Stellar collapse is accompanied by emission of E sub neutrino approximately 10 MeV neutrinos and antineutrinos with the energy output W sub neutrino approximately 10 to the 53rd power to 10 to the 54th power erg. Annihilation of these particles in the vicinity of collapsar is considered. The physical consequences are discussed

Berezinsky, V. S.

Prilutsky, O. F.

English

NASA Technical Reports Server

2 9 OG I.l.IO
NEUTRI_ O-AN TINEUTRINO J_N IKILATION:
AROUND COLLAPSING STAR
V.Z.Berezinsky and O.F.Prilutsky
Institute for Nuclesr Research, Academy
of Sciencies of the USSR
60th Anniversary of the October Re_olu-
tion Prospect 7a, 117312 Moscow, USSR
ABSTRAC_
Stellar collapse is accompanied by emission of E_ I0 MeV
neutrinos and antineutrinos with the energy output W_
IOS_-IO_erg. Annihilation of these particles(_+V-_ e++e- )
im the vicinity.,of ccllapsar is considered.The physical
consequenoies are discussed.
I. Introduction. Our interest to the problem of _-annihilation in
the vicinity of collapsing object(collapsar) is stimulated by expec-
ted possibility 0£ "quiet collapses" and by prospects of their detec-
tion using neutriz_o radiation/I-6/. Can collapse occur in such a way
that neutrino emission will be the only observational consequence?
_e think that in many cases, if not in all, neutrimo burst will be
accompanied by X,ray burst. Here we suggest a mechanism of energy _de-
position in; outer layer of collapsing star and beyond it, which can
result in ejection of small mass and in generation of X-ray burst.
This mechanism is _V-annihilation. Ai latest stages of evolution of
a massive star an isolated stellar core is produced. For a star with
N_2M O collapse results in the formati_ of a hot neutron star which
is cooling during I0-20 s mostly by neutrino radiation. For a star
with M_IO M@a hot compact core exists during several seconds follo-
wed by the formation of a black hole-. The similar compact hot core
can be produced as a result of gas accretio_ to white dwarf in a bi-
nary system. In all these cases neutrinos are emitted from "neutrino-
sphere"(analogous to photosphere). Its radius R9 is defined by cohe-
rent 9 A-_A scattering. The efficiency of _ +_-_e.+e - scattering
depends on c.m.-energy of two neutri_uos and thus it increases at
large angles between neutrin_oa. Therefore the annihilati_ beyond the
outer boundary of a star heavily depends on the radius of neutrino-
sphe re.
2. Probabilit[ of annihilation. Neutrinos emitted from neutriz_osphere
of radius R9 have Planr k spectrum characterize_ by temperature T.
Neutrinos (and antineutrincs) of all three flavours (_ ,_ ands) are
equally presented in the flux. Consider antineutrino (_)moving; in
radial direction. Colliding with the other neutrimos emitted from
neutrinosphere it undergoes at the distance dr d9 annihilation col-
lisions •
d< nv( ,e)dg-O CE )(4-ooze)da,
where _q_(g,8)is a space density of neutriz_os with energy Z moving at
an angle _ to radial direction. At e-_m_the density _9(£_e_ is gi-
ven by
.. 
29 
'l' JN O-AN 'l'llmUf1' l  lINN IHILNI'I(,)  
AllOOO  C PSDW STA  
V.S .Berezinsky and O.]'.Prilutsky, 
1nsti tute for Nuclasr Research..,Acade:my 
of Scie cies of the USS  
60th, Anniversary of the October Rewo~u­
tion. Prospec~, 7a, 117312 Moscow, USSR 
AJ3S~'RACm 
OQ, 1.1-10 
Stellar collapse is accompanied by emission. of Ev""IO MeV 
neutrinos and antineutrinos with the energy output Wv rV 
Id'"3 _Ir§Lf erg. Annihilation. of these particles(-v + 15'-7 e+ +e ) 
in. the vicinity. of collapsar is considered.The physical 
consequencies are discussed. 
I. Introduction. Our interest '~o the problem of "i7V-annihilation. in 
the vicinity of collapsing object(collapsar) is stimulated by expec-
ted possibility of "quiet collapses" and by prospects of their detec-
tion. using neutr~o radiation/I-6j. Can collapse occur in such a way 
that neutrino emission will be the only Observational consequence? 
We think that in many cases, if not in all, neutrino burst, will be 
accompanied by X-ray burst. Here we suggest a mechanism of energy de-
position in, outer layer of collapsing star and beyond it, which can 
result in ejection of small mass and in generation. of X-ray burst. 
This mechanism is '\JV -a.nnihila tion. At latest stage,s of evolution of 
a massive star an isolated stellar core is produced. For a star with 
M=2M()collapse results in the formati~ of a hot neutron star which 
is cooling during 10-20 s mostly by neutrino radiation. Fora star 
wi th MeoIO M0a hot compaot core exists during several seoonds follo-
wed by the for ation of a blaok hole. The si ilar compact hot oore 
can be produced as a result of gas acoretion. to white dwarf in a bi-
nary system. In all these cases ne~trinos are emitted from "neutrino-
sphere"(analogous to photosphere). Its rad-ius R)) is defined by oohe-
rent VA~YA scattering. The efficiency of"\) +\> -"e++e- scattering 
depends 'on o.m.-energy of two neutrinDs and thus it inoreases at 
large angles between neutrin.os,. Therefore the annihilation. beyond- the 
outer boundary of a star heavily depends on. the radius of neutriuo-
sphere • 
2. Probability of annihilation .• Ne,utrinos emitte.d from neutriaosphere 
of radius Rv have Planck speotrum oharacterized by temperature 'l!'. 
Neutrinos (and antineutrinos) of. all three flavours (e._,{ and -z:.) are 
equally presented in the flux. Con.sider antineutrino ()) moving. in 
radial direotion. Colliding with the other neutriRos emitted from 
neutrinosphere it undergoes at the distanoe dr d-v annihilation col-
lisions: 
d 'V =- d., h v (E ) e) 01 $2 0---( E c) (-1 - cos e ) vi E.. ) (r) 
where I'l,,(€,s) is a spaoe density of neutr~os with energy £ moving at 
an angle e to rad-ial direotion. At e=e'M~ the density 11,,(£)9) :hs gi-
ven by 
https://ntrs.nasa.gov/search.jsp?R=19850025598 2020-03-20T17:55:30+00:00Z
30
OD I.I-I0
where _ax = arcsin R2/r , B is neutrino brigh±ness of the neutrino-
sphere, gv =I is a statistical fact ore for massless neutrinos, dR is
a ,qolid angle _(Ec) is the oross_sectiono of V+_-_+_ -soat terimg at
energy Ec in c.m.-system. Reactions _._/_,_-and_)=._-_%_- pro-
ceed thr,ough neutral currents (Z -exc_amge). The oross-sectlon is:gi-
ven_ by
7(Ec.,_
9....
where _ =s_ _. _- 0.23, GF is Fermi eonatant., _c =E¢/2 and
Pc=(£2j m_cw) _Im_. For 9_.9z-* _+*¢- the oontributio_ oomea, from hoth_
CC(_.= -exchange) and NC(Z ° -exchange) and cross_section is
O"CE_)- 9,.. _- c
Integrating; (I) over r from R to oo one fin_s the number o_ collisi-
ons h) auffered by neutrino with energy E=KT:
o o m_, (6)
_- _ _- _ -45 2 _ -- -
_..+._.- ana _-r_..+_-c.._e+.e. ana (I..Z8/_)G,m m_o_ ,,.5.2.1,0 _'_'om_
£or _e._-> _++_-. For two cases the approximate analytical formu-
lae can_be giv_nm 2
i) at R_R_ and _T>> 2mac
R/R9
(ii) at R>k R_
fr
(8)
30 
00 1.1-10 
h (E e) = J... oIB =. <}v £2.. (exp s/K T 1- 1)-1 
v) c cit. (hc.)~ ( 2) 
where 8h\lM<. = arcsin Ry/r, B is neutrino brightness. of the neutrino-
sph re f gy -I is, a s atistioal faot.oIl. for mas ~ss neutrmos, d52. is 
a solid angle O(Ec) is the ros  ... seoti n, of v.j.v~e~e -soatterimg at 
nergy Ec in c.m.- ystem. Reactions V +Vr~e;-fe..- and ~-r;+\)-z:.~e..++e.- pro-
ceed thr.ough neutral ourrents (ZO -exohange). The ross-se tion is gi-
venl by 
:t.l.. V(Ec.J=:~(~~~f4- ~)(1+ ;:::) G~Sc-Pc-C) (3) 
where ~ =SUL '.Lew % 0.23, GF is Fermi ooniStant" E.c. -Ec/2 and 
Pc = (£::- - i'YI~C'ly(2.. • For ve.+Ve. ~ e+-+e..- the oontribution... oomes, from b;oth 
CC(v0 -exchange) and NC(ZO -exchange) and ross.,....seotion is 
R"- 2.. ':l 
()eEL ) ::. ~ (2, ~ l..-j: f + ~ ) (1+ ;::1- ) G~ ~c- Pc-c . 
c. 
1ntegrating~ (I) over r from R to oD one finds the number of oollisi-
ons V suffered by neutrino with energy E=KT: 
(5) 
Where f(Rv/R)T)=. 
R,,/R (- V(-X'- 00 
= )~ ) ~~d~ ~ ct~ -e.ii-~-1 (1- ~"'t)[i+~(1- ~') ] 
o 0 ~ ( 6) 
ZtJ,..41/ 2'Ji 2me.C /KT}; Uais (O.26/.1()G F m~ o'-{ _LI.10-45 cm2 for' VI: +Vr: 7-
e,++e- and v-c+v-z:..-'7e++e- and (I .• I8/Jr)Gi~m~c'{ _5.2.JjO-'{Som~ 
for Ve+ve.--> e.++e-. For two ca es the appraximate nalytical. formu-
~ae oan" be gi v.en.:, 2 
~) at >r-Rv and K.. T > > 2me c 
( 1) 
( 8) 
• 
31
OG I.I-IO
For the fu_her numerical estimates we shall use the calculations of
Nadyozhin./7/ for collapse of iron_Qxygen core with mass, _I=2MO . Ac-
cording to these calculations after neutronization of the core the
collapse is slowed down and stops for IO-20s untill the core (hot ne-
utron_ star) is cooled due to neutrino radiation,. At this stage the
core is characterized by the following parameters: radius and tempe-
rature of neutrinosphere are respectively R =IIkm and T=6.5.IO_°K,
the mass abo_ neutrinosphere is M=0.OII M:O, the outer radius of the
star is R=I2.7 ks, neutrino luminosity is [vq =I-65 .I0_ erg/s and
the total energy of neutrinD burst is W_ =5.8.I0 y3 erg. Inserting
these parameters inlo (7) one finds for_e _ _ 9.10 -6 • For the
case (ii) and ad hoc parameters R9 =I3 ks, R=260 km and _2 Me_ we
find _ _ 2.I0-If . Probability for _a to annihilate beyond the
neutrinosphere radius is _ _ 4.10 -_ •
3. Application_:. The most interesting consequencies are connected
with _+_-*_+._- annihilatio_l beyond the outer surface of the star.
The energy released per Is in_ the form of e+-e--pairs is _ L_v
1.5.IO _v erg/s. The production of the new particles (e_ ,e_ ,¥) i_ the
collisions of e+ and e- as well as radiatio_ im magnetic field re-
sults in formation of a fireball /8/ and finally, in X-ray burst. A
duration_ of the burst is a delicate problem connected with the stel-
lar wind from the surface of the star. Unless neutrino luminosity is
higher thanL [v_IO_erg/s neutrino pressure cannot produce the
stellar wind from the surface. The stellar wind at the considered
Kelvin; stage of collapsing star results from the heating of the star
surface to the temperature T S _ 2.2.I0 _ K corresponding to Edding-
ton luminosity. The heating is caused by 3 reasons: (i) by thermal
flux from neutrinosphere, (ii) by _-scattering of neutrino flux and
(iii) by _V -annihilation beyond the neutrimosphere. If outer shell
is composed mainly of carbon, the depth of photosphere is x_3Og/cm
The energy deposition by neutrinos inside this depth results in
equlibrium temperature T S _- 2.I0 _ K. Therefore_ the surface tempera-
ture depends o_ the. thermal flux from the deeper layers of the shell
and hence on_ the temperature gradient. It is interesting to note that
_ -annihilation diminishes the temperature gradient, since the re-
leased energy per particle is increaaing outward due to diminishing
of density. During the time the surface is heated to supereddington
temperature and stellar wind makes the surroundings of the star
opaque fon X-rays, the fireball expands and leaves the star as X-ray
hurst. If timescale of the surface heating and of the filling of the
star surroundings with the gas is _ _ I ms, then energy transferred
to the fireball is W o_ _ [v _ _ IO _W erg ....Such_ a bursh undoubily
can be detected if the collapse occurs in our Galaxy. To make the
star opaque for X-ray radiatior_ the mass loss M driven by the stel-
lar wind must be rather large. The column density X at. the time t
" tdue to mass loss M and gas velocity w (_M/g) _z is _=_t/W_(K+v _)
E_en_ for supereddington regime [ _- IO L s_ /8/ _2.10_s g/s
and the column_ density_ at t --*co , _ _ _6g/cm , is less than
critical value k c _.30g/cm _ •
1 
 1.1-10 
or t e f tther umerical sti ates e a l se t  alculations f 
Uadyozhin. /1/ for collapse of ironJ-oxygen core with mass' M:=2NIQ. Ac-
cording t  these oalculations fter eutronization of the core the 
collapse is slo ed do n and stops f r 10-2013 ntill the core ( ot e-
utron, star) is cooled due to neutrin:o radiation,. At this stage the 
core is characterized by the follo ing arameters: ra i s and te pe-
rat re of neutrinosphere are res ectively  lIk  and 1]::.6.5.1010 K, 
the ass abov:a neutrinosphere is. M=O .011 ev, the outer radius of the 
st r i  :;:sI2.1 km, eutrino l inosity i  Lvv I. 5.I 5 2.. r /s and 
the total energy of neutrino burst isWv =5.8 .10
53 erg. Inserting 
these parameters into (1) one fillda f.or ve j) ~ 9.10-6 • ]'or' the 
case (ii) and ad hoc para eters Rv =13 km" R=260 km and KT=I2 MeV we 
find )J ~ 2.10- 11 • robability for ve t  annihilate beyond the 
neutrinosphere radius is 'i) ~ 4.10-5 • 
3. Applications. The most interesting consequencies, are connected 
i t  V +-v --.'>e,++e- a nihila tion. beyond the oute r surface of the st r. 
The energy. released. per Is in, the for  o:fj' e+ -e- -pairs is '0 LvV' ~ 
I.5.I04~ erg/s. The production of the new particles (e~ ,e- ,X) in the 
o lisi~s f   - s ell s iati n in agnetic i l  -
sults in for ation. of a fireball /8/ and finally in -ray burst. A 
duration, of the rst is a elicate proble  connected ith the st,el-
r ind   rf ce f  r. nle s utrillo inosity  
higher than.; L'IIv~IO 55 erg/ s neutrino pressure cannot produce the 
ll r ind o  t  rf ce. he t llar ind t t  sidered 
Kelvin, stage of collapsing star results from the heating of the star 
surface to the te perature '.£1 s?;- 2.2.101- K corresponding to l~dding­
ton lu inosity. 'llhe heating is caused by 3 reasons: (i) by ther al 
flux: fro  neutrinosphere, (ii) by ve... -scattering of neutrino flux. and 
(iii) by ~~ -annihilation beyond the neutriruosphere. If outer shell 
is co posed ainly of carbon, the depth of photosphere is x %30g/ cm 
The energy deposition by neutrinos inside this depth results in 
equlibrium temperature Ts :::::.. 2.106 K. Therefore) the surface tempera-
ture depends ~. the, ther al flux from the deeper layers of the shell 
and hence on, the te perature gradient. It is interesting to note that, 
~V -annihilation, di inishes the te perature, radient, since the re-
leased energy- per particle is increaaing outward due to di inishing 
of density. uring the time the surface is heated to supereddingt.on. 
te perature and stellar wind makes the surroundings of the star 
opaque foI!. -rays, the fireb.all expands and leaves the star as X-ray 
b rst. If ti escale of the surface heating and of the fillin  of tho 
star surroundings with the gas is ~~ I ms, then energy transferred 
to the fireball is  "X- V Lv T..- ~ 10'-ll( erg •. Such. a burst., undoubtly 
can be dete cted if the collapse occurs in, our Galaxy. fro make the 
star opaque for X-ray radiation.; the mass loss M: driven by the stel-
l r ind ust be rat er lcnge .• , he colu n den.si t.y  at, the time t 
due to mass loss  and gas velocity v= (2-oe.M IRYf2. is ~=. Mt:(t-fJrR,(R+vt..) 
Bvenl for supe reddingt on: regime L?;:.. 10 L Ed.ol /8/ M=2 .10 (8 g/ s 
and the coluffil1j density; at t ~ 00 , )\ 00 =6g/ cm ,is less than 
critical value Xc -;::::..30g/ cm 'L • 
32 OO. l.I-lO
A oknowledgme_ts_. We are grateful to D.K.Nadyozhin for useful dis-
cusmionm •
Refe tence s.
/I/ Zeldowich Ya.B. and Gusein_ _O.K., _1965, Pisma ZhETP, 1,4
/2/Zaldovich Ya.B • and N ovikov I .D.,I9 71, The ory of Gra_i_atiom
and Stellar E_olution, Moscow, Nauka.
143_ Imshennik V.S. and Nadyozhim_ D.K.,I980, Pmepri_t ITEP N9_,N98.Domogats y G.V. and Zatsep n G T I965, Proc. 9th ICRC(London)
2,I030
/5/ Domogatsky G.VJ. et al, I977, Proc. of Int. Conf. "Neutrimo-77"
(Baksan.), 1,85.
/6/ Chudako_ A.E. and l_vazhskaya G.G_I977, Proc. of Imt. Conf.
"Neutrino-77" (Baksan), I, I55.
/7/ Nadyozhi_D.K_I978, Ap._p.Sci., 53, 1311
Yahel R.Z.. et al, 1984, Astro_. and Astrophys., 139, 359
32 00 1.1,...10 
A,cknowledgmen.ts,. We are grateful to D .• K.Nadyozhin for useful dis-
oussions. 
References. 
/ II Ze ldoViieh Ya.B. and Ouse inoVi' O.K., ' 965, Pisma ZhETP, 1,4 
/ / Ze.ldovich Ya.B. and Novikov I. .,I97I, Theory of Ora'Witatioll. 
and Stellar Ev;olution" Moscow, Nauka. 
/3/ Imshennik. V.S. and Nadyozhin. D.K.,I980, Preprint ITEP N9I.,N98. 
/4/ Domogatslq G.V. and Zatsepin. G.T., 1965, Proe. 9th ICRC(London) 
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• 


Neutrino-antineutrino annihilation around collapsing star

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