ASTROPHYSICS, VOLUME 2, NUMBER 1 65

THE BREAK IN THE RADIO EMISSION SPECTRUM OF CASSIOPEIA A

V. G. Malumyan

Astrofizika, Vol. 2, No. I, pp. 128--131, 1966

Accord ing to [1, 2], the r ad io e m i s s i o n s p e c t r u m

of C a s s i o p e i a A e x p e r i e n c e s a b r e a k n e a r the f r e -

quency v m ~ 30 M e / s e e . At f r equenc i e s v > u m the r ad io e m i s s i o n s p e c t r u m

of this s o u r c e has the f o r m S u ~ u - a , where S v is the s p e c t r a l f lux dens i ty and the s p e c t r a l exponent is

~ 0 . 8 . However , "at f r equenc i e s u < v m, Sv ~v/3, whe re ~ > 0.

Thus, nea r the f r equency v m the s p e c t r a l exponent Of the r ad io e m i s s i o n f rom Cas s iope i a A changes s ign and the flux dens i ty at this f r equency is a m a x i m u m . The fol lowing a r e the two mos t probable m e c h a n i s m s for expla in ing the b r e a k in the s p e c t r u m of Cass iope i a A [2--4]:

1. Absorp t ion in r eg ions of ion ized hydrogen p r o - j e t t e d aga ins t the s o u r c e .

2. The inf luence of a medium with a r e f r a c t i v e

index n(u) < 1, s i tua ted in the s o u r c e i t se l f . (Such a medium may be ionized gas.) These m e c h a n i s m s have been d i s c u s s e d in [2--5], and t h e r e f o r e they wil l not

be d e s e r i b e d in deta i l he r e . Cas s iope i a A is s i tua ted n e a r the gaIac t ic plane

(b = -2~ which f avo r s the m e c h a n i s m of absorp t ion

in HII r eg ions s i tua ted in the d i r ec t i on of the s o u r c e . In this ea se the f r equency Vm and the e m i s s i o n m e a s - ure ME of the ItII abso rb ing reg ions a r e r e I a t ed by

the fol lowing e x p r e s s i o n [2]:

ME ~ 1.15 ~ (1)

(v m is e x p r e s s e d in M e / s e e , c~ is the s p e c t r a l expon- ent of the rad io e m i s s i o n f r o m the sou rce ) . In the case of Cas s iope i a A, we obtain ME ~ 800 using (1).

When r e l a t i v i s t i c e l e c t r o n s a r e emi t t ed in a m e d - ium with a r e f r a c t i v e index n(v) < 1, the in tens i ty of the r ad i a t i on f r o m r e l a t i v i s t i c e l e c t r o n s d e c r e a s e s

sha rp ly at r e l a t i v e l y low f r e q u e n c i e s [4, 5]. This leads to a change in the s ign of the s p e c t r a l exponent for radiation from relativistic electrons.

If this mechanism is the cause of the break in the spectrum of the source, we have [4, 5] at a frequency

Pm

vm -- f ( 7 ) ecNe, (2) H i

w h e r e f(7) i s a f u n c t i o n w h i c h depends on the exponent of the e n e r g y s p e c t r u m for r e l a t i v i s t i c e l e c t r o n s 7, e is e l e c t r o n cha rge , c is the ve loc i t y of l ight in a

vacuum, N e is the e l e c t r o n dens i ty in the ionized gas, H• is the component of magnetic field strength per- pendicular to the velocity vector of the radiating elec- trons.

For Cass iope ia A, 7 = 2~ + 1 = 2.6 and f(Y) ~ 3, so that

~,,.~.3ecN~ =40 Ne. (3) H• H~.

N e, H / a n d v m a r e e x p r e s s e d in am -3, gaus s , and cps , r e s p e c t i v e l y .

F r o m (3), on the assumpt ion that HA- = 10-4--10 -5 G, we have for the e m i s s i o n m e a s u r e of the ionized gas,

2 2

M E - ~.~H• - 2.10 ~ - 2 . 1 0 ~ (4) 1.6.10 3

(l is the size of the source in parsecs; for Cassio-

peia A, l ~ 4 parsecs). Lack of knowledge of the pre-

cise value of H I in Cassiopeia A makes the evaluation

of ME on the basis of (4) very unreliable.

A comparison of the values of ME obtained using

(1) and (4) reveals that even if a nebu]a with an emis-

sion measure 103--102 is discovered in the direction

of Cassiopeia A, we still cannot arrive at any definite

conclusion concerning the mechanism responsible for the break in the source spectrum. The authors of

[2, 4] cite several factors indicating that this break is

apparently caused by absorption in HII regions. In these same studies it is noted that this conclusion

cannot be considered final.

We wish to mention one circumstance which in our

opinion makes it possible to clarify the cause of the

break in the spectrum of Cassiopeia A. Cassiopeia A belongs to the class of radio sources identified with

the expanding remnants of a supernova flare. The

type-If supernova responsible for the radio emission from Cassiopeia flared up approximately 300 years

ago [6]. Because of its youth this source is expanding

relatively rapidly. According to [6], the velocity of

expansion is 7500 km/sec. Due to the expansion of the source the magnetic field strength and the energy of

the relativistic particles in it decrease continuously,

which leads to a systematic decrease in the radio

flux [7]. A number of specially formulated observa- tions have made it possible to detect a decrease in the

radio flux of Cassiopeia A [8--10]. We will show that if the break is caused by the in-

fluence of an ionized medium with n(v) < 1, localized in the source, the expansion of the remnant of the

supernova should lead to a systematic decrease in

the frequency Vr~ of the break (as yet the remnant has not been slowed down significantly by the interstellar

medium).

As a result of expansion the electron density N e of the ionized gas should change. From the condition for

66 ASTROFIZIKA, JANUARY--MARCH 1966

conserva t ion of the number of e l ec t rons in the source we have

3 Neoro --NeTr 3, (5)

where Ne0, NeT, r 0 and r T a r e the e l ec t ron dens i ty and the rad ius of the source at some in i t ia l t ime T o and at t ime T re spec t ive ly .

The condi t ion for the conse rva t ion of the magnet ic flux gives

Hor~ =: Hr r~. ( 6 )

As before , the subsc r ip t s 0 and T apply to some i n i - t ia l t ime T o and a t ime T af ter the supernova f la re . The magnet ic field component H A a lso changes in con- fo rmi ty with the law (6). It follows f r o m the con- s e rva t ion of the ad iabat ic i nva r i an t (P s in 0)2/H = = const (P = E / e is the momentum of a r e l a t i v i s t i c par t ic le , E is its energy) that the angle 0 between the veloci ty vec tor of a r e l a t i v i s t i c e l ec t ron and the d i - r ec t ion of the magnet ic field, when H ~ r -2 and E ~ r -1, r e m a i n s cons tant [5, 7]. Thus,

H~. ,>r~ = H~ r r~. (7)

F r o m (5) and (7) we have NeT = Ne0(r0/rT) 3 and HAT = H• 2" Subst i tut ing these va lues into (3), we obtain

~ ~= 40 N~o ro 1"o - - "~,,,o ( 8 )

H : o rT rT

Due to the youth of Cass iopeia A, it can be a s s u m e d that the expansion is p ropor t iona l to t ime T, s ince in t h e in i t ia l s tages of expansion dece le ra t ion b y the i n t e r s t e l l a r medium has l i t t le effect. Then we f inal ly obtain for v m

7; f

The d e c r e a s e of v m for Cass iopeia A, de t e rmined f rom (9), is approx imate ly 0.1 M c / s e c per y e a r . If such a change is, in fact, occu r r ing , i t may be de t ec - ted by specia l observa t ions in the d e c a m e t e r r a n g e ,

If the b reak is caused by the absorp t ion of long- wave radio e m i s s i o n in zones of ion ized hydrogen projec ted onto tt!e s ouree~ no change in the f requency v m should be obserVed.

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t0 December 1965 Byurakan As t rophys ica l Obse rva to ry