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RAYLEIGH-TAYLOR CONVECTIVE OVERTURN AS A POSSIBLE SOLUTION TO THE SUPERNOVA
PUZZLE
Mario Livio, J. Robert Buchler
To cite this version:
Mario Livio, J. Robert Buchler. RAYLEIGH-TAYLOR CONVECTIVE OVERTURN AS A POSSI-
BLE SOLUTION TO THE SUPERNOVA PUZZLE. Journal de Physique Colloques, 1980, 41 (C2),
pp.C2-155-C2-157. �10.1051/jphyscol:1980225�. �jpa-00219817�
RAYLEIGH-TAYLOR CONVECTIVE OVERTURN AS A POSSIBLE SOLUTION TO THE SUPERNOVA PUZZLE *
Abstract.-Strong neutronization above the neutrinosphere produces a convectively unstable gradient of the electron to baryon ratio Y . An I = 2 Rayleigh-Taylor overturn of the whole core is expected to ensue. A sea result the trapped neutrini are released on a short timescale, thus providing the necessary boost to cause a violent explosion.
The final word for the growth of this instability calls for a full two-dimensional calculation. Such a study is now in progress. A one-dimensional hydrodynamic para- metrization of the overturn shows that explosion results whenever mixing occurs
significantly beyond the neutrinosphere. The main cause for explosion is energy deposition in the mantle by Comptonization as well as by absorption and re-emis-
sion.
The Rayleigh-Taylor overturn of the core could thus well resolve the present puzzle of only marginally exploding supernova models.
Recent studies of stellar core collapse are still unable to poduce a conclusive answer to the problem of supernova explosions.
Hydrodynamic calculations indicate that the collapse is halted and reversed as a result of the sudden stiffening of the equation of state, at about nuclear matter densities.
An outward moving Shockwave results from this bounce (Wilson 1979a, Van Riper and Arnett 1978, Bruenn 1975).
Although the Shockwave has been demonstra- ted to produce mass ejection under adiaba- tic conditions (Lichtenstadt et al.1979, Van Riper 1978) the explosion is still gene- rally marginal (see also Mazurek 1979, Bruenn, Buchler and Yueh 1978) and too sen- sitively dependent on various parameters, in particular the adiabatic index y and the density. Furthermore, the use of a more rea-
listic equation of state in the calulation results in a standing shock (Wilson 1979b).
The expectation that a large neutrino flux would impart enough energy (Colgate and White 1966) or mementum to the mantle, thus causing its ejection, has also not been rea- lized. Neutrino transport calculations have demonstrated that the neut rlni are trapped at densities above 10 g/cc (Arnett 1977, 12
Yueh and 3uchler 1977, Mazurek 1977, Tubbs 1977) . As a result, insufficient stresses are obtained.
Epstein (1978) has observed, that be- cause of strong neutronization above the neutrinosphere ( neutrino "photosphere") a convectively unstable gradient of the electron to barvon ratio Y develoos.
e
An examination of the collapse calculations of Wilson ( 1979a), Arnett (1979) and Bruenn, Buchler, and Livio (1979), reveals, that the inversion in Y becomes even more
e
•pronounced after several bounces. This potentially unstable configuration led Colgate (1978) to suggest that a delayed Rayleigh-Taylor core overturn may occur.
The effect of such an overturn may be in the enhancement of neutrino release on one hand the release of gravitational and thermal energy on the other (Colgate and Petschek 1979), both leading possibly to an explosion.
The two important questions that need, therefore, to be answered are: (i) Can a large scale Taylor mode really grow (how fast and what is the relevant wavelength)?
and (ii) is such an overturn (provided it occurs) really capable of producing an X Paper presented at the "International Colloquium on the Physics of Dense Matter" held at
the Institut d'Astrophysique, Paris, September 17-22, 1979.
11
JOURNAL DE PHYSIQUE Colloque C2, supplément au n° 3, Tome 41, mars 1980, page C2-155
Mario Livio and J.Robert Buchler
Department of physics and Astronome University of Florida Gainesville, FL 32611 and University of California Los Alamos Scientific Laboratory LOJS Alamos, NM 87545
Résumé.-Au c o u r s du c o l l a p s e s t e l l a i r e , l a n e u t r o n i s a t i o n i n t e n s e a u - d e s s u s de l a n e u t r i n o s p h è r e c r é e un g r a d i e n t de l a c o n c e n t r a t i o n des é l e c t r o n s q u i c a u s e une i n s t a b i l i t é de R a y l e i g h - T a y l o r d ' o r d r e H=2. I l en r é s u l t e un chamboulement q u i l i b è r e l e s n e u t r i n i emprisonnés dans l e coeur de l ' é t o i l e q u i eux à l e u r t o u r c a u s e n t l ' e x p l o s i o n v i o l e n t e de l ' e n v e l o p p e s t e l l a i r e .
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1980225
JOURNAL DE PHYSIQUE
explosion?
The f i n a l word concerning t h e f i r s t ques- t i o n c a l l s f o r a f u l l two-dimensional hydro dynamic c a l c u l a t i o n . Such a s t u d y i s now i n iDrogress ( L i v i o
,
Ruchler,
and ~ o l g a t e (1 97 9).A t t h e p r e s e n t time we can only g i v e an answer i n terms of p l a u s i b i l i t y arguments.
Lattimer (1979) h a s shown t h a t n e u t r i n o l o s - s e s from m a t t e r j u s t above t h e n e u t r i n o - s p h e r e (even a t t h e l i m i t of z e r o k i n e t i c energy) l e a d t o a r e d u c t i o n i n t h e p r e s s u r e . This i n t u r n means, t h a t a c o n v e c t i v e l y uns- t a b l e s i t u a t i o n w i l l a r i s e , provided t h a t t h e ( s t a b i l i z a t i n g ) e n t r o p y g r a d i e n t i s n o t t o o s t e e p and t h e p r e s s u r e depends o n l y wea- k l y on t h e e n t r o p y . Cogate and Petschek
(1979) argue, t h a t s i n c e t h e n u c l e i have a v e r y l a r g e s p e c i f i c h e a t , t h e thermal energy i s p r i m a r i l y absorbed by t h e l a r g e number of n u c l e a r e x c i t e d s t a t e s and t h u s h a s o n l y a l i t t l e e f f e c t on t h e p r e s s u r e . I n a d d i t i o n , t h e y n o t e , t h a t according t o t h e c a l c u l a - t i o n s of L i c h t e n s t a d t e t a l . (1979)
,
a shock g e n e r a t e d , l a r g e entropy g r a d i e n t , can cause mass e j e c t i o n i n i t s e l f , even w i t h o u t any c o r e o v e r t u r n . They t h e r e f o r e conclude t h a t t h e combination of Ye and entropy g r a d i e n t s s h o u l d be c o n v e c t i v e l y u n s t a b l e .The !2 = 2 u n s t a b l e mode, corresponding t o an eddy s i z e X
-
aR i s expected t o have t h e l a r g e s t i n i t i a l amplitude, s i n c e it i s exci- t e d by s t e l l a r r o t a t i o n . This mode w i l l a l s o have t h e l a r g e s t p o t e n t i a l energy a v a i l a b l e and t h e r e f o r e l e a d t o h i g h e r v e l o c i t i e s . The i m p o r t a n t t h i n g t o n o t e i s t h a t t h e develop- ment of such an u n s t a b l e mode w i l l i n v o l v e a n o v e r t u r n of t h e whole c o r e r a t h e r t h a n j u s t *he u n s t a b l e r e g i o n . The growth time of a p e r t u r b a t i o n of wave nunber K i s g i v e n byT - [(p2-p,) K a / ( ~ ~ + p ~ q ~ / ~ , where a
i s
t h e a c c e l e r a t i o n and K t h e wave number and i s of t h e o r d e r of a few m i l l i s e c o n d s f o r t h e R = 2 mode. I n t h e non l i n e a r regime t h e growthtime i s given roughly by t h e c o r e t r a v e r s a l time which i s of t h e o r d e r of 0.3 m s (Col- g a t e and Petschek 1979). Thus, t h k growth r a t e i s f a s t compared t o t h e d e l e p t o n i z a - t i o n time of t h e o u t e r p o r t i o n of t h e c o r e ,
which i s of t h e o r d e r of 30 m s (Wilson 197%) .One t h e r e f o r e e x p e c t s t h a t t h e neu- t r i n i t h a t have been trapped i n t h e c o r e p r i o r t o t h e o v e r t u r n w i l l be dredged i n t o t h e s e m i t r a n s p a r e n t r e g i o n s , e n a b l i n g them t o impart energy and momentum t o t h e mant- l e . I n a d d i t i o n , t h e r e l e a s e of g r a v i t a - t i o n a l energy by t h e plume can a l s o a s s i s t i n e j e c t i n g t h e mantle.
I n o r d e r t o answer t h e second q u e s t i o n (whether t h e o v e r t u r n s u p p l i e s enough e n e r gy f o r t h e e x p l o s i o n ) , Bruenn, Buchler and L i v i o (1 97 9) have developed t h e f o l l o w i n g scheme : t h e convection i s parametrized by mixing l e p t o n s , s t a r t i n g a time A t a f t e r
t h e bounce. The mixing i s performec? o u t t o a r a d i u s R m i x r on a time s c a l e t
mix
'
where YL i s t h e l e p t o n t o baryon r a t i o and t h e average i s mass weighted t o ensure l e p t o n c o n s e r v a t i o n i n t h e p r o c e s s . I n s i d e t h e n e u t r i n o s p h e r e , d e f i n e d by a d e n s i t y p% l o c a l b e t a e q u i l i b r i u m i s assumed b e t -
ween e l e c t r o n s and n e u t r i n i . Outside t h e n e u t r i n o s p h e r e , t h e n e u t r i n o d i l u t i o n i s approximated w i t h t h e r e l a t i o n
where d i s a d i l u t i o n parameter which sh- ould be between 2 (decoupled n e u t r i n i ) and 3 (volumic expansion). The spectrum of t h e n e u t r i n i i s chosen a s t h e one t h e y had a t t h e decoupling p o i n t r* (corresponding t o p*). Neutrino t r a n s p o r t h a s been t r e a t e d by t h e m u l t i g r o u p d i f f u s i o n scheme (Bruenn Buchler and Yueh 1978) and a 1-D hydrocode (Bruenn, 1975) followed t h e e v o l u t i o n . A l l c a l c u l a t i o n s s t a r t e d a s an i r o n c o r e poly- t r o p e of index 3. The c e n t r a l d e n s i t y was pc= 5 x 1 0 ~ g / c m 3 and temperature Tc = 1 . l x 1010 K. T h i s p a r t i c u l a r model, when c o l a - psed and followed through s e v e r a l bounces d i d n o t produce a n e x p l o s i o n ; it w i l l s e r v e u s a s a r e f e r e n c e model.
A s we h a v e a l r e a d y m e n t i o n e d t h e m i x i n g t i m e i s e x p e c t e d t o b e o f t h e o r d e r o f a few m i l l i s e c o n d s ; i t s v a l u e h a s b e e n v a r i e d b e t w e e n ' l m s and 30 m s . S i n c e t h e e x a c t den- s i t y o f n e u t r i n o d e c o u p l i n g i s n o t c l e a r , P* h a s b e e n v a r i e d i n t h e r a n g e 1 0 ' ~ - 1 0 ~ ~ g /
c m 3 . A t t h e o n s e t o f t h e m i x i n g p r o c e s s t h e i r model had 10 z o n e s between
r
% and t h e s h o c k . Rmix h a s b e e n v a r i e d from 2 z o n e s beyond r i t o 2 z o n e s b e h i n d t h e s h o c k . A l l m o d e l s t h a t h a v e b e e n mixed s i g n i f i c a n t l y beyond t h e n e u t r i n o s p h e r e r e s u l t i n a n e x p l -/ 3 / Bruenn, S.W., 1975, Ann. N.Y. Acad.
S c i . ,
262,
8 0 ./4/ Bruenn, S.W., B u c h l e r , J . R . and Yueh W.R. 1 9 7 8 , Ap. Space S c i .
59,
261./5/ Bruenn, S.W., B u c h l e r , J . R . a n d L i v i o P4. 1 9 7 9 , S u b m i t t e d t o Ap. J . L e t t e r s ,
" R a y l e i g h t T a y l o r C o n v e c t i v e Over-
t u r n i n S t e l l a r C o l l a p s e " .
/ 6 / 'lueh, Y.?. and 3uc:iler, T . 7 . 1 9 7 7 , P.p. J . L e t t .
G ,
Ll21.J7/ L i r 7 i b , 1:.
,
Buckler, Z. R. and C o l g a t e , S.A. 1979, i n p r e p a r a t i o n ./8/ C o l g a t e ; S.A. 1978, LASL p r e p r i n t , l A - UR-78-203 0,
"
Supernova Plass E j e c t i o n and C o r e Hydrodynamics".o s i o n . A l t h o u q h n e u t r i n o s t r e s s e s a r e i n c r e - /9/ C o l q a t e , S.A. and P e t s c h e k , A.G.,197g a s e d , t y p i c a l l y by a f a c t o r o f 5 , t h e main p r e p r i n t , "Dynamical Supernova
cbre
O v e r t u r n a n d Plass E j e c t i o n " .
f a c t o r i n c a u s i n g t h e e x p l o s i o n i s e n e r g y
/ l o /
C o l g a t e , s . A . andmite,
R . H . , 1966, d e p o s i t i o n ( b o t h b y c o m p t o n i z a t i o n and by Ap. J .143,
626.a b s o r p t i o n a n d r e - e m i s s i o n ) . A tremendous /11/ E p s t e i n , R . I . , 1 9 7 8 , "Lepton D r i v e n s t r e n g t h e n i n g o f t h e shock a s a r e s u l t o f t h e C o n v e c t i o n i n Supernova" Mon. Not.
Roy. A s t r o n . Soc., i n p r e s s .
d e p o s i t e d e n e r g y i s o b t a i n e d . Two non e x p l o - 21 L a t t i m e r , .M., 979, private colmu- d i n g m o d e l s had u n r e a l i s t i c a l l y s m a l l v a l u e s n i c a t i o n
.
o f (Rmix-r* )
,
d e m o n s t r a t i n g t h e i m p o r t a n c e of n e u t r i n o d r e d g i n g t o t h e s e m i t r a n s p a r e n t r e g i o n s o u t s i d e t h e n e u t r i n o s p h e r e . Theto-
t a l e n e r g y o f t h e o u t w a r d moving z o n e s i n t h e e x p l o d i n g m o d e l s i s i n t h e r a n g e 4.1 x1051
-
7.0 x e r g s .W e r e g a r d a s v e r y e n c o u r a g i n g t h e f a c t t h a t we c a n answer a f f i r m a t i v e l y t h e s e c o n d q u e s t i o n we h a v e p o s e d . T a y l o r o v e r t u r n ( i f it o c c u r s ) c o u l c ? t h e r e f o r e w e l l b e t h e a n s - wer t o t h e p r e s e n t s u p e r n a v a i m p a s s e . The c o n c l u s i v e a n s w e r c o n c e r n i n g t h e g r o w t h 0 5 t h e i n s t a b i l i t y , however, w i l l h o p e f u l l y b e g i v e n by a two d i m e n s i o n a l hydrodynamic c a l - c u l a t i o n ( L i v i o , B u c h l e r and C o l g a t e 1 9 7 9 ) .
W e g r a t e f u l l y a c k n o l e d g e f r u i t f u l d i s c u s - s i o n s w i t h S t e v e Bruenn a n c ' s t i r l i n g C o l g a t e .
T h i s work h a s b e e n s u p p o r t e d i n p a r t by t h e N a t i o n a l S c i e n c e F o u n d a t i o n (AST 77- 17572) a t t h e U n i v e r s i t y of F l o r i d a and b y t h e Department of Energy a t LASL.
L i c h t e n s t a d t , I . , S a c k , N . and Blud- man, S.A., 1 9 7 9 , p r e p r i n t I w E f f e c t s o f E q u a t i o n of S t a t e o n t h e Outcome o f S t e l l a r C o l l a p s e " .
Mazurek, T . J . , 1977, Comments i n Ap.
S p a c e S c i . ,
1,
77.Mazurek, T.J., 1979, p r i v a t e communi- c a t i o n .
Tubbs, D.L., 1977, " D i r e c t S i m u l a t i o n Y e u t r i n o T r a n s g o r t A s p e c t s Of eciui- l i b r a t i o n " , S u b m i t t e d t o A p . J . Sup- p l e m e n t .
Van R i p e r , K . , 1978, Ap. J.
221,
304 Van R i p e r , K . and A r n e t t , D.W., 1978, Ap.J. L e t t .225,
L129.Wilson, J . R . , 1 9 7 9 a , p r e p r i n t ,
" N e u t r i n o Flow a n d S t e l l a r C o l l a p s e " . Wilson, J.R., 197913, "all: q i v e n . a t tlke Aspen Florkshop o n S t e l l a r C o l l a - p s e .
R e f e r e n c e s
/1/ A r n e t t D.W., 1977, Ap. J . 2 1 8 , 8 1 5 /2/ A r n e t t ,D .W., 1979, p r i v a t e communica-
t i o n .
