ELSEVIER Nuclear Physics A718 (2003) 333c-336c
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The r-process in the neutrino wind and U-Th cosmochronology
Shinya Wanajo , Naoki Itoh , Kiliri Ishimarii, Satoshi Nozawa and Timot,hy C. Beersd Depart,ment, of Physics, Sophia University, 7-1 Kioi-cho, Chiyoda-ku, Tokyo, 102-8554, .Japan
Depart,ment of Physics, Ochanomizii University, 2-1-1 Otsiika, Biinkyo, Tokyo 112-8610, Japan
Josai Junior College for Women, 1-1 Keyakidai, Sakado-shi, Saitama, 350-0290, J a p a n dDepartment, of Physics/Ast,ronomy, Michigan St,at,e Universit,y, E. Lansing, MI 48824
T h e discovery of t h e highly r-process-enhanced, extremely metal-poor star,
CS
31082- 001 ([Fe/H] = -2.9) has provided a powerful new tool for age determination, by virtue of t h e det,ect,ion and measiirement, of t h e radioactive species uranium and thorium. We det,ermine t h e lower limit on t h e age of t h e universe by comparison of the niicleosynt,hesis results based on the neutrino wind scenario with t h e available spectroscopic element,al abundance ( M a ofCS
31082-001.1 . Introduction
Uranium and thorium are regarded as potentially iiseftil cosrnochronometers because their long radioactive decay half-lives (232Th: 14.05 Gyr, 238U: 4.468 Gyr) are significant fractions of t,he expected age of t,he universe. T h e excellent, agreement of t h e relat,ive abundances of neutron-capture elements in the extmmely m e h - p o o r ([Fe/H] = -3.1), r-process-elemerit,-enhanced star CS 22892-052 with t h e solar r-process patt,ern initially suggested t h a t thorium might serve as a precise cosmochronomet,er [l]. T h e time t h a t has d since the prodiict,iori of t h e thorium t h a t is now observed in t h e outer atmosphere of such a n old halo s t a r can be regarded as a hard lower limit, on the age of t h e universe.
T h e second discovered r-process-enhanced, extremely metal-poor star,
CS
31082-001 ([Fe/H] = -2.9) has provided a new, potentially quite poiverfiil cosmochronometer, ura- nium[a].
In principle, uranium might be expecked t,o he a more precise chronometer t h a n t,horiiirn owing to it,s short,er half life. Howewr, analysis of this star has also provided conclusive evidence t,hat, t,he r-procrss pattern is n o t u.n.iversal over t h e actinides. Hence, any agt: est,imat,rs t,hat, demand assiimpt,ioii of t h e iiniversalit,y of the r-process pat,t,erri may in fact, be iirixeliable. T h e purpose of this paper is t o constriict, a realistsic r-process model bascd on t,he neiit,rino-wind scenario, i n ordcr t,o derive init,ial productlion ratios t,hat, might, be iisefiil for est,imat,ion of the minimum age of tlhe universe, in part,iciilar by use of t,he U-Th chronomet,er pair. T h e age ofCS
31082-001 is derived by comparison of t,tic riiicleosyiit,hesis rcsiilt,s wit,h t,he abiiritlarice pattjerri of heavy element)s in t,liis st,ar[3].0375-9474/03/$ - see front matter 0 2003 Elsevier Science B.V. All rights reserved doi: 10.1016/S0375-9474(03)00735-8
334c S. Wanajo et al. /Nuclear Physics A718 (2003) 333c-336c
2. The r-process in the neutrino wind
Neutrino wind, in which t,he free nucleons accelerated by the intense neutrino flux near t h e neutrino sphere of a core-collapse supernovae assemble t o heavier niiclei; has been believed t,o be the most, promising astrophysical site of the r-process[4]. R.ecent,ly, Otsnki e t al. (2000) have stndicd t h e physical condit,ions required for t,he r-process in detail, using a semi-analytic model of a spherical, steady neutrino wind, taking general relativistic effectas int,o accoiint,[5]. They suggested t h a t robust, physical conditions for were obt,ained only if tjhe proto-neutron star was as massive a s
-
2.0Me.Furthermore, Wanajo et, al. (2001) showed from niicleosynthesis calculations t,hat, t h e r-process yields for the compact, prot,o-neut,ron star models (with a mass of 1.9 - 2.0MG and radius of 10 km) were in good agreement with t,he solar r-process pattern[6]. We use a model with a proto-neutron star with (gravitational) mass of 2.0MB and radius of 10 km, as in [6], whose nucleosynthesis results are in good agreement with t,he solar r-pattern for nuclei A zs 120 - 200.
T h e r-process of nucleosynthesis, adopting t h e model described above for t h e physical conditions, is obtained by application of a n extensive nuclear-reaction network code. T h e network consists of
-
3600 species, all t h e way from single neut,rons and protons up to t h e fermium isot,opes. We inclnde all relevant, react,ions, i.e., ( n , y), ( p , y), ( a , y), ( p ; n ) , ( a , p ) , ( a , n,), and their inverses[7][8]. T h e a-deca chains and spont,aneoiis fission processes are taken into account only after t h e freezeout, of all other reactions. For t h e latter, all nuclei with A2
256 are assnmed t o decay by spontaneous fission only. T h e few known nuclei undergoing spontaneous fission for A<
256 are also included, along with their branching ratios. Neutron-indnced arid P-delayed fissions, as well as t h e contribution of fission fragments t o the lighter nuclei, are neglected. T h e electron fraction, Ye, is varied from 0.39 t o 0.49 t o examine its effect on t h e r-process. In order t o calciilat,e t h e mass- int,egrat,ed r-process yields, the time evolution of t,he neutrino luminosity, L,, is assumed t o be L,(t) = L,o(t/to)-’. L,o and to are taken t o be 1052.fi ergs s-’ (z 4 x los* ergs s - ’ ) and 0.2 s , respectively, being in reasonable agreement with the hydrodynamic resiilt,s[4].3. The U-Th cosmochronology
In Figure 1 t h e available spect,roscopic abundance d a t a for
CS
31082-001[9] (dots) are compared with t h e niicleosynthesis results (thick line) and witah the solar r-pattern (thin line), scaled a tEu
(2 = 63). Nucleosynthesis resiilts for all Ye cases are in good agreement with t h e abundance pattern of CS 31082-001 for t h e elements between P r(2
= 59) and T m ( Z = 69), with t,he exception of T b . Note t h a t a few of the predicted abundances for elements near t h e second peak (Ba, La, and Ce) are significantly deficient compared t o both t,he observational and solar patt,erns. T h i s might be due t o t h e properties of t h e nuclear mass model employed in t,his study.. T h e plat,iniim-peak element,s 0 s and Ir are in reasonable agreement,, except, for the Ye = 0.49 case: althongh the height of t h e ’"Pt differs.T h e age of CS 31082-001 can be inferred by application of one or more of t,he following t,hrce relations[9]:
&,,,
= 46.67 [log(Th/r)o - log(Th/r),,,] Gyr (1)S. Wanajo et al. /Nuclear Physics A718 (2003) 333c-336c 335c
1 N
-
+ o
-
I=
-
- 1- rn - 2
1 N
-
+ 0
-
I=
-
- 1rn - 0
- 2
1 N
-
+ o
-
I-
- 1=
0 0 -
- 2
40 60 80 40 60 80
atomic number atomic number
Figure 1. Comparison of t h e mass-integrated yields (the thick line) for Ye = (a) 0.39; (b) 0.40, (c) 0.41, (d) 0.42, (e) 0.43, a n d (f) 0.49, scaled at Eu (2 = 63); with t h e abundance p a t t e r n of
CS
31082-001 (filled circles, with observational error bars), as functions of at,omic number. For Pb, t h e observed upper limit is shown by t h e open circle. T h e scaled solar r-pattern is shown by t h e thin line.t t , , = 14.84 [Iog(U/r)o - log(U/r),,,] Gyr th,T,, = 21.76 [log(U/Th)o - log(U/Th),,,] Gyr,
where T is a stable r-element, a n d t h e siibscripts 0 and now denote t h e initial a n d current values derived by theory a n d observation, respectively. With the use of these ratios as t,he initial vahies, t,he age of CS 31082-001 is derived as shown in in Figure 2. It is noteworthy t,hat t h e age obt,ained from t h e U-Th chronometer pair is considerably more robust, t h a n the alt,ernat,ives, resulting in a range N 13.5 - 14.2 Gyr, wit,h an exception of 12.2 Gyr for the Ye = 0.49 case. Therefore, we use only t.he U-Th chronomet,er for dating of t,his s t a r , while t,he others are regarded as consistency checks only. Ye is constrained t o be M 0.40, owing to t h e consistency between ages based on t,he U-Th pair and others.
T h e difference between t h e ages obtained from U-Th bet.ween Ye = 0.39 and 0.41 is only
336c S. Wanajo et al. /Nuclear Physics A718 (2003) 333c-336c
-40 I I I
Th/EuTh/Os Th/lr U/Eu U/Os U/lr U/Th
Figure 2. Ages of CS 31082-001 derived from various chronometer pairs. The robustness of t,he U-Th pair is clearly shown. The superiority of the U-r pairs compared to those of Th-r can also be seen.
0.1 Gyr. On the other hand, the observational error associated with the U/Th ratio, 0.11 dex, leads to an uncertainty of 2.4 Gyr from application of equation (3). We conclude, therefore, that the age of CS 31082-001 is 14.1
It, should be emphasized that the age determination made in the present paper is derived from the explorat,ion of a single specific model based on the neutrino-wind scenario, and relies as well on the choice of one of the many exist,ing nuclear data sets[lO]. Thus, it is clear that our final result, may be changed if we were to make use of other astrophysical models. Obviously, more study with other astrophysical models, as well as with a number of different nuclear data sets, are needed to derive the final results.
2.5 Gyr.
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