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Radioactive nuclei on accreting neutron stars
Nuclear Physics A 746 (2004) 347c–353c
Radioactive nuclei on accreting neutron stars H. Schatza a
Dept. of Physics and Astronomy, National Superconducting Cyclotron Laboratory, and Joint Institute for Nuclear Astrophysics, Michigan State University, East Lansing, MI 48824, USA With new data from RXTE, Chandra, and XMM X-ray astronomy of accreting neutron stars enters a precision era. Precision nuclear physics from experiments with radioactive beams is needed to interpret the data. We review status and prospects of the nuclear physics, focusing on the nuclear reactions in X-ray bursts, in particular with heavy unstable nuclei beyond magnesium. At the NSCL Coupled Cyclotron Facility some of the major nuclear physics uncertainties are now being addressed using neutron removal reactions with radioactive beams. 1. INTRODUCTION Type I X-ray bursts are thermonuclear explosions on the surface of an accreting neutron star (see reviews [1–3]). Most of the bursts are powered by a mix of explosive helium and hydrogen burning via the 3α reaction, the αp process and the rapid proton capture process (rp-process) [4,5]. X-ray observatories such as Beppo SAX, RXTE, Chandra, and XMM provide a wealth of new high quality data on X-ray bursts. These include discoveries, such as nearly coherent oscillations in the 100-1000 Hz range, or rare superbursts, but also precision data on long term bursting behavior of regular ”textbook” bursters such as GS 1826-24 [6]. As accretion rates change slowly over decades such long term observations probe burst properties as a function of accretion rate, and can be directly compared to model predictions. 1D X-ray burst model simulations with the full nuclear physics of the rp process became possible recently [7,8]. Together with the new observations and a reliable nuclear physics database this could be the beginning of a precision era in the field. In fact, first detailed comparisons of predicted and observed X-ray burst light curves for specific systems are now being preformed [6,9], but suffer from large nuclear physics uncertainties [10,7]. Nuclear physics enters X-ray burst models in many ways. Spallation reactions can modify the material impinging on the neutron star surface. This might be directly observable through absorption line features in the X-ray spectra [11]. Explosive hydrogen and helium burning in the layer of accreted material on the surface of the neutron star powers the observed X-ray bursts via the rp- and αp-processes [4,5], which involve extremely neutron deficient unstable nuclei. Nuclear physics determines directly duration and shape of the burst lightcurves [7,8,12,13,10]. Stable hydrogen burning between bursts modifies the composition of the burst fuel prior to ignition, and is the dominant burning mechanism at 0375-9474/$ – see front matter © 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.nuclphysa.2004.09.151
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H. Schatz / Nuclear Physics A 746 (2004) 347c–353c
very high accretion rates, for example in X-ray pulsars [14]. While the products of surface burning processes most likely are not ejected into space, knowledge of the composition of the ashes is critical for modeling the neutron star crust. In particular, the amount of potential fuel for deeper burning processes in the burst ashes is critcial. This includes carbon, which could explode deep in the crust triggering the recently discovered rare superbursts [15,16]. Important are also amount and exact compositon of the nuclei beyond iron that can serve as fuel for a photodisintegration runaway during superbursts [17]. Still deeper in the crust nuclei undergo another sequence of nuclear reactions - electron captures and pycnonuclear fusion (pressure induced fusion) determining composition and thermal properties of the crust. These processes produce extremely neutron rich unstable nuclei and their energy generation can be observed directly in transient systems during the off-phase when accretion shuts off and X-ray emission from the surface of the neutron star can be detected [18]. Deep crust processes also set the termal structure of the crust, which serves as a boundary condition for X-ray burst and superburst models [19]. Another observable of the deep crust processes might be gravitational wave emission if the thermal structure is unisotropic [20]. 2. NUCLEAR DATA NEEDS In this paper we focus on the nuclear physics of the αp- and rp-processes in X-ray bursts. These reaction sequences have the most direct observational consequences and set the stage for all subsequent nuclear processes deeper in the crust. Fig. 1 shows the path of the rp process during an X-ray burst calculated with a one zone model coupled selfconsistently to a complete reaction network [13]. The endpoint of the rp process depends on the amount of hydrogen available at burst ignition, which in turn varies with the parameters of the system such as accretion rate, heat flux from the neutron star surface and composition of the accreted material. However, even for large hydrogen to seed ratios the rp process is limited by a SnSbTe cycle, which forms because of the very low α binding energies of proton rich Te isotopes [13]. In principle the rp-process could proceed beyond the SnSbTe cycle in a multiburst rp-process (the rp2 process [21]). In this scenario the freshly synthesized nuclei decay back to stability and are then again bombarded with protons in a second burst thus bypassing the SnSbTe cycle. Recent 1D multizone calculations indicate that reirradiation of incompletely burned ashes indeed occurs in X-ray bursts [7,8]. However, the first burst happens through heating from the underlying ignition layers at lower temperatures. This reduces the overall hydrogen to seed ratio as lower temperature helium fusion produces more lighter seed nuclei as opposed to fewer heavy seed nuclei. Overall the rp-process therefore tends to be shorter, so even with multibursts the SnSbTe cycle is only barely reached. However, the full system parameter space has not been explored yet. For now it is reasonable to assume that the reaction path outlined in Fig. 1 encompasses the maximum range of nuclear physics data needed for rp-process calculations. The critical data are nuclear masses, β decay rates, and the rates of (p,γ) and (α,p) reactions. In particular it is the interplay of masses and β decays along the proton drip line that sets the path and timescale of the rp process. Proton separation energies determine where in the rp-process path (γ,p) photodisintegration reactions hamper the reaction flow and
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H. Schatz / Nuclear Physics A 746 (2004) 347c–353c
Xe (54) I (53) Te (52)
(g,a) 105Te
106Te
107Te
108Te
104Sb
105Sb
106
107Sb
Sb
Sb (51) Sn (50) In (49) Cd (48) Ag (47) Pd (46) Rh (45) Ru (44)
(p,)g 103Sn
104Sn
105Sn
106Sn
102In
103In
104In
105In
5
5758
Tc (43) Mo (42) Nb (41) Zr (40) Y (39) Sr (38)
b+
56 5455 53
Rb (37) Kr (36) Br (35) Se (34)
5152 4950
As (33) Ge (32) Ga (31) Zn (30)
45464748 424344 41
37383940 Cu (29) Ni (28) 33343536 Co (27) Fe (26) 3132 Mn (25) Cr (24) 2930 V (23) Ti (22) 25262728 Sc (21) Ca (20) 2324 K (19) Ar (18) 2122 Cl (17) S (16) 17181920 P (15) Si (14) 1516 Al (13) Mg (12) 14 Na (11) Ne (10) 11 1213 F (9) O (8) 9 10 N (7) C (6) B (5) 7 8 Be (4)
rp process
ap process
Li (3) He (2) 5 6 H (1) 3 4 n (0) 2 0 1
3a reaction
Figure 1. Reaction flow time integrated over a complete x-ray burst [13]. The inset shows the SnSbTe cycle in detail.
create waiting points. The β decay lifetime of the waiting point nucleus then determines together with the remaining net proton capture lifetime the timescale of the rp-process and the final abundance pattern. Therefore masses and β decay lifetimes strongly impact calculated X-ray burst lightcurves. This has been qualitatively demonstrated in a series of one-zone model calculations [12,13]. In a more recent study lightcurve variations were calculated based on actual uncertainties in state of the art mass predictions, again in a onezone model [10]. These findings have now been confirmed by multizone calculations with full nuclear physics, where the impact of mass uncertainties was simulated by changing β-decay lifetimes [7]. Proton capture rates and (α,p) reaction rates can play an important role at lower temperature when they compete with β-decay rates or become comparable to the burst timescale. This happens inbetween bursts, during burst ignition and cooling, and for burning at shallower depths above the ignition zone. Because of the latter issue, 1D multizone models are needed to investigate the sensitivity of X-ray burst calculations to reaction rates. The importance of proton captures on heavy nuclei closer to stability, such as 27 Si, 31 S, 35 Ar, and 39 Ca for burst ignition has already been pointed out [22]. Recently it has been demonstrated that slow (α,p) reaction rates at the 22 Mg, 26 Si, 30 S, and 34 Ar waiting points could cause double peaked bolometric X-ray burst lightcurves,
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which are observed occasioanlly and could not be explained before [8]. These waiting points had been identified before in one-zone calculations [23], but the observable effect is produced by an interplay of different burning zones with different conditions, which cannot be modeled in a one zone model. 3. EXPERIMENTAL STATUS AND NEW TECHNIQUES Radioactive beam experiments at many facilities have provided a wealth of new data on the location of the proton drip line between Ni and Te. These include experiments at LBL [24], GANIL [25–28], GSI [29–32], ISOLDE [33,34], MSU/NSCL [35–37], and ORNL [38]. These experiments focused on the determination of the transition from β to proton decay as one moves away from stability, either by measuring β decay rates or by obtaining lifetime limits from the nonobservation of isotopes with known production rates. Proton emitters have in most cases been identified on the basis of such lifetime limits - with the exception of 105 Sb [24,30] no direct proton emission has been observed in this element range. In addition these experiments provided data on the majority of β decay half-lives in the rp process, with the exception of 74 Sr, 87 Ru, 95,96 Cd. The lack of sufficiently precise proton separation energies (accuracy of at least ≈ kT = 80 keV needed) along the proton drip line between Ni and Te has been the major nuclear physics uncertainty in rp-process calculations for a long time [10]. Recently a number of new techniques have been used to measure masses of exotic nuclei in the path of the rp process. These include time-of-flight measurements at the ESR storage ring at GSI in the Ti-Mn region [39] and ion trap experiments at ISOLTRAP [40] and the Canadian Penning Trap at ANL [42]. Of particular importance are the proton separation energies of 61 Ga, 65 As, 69 Br, 73 Rb, and 77 Y which are related to the longest lived waiting points in the rp process. Here, the situation has been improved considerably. The masses of 61 Ga [41], 68 Se [42,43], and 76 Sr [40] masses have been measured using β-endpoint techniques and Penning traps removing the major uncertainties in the N = Z nuclei. At the same time, new mass predictions based on Coulomb shift calculations can now provide quite reliable data for masses beyond the N = Z line, provided the mass of the mirror nucleus is experimentally known [10]. Nevertheless, an experimental determination of the 69 Br, 73 Rb, and 77 Y masses would be important. The former two isotopes are proton unbound and are therefore out of reach for time-of-flight or Penning trap measurements, but transfer reactions with radioactive beams could be used to determine their masses. Experimental information is sparse for the rates of proton capture and (α,p) reactions on unstable nuclei along the αp- and rp-process paths. Theoretical predictions of these rates are highly uncertain as level densities tend to be low. In this case statistical methods are not generally applicable [44] and shell model calculations, available up to A = 63 [45,46], cannot predict the properties of individual resonances with sufficient accuracy (see below) even when information from mirror nuclei is available. Direct measurements of proton capture rates with radioactive beams at low astrophysical energies of a few MeV are difficult and have only been done in a few cases such as 13 N(p,γ)14 O at Louvain-la-Neuve [47] and more recently 21 Na(p,γ)22 at TRIUMF [48]. For the time being, indirect methods using stable and radioactive beams are needed to obtain experimental information on the majority of proton and α induced reaction rates.
H. Schatz / Nuclear Physics A 746 (2004) 347c–353c
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So far, such efforts have mainly concentrated on lighter nuclei with Z ≤ 12, which are of potential importance during the X-ray burst ignition process. Experimental information beyond Z = 12 is very limited because the reaction path moves further away from stability, because of technical limitations, and because many experimental studies are motivated by the nova problem. In the Z = 12–21 range some relevant information on nuclei closer to stability is available from stable beam transfer reaction measurements, for example using (3 He,np) and (3 He,t) reactions (see [49] for a review of the A = 20–40 mass range). Only recently, stable beam multinucleon transfer reaction measurements have provided information about more unstable nuclei. These include reactions such as ( 4 He,8 He) for 24 Si [50], (3 He,6 He) and (p,t) for the 26 Si [51,52], and (7 Li,8 He) for the 27 P [53], which are relevant for the 23 Al(p,γ)24 Si, 25 Al(p,γ)26 Si, and 26 Si(p,γ)27 P reaction rates, respectively. The inverse kinematics reaction 1 H(58 Ni,57 Cu)2n has been used to determine resonance energies in the 56 Ni(p,γ)57 Ni reaction rate [54] via γ-ray spectroscopy. Such multinucleon transfer reactions typically provide only information on excitation energies but as resonant reaction rates depend exponentially on resonance energies this removes the major uncertainty in the reaction rates. However, transfer reactions with stable beams have limitations because they cannot reach nuclei that are too far from stability because of the difficulty to manufacture targets for certain elements, and because of the selectivity of the reaction to only a subset of the relevant states. Even in the cases where critical levels have been observed with particle spectroscopy, the precision of the extracted resonance energy is on the order of 20-100 keV. Because of the sensitivity of resonant reaction rates to level energies, accuracies of the order of 1-10 keV are needed. Transfer reactions with radioactive beams can provide a way to overcome these limitations. Rehm et al. 1998 [55] determined neutron spectroscopic factors in 57 Ni using a (d,p) reaction in inverse kinematics with a radioactive 56 Ni beam at ANL. This allowed to constrain proton spectroscopic factors in the 57 Cu mirror, which are relevant for the 56 Ni(p,γ) reaction in the rp-process. More recently, a new method has been developed at the National Superconducting Cyclotron Laboratory to measure excitation energies directly in the relevant neutron deficient nuclei using neutron removal reactions in inverse kinematics [56]. A first application was the measurement of excitation energies in 33 Ar using neutron removal of a 84 MeV/u radioactive 34 Ar beam on a plastic target. γ-rays from the deexcitation of the resulting 33 Ar nuclei were detected in coincidence with the observation of the 33 Ar residual in the S800 spectrometer. With this technique the energies of all relevant states could be determined with accuracies of 2–9 keV. Together with shell model calculations for the remaining parameters this reduced the uncertainty in the 32 Cl(p,γ)33 Al reaction rate from a factor of around 1000 to a factor of 2-3. This method has great future potential. Because of the relatively large cross sections for neutron removal, and the high beam intensities provided by the NSCL Coupled Cyclotron Facility all nuclei in the rp-process up to Z ≈ 36 are within reach. A complementary method to also measure exitation energies of predominatly proton decaying states is being developed. Together with shell model calculations, now available up to A = 63 [45,46] a drastically improved set of proton capture rates for rp-rprocess studies is within reach. This could form a basis for meaningful sensitivity studies to determine the reactions that
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need to be measured more accurately with other techniques, for example directly with low energy radioactive beams at the future rare isotope accelerator RIA. 4. ACKNOWLEDGEMENTS The neutron removal technique at the NSCL has been developed in a collaboration with R.R.C. Clement, D. Bazin, W. Benenson, B.A. Brown, A.L. Cole, M.W. Cooper, P.A. DeYoung, A. Estrade, M.A. Famiano, N.H. Frank, A. Gade, T. Glasmacher, P.T. Hosmer, W.G. Lynch, F. Montes, W.F. Mueller, G.F. Peaslee, P. Santi, B.M. Sherrill, M-J. van Goethem, and M.S. Wallace. The one zone X-ray burst model was developed with L. Bildsten and A. Cumming, using a reaction network solver provided by F.-K. Thielemann. The reaction library is maintained in collaboration with M. Wiescher. This work has been supported by NSF grants PHY-0110253 and PHY-0110253 (Joint Institute for Nuclear Astrophysics). H. S. is an Alfred P. Sloan fellow. REFERENCES 1. W. H. G. Lewin, J. van Paradijs, and R. E. Taam, in X-Ray Binaries, edited by W. H. G. Lewin, J. van Paradijs, and E. P. J. van den Heuvel (Cambridge Univ. Press, Cambridge) p. 175 (1997). 2. L. Bildsten, ”Rossi 2000: Astrophysics with the Rossi X-ray Timing Explorer, March 22-24, 2000 at NASA’s Goddard Space Flight Center, Greenbelt, MD USA”, E65, (astro-ph/0001135) (2000). 3. T. E. Strohmayer and L. Bildsten, To appear in Compact Stellar X-ray Sources, eds. W.H.G. Lewin and M. van der Klis, Cambridge University Press, astro-ph/0301544, 2003. 4. R. K. Wallace and S. E. Woosley, Ap. J. Suppl. 45 (1981) 389. 5. H. Schatz et al., Phys. Rep. 294 (1998) 167. 6. D. K. Galloway et al.. astro-ph/0308122 (2003). 7. S. E. Woosley et al., astro-ph/0307425 (2003). 8. J. L. Fisker and F.-K. Thielemann, astro-ph/0312361 (2003). 9. A. Cumming, astro-ph/0309626 (2003). 10. B. A. Brown et al. Phys. Rev. C 65 (2002) 5802. 11. L. Bildsten, P. Chang, and F. Paerels, astro-ph/0303147 (2003). 12. O. Koike, M. Hashimoto, K. Arai, and S. Wanajo, Astron. Astrophys. 342 (1999) 464. 13. H. Schatz et al., Phys. Rev. Lett. 86 (2001) 3471. 14. H. Schatz, L. Bildsten, and A. Cumming, Ap. J. 524 (1999) 1014. 15. A. Cumming, and L. Bildsten, ApJ, 559 (2001) L127. 16. E. F. Brown, and T. E. Strohmayer, Ap. J. 566 (2002) 1045. 17. H. Schatz, L. Bildsten, and A. Cumming, Ap. J. 583 (2003) L87. 18. E. F. Brown, L. Bildsten, R. E. Rutledge Ap. J. 504 (1998) 95. 19. E. F. Brown, Ap. J. 529 (2000) 985. 20. L. Bildsten, Ap. J. 501 (1998) 89. 21. R. N. Boyd, M. Hencheck, and B. S. Meyer, in International Symposium on Origin of Matter and Evolution of Galaxies 97, Atami, Japan, edited by S. Kubono, T. Kajino,
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22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39. 40. 41. 42. 43. 44. 45. 46. 47. 48. 49. 50. 51. 52. 53. 54. 55. 56.
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K. I. Nomoto, and I. Tanihata (World Scientific, New Jersey, Singapore, 1998), p. 350. F.-K. Thielemann et al. Prog. Part. Nucl. Phys. 46 (2001) 5. M. Wiescher and H. Schatz, Journ. Phys. G Topical Review 25 (1999) R133. R. J. Tighe et al., Phys. Rev. C 49 (1994) R2871. B. Blank et al., Phys. Rev. Lett. 74 (1995) 4611. K. Rykaczewski et al., Phys. Rev. C 52 (1995) R2310. Z. Janas et al., Phys. Rev. Lett. 82 (1999) 295. M. J. Lopez Jimenez et al. Phys. Rev. C 66 (2002) 025803. A. Plochocki et al., Nucl. Phys. A 388 (1982) 93. R. Schneider, PhD Thesis, TU M¨ unchen, 1996. M. Shibata et al., Journ. Phys. Soc. Japan 65 (1996) 3172. P. Kienle et al., Prog. Part. Nucl. Phys. 46 (2001) 73. A. Jokinen et al., Z. Phys. A 355 (1996) 227. M. Oinonen et al., Phys. Rev. C 61 (2000) 035801. M. F. Mohar et al., Phys. Rev. Lett. 66 (1991) 1571. J. Winger et al., Phys. Lett. B 299 (1993) 214. R. Pfaff et al., Phys. Rev. C 53 (1996) 1753. J. J. Ressler et al., Phys. Rev. Lett 84 (2000) 2104. M. Hausmann et al., Nucl. Phys. A701 (2002) 561. F. Herfurth et al J. Phys. B: At. Mol. Opt. Phys. 36 (2003) 931. Weissman, L. et al. Phys. Rev. C 65 (2002) 024321. G. Savard, private communication (2003). A. Woehr, private communication (2003). T. Rauscher, F.-K. Thielemann, K.-L. Kratz, Phys. Rev. C 56 (1997) 1613. H. Herndl et al. Phys. Rev. C 52 (1995) 1078. J.L. Fisker et al., ADNDT 79 (2001) 241. P. Decrock et al., Phys. Lett. B 304 (1993) 50. S. Bishop et al., Phys. Rev. Lett. 90 (2003) 162501. C. Iliadis et al. Ap. J. Suppl. 134 (2001) 151. H. Schatz et al., Phys. Rev. Lett. 79 (1997) 3845. J. Caggiano et al. Phys. Rev. C 65 (2002) 5801. D. W. Bardayan et al Nucl. Phys. A 718 (2003) 505b. J. Caggiano et al. Phys. Rev. C 64 (2001) 5802. X. G. Zhou et al. Phys. Rev. C 53 (1996) 982. K. E. Rehm et al. Phys. Rev. Lett. 80 (1998) 676. R. R. C. Clement et al., submitted to Phys. Rev. Lett. (2004).
Radioactive nuclei on accreting neutron stars H. Schatza a
Dept. of Physics and Astronomy, National Superconducting Cyclotron Laboratory, and Joint Institute for Nuclear Astrophysics, Michigan State University, East Lansing, MI 48824, USA With new data from RXTE, Chandra, and XMM X-ray astronomy of accreting neutron stars enters a precision era. Precision nuclear physics from experiments with radioactive beams is needed to interpret the data. We review status and prospects of the nuclear physics, focusing on the nuclear reactions in X-ray bursts, in particular with heavy unstable nuclei beyond magnesium. At the NSCL Coupled Cyclotron Facility some of the major nuclear physics uncertainties are now being addressed using neutron removal reactions with radioactive beams. 1. INTRODUCTION Type I X-ray bursts are thermonuclear explosions on the surface of an accreting neutron star (see reviews [1–3]). Most of the bursts are powered by a mix of explosive helium and hydrogen burning via the 3α reaction, the αp process and the rapid proton capture process (rp-process) [4,5]. X-ray observatories such as Beppo SAX, RXTE, Chandra, and XMM provide a wealth of new high quality data on X-ray bursts. These include discoveries, such as nearly coherent oscillations in the 100-1000 Hz range, or rare superbursts, but also precision data on long term bursting behavior of regular ”textbook” bursters such as GS 1826-24 [6]. As accretion rates change slowly over decades such long term observations probe burst properties as a function of accretion rate, and can be directly compared to model predictions. 1D X-ray burst model simulations with the full nuclear physics of the rp process became possible recently [7,8]. Together with the new observations and a reliable nuclear physics database this could be the beginning of a precision era in the field. In fact, first detailed comparisons of predicted and observed X-ray burst light curves for specific systems are now being preformed [6,9], but suffer from large nuclear physics uncertainties [10,7]. Nuclear physics enters X-ray burst models in many ways. Spallation reactions can modify the material impinging on the neutron star surface. This might be directly observable through absorption line features in the X-ray spectra [11]. Explosive hydrogen and helium burning in the layer of accreted material on the surface of the neutron star powers the observed X-ray bursts via the rp- and αp-processes [4,5], which involve extremely neutron deficient unstable nuclei. Nuclear physics determines directly duration and shape of the burst lightcurves [7,8,12,13,10]. Stable hydrogen burning between bursts modifies the composition of the burst fuel prior to ignition, and is the dominant burning mechanism at 0375-9474/$ – see front matter © 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.nuclphysa.2004.09.151
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very high accretion rates, for example in X-ray pulsars [14]. While the products of surface burning processes most likely are not ejected into space, knowledge of the composition of the ashes is critical for modeling the neutron star crust. In particular, the amount of potential fuel for deeper burning processes in the burst ashes is critcial. This includes carbon, which could explode deep in the crust triggering the recently discovered rare superbursts [15,16]. Important are also amount and exact compositon of the nuclei beyond iron that can serve as fuel for a photodisintegration runaway during superbursts [17]. Still deeper in the crust nuclei undergo another sequence of nuclear reactions - electron captures and pycnonuclear fusion (pressure induced fusion) determining composition and thermal properties of the crust. These processes produce extremely neutron rich unstable nuclei and their energy generation can be observed directly in transient systems during the off-phase when accretion shuts off and X-ray emission from the surface of the neutron star can be detected [18]. Deep crust processes also set the termal structure of the crust, which serves as a boundary condition for X-ray burst and superburst models [19]. Another observable of the deep crust processes might be gravitational wave emission if the thermal structure is unisotropic [20]. 2. NUCLEAR DATA NEEDS In this paper we focus on the nuclear physics of the αp- and rp-processes in X-ray bursts. These reaction sequences have the most direct observational consequences and set the stage for all subsequent nuclear processes deeper in the crust. Fig. 1 shows the path of the rp process during an X-ray burst calculated with a one zone model coupled selfconsistently to a complete reaction network [13]. The endpoint of the rp process depends on the amount of hydrogen available at burst ignition, which in turn varies with the parameters of the system such as accretion rate, heat flux from the neutron star surface and composition of the accreted material. However, even for large hydrogen to seed ratios the rp process is limited by a SnSbTe cycle, which forms because of the very low α binding energies of proton rich Te isotopes [13]. In principle the rp-process could proceed beyond the SnSbTe cycle in a multiburst rp-process (the rp2 process [21]). In this scenario the freshly synthesized nuclei decay back to stability and are then again bombarded with protons in a second burst thus bypassing the SnSbTe cycle. Recent 1D multizone calculations indicate that reirradiation of incompletely burned ashes indeed occurs in X-ray bursts [7,8]. However, the first burst happens through heating from the underlying ignition layers at lower temperatures. This reduces the overall hydrogen to seed ratio as lower temperature helium fusion produces more lighter seed nuclei as opposed to fewer heavy seed nuclei. Overall the rp-process therefore tends to be shorter, so even with multibursts the SnSbTe cycle is only barely reached. However, the full system parameter space has not been explored yet. For now it is reasonable to assume that the reaction path outlined in Fig. 1 encompasses the maximum range of nuclear physics data needed for rp-process calculations. The critical data are nuclear masses, β decay rates, and the rates of (p,γ) and (α,p) reactions. In particular it is the interplay of masses and β decays along the proton drip line that sets the path and timescale of the rp process. Proton separation energies determine where in the rp-process path (γ,p) photodisintegration reactions hamper the reaction flow and
349c
H. Schatz / Nuclear Physics A 746 (2004) 347c–353c
Xe (54) I (53) Te (52)
(g,a) 105Te
106Te
107Te
108Te
104Sb
105Sb
106
107Sb
Sb
Sb (51) Sn (50) In (49) Cd (48) Ag (47) Pd (46) Rh (45) Ru (44)
(p,)g 103Sn
104Sn
105Sn
106Sn
102In
103In
104In
105In
5
5758
Tc (43) Mo (42) Nb (41) Zr (40) Y (39) Sr (38)
b+
56 5455 53
Rb (37) Kr (36) Br (35) Se (34)
5152 4950
As (33) Ge (32) Ga (31) Zn (30)
45464748 424344 41
37383940 Cu (29) Ni (28) 33343536 Co (27) Fe (26) 3132 Mn (25) Cr (24) 2930 V (23) Ti (22) 25262728 Sc (21) Ca (20) 2324 K (19) Ar (18) 2122 Cl (17) S (16) 17181920 P (15) Si (14) 1516 Al (13) Mg (12) 14 Na (11) Ne (10) 11 1213 F (9) O (8) 9 10 N (7) C (6) B (5) 7 8 Be (4)
rp process
ap process
Li (3) He (2) 5 6 H (1) 3 4 n (0) 2 0 1
3a reaction
Figure 1. Reaction flow time integrated over a complete x-ray burst [13]. The inset shows the SnSbTe cycle in detail.
create waiting points. The β decay lifetime of the waiting point nucleus then determines together with the remaining net proton capture lifetime the timescale of the rp-process and the final abundance pattern. Therefore masses and β decay lifetimes strongly impact calculated X-ray burst lightcurves. This has been qualitatively demonstrated in a series of one-zone model calculations [12,13]. In a more recent study lightcurve variations were calculated based on actual uncertainties in state of the art mass predictions, again in a onezone model [10]. These findings have now been confirmed by multizone calculations with full nuclear physics, where the impact of mass uncertainties was simulated by changing β-decay lifetimes [7]. Proton capture rates and (α,p) reaction rates can play an important role at lower temperature when they compete with β-decay rates or become comparable to the burst timescale. This happens inbetween bursts, during burst ignition and cooling, and for burning at shallower depths above the ignition zone. Because of the latter issue, 1D multizone models are needed to investigate the sensitivity of X-ray burst calculations to reaction rates. The importance of proton captures on heavy nuclei closer to stability, such as 27 Si, 31 S, 35 Ar, and 39 Ca for burst ignition has already been pointed out [22]. Recently it has been demonstrated that slow (α,p) reaction rates at the 22 Mg, 26 Si, 30 S, and 34 Ar waiting points could cause double peaked bolometric X-ray burst lightcurves,
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which are observed occasioanlly and could not be explained before [8]. These waiting points had been identified before in one-zone calculations [23], but the observable effect is produced by an interplay of different burning zones with different conditions, which cannot be modeled in a one zone model. 3. EXPERIMENTAL STATUS AND NEW TECHNIQUES Radioactive beam experiments at many facilities have provided a wealth of new data on the location of the proton drip line between Ni and Te. These include experiments at LBL [24], GANIL [25–28], GSI [29–32], ISOLDE [33,34], MSU/NSCL [35–37], and ORNL [38]. These experiments focused on the determination of the transition from β to proton decay as one moves away from stability, either by measuring β decay rates or by obtaining lifetime limits from the nonobservation of isotopes with known production rates. Proton emitters have in most cases been identified on the basis of such lifetime limits - with the exception of 105 Sb [24,30] no direct proton emission has been observed in this element range. In addition these experiments provided data on the majority of β decay half-lives in the rp process, with the exception of 74 Sr, 87 Ru, 95,96 Cd. The lack of sufficiently precise proton separation energies (accuracy of at least ≈ kT = 80 keV needed) along the proton drip line between Ni and Te has been the major nuclear physics uncertainty in rp-process calculations for a long time [10]. Recently a number of new techniques have been used to measure masses of exotic nuclei in the path of the rp process. These include time-of-flight measurements at the ESR storage ring at GSI in the Ti-Mn region [39] and ion trap experiments at ISOLTRAP [40] and the Canadian Penning Trap at ANL [42]. Of particular importance are the proton separation energies of 61 Ga, 65 As, 69 Br, 73 Rb, and 77 Y which are related to the longest lived waiting points in the rp process. Here, the situation has been improved considerably. The masses of 61 Ga [41], 68 Se [42,43], and 76 Sr [40] masses have been measured using β-endpoint techniques and Penning traps removing the major uncertainties in the N = Z nuclei. At the same time, new mass predictions based on Coulomb shift calculations can now provide quite reliable data for masses beyond the N = Z line, provided the mass of the mirror nucleus is experimentally known [10]. Nevertheless, an experimental determination of the 69 Br, 73 Rb, and 77 Y masses would be important. The former two isotopes are proton unbound and are therefore out of reach for time-of-flight or Penning trap measurements, but transfer reactions with radioactive beams could be used to determine their masses. Experimental information is sparse for the rates of proton capture and (α,p) reactions on unstable nuclei along the αp- and rp-process paths. Theoretical predictions of these rates are highly uncertain as level densities tend to be low. In this case statistical methods are not generally applicable [44] and shell model calculations, available up to A = 63 [45,46], cannot predict the properties of individual resonances with sufficient accuracy (see below) even when information from mirror nuclei is available. Direct measurements of proton capture rates with radioactive beams at low astrophysical energies of a few MeV are difficult and have only been done in a few cases such as 13 N(p,γ)14 O at Louvain-la-Neuve [47] and more recently 21 Na(p,γ)22 at TRIUMF [48]. For the time being, indirect methods using stable and radioactive beams are needed to obtain experimental information on the majority of proton and α induced reaction rates.
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So far, such efforts have mainly concentrated on lighter nuclei with Z ≤ 12, which are of potential importance during the X-ray burst ignition process. Experimental information beyond Z = 12 is very limited because the reaction path moves further away from stability, because of technical limitations, and because many experimental studies are motivated by the nova problem. In the Z = 12–21 range some relevant information on nuclei closer to stability is available from stable beam transfer reaction measurements, for example using (3 He,np) and (3 He,t) reactions (see [49] for a review of the A = 20–40 mass range). Only recently, stable beam multinucleon transfer reaction measurements have provided information about more unstable nuclei. These include reactions such as ( 4 He,8 He) for 24 Si [50], (3 He,6 He) and (p,t) for the 26 Si [51,52], and (7 Li,8 He) for the 27 P [53], which are relevant for the 23 Al(p,γ)24 Si, 25 Al(p,γ)26 Si, and 26 Si(p,γ)27 P reaction rates, respectively. The inverse kinematics reaction 1 H(58 Ni,57 Cu)2n has been used to determine resonance energies in the 56 Ni(p,γ)57 Ni reaction rate [54] via γ-ray spectroscopy. Such multinucleon transfer reactions typically provide only information on excitation energies but as resonant reaction rates depend exponentially on resonance energies this removes the major uncertainty in the reaction rates. However, transfer reactions with stable beams have limitations because they cannot reach nuclei that are too far from stability because of the difficulty to manufacture targets for certain elements, and because of the selectivity of the reaction to only a subset of the relevant states. Even in the cases where critical levels have been observed with particle spectroscopy, the precision of the extracted resonance energy is on the order of 20-100 keV. Because of the sensitivity of resonant reaction rates to level energies, accuracies of the order of 1-10 keV are needed. Transfer reactions with radioactive beams can provide a way to overcome these limitations. Rehm et al. 1998 [55] determined neutron spectroscopic factors in 57 Ni using a (d,p) reaction in inverse kinematics with a radioactive 56 Ni beam at ANL. This allowed to constrain proton spectroscopic factors in the 57 Cu mirror, which are relevant for the 56 Ni(p,γ) reaction in the rp-process. More recently, a new method has been developed at the National Superconducting Cyclotron Laboratory to measure excitation energies directly in the relevant neutron deficient nuclei using neutron removal reactions in inverse kinematics [56]. A first application was the measurement of excitation energies in 33 Ar using neutron removal of a 84 MeV/u radioactive 34 Ar beam on a plastic target. γ-rays from the deexcitation of the resulting 33 Ar nuclei were detected in coincidence with the observation of the 33 Ar residual in the S800 spectrometer. With this technique the energies of all relevant states could be determined with accuracies of 2–9 keV. Together with shell model calculations for the remaining parameters this reduced the uncertainty in the 32 Cl(p,γ)33 Al reaction rate from a factor of around 1000 to a factor of 2-3. This method has great future potential. Because of the relatively large cross sections for neutron removal, and the high beam intensities provided by the NSCL Coupled Cyclotron Facility all nuclei in the rp-process up to Z ≈ 36 are within reach. A complementary method to also measure exitation energies of predominatly proton decaying states is being developed. Together with shell model calculations, now available up to A = 63 [45,46] a drastically improved set of proton capture rates for rp-rprocess studies is within reach. This could form a basis for meaningful sensitivity studies to determine the reactions that
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need to be measured more accurately with other techniques, for example directly with low energy radioactive beams at the future rare isotope accelerator RIA. 4. ACKNOWLEDGEMENTS The neutron removal technique at the NSCL has been developed in a collaboration with R.R.C. Clement, D. Bazin, W. Benenson, B.A. Brown, A.L. Cole, M.W. Cooper, P.A. DeYoung, A. Estrade, M.A. Famiano, N.H. Frank, A. Gade, T. Glasmacher, P.T. Hosmer, W.G. Lynch, F. Montes, W.F. Mueller, G.F. Peaslee, P. Santi, B.M. Sherrill, M-J. van Goethem, and M.S. Wallace. The one zone X-ray burst model was developed with L. Bildsten and A. Cumming, using a reaction network solver provided by F.-K. Thielemann. The reaction library is maintained in collaboration with M. Wiescher. This work has been supported by NSF grants PHY-0110253 and PHY-0110253 (Joint Institute for Nuclear Astrophysics). H. S. is an Alfred P. Sloan fellow. REFERENCES 1. W. H. G. Lewin, J. van Paradijs, and R. E. Taam, in X-Ray Binaries, edited by W. H. G. Lewin, J. van Paradijs, and E. P. J. van den Heuvel (Cambridge Univ. Press, Cambridge) p. 175 (1997). 2. L. Bildsten, ”Rossi 2000: Astrophysics with the Rossi X-ray Timing Explorer, March 22-24, 2000 at NASA’s Goddard Space Flight Center, Greenbelt, MD USA”, E65, (astro-ph/0001135) (2000). 3. T. E. Strohmayer and L. Bildsten, To appear in Compact Stellar X-ray Sources, eds. W.H.G. Lewin and M. van der Klis, Cambridge University Press, astro-ph/0301544, 2003. 4. R. K. Wallace and S. E. Woosley, Ap. J. Suppl. 45 (1981) 389. 5. H. Schatz et al., Phys. Rep. 294 (1998) 167. 6. D. K. Galloway et al.. astro-ph/0308122 (2003). 7. S. E. Woosley et al., astro-ph/0307425 (2003). 8. J. L. Fisker and F.-K. Thielemann, astro-ph/0312361 (2003). 9. A. Cumming, astro-ph/0309626 (2003). 10. B. A. Brown et al. Phys. Rev. C 65 (2002) 5802. 11. L. Bildsten, P. Chang, and F. Paerels, astro-ph/0303147 (2003). 12. O. Koike, M. Hashimoto, K. Arai, and S. Wanajo, Astron. Astrophys. 342 (1999) 464. 13. H. Schatz et al., Phys. Rev. Lett. 86 (2001) 3471. 14. H. Schatz, L. Bildsten, and A. Cumming, Ap. J. 524 (1999) 1014. 15. A. Cumming, and L. Bildsten, ApJ, 559 (2001) L127. 16. E. F. Brown, and T. E. Strohmayer, Ap. J. 566 (2002) 1045. 17. H. Schatz, L. Bildsten, and A. Cumming, Ap. J. 583 (2003) L87. 18. E. F. Brown, L. Bildsten, R. E. Rutledge Ap. J. 504 (1998) 95. 19. E. F. Brown, Ap. J. 529 (2000) 985. 20. L. Bildsten, Ap. J. 501 (1998) 89. 21. R. N. Boyd, M. Hencheck, and B. S. Meyer, in International Symposium on Origin of Matter and Evolution of Galaxies 97, Atami, Japan, edited by S. Kubono, T. Kajino,
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