Äîêóìåíò âçÿò èç êýøà ïîèñêîâîé ìàøèíû. Àäðåñ îðèãèíàëüíîãî äîêóìåíòà : http://www.iki.rssi.ru/galeev/astro2007/2012_Potashov.pdf Äàòà èçìåíåíèÿ: Tue Aug 28 17:45:39 2012 Äàòà èíäåêñèðîâàíèÿ: Tue Oct 2 14:24:19 2012 Êîäèðîâêà: ISO8859-5 Ïîèñêîâûå ñëîâà: ï ï ï ï ï ï ï ï ï ï ï ï ï ï ï ï

à éà è ãâç ã èá É äâ

çéä æâãê

çä èæ È è

â

âèã

ãéâè æ ãâç

âè ÖÔÜ âè Ûã

äæã çç ç ãà ê

ãæ áéàè äàí

ääæãì á è ãâÊ

M.Sh.Potashov
S.I.Blinnikov, P.V.Baklanov, A.A.Andronova
á æ èÊä ãè ç ãê á àÊ ãá

ITEP

Tarusa 19.01.2012 - p. 1


SN 1987A

Tarusa 19.01.2012 - p. 2


H line is weak, SN1999em, day 37

Dessart, L., Hillier, J. 2005, CMFGEN
Tarusa 19.01.2012 - p. 3


Time dependent effects

Ç Utrobin, V. U., Chugai, N. 2002 - 2005

A time-dependent hydrogen ionization in the atmosphere of SN 1987A.

Tarusa 19.01.2012 - p. 4


Time dependent effects

Ç Utrobin, V. U., Chugai, N. 2002 - 2005

A time-dependent hydrogen ionization in the atmosphere of SN 1987A.
Ç Zeldovich, Ya. B., Kurt, V. G., and Sunyaev, R. A. 1968

Importance of the ionization freeze-out effect in cosmology.
Tarusa 19.01.2012 - p. 4


Spectra calculation

Ç Advantages and disadvantages of the

radiations-hydrodynamic STELLA code + CMFGEN - hydrodynamic is NOT included + Utrobin, Chugai - grey atmosphere - LTE

Tarusa 19.01.2012 - p. 5


Spectra calculation

Ç Advantages and disadvantages of the

radiations-hydrodynamic STELLA code + CMFGEN - hydrodynamic is NOT included + Utrobin, Chugai - grey atmosphere - LTE
Ç Hydrodynamic profiles and photosphere continuum
from STELLA

Tarusa 19.01.2012 - p. 5


Spectra calculation

Ç Advantages and disadvantages of the

radiations-hydrodynamic STELLA code + CMFGEN - hydrodynamic is NOT included + Utrobin, Chugai - grey atmosphere - LTE
Ç Hydrodynamic profiles and photosphere continuum
from STELLA

Ç Rate equations

Tarusa 19.01.2012 - p. 5


Spectra calculation

Ç Advantages and disadvantages of the

radiations-hydrodynamic STELLA code + CMFGEN - hydrodynamic is NOT included + Utrobin, Chugai - grey atmosphere - LTE
Ç Hydrodynamic profiles and photosphere continuum
from STELLA

Ç Rate equations Ç Transfer equations in Sobolev approximation

and taking into account multiplet coupling

Tarusa 19.01.2012 - p. 5


Initial conditions

Ç First path: SAHA or LUCY (Tm Tc ) and Boltzmann

Tarusa 19.01.2012 - p. 6


Initial conditions

Ç First path: SAHA or LUCY (Tm Tc ) and Boltzmann Ç Second path: Number densities from first path

Tarusa 19.01.2012 - p. 6


Rate equations
Ç
nz , t
i

= -div (nz, i - ) + v
j =i

(nz, j Pj, i - nz, i Pi, j )

Tarusa 19.01.2012 - p. 7


Rate equations
Ç
nz , t
i

= -div (nz, i - ) + v
j =i

(nz, j Pj, i - nz, i Pi, j )

Ç

Dnz,i Dt

=-

3nz t

,i

+
j
(nz,j Aij + nz,i Bij Jj i - nz,j Bj i Jj i )

-
j >i

(nz,j Aj i + nz,j Bj i Jij - nz,i Bij Jij ) nz,j Cj i - ne nz,
j =i z,ic i j =i

+ne
n

C

ij z,ci

-nz,i (B +
nz,i nz

+ ne C

z,ic

) + ne nz+ (B + ne C
z- ,j c

+ ne C

z,ci

)

nz- ,j (B
j =1 n

z- ,j c

)

-nz,

i j =1

ne (B

z- ,cj

+ ne C

z- ,cj

), i = 1, 2 . . .

Tarusa 19.01.2012 - p. 7


Rate equations
Ç
nz , t
i

= -div (nz, i - ) + v
j =i

(nz, j Pj, i - nz, i Pi, j )

Ç

Dnz,i Dt

=-

3nz t

,i

+
j
(nz,j Aij + nz,i Bij Jj i - nz,j Bj i Jj i )

-
j >i

(nz,j Aj i + nz,j Bj i Jij - nz,i Bij Jij ) nz,j Cj i - ne nz,
j =i z,ic i j =i

+ne
n

C

ij z,ci

-nz,i (B +
nz,i nz

+ ne C

z,ic

) + ne nz+ (B + ne C
z- ,j c

+ ne C

z,ci

)

nz- ,j (B
j =1 n

z- ,j c

)

-nz,
Ç
Dne Dt

i j =1

ne (B

z- ,cj

+ ne C

z- ,cj

), i = 1, 2 . . .
z,ci

= nz,i (B

z,ic

+ ne C

z,ic

) - ne nz+ (B

+ ne C

z,ci

)

Tarusa 19.01.2012 - p. 7


Rate equations

Two photon decay
DnH, Dt DnH, Dt
1

= =

2

DnH, Dt DnH, Dt

1

+ A2q - A2q

2

System closure
Dnz,p Dt

=-

3nz t

,p

-
j =p

Dnz,j Dt

Tarusa 19.01.2012 - p. 7


Line transfer

ÇJ

lu

= (1 - lu )Slu + lu I Ç W

Tarusa 19.01.2012 - p. 8


Line transfer

ÇJ

lu ul

= (1 - lu )Slu + lu I Ç W =
1-exp(-lu ) lu c3 1 gl 8 lu 3 gu Aul
3 2hlu c2

Ç

lu = S
lu

t nl -
-1

gl gu

nu

=

g u nl g l nu

-1

Tarusa 19.01.2012 - p. 8


Steady state at 15 Day
15 day H, CA
1.6ç1014

steady state

f (er g /s/cm2/H z )

0. 0

0. 2

0. 4

0. 6

0. 8

1. 0

1. 2

1. 4

3000

3500

4000

4500

5000

5500

6000

6500

7000

7500

8000

8500

9000



Tarusa 19.01.2012 - p. 9


Time dependent at 15 Day
1.8ç10
14

15 day H, CA
time dep endent

f (er g /s/cm2/H z )

0. 0

0. 2

0. 4

0. 6

0. 8

1. 0

1. 2

1. 4

1. 6

3000

3500

4000

4500

5000

5500

6000

6500

7000

7500

8000

8500

9000



Tarusa 19.01.2012 - p. 10


Steady state, time dependent at 15 Day
1.8ç10
14

15 day H, CA
time dep endent steady state

f (er g /s/cm2/H z )

0. 0

0. 2

0. 4

0. 6

0. 8

1. 0

1. 2

1. 4

1. 6

3000

3500

4000

4500

5000

5500

6000

6500

7000

7500

8000

8500

9000



Tarusa 19.01.2012 - p. 11


Steady state, multiplet coupling at 15 Day
15 day H, CA
1.6ç10
14

multiplet coupling steady state

f (er g /s/cm2/H z )

0. 0

0. 2

0. 4

0. 6

0. 8

1. 0

1. 2

1. 4

3000

3500

4000

4500

5000

5500

6000

6500

7000

7500

8000

8500

9000



Tarusa 19.01.2012 - p. 12


Time dependent, multiplet coupling at 15 Day
1.8ç1014

15 day H, CA
multiplet coupling time dep endent

f (er g /s/cm2/H z )

0. 0

0. 2

0. 4

0. 6

0. 8

1. 0

1. 2

1. 4

1. 6

3000

3500

4000

4500

5000

5500

6000

6500

7000

7500

8000

8500

9000



Tarusa 19.01.2012 - p. 13


All, multiplet coupling at 15 Day
1.8ç1014

15 day H, CA
time dep endent steady state

f (er g /s/cm2/H z )

0. 0

0. 2

0. 4

0. 6

0. 8

1. 0

1. 2

1. 4

1. 6

3000

3500

4000

4500

5000

5500

6000

6500

7000

7500

8000

8500

9000



Tarusa 19.01.2012 - p. 14


20 Day
20 day H, CA
1.0ç10
14

time dep endent steady state

f (er g /s/cm2/H z )

0. 0

0. 2

0. 4

0. 6

0. 8

3000

3500

4000

4500

5000

5500

6000

6500

7000

7500

8000

8500

9000



Tarusa 19.01.2012 - p. 15


30 Day
30 day H, CA
4.5ç10
13

time dep endent steady state

f (er g /s/cm2/H z )

0. 0

0. 5

1. 0

1. 5

2. 0

2. 5

3. 0

3. 5

4. 0

3000

3500

4000

4500

5000

5500

6000

6500

7000

7500

8000

8500

9000



Tarusa 19.01.2012 - p. 16


50 Day
50 day H, CA
1.4ç10
13

f (er g /s/cm2/H z )

0. 0

0. 2

0. 4

0. 6

0. 8

1. 0

1. 2

time dep endent steady state

3000

3500

4000

4500

5000

5500

6000

6500

7000

7500

8000

8500

9000



Tarusa 19.01.2012 - p. 17


15 Day
15 day H, CA, Fe
1.8ç10
14

time dep endent steady state

f (er g /s/cm2/H z )

0. 0

0. 2

0. 4

0. 6

0. 8

1. 0

1. 2

1. 4

1. 6

3000

3500

4000

4500

5000

5500

6000

6500

7000

7500

8000

8500

9000



Tarusa 19.01.2012 - p. 18


20 Day
20 day H, CA, Fe
1.0ç1014

time dep endent steady state

f (er g /s/cm2/H z )

0. 0

0. 2

0. 4

0. 6

0. 8

3000

3500

4000

4500

5000

5500

6000

6500

7000

7500

8000

8500

9000



Tarusa 19.01.2012 - p. 19


30 Day
30 day H, CA, Fe
4.5ç1013

time dep endent steady state

f (er g /s/cm2/H z )

0. 0

0. 5

1. 0

1. 5

2. 0

2. 5

3. 0

3. 5

4. 0

3000

3500

4000

4500

5000

5500

6000

6500

7000

7500

8000

8500

9000



Tarusa 19.01.2012 - p. 20


50 Day
50 day H, CA, Fe
1.4ç1013

time dep endent steady state

f (er g /s/cm2/H z )

0. 0

0. 2

0. 4

0. 6

0. 8

1. 0

1. 2

3000

3500

4000

4500

5000

5500

6000

6500

7000

7500

8000

8500

9000



Tarusa 19.01.2012 - p. 21