Nagataki, S

Suzuki, T

Wanajo, S

CERN Document Server

PoS(NIC-IX)200R-Process Nucleosynthesis in AlfvØn Wave-drivenProto-Neutron Star WindsTakeru K. Suzuki∗, Shigehiro Nagataki, Shinya WanajoE-mail: stakeru@provence.c.u-tokyo.ac.jp,nagataki@yukawa.kyoto-u.ac.jp, wanajo@astron.s.u-tokyo.ac.jpWe propose magnetic proto-neutron star (PNS) winds driven by Alfvén waves as well as the neu-trino heating as an appropriate site for the r-process nucleosynthesis. Alfvén waves excited bysurface motions of a PNS propagate outwardly, and they heat and accelerate the wind by dissipa-tion. In the Alfvén wave-driven wind, larger entropy per baryon and shorter dynamical time scaleare achieved, which favors the r-process. A PNS with surface B0>∼ 5× 1014G, gives suitablewind properties for the r-process in a typical case. We also perform nuclear reation calcuationsand confirm this result; the 3rd peak elements are sufficiently synthesized in the Alfvén wave-driven wind in such a condition.International Symposium on Nuclear Astrophysics  Nuclei in the Cosmos  IXJune 25-30 2006CERN, Geneva, Switzerland∗Gradate School of Arts & Sciences, University of Tokyo†Yukawa Institute for Theoretical Physics, Kyoto University; Kavli Institute for Particle Astrophysics and Cosmol-ogy Stanford Linear Accelerator Center‡Department of Astronomy, University of Tokyoc© Copyright owned by the author(s) under the terms of the Creative Commons Attribution-NonCommercial-ShareAlike Licence. http://pos.sissa.it/PoS(NIC-IX)200R-process in AlfvØn Wave-driven Winds1. IntroductionA neutrino-driven wind is probably the most promising site of the rapid neutron capture pro-cess (r-process). However, it is difficult to realize the suitable condition for the r-process in thewind of the standard proto-neutron star (PNS) (e.g. [1]). Recently roles of magnetic fields arehighlighted to suitable circumstances for the r-process, namely short dynamical timescale, texp, andlarge entropy per baryon, S. Thompson (2003) [2] considered large-scale scale magnetic fieldswhich confine the plasma to achieve enough S. As another possibility, Suzuki & Nagataki [3]proposed that Alfvén waves generated from magnetic PNS give faster acceleration (smaller texp)and larger heating (larger S) in the wind by the additional momentum and energy inputs. In thiscontribution, we firstly introduce basic properties of Alfvén wave-driven winds, and then, presentresults of nucleosynthesis calculations.2. ModelWe consider steady-state winds from PNSs with radius, RNS = 10 km, under the Newtoniangravity. We assume radial expansion of magnetic flux tubes in which the winds flow out, givingmagnetic flux conservation, Br2 = B0r20 , where B0 is the surface magnetic field strength. Differencefrom the standard neutrino-driven wind is that we take into account the acceleration by the wavepressure, Pw, in the momentum equation and the heating, q˙w, by the wave dissipation in the energyequation which arevdvdr=−GMr2−1ρdPdr−1ρdPwdr(2.1)andq˙ν + q˙w = v(dEdr−Pρ2dρdr), (2.2)respectively, where q˙ν is cooling/heating by neutrino and the other variables have the usual mean-ings. The acceleration ( dPwdr ) and heating (q˙w) by the Alfvén wave are determined by a suitabledissipation model. Here, We assume wave action, defined as Hw ≡ δB28pi(vA+v)(vA + v)vAwhich is anadiabatic constant in unit of energy flux, follows an exponential decay on r with dissipation length,l:Hw =R2NSr2Hw,0 exp(RNS− rl), (2.3)We inject Alfvén waves with initial amplitude, δB0/B0 = 0.1 at the surface, and we construct tran-sonic wind solutions (see [3] for more detailed setting of the model and subsonic cases. ) We onlyconsider strong magnetic field cases, B0 = 1014−1015G, because otherwise the Alfvén waves onlygive a tiny effect on the winds. l can be estimated from the solar wind studies by one of the authors[4 – 6], in which weakly nonlinear (δB0/B0 ∼ 0.1) waves dissipate typically after propagating ∼ 10wavelengths, corresponding to l <∼ 10RNS in the present PNS conditions.3. ResultsFigure 1 shows the structures of the Alfvén wave-driven winds. The left panels present depen-dence on surface magnetic field, B0, and the right panels present dependence on dissipation length,2PoS(NIC-IX)200R-process in AlfvØn Wave-driven WindsFigure 1: Structures of Alfvén wave-driven winds. The top panels show density in unit of 105 g cm−3, ρ5,temperature in 109 K, T9, and velocity in 107 cm s−1, v7. The middle panels exhibit entropy per baryon, S.The bottom panels show the heating by waves, q˙w, and by neutrinos, q˙ν . The left panels show dependenceon B0 (= 5×1014 G; solid, 3×1014 G; dotted, 0 G; dashed) for fixed l = 10RNS and the right panels showdependence on l (= 5RNS; solid, 30RNS; dashed) for fixed B0 = 5×1014 G.l. Thanks to the wave pressure, the wind is accelerated faster as B0 increases. The heating dueto the wave dissipation also gives larger S in the larger B0 case. Therefore, the conditions in theAlfvén wave-driven winds are favorable for the r-process. Faster dissipation (smaller l) leads tomore rapid increase of S, which is also better for the r-process.In Figure 2 we compare the results of texp and S with the r-process condition1 by [1],S >∼ 2×103Ye( texps)1/3, (3.1)where Ye is electron fraction which our model does not explicitly include. For standard Ye(= 0.4−0.5), Alfvén -driven winds of PNSs with B0>∼ 5× 1014 G satisfy the condition, provided l <10RNS.Next, we calculate the actual nucleosynthesis in the Alfvén wave-driven winds [8]. We per-form nuclear reaction network calculations by adopting the physical conditions (ρ and T ) whichchange with time according to the outward velocities along with the flows. Figures 3 and 4 showthe dependences of the synthesized elements on B0 and l, where we assume electron fraction = 0.4.1This is strictly the condition for α-process [7] which determines a neutron-to-seed ratio before the neutron captureoccurs.3PoS(NIC-IX)200R-process in AlfvØn Wave-driven WindsFigure 2: texp(s) (X-axis) and S at T = 0.2MeV (Y-axis) for various parameters of Alfvén waves. Opencircles, filled triangles, and open squares are results with l = 5, 10, & 30, respectively. Numbers denotemagnetic field strength at the surface. For example 6(14) indicates B0 = 6× 1014G. Results with the sameB0 are connected by dashed lines. Solid lines are the conditions for the r-process by [1] for Ye = 0.4 & 0.5.Figure 3: Results of the synthesized elements in the Alfvén wave-driven winds. The red, black, and bluelines correspond to B0 = 6× 1014 G, 5× 1014 G, and 4× 1014 G, respectively, where we adopt constantl = 5RNS.4PoS(NIC-IX)200R-process in AlfvØn Wave-driven WindsFigure 4: The same as Figure 3 but for the ł dependence. The red, black, and blue lines correspond tol = 2RNS, 5RNS, and 10RNS, respectively, for B0 = 5×1014 G.Figure 3 illustrates that larger B0 favors the r-process. While the 3rd peak elements (massnumber, A ≈ 195) are not produced in the B0 = 4× 1014 G case (see [8] for non magnetic fieldcase), they are synthesized in the B0 = (5,6)×1014 G cases. In the B0 = 6×1014 G case, sizableamounts of elements with A = 230−240 are also synthesized. This is because the nonequilibriumcircumstances with small texp and large S are achieved in larger B0, which is suitable for the r-process.Figure 4 exhibits that smaller l is favorable to the synthesis of the r-process elements; the 3rdpeak elements are produced in the cases with l = (2,5)RNS, while they are not in the case with10RNS. This is because S should be large in the inner region where the α-process [7] takes placeto give a sufficiently large neutron-to-seed ratio, which requires small l. Otherwise if l is large, thewave heating occurs in the outer region and the increase of S is a little to slow; in the case withl = 10RNS, the 3rd peak elements are not synthesized.References[1] Hoffman, R. D., Woosley, S. E., & Qian, Y.-Z. 1997, ApJ, 482, 951[2] Thompson, T. A. 2003, ApJ, 585, L33[3] Suzuki, T. K. & Nagataki, S. 2005, ApJ, 628, 914[4] Suzuki, T. K. 2004, MNRAS, 349, 1227[5] Suzuki, T. K. & Inutsuka, S. 2005, ApJ, 632, L49[6] Suzuki, T. K. & Inutsuka, S. 2006, JGR, 111, A06101[7] Woosley, S. E. & Hoffman, R. D. 1992, ApJ, 395, 202[8] Wanajo, S., Suzuki, T. K. & Nagataki, S. 2006, submitted to ApJL5

R-process Nucleosynthesis in Alfven Wave-Driven Proto-Neutron Star Winds

Abstract

Similar works

Full text

Available Versions

CERN Document Server