Physics Letters B 291 (1992) 97,98 North-Holland PHYSICS LETTERS B

Constraints on mass of the DFSZ axions from the carbon-oxygen burning stage of stars

Jin W a n g Department of Astronomy and Astrophvsics University of lllinois, Urbana, IL 61801, USA

Received 29 January 1991; revised manuscript received 1 July 1992

It is believed that carbon burning of detonation or deflagration is an essential process for producing type I supernovae. We consider the effect of the energy loss due to the DFSZ axions on the core temperature of the star, and we use the min imum core temperature needed for a type I supernova to constrain the mass of DFSZ axions.

The most plausible model for type I supernovae which is consistent with observat ions is the thermo- nuclear explosion of accreting white dwarfs [ 1 ]. It should be noted that [ 2 ] Hoyle and Fowler first pre- sented the idea that type I supernovae are triggered by the thermonuclear runaway o f carbon burning in electron-degenerate cores. This idea was refined to the carbon de tonat ion SN model [ 3 ] and later to the car- bon deflagrat ion SN model [4]. The de tona t ion /de - flagration type of explosion disrupts the white dwarf completely except for the single detonat ion that leaves a white dwarf remnant behind.

Carbon burning is essential for type I SN. In this paper we use this proper ty to constrain the mass of axions [5] . The basic idea is simple: with extra en- ergy loss due to the axions, the tempera ture of the core of the star drops; if the energy loss is too much, then there will be no ignition of carbon burning of ei ther de tonat ion or deflagration, therefore a type I SN could not occur. We consider the effect of the en- ergy loss due to the DFSZ axions on the core temper- ature of the star. We use the min imum core temper- ature needed for a type I supernova to constrain the mass of DFSZ axions. So from this fact, we get the upper bound of the mass ofaxions .

Let us now be a little bit more quanti ta t ive. As the carbon-oxygen core increases in mass due to hel ium burning, the size of the core contracts (the core is de- generate, MR 3= C where C is a cons tant ) , thereby releasing gravi ta t ional energy:

Egrav d(3GM2 7 G -~" dt \ 5 ~ . ] = 5 C I/3 M4/3~I" ( l )

In the absence of neutr ino magnetic moment cool- ing, the dominan t cooling mechanism for the approx- imately isothermal core is usually taken to be neu- tr ino emission. In this analysis, we assume that axion cooling dominates , so we can de termine the axion mass necessary to prevent the ignit ion of carbon burning of de tonat ion or deflagration. The energy generation rate of DFSZ axions is given by [6,8] (here the Bremsstrahlung process domina tes )

Z 2 ea = 1.08× 1023 erg g-1 s-~ aa--£ T4F, (2)

where Z = 6 , A = 1 2 , F = 5 . 4 , O : a = 5 . 8 X 1 0 -22 (ma/

eV) 2. From the energy equil ibrium condit ion we have

ea = egrav = / ~ g r a v / M • ( 3 )

This equat ion determines the core temperature ,

T7 = CoMl/X2j~ll/ama 1/2, ( 4 )

where Co is a constant. Note that the larger the DFSZ axion mass is, the

lower is the tempera ture of the core. One can easily see how a sufficiently massive axion mass can pre- vent the core from reaching the tempera ture required to ignite carbon.

Now we use the results of some previous stellar

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Volume 291, number 1,2 PHYSICS LETTERS B 17 September 1992

evolution investigations [4,8] on carbon burn ing to get the input physical quant i ty such as M, M, and p, T. We have that

provides a new way of constraining the various dark matter candidates, such as axions, the neutr ino mag-

netic moment and so on.

M=O.26Mo = 5 . 2 X 1032 g , (5)

h~/= 6.5 X t0-13Mo s - I = 1.3× 1021 g s - ' , (6)

T : 109K= 102T7 , (7)

p = 3 . 5 X l09 gcm -3 , (8)

C=MR3=M2/(p.~z) = 1.85X 1055 g cm 3 . (9)

Substituting all the values above into eq. (4) , we get rna < 0.03 eV. This definitely suggests we can now put a safe upper bound on the mass of the DFSZ ax- ions: ma < 0.03 eV.

We notice that this constraint is tighter than what in previous analyses had been obtained from study- ing the main sequence and red giant stars and is close

to the white dwarf cooling bound [ 6 ]. Our method

References

[ 1 ] J.C. Wheeler, in: Supernovae: A survey of current research, eds. M.J. Rees and R.J. Stoneham (Reidel, Dordrecht, 1982) p. 167.

[2] F. Hoyle and W.A. Fowler, Astrophys. J. 132 (1960) 565. [3] W.D. Arnett, Astrophys. Space Sci. 5 (1969) 180. [4] K. Nomoto, D. Sugimoto and S. Neo, Astrophys. Space Sci.

39 (1976) L37. [5] R.D. Peccei and H.R. Quinn, Phys. Rev. Lett. 38 (1977)

1440. [6] G. Raffelt and D. Dearborn, Phys. Rev. D 36 (1987) 2211;

D37 (1988) 549. [7] G. Raffelt, Phys. Lett. B 166 (1986) 402;

M. Nakagama, Y. Kohyama and N. Itoh, Astrophys. J. 322 (1987) 291.

[8] I. Iben, Astrophys. J. 226 (1978) 996.

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