From core collapse to superluminous: the rates of massive stellar explosions from the Palomar Transient Factory

ABSTRACT We present measurements of the local core-collapse supernova (CCSN) rate using SN discoveries from the Palomar Transient Factory (PTF). We use a Monte Carlo simulation of hundreds of millions of SN light-curve realizations coupled with the detailed PTF survey detection efficiencies to forward model the SN rates in PTF. Using a sample of 86 CCSNe, including 26 stripped-envelope SNe (SESNe), we show that the overall CCSN volumetric rate is $r^\mathrm{CC}_v=9.10_{-1.27}^{+1.56}\times 10^{-5}\, \text{SNe yr}^{-1}\, \text{Mpc}^{-3}\, h_{70}^{3}$ at 〈z〉 = 0.028, and the SESN volumetric rate is $r^\mathrm{SE}_v=2.41_{-0.64}^{+0.81}\times 10^{-5}\, \text{SNe yr}^{-1}\, \text{Mpc}^{-3}\, h_{70}^{3}$. We further measure a volumetric rate for hydrogen-free superluminous SNe (SLSNe-I) using eight events at z ≤ 0.2 of $r^\mathrm{SLSN-I}_v=35_{-13}^{+25}\, \text{SNe yr}^{-1}\text{Gpc}^{-3}\, h_{70}^{3}$, which represents the most precise SLSN-I rate measurement to date. Using a simple cosmic star formation history to adjust these volumetric rate measurements to the same redshift, we measure a local ratio of SLSN-I to SESN of ${\sim}1/810^{+1500}_{-94}$, and of SLSN-I to all CCSN types of ${\sim}1/3500^{+2800}_{-720}$. However, using host galaxy stellar mass as a proxy for metallicity, we also show that this ratio is strongly metallicity dependent: in low-mass (logM* < 9.5 M⊙) galaxies, which are the only environments that host SLSN-I in our sample, we measure an SLSN-I to SESN fraction of $1/300^{+380}_{-170}$ and $1/1700^{+1800}_{-720}$ for all CCSN. We further investigate the SN rates a function of host galaxy stellar mass, and show that the specific rates of all CCSNe decrease with increasing stellar mass.

Dense gas formation and destruction in a simulated Perseus-like galaxy cluster with spin-driven black hole feedback

Context. Extended filamentary Hα emission nebulae are a striking feature of nearby galaxy clusters but the formation mechanism of the filaments, and the processes which shape their morphology remain unclear. Aims. We conduct an investigation into the formation, evolution and destruction of dense gas in the centre of a simulated, Perseus-like, cluster under the influence of a spin-driven jet. The jet is powered by the supermassive black hole (SMBH) located in the cluster’s brightest cluster galaxy. We particularly study the role played by condensation of dense gas from the diffuse intracluster medium, and the impact of direct uplifting of existing dense gas by the jets, in determining the spatial distribution and kinematics of the dense gas. Methods. We present a hydrodynamical simulation of an idealised Perseus-like cluster using the adaptive mesh refinement code RAMSES. Our simulation includes a SMBH that self-consistently tracks its spin evolution via its local accretion, and in turn drives a large-scale jet whose direction is based on the black hole’s spin evolution. The simulation also includes a live dark matter (DM) halo, a SMBH free to move in the DM potential, star formation and stellar feedback. Results. We show that the formation and destruction of dense gas is closely linked to the SMBH’s feedback cycle, and that its morphology is highly variable throughout the simulation. While extended filamentary structures readily condense from the hot intra-cluster medium, they are easily shattered into an overly clumpy distribution of gas during their interaction with the jet driven outflows. Condensation occurs predominantly onto infalling gas located 5−15 kpc from the centre during quiescent phases of the central AGN, when the local ratio of the cooling time to free fall time falls below 20, i.e. when tcool/tff < 20. Conclusions. We find evidence for both condensation and uplifting of dense gas, but caution that purely hydrodynamical simulations struggle to effectively regulate the cluster cooling cycle and produce overly clumpy distributions of dense gas morphologies, compared to observation.

Geometric cues stabilise long-axis polarisation of PAR protein patterns in C. elegans

In the Caenorhabditis elegans zygote, PAR protein patterns, driven by mutual anatagonism, determine the anterior-posterior axis and facilitate the redistribution of proteins for the first cell division. Yet, the factors that determine the selection of the polarity axis remain unclear. We present a reaction-diffusion model in realistic cell geometry, based on biomolecular reactions and accounting for the coupling between membrane and cytosolic dynamics. We find that the kinetics of the phosphorylation-dephosphorylation cycle of PARs and the diffusive protein fluxes from the cytosol towards the membrane are crucial for the robust selection of the anterior-posterior axis for polarisation. The local ratio of membrane surface to cytosolic volume is the main geometric cue that initiates pattern formation, while the choice of the long-axis for polarisation is largely determined by the length of the aPAR-pPAR interface, and mediated by processes that minimise the diffusive fluxes of PAR proteins between cytosol and membrane.

On a unified breaking onset threshold for gravity waves in deep and intermediate depth water

We revisit the classical but as yet unresolved problem of predicting the breaking onset of 2D and 3D irrotational gravity water waves. Based on a fully nonlinear 3D boundary element model, our numerical simulations investigate geometric, kinematic and energetic differences between maximally tall non-breaking waves and marginally breaking waves in focusing wave groups. Our study focuses initially on unidirectional domains with flat bottom topography and conditions ranging from deep to intermediate depth (depth to wavelength ratio from 1 to 0.2). Maximally tall non-breaking (maximally recurrent) waves are clearly separated from marginally breaking waves by their normalised energy fluxes localised near the crest tip region. The initial breaking instability occurs within a very compact region centred on the wave crest. On the surface, this reduces to the local ratio of the energy flux velocity (here the fluid velocity) to the crest point velocity for the tallest wave in the evolving group. This provides a robust threshold parameter for breaking onset for 2D wave packets propagating in uniform water depths from deep to intermediate. Further targeted study of representative cases of the most severe laterally focused 3D wave packets in deep and intermediate depth water shows that the threshold remains robust. These numerical findings for 2D and 3D cases are closely supported by our companion observational results. Warning of imminent breaking onset is detectable up to a fifth of a carrier wave period prior to a breaking event.

Loss Mechanisms of Interplatform Steps in a 1.5-Stage Axial Flow Turbine

In this paper, the detailed steady and unsteady numerical investigations of a 1.5-stage axial flow turbine are conducted to determine the specific influence of interplatform steps in the first stator—as caused by deviations in manufacturing or assembly. A basic first stator design and a design consisting of a bow and endwall contours are compared. Apart from step height, the position and geometry of the interplatform border are varied for the basic design. To create the steps, every third stator vane was elevated, together with its platforms at hub and shroud, such that the flow capacity is only little affected. The results show that the effects of steps on the platform borders in front and aft of the first stator can be decoupled from those occurring on the interplatform steps. For the latter, being the main contributor to the additional loss, the intensity of recirculation zones and losses increase substantially when the platform border is located close to the suction side. Using a relative step height of 1.82% span, the entropy production doubles when compared to a position close to the pressure side, which can be explained by differences in local flow velocity level. Regarding a circular-arc-shaped platform, the losses can be more than halved—mainly due to lower included angles between step and endwall flow streamlines. The findings can be explained by a nondimensional relation of the local entropy production using local values for step height and characteristic flow quantities. Furthermore, a reduction in step height leads to an attenuation of the otherwise linear relationship between step height and entropy production, which is mainly due to lower local ratio of step height and boundary layer thickness. In the case of laminar or transitional flow regions on the endwall, typical for turbine rigs with low inlet turbulence and low-pressure turbines under cruise conditions, the steps lead to immediate local flow transition and thus substantially different results.

Loss Mechanisms of Inter-Platform Steps in a 1.5 Stage Axial Flow Turbine

In this paper detailed steady and unsteady numerical investigations of a 1.5 stage axial flow turbine are conducted to determine the specific influence of inter-platform steps in the first stator — as caused by deviations in manufacturing or assembly. A basic first stator design and a design consisting of a bow and endwall contours are compared. Apart from step height, the position and geometry of the inter-platform border are varied for the basic design. To create the steps, every third stator vane was elevated, together with its platforms at hub and shroud — such that the flow capacity is only little affected. The results show that the effects of steps on the platform borders in front and aft of the first stator can be decoupled from those occurring on the inter-platform steps. For the latter — being the main contributor to the additional loss — the intensity of recirculation zones and losses increase substantially when the platform border is located close to the suction side. Using a relative step height of 1.82 % span, the entropy production doubles when compared to a position close to the pressure side, which can be explained by differences in local flow velocity level. Regarding a circular-arc shape platform, the losses can be more than halved — mainly due to lower included angles between step and endwall flow streamlines. The findings can be explained by a non-dimensional relation of the local entropy production using local values for step height and characteristic flow quantities. Furthermore, a reduction in step height leads to an attenuation of the otherwise linear relationship between step height and entropy production, which is mainly due to lower local ratio of step height and boundary layer thickness. In the case of laminar or transitional flow regions on the endwall — typical for turbine rigs with low inlet turbulence and low-pressure turbines under cruise conditions — steps lead to immediate local flow transition and thus substantially different results.