ASTROPHYSICAL SHRAPNEL: DISCRIMINATING AMONG NEAR-EARTH STELLAR EXPLOSION SOURCES OF LIVE RADIOACTIVE ISOTOPES

SNe include both CCSNe and TNSNe; CCSNe are the results of massive stars completing Fe/Ni fusion in their cores and collapsing under the influence of gravity whereas TNSNe result from runaway nuclear fusion in a C-O white dwarf near its Chandrasekhar limit. Both types have similar explosive energies and modes of transporting ejecta. However, although known to be sources of stable iron isotopes, TNSNe are calculated to produce relatively little ⁶⁰Fe, namely ∼2.3 × 10⁻⁹ M_☉, according to the W7 Type Ia Model of Nomoto et al. (1984). ECSNe form a special subcategory of CCSNe with significantly different radioactive isotope yields. While the ⁶⁰Fe yields for CCSNe and ECSNe are similar (∼10⁻⁶–10⁻³ M_☉, Rauscher et al. 2002; Limongi & Chieffi 2006), their yields for other isotopes (e.g., ²⁶Al and ⁵³Mn) are vastly different (Wanajo et al. 2013). For the purposes of this paper, ECSNe will refer to SNe from 8–10 M_☉ stars, CCSNe will refer to SNe with progenitor masses > 10 M_☉, and SNe will refer to CCSNe, ECSNe, and TNSNe. It should be noted that the yields for ²⁴⁴Pu were calculated using the same method from Fields et al. (2005); the proportions of r-process elements are generally consistent to that found in metal-poor globular clusters and in the Sun. In this paper, however, the yields for ²⁴⁴Pu were based on the yields for ¹⁸²Hf from Rauscher et al. (2002) using the ratios given in Fields et al. (2005).

SNe can show large variations in their isotope yields. TNSN ⁶⁰Fe yields show variations over several orders of magnitude (∼10⁻¹⁸–10⁻⁷ M_☉) due to variations in the number and location of ignition points and the transition from deflagration to detonation (Seitenzahl et al. 2013).⁴ CCSNe/ECSNe yields are highly dependent on a number of factors including when different layers are mixed. This can be seen in the variations of yields from one mass to another (Rauscher et al. 2002). The yields within a given mass are also subject to uncertainties in nuclear reaction rates (3-α and ¹²C(α,γ)¹⁶O) which can lead to an almost order of magnitude shift in the production of ²⁶Al and ⁶⁰Fe (Tur et al. 2010). In Section 6, Figure 3, we show the calculated distances with uncertainties indicated by dashed lines for a factor of five variation in the ⁶⁰Fe yield for each CCSN/ECSN type.

Fiducial parameters for the explosions and the ISM are chosen as follows. We assume CCSNe and TNSNe deposit $E_{\rm CCSN \ \& \ TNSN} = 10^{51}$ erg into their ejecta, while ECSNe deposit E_ECSN = 10⁵⁰ erg (Wanajo et al. 2009). Because the Local Bubble shows evidence of multiple SN explosions, we will assume that if an SN were the source of the ⁶⁰Fe signal, it would be the most recent SN, meaning the SN occurred in an already depleted ISM, but not as depleted as the current density of the Local Bubble (i.e., n_{Average ISM} = 1.0 cm⁻³ > n_ISM > n_{Local Bubble} = 0.005 cm⁻³). Therefore, we estimated an SN would have occurred in an ISM of density, n_ISM = 0.1 cm⁻³, temperature, T = 8000 K, and sound speed, c_s = 10 km s⁻¹ (i.e., approximate values for the Local Cloud, Fields et al. 2008).

KNe are thought to result from Neutron Star–Neutron Star (NS–NS) or in some cases Neutron Star–Black Hole (NS-BH) mergers (Li & Paczyński 1998; Metzger et al. 2010; Tanvir et al. 2013). For this paper, we only consider the KN explosion's lower-energy, spherical/torical ejection and not its highly beamed gamma-ray burst (GRB) jet. The rapid decompression and ejection of neutron-rich NS matter makes these events a natural site for the r-process (Lattimer & Schramm 1974; Symbalisty & Schramm 1982). While KNe are less energetic than SNe (E_KN = 10⁴⁹ erg, Goriely et al. 2011), we will consider a possible KN source of the ⁶⁰Fe signal as occurring in the same ISM conditions as an SN. However, given the axisymmetric nature of NS–NS mergers, we will not apply the same constraints to KNe as SNe, but will instead evaluate KNe with respect to isotope yields and frequency.

While there has been some modeling of KN yields, none we are aware of have specifically stated a yield for ⁶⁰Fe. However, it is possible to determine an upper limit on the range for a KN. In Goriely et al. (2011), they list mass fractions for every atomic number up to ∼200 for a NS–NS merger with a total merger mass of 2.7 M_☉. If we assume all of the isotopes with A = 60 are in the form of ⁶⁰Fe (M_{ej, total} = 10⁻³–10⁻², $X_{{60}_{\rm Fe}} = 10^{-5}$) then the upper limit to the mass of ejecta in ⁶⁰Fe is 10⁻⁷ M_☉.

SAGBs (6.5–9 M_☉) are post-main-sequence stars that produce large amounts of dust (see, e.g., Ventura et al. 2012) and have strong winds (∼30 km s⁻¹) capable of carrying dust great distances. SAGBs produce 10⁻⁶–10⁻⁵ M_☉ of ⁶⁰Fe (Doherty et al. 2013), but are distinguishable from SNe in that they produce practically no ⁵³Mn (Wasserburg et al. 2006; Fimiani et al. 2014). We note that SAGB yields are subject to an uncertainty in the onset of the super-wind phase (Doherty et al. 2013); a delayed onset results in generally increased yields. The implication for distance is shown with dashed error bars on SAGB results in Section 6, Figure 3. In contrast to SNe, we do not expect an SAGB wind to affect the density of the Local Bubble appreciably, and we assume that an SAGB source for the ⁶⁰Fe signal would have occurred in an ISM like that found in the Local Bubble today (i.e., n_ISM = 0.005 cm⁻³, temperature, T = 10⁶ K, and sound speed, c_s = 100 km s⁻¹). Finally, we assume the initial velocity of the SAGB grains to be: v_{grain, 0} = 30 km s⁻¹.

Regardless of the source, any ⁶⁰Fe arriving in the solar system will need to be in the form of dust. Fields et al. (2008) showed that the solar wind will keep any gaseous isotopes from reaching the Earth (unless an SN is sufficiently close, but this will be used as a constraint later in Sections 3.1 and 6). We assume that the dust grains are spherical and select as our fiducial values for dust grains: density, ρ_grain = 3.5 g cm⁻³ (an average value for silicates), radius, a = 0.2 μm (this selection is based on discussion in Section 4.2), and voltage, ${\cal V} = 0.5 \ {\rm V}$. Departures from these values will be specifically stated.

For SNe in the adiabatic/energy-conserving phase, the shock follows a self-similar or Sedov–Taylor expansion profile. With the explosion at time t = 0, a shock is launched with radius, R_SN, at elapsed time, t, given by

$$\begin{equation} R_{\rm SN}= \xi _0 \left(\frac{E_{\rm SN}t^2}{\rho _{\rm ISM}} \right)^{1/5} \end{equation} \tag{ 2 }$$

for an SN explosion depositing energy E_SN into the ejecta, propagating into a local ISM of density ρ_ISM = m_un_ISM. The quantity ξ₀ is a dimensionless constant that is of the order of unity for γ = 5/3 using the derivation in Zel'dovich & Raizer (1967). Thus the time interval to traverse distance, D, is

$$\begin{equation} t_{\rm travel, SN} = \left(\frac{D}{\xi _{0}} \right)^{5/2} \left(\frac{\rho _{\rm ISM}}{E_{\rm SN}} \right)^{1/2} \end{equation} \tag{ 3 }$$

where we have assumed a uniform ISM density. While we know this is a crude approximation (see, e.g., Abt 2011), deviations from the uniform case would be encoded into the signal and could be determined if the signal is time-resolved (for examples of non-uniform media, see Book 1994). We use the uniform ISM case as a baseline.

The density versus radius profile for an SN signal may be approximated by a "saw-tooth" profile. As will be described in greater detail in Section 3.3, Section 3.4, and Appendix B, measurements in sediment open the possibility to making time-resolved fluence measurements. A saw-tooth pattern gives a better approximation of the more exact Sedov solution than a uniform shell profile. The saw-tooth pattern reaches its maximum density value at the outer edge of the shock, then decreases linearly to a fraction of the total shock radius, , where the density is zero from that point to the center of the remnant. See Appendix B for a comparison of the exact Sedov, saw-tooth, and uniform shell profiles.

Possible SNe will be constrained by an inner "kill" distance and an outer "fadeaway" distance. The kill distance is the range at which an SN can occur and create extinction-level disruptions to the Earth's biosphere. The primary mechanism for an SN to accomplish this is for ionizing radiation (i.e., gamma-rays, hard X-rays, and cosmic-rays) to destroy O₃ and N₂ in the atmosphere producing nitric oxides (NO_y) and leaving the biosphere vulnerable to UVB rays from the Sun (first described by Shklovskii & Sagan 1966, described in detail by Ruderman 1974, and updated by Ellis & Schramm 1995). This can be accomplished either by direct exposure (i.e., an X-ray flash from the SN) or by a "descreening" boost in cosmic-ray flux.⁶ Gehrels et al. (2003) calculated a kill distance R_kill ≲ 8 pc for the direct exposure case using the galactic gamma-ray background and SN rates, although, as pointed out by Melott & Thomas (2011), this is probably an underestimation based on more recent rate estimations. This work was expanded upon by Ejzak et al. (2007) and Thomas et al. (2008) to include X-rays and showed that for exposure durations up to 10⁸ s, the effects on the biosphere were the same and that the critical value for an extinction-level SN event was an energy fluence of 10⁸ erg cm⁻² (not to be confused with the description of fluence used throughout the rest of this paper). As noted in Melott & Thomas (2011), these direct exposure calculations use SN rate and photon and cosmic-ray emission information that are improving, but still subject to large uncertainties.

Here we calculate the kill distance using the descreening case described in Fields et al. (2008); it yields the same range as the direct exposure calculations, and is scalable to the energy of the SN, E_SN. The descreening kill distance is the range at which an SN can occur and its shock will penetrate the solar system to within 1 AU of the Sun. It is determined by setting the solar wind pressure, P_SW, equal to the pressure of the SN shock (see, e.g., Fields et al. 2008). In this case, the pressure from the SN has little effect on the Earth, but by pushing back the solar wind, the Earth is inside the SN remnant and now directly exposed to the SN cosmic-rays that would normally diffuse out over 10⁴ yr (Fujita et al. 2010) in addition to an increased galactic cosmic-ray background. In-turn, these destroy O₃ and N₂ in the atmosphere, just as in the direct exposure case, in addition to increased radionuclide deposition (Melott & Thomas 2011). Using our fiducial SN values, we find

$$\begin{equation} R_{\rm kill} = 10 \ {\rm pc} \ \left(\frac{E_{\rm SN}}{10^{51} \ {\rm erg}} \right)^{1/3} \left(\frac{2 \times 10^{-8} \ {\rm dyne \ cm^{-2}}}{P_{\rm SW}} \right)^{1/3} \end{equation} \tag{ 4 }$$

The fadeaway distance is the range at which the SN shock dissipates and slows to the sound speed of the ISM. Because of uncertainty in when SN dust decouples from the rest of the shock, the fadeaway distance is not an absolute limitation like the kill distance, but can serve as a guide to the likelihood of a progenitor. Using the derivation from Draine (2011, Equation (39.31)), we find

$$\begin{equation} R_{\rm fade} = 160 \ {\rm pc} \left(\!\frac{E_{\rm SN}}{10^{51} \ {\rm erg}} \!\right)^{0.32} \left(\!\frac{0.1 \ {\rm cm^{-3}}}{n_{\rm ISM}}\! \right)^{0.37} \left(\!\frac{10 \ {\rm km\,s^{-1}}}{c_{s}}\! \right)^{2/5} \end{equation} \tag{ 5 }$$

In the case of SAGBs, we assume the dust is ejected radially and that the distance traveled by SAGB dust is determined only by a drag force, F_drag (magnetic forces will be considered later in this section as a constraint). Using the description in Draine & Salpeter (1979), the drag force due to only collisional forces (in cgs units) is⁷

$$\begin{equation} F_{\rm drag} = 2 \pi a^{2} kT \left(\sum _{j} n_{j} [ G_{0}(s_{j}) ] \right) \end{equation} \tag{ 6 }$$

with

$$\begin{equation} G_{0}(s) \approx \frac{8s}{3 \sqrt{\pi }} \left(1+\frac{9 \pi }{64} s^{2} \right)^{1/2}, \; \; s_{j} \equiv \left(m_{j} v^{2}/2kT \right)^{1/2} \, \end{equation} \tag{ 7 }$$

where j is the respective species in the ISM (we consider only ionized H; He and free electrons will be neglected), m_j is the particle mass of that respective species, k is the Boltzmann constant, T is the temperature of the ISM, and v is the velocity of the particle relative to the medium. For small v (i.e., v_grain ≲ 100 km s⁻¹) the first term in G₀ will dominate, leaving $G_{0}(s) \approx 8s/(3 \sqrt{\pi })$. Making these simplifications, we find

$$\begin{equation} F_{\rm drag} = 2 \pi a^{2} kT n_{\rm ISM} v_{\rm grain} \left(\frac{8}{3 \sqrt{\pi }} \right) \left(\frac{m_{p}}{2kT} \right) ^{1/2} = m_{\rm grain} \ddot{R}_{\rm SAGB} \end{equation} \tag{ 8 }$$

where R_SAGB is the distance the dust grain has traveled from the SAGB, and $v_{\rm grain} \equiv \dot{R}_{\rm SAGB}$. Integrating twice and setting R_SAGB equal to the traverse distance from the progenitor to Earth, D, gives the transit interval:

$$\begin{equation} t_{\rm travel, SAGB} = -\zeta _{0} \left(\frac{a \rho _{\rm grain}}{c_{s} \rho _{\rm ISM}} \right) \ln \left(1 - \frac{1}{\zeta _{0}} \frac{c_{s} \rho _{\rm ISM}}{a \rho _{\rm grain}} \frac{D}{v_{\rm grain, 0}} \right) \end{equation} \tag{ 9 }$$

where ζ₀ is a dimensionless constant and of the order of unity for γ = 5/3, c_s is the sound speed in the ISM, and v_{grain, 0} is the initial velocity of the dust grain when it leaves the SAGB.

We approximate the density profile for an SAGB signal by a uniform shell or "top-hat" shape (we will use the "top-hat" profile to avoid confusion with the SN profile discussion). This corresponds to a uniform, steady wind. The top-hat pattern reaches its maximum density value at the leading edge of the signal, retains this value for the duration of the signal, and afterward the density returns to zero. The SAGB phase is characterized by thermal-pulsing of the star's envelope. Since the duration of each pulse (Δt_pulse ∼ 1 yr) and interval between pulses (Δt_inter ∼ 100 yr) are much shorter than the SAGB phase (Δt_SAGB ∼ 100 kyr ≫ Δt_inter > Δt_pulse) we assume that the amount of ejected material is approximately constant for the duration of the SAGB phase (see Siess 2010). Furthermore, we assume all parts of the signal experience the same forces from the SAGB to the Earth, so that the duration of the signal remains the same (i.e., Δt_{signal, SAGB} = Δt_SAGB = 100 kyr).

Because SAGB winds would not be as devastating to the Earth as an SN shock, we forego establishing an inner kill distance, but establish two outer distances: the drag stopping distance, R_drag, and the magnetic deflection distance, R_mag. The distance, R_drag, is the range of the SAGB dust grains' e-folding velocity, and the R_mag is the range at which deflection of the dust grain's trajectory by the ISM's magnetic field becomes significant. Using the derivations from Murray et al. (2004), we find

$$\begin{eqnarray} R_{\rm drag} &=& 93 \ {\rm kpc} \left(\frac{\rho _{\rm grain}}{3.5 \ {\rm g \ cm^{-3}}} \right) \left(\frac{a}{0.2 \ \mu {\rm m}} \right) \left(\frac{0.005 \ {\rm cm^{-3}}}{n_{\rm ISM}} \right)\nonumber\\ &&\times \left(\frac{10^{6} \ {\rm K}}{T} \right)^{1/2} \left(\frac{v_{\rm grain, 0}}{30 \ {\rm km\,s^{-1}}} \right) \end{eqnarray} \tag{ 10 }$$

$$\begin{eqnarray} R_{\rm mag} &=& 1 \ {\rm pc} \left(\frac{\rho _{\rm grain}}{3.5 \ {\rm g \ cm^{-3}}} \right) \left(\frac{0.5 \ {\rm V}}{\cal V} \right) \left(\frac{5 \ \mu {\rm G}}{B} \right)^{1/2}\nonumber\\ &&\times \left(\frac{v_{\rm grain, 0}}{30 \ {\rm km\,s^{-1}}} \right) \left(\frac{a}{0.2 \ \mu {\rm m}} \right)^{2} \end{eqnarray} \tag{ 11 }$$

The implications of these limits will be discussed in greater detail in Section 6.

To estimate the distance, D, to the explosion, we wish to invert Equation (1). When the transit time (the time for the shock to travel from the source to Earth) is negligible (t_travel ≪ τ_i), the procedure is straightforward, since the only distance dependence is the inverse square dilution of the ejecta, and so $D \propto 1/\sqrt{{\cal F}_{{\rm obs}, i}}$.⁸ This has been assumed in work to date. However, if D is sufficiently large, then via Equation (2), the distance-dependent transit time can become important and must be included in solving Equation (1); we have done this in all of our results.

Another effect occurs when the radioisotope signal is sampled sufficiently finely to resolve the time history of the deposition signal. This occurs when the signal width (the time from the arrival of the signal's leading edge to the departure of the signal's trailing edge) is larger than the sampling time resolution (Δt_signal > Δt_res). In this case, the total radioisotope signal, summed over all time bins, should be used in solving the distance via Equation (1); and as we show in Section 3.5 below, the width of Δt_signal for an SN probes independently the explosion distance. However, the available Knie et al. (2004) data has a time sampling of Δt_res ∼ 880 kyr, and shows no evidence for a signal that is extended in time. Thus we infer that the signal width Δt_signal ≲ Δt_res, and indeed we find Δt_signal ≲ 880 kyr for most of our possible progenitors. In addition, when solving for distance using the Knie results, we assumed the signal arrived halfway through the sample. Therefore, half of the sampling width is used as a median value rather than assuming the signal arrives right as the sampling window begins or just before it ends.

Although the time resolution of the deep-ocean ⁶⁰Fe crust measurements in Knie et al. (2004) data preclude resolution of the time structure of the radioisotope deposition, measurements in sediments can achieve much better time resolution, and so it is of interest to explore the time dependence of the explosion signal. Such work was pioneered by Ammosov et al. (1991) in the context of the ¹⁰Be anomalies ∼35 and 60 kyr ago in Antarctic ice cores (Raisbeck et al. 1987).

In developing a model for deposition, we examine a Sedov-Taylor profile for an SN shock (a similar examination could be done for the SAGB case if we had more detailed description of its signal width dependence), which implies an energy-conserving (adiabatic) evolution. This also means the shock will remain self-similar as it progresses and that the majority of the material is concentrated near the leading edge. Although the remnant density profile changes once the remnant transitions to the radiative/momentum-conserving phase, we have chosen to maintain the Sedov profile. We did this, firstly, because the profiles are similar in shape (the radiative profile is a thicker shell profile, see, e.g., Shu 1992, Figure 17.4). Secondly, because the dust will decouple from the gas at some point, either when the shock meets back pressure from encountering the solar wind or at the transition from the adiabatic to the radiative phase when the shock loses its internal radiation pressure (Draine 2011). The exact nature of this decoupling and resulting profile would require detailed calculations that are beyond the scope of this paper.

We assume that the explosion ejecta are well-mixed within the swept-up matter, so that the ejecta density profile follows that of the blast itself. As described in Appendix B, we approximate the Sedov density profile as a "saw-tooth" that drops linearly from a maximum behind the shock radius R_SN to zero at an inner radius r_in = (1 − )R_SN, with ≈ 1/6. We note that the leading edge of the blast from an event at distance D arrives at a time t_travel since the explosion which corresponds to geological time t_arr; this is given by D = R_SN(t_arr), whereas the trailing edge of the shell arrives at time t_dep given by D = (1 − )R_SN(t_dep). Thus we have t_dep = t_arr/(1 − )^5/2.

With these assumptions we can model the global-averaged flux time profile, $\mathbb {F}$. For radioisotope i, we have:

$$\begin{equation} \mathbb {F}_i(D,t) = \left(\!\frac{t}{t_{\rm arr}}\! \right)^{-11/5} \! \left[\! \frac{(t/t_{\rm arr})^{-2/5}-(t_{\rm dep}/t_{\rm arr})^{-2/5}}{1-(t_{\rm dep}/t_{\rm arr})^{-2/5}}\! \right] \! \mathbb {F}_i(D,t_{\rm arr}) \end{equation} \tag{ 12 }$$

as shown in Appendix B; note that here all times are geological and thus increase toward the past.⁹ This describes a cusp-shaped decline from an initial flux:

$$\begin{eqnarray} \mathbb {F}_i(D,t_{\rm arr}) &= & \frac{2{\cal F}_{1}}{5t_{\rm arr}} = \frac{3}{40\pi } \frac{\gamma +1}{\gamma -1} \frac{M_{{\rm ej}, i}/m_i}{D^2} \ \left(\!\frac{\xi _0^5 E_{\rm SN}}{m_p n_{\rm ISM} D^5} \!\right)^{1/2}\nonumber \\ \end{eqnarray} \tag{ 13 }$$

$$\begin{eqnarray} & = & 9.5 \times 10^5 \ {\rm atoms \ cm^{-2} \ kyr^{-1} } \nonumber \\ & & \ \times \ \left(\frac{0.1 \ \rm cm^{-3}}{n_{\rm ISM}} \right)^{1/2} \ \left(\frac{E_{\rm SN}}{10^{51} \ \rm erg} \right)^{1/2} \ \left(\frac{M_{{\rm ej}, i}}{3 \times 10^{-5} \, M_\odot } \right) \nonumber \\ & & \ \times \ \left(\frac{60}{A_{i}} \right) \ \left(\frac{100 \ \rm pc}{D} \right)^{9/2} \end{eqnarray} \tag{ 14 }$$

where the numerical values are m_i = 60m_u and the yield is appropriate for ⁶⁰Fe.

To test the profile in Equation (12), one can fit observed time-resolved data to this form, letting t_arr and t_dep, and $\mathbb {F}_i(D,t_{\rm arr})$ be free parameters. For the Sedov profile, the time endpoints should obey t_dep = t_arr/(1 − )^5/2, which provides a consistency check for the Sedov (adiabatic) approximation. Moreover, as we show in Section 3.5, the interval t_dep − t_arr provides an independent measure of the explosion distance.

If the radioisotope abundance is sampled over a time interval [t₁, t₂], then the fluence (without radioactive decays) will be the integral of the surface flux over this interval: ${\cal F}_i(t_1,t_2) = \int _{t_1}^{t_2} \mathbb {F}_i(t) \ dt$, where we have suppressed the dependence on time-independent parameters such as distance. If the observed time resolution Δt_res is small compared to t_arr and t_dep, then the fluence profile ${\cal F}_i(t-\Delta t_{\rm res}/2,t+\Delta t_{\rm res}/2) \approx \mathbb {F}_i(t) \ \Delta t_{\rm res}$ will recover the flux history.

So far we have calculated the observed fluence without the effect of decay. Since all the atoms were created at the same time, the observed fluence is reduced by a factor of $e^{-(t_{\rm arr}+t_{\rm travel})/\tau _i}$. The effects of uptake (Section 4.1) and dust depletion (Section 4.2) introduce further factors of U_i and f_i. We thus arrive at the observed fluence:

$$\begin{equation} {\cal F}_{{\rm obs}, i}(t_1,t_2) = U_i f_i e^{-(t_{\rm arr}+t_{\rm travel})/\tau _i} \int _{t_1}^{t_2} \mathbb {F}_i(t) \ dt . \end{equation} \tag{ 15 }$$

One can show that the total integrated fluence ${\cal F}_{{\rm obs}, i}(t_{\rm arr},t_{\rm dep})$ takes precisely the value in Equation (1). This reflects the number conservation (aside from decays) of the atoms in the SN ejecta. This also implies that, in a time-resolved measurement, the total fluence is conserved, which means that the area under a fluence versus time curve will be constant for fixed explosion parameters. This implies that fluence measurements of ⁶⁰Fe/Fe will show lower values when measured over fewer bins, and finer sampling will show higher fluence over more bins (see Figure 1).

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A time-resolved signal not only encodes information about the shape of the blast density profile, but also about the distance. The relation D = (1 − )R_SN(t_dep) also allows us to write t_dep = t_arr/(1 − )^5/2 and thus that

$$\begin{equation} \Delta t_{\rm signal}= t_{\rm dep}- t_{\rm arr}\equiv \alpha t_{\rm arr} \end{equation} \tag{ 16 }$$

where we define a dimensionless parameter, α, that relates the signal width in terms of the arrival time. For our profile, α = (1 − )^−5/2 − 1 ≈ 0.577. We see that the radioisotope width grows in proportion to the blast transit time to Earth, t_travel, which itself depends on distance. Thus a measurement of Δt_signal from a time resolved radioisotope signal gives an measure of the explosion distance. Within this Sedov model, D = R_SN(t_arr), and so we can solve for the distance based on "blast timing:"

$$\begin{eqnarray} D & = & \xi _0 \left(\frac{E_{\rm SN}\Delta t_{\rm signal}^2}{\alpha ^2 \rho } \right)^{1/5} \end{eqnarray} \tag{ 17 }$$

$$\begin{eqnarray} & = & 65 \ {\rm pc} \ \left(\frac{\Delta t_{\rm signal}}{100 \ \rm kyr} \right)^{2/5} \ \left(\frac{E_{\rm SN}}{10^{51} \ \rm erg} \right)^{1/5} \ \left(\frac{0.1 \ \rm cm^{-3}}{n_{\rm ISM}} \right)^{1/5}\qquad \end{eqnarray} \tag{ 18 }$$

This distance measure is independent of the "radioactivity distance" and its associated uncertainties, notably due to uptake, dust fraction, and radioisotope yields. Moreover, as characteristic for Sedov blast waves, the blast-timing distance in Equation (17) scales as small powers of the timescale, as well as the energy and density. This will weaken the uncertainties in distance estimate.

Having two independent distance estimates allows a consistency check for the model. Alternatively, if we adopt one of the distance estimates as the correct value, we can deduce the parameters in the other. For example, adopting the blast-timing distance we can use the observed fluence and solve for the product of radioisotope yield, uptake, and dust fraction: $M_{{\rm ej}, i} U_i f_i \propto D^2 \ {\cal F}_{{\rm obs}, i}$. Given a geophysical estimate of uptake, this allows for a measure of the yield and thus a direct probe of the nucleosynthesis output and thus the nature of the explosion (see Figure 1 for examples).

Uptake in the Fe-Mn crust involves a complex chemical process that incorporates material into the crust with a low accumulation rate ∼2 mm/Myr. Usual deep-ocean sediments, on the other hand, do not make such a geochemical selection, and have greater accumulation rates ∼3–4 mm/kyr (Feige et al. 2012). The Fe uptake factor was calculated by Knie et al. (2004) using the relative concentrations of Fe and Mn in water and the Fe-Mn crust and the uptake of Mn (4%), leading to an estimate for the Fe uptake, U_Fe = 0.6%. However, recent studies have suggested that U_Fe = 0.5–1 (Bishop & Egli 2011; Feige et al. 2012). Using the smaller estimate of U_Fe, Knie et al. (2004) calculated an SN distance of D ≈ 40 pc; a reasonable distance considering the Local Bubble is ∼200 pc in diameter in the Galactic plane extending 600 pc perpendicular to the plane (Fuchs et al. 2006) and superbubbles in the Large Magellanic Cloud are typically ∼100–200 pc in diameter (for a single round of star formation, Chu 2008). Changing the uptake factor has the immediate effect of changing the implied distance to the explosion. This can be roughly understood if we ignore the effect of the debris decays in transit, in which case the signal follows the inverse square law and we have $D \propto \sqrt{U_{i}/{\cal F}_{{\rm obs}, i}}$. The effect of decays en route softens this dependence somewhat.

If U_Fe is an order of magnitude larger, the implied distance increases by a factor ≳ 2. With a Fe-Mn crust uptake factor of U_Fe = 0.5–1, the implied distances are around D ∼ 200 pc. This seems an unlikely distance, given that the solar system is roughly in the center of the Local Bubble (see Berghöfer & Breitschwerdt 2002, Figure 2), and an SN would have had to occur outside the Local Bubble in order to produce the signal (assuming the progenitor is in the Galactic plane).

However, implicit in the Knie et al. (2004) calculation is the assumption that the dust fraction, f_Fe = 1. As we will show in Section 4.2, this is most likely not the case, and the combination of a higher uptake value (we chose U_Fe = U_Al = 0.5) with a smaller dust fraction (f_i ≪ 1) can still yield reasonable progenitor distances.

It was shown in Fields et al. (2008), that for an SN further than D ∼ 10 pc, the solar wind would keep the SN blast plasma outside of 1 AU, and thus the Earth will not find itself inside gas-phase SN debris. However, refractory SN ejecta will be condensed into dust grains. As discussed in Athanassiadou & Fields (2011), we expect these grains to be entrained in the SN blast as it reaches the heliosphere, but then decouple at the SN-solar wind shock and move essentially ballistically through the inner solar system. Once the dust decouples from the gas in the shock, it can travel great distances. At this point, both SNe and SAGBs behave the same, as they are subject to the same drag stopping distance, R_drag discussed in Section 3.2. This is more than sufficient to reach the Earth in spite of the solar wind, and indeed should carry dust grains beyond the SN remnant when it finally comes to rest. Thus, for the D > 10 pc events of interest, the amount of any radioisotope i that comes to Earth will be proportional to the fraction, f_i, of the isotope that reaches Earth via dust, as seen in Equations (1) and (15).

Determining f_i requires examining a number of factors (the results are summarized in Table 2).

• 1.  
  How much of the isotope condenses into dust at departure from source?
• 2.  
  How much of that dust survives the interstellar journey from the source to the solar system?
• 3.  
  How much of the remaining dust can filter through the heliopause and enter the solar system?
• 4.  
  How much of the filtered dust can overcome the solar wind/radiation pressure and reach the Earth's orbit?

In order to determine the isotope fraction that condenses into dust, we use recent observations of SN 1987A. Herschel observations in the far infrared and sub-millimeter wavelengths were modeled in Matsuura et al. (2011) with different elemental abundances and dust compositions. In both models studied, the synthesized Fe mass was nearly identical to the Fe condensed into dust. This suggests that after less than 30 yr (much less time than required to travel to a nearby solar system), practically all of the iron from the SN is in the form of dust. Furthermore, when comparing condensation temperatures (Spitzer & Jenkins 1975), one finds that T_{C, Al} = 1800 K > T_{C, Fe} = 1500 K, suggesting Al would condense into dust at the same time as Fe, if not sooner. Based on this reasoning, we assume 100% of Al and Fe condenses into dust for both SNe and SAGBs.

While refractory elements seem to condense rapidly after ejection, only the dust that survives transport to the solar system will reach the Earth. Dust leaving from SAGBs will be subject to shocks from neighboring star systems as well as sputtering from radiation and collisions with other dust grains. However, for the purposes of this paper, we will assume these affects are negligible compared to other filtering effects examined. Therefore, we will assume all of the dust from SAGBs is able to pass from the SAGB to the solar system (a more in-depth discussion of interstellar effects on dust grains is discussed in Murray et al. 2004).

Conversely, SN remnants are likely to be much harsher environments for dust, leading to predictions of very small survival probabilities for some dust species and thus for some radioisotopes. Dust formed from ejecta in a newborn SN remnant will encounter a reverse shock as the remnant transitions from the free expansion to the Sedov/adiabatic phase. The reverse shock propagates from the outer edge of the remnant back to the source and is generally stronger than the interface between the outer edge of the remnant and general ISM. The reverse shock causes large-scale sputtering/destruction of grains resulting in gas phase emission from previously refractory elements (e.g., see emission from Cassiopeia A, Rho et al. 2008). Silvia et al. (2010, 2012) studied this interaction and found grains ≲ 0.1 μm to be most affected; ∼1% of Al₂O₃ (corundum), ∼50% of FeS (troilite), and ∼100% of Fe (metallic iron) previously condensed into dust survives.

Once the dust reaches the solar system, it must pass through the heliosphere to reach the Earth. Linde & Gombosi (2000) suggested a cut-off grain size of 0.1–0.2 μm for filtering by the heliosphere for grains with speeds of 26 km s⁻¹ corresponding to the Sun's motion through the local ISM. This filtering is less severe for faster dust grains (Athanassiadou & Fields 2011), but for our larger SN distances we find slower speeds in Table 3. Since magnetohydrodynamic simulations by Slavin et al. (2010) showed penetration but strong deflection of 0.1 μm grains, we chose a minimum grain size of 0.2 μm for entering the solar system. For SN dust, this cut-off means that negligible amounts of Al₂O₃ and FeS grains will enter the solar system, while ∼10% of Fe grains will be large enough to pass through. For SAGB dust, we assume the Fe is in elemental Fe and silicate grains (distributed according to Pollack et al. 1994 with FeS assumed to be Fe); Al will be in Al₂O₃, but with a larger grain size (Hoppe & Zinner 2000). The Fe size distribution is assumed to be the same as for SN (Sterken et al. 2013), and silicate grains are assumed to follow the Mathis et al. (1977) distribution (dN/da∝a^−3.5) ranging from 0.5–350 nm (Weingartner & Draine 2001). This means ∼10% of Fe, ∼25% of silicates, and ∼100% of Al from SAGBs will enter the solar system.

Table 3. Predicted Parameters for Possible ⁶⁰Fe Signal Sources

Progenitor	Distance to Source, D,	Time en route, ttravel,	Signal Width, Δtsignal,	Arrival Speed, varr,
	pc	Myr	kyr	km s−1
6.5-M☉ SAGB	79$_{-8}^{+13}$	2.8	100	25
7.0-M☉ SAGB	66$_{-7}^{+11}$	2.3	100	26
7.5-M☉ SAGB	73$_{-8}^{+12}$	2.6	100	25
8.0-M☉ SAGB	97$_{-9}^{+14}$	3.5	100	24
8.5-M☉ SAGB	110$_{-10}^{+15}$	4.2	100	23
9.0-M☉ SAGB	110$_{-10}^{+15}$	4.1	100	23
15-M☉ CCSN	94$_{-12}^{+19}$	0.44	250	84
19-M☉ CCSN	120$_{-13}^{+18}$	0.74	430	61
20-M☉ CCSN	71$_{-9}^{+15}$	0.22	130	130
21-M☉ CCSN	59$_{-8}^{+13}$	0.14	80	170
25-M☉ CCSN	130$_{-13}^{+17}$	0.98	570	52
8-10-M☉ ECSN	67$_{-8}^{+12}$	0.61	351	43

Notes. Errors are only for variances in the Knie et al. (2004) decay-corrected fluence value and do not include variations in nuclear reaction rates (SNe) or delayed super-wind phase (SAGBs). These parameters are calculated with the Fe uptake factor, U_Fe = 0.5.

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Lastly, the dust grain must overcome the Sun's radiation pressure once it is in the solar system. For this, we consider the parameter β (Burns et al. 1979) that characterizes the ratio of the Sun's radiation force, F_r, to the gravitational force, F_g:

$$\begin{equation} \beta \equiv \frac{F_{r}}{F_{g}}= C_{\rm r}Q_{\rm pr}\frac{3}{4a\rho _{\rm grain}} \end{equation} \tag{ 19 }$$

where C_r is 7.6 × 10⁻⁵ g cm⁻² and Q_pr is the efficiency of the radiation on the grain (we will assume Q_pr ∼ 1 for the size of grains we are interested in, Gustafson 1994). From Sterken et al. (2013), only dust grains with β ≲ 1.3 will reach Earth's orbit; based on the densities of the minerals considered, if the grain can enter the solar system, it will be able to reach Earth's orbit.

Combining each of these factors, we find for SNe: f_{Fe, SN} ≈ 0.01 and f_{Al, SN} is negligible. For SAGBs: f_{Fe, SAGB} ≈ 0.2 and f_{Al, SAGB} ≈ 1. In spite of the number of considerations in determining these quantities, there are still others that could be included, namely a velocity dependence on the filtering by the heliopause. We would expect dust grains with a sufficiently high velocity (i.e., v_grain > v_{esc, ☉}) to ignore size filtering limitations, but including these effects will be left for a future work.

The primary data value for our analysis is the decay-corrected ⁶⁰Fe fluence measured by Knie et al. (2004) in a deep-ocean Fe-Mn crust. They found an isotopic ratio of ${{}^{60}{\rm Fe}}/{\rm Fe} = 1.9 \times 10^{-15}$ within the crust; this corresponds to a decay-corrected fluence of ${\cal F}_{{\rm arr},60} = (2.9 \pm 1.0) \times 10^{6} \ \rm atoms\,cm^{-2}$. This may be used to determine the distance from the progenitor. At the time of the original measurements, the half-life of ⁶⁰Fe was estimated to be 1.49 Myr and that of ¹⁰Be was estimated to be 1.51 Myr, resulting in an arrival time, t_arr = 2.8 Myr ago. Since then, the half-lives have been refined: current best estimates being $\tau _{1/2, {}^{60}{\rm Fe}}$ = 2.62 Myr and $\tau _{1/2, {}^{10}{\rm Be}} = 1.387$ Myr, and this places the signal arrival at 2.2 Myr ago. To update the Knie ⁶⁰Fe fluence, we use ratios to convert the previous results to the updated values that are similar in method to those employed by Bishop & Egli (2011) and Feige et al. (2012): ${\cal F}_{\rm 60, update}/{\cal F}_{\rm 60, previous} = e^{-t_{\rm 60, update}/\tau _{\rm 60, update}}/e^{-t_{\rm 60, previous}/\tau _{\rm 60, previous}}$, which gives the following updated, decay-corrected fluence in the crust.

$$\begin{equation} {\cal F}_{\rm arr, 60 (updated)} = (1.41 \pm 0.49) \times 10^{6} \ \rm atoms\,cm^{-2} \end{equation} \tag{ 20 }$$

The ⁶⁰Fe measurement in the crust has been verified by Fitoussi et al. (2008), but within this same work, no comparable ⁶⁰Fe signal was detected in a sea sediment sample. Fitoussi et al. (2008) suggested several reasons for the non-detection in the sediment, including differences in uptake and divergences in the sediment from the global background. In addition, we note that the fluence calculation assumes an even distribution of dust over the Earth's surface. However, the Earth's wind patterns are not uniform, nor is Earth's precessional axis necessarily orthogonal to the progenitor's position. Consider, for example, a spherical dust grain of radius 0.2 μm falling at terminal velocity (∼0.1 m s⁻¹) through a 1500 m-thick jet stream flowing horizontally at 100 km hr⁻¹ with a density of 4 × 10⁻⁴ g cm⁻³ (the assumption of falling at terminal velocity should be valid as the Earth's atmosphere will have dissipated most of the dust grain's remaining interstellar kinetic energy). As the dust grain falls, the pressure from the jet stream will quickly accelerate the grain horizontally to the same velocity and push the grain ∼300 km before it falls out of the jet stream. In view of the non-uniformity of the jet stream's flow as well as other terrestrial winds, anisotropies in the observed fluences are expected. Furthermore, one should also consider the source's orientation to the Earth's precessional axis; the Fe-Mn crust used by Knie et al. (2004) is from 9°18' N, 146°03' W (∼1, 000 mi/1,600 km SE of Hawaii), and the sediment used by Fitoussi et al. (2008) is from 66°565 N, 6°270 W (∼250 mi/400 km NW of Iceland). The crust sample's location relative to the equator would make it more likely to receive a signal over a range of arrival angles while the northern hemisphere could be partially shielded from a more southerly progenitor. Rather than the Fe-Mn crust signal being due to a misinterpretation of the global background, the absence of a sediment signal could be due to the geometry of the source's position. If this is the case, a sediment sample from the southern hemisphere (e.g., ELT49-53, 38°587 S, 103°431 E and ELT45-21, 37°516 S, 100°017 E used by Feige et al. 2013) should have an ⁶⁰Fe signal.

In addition to sea sediment and Fe-Mn crusts, lunar surface (regolith) samples can also be used to search for a nearby progenitor signal. The lunar surface is not affected by wind or water erosion, but, as pointed out by Feige et al. (2013), the sedimentation rate is low (precluding the possibility of time-resolved measurements) and regular impacts by a range of impactors (Langevin & Arnold 1977), continually churn up the regolith, mixing different levels. Lunar samples would be better suited to providing a "first hint" of a signature (Feige et al. 2013). Apollo core samples were analyzed by Cook et al. (2009), Fimiani et al. (2012), and Fimiani et al. (2014); in particular, these authors found both the Apollo 12 sample 12025 and Apollo 15 sample 15008 to have an ⁶⁰Fe signal above the background. Nishiizumi et al. (1979) and Nishiizumi et al. (1990) found that the Apollo 12 and 15 cores, respectively, showed little to no large-scale mixing just prior to, during, and/or since the potential arrival of the signal, meaning no large impactor could have ejected part of the regolith thus diluting the signal. However, as we show in the next section, another issue arises with the dust's arrival at the Moon's surface that can dilute the signature.

As noted above, there are putative detections of a non-meteoric ⁶⁰Fe lunar anomaly, which seem to verify the presence of the deep-ocean signal; an amazing confirmation. However, having argued that the ⁶⁰Fe will arrive in the form of high-velocity dust grains, we now consider the implications for the deposition onto the lunar surface.

Cintala (1992) made a detailed study of impacts on the lunar regolith and found semi-empirical fits to the volume of vapor produced as a function of impactor size and velocity and of the target composition. It was found that impactor velocity is the dominant factor and that, for v_grain > 100 km s⁻¹, the volume of target material that is vaporized is ∼10–100 times the volume of the impactor itself. More recently, Cremonese et al. (2013) showed that micrometeor impacts can be a non-negligible source of the lunar vapor atmosphere. They use the Cintala (1992) model and find that the contribution may be 8% of the photo-stimulated desorption at the subsolar point, becoming similar in the dawn and dusk regions and dominant on the night side. Moreover, Collette et al. (2014) did laboratory experiments to simulate micrometeorite impacts, studying the neutral gas created as a result. They find that the number of neutrals produced per unit impactor mass scales as ${\sim } v_{\rm grain}^{2.4}$, and they conclude that complete vaporization is expected for speeds exceeding 20 km s⁻¹.

With these results in mind, we now consider the conditions surrounding the arrival of the dust signal in question at the lunar surface. After entering the solar system, the dust grains continue to the Earth/Moon at essentially the same speed. However, whereas the Earth's atmosphere slows the arriving dust grains prior to reaching the surface, the Moon's tenuous atmosphere has practically no influence, and the dust grains' velocities are unchanged before arrival at the lunar surface. The dust grains are estimated to be ∼0.2 μm in size, and moving at ∼20–100 km s⁻¹ depending on the progenitor's distance. Thus the grains behave as "micrometeorites" moving at very high speeds similar to those examined above.

Consider a silicate dust grain (ρ_grain ∼ 3.5 g cm⁻³) impacting the lunar surface (ρ_regolith ∼ 1.6 g cm⁻³) at v_grain ∼ 20 km s⁻¹. The grain arrives with kinetic energy $E_{\rm grain} = m_{\rm grain}v_{\rm grain}^2/2 \sim 0.23 \ \rm erg$, where m = 4πρ_graina³/3 is the mass of a spherical grain of radius a. The dust grain will penetrate the regolith to a depth comparable to its diameter and will vaporize some of the surrounding material; we will assume V_vapor = 10 V_grain⇒m_vapor ≈ 4.6 m_grain. Given the grain's high speed and shallow penetration, the vaporization will happen quickly (i.e., very little expansion occurs before the entire mass is vaporized). Moreover, since the initial density of the vaporized regolith is much greater than the density of the Moon's atmosphere, the gas will behave as if it is expanding isentropically into a vacuum. The grain's kinetic energy will go into vaporizing the grain and regolith and into the thermal and kinetic energy of the resulting gas. To determine the vaporization energy, the standard enthalpy of formation for the lunar regolith is ∼1.5 × 10¹¹ erg g⁻¹ = (3.9 km s⁻¹)². This is an approximate value for both of the lunar regolith's main constituents, silica, SiO₂, and aluminum oxide, Al₂O₃, (Nava & Philpotts 1973), and includes both the vaporization and dissociation energies for the molecules. Therefore, the total energy consumed in vaporization is 0.1 erg, leaving 0.13 erg for the thermal and kinetic energy, E_vapor, of the gas.

As the gas expands, the thermal portion vanishes asymptotically, with all the energy becoming kinetic. Thus, after this cooling, the asymptotic expansion speed of the vaporized material is:

$$\begin{equation} v_{\infty } = \sqrt{\frac{2E_{\rm vapor}}{m_{\rm vapor} + m_{\rm grain}}} \approx 6 \ {\rm km\,s^{-1}} \end{equation} \tag{ 21 }$$

[For further discussion, see Zel'dovich & Raizer (1967, p. 101–104, 844–846)].

The vapor speed is much larger than the lunar escape velocity, v_{esc, Moon} = 2.4 km s⁻¹. This suggests that much of the vaporized material, including the dust impactor with its ⁶⁰Fe material, would escape from the Moon. This would imply that the Moon has an uptake factor U_Moon ≪ 1. Thus, we should not be surprised that the lunar results for ⁶⁰Fe are lower than expected naively from the terrestrial Fe-Mn crust results. While lunar samples confirm the signal found in the Fe-Mn crust, they are less suitable for determining the fluence given the difficulties in determining U_Moon.

Several searches for live ²⁴⁴Pu have been performed, beginning with Wallner et al. (2000) looking at Fe-Mn nodules. Studies of top layer sea sediment by Paul et al. (2001); Paul et al. (2003), and Paul et al. (2007) have shown there is a very low background in ²⁴⁴Pu, making ²⁴⁴Pu an excellent candidate to confirm an ⁶⁰Fe signal from an extra-solar source (presumably from a CCSN). Wallner et al. (2000, 2004) reported the detection of a single ²⁴⁴Pu atom in the same Fe-Mn crust sample used by Knie et al. (1999) and Knie et al. (2004) covering the entire time interval of 1–14 Myr. Separately, Raisbeck et al. (2007) looked in sea sediment for a ²⁴⁴Pu signal, but did not find any evidence for a signal. It should be noted, however, that the Raisbeck study was using the previous arrival time (2.8 Myr ago) for his search. The samples were dated using magnetic polarization analysis and did not cover a large enough time interval to include the appropriate dating interval using the new value for the ¹⁰Be lifetime (Meynadier et al. 1994).

Feige et al. (2013) reported on searches for ¹⁰Be and ²⁶Al using ∼3 kyr time intervals in samples from sea sediments ELT 49-53 and ELT 45-21. In the case of ²⁶Al, the measurements showed only variations consistent with fluctuations around the background level, and found no evidence for an extra-solar signal. The paper also reported that ⁵³Mn measurements are planned.

Figure 3 shows the calculated distances for our examined CCSNe and ECSN; they range from ∼60–130 pc. All CCSNe from our set lie outside of the kill distance and within the fadeaway distance for both their average fluence values and errors. Similarly, the ECSN lies outside the kill distance and within the fadeaway distance (the ECSN kill and fadeaway distances are shorter due to its lower explosive energy). The ECSN upper error is outside the fadeaway distance, but because SN dust can still travel great distances after decoupling, this is not an absolute limitation. Based on these distances, either a CCSN or an ECSN could have produced the measured ⁶⁰Fe signal.

TNSN produce so little ⁶⁰Fe that it would require a TNSN to have been at a distance of ∼0.6 pc in order to produce the signal measured by Knie et al. (2004). This is an implausibly short distance, and any uncertainty in the fluence measurement would not change this determination. At that range, the TNSN would have killed nearly all life on Earth, so we can exclude a TNSN as the source of the ⁶⁰Fe signal (in this case, the descreening kill distance for a TNSN is ∼10 pc and the ionizing radiation kill distance from 10⁴⁸ erg of γ-rays is ∼20 pc, Smith et al. 2004). Adopting the largest yield ($M_{\rm ej,{}^{60}{\rm Fe}}\sim 10^{-7} \, M_\odot$) from Seitenzahl et al. (2013) extends the distance to ∼6 pc, which is still inside the kill radius and does not change this conclusion.

Our calculations give a possible KN distance of ∼5 pc. Of the little that is known observationally or even theoretically about KNe, we are unaware of any estimates of their ionizing radiation output. In addition, the strength and shape of the shock from ejected material is highly dependent on the orientation of the merger. Thus, we are unable to estimate the corresponding kill distance either by direct exposure or descreening. The ejecta from KNe are certainly energetic (explosive velocities ∼0.3 c, Goriely et al. 2011), and one might imagine decompressing neutron star matter initially emitting in the UV or at shorter wavelengths. However, the observed radiation for the KN candidate associated with GRB 130603B is very red at times ≳ 8 hr (Berger et al. 2013). Moreover, while the KN shock and radiation is expected to be much more isotropic than the GRB, more study of the geometry of the resulting blast is needed to determine a definitive kill distance like that used for TNSN. Consequently, a biohazard argument cannot rule out a KN explosion as the source of the ⁶⁰Fe anomaly.

However, a much better discriminator for a KN source would be the ²⁴⁴Pu/⁶⁰Fe ratio. The single ²⁴⁴Pu atom detected by Wallner et al. (2000, 2004) yields a surface fluence of 3  ×  10⁴ atoms cm⁻² for the period 1–14 Myr ago. Looking at the yields from Goriely et al. (2011) again, we can infer the yield for A = 244 should be at least on the order of the yield for A = 60 (i.e., $({{}^{244}{\rm Pu}}/{{}^{60}{\rm Fe}})_{\rm KN} \,{\ge}\, 1$).¹⁰ Based on this assumption and the surface fluence for ⁶⁰Fe during the signal passing (1.41  ×  10⁶ atoms cm⁻²/0.5  =  3  ×  10⁶ atoms cm⁻²), then

$$\begin{equation*} ({{}^{244}{\rm Pu}}/{{}^{60}{\rm Fe}})_{\rm measured} \approx 10^{-2} \ll 1 \lesssim ({{}^{244}{\rm Pu}}/{{}^{60}{\rm Fe}})_{\rm KN \ predicted} \end{equation*}$$

even though ²⁴⁴Pu was measured over 10 times the time period as ⁶⁰Fe (Note: this assumes the dust fraction for Pu is the same as Fe, f_Pu ∼ f_Fe).

Additionally, KN occur infrequently (∼10 Myr⁻¹ galaxy⁻¹, Goriely et al. 2011) compared to CCSN & ECSN (∼30 kyr⁻¹ galaxy⁻¹).¹¹ If we approximate the Milky Way as a thin cylinder of radius 10 kpc and thickness 200 pc, the rates (Γ) of a KN occurring within ∼5 pc or a CCSN/ECSN occurring within ∼75 pc of the Earth are:

$$\begin{equation*} \Gamma _{\rm nearby \ source} = \Gamma _{\rm galaxy} \frac{V_{\rm nearby \ source}}{V_{\rm galaxy}} \end{equation*}$$

$$\begin{equation*} \Gamma _{\rm nearby \ KN} = \left(\frac{1}{10^{7}{\rm \ Myr}} \right) \left(\frac{D}{5 {\rm \ pc}} \right)^3 \end{equation*}$$

$$\begin{equation*} \Gamma _{\rm nearby \ SN} = \left(\frac{1}{1{\rm \ Myr}} \right) \left(\frac{D}{75 {\rm \ pc}} \right)^3 \end{equation*}$$

After inverting these quantities, we can expect a nearby SN every ∼1 Myr compared to a nearby KN every ∼10⁷ Myr ≫ 1/H₀ (the Hubble time). This makes a KN an unlikely source for the ⁶⁰Fe signal. However, this result should be revisited as specific yields for ⁶⁰Fe become available and especially if a signal from strong r-process isotopes is detected (e.g., ¹⁴⁶Sm, ¹⁸²Hf, and ²⁴⁴Pu).

Figure 3 plots three of our six examined SAGBs (all are listed in Table 3). Their distances range ∼60–110 pc; similar to those of CCSNe. With errors, all SAGBs lie well within the distance for dust stopping due to drag (∼90 kpc) but well outside the magnetic deflection distance (∼1 pc). While it is tempting to rule out SAGBs as a source under the assumption that any dust would be quickly deflected, we have decided not to rule out SAGBs (see, e.g., Frisch 1995; Cox & Helenius 2003; Florinski et al. 2004; Frisch et al. 2012) since there is uncertainty in the strength, direction, and uniformity of the Local Bubble's magnetic field. Depending on the nature of the Local Bubble's magnetic field, charged dust particles could travel with very little deflection. Instead, we will be examining an alternate search in a future work.

In Figure 4, we plot ²⁶Al predictions for various progenitors, and the expected background in the accelerator mass spectrometry (AMS) data from Feige et al. (2013) using the same 3-kyr sampling intervals used in this experiment. Because f_{Al, SN} ≈ 0, we do not expect any signal to be present if the source was an SN. The calculated signal from a 15-M_☉ CCSN with f_{Al, SN} = 1 is plotted simply as an example if the dust fraction was significantly higher. Additionally, while we would expect some Al from SAGBs to reach Earth, it would not be visible above the variations in the ²⁶Al background.

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In anticipation of AMS ⁵³Mn measurements mentioned by Feige et al. (2013), in Figure 5 we plot predictions for ⁵³Mn based on the distance determined by the ⁶⁰Fe fluence. Since the survival and grain size for Mn from an SN has not been described to our knowledge, we plotted a range of SN progenitors (since SAGBs are not expected to produce ⁵³Mn) and dust fractions, using the largest possible signal source (21-M_☉ CCSN), a mid-range source (15-M_☉ CCSN), and the lowest source (ECSN). We varied the dust fraction from an order of magnitude above to an order of magnitude below f_{SN, Fe}. As can be seen for the 15- and 21-M_☉ CCSN with f_{SN, Mn} ≳ f_{SN, Fe}, a signal should be readily detectable the given the AMS detection threshold of ∼10^{−15 53}Mn/⁵⁵Mn (Poutivtsev et al. 2010). However, for the ECSN and most CCSNe with f_{SN, Mn} < f_{SN, Fe} (even a 21-M_☉ case could be difficult to detect depending on the fluctuations in the ⁵³Mn/⁵⁵Mn background), it should be improbable for an SN progenitor to be detected with ⁵³Mn.

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