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Collective oscillations and r-process nucleosynthesis
Nuclear Physics B (Proc. Suppl.) 217 (2011) 121–123 www.elsevier.com/locate/npbps
Collective oscillations and r-process nucleosynthesis Rebecca Surmana , Gail C. McLaughlinb , Alexander Friedlandc , and Huaiyu Duand a
Department of Physics and Astronomy, Union College, Schenectady, NY 12308 USA b
Department of Physics, North Carolina State University, Raleigh, NC 27695, USA c
Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM 87544, USA d
Department of Physics and Astronomy, University of New Mexico, Albuquerque, NM 87131, USA Neutrinos have recently been shown to have collective phenomenon which causes them to flavor transform near the center of the supernova. These flavor transformations can potentially impact supernova nucleosynthesis, particularly for processes that occur near the core, such as the r-process. In this paper we explore the effects of collective oscillations on a supernova r-process. We find that magnitude of the effect depends senstivitely on the astrophysical conditions—in particular on the interplay between the time when nuclei begin to exist in significant numbers and the time when the collective oscillation begins. Because of this delicate balance, a more definitive understanding of the astrophysical conditions is necesssary. Here, we explore scenarios based on outflow models currently in use and discuss their implications.
Recent advances have been made in the understanding of neutrino flavor transformations in supernovae. It is now widely thought that neutrinos transform “collectively” much deeper in the supernovae than previously thought [1–5]. This means that neutrino flavor transformations have a greater potential to impact nucleosynthesis, particularly for types of element synthesis that occur near the core, such as the r-process [6,7]. While the site of r-process, or rapid neutron capture, nucleosynthesis has not yet been conclusively determined (see, e.g., [8] for a review), observational data points to astrophysical events that operate early in galactic history and produce a consistent abundance pattern for the heaviest elements [9–12]. This seems to favor a site within a core-collapse supernova over other possible options, such as compact object mergers [13,14]. Though the requisite conditions for the r-process are difficult to obtain, e.g. [15,16] and references therein, the most promising and well-studied po0920-5632/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.nuclphysbps.2011.04.081
tential site is that of the neutrino-driven wind that develops at late times close to the newlyformed neutron star, first examined in [17,18]. In this paper we study the effects of collective neutrino flavor oscillations on neutron rich nucleosynthesis. We pick astrophysical conditions which produce neutron rich outflow and then examine the interplay between the nuclear reactions and the neutrinos, and describe the impact of changing the neutrino flux at different points above the neutrino surface on the abundance pattern. Collective effects cause rapid oscillations above the neutrino surface, so we present a couple of examples of calculations of a neutrino transformation calculation coupled to a nuclear reaction network. In the traditional picture, a supernova neutrino-driven wind r-process proceeds as follows. A mass element composed of free nucleons is heated to high entropies by the protoneutron star neutrino emission, and its neutron-to-proton
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R. Surman et al. / Nuclear Physics B (Proc. Suppl.) 217 (2011) 121–123
ratio is set by the competing weak interactions: νe + n ν¯e + p
p + e−
(1)
n+e
(2)
+
As long as the electron antineutrino spectrum is sufficiently hotter than the electron neutrino spectrum, antineutrino captures dominate and the material becomes neutron rich. As the material accelerates away from the center, it cools and nuclei reassemble, first to alpha particles, then to heavier r-process seed nuclei. The subsequent r-process consists of the rapid captures of the remaining neutrons on the seed nuclei. Note that once alpha particles form, the protons are all bound in alphas, and so the forward reaction of Eqn. 2 is cut off. The remaining neutrons can then be depleted by the forward reaction of Eqn. 1, forming protons that then bind into additional alphas. This is the so-called ‘alpha effect’ [19], and it acts to reduce the effectiveness of the subsequent r-process. Since the operation of the alpha effect is sensitive to the electron neutrino spectrum, flavor transformations between electron and the hotter mu and tau neutrinos can only act to strengthen the effect. The impact of neutrino flavor transformations on supernova nucleosynthesis depends sensitively on what stage of nucleosynthesis the material is in when the transformation occurs, with earlier flavor transformations resulting in more dramatic effects. This is determined by the hydrodynamic trajectory of the outflowing material. As the conditions in the neutrino-driven wind are uncertain, we examine a range of possible trajectories, with two examples shown in Fig. 1. The trajectories are shown along with the approximate temperature ranges for each stage of nucleosynthesis, and a sample electron neutrino survival probability, calculated as in [20]. In the trajectory shown with the dashed line, the flavor transformation occurs during the formation of seed nuclei, and so we expect an enhancement of the alpha effect. In the second trajectory, shown with the dot-dashed line, the flavor transformation occurs earlier, while alphas are forming. In this case the altered neutrino spectra can cause a shift in the neutron-to-proton ratio in addition to the strengthened alpha effect.
Figure 1. Shows temperature T9 as a function of radius in km (dashed line) for two sample thermodynamic trajectories, one with lower density and entropy s/k = 300 (dot-dashed line) and the other with higher density and s/k = 200 (dashed line). The solid line shows a sample electron neutrino survival probability P (e) for 20 MeV neutrinos, as calculated assuming an inverted hierarchy.
We examine these effects in simulations that couple a nuclear network calculation, described in [21], to a full neutrino oscillation calculation as in [20]. We use late-time neutrino spectra from [22] and hydrodynamic trajectories similar to [23]. Abundance patterns for a sample set of simulations are shown in the bottom panel of Fig. 2. Note that the influence of the flavor transformations here is to enhance the influence of neutrino interactions on the r-process and further weaken the third r-process peak. In the single-angle calculation, the third peak is entirely absent. These results can be understood by examining the evolution of the neutron and alpha particle abundances shown in the top panel of Fig. 2. In the multiangle calculation, the flavor transformation occurs around r ∼ 100 km or so, late in the alpha particle formation stage, so here the oscillations tend to intensify the alpha effect. When using the oscillation calculation with the single angle approximation, however, the flavor transformation occurs much earlier, while the initial neutron-toproton ratio is still being set. This results in a sufficiently large drop in the free neutron abun-
R. Surman et al. / Nuclear Physics B (Proc. Suppl.) 217 (2011) 121–123
dance to (erroneously) prevent the formation of the third r-process peak. A careful description of our full calculation along with additional results and discussion appear in [24].
Figure 2. Bottom panel shows final abundances Y versus mass number A for simulations with s/k = 200 and τ = 15 ms and with no neutrino oscillations (solid line) and single-angle (short dashes) and full multiangle (long dashes) oscillation calculations, both assuming an inverted hierarchy. The top panel shows mass fractions of neutrons (black lines) and alpha particles (grey lines) as a function of radius r in km for the same three simulations.
While the astrophysical site of the r-process has yet to be pinned down, most of the potential environments are characterized by high temperatures, densities, and neutrino emission. We have found that neutrino collective oscillations act only to enhance the role that neutrinos play in heavy el-
123
ement nucleosynthesis in these environments and should therefore not be neglected. REFERENCES 1. G. M. Fuller, R. W. Mayle, J. R. Wilson and D. N. Schramm, Astrophys. J. 322 (1987) 795. 2. D. Notzold and G. Raffelt, Nucl. Phys. B 307 (1988) 924. 3. J. T. Pantaleone, Phys. Lett. B 287 (1992) 128. 4. G. Sigl and G. Raffelt, Nucl. Phys. B 406 (1993) 423. 5. H. Duan et al., Phys. Rev. Lett. 97 (2006) 241101. 6. A. B. Balantekin and H. Yuksel, New J. Phys. 7 (2005) 51. 7. S. Chakraborty et al., JCAP 1006 (2010) 007. 8. M. Arnould, S. Goriely, and K. Takahashi, Phys. Rept. 450 (2007) 97. 9. C. Sneden et al., Astrophys. J. 467 (1996) 819. 10. S. G. Ryan, J. E. Norris, and T. C. Beers, Astrophys. J. 471 (1996) 254. 11. Y. Ishimaru and S. Wanajo, Astrophys. J. 511 (1999) L33. 12. J. W. Truran et al., Pub. Astron. Soc. Pac. 114 (2002) 1293. 13. D. Argast et al., Astron. Astrophys. 416 (2004) 997. 14. S. Wanajo and I. Ishimaru, Nucl. Phys. A 777 (2006) 676. 15. T. Fischer et al., Astron. Astrophys. 517 (2010) A80. 16. L. Huedepohl et al., arXiv:0912.0260. 17. B. S. Meyer et al., Astrophys. J. 399 (1992) 656. 18. S. E. Woosley et al., Astrophys. J. 433 (1994) 229. 19. B. S. Meyer, G. C. McLaughlin, G. M. Fuller, Phys. Rev. C 58 (1998) 3696. 20. H. Duan and A. Friedland, arXiv:1006.2359. 21. R. Surman et al., Astrophys. J. 679 (2008) L117. 22. M. Keil, G. G. Raffelt, and H.-Th. Janka, Astrophys. J. 590 (2003) 971. 23. I. V. Panov and H.-Th. Janka, Astron. Astrophys. 494 (2009) 829. 24. H. Duan et al., arXiv:1012.0532.
Collective oscillations and r-process nucleosynthesis Rebecca Surmana , Gail C. McLaughlinb , Alexander Friedlandc , and Huaiyu Duand a
Department of Physics and Astronomy, Union College, Schenectady, NY 12308 USA b
Department of Physics, North Carolina State University, Raleigh, NC 27695, USA c
Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM 87544, USA d
Department of Physics and Astronomy, University of New Mexico, Albuquerque, NM 87131, USA Neutrinos have recently been shown to have collective phenomenon which causes them to flavor transform near the center of the supernova. These flavor transformations can potentially impact supernova nucleosynthesis, particularly for processes that occur near the core, such as the r-process. In this paper we explore the effects of collective oscillations on a supernova r-process. We find that magnitude of the effect depends senstivitely on the astrophysical conditions—in particular on the interplay between the time when nuclei begin to exist in significant numbers and the time when the collective oscillation begins. Because of this delicate balance, a more definitive understanding of the astrophysical conditions is necesssary. Here, we explore scenarios based on outflow models currently in use and discuss their implications.
Recent advances have been made in the understanding of neutrino flavor transformations in supernovae. It is now widely thought that neutrinos transform “collectively” much deeper in the supernovae than previously thought [1–5]. This means that neutrino flavor transformations have a greater potential to impact nucleosynthesis, particularly for types of element synthesis that occur near the core, such as the r-process [6,7]. While the site of r-process, or rapid neutron capture, nucleosynthesis has not yet been conclusively determined (see, e.g., [8] for a review), observational data points to astrophysical events that operate early in galactic history and produce a consistent abundance pattern for the heaviest elements [9–12]. This seems to favor a site within a core-collapse supernova over other possible options, such as compact object mergers [13,14]. Though the requisite conditions for the r-process are difficult to obtain, e.g. [15,16] and references therein, the most promising and well-studied po0920-5632/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.nuclphysbps.2011.04.081
tential site is that of the neutrino-driven wind that develops at late times close to the newlyformed neutron star, first examined in [17,18]. In this paper we study the effects of collective neutrino flavor oscillations on neutron rich nucleosynthesis. We pick astrophysical conditions which produce neutron rich outflow and then examine the interplay between the nuclear reactions and the neutrinos, and describe the impact of changing the neutrino flux at different points above the neutrino surface on the abundance pattern. Collective effects cause rapid oscillations above the neutrino surface, so we present a couple of examples of calculations of a neutrino transformation calculation coupled to a nuclear reaction network. In the traditional picture, a supernova neutrino-driven wind r-process proceeds as follows. A mass element composed of free nucleons is heated to high entropies by the protoneutron star neutrino emission, and its neutron-to-proton
122
R. Surman et al. / Nuclear Physics B (Proc. Suppl.) 217 (2011) 121–123
ratio is set by the competing weak interactions: νe + n ν¯e + p
p + e−
(1)
n+e
(2)
+
As long as the electron antineutrino spectrum is sufficiently hotter than the electron neutrino spectrum, antineutrino captures dominate and the material becomes neutron rich. As the material accelerates away from the center, it cools and nuclei reassemble, first to alpha particles, then to heavier r-process seed nuclei. The subsequent r-process consists of the rapid captures of the remaining neutrons on the seed nuclei. Note that once alpha particles form, the protons are all bound in alphas, and so the forward reaction of Eqn. 2 is cut off. The remaining neutrons can then be depleted by the forward reaction of Eqn. 1, forming protons that then bind into additional alphas. This is the so-called ‘alpha effect’ [19], and it acts to reduce the effectiveness of the subsequent r-process. Since the operation of the alpha effect is sensitive to the electron neutrino spectrum, flavor transformations between electron and the hotter mu and tau neutrinos can only act to strengthen the effect. The impact of neutrino flavor transformations on supernova nucleosynthesis depends sensitively on what stage of nucleosynthesis the material is in when the transformation occurs, with earlier flavor transformations resulting in more dramatic effects. This is determined by the hydrodynamic trajectory of the outflowing material. As the conditions in the neutrino-driven wind are uncertain, we examine a range of possible trajectories, with two examples shown in Fig. 1. The trajectories are shown along with the approximate temperature ranges for each stage of nucleosynthesis, and a sample electron neutrino survival probability, calculated as in [20]. In the trajectory shown with the dashed line, the flavor transformation occurs during the formation of seed nuclei, and so we expect an enhancement of the alpha effect. In the second trajectory, shown with the dot-dashed line, the flavor transformation occurs earlier, while alphas are forming. In this case the altered neutrino spectra can cause a shift in the neutron-to-proton ratio in addition to the strengthened alpha effect.
Figure 1. Shows temperature T9 as a function of radius in km (dashed line) for two sample thermodynamic trajectories, one with lower density and entropy s/k = 300 (dot-dashed line) and the other with higher density and s/k = 200 (dashed line). The solid line shows a sample electron neutrino survival probability P (e) for 20 MeV neutrinos, as calculated assuming an inverted hierarchy.
We examine these effects in simulations that couple a nuclear network calculation, described in [21], to a full neutrino oscillation calculation as in [20]. We use late-time neutrino spectra from [22] and hydrodynamic trajectories similar to [23]. Abundance patterns for a sample set of simulations are shown in the bottom panel of Fig. 2. Note that the influence of the flavor transformations here is to enhance the influence of neutrino interactions on the r-process and further weaken the third r-process peak. In the single-angle calculation, the third peak is entirely absent. These results can be understood by examining the evolution of the neutron and alpha particle abundances shown in the top panel of Fig. 2. In the multiangle calculation, the flavor transformation occurs around r ∼ 100 km or so, late in the alpha particle formation stage, so here the oscillations tend to intensify the alpha effect. When using the oscillation calculation with the single angle approximation, however, the flavor transformation occurs much earlier, while the initial neutron-toproton ratio is still being set. This results in a sufficiently large drop in the free neutron abun-
R. Surman et al. / Nuclear Physics B (Proc. Suppl.) 217 (2011) 121–123
dance to (erroneously) prevent the formation of the third r-process peak. A careful description of our full calculation along with additional results and discussion appear in [24].
Figure 2. Bottom panel shows final abundances Y versus mass number A for simulations with s/k = 200 and τ = 15 ms and with no neutrino oscillations (solid line) and single-angle (short dashes) and full multiangle (long dashes) oscillation calculations, both assuming an inverted hierarchy. The top panel shows mass fractions of neutrons (black lines) and alpha particles (grey lines) as a function of radius r in km for the same three simulations.
While the astrophysical site of the r-process has yet to be pinned down, most of the potential environments are characterized by high temperatures, densities, and neutrino emission. We have found that neutrino collective oscillations act only to enhance the role that neutrinos play in heavy el-
123
ement nucleosynthesis in these environments and should therefore not be neglected. REFERENCES 1. G. M. Fuller, R. W. Mayle, J. R. Wilson and D. N. Schramm, Astrophys. J. 322 (1987) 795. 2. D. Notzold and G. Raffelt, Nucl. Phys. B 307 (1988) 924. 3. J. T. Pantaleone, Phys. Lett. B 287 (1992) 128. 4. G. Sigl and G. Raffelt, Nucl. Phys. B 406 (1993) 423. 5. H. Duan et al., Phys. Rev. Lett. 97 (2006) 241101. 6. A. B. Balantekin and H. Yuksel, New J. Phys. 7 (2005) 51. 7. S. Chakraborty et al., JCAP 1006 (2010) 007. 8. M. Arnould, S. Goriely, and K. Takahashi, Phys. Rept. 450 (2007) 97. 9. C. Sneden et al., Astrophys. J. 467 (1996) 819. 10. S. G. Ryan, J. E. Norris, and T. C. Beers, Astrophys. J. 471 (1996) 254. 11. Y. Ishimaru and S. Wanajo, Astrophys. J. 511 (1999) L33. 12. J. W. Truran et al., Pub. Astron. Soc. Pac. 114 (2002) 1293. 13. D. Argast et al., Astron. Astrophys. 416 (2004) 997. 14. S. Wanajo and I. Ishimaru, Nucl. Phys. A 777 (2006) 676. 15. T. Fischer et al., Astron. Astrophys. 517 (2010) A80. 16. L. Huedepohl et al., arXiv:0912.0260. 17. B. S. Meyer et al., Astrophys. J. 399 (1992) 656. 18. S. E. Woosley et al., Astrophys. J. 433 (1994) 229. 19. B. S. Meyer, G. C. McLaughlin, G. M. Fuller, Phys. Rev. C 58 (1998) 3696. 20. H. Duan and A. Friedland, arXiv:1006.2359. 21. R. Surman et al., Astrophys. J. 679 (2008) L117. 22. M. Keil, G. G. Raffelt, and H.-Th. Janka, Astrophys. J. 590 (2003) 971. 23. I. V. Panov and H.-Th. Janka, Astron. Astrophys. 494 (2009) 829. 24. H. Duan et al., arXiv:1012.0532.