Lower Limits on the Nucleosynthesis of ⁴⁴Ti and ⁶⁰Fe in the Dynamic Spiral-arm Cosmic-Ray Propagation Model

The composition of cosmic rays (CRs) has fascinated researchers for almost half a century: both the composition of CRs that reach the solar system and the primary composition, which is accelerated by supernova remnants (e.g., Ackermann et al. 2013, and references therein). In Benyamin et al. (2016), we studied the composition and propagation of two separate element groups: the "light" elements, Boron through Silicon; and the "heavy" elements, Scandium through Nickel. We found that the optimal primary composition for the "heavy" elements group that best fit the Ni/Fe ratio observation is 95% Iron and 5% Nickel.

In this paper, we continue our study of this group by focusing on two radioactive isotopes,⁴⁴Ti and ⁶⁰Fe. We will show that our set of models cannot explain the observation of the two isotopes by only including secondary ⁴⁴Ti and ⁶⁰Fe, i.e., nuclei created as spallation products through collision with the interstellar medium (ISM) gas.¹

The production of Iron group nuclei is through fusion in the last evolutionary phase of the progenitor stars or the supernova (SN) event itself. Indeed, ⁴⁴Ti is spectrally detected in supernova remanents (SNRs) Casssiopeia A and SNR 1987A (Iyudin et al. 1994; The et al. 1996; Vink et al. 2001; Grebenev et al. 2012). Since ⁴⁴Ti is produced through the reaction ⁴⁰Ca(α, γ)⁴⁴Ti (The et al. 1998), its detection in remnants is evidence of a rich α particle supply in the supernova explosion, which exists inside the core-collapse supernova during the α-rich freeze-out phase. However, if the acceleration process of the CR isotopes coming from the SNe is relatively long, then by the time the nuclei are accelerated those nuclei that are unstable through electron capture (EC) should decay. A short acceleration process will, however, strip the nuclei of their electrons and allow them to be long-lived CRs.

There is, however, another source of ⁴⁴Ti in the CRs—CR nuclei are also created through spallation during their propagation in the galaxy. Since they are formed stripped, these EC unstable isotopes can survive as long as they remain at high energies. As a consequence, nuclei that decay through EC have a mean half-life time, which depends strongly on the energy. This can be seen with the Niebur et al. (2000) measurements that show how the ⁴⁹Ti/⁴⁹V and ⁵¹V/⁵¹Cr ratios decrease with energy, as expected from the longer decay time of the EC isotopes, ⁴⁹V and ⁵¹Cr, at higher energies.

In Benyamin et al. (2014, 2016), we developed the first CR propagation code that includes dynamic spiral arms as the main source of the CRs in the galaxy and showed how changing the CRs source distribution from the "standard" azimuthal symmetry to a dynamic spiral-arms source distribution solves several "standard" model anomalies.

Within the Iron group nuclei (Scandium through Nickel), there are a few CR isotopes that are known to decay through EC in the lab, and these isotopes can provide an interesting fingerprint on the process of reacceleration (e.g., Strong et al. 2007, and references therein). In Benyamin et al. (2017), we focused on investigating these isotopes and showed that, in principle, they can also be used to constrain CRs propagation models, though present day uncertainties in the nuclear cross sections are a limitation.

Our model considers ⁴⁴Ti, ⁴⁹V, ⁵¹Cr, ⁵³Mn, ⁵⁵Fe, ⁵⁷Co, and ⁵⁹Ni as EC isotopes² whose effective half-life can be governed by the electron attachment rate or radioactive decay. The timescale for stripping electrons by the ISM for these isotopes is roughly τ_stripping ≈ 5 × 10⁻³ Myr (Letaw et al. 1985). For the ⁴⁴Ti, ⁴⁹V, ⁵¹Cr, ⁵⁵Fe, and ⁵⁷Co, the decay timescale is on the order of several days to a few years, which is much smaller than τ_stripping. This implies that we can neglect the stripping process for these isotopes and assume that they decay immediately after they attach to an electron from the ISM. However, the EC half-life time of ⁵³Mn and ⁵⁹Ni is 3.7 Myr and 0.076 Myr, respectively, which is much longer than τ_stripping. Here, one can neglect the decay process and assume that these isotopes will become stripped of their electrons before being able to decay and can, therefore, be assumed to be stable. In Benyamin et al. (2017), we considered isotopes governed by the attachment timescale and empirically obtained the energy dependence of this process using the observation of ⁴⁹Ti/⁴⁹V and ⁵¹V/⁵¹Cr ratios.

When an EC isotope is created through fusion, it has relatively low energy within the star or subsequent supernova. This leads to a very high electron attachment cross section, such that it will decay to its daughter isotope if produced. Several observations detected hard X-ray lines from supernova remnants, such as Casssiopeia A and SN 1987A, which are associated with the decay of ⁴⁴Ti to ⁴⁴Sc (through EC with a half-life time of about 60 years in the lab), 67.9 KeV and 78.4 KeV, and the decay of ⁴⁴Sc to ⁴⁴Ca through β⁺ with a half-life time of about 4 hr in the lab), 1.157 MeV (OSSE, The et al. 1996; COMPTEL, Iyudin et al. 1994; BeppoSAX, Vink et al. 2001; and γ-rays, Grebenev et al. 2012). Since ⁴⁴Ti is an EC isotope with a half-life of 60 years, it implies two things. First, the ⁴⁴Ti should have been formed within this timescale preceding the supernova. Second, if this ⁴⁴Ti is to accelerate and become ⁴⁴Ti CRs, it should be accelerated through the SNR shocks, and get stripped, before being able to decay to its daughter isotope.³ Although there is no explicit acceleration timescale, there is one implicitly set by the decay timescale of ⁴⁴Ti. Namely, any acceleration process, which will strip the 44Ti as fast or much faster than its 60 year decay time, would give the same results.

⁴⁴Ti is produced through the ⁴⁰Ca(α, γ)⁴⁴Ti reaction (The et al. 1998), which requires a rich α particles supply, as is the case inside a core-collapse (Type II) supernova during the α-rich freeze-out phase. The et al. (1998) also showed the importance of secondary reactions, such as ⁴⁵V(p,γ)⁴⁶Cr, ⁴⁴Ti(α, p)⁴⁷V, and ⁴⁴Ti(α, γ)⁴⁸Cr, on the rate of production and the amount of ⁴⁴Ti in the supernova explosion, but due to the unstable nature of these isotopes, it is hard to measure the reactions in the lab and provide meaningful constraints.

Woosley & Hoffman (1991) constrained the production of ⁴⁴Ti in SN 1987A using the ⁴⁴Ca/⁵⁶Fe ratio of CRs that reach the solar system. Given that ⁴⁴Ca is mainly produced by the decay of ⁴⁴Ti, they concluded that the ⁴⁴Ti/⁵⁶Fe ratio at the source is about the same as the ⁴⁴Ca/⁵⁶Fe ratio in CRs that reach the solar system. In later work (Diehl et al. 2006, and references within), this result was recovered and extended for SN 1987A and Cas A.

The connection between ⁶⁰Fe (which decay through β⁻ with half-life time of about 2.6 million years) and γ-ray astronomy is extensively discussed in Diehl et al. (2011). The 1.173 MeV and 1.332 MeV lines associated with the decay modes of ⁶⁰Fe were detected by the space-based telescopes RHESSI (Smith 2004) and International Gamma-Ray Astrophysics Laboratory/SPectrometer for INTEGRAL (INTEGRAL/SPI; Harris et al. 2005), which give an instantaneous snapshot of the on-going nucleosynthesis of this isotope in the Milky Way (Prantzos 2010; Diehl 2013).

The production of ⁶⁰Fe is associated with core-collapse supernovae, which is expected to be produced in two locations before the supernovae explosion—the neon shell and at the base of the helium shell. In the neon shell, ²²Ne and ^25,26Mg are mixed into the superheated neon burning region, which allows free neutrons to be captured by the ⁵⁸Fe seed. The seed itself is previously produced by the s-process during the helium burning phase, and then by the intermediate radioactivity of ⁵⁹Fe, to form ⁶⁰Fe. At the base of the helium shell, ⁶⁰Fe is produced by mild r-process during explosive helium burning (Woosley & Weaver 1995).

Meyer & Clayton (2000) calculated the nucleosynthesis production of the short-lived radioactive isotopes in massive stars, type Ia supernova, and neutron star disruption. In massive stars, they predicted that the ratio between ⁶⁰Fe to ⁵⁶Fe should be around 3 × 10⁻⁵.

Recently, Binns et al. (2016) reported the observation of ⁶⁰Fe using the Advanced Composition Explorer-Cosmic Ray Isotope Spectrometer (ACE-CRIS) instrument in the energy range of 195 MeV to 500 MeV. They detected 15 ⁶⁰Fe nuclei, a total Fe number of 3.55 × 10⁵, and calculated the ⁶⁰Fe/⁵⁶Fe and ⁶⁰Fe/Fe ratios to be (4.6 ± 1.7) × 10⁻⁵ and (3.9 ± 1.4) × 10⁻⁵, respectively. Using the leaky-box model, they concluded that the ratios at the source are (7.5 ± 2.9) × 10⁻⁵ and (6.2 ± 2.4) × 10⁻⁵, respectively.

We begin in Section 2 by briefly describing the model we developed and our nominal model parameters. In Section 3, we carry out an analysis of the model to find the amount of primary ⁴⁴Ti and ⁶⁰Fe required to explain the observations obtained by CRIS, using a more modern 3D model than the leaky-box model, namely, the dynamic spiral-arms model. The implications of these results are then discussed in Section 4.

In Benyamin et al. (2014), we developed a fully three-dimensional numerical code describing the diffusion of CRs in the Milky Way. The code is presently the only model to consider dynamic spiral arms as the main source of the CR particles. With the model, Benyamin et al. (2014) recovered the Boron to Carbon (B/C) ratio and showed how the dynamics of the arms is important for understanding the behavior of nuclei secondary to primary ratios, which, below 1 GeV/nuc., increase with the energy.

In Benyamin et al. (2016), we upgraded the code to be faster and more accurate and showed how a spiral-arms model, unlike a disk-like model, can explain the discrepancy between the grammage required to explain the B/C ratio and the sub-Fe/Fe ratio. The optimal parameters of the model are summarized in Table 1. The two main parameters that change when moving from a "disk-like" model to a spiral-arms model are the diffusion coefficient and the halo size, which are smaller by about a factor of 10 from the "standard" parameters. This change in the derived diffusion coefficient and halo size elucidate that the canonical values for the parameters that describe the CR diffusion were obtained under a given set of model assumptions. Once we change the underlying assumptions, we should reanalyze the various parameters accordingly and not assume that their canonical values still hold.

Our code is different from present day simulations (such as galprop, Strong & Moskalenko 1998; and dragon, di Bernardo et al. 2010), which solve the diffusion partial differential equations (PDE) that we use in a Monte Carlo methodology. It allows for more flexibility in adding various physical aspects to the code (such as the spiral-arm advection), though at the price of reduced speed. The full details of the code and of the model can be found in Benyamin et al. (2014, 2016).

In Benyamin et al. (2017), we focused on the EC isotopes and carried out a full parameter analysis of the electron attachment cross-section formula using measurements of ⁴⁹Ti/⁴⁹V and ⁵¹V/⁵¹Cr ratios in CRs. An empirical relation was derived from these results and is here applied to ⁴⁴Ti, ⁴⁹V, ⁵¹Cr, ⁵⁵Fe, and ⁵⁷Co isotopes. This relation is ${\sigma }_{a}{(E,Z)=N({z}_{{\rm{h}}})\times {Z}^{4.5}\times (E/500\mathrm{MeV})}^{-1.8}$, with a normalization given by N_SA(z_h, τ_arm) = 7.98 × 10⁻⁵ mb ×(τ_arm/10 Myr)^−0.278 × (z_h/1 kpc)^0.236. The full details on the analysis can be found in Benyamin et al. (2017).

Many of the partial cross sections are poorly measured, and the values used are often the results of fits and extrapolations, giving rise to large uncertainties (Webber et al. 2003; Moskalenko 2011). The problem is aggravated below a few GeV/nuc., where the cross sections have larger energy dependences (Schwaller et al. 1979; Moskalenko & Mashnik 2003) and become more acute as Z increases (e.g., see Appendix II in Garcia-Munoz et al. 1987; Sisterson & Vincent 2006; Titarenko et al. 2008). The same can be said about the attachment cross section, whose measurements were carried out half a century ago (Wilson 1978; Crawford 1979). The best that the analysis of Letaw et al. (1985) and our extrapolation of the data (Benyamin et al. 2017) could provide is that there is at least a 20% uncertainty on the attachment cross sections. With that in mind, we use the model itself to constrain the cross sections, which leads to model parameters appearing in the cross-section fits.

For ⁵³Mn and ⁵⁹Ni, the half-life time for the EC decay is 3.7 Myr and 0.076 Myr, respectively, which is much longer than τ_stripping ≈ 5 × 10⁻³ Myr (Letaw et al. 1985). Consequently, this allows one to neglect the decay process and assume that these isotopes will become stripped of their electrons before decaying and remain stable. For these isotopes, it is irrelevant to apply the above formula, as their identity will not change.

3.1. Primary ⁴⁴Ti

We begin by implementing the attachment rate formula to the EC isotopes, specifically to ⁴⁴Ti. This allows us to predict the amount of ⁴⁴Ti and compare it to its daughter isotope, ⁴⁴Ca. The results are depicted in Figure 1. With our simulation, we find a ratio that is lower by about a factor of 2 from the observations. This can be explained by the fact that we did not include any ⁴⁴Ti in the initial composition—any additional ⁴⁴Ti that is initially present will increase the ⁴⁴Ti/⁴⁴Ca ratio. In order for the ⁴⁴Ti not to decay, it has to accelerate quickly by the SNR shocks to a sufficiently high energy and to be stripped of its electrons, compared with its decay half-life of 60 years. By fitting our model results to the observations, we can determine the minimal amount of ⁴⁴Ti in the initial composition that escapes the SNR obtained if the acceleration is fast. If some of the ⁴⁴Ti can decay, then the required ⁴⁴Ti at the source should be correspondingly higher.

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The optimal amount of primary ⁴⁴Ti required to recover ACE/CRIS's (Scott 2005) observations is ⁴⁴Ti/Fe = 0.40% ± 0.03%, which means that the ratio ⁴⁴Ti/⁵⁶Fe is = 0.44% ± 0.03%.

Scott (2005) also report the observations of the ⁴⁴Ca/⁵⁶Fe, which is about 0.5% ± 0.1%. According to Diehl et al. (2006) and Woosley & Hoffman (1991), the initial ⁴⁴Ti/⁵⁶Fe ratio should be about the same as the ⁴⁴Ca/⁵⁶Fe ratio measured in CRs that reach the solar system, which is in good agreement with our results.

3.2. Primary ⁶⁰Fe

The next step is to estimate the amount of ⁶⁰Fe in the initial composition. To do so, we carry out a similar analysis to the one described above for ⁴⁴Ti and estimate the initial amount of ⁶⁰Fe required to fit the recent CRIS results (Binns et al. 2016).

Figure 2 depicts the ⁶⁰Fe/⁵⁶Fe ratio in our model, with and without the primary ⁶⁰Fe. The optimal fit corresponds an to initial ⁶⁰Fe/⁵⁶Fe ratio of (4.5 ± 2) × 10⁻⁵. Our results agree with Meyer & Clayton (2000), who predict ⁶⁰Fe/⁵⁶Fe = 3 × 10⁻⁵, and with Binns et al. (2016)'s estimate of ⁶⁰Fe/⁵⁶Fe = (7.5 ± 2.9) × 10⁻⁵.⁴

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Given the parameters in Table 1, the diffusion length of the ⁶⁰Fe is only few hundreds pc's. which is about the distance that ⁶⁰Fe travels over its half-life time. Thus, the source of ⁶⁰Fe, i.e., the spiral arm, is relatively local. This is consistent with the detections of ⁶⁰Fe in deep-sea crusts in all major oceans of the world (Knie et al. 2004; Wallner et al. 2016), with detections of ⁶⁰Fe in lunar samples (Fimiani et al. 2016, 2014, 2012), and with Binns et al. (2016, p. 680)'s conclusion that, "Our distance from the source of this nuclide cannot greatly exceed the distance that CRs can diffuse over this timescale, which is ≤1 kpc."

It is generally accepted that a bulk of the galactic CRs (whether in number or energy) are accelerated in supernova remnants (e.g., Ackermann et al. 2013, and references therein), while the production of Iron group nuclei is through fusion in the last evolutionary phase of the progenitor stars or in the SN event itself. Indeed, ⁴⁴Ti is spectrally detected in SNRs Casssiopeia A and SNR 1987A (Iyudin et al. 1994; The et al. 1996; Vink et al. 2001; Grebenev et al. 2012). Since ⁴⁴Ti is produced through the reaction ⁴⁰Ca(α, γ)⁴⁴Ti (The et al. 1998), its detection in remnants is evidence of a rich α particle supply in the supernova explosion, which existed inside the core-collapse supernova during the α-rich freeze-out phase. However, if the acceleration process of the CR isotopes coming from the SNe is relatively long, then by the time the nuclei are accelerated, those nuclei that are unstable through EC should decay. A short acceleration process will, however, strip the nuclei of their electrons and allow them to be long-lived CRs.

There is, however, another source of ⁴⁴Ti in the CRs—CR nuclei are also created through spallation during their propagation in the galaxy. Since they are formed stripped, these EC unstable isotopes can survive as long as they remain at high energies. As a consequence, nuclei that decay through EC have a mean half-life time that depends strongly on the energy. This can be seen with the Niebur et al. (2000) measurements that show how the ⁴⁹Ti/⁴⁹V and ⁵¹V/⁵¹Cr ratios decrease with energy, as expected from the longer decay time of the EC isotopes (i.e., ⁴⁹V and ⁵¹Cr) at higher energies.

In our previous analyses (Benyamin et al. 2014, 2016), we showed how our propagation model can be used to describe the CR propagation by fitting the secondary to primary ratios in the Beryllium–Oxygen and Scandium–Nickel elements groups.

Jones et al. (2001) and Niebur et al. (2001) suggested that a standard diffusion model cannot explain the behavior of EC isotopes and cannot explain the decrease in the ratios of the daughter EC isotopes to the EC isotopes: for example, the ratios ⁴⁹Ti/⁴⁹V and ⁵¹V/⁵¹Cr. Jones et al. (2001) and Niebur et al. (2001) were in agreement that nominal diffusion models cannot give a strong enough decrease as the energy increases. Their solution for the decrease of ⁴⁹Ti/⁴⁹V and ⁵¹V/⁵¹Cr was to add an ad hoc assumption to their propagation model on the reacceleration of the nuclei on their way to Earth in order to fit these observations.

In our previous work on EC isotopes (Benyamin et al. 2017), we suggested another explanation for the decrease in the ratio of ⁴⁹Ti/⁴⁹V and ⁵¹V/⁵¹Cr. We showed that a energy-dependent cross section for the attachment of electrons from the ISM can explain the observed behavior, without having to add any additional primary CRs at the source. When the isotope attaches an electron, it subsequently decays through EC. The fitted functional form for the electron attachment cross section that we obtained in Benyamin et al. (2017) is ${\sigma }_{a}{(E,Z)=N({z}_{{\rm{h}}})\times {Z}^{4.5}\times (E/500\mathrm{MeV})}^{-1.8}$, with a normalization given by ${N}_{{SA}}({z}_{{\rm{h}}},{\tau }_{\mathrm{arm}})=7.98\,\times \,{10}^{-5}\,$ mb × (τ_arm/10 Myr)^−0.278 × (z_h/1 kpc)^0.236.

With the help of the empirical fit obtained in Benyamin et al. (2017), we simulated the ⁴⁴Ti/⁴⁴Ca ratio here and found that the ratio is lower than the observations by a factor of about 2. This can be explained away by adding ⁴⁴Ti to the list of injected isotopes, as is corroborated by the observations (Iyudin et al. 1994; The et al. 1996; Vink et al. 2001; Grebenev et al. 2012). We found out that the amount of ⁴⁴Ti/⁵⁶Fe required to be injected as part of the initial composition is 0.44% ± 0.03% in order to match the CRIS observations (Scott 2005). Our results agree with Diehl et al. (2006) and Woosley & Hoffman (1991), who predict it to be about the same as the ⁴⁴Ca/⁵⁶Fe ratio measured in CRs reaching the solar system, which is about 0.5% ± 0.1% (Scott 2005).

Recently, Binns et al. (2016) reported the detection and measurement of ⁶⁰Fe in CRs using the ACE-CRIS instrument. The ratios ⁶⁰Fe/⁵⁶Fe and ⁶⁰Fe/Fe found are (4.6 ± 1.7) × 10⁻⁵ and (3.9 ± 1.4) × 10⁻⁵, respectively. We found that we need to have an initial ⁶⁰Fe/⁵⁶Fe ratio of (4.5 ± 2) × 10⁻⁵ to the initial composition in order to fit the observed ⁶⁰Fe/⁵⁶Fe. Our results also agree with Meyer & Clayton (2000), who predict ⁶⁰Fe/⁵⁶Fe = 3 × 10⁻⁵, and with Binns et al. (2016), who estimated a ratio of ⁶⁰Fe/⁵⁶Fe = (7.5 ± 2.9) × 10⁻⁵.

By noting the 25% difference between the spiral-arm and disk models, it is evident that these are the type of uncertainties in the prediction from the Galactic parameters. Moreover, together with the similarly large uncertainties in the spallation cross section, it implies that the predictions have an uncertainty of at least 40%.

As a word of caution, one should emphasize that some of the EC radioactive isotopes could decay during the acceleration phase before escaping the SNR; thus, the amount of ⁴⁴Ti/⁵⁶Fe = 0.44% ± 0.03% and of ⁶⁰Fe/⁵⁶Fe = (4.5 ± 2) × 10⁻⁵ that is required to add to the initial composition of CRs is actually only a lower limit on the nucleosynthesis of these isotopes. On top of that, if one wants to calculate the ratios before the acceleration, one needs also to consider that there might be a difference in the acceleration efficiencies (Meyer et al. 1997); thus, the actual ratios will be ${({}^{44}\mathrm{Ti}{/}^{56}\mathrm{Fe})}_{\mathrm{CR},\mathrm{source}}={({}^{44}\mathrm{Ti}{/}^{56}\mathrm{Fe})}_{\mathrm{SN}}\times {{ \mathcal E }}_{{}^{44}\mathrm{Ti}}/{{ \mathcal E }}_{{}^{56}\mathrm{Fe}}$ and ${({}^{60}\mathrm{Fe}{/}^{56}\mathrm{Fe})}_{\mathrm{CR},\mathrm{source}}={({}^{60}\mathrm{Fe}{/}^{56}\mathrm{Fe})}_{\mathrm{SN}}\times {{ \mathcal E }}_{{}^{60}\mathrm{Fe}}/{{ \mathcal E }}_{{}^{56}\mathrm{Fe}}$, with ${ \mathcal E }$ denoting the acceleration efficiency.

The authors wish to thank Michael Paul for use valuable suggestions. N.J.S. gratefully acknowledges the support of the Israel Science Foundation (grant No. 1423/15) and the I-CORE Program of the Planning and Budgeting Committee and the Israel Science Foundation (center 1829/12).