Progenitor Core Research Articles

OneSC: A computational platform for recapitulating cell state transitions.

Computational modelling of cell state transitions has been a great interest of many in the field of developmental biology, cancer biology and cell fate engineering because it enables performing perturbation experiments in silico more rapidly and cheaply than could be achieved in a wet lab. Recent advancements in single-cell RNA sequencing (scRNA-seq) allow the capture of high-resolution snapshots of cell states as they transition along temporal trajectories. Using these high-throughput datasets, we can train computational models to generate in silico 'synthetic' cells that faithfully mimic the temporal trajectories. Here we present OneSC, a platform that can simulate synthetic cells across developmental trajectories using systems of stochastic differential equations govern by a core transcription factors (TFs) regulatory network. Different from the current network inference methods, OneSC prioritizes on generating Boolean network that produces faithful cell state transitions and steady cell states that mimic real biological systems. Applying OneSC to real data, we inferred a core TF network using a mouse myeloid progenitor scRNA-seq dataset and showed that the dynamical simulations of that network generate synthetic single-cell expression profiles that faithfully recapitulate the four myeloid differentiation trajectories going into differentiated cell states (erythrocytes, megakaryocytes, granulocytes and monocytes). Finally, through the in-silico perturbations of the mouse myeloid progenitor core network, we showed that OneSC can accurately predict cell fate decision biases of TF perturbations that closely match with previous experimental observations.

Physical Correlations and Predictions Emerging from Modern Core-collapse Supernova Theory

In this paper, we derive correlations between core-collapse supernova observables and progenitor core structures that emerge from our suite of 20 state-of-the-art 3D core-collapse supernova simulations carried to late times. This is the largest such collection of 3D supernova models ever generated and allows one to witness and derive testable patterns that might otherwise be obscured when studying one or a few models in isolation. From this panoramic perspective, we have discovered correlations between explosion energy, neutron star gravitational birth masses, 56Ni and α-rich freezeout yields, and pulsar kicks and theoretically important correlations with the compactness parameter of progenitor structure. We find a correlation between explosion energy and progenitor mantle binding energy, suggesting that such explosions are self-regulating. We also find a testable correlation between explosion energy and measures of explosion asymmetry, such as the ejecta energy and mass dipoles. While the correlations between two observables are roughly independent of the progenitor zero-age main-sequence (ZAMS) mass, the many correlations we derive with compactness cannot unambiguously be tied to a particular progenitor ZAMS mass. This relationship depends on the compactness/ZAMS mass mapping associated with the massive star progenitor models employed. Therefore, our derived correlations between compactness and observables may be more robust than with ZAMS mass but can nevertheless be used in the future once massive star modeling has converged.

Kinematics and Metallicity of Red Giant Branch Stars in the Northeast Shelf of M31* *The data presented herein were obtained at the W. M. Keck Observatory, which is operated as a scientific partnership among the California Institute of Technology, the University of California, and the National Aeronautics and Space Administration. The Observatory was made possible by the generous financial support

We obtained Keck/DEIMOS spectra of 556 individual red giant branch stars in four spectroscopic fields spanning 13−31 projected kpc along the northeast (NE) shelf of M31. We present the first detection of a complete wedge pattern in the space of projected M31-centric radial distance versus line-of-sight velocity for this feature, which includes the returning stream component of the shelf. This wedge pattern agrees with expectations of a tidal shell formed in a radial merger and provides strong evidence in favor of predictions of Giant Stellar Stream (GSS) formation models in which the NE shelf originates from the second orbital wrap of the tidal debris. The observed concentric wedge patterns of the NE, west (W), and southeast (SE) shelves corroborate this interpretation independently of the models. We do not detect a kinematical signature in the NE shelf region corresponding to an intact progenitor core, favoring GSS formation models in which the progenitor is completely disrupted. The shelf’s photometric metallicity ([Fe/H]phot) distribution implies that it is dominated by tidal material, as opposed to the phase-mixed stellar halo or the disk. The metallicity distribution ([Fe/H]phot = −0.42 ± 0.01) also matches the GSS, and consequently the W and SE shelves, further supporting a direct physical association between the tidal features.

Supernova Fallback as Origin of Neutron Star Spins and Spin-kick Alignment

Abstract Natal kicks and spins are characteristic properties of neutron stars (NSs) and black holes (BHs). Both offer valuable clues to dynamical processes during stellar core collapse and explosion. Moreover, they influence the evolution of stellar multiple systems and the gravitational-wave signals from their inspiral and merger. Observational evidence of a possibly generic spin-kick alignment has been interpreted as an indication that NS spins are either induced with the NS kicks or inherited from the progenitor rotation, which thus might play a dynamically important role during stellar collapse. Current three-dimensional supernova simulations suggest that NS kicks are transferred in the first seconds of the explosion, mainly by anisotropic mass ejection and, on a secondary level, anisotropic neutrino emission. By contrast, the NS spins are only determined minutes to hours later by the angular momentum associated with the fallback of matter that does not become gravitationally unbound in the supernova. Here, we propose a novel scenario to explain spin-kick alignment as a consequence of tangential vortex flows in the fallback matter that is accreted mostly from the direction of the NS’s motion. For this effect the initial NS kick is crucial, because it produces a growing offset of the NS away from the explosion center, thus promoting one-sided accretion. In this new scenario conclusions based on traditional concepts are reversed. For example, pre-kick NS spins are not required, and rapid progenitor core rotation can hamper spin-kick alignment. We also discuss implications for natal BH kicks and the possibility of tossing the BH’s spin axis during its formation.

From the CMF to the IMF: beyond the core-collapse model

ABSTRACT Observations have indicated that the pre-stellar core mass function (CMF) is similar to the stellar initial mass function (IMF), except for an offset towards larger masses. This has led to the idea that there is a one-to-one relation between cores and stars, such that the whole stellar mass reservoir is contained in a gravitationally bound pre-stellar core, as postulated by the core-collapse model, and assumed in recent theoretical models of the stellar IMF. We test the validity of this assumption by comparing the final mass of stars with the mass of their progenitor cores in a high-resolution star formation simulation that generates a realistic IMF under physical condition characteristic of observed molecular clouds. Using a definition of bound cores similar to previous works we obtain a CMF that converges with increasing numerical resolution. We find that the CMF and the IMF are closely related in a statistical sense only; for any individual star there is only a weak correlation between the progenitor core mass and the final stellar mass. In particular, for high-mass stars only a small fraction of the final stellar mass comes from the progenitor core, and even for low-mass stars the fraction is highly variable, with a median fraction of only about 50 per cent. We conclude that the core-collapse scenario and related models for the origin of the IMF are incomplete. We also show that competitive accretion is not a viable alternative.

Inferring physical properties of stellar collapse by third-generation gravitational-wave detectors

Galactic core-collapse supernovae are among the possible sources of gravitational waves. We investigate the ability of gravitational-wave observatories to extract the properties of the collapsing progenitor from the gravitational waves radiated. We use simulations of supernovae that explore a variety of progenitor core rotation rates and nuclear equations of state and examine the ability of current and future observatories to determine these properties using gravitational-wave parameter estimation. We use principal component analysis of the simulation catalog to determine the dominant features of the waveforms and create a map between the measured properties of the waveform and the physical properties of the progenitor. We use Bayesian parameter inference and the parameter map to calculate posterior probabilities for the physical properties given a gravitational-wave observation. We estimate the ratio of the progenitor's core rotational kinetic energy to potential energy ($\beta$) and the post bounce oscillation frequency. For a supernovae at the distance of the galactic center (8.1 kpc) with $\beta = 0.02$ our method can estimate $\beta$ with a $90\%$ credible interval of $0.004$ for Advanced LIGO, improving to $0.0008$ for Cosmic Explorer. We demonstrate that if the core is rotating sufficiently rapidly for a signal observed by Cosmic Explorer, our method can also extract the post bounce oscillation frequency of the protoneutron star to a precision of within $5$~Hz ($90\%$ credible interval) allowing us to constrain the nuclear equation of state. For a supernovae at the distance of the Magellanic Clouds (48.5 kpc) Cosmic Explorer's ability to measure these parameters decreases slightly to $0.003$ for rotation and $11$~Hz for the postbounce oscillation frequency ($90\%$ credible interval). Sources in Magellanic Clouds will be too distant for Advanced LIGO to measure these properties.

Origin of Sources of Repeating Fast Radio Bursts with Periodicity in Close Binary Systems

Abstract It is proposed that sources of repeating fast radio bursts with detected periodicity are magnetars with extremely short initial spin periods at the protoneutron star stage, formed in binaries after tidal synchronization of their progenitor cores during late stages of thermonuclear burning in very close systems with orbital periods about a few days. This formation channel is in several respects different from evolution of progenitors of normal magnetars, and thus, it explains some differences between repeating and non-repeating sources of fast radio bursts.

The Preservation of Super-Earths and the Emergence of Gas Giants after Their Progenitor Cores Have Entered the Pebble-isolation Phase

Abstract The omnipresence of super-Earths suggests that they are able to be retained in natal disks around low-mass stars, whereas exoplanets’ mass distributions indicate that some cores have transformed into gas giants through runaway gas accretion at ≳1 au from solar-type stars. In this paper, we show that transition to runaway gas accretion by cores may be self-impeded by an increase of the grain opacity in their envelope after they have acquired sufficient mass (typically ∼ 10M ⊕) to enter a pebble-isolation phase. The accumulation of approximately millimeter- to meter-sized pebbles in their migration barriers enhances their local fragmentation rates. The freshly produced submillimeter grains pass through the barrier, elevate the effective dust opacity, and reduce the radiative flux in the core’s envelope. These effects alone are adequate to suppress the transition to runaway accretion and preserve super-Earths in the stellar proximity (∼0.1 au), albeit entropy advection between the envelope and the disk can further reduce the accretion rate. At an intermediate distance (∼1 au) from their host stars, the escalation in the dust opacity dominates over entropy advection in stalling the transition to runaway accretion for marginally pebble-isolated cores. Beyond a few astronomical unit, the transformation of more-massive cores to gas giants is reachable before severe depletion of disk gas. This requirement can be satisfied either in extended disks with large scale height via orderly accretion of migrating pebbles or through the mergers of oligarchic protoplanetary embryos, and can account for the correlated occurrence of long-period gas giants and close-in super-Earths.

SN 2016coi (ASASSN-16fp): An Energetic H-stripped Core-collapse Supernova from a Massive Stellar Progenitor with Large Mass Loss

Abstract We present comprehensive observations and analysis of the energetic H-stripped SN 2016coi (a.k.a. ASASSN-16fp), spanning the γ-ray through optical and radio wavelengths, acquired within the first hours to ∼420 days post explosion. Our observational campaign confirms the identification of He in the supernova (SN) ejecta, which we interpret to be caused by a larger mixing of Ni into the outer ejecta layers. By modeling the broad bolometric light curve, we derive a large ejecta-mass-to-kinetic-energy ratio (M ej ∼ 4–7 M ⊙, E k ∼ (7–8) × 1051 erg). The small [Ca ii] λλ7291,7324 to [O i] λλ6300,6364 ratio (∼0.2) observed in our late-time optical spectra is suggestive of a large progenitor core mass at the time of collapse. We find that SN 2016coi is a luminous source of X-rays (L X > 1039 erg s−1 in the first ∼100 days post explosion) and radio emission (L 8.5 GHz ∼ 7 × 1027 erg s−1 Hz−1 at peak). These values are in line with those of relativistic SNe (2009bb, 2012ap). However, for SN 2016coi, we infer substantial pre-explosion progenitor mass loss with a rate ∼ (1–2) × and a sub-relativistic shock velocity v sh ∼ 0.15c, which is in stark contrast with relativistic SNe and similar to normal SNe. Finally, we find no evidence for a SN-associated shock breakout γ-ray pulse with energy E γ > 2 × 1046 erg. While we cannot exclude the presence of a companion in a binary system, taken together, our findings are consistent with a massive single-star progenitor that experienced large mass loss in the years leading up to core collapse, but was unable to achieve complete stripping of its outer layers before explosion.

A successful 3D core-collapse supernova explosion model

In this paper, we present the results of our three-dimensional, multigroup, multineutrino-species radiation/hydrodynamic simulation using the state-of-the-art code fornax of the terminal dynamics of the core of a non-rotating 16 M⊙ stellar progenitor. The calculation incorporates redistribution by inelastic scattering, a correction for the effect of many-body interactions on the neutrino–nucleon scattering rates, approximate general relativity (including the effects of gravitational redshifts), velocity-dependent frequency advection, and an implementation of initial perturbations in the progenitor core. The model explodes within ∼100 ms of bounce (near when the silicon–oxygen interface is accreted through the temporarily stalled shock) and by the end of the simulation (here, ∼677 ms after bounce) is accumulating explosion energy at a rate of ∼2.5 × 1050 erg s−1. The supernova explodes with an asymmetrical multiplume structure, with one hemisphere predominating. The gravitational mass of the residual proto-neutron star at ∼677 ms is ∼1.42 M⊙. Even at the end of the simulation, explosion in most of the solid angle is accompanied by some accretion in an annular region at the wasp-like waist of the debris field. The ejecta electron fraction (Ye) is distributed between ∼0.48 and ∼0.56, with most of the ejecta mass proton-rich. This may have implications for supernova nucleosynthesis, and could have a bearing on the p- and νp-processes and on the site of the first peak of the r-process. The ejecta spatial distributions of both Ye and mass density are predominantly in wide-angle plumes and large-scale structures, but are nevertheless quite patchy.

Testing the Formation Scenarios of Binary Neutron Star Systems with Measurements of the Neutron Star Moment of Inertia

Abstract Two low-mass (M < 1.4 M ⊙) neutron stars, J0737-3039B and the companion to J1756-2251, show strong evidence of being formed in an ultra-stripped supernova explosion (US-SN) with a ONeMg or Fe progenitor. Using systematically generated sets of equations of state we map out the relationship between the moment of inertia of J0737-3039A, a candidate for a moment of inertia measurement within a decade, and the binding energy of the two low-mass neutron stars. This relationship, similar to the I-Love-Q relations, is more robust than a previously explored correlation between the binding energy and the slope of the nuclear symmetry energy L. We find that, if either J0737-3039B or the J1756-2251 companion were formed in a US-SN, no more than 0.06 M ⊙ could have been lost from the progenitor core. Furthermore, a measurement of the moment of inertia of J0737-3039A to within 10% accuracy can discriminate between formation scenarios and, given current constraints on the predicted core mass loss, potentially rule them out. Advanced LIGO can potentially measure the neutron star tidal polarizability to equivalent accuracy which, using the I-Love-Q relations, would obtain similar constraints on the formation scenarios. Such information would help constrain important aspects of binary evolution used for population synthesis predictions of the rate of binary neutron star mergers and resulting electromagnetic and gravitational wave signals. Further progress needs to be made in modeling the core-collapse process that leads to low-mass neutron stars, particularly in making robust predictions for the mass loss from the progenitor core.

Estimating the core compactness of massive stars with Galactic supernova neutrinos

We suggest the future detection of neutrinos from a Galactic core-collapse supernova can be used to infer the progenitor’s inner mass density structure. We present the results from 20 axisymmetric core-collapse supernova simulations performed with progenitors spanning initial masses in the range 11–, and focus on their connections to the progenitor compactness. The compactness is a measure of the mass density profile of the progenitor core and recent investigations have suggested its salient connections to the outcomes of core collapse. Our simulations confirm a correlation between the neutrinos emitted during the accretion phase and the progenitor’s compactness, and that the ratio of observed neutrino events during the first hundreds of milliseconds provides a promising handle on the progenitor’s inner structure. Neutrino flavor mixing during the accretion phase remains a large source of uncertainty.

Updated constraints on self-interacting dark matter from Supernova 1987A

We revisit SN1987A constraints on light, hidden sector gauge bosons ("dark photons") that are coupled to the standard model through kinetic mixing with the photon. These constraints are realized because excessive bremsstrahlung radiation of the dark photon can lead to rapid cooling of the SN1987A progenitor core, in contradiction to the observed neutrinos from that event. The models we consider are of interest as phenomenological models of strongly self-interacting dark matter. We clarify several possible ambiguities in the literature and identify errors in prior analyses. We find constraints on the dark photon mixing parameter that are in rough agreement with the early estimates of Dent et al., but only because significant errors in their analyses fortuitously canceled. Our constraints are in good agreement with subsequent analyses by Rrapaj & Reddy and Hardy & Lasenby. We estimate the dark photon bremsstrahlung rate using one-pion exchange (OPE), while Rrapaj & Reddy use a soft radiation approximation (SRA) to exploit measured nuclear scattering cross sections. We find that the differences between mixing parameter constraints obtained through the OPE approximation or the SRA approximation are roughly a factor of $\sim 2-3$. Hardy & Laseby include plasma effects in their calculations finding significantly weaker constraints on dark photon mixing for dark photon masses below $\sim 10\, \mathrm{MeV}$. We do not consider plasma effects. Lastly, we point out that the properties of the SN1987A progenitor core remain somewhat uncertain and that this uncertainty alone causes uncertainty of at least a factor of $\sim 2-3$ in the excluded values of the dark photon mixing parameter. Further refinement of these estimates is unwarranted until either the interior of the SN1987A progenitor is more well understood or additional, large, and heretofore neglected effects, are identified.

Dynamic collapses of relativistic degenerate stellar cores and radiation pressure dominated stellar interiors

We investigate and explore self-similar dynamic radial collapses of relativistic degenerate stellar cores (RDSCs) and radiation pressure dominated stellar interiors (RPDSIs) of spherical symmetry by invoking a conventional polytropic (CP) equation of state (EoS) with a constant polytropic index γ=4/3 and by allowing free-fall non-zero RDSC or RPDSI surface mass density and pressure due to their sustained physical contact with the outer surrounding stellar envelopes also in contraction. Irrespective of the physical triggering mechanisms (including, e.g., photodissociation, electron-positron pair instability, general relativistic instability etc.) for initiating such a self-similar dynamically collapsing RDSC or RPDSI embedded within a massive star, a very massive star (VMS) or a supermassive star (SMS) in contraction and by comparing with the Schwarzschild radii associated with their corresponding RDSC/RPDSI masses, the emergence of central black holes in a wide mass range appears inevitable during such RDSC/RPDSI dynamic collapses inside massive stars, VMSs, and SMSs, respectively. Radial pulsations of progenitor cores or during a stellar core collapse may well leave imprints onto collapsing RDSCs/RPDSIs towards their self-similar dynamic evolution. Massive neutron stars may form during dynamic collapses of RDSC inside massive stars in contraction under proper conditions.

450 d of Type II SN 2013ej in optical and near-infrared

We present optical and near-infrared photometric and spectroscopic observations of SN 2013ej, in galaxy M74, from 1 to 450 days after the explosion. SN 2013ej is a hydrogen-rich supernova, classified as a Type IIL due to its relatively fast decline following the initial peak. It has a relatively high peak luminosity (absolute magnitude M$_\rm{V}$ = -17.6) but a small $^{56}$Ni production of ~0.023 M$_\odot$. Its photospheric evolution is similar to other Type II SNe, with shallow absorption in the H{\alpha} profile typical for a Type IIL. During transition to the radioactive decay tail at ~100 days, we find the SN to grow bluer in B - V colour, in contrast to some other Type II supernovae. At late times, the bolometric light curve declined faster than expected from $^{56}$Co decay and we observed unusually broad and asymmetric nebular emission lines. Based on comparison of nebular emission lines most sensitive to the progenitor core mass, we find our observations are best matched to synthesized spectral models with a M$_\rm{ZAMS}$ = 12 - 15 M$_\odot$ progenitor. The derived mass range is similar to but not higher than the mass estimated for Type IIP progenitors. This is against the idea that Type IIL are from more massive stars. Observations are consistent with the SN having a progenitor with a relatively low-mass envelope.

PROBING THE ROTATION OF CORE-COLLAPSE SUPERNOVA WITH A CONCURRENT ANALYSIS OF GRAVITATIONAL WAVES AND NEUTRINOS

The next time a core-collapse supernova (SN) explodes in our galaxy, vari- ous detectors will be ready and waiting to detect its emissions of gravitational waves (GWs) and neutrinos. Current numerical simulations have successfully introduced multi-dimensional effects to produce exploding SN models, but thus far the explosion mechanism is not well understood. In this paper, we focus on an investigation of progenitor core rotation via comparison of the start time of GW emission and that of the neutronization burst. The GW and neutrino de- tectors are assumed to be, respectively, the KAGRA detector and a co-located gadolinium-loaded water Cherenkov detector, either EGADS or GADZOOKS!. Our detection simulation studies show that for a nearby supernova (0.2 kpc) we can confirm the lack of core rotation close to 100% of the time, and the presence of core rotation about 90% of the time. Using this approach there is also po- tential to confirm rotation for considerably more distant Milky Way supernova explosions.

DIVERSITY OF EXTRASOLAR PLANETS AND DIVERSITY OF MOLECULAR CLOUD CORES. II. MASSES OF GAS GIANT PLANETS

In Paper I, we suggested that the diversity of extrasolar planets might originate from the diversity of molecular cloud cores and specifically illustrated the relationship between semi-major axes of planets in a planetary system and the properties of its progenitor cloud core. In this paper, we investigate the dependence of the mass of a giant planet on the progenitor core properties. We give numerical results of planet masses as a function of the core properties by using the core accretion model of planet formation. Comparing with observations, our model could explain the range and the most frequent values of observed masses of gas giant planets. Our calculations could interpret the observed pileup of gas giants at and the distinct deficit of gas giants from ∼0.05 to . Our calculations indicate that it is difficult to form gas giant planets outside and the intermediate mass planets might be found at ∼15–30 AU as the observing technique advances. We suggest a formation mechanism of super-Jupiters in the framework of the core accretion model of planet formation. A super-Jupiter can form under the condition that a disk is gravitationally unstable (high viscosity) when a protoplanet opens the deep gap. Our calculations infer that the upper limit of super-Jupiter masses, the range of semi-major axes, and the occurrence rate of super-Jupiters increase with the central star mass. We find that gas giant planets should commonly exist around various stellar masses.

THE EVOLUTION OF THE SNOW LINE IN A PROTOPLANETARY DISK

We study the evolutionary behavior of the snow line with a time-dependent disk model that includes the mass influx onto the disk from the collapse of the progenitor cloud core. We are able to investigate the evolution of the snow line during the disk formation and early evolution. We find that the radius of the snow line in a disk first increases with time, reaches a maximum, , and then decreases with time. The mass influx in our model inherits the progenitor core properties and we quantitatively illustrate the relationship between the behavior of the snow line and the core properties. We find that the mass influx onto the disk becomes dilute for high core angular momentum and that surface density near the snow line decreases. Thus viscosity heating decreases and becomes small. When the angular momentum is low, the amount of material falling onto the disk is small and thus the surface density is small. This limits the value of . We find that the maximum value of is for the core mass . We suggest that diffusion of water vapor to makes a preferred location for gas giant planet formation. Water inside is substantially depleted due to diffusion. The observed lack of cold water vapor in protoplanetary disks by Herschel might be related to the depletion of water inside .

EVOLUTIONARY CHANNELS FOR THE FORMATION OF DOUBLE NEUTRON STARS

We analyze binary population models of double-neutron stars and compare results to the accurately measured orbital periods and eccentricities of the eight known such systems in our Galaxy. In contrast to past similar studies, we especially focus on the dominant evolutionary channels (we identify three); for the first time, we use a detailed understanding of the evolutionary history of three double neutron stars as actual constraints on the population models. We find that the evolutionary constraints derived from the double pulsar are particularly tight, and less than half of the examined models survive the full set of constraints. The top-likelihood surviving models yield constraints on the key binary evolution parameters, but most interestingly reveal (i) the need for electron-capture supernovae from relatively low-mass degenerate, progenitor cores, and (ii) the most likely evolutionary paths for the rest of the known double neutron stars. In particular, we find that J1913+16 likely went through a phase of Case BB mass transfer, and J1906+0746 and J1756-2251 are consistent with having been formed in electron-capture supernovae.

Neutrino viscosity and drag: impact on the magnetorotational instability in protoneutron stars

The magnetorotational instability (MRI) is a promising mechanism to amplify the magnetic field in fast rotating protoneutron stars. The diffusion of neutrinos trapped in the PNS induces a transport of momentum, which can be modelled as a viscosity on length-scales longer than the neutrino mean free path. This neutrino-viscosity can slow down the growth of MRI modes to such an extent that a minimum initial magnetic field strength of $\gtrsim 10^{12}\, {\rm G}$ is needed for the MRI to grow on a sufficiently short time-scale to potentially affect the explosion. It is uncertain whether the magnetic field of fast rotating progenitor cores is strong enough to yield such an initial magnetic field in PNS. At MRI wavelengths shorter than the neutrino mean free path, on the other hand, neutrino radiation does not act as a viscosity but rather induces a drag on the velocity with a damping rate independent of the wavelength. We perform a linear analysis of the MRI in this regime, and apply our analytical results to the PNS structure from a one-dimensional numerical simulation. We show that in the outer layers of the PNS, the MRI can grow from weak magnetic fields at wavelengths shorter than the neutrino mean free path, while deeper in the PNS MRI growth takes place in the viscous regime and requires a minimum magnetic field strength.