Short-lived 244 Pu points to compact binary mergers as sites for heavy r-process nucleosynthesis

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1 SUPPLEMENTARY INFORMATION DOI: /NPHYS3574 Short-lived 244 Pu points to compact binary mergers as sites for heavy r-process nucleosynthesis 1 Interpretation of the deep sea measurement Wallner et al 1 measured the number of live 244 Pu particles in deep-sea archives, which consist of two samples, crust and sediment. Using the crust sample the estimated flux of 244 Pu particles on the Earth s orbit is f Pu = cm 2 Myr 1 and it is cm 2 Myr 1 with the sediment sample. The upper and lower values are 2σ limits. The crust sample spans an accumulation time of 25 Myr and the sediment one spans 1.64 Myr. The two estimates are consistent with each other within the 2σ level. Here, we use only on the crust sample since it statistically dominates over the sediment one and it spans a longer accumulation time. Even if one combines the two data, our conclusion does not change significantly. The estimated flux with the two samples combined is cm 2 Myr 1 where again we take 2σ limits. This is only slightly larger than the one estimated using the crust sample alone. The value of f Pu, which is the mean value over the last 25 Myr, is converted to the 244 Pu number density in the ISM around the Solar System as ISM = f Pu (, cm 3 ϵv rel n Pu )( f Pu 250 cm 2 Myr 1 v rel 26 km/s ) 1 ( ϵ 0.05) 1, (1) where v rel is the relative velocity between the Solar System and the ISM. The efficiency ϵ takes into account (i) the penetration efficiency of the 244 Pu flux from the ISM outside the heliosphere to the Earth s orbit and (ii) the difference between the mean ISM density around the solar circle NATURE PHYSICS 1

2 SUPPLEMENTARY INFORMATION DOI: /NPHYS3574 and the local ISM density where the Solar System has been traveling during the last 25 Myr. Wallner et al. 1 used ϵ = Here we use ϵ =0.05. In the following, we discuss how this efficiency is estimated. The dust flux of the ISM inside the heliosphere have been measured by the Ulysses, Galileo, Cassini, and Helios spacecrafts (see Mann 2 for a review). The measurements yield a lower limit on the gas-mass to dust-mass ratio in the local ISM 3, 150, which is roughly consistent with astronomical estimates based on star-light extinction of nearby stars. In addition, the dust flux in a mass range of to g measured by Cassini around 1 AU agrees with the one measured around 3 AU by Ulysses during the same period 4, 5. Based on these facts, we assume that the 244 Pu flux on Earth s orbit is the same as the one at the heliopause. We also assume that the 244 Pu abundance in the ISM dust grains is independent of the grain size. As the ISM is highly inhomogeneous, one should take into account the depletion of the local ISM relative to the average galactic ISM density when evaluating the implied radioactive nuclide s density. The Solar System is currently traveling inside a small interstellar cloud 6 with a mean density of cm 3. This cloud is within the Local Bubble that has a very low mean density of cm 3 and a radius of pc. Based on the solar motion and the size of the Local Bubble 7, the Solar System has been in a very low density region for the last 3 10 Myr. Before that time it had been outside the Local Bubble, where the ISM density is in the range 2 NATURE PHYSICS

3 DOI: /NPHYS3574 SUPPLEMENTARY INFORMATION of cm 3. Therefore the ISM density surrounding the Solar System averaged over the last 25 Myr can be estimated as cm 3. Based on the above consideration, a plausible range of ϵ is 0.05 to 0.9. Here we use ϵ =0.05 as a reference value that corresponds to a conservative choice in terms of the depletion of 244 Pu in the ISM. Clearly this is the largest source of uncertainty in our estimates. Still this uncertainty does not affect the qualitative nature of our results. In the following we also consider ϵ =0.01. Even with this low value (see Fig. 1 of the Supplementary material), cc-sne are only marginally consistent with the deep-sea the measurements. We note also that the penetration of ISM dust to the Earth s orbit in deep-sea archives is confirmed by the observation of a spike of live 60 Fe (half-live of 2.6 Myr) in the deep-sea crust 8 and sediments 9, 10. This 60 Fe spike is interpreted as direct ejecta of a close-by supernova about 2.5 Myr BP. 2 Mixing process in the Galactic disk Heavy nuclei ejected into the ISM are homogenized via different processes on different timescales 11. Initially, the gas containing heavy nuclei expands into the ISM as a blast wave until after a couple of Myr 12, depending on the ejecta s kinetic energy, initial velocity and external density. In the literature, it has been often assumed that at this stage the ejected material remains within this fluid element, yielding a very slow process of mixing within the galaxy. However, the ISM turbulence efficiently homogenizes the ejected material 13. The diffusion timescale of the nuclei is determined by the turnover timescale of the largest eddies 14. The diffusion coefficient can 3 NATURE PHYSICS 3

4 SUPPLEMENTARY INFORMATION DOI: /NPHYS3574 be described as D v t l mix /3 α kpc 2 /Gyr (v t /7 km s 1 )(H/0.2 kpc), where v t is the typical turbulent velocity of the ISM, l mix =3αH is the turbulence mixing length and H is the scale-height of the local ISM. Here we have introduced a mixing length parameter α, choosing α =0.1as a reference value. A numerical simulation of the turbulent mixing in the Galactic disk shows this level of efficiency of the mixing Sensitivity of the results to the choice of parameters Estimates of the rates and yields involve two unknown parameters: ϵ and α. The first, ϵ, introduces the largest uncertainty in the results. For larger values of ϵ, smaller yields are sufficient, as the depletion of the current ISM 244 Pu is more significant. Figure S1shows the rate-yield estimates for ϵ =0.01 (top panel) and for 0.9 (bottom panel). For ϵ =0.01, the estimated rate is R 0 < 7000 Myr 1 within the 2σ level. Even though this rate is quite high it is still smaller than the rate of normal cc-sne by a factor of a few. For ϵ =0.9, the allowed event rate is small R 0 < 7 Myr 1. The rate-yield estimates with different choices of α (0.3, 0.03, and 0.01) are shown in Fig. S2. For α =0.3 (top panel of Fig. S2), the mixing timescale is shorter, implying that a single event can injects live 244 Pu particles into a larger volume. As a result, observes measure larger 244 Pu densities and the allowed rate-yield region in the figure shifts to the lower event rate compared to those with α = 0.1. On the contrary, with a smaller, α = 0.03 (bottom panel of Fig. S2) and 0.01 in Fig. S3, higher rates and smaller yields are allowed. Although 4 NATURE PHYSICS

5 DOI: /NPHYS3574 SUPPLEMENTARY INFORMATION the overlap region of the 244 Pu measurements and total mass of r-process elements depends on the value of ϵ and α, the estimate ranges of the rate and yield are consistent with those of compact binary mergers irrespective of the exact choice of these two parameters. Thus we can generally conclude that the high-yield/small-rate scenario, or more specifically the compact binary merger scenario is preferred while the low-yield/high-rate scenario, or more specifically the cc-sne scenario, is ruled out. 4 Numerical Simulation To study the fluctuations of 244 Pu abundance in the ISM around the solar circle, we performed a Monte-Carlo simulation of the history of the injections of live 244 Pu particles in the ISM taking into account the radioactive decay and the turbulent diffusion processes. The r-process events are generated randomly in a 4-dimensional box with dimensions 7 Gyr in time, 16.66π kpc in the x-direction (the circumference of the solar circle), 2 kpc in the y-direction (the width of the circle), and an exponential decay in the z-direction (the height from the Galactic plane). The events are distributed following the stellar mass distribution in the Galactic disk 16 and the redshift evolution following the SGRB rate 17 or the cosmic star formation history 18. Each event ejects a fixed amount of r-process material heavier than A = 90 with the solar abundance pattern 19, 20. The number density of a radioactive nuclide with a mean-life of τ i at a given time t and a point r is computed by n i (t, r )= j t>t j N i ( K j (t) exp r r j 2 t ) j, (2) 4D t j τ i NATURE PHYSICS 5

6 SUPPLEMENTARY INFORMATION DOI: /NPHYS3574 where r j and t j are the location and time of an event labeled by j, t j t t j, and } K j (t) = min {(4πD t j ) 3/2, 8πHD t j (3) where the density evolution changes from the 3-dimensional evolution to the 2-dimensional one appropriately. Here N i is the total number of the nuclide i ejected in each event. For 244 Pu particles, the total number is given by N Pu =( 244 Pu/ 238 U) 0 N 238U, where N 238U is the number of 238 U particles and ( 244 P/ 238 U) 0 is the initial production ratio. This quantity depends on the details of the ejecta properties as well as on the nuclear fission model. In the context of supernova explosions, Cowan et al. 21 estimated that a ratio of 0.4 reproduces the solar abundance pattern. For compact binary merger ejecta, Eichler et al. 22 computed a production ratio of Here we use ( 244 Pu/ 238 U) 0 = The dependence on the production history The time evolution of the mean abundance of 244 Pu and its fluctuations depend on the history of the production rate. Figure S4, depicts the rate-yield results with the production rate following the SGRB rate 17 (top panel) and the cosmic star formation history (modified Salpeter A IMF model 18 ; bottom panel). In both cases, the rate decreases with time for the epoch that we are interested in here. The production rate at 4.6 Gyr BP is higher than the current one by a factor of 3 for the former and 4 for the latter. As long as the event rate decreases by these factors, the results do not depend sensitively on the choice of the production-rate history. However, if the event rate is constant with time, very large fluctuations, i.e., small event rates, are required to be 6 6 NATURE PHYSICS

7 DOI: /NPHYS3574 SUPPLEMENTARY INFORMATION consistent with both the ESS and current measurements as shown in Fig. S5. 6 Estimates of the rate of detectable gravitational-wave events We estimated the rate of detectable gravitational-wave events R GW using the current Galactic merger rate R 0 as R GW V GW n MW R 0. Here V GW is the detectable volume of compact binary mergers and n MW 0.01 Mpc 3 is the number density of Milky-Way size galaxies. Assuming the horizon distance of the advanced detectors of 200 Mpc for binary neutron star mergers, we get R GW 30 yr 1 (R 0 /90 Myr 1 ). References 1. Wallner, A. et al. Abundance of live 244 Pu in deep-sea reservoirs on Earth points to rarity of actinide nucleosynthesis. Nature Commun., 6, 5956 (2015). 2. Mann, I. Interstellar Dust in the Solar System. Annu. Rev. Astro. Astrophys, 48, (2010). 3. Frisch P. C. & Slavin, J. D. Interstellar dust close to the Sun. Earth and Planet Space, 65, (2013). 4. Altobelli, N. et al. Cassini between Venus and Earth: Detection of interstellar dust. J. Geophys. Res., 108, 8032 (2003). NATURE PHYSICS 7

8 SUPPLEMENTARY INFORMATION DOI: /NPHYS Landgraf, M. et al. Penetration of the heliosphere by the interstellar dust stream during solar maximum. J. Geophys. Res., 108, 8030 (2003). 6. Frisch, P. C. et al. The Interstellar Medium Surrounding the Sun. Annu. Rev. Astro. Astrophys, 49, (2011). 7. Frisch, P. C. & Slavin, J. D. The Sun s journey through the local interstellar medium: the paleolism and paleoheliosphere. Astrophys. Space Sci. Trans., 2, (2006). 8. Knie, K. et al. 60 Fe Anomaly in a Deep-Sea Manganese Crust and Implications for a Nearby Supernova Source. Phys. Rev. Lett., 93, (2004). 9. Fitoussi, C. et al. Search for Supernova-Produced Fe60 in a Marine Sediment. Phys. Rev. Lett., 101, (2008). 10. Wallner, A. et al. in preparation. 11. Roy J.-R. & Kunth, D. Dispersal and mixing of oxygen in the interstellar medium of gas-rich galaxies. Astron. Astrophys., 294, (1995). 12. Cioffi, D. F., McKee, C. F. & Bertschinger, E. Dynamics of radiative supernova remnants. Astrophys. J, 334, (1988). 13. Scalo, J. & Elmegreen, B. G. Interstellar Turbulence II: Implications and Effects. Annu. Rev. Astro. Astrophys., 42, (2004). 8 NATURE PHYSICS

9 DOI: /NPHYS3574 SUPPLEMENTARY INFORMATION 14. Pan, L. & Scannapieco, E. Mixing in Supersonic Turbulence. Astrophys. J., 721, (2010) 15. Yang, C.-C. & Krumholz, M. Thermal-instability-driven Turbulent Mixing in Galactic Disks. I. Effective Mixing of Metals. Astrophys. J., 758, 48 (2012). 16. McMillan, P. J. Mass models of the Milky Way. MNRAS, 414, (2011). 17. Wanderman, D. & Piran, T. The rate luminosity function and time delay of non-collapsar short GRBs. MNRAS, 448, (2015). 18. Hopkins, A. M. & Beacom, J. F. On the Normalization of the Cosmic Star Formation History. Astronphys J., 651, (2006). 19. Goriely, S. Uncertainties in the solar system r-abundance distribution. Astron. and Astrophys., 342, (1999). 20. Lodders, K., Palem, H. & Gail, H.-P. Abundances of the Elements in the Solar System. Landolt Börnstein, 44 (2009). 21. Cowan, J. J., Thielemann, F.-K. & Truran, J. W. Nuclear chronometers from the r-process and the age of the galaxy. Astrophys. J., 323, (1987). 22. Eichler, M. et al. The Role of Fission in Neutron Star Mergers and Its Impact on the r-process Peaks. Astrophys. J,, 808, 30 (2014) NATURE PHYSICS 9

SHORT-LIVED 244 PU POINTS TO COMPACT BINARY MERGERS AS SITES FOR HEAVY R-PROCESS NUCLEOSYNTHESIS

Draft version July 26, 208 Preprint typeset using L A TEX style emulateapj v. 08/22/09 SHORT-LIVED 244 PU POINTS TO COMPACT BINARY MERGERS AS SITES FOR HEAVY R-PROCESS NUCLEOSYNTHESIS Kenta Hotokezaka,