
2/14

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!


3/14

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


4/14

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


5/14

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

.


6/14

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


7/14

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


8/14

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!


9/14

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?


10/14

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.


11/14

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


12/14

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


13/14

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.


14/14

Supernova Rates Star Formation

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