Energy spectra of photons emitted from Bremsstrahlung (BR) of energetic electrons with matter, is obtained from the deconvolution of the electron energy spectra. It can be inferred that the scenario for the production of X-rays and gamma rays in solar flares may vary from event to event. However, it is possible in many cases to associated low energy events to impulsive acceleration, and the high energy phase of some events to stochastic acceleration. In both cases, flare particles seem to be strongly modulated by local energy losses. Electric field acceleration, associated to neutral current sheets is a suitable candidate for impulsive acceleration. Finally, that the predominant radiation process of this radiation is the inverse Compton effect due to the local flare photon field

Alvarez, M.

Gallegos, A.

Laville, A.

Perez-Peraza, J.

English

NASA Technical Reports Server

34 SH I. 2-3
STUDY OF NON-THERMAL PHOTON PRODUCTION UNDER DIFFERENT SCENARIOS IN
SOLAR FLARES. II. THE COMPTONIN_ERS£ AND BREMSSTRAHLUNGMODELS AND
FITTINGS.
J. P_rez-Peraza* and M. Alvarez*;A, Lavi!le**
Instituto de Geoffsica UNAM, 04510-C.U., M6xico, D. F,, MEXICO
A.Gallegos
Depto. de FTsica, UPICSA, 08400 - M_xico, D. F., MEXICO
1. Introduction. Energy spectra of photons emitted from Bremsstrahlung
(BR) of energetic electrons with matter, is obtained from the deconvolu-
tion of the electron energy spectra derived in _H 1,2,-2, According to
Kane and Anderson (1970), the differential photon flux at the earth
level is
Em
dJ(h_) _ 3.53x10"28E.M. f do(E,hv) N(E)dE (photons/s KeV cm 2) [I]
d(h_) n E dE
where do(E,hv)/dE is the differential cross-section for electron_proton
(BR), given in the non-relativistic range by the Bethe-Heitler formula
(Jackson, 1962) and in the relativistic domain by the Koch and MQtz
formula (Bai and Ramaty, 1976); E.M. = n2V is the emission measure, with
n and V the number density and volume respectively. For Inverse Compton
(IC) we followed Sheng (1972), introducing o(W,h_) = ot_[h_-(4/3)_
(W/m c2) 2] in eq.(1) for W<(m c2)2/4_m 290 MeV, where W=total electrone e
energy, o.=6.65xi0 -25 cm2=Thompson cross-section and _=2.7kT=mean
thermal p_oton energy, and we obtained at I Astronomical Unit.
dJ (h_)/d(h_)= (4.39xi0-31 E.M"_ph(hv)½/n2T3/2) N(E=meC2{ (3h_/4_)½-I })
(photons/s KeY cm2) [2]
For the evaluation of the electron energy spectra we have explored dif-
ferent combinations of the source physical parameter in the scenarios
displayed in SH 1.2-2= n=lOl°-lO 13 cm-3 with T=lOS-lO 7 °K in scenario
(a), n=101°-1012 cm-3 with T=lOS-107°K in scenario (b). For scenario (c)
we used the combination of the two previous parameter sets. Values of
B were delimited from the thermal flux No in SH 1.2-2, for every couple
(n,T), by normalization of No with the point of maximum flux and minimum
energy in the observational photon spectra. For the evaluation of the
spectrum [10] of scenario (d) we sweped n=101°-1013cm -3, L=108-109cm,
B=102-103 gauss and £=10"3-10 V/cm; in this case two assumptions were
worked out for the transport and photon emission regions respectively,
first n=101°-1011 cm'3,T=lOS-lO 6 °K with n=109-101° cm"3, T=106-108 °K,
and on the other hand n=101°-1012 cm-3 , T=lOS-lO 6 oK with n=I012-1013
cm-3 , T=104-10 s °K. For the acceleration efficiencies of the Fermi,
Betatron and electric field acceleration processes in scenarios (a)-(c)
we have required that the net energy change rate dE/dt>O in eqs. [7] and
[8] of paper SH 1.2-2. The mean acceleration time T in eq. [6] is the
free parameter of our analysis, however, we have restricted it to physi-
cally reasonably values quoted in the literature. Similarly we have
proceeded for the selection of the three characteristic times of scenario
(d): the characteristic time _ of the injection rate in eq. [5] of
SH 1.2-2, and the mean remain times T1 and T2 of particles in the trans-
**INAOE
* On leave for the Instituto Naciona! de Astrof[sica, Opt[ca y Electr6nica_
A.P. 5!, Z.P. 7200 - Puebla, M_xico.
34 SH 1.2-  
TUDY F N-THERMAL PHOTON RODUCTION UNDER I ENT CENARIOS I  
OLAR . I . THE OMPTON I \L [ ND BREMS TRAHLUNG ODELS AND 
I GS. 
J. P~rez-Peraza* and M. lvarez*;A. Laville** 
I stituto de eoffsica UNAM, 04510-C.U., M~xico, . ., EXICO 
. allegos 
epto. de fsica, PI S , 08400 - M~xico, . ., E ICO 
. I troduction. er y s ctra f tons e itted fr  re sstrahlung 
(BR) of energetic electrons ith atter, is obtained fro  the deconvolu-
tion f t e electron energy s ectra derived in ~H .2,-2. ccording t  
ane and nderson (1970), the differential photon flux at the earth 
l el i  
 
dJ(hv) = 3.53xl0- 28 E.M. J da(E,hv) N(E)dE (photons Is KeV cm 2) [1] 
d(hv) n E dE 
here da( ,hv)/d  is the differential cross-section for electron~proton 
( ), i  in th  n-relativistic ran   th  et e- eitler form l  
(Jac s , ) a  in t e r l ti i ti  ai  by the och a  tz 
f r l  ( i  at , ); . .  2  is th  issi  easure, it  
n and V the nu ber density and volu e respectively. For Inverse Co pton 
(IC) we followed Sheng (1972), Jntroducing a(W,hv) = a 6[hv-(4/3)i 
( /m C 2) ] in e . ( ) f r «m C 2) /4E'V  e , here t \·/=total l tr  
  
r , a 6. 10- 25 c 2 pson r - ti   € .  mean 
l ~  r y,   t   1 st ical nit  
dJ(hv)/d(hv)=(4.39x10- 31 E.M.w h(hv)~/n2T3/2)N(E=m c2{(3hv/4£)~-1})   
( hotons/s eV c 2) [ ] 
or the evaluation of the electron energy spectra e have explored if-
ferent binations f t e s urce hysical rameter i  t e enarios 
isplayed i  S  .2-2: 10 10-10 13 - 3 ith 105-107 O  i  enario 
(a), n=10 10-10 12 c - 3 ith T=106-107°K in scenario (b). For scenario (c) 
e used t e co bination f the t o previous parameter s ts. alues of 
B ere del imited fro  the thermal flux No in SH 1.2-2, for p.very couple 
(n,T),  r al ization f o ith the int f i  flux  i i u  
energy in the bservational photon s ectra. or the e aluation f the 
spectrum [10] of scenario (d) we sweped n=1010-1013cm-3, L=10 B-10 9cm, 
B=10 2-10 3 gauss and E=10- 3 -10 V/cm; in this case two assumptions were 
worked out for the transport and photon emission regions respectively, 
first n=10 10-10 11 CM- 3 ,T=10 5-10 6 OK with n=10 9-10 10 cm- 3, T=10 6-10 B OK, 
and on the other hand n=1010-1012 c - 3, T=10 5-10 6 OK ith n=10 12-10 13 
cm- 3, T=104_105 OK. For the acceleration efficiencies of the Fermi, 
Betatron and electric field acceleration processes in scenarios (a)-(c) 
we have required that the net energy change rate dE/dt>O in eqs. [71 and 
[8] of paper SH 1.2-2. The mean acceleration time l in eq. [6] is the 
free parameter of our analysis, however, we have restricted it to physi-
cally reasonably values quoted in the I iterature. Similarly we have 
proc eded for the selection f the thr e haracteristic times f cenario 
(d): the characteristic time ~ of the injection rate in eq. [5] of 
SH 1.2-2, and the mean remain times II and l2 of particles in the trans-
;',;~ I NAOE 
* On leave for the Instituto Nacional de Astroftsica, Optica y Electr6nica, 
.P. 1, .P. 00 - Puebla, ~1exico. 
https://ntrs.nasa.gov/search.jsp?R=19850026426 2020-03-20T16:52:54+00:00Z
8S SH 1.2-3
port and emission regions respectively. It should be noted that,although
electric field acceleration in scenario (a) and neutral sheet accelera-
tion in scenario (d) is basically the same process_in the former case we
are adopting a thick geometry, while in the later energy losses in the
acceleration volume are neglected (thin geometry_ and the spectrum is
derived in a quite a different form, by following particle trajectories
in the electromagnetic field of the sheet is diffusion region, for the
photon field we sweped from _ph = 1012"1018 eV/cm3'
2. Results. Low energy events and the impulsive phase of high energy
events are better described within the frame of scenario (a) rather than
with (d)(Figs.1-3). Acceleration in those events is better described by
impulsive electric field acceleration in the context of thick geometries,
while the dominant radiation process is the (IC) effect, even whithin the
frame of the thin geometry of scenario (d). The range of accelerating e-
lectrid fields falls between 6.5xi0"3-I0 "2 V/cm, whereas in scenario (d)
higher fields are required (I-15) V/cm. Similarly, the adequate magnetic
field strengths are 50-100 gauss, whereas in scenario (d) it is needed
400-500 gauss. Typical number densities are I0II cm-_, but 10I° cm"3 in
the acceleration region with !013 cm"3 in the emission region in scena-
rio (d). Temperatures of 106 °K and photon fields > 1017eV/cm 3 prevail
in the source. Characteristic acceleration times are 0.03-0.06 s and
much higher (30-50)s in scenario (d), where corresponding emission times
are _80-I00 s. Non-impulsive energy spectra of low and high energy events
(usually associated to 2nd acceleration stage) are better described by
stochastic acceleration from thermal energies, scenario (b), and radia-
tion from (IC) than with injection from a preliminar acceleration phase
within the volume of secondary _tochastlc acceleration scenario (c), in
which case radiation appears from (BR). The acceleration efficiency in
this kind of events must be very high (_=I0-20 s'1), while the corres-
ponding acceleration times are quite shorter m 0.002 s, but if the con-
tribution of a first acceleration step is considered the acceleration
efficiency turns to be lower. Typical parameters involved in these events
are n=10_Icm "3, T_IO 6 °K, Bm50 gauss, while _ph values (1016-1017)eV/cm3
are lower than in impulsive events. On the other hand, the global des-
cription of energy spectra composed of two different components (usually
associated with two acceleration phases) is better assuming scenario
(c) than with (b), in which case radiation from (IC) is dominant, with
_ph_1017eV/cm3 I T:O 02S n=1011cm "3 T=IO6 °K and B=50 gauss, _ _ I s" , . , ,
Optimum fits to the observational spectra are sumarized in table I.
3. Conclusions. From this study it can be infered that the scenario for
the production of (X'T) rays continum in solar flares may vary from
event to event, however, it is possible in many cases to associate low
energy events to impulsive acceleration, and the high energy phase of
some events to stochastic acceleration. In both cases, flare particles
seems to be strongly modulated by local energy losses, Electric field
acceleration, associated for instance to neutral current sheets is a
suitable candidat for impulsive acceleration, Finally we claim that the
predominant radiation process of this radiation is the (IC) effect due
to the local flare photon field.
35 SH 1.2-3 
port and emission regions respectively. It should be noted that,although 
electric fi l  acceleration i  scenario ( ) a  eutral sheet ccelera-
tion in scenario (d) is asically the sa e process) in the for er case e 
are adopting a thick geometry, hile in the later energy losses in the 
acceleration ol e r  eglected (t i  e etrYh a  t e s ectr  is 
derived in a uite a ifferent for , by follo ing article traject ries 
in the electr agnetic fiel  of the sheet is iff si n region. f r the 
photon field we sweped from wph = 10
12
_10 18 eV/cm 3. 
. esults. o  energy events a  t  i pulsi e hase f i  e er y 
ents r  e ter escri d ithin t  a  f enario  t r t  
ith ( )( igs.I-3). cceleration in those events is etter described by 
i pulsive electric field acceleration in the context of thick geometries, 
hile the do inant radiation process is the (I ) effect, even hithin the 
fr e f t  t i  etry f s nari  ( ). he r  f ccelerati g -
l tri  i l  ll  t e  . xl0- 3-10- 2 / , hereas i  nari  ( ) 
higher fields are required (1-15) V/c . Si ilarly, the adequate agnetic 
field strengths are 50~100 gauss, hereas in scenario (d) it is needed 
400-500 gauss. Typical number densities are 1011 cm- 3, but 1010 cm- 3 in 
t e accelerati n region ith 10 13 c - 3 in t e e ission region in sce a-
rio (d). Temperatures of 10 6 oK and photon fields> 10 17eV/cm 3 prevail 
  rce. haracteristic celerati n t s  . - .  an  
uch i er ( - )s in sce ari  ( ), here c rres di g e issi n ti es 
are ~0-1  s. on-i pulsive energy spectra of low and high energy events 
(usually associated to 2nd acceleration stage) are better described by 
hastic celerati n o  t l ergies, ari  ,  i -
ti  fro  (I ) t a  it  i j ti  from a rel i inar celerati n ase 
ithin the volu e of secondary £tochastic acceleration scenario (c), in 
which case radiation appears from (BR). The acceleration efficiency in 
this kind of events ust be very high (a=10-20 S-l), hile the corres-
ponding acceleration times are quite shorter ~ 0.002 s, but if the con-
tribution of a first acceleration step is considered the acceleration 
efficiency turns to be lo er. Typical para eters involved in these events 
are n=10 11cm- 3, T~106 oK, B~50 gauss, while woh values (1016-10 17 )eV/cm 3 
are lo er t a  i  i ulsi e e ents. n t e t er a , t e l al es-
cription of energy spectra composed of two different components (usually 
associated with two acceleration phases) is better assu ing scenario 
(c) th,C'1n with (b), in which case radiation from (IC) is dominant, with 
wph~1017eV/cm3, a ~ 1 S-l, T=0.02s, n=10 11 cm- 3, T=10 6 oK and B=50 gauss. 
Optimum fits to the observational spectra are sumarized in table 1. 
3. Conclusions. From this study it can be infered that the scenario for 
the production of (X-y) rays continu  in solar flares may vary from 
event to event, however, it is possible in many cases to associate low 
energy events to impulsive acceleration, and the high energy phase of 
some events to st c astic accelerati . In both cases, flare articles 
seems to be strongly odulated by local energy losses. lectric field 
acceleration, associated for instance to neutral current sheets is a 
suitable candidat for impulsive acceleration. Finally we claim that the 
predo inant radiation process of this radiation is the (lC) effect due 
to the local flare photon field. 
TABLE 1 SH 1.2-3
ACCEL. PARAHETERS FLAREPARAMETERS BEST FITTING
BEST
EVENT SCENA- ACCEL. & LOSSES P_O. Wph _(V/cm) T(s) n(cm"_) T(_K) B(gauss) (FIGS.I-6)
RIO PROCESSES PROC. (eV/cm s) _(s "z) T',Xl,T2(S)
1-111- 970 (a) EFA=electrzc £_eldlC 5xlO 17 E=I0 -2 6xlO -s 1011 106 90 EFA-IC
acceleratzon
X-PAYS (a) BETA= betatron IC 3xi0IG _-I 0,3 1011 107 10035-16oKeV
... neutrBl sheet 101o.101 $ONEPHASE (d) 8_a= accelera_lon BR E-IO 50,500,100 106 500
30-111-1969 (a) EFA IC 10 z; €-6 5xlO-s 6x10 -s 1011 10s 50 EFA-IC
X-RAYS (a) EFA BR €-2 10 101_ 2x10 s 10028-25_ KeY
ONEPHASE (d) NSA IC 3x1017 €-15 5Ot200Ot100 101°-1.0 is 10s 400
4-111-1972 (a) EFA IC 10 z_ E-SxlO "2 3x10"2 10zz 106 50 EFA-tC
y-RAYS (a) BETA IC 1016 u-i 0.2 10zz I0 T 1200.4-0.7 MeV
1st PHASE (a) BETA BR _-10 I. 10_1 10_ 50
(d) NSA IC 2.511017 _-_ 30,400,80 lOZ°-tO 12 _06 _00 _10
¢D
4-111-1972 (b) FERHI IC 1017 _-20 2x10 -s 10zz 106 50 FERHI-IC
y-RAYS (b) FERHI BR _-1 1. 1011 10s 500.8-7HeV
2nd. PHASE (c) (BETA-IC)-FERHI BR I0 z_ Q-1 5x10"2 10_z 107 160
30-111-1969 (b) FERHI IC 10_6 u-lO 2x10 -_ 10_x 106 45 FERNI-IC
X-RAYS (b) FERHI BR - _-0.5 0.5 I0 sl 106 4028-254 KeY
2nd. PHASE (c) (EFA-IC)-FERHI BR 1017 €-10 2x10 "2 1012 106 100
_-Vtit-1972 (b) FERH! IC I016 _-10 1,5x10 "s 109 107 _5
y-RAYS (b) FERHI BR - _-1 0.3 10 z° 106 500.4-7 HeV
1st. _ 2nd. (c) (EFA-IC)-FER IC 101_ 5xiO -_ 2.5x10 -_ 10z_ 106 50
PHASE (c) (BETA-IC)-FERHI IC 2x10z? I. 0.02 10 zz 106 50 (BETA-IC)-FERHI-IC
(c) (BETA-IC)-FERHI BR 3xI0 z¢ _-10 7x10"z 1011 107 100
09
I,o
i
TABLE 1 SH 1.2-3 
ACCEL. PARAMETERS FLARE PARAMETERS BEST FITTING 
BEST wph EVENT SCENA- ACCEL. & LOSSES RAD. £lV/em) T(S) n(em-') T(OK) B(gauss) (FIGS.I-6) 
RIO PROCES ES PROC. (eV/em') ~(S-l) T',Tl'T2(S) 
1-1" - 970 (a) EFA=el ec tn.c fl.eld IC 5xl017 £_10. 2 6xI0-' loll 106 90 EFA-IC 
X-RAYS acceleratl.on 
35-160 KeV (a) BETA = betatron IC 3xl016 a-I 0.3 1011 10
7 100 
ONE PHASE (d) NSA=n~g~~f~r~€r8~ BR £-10 50,500,100 lOU-lOU 106 500 
30- " 1-1969 (a) EFA IC 1017 £-6 5x10- s 6xl0-' lOll 106 50 EFA-IC 
X-RAYS (a) EFA BR £-2 10 1019 2xl0s 100 28-251t KeV 
ONE PHASE (d) NSA IC 3xl017 £-15 50 12000 1100 1010-10lS 106 Itoo 
It-" 1-1972 (a) EFA IC 1017 £-5xI0- 2 3xl0- 2 lOll 106 50 EFA-IC 
y-RAYS (a) BETA IC 1016 a-I 0.2 lOll 107 120 0.It-0.7 MeV 
1st PHASE (a) BETA BR 0-10 1. lOll 106 50 
(d) NSA IC 2.5xl0P £-1 30,400,80 1010 -1012 106 400 fit 
4-111-1972 (b) FERMI IC 1017 a-20 2x10- 3 loll 106 50 FERMI-IC C. 
y-RAYS (b) FERMI BR a-I 1. lOll 106 50 0.8-7MeV 
2nd. PHASE (e) (BETA-IC)-FERMI BR IOu a-I 5xl0- 2 lOll 107 160 
'" 
30-111-1969 (b) FERMI IC 1016 a-IO 2x10-s lOll 106 45 FERMI-IC 
X-RAYS (b) FERMI BR a-0.5 0.5 lOll 106 40 28-254 KeV 
2nd. PHASE (e) (EFA-IC)-FERMI BR 1017 e:-l0 2x10-2 IOU 106 100 
'" 
4-VIIl-1972 (b) FERMI IC 1016 a-l0 1.5xl0- s 10 9 107 45 
'" y-RAYS (b) FERMI BR a-I 0.3 1010 106 50 0.4-7 MeV 
1st. & 2nd. (e) (EFA-IC)-FER IC 1017 5xl0- 2 2.5xl0- 2 1011 106 50 
PHASE (e) (BETA-IC)-FERMI IC 2xl017 1. 0.02 lOll 106 50 (BETA-IC)-FERMI-IC 
(e) (BETA-IC)-FERMI BR 3xl016 a-IO 7xl0- 2 1011 107 100 
Vl 
:c 
N 
I 
W 
3
7
SH
I
.2
-3
R
eferences
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_3,415,
19
-
-
-75
d 
;; 
~ 
~ 
... 
! 
'" '2 , 
010 
o 
:J: 
a. 
Mi 
10' 
R Ay S ":'''., FIG 1 x- '\'., 1~11-I910 ',\ "-
OIIE ~.,S (J91t) ,\ \ .......... (rao_. ". ""-
, 
'..\\ 
\\~ 
PI EFA-IC --
~l BETA-IC - - --
(01 fFA- BR 
(Ill BETA-BR--'-1 
~) NSA-BR •••••• 
(eI) NSA -Ie ------
, 
PWOTON ENERGY 10' (ke") 
~~r/--~~'-~----------'------r---r--, 
10' 
~ 
~ 
.. '? 
5 
't;-
~ 
o 
a: 
'0'" 
F IG4 
t-RA'fS 
4.'1111-191'2 
f '~ Z~P~ASE \ •• ~ SURI e4~(~,~ '1.\\'., 
,,\ ',,, 
(~FER-IC­
(hj H: R-BR- --
(d CEfA Ulf'ER-IC ---
ee) lBfr-10.fER-1C 
Ie) (8ET-lc).fE~.,--. 
(C:)(sETA-IOFER-BR ...... 
5.161 , • • • • . .; t \! 
5a lCf' 10· ... It 10· 
PHOTON HJER6Y (M.V) 
Id 
'> ~ 
"',; ~ § 
"(;;-
'2 0-15\0 
::r 
Q. 
kl 
(eU HA Ie---
(0) 8n~-lC---­
raj EFA-SR 
(0) BET~-BR--'­
"I ~SA-~·· .. • .. 
(0) 1lY>.· Ie - ---
FIG 2 
x- RA. 'IS 
30-1I\-196~ 
ONE PIlAU 
FROu ... III'm) 
.J I 
10 , 10' ·1 i.. 
PH OT 0 III 
~drl--~--~~~--~~----------~-' 
let 
::; 
"'f 
~ 
t 
! 
~ 
~ 
.<j 
~ -. 
'\ -
Flas 
x-RA.'fS 
30 1II-\~i9 
2'!! PHASE 
F ROsh+ 01 (1911 
~ . ~~~;. . ..•.• 
X '. 
\ '. 
\ ~ ~ 
\ '\ .. 
'\ : 
(b)HlHC -- \ '\ l 
(b) FER-BR - .... - ~,. : 
eel (EFA-IC)fER-IC ----- ,,-: 
(t) (EFA BR)-HR-IC \: 
(e)(EFA-IC)fER-8R - - - • 1 
(CJ(SETA-lc)H2 -BR" .... : I 
50162 1 .L. .\ 
"10' 
~ 
~ 
~ 
10' 
1 ..., 
~lCt 
I:; 
if 
16' 
It' 
;:.. 
~ 
u ~4-~ 
S 
::,. 
~ 
<:> 
o 
:x 
l. 
YO-RAYS 
4-v1I11912 
t'! PHASE 
SUI11atol (1915) 
(0) EFA-IC --
(0) 8ETA-IC - --
(0) EFA-BR ---
(0) BETA-BR --0 
(d) ~SA-IC •••••• 
(d) NSA-BR 
FIG3 
IO-~1 .• . I I I. , 
2.16' 4.'o~ 10· 
PI-IOTOAJ OJ ERG Y (MeV) 
\\ 
. \
\~ 
F=IGG 
'I-RAYS 
4-'1111-\912 
SURI .01 (191 
\ ,,---\I~' \ ,\ 
\ 
. \\ -
(b)FER-]C --- \\\t 
(ij FER-SR -- \ 
(c) (II'A-lq-FER 1C---- \\ 
(c) CEA-IC)fEl/-IC - \: 
(Cl(IlT-IC)-FfR-BR - -- ,I 
2.,cS' 10' 
PUOTOAI EAJERGY (Ii.V) 
(/);;o;:c..."T)nnnO:!;;o 
CIlIIlI,,::r::rIllCD 
,:JOOIllCC-·-n 
-·CD A'IJI:J"'O:J~ CD 
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Study of non-thermal photon production under different scenarios in solar flares. 2: The Compton inverse and Bremsstrahlung models and fittings

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