M
# 3"10-5 yr -1.
.
(t) = e"t/ t
#
t
1
t"
gas
S(t) = 1! e!t/t
"( )/!
t
1
"
t"
stars
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What Star Formation Efficiency
and Yields of H, He and Metals ?X = 0.75
Y = 0.25
Z = 0.00
X = ?
Y = ?
Z = ?
MG = M0
MS= 0
MG = 0
MS= M0
MG = (1-!) M0
MS= !M0
!= ?
KABOOM!
KABOOM!
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Estimates for efficiency !, yield in X, Y, Z
Assume:
1.
Type-II SNe enrich the ISM.(Neglect: Type-I SNe, stellar winds, PNe, ....)
2. Closed Box Model:(Neglect: Infall from the IGM, outflow to the IGM)
3.
SN 1987A is typical Type-II SN.
Better models include these effects.
What do we know about SN 1987A?
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SN 1987A
23 Feb 1987 in LMC
Brightest SN since 1604!
First SN detected in neutrinos.
Visible (14 --> 4.2 mag) to naked eye,
in southern sky.
Progenitor star visible:
~20 Msun blue supergiant.
3- ring structure (pre-SN wind)
UV flash reached inner ring in 80 d.Fastest ejecta reached inner ring in ~6 yr.Fast ejection velocity v~c/30~11,000 km/s.
Slower (metal-enriched) ejecta asymmetric.
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SN 1987A
23 Feb 1987 in LMC
Brightest SN since 1604!
First SN detected in neutrinos.
Visible (14 --> 4.2 mag) to naked eye,
in southern sky.
Progenitor star visible:
~20 Msun blue supergiant.
3- ring structure (pre-SN wind)
Shockwave reaches inner ring 2003.
20032010
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Use SN 1987A to calculate !and yield.
SN 1987A: progenitor star mass = 20 M!
remnant neutron star mass = 1.6 M!
mass returned to the ISM = 18.4 M!
From IMF, 7.2% ofMSis in stars withM> 8 M
!
"
= Fraction ofMSreturned to ISM:
Star Formation Efficiency
!= fraction ofMSretained in stars:
! =mass returned to gas
mass turned into stars= 0.072!
18.4
20" 6.6%
! =1!"= 93%
Star Formation Efficiency
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SN 1987A Lightcurve
56Ni => 56 Co 6d half-life56Co => 56 Fe 78d half-life
Powered by radioactive decay of r-process nuclei.
Use to measure metal abundances in ejected gas.
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