In this response, I leave the reviewer comments as written and insertmy responses in bold italics
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Reviewer #1: I have reviewed the submission `Nuclear Criticality as a Contributor to Gamma-Ray Burst Events' by R. Hayes. In this paper, the author puts forward the idea that fissile material could accumulate in an astrophysical environment, such as following the production and ejection of r-process elements in a core-collapse supernovae. The author suggests that if the right conditions are reached in this accumulation for a runaway fission event (`nuclear criticality'), then the burst of high energy emission could result, which it is suggested could contribute to the population of observed gamma-ray bursts (GRBs). This is a correct assessment of the work.
The main idea of the paper, namely that nuclear criticality could be regularly achieved in astrophysical environments, is highly speculative and its plausibility is not well quantified. I have included further qualification on plausibility but quantitative frequency is not offered outside of postulating measured fast rise exponential decay type galactic events which could be attributed to criticality GRBemissions placing only an upper bound on frequency estimates. Furthermore, basic energetic arguments show that such fission-powered GRBs could only contribute to events within our galaxy (see below), despite overwhelming evidence that most GRBs are cosmological. I have added text clarifying that the galactic origin is more consistent with current measurements. Despite these and other objections, it cannot be entirely ruled out that a small fraction of GRBs could originate from such events, although to prove that the requisite conditions are indeed achieved at a reasonable rate would require work far beyond that presented here. Agreed, this is intended to be a paper introducing the potential for such events and not to fully characterize the various parametric dependencies The paper also highlights physics that could in principle be at work in other astrophysical environments, such as accretion onto neutron stars - with possible relevance e.g. to what are normally-interpreted as magnetically-powered flares on Galactic magnetars. Spot on, the paper demonstrates that some of these events could have a fission related component.
Despite the deep reservations I hold about the likely relevance of the proposed ideas to actual astrophysics events, the paper is original and should stimulate further thought and future work into whether such a process could indeed be relevant in an astrophysical setting.Correct, this is the intended purpose of the original paper with this revision attempting to address the pertinent issues raised by the referee.In other words, although the paper would be strengthened greatly by a more quantitative argument, it still serves as useful 'ideas' paper to be developed later by others. Agreed, I have tried to include more discussion on potential relevance with some quantitative additions but the reviewer is correct, this paper is limited to a novel mechanism which very well could prove of little useif it is never backed by predicted measurement evidence but on the flip side could very well be the fundamental basis of some substantially interesting physical phenomenon.
Below, I provide several broad issues that should be addressed before I can recommend the paper for publication.
*** It is understood that the author is not an expert in astrophysics phenomenology, so a detailed comparison to the known or expected conditions in astrophysical environments may not necessarily be warranted. AgreedNevertheless, when reading the paper as someone who might wish to make more quantitative comparisons, I was left with several unanswered questions, such as:
- What conditions on density/temperature/elemental abundances are required for criticality to be maintained?I have expanded the section on the fundamentals of criticality to give the basic requirements and to clarify that these can take wide variations, over many orders of magnitude with the more sensitive parameters being total fissile mass and for moderated systems the fissile to moderator ratio with only minimum density being set by the neutron half-life. I have added equation 1 which to first order can approximate the basic conditions expected on density, temperature and pressure, at least as well as any closed form equation can do. Sophisticated modeling may very well be necessary for accretion disks and torroidal shapes along with extreme variations of temperature and pressure (i.e., the equation is for a homogenous, unreflected, spherical, moderated mass where neutron lifetime is negligible).
- How likely is 'feedback' - namely, once runaway occurs, can the system respond sufficiently rapidly (i.e. 'explode') to terminate the runaway before all of the potential nuclear energy is released? I believe this comment is now addressed by adding discussion on the difference between delayed critical (as in a power reactor) and prompt critical as done in weapons systems and the thermal response times of each. Short answer is yes, the system would be expected to disassemble at least temporarily before a majority of the potential nuclear energy is released per event.
- Are the conditions for criticality consistent with what is expected in terms of the known yield of r-process elements? For instance, there is evidence from metal-poor stars (e.g. Sneden et al. 2003) that the r-process is produced with fairly universal abundance distribution; is the ratio of fissioning nuclei to 'poison' nuclei (or moderators) given this distribution sufficient for a runaway at any density/temperature? Excellent question, the text clarifies that a homogenous mix of the fissile/transuranic elements being produced/ejected in the standard r-process is not adequate to sustain criticality. Rather, the potential ejecta from neutron star mergers certainly is. Similarly, with r-process evolution, critical distributions could be obtainable based on differential production of actinides being proportional to neutron flux rates so that if the peak neutron flux creating the majority of the actinides such that the result has an hydrogen to actinide ratio ~1e3 would then provide conditions favorable to criticality. Isotopic fractionation of this detail does not appear to be available in literature models of which I could locate leaving it as speculative although in my opinion reasonable as an attainable physical effect.
- How does an admixture of hydrogen (as is likely to also be present in the ejecta from most core collapse supernovae) affect the requisite conditions? I have added that this will substantially lower the requisite critical mass once the fissile to hydrogen atom ratio falls into the appropriate range, this does thermalize the system which changes the resultant prompt gamma spectrum and the subsequent fission product decay gamma spectrum.
*** Although the author discusses GRBs as a potential consequence of runaway fission events, he does not discuss how this is consistent with our current understanding of the origin of GRBs. For instance, it is now well established that most long-duration GRBs originate from collapsing massive stars in the distant, high redshift universe (e.g. Woosley & Bloom 2006 for a review). I have included text to now discuss these results accordingly. These cosmological distances imply that GRBs have enormous energies ~1e50-1e53 ergs. A basic analysis (below) shows that runaway fission events cannot produce such energetic phenomenon. The concepts and arguments have now been fully incorporated into the paper.
For instance, a gamma-ray burst of typical duration T ~ 1 min must originate from a region of characteristic size L < T*c ~ 1e12 cm, since otherwise its duration would be increased due to light crossing time delay (this is actually a conservative upper limit on the emission size, since what truly matters is the variability timescale, which is typically ~ 1 second or less). In addition to being smaller than the light crossing size, the emission region must be transparent to gamma-rays. The requirement that the critical region must be transparent to gamma-ray photons can be translated into a constraint on the optical depth tau_es = n_e*sigma_T*L < 1 to Thomson scattering, where sigma_T ~ 7e-25 cm^2 is the Thomson scattering opacity; n_e ~ N_e/L^3 is the average number density of electrons and N_e is the total number of electrons. Requiring both tau_e < 1 and L < 1e12 cm implies that N_e < 1e48. Assuming fully ionized gas, the number of electrons N_e is similar to thenumber of nucleons N_n. If every fission reaction released E_fiss ~ 1 MeV per nucleon (optimistic since most of the nuclei are unlikely to fission), then this places an upper limit of E_tot < E_fiss*N_e ~ 1e42 erg. Given that GRBs have typical fluence (time-integrated flux) of F ~ 1e-6 erg/cm^2, such an event would have to originate from a typical distance D ~ (E_tot/F*4*pi)^0.5 ~ 100 kpc or less, i.e. in our Galaxy or its halo. Of course I do not disagree, I assume the referee felt this derivation was important to be included as such rather than to be included here just for my benefit. Otherwise, I am happy to simply reference Woolsey and Bloom and/or similar work to make this point.
The author should acknowledge how the maximum energy of such fission events could be reconciled with the known large energies of GRBs, or it should be acknowledged that only a small fraction of GRBs could originate from such events. Done, note the beaming potential near a magnetar could bias emission along the magnetic axis with an assumed preferential orientation aligned with the galactic axis. This would tend to generate a more isotropic distribution pattern as more distant events in the galaxy would preferentially emit perpendicular to the galactic plane and not towards us.
** Despite its exclusion as a cosmological GRB source, runaway fission could in principle still be relevant to the small subset of gamma-ray transients that could have galactic origin. If runaway fission events were really associated with recent supernovae (as the author seems to suggest), then they would be concentrated in the galactic plane - yet the GRB distribution is largely isotropic on the sky (for recent work on the fraction of sources detected by Swift that could be galactic, see J.C. Tello et al. 2012, ). This consideration is now included in the revised submission.
Some galactic gamma-ray flares are known (soft gamma-ray [SGR] repeaters), but these are generally thought to be associated with flares on galactic magnetars. Although these are indeed young neutron stars (which could in principle be accreting r-process material from their natal supernova), the standard model is that the flaring is powered by the release of magnetic energy, as is supported by other observations such as the large surface magnetic fields inferred from the rate of electromagnetic spin-down as measured from X-ray pulsation (e.g. Kouveliotou et al. 1998). The revision now includes discussion acknowledging these models.
If fission runaway on the neutron star surface was responsible for powering this flaring, it is unclear why this would occur only on highly magnetized neutron stars? The occurrence near neutron stars is only offered as a means to provide some beaming through beta decay related fission product gamma emission. The vast majority of gamma emission from fission products occurs with beta decay which is known to not produce isotropic gamma emission in a strong magnetic field. Criticality does not require in any way for this magnetic field to be present. (although I suggest checking out Cooper, Randall L & Kaplan, David L. ApJL, 708, L80 for some interesting ideas about how thermodynamic conditions might be different as matter settles onto the magnetar surface). The discussion section has been revised to have a brief comparison and characterization to the fission model. At a minimum the author should address more explicitly whether he has SGR flares (as opposed to cosmological GRBs) in mind as a potential astrophysical site for nuclear criticality. Indeed, the most credible source term are the FRED events described by Tello et al (2012) but the gamma emission anisotropy from beta decay related gamma emission of fission products still leaves the door open for additional magnetar related beamingout of our galaxy masking many disk events and so deserves mention.