Ouyed et al. (1998) proposed Deuterium (DD) fusion at the core-mantle interface of giant planets as a mechanism to explain their observed heat excess. But rather high interior temperatures (~10^5 K) and a stratified D layer are needed, making such a
scenario unlikely. In this paper, we re-examine DD fusion, with the addition of screening effects pertinent to a deuterated core containing ice and some heavy elements. This alleviates the extreme temperature constraint and removes the requirement of a stratified D layer. As an application, we propose that, if their core temperatures are a few times 10^4 K and core composition is chemically inhomogeneous, the observed inflated size of some giant exoplanets (hot Jupiters) may be linked to screened DD fusion occurring deep in the interior. Application of an analytic evolution model suggests that the amount of inflation from this effect can be important if there is sufficient rock-ice in the core, making DD fusion an effective extra internal energy source for radius inflation. The mechanism of screened DD fusion, operating in the above temperature range, is generally consistent with the trend in radius anomaly with planetary equilibrium temperature $T_{rm eq}$, and also depends on planetary mass. Although we do not consider the effect of incident stellar flux, we expect that a minimum level of irradiation is necessary to trigger core erosion and subsequent DD fusion inside the planet. Since DD fusion is quite sensitive to the screening potential inferred from laboratory experiments, observations of inflated hot Jupiters may help constrain screening effects in the cores of giant planets.
LSQ14bdq and SN 2006oz are super-luminous, hydrogen-poor, SNe with double-humped light curves. We show that a Quark-Nova (QN; explosive transition of the neutron star to a quark star) occurring in a massive binary, experiencing two Common Envelope (C
E) phases, can quantitatively explain the light curves of LSQ14bdq and SN 2006oz. The more massive component (A) explodes first as a normal SN, yielding a Neutron Star which ejects the hydrogen envelope of the companion when the system enters its first CE phase. During the second CE phase, the NS spirals into and inflates the second He-rich CE. In the process it gains mass and triggers a Quark-Nova, outside of the CO core, leaving behind a Quark Star. The first hump in our model is the QN shock re-energizing the expanded He-rich CE. The QN occurs when the He-rich envelope is near maximum size (~ 1000R_sun) and imparts enough energy to unbind and eject the envelope. Subsequent merging of the Quark Star with the CO core of component B, driven by gravitational radiation, turns the Quark star to a Black Hole. The ensuing Black Hole accretion provides sufficient power for the second brighter and long lasting hump. Our model suggests a possible connection between SLSNe-I and type Ic-BL SNe which occur when the Quark Nova is triggered inside the CO core. We estimate the rate of QNe in massive binaries during the second CE phase to be ~ 5x10^(-5) of that of core-collapse SNe.
We propose a simple model explaining two outstanding astrophysical problems related to compact objects: (1) that of stars such as G87-7 (alias EG 50) that constitute a class of relatively low-mass white dwarfs which nevertheless fall away from the C/
O composition and (2) that of GRB 110328A/Swift J164449.3+57345 which showed spectacularly long-lived strong X-ray flaring, posing a challenge to standard GRB models. We argue that both these observations may have an explanation within the unified framework of a Quark-Nova occurring in a low-mass X-ray binary (neutron star- white dwarf). For LMXBs where the binary separation is sufficiently tight, ejecta from the exploding Neutron Star triggers nuclear burning in the white dwarf on impact, possibly leading to Fe-rich composition compact white dwarfs with mass 0.43M_sun < M_WD < 0.72M_sun, reminiscent of G87-7. Our results rely on the assumption, which ultimately needs to be tested by hydrodynamic and nucleosynthesis simulations, that under certain circumstances the WD can avoid the thermonuclear runaway. For heavier white dwarfs (i.e. M_WD > 0.72M_sun) experiencing the QN shock, degeneracy will not be lifted when Carbon burning begins, and a sub-Chandrasekhar Type Ia Supernovae may result in our model. Under slightly different conditions, and for pure He white dwarfs (i.e. M_WD < 0.43M_sun), the white dwarf is ablated and its ashes raining down on the Quark star leads to accretion-driven X-ray luminosity with energetics and duration reminiscent of GRB 110328A. We predict additional flaring activity towards the end of the accretion phase if the Quark star turns into a Black Hole.
We show that several features reminiscent of short-hard Gamma-ray Bursts (GRBs) arise naturally when Quark-Novae occur in low-mass X-ray binaries born with massive neutron stars (> 1.6M_sun) and harboring a circumbinary disk. Near the end of the firs
t accretion phase, conditions are just right for the explosive conversion of the neutron star to a quark star (Quark-Nova). In our model, the subsequent interaction of material from the neutron stars ejected crust with the circumbinary disk explains the duration, variability and near-universal nature of the prompt emission in short-hard GRBs. We also describe a statistical approach to ejecta break-up and collision to obtain the photon spectrum in our model, which turns out remarkably similar to the empirical Band function (Band 1993). We apply the model to the fluence and spectrum of GRB 000727, GRB 000218, and GRB980706A obtaining excellent fits. Extended emission (spectrum and duration) is explained by shock-heating and ablation of the white dwarf by the highly energetic ejecta. Depending on the orbital separation when the Quark-Nova occurs, we isolate interesting regimes within our model when both prompt and extended emission can occur. We find that the spectrum can carry signatures typical of Type Ib/c SNe although these should appear less luminous than normal type Ib/c SNe. Late X-ray activity is due to accretion onto the quark star as well as its spin-down luminosity. Afterglow activity arise from the expanding shell of material from the shock-heated expanding circumbinary disk. We find a correlation between the duration and spectrum of short-hard GRBs as well as modest hard-to-soft time evolution of the peak energy.
European options can be priced when returns follow a Students t-distribution, provided that the asset is capped in value or the distribution is truncated. We call pricing of options using a log Students t-distribution a Gosset approach, in honour of
W.S. Gosset. In this paper, we compare the greeks for Gosset and Black-Scholes formulae and we discuss implementation. The t-distribution requires a shape parameter u to match the fat tails of the observed returns. For large u, the Gosset and Black-Scholes formulae are equivalent. The Gosset formulae removes the requirement that the volatility be known, and in this sense can be viewed as an extension of the Black-Scholes formula.
[Abridged] Superluminous Supernovae (SN2006gy, SN2005gj, SN2005ap, SN2008fz, SN2003ma) have been a challenge to explain by standard models. We present an alternative scenario involving a quark-nova (QN), an explosive transition of the newly born neut
ron star to a quark star in which a second explosion (delayed) occurs inside the already expanding ejecta of a normal SN. The reheated SN ejecta can radiate at higher levels for longer periods of time primarily due to reduced adiabatic expansion losses, unlike the standard SN case. Our model is successfully applied to SN2006gy, SN2005gj, SN2005ap, SN2008fz, SN2003ma with encouraging fits to the lightcurves. There are four predictions in our model: (i) superluminous SNe optical lightcurves should show a double-hump with the SN hump at weaker magnitudes occurring days to weeks before the QN; (ii) Two shock breakouts should be observed vis-a-vis one for a normal SN. Depending on the time delay, this would manifest as two distinct spikes in the X-ray region or a broadening of the first spike for extremely short delays; (iii) The QN deposits heavy elements of mass number A> 130 at the base of the preceeding SN ejecta. These QN r-processed elements should be visible in the late spectrum (few days-weeks in case of strong ejecta mixing) of the superluminous SN; (iv) The QN yield will also contain lighter elements (Hydrogen and Helium). We expect the late spectra to include H_alpha emission lines that should be distinct in their velocity signature from standard H_alpha emission.
If a quark-nova occurs inside a collapsar, the interaction between the quark-nova ejecta (relativistic iron-rich chunks) and the collapsar envelope, leads to features indicative of those observed in Gamma Ray Bursts. The quark-nova ejecta collides wi
th the stellar envelope creating an outward moving cap (Gamma ~ 1-10) above the polar funnel. Prompt gamma-ray burst emission from internal shocks in relativistic jets (following accretion onto the quark star) become visible after the cap becomes optically thin. Model features include: (i) precursor activity (optical, X-ray, gamma-ray), (ii) prompt gamma-ray emission, and (iii) afterglow emission. We discuss SN-less long duration GRBs, short hard GRBs (including association and non-association with star forming regions), dark GRBs, the energetic X-ray flares detected in Swift GRBs, and the near-simultaneous optical and gamma-ray prompt emission observed in GRBs in the context of our model.
Astrophysical jets are associated with the formation of young stars of all masses, stellar and massive black holes, and perhaps even with the formation of massive planets. Their role in the formation of planets, stars, and galaxies is increasingly ap
preciated and probably reflects a deep connection between the accretion flows - by which stars and black holes may be formed - and the efficiency by which magnetic torques can remove angular momentum from such flows. We compare the properties and physics of jets in both non-relativistic and relativistic systems and trace, by means of theoretical argument and numerical simulations, the physical connections between these different phenomena. We discuss the properties of jets from young stars and black holes, give some basic theoretical results that underpin the origin of jets in these systems, and then show results of recent simulations on jet production in collapsing star-forming cores as well as from jets around rotating Kerr black holes.
Magnetic reconnection plays a critical role in many astrophysical processes where high energy emission is observed, e.g. particle acceleration, relativistic accretion powered outflows, pulsar winds and probably in dissipation of Poynting flux in GRBs
. The magnetic field acts as a reservoir of energy and can dissipate its energy to thermal and kinetic energy via the tearing mode instability. We have performed 3d nonlinear MHD simulations of the tearing mode instability in a current sheet. Results from a temporal stability analysis in both the linear regime and weakly nonlinear (Rutherford) regime are compared to the numerical simulations. We observe magnetic island formation, island merging and oscillation once the instability has saturated. The growth in the linear regime is exponential in agreement with linear theory. In the second, Rutherford regime the island width grows linearly with time. We find that thermal energy produced in the current sheet strongly dominates the kinetic energy. Finally preliminary analysis indicates a P(k) 4.8 power law for the power spectral density which suggests that the tearing mode vortices play a role in setting up an energy cascade.
Relativistic outflows carrying large scale magnetic fields have large inductive potential and may accelerate protons to ultra high energies. We discuss a novel scheme of Ultra-High Energy Cosmic Ray (UHECR) acceleration due to drifts in magnetized, c
ylindrically collimated, sheared jets of powerful active galaxies (with jet luminosity $geq 10^{46}$ erg s$^{-1}$). A positively charged particle carried by such a plasma is in an unstable equilibrium if ${bf B} cdot abla times {bf v}< 0$, so that kinetic drift along the velocity shear would lead to fast, regular energy gain. The highest rigidity particles are accelerated most efficiently implying the dominance of light nuclei for energies above the ankle in our model: from a mixed population of pre-accelerated particle the drift mechanism picks up and boosts protons preferably.
