NUCLEOSYNTHESIS INSIDE GAMMA-RAY BURST ACCRETION DISKS AND ASSOCIATED OUTFLOWS

Transcription

1 NUCLEOSYNTHESIS INSIDE GAMMA-RAY BURST ACCRETION DISKS AND ASSOCIATED OUTFLOWS Indrani Banerjee Indian Institute of Science Bangalore The work has been done in collaboration with Banibrata Mukhopadhyay XXVII texas symposium on relativistic astrophysics 8-13 December 2013

2 Plan of the talk Collapsar Model: A brief overview Disk Model and Input Physics Nuclear Reaction Network used Nucleosynthesis in the disks Outflow model Nucleosynthesis in the outflow: few examples Conclusion & Discussions

3 COLLAPSar model considered Progenitor stars have M MS between M sun Form proto-neutron star initially, later transformed to a black hole fallback collapsars. Mild supernova explosion Accretion rate : (in M Sun s -1 ) Ideal sites for the nucleosynthesis of heavy elements origin of which is still not well understood MacFadyen, Woosley & Heger (ApJ 2001)

4 DISK MODEL & INPUT PHYSICS Height averaged equations based on Newtonian dynamics were used. Strong gravity around the black hole was mimicked in terms of the well established pseudo-newtonian potential (Mukhopadhyay, 2002) The continuity equation gives the mass accretion rate : where, Additionally we have the viscous momentum balance equations : Kohri, Narayan & Piran ApJ 2005 Chen & Beloborodov ApJ 2007

5 Contributions from radiation pressure, gas pressure, electron degeneracy pressure and neutrino pressure were included in the equation state : X f : Free nucleon mass fraction τ ν : optical depths of neutrinos

6 The energy equation is given by :

7 DENSITY AND TEMPERATURE PROFILE M BH = 3M Sun α = 0.01 in units of M sun s -1

8 Nuclear Reaction Network Well tested nuclear reaction / network code has been used which has been implemented by : Chakrabarti, S. K., Jin, L., Arnett, D. (1987, ApJ) Mukhopadhyay B., Chakrabarti S. K. (2000, A&A) Cooper R., Mukhopadhyay B., Steeghs D, Narayan R. (2006, ApJ) We have increased the nuclear network and included reaction rates from the JINA Reaclib Database

9 Nucleosynthesis in the disks

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11 Formation of zones characterized by dominant elements M BH = 3 M Sun a=0 α = 0.01 He He Si/S Ni/Fe/Si/S Ca/Ti/Cr Ni/Fe Initial abundance : He rich Initial abundance : Si rich

12 Why iron group elements synthesized during Si burning? Photodisintegration reactions: X + γ z + Y where, z : p, n, α The temperature attained in the disk is high enough for photodisintegration reactions and their reverses to come in equilibrium. Photoejected particles recaptured by nuclei existing in the system nuclei with higher binding energy from where they are ejected photodisintegration rearrangement reactions. The density and temperature is such that T β-decay >> T photodisintegration rearrangement The result of photodisintegration rearrangement is the synthesis of iron group elements with 54 Fe or 56 Ni being the most abundant element.

13 outflow and supernovae High accretion rate matter gets stagnated onto the disk favors outflow unless cooling takes over to aid accretion. Outflows often result in stellar explosions observable as supernovae, e.g. SN1998bw and SN1997ef. Stellar explosion does not necessarily mean that there is a supernova. For a supernova to occur, continuous energy has to be emitted in the visible part of the spectrum to power the observable light curve for long times of the order of weeks to months. The time evolution of the light curve of Type Ibc supernovae results from the decay of 56 Ni 56 Co 56 Fe.

14 OUTFLOW MODEL Our hydrodynamic model of the wind assumes that the gases are adiabatic and spherically expanding. The temperature of the ejecta is given by : r ej is the ejection radius of the wind T 0 is the temperature at r ej γ is the adiabatic index v ej is the ejection velocity v & h ej are obtained after solving the hydrodynamics of the disk The entropy per baryon, S, of the ejecta expressed in units of Boltzmann constant is assumed to be constant throughout the flow : Fujimoto et al Pruet et al. 2003

15 Outflow from He-rich zone of the Si-rich disk

16 Trough-like feature in the abundance evolution pattern of α-elements 28 Si + 4 He p + 31 P 31 P + 4 He p + 34 S 34 S + 4 He n + 37 Ar 37 Ar + 4 He p + 40 K 40 K + 4 He n + 43 Sc 43 Sc + 4 He p + 46 Ti 46 Ti + 4 He n + 49 Cr 49 Cr + 4 He p + 52 Mn 52 Mn + n 53 Mn 53 Mn +p n + 53 Fe 53 Fe + 4 He n + 56 Ni Later, (p,α), (n,α) reactions enhance the mass fraction of the α-elements. Mass fractions of α-elements saturate once the forward and reverse reactions come in equilibrium.

17 Outflow from Si-rich zone of the Si-rich disk

18 Estimation of elemental contamination in the Galaxy Assuming: Typical mass of the galaxy M Sun Typical age of the galaxy years 1 supernova event in every 100 years during the lifetime of the galaxy Typical change in mass fraction of i-th species during one such supernova event, 10-3 For e.g., to estimate the maximum contamination of 60 Zn in the galaxy: Consider outflow model(s) where mass fraction of 60 Zn is maximum (here X max = X i ~0.036) T S (no. of years per supernova) = 100 years T G (age of galaxy) = years M G (mass of galaxy) = M Sun < X i > ~ 3.6 X 10-5

19 Summary & Conclusions We report the synthesis of several isotopes of iron, cobalt, nickel, sulphur, silicon, argon and calcium in the disk as was reported by previous authors. We also report for the first time the synthesis of 31 P, 39 K, 43 Sc, 35 Cl and various isotopes of titanium, vanadium, chromium, manganese and copper in the disk. Presence of 56 Ni in the outflow indicates that there will be a supernova explosion. Apart from 56 Ni, isotopes of copper, zinc, iron and alpha elements are formed in the outflow. We give an estimate of the elemental contamination of the galaxy. Emission lines of many of these elements have been discovered in the X-ray afterglows of GRBs: Fe lines in GRB (Piro et al. 1995), GRB (Yoshida et al. 1999) and GRB (Antonelli et al. 2000); S, Ar, Ca lines in GRB (Reeves et al. 2003) by Chandra, BeppoSAX, XMM-Newton, but Swift is yet to detect these lines (Zhang et al. 2006; Hurkett et al. 2008).

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21 ABUNDANCE OF ELEMENTS BECOMES IDENTICAL IN THE INNER DISK M BH = 3 M Sun a=0 α = 0.01

22 THE SUPERNOVA-GAMMA-RAY BURST CONNECTION Various layers of an evolved massive star with M MS > 20M Sun are organized in the manner of an onion. These stars, when losing mass rapidly by means of a strong stellar wind are often called Wolf Rayet stars. When these stars undergo core collapse after losing their hydrogen and/or helium envelope they form black holes. As the core collapses the star s bulk explodes into the surrounding ISM leading to a supernova event. The onion-like layers of an evolved massive star (not to scale) Black hole pulls in more stellar material. If the progenitor star has enough spin, a high density accretion disk develops around the black hole. This is the collapsar model of gamma-ray bursts. Rotating conducting fluids create a magnetic field and due to differential rotation the magnetic field lines twist violently. This causes a jet of material to blast outward perpendicular to the accretion disk.

23 THE RELATIVISTIC FIREBALL SHOCK MODEL The jet of material that comes out contains matter and antimatter in the form of electrons and positrons. As the jet moves nearly at the speed of light relativistic effects take over. The jet referred to as the fireball is more like a fire hose. It behaves like a shock wave as it races outward, plowing into and sweeping up matter in its way. Inside the fireball, pressure, density and temperature vary, resulting in a series of internal shock waves moving back and forth within the fireball as faster moving blobs of material overtake slower moving blobs. Gamma rays are produced as a result of the collisions of blobs of matter. Initially, the fireball medium does not allow light to escape. When it cools enough to become transparent, the gamma ray photons race outward in the direction of motion of the jet, just ahead of the lead shock front. Afterglow results when material in the jet collides with the interstellar medium to create a wide array of less energetic light. Initially X rays result, but as the blobs of matter bump into each other, they lose their kinetic energy and the resulting energies decrease through visible light and eventually into radio waves.

24 WHEN DOES A STAR EVOLVE ALL THE WAY TO A GAMMA-RAY BURST? Three very special conditions are required for a star to evolve all the way to gamma-ray burst : 1. The star must be massive enough so that it forms a central black hole via core collapse. 2. The star must be rapidly rotating to develop an accretion disk. 3. The star must have low metallicity in order to strip off its hydrogen envelope so the jets can reach the surface. (Heger et al., ApJ 2003)

25 Significant processes emitting neutrinos 1. Electron -positron pair annihilation: The neutrino cooling rate per unit volume : 2. Nucleon nucleon bremsstrahlung : The neutrino cooling rate per unit volume :

26 3. Plasmon decay : The neutrino cooling rate per unit volume : 4. Neutronization reactions : The neutrino cooling rate per unit volume :

27 Neutrino Opacities Each neutrino emission process has an inverse process corresponding to absorption. The various absorptive optical depths are : 1. Interaction of neutrinos with one another : 2. Absorption onto protons and neutrons : Scattering impedes the free escape of neutrinos from the disk. Total scattering optical depth is given by :

28 Time evolution of the isotopic abundances Our nuclear reaction network contains 340 nuclear species upto 87 Y and all possible reactions between the various isotopes. In our nucleosynthesis code the reaction rates have been updated suitably from time to time. For simplicity let us consider four isotopes and three reactions : p + p e + + ν e + D D + D 4 He 3 4 He 12 C The corresponding rate equations can be expressed as The above equation can be written as where, v(t) is the linear combination of all the eigenvectors such that,

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31 Initial abundances The disk is made from the fallback material of the successfully driven supernova. The chemical composition of the fallback material is changed from the pre-sn composition due to SN shock heating. Composition of the explosively burned O-rich layer is similar to the pre-sn composition of the Si-rich layer (Hashimoto, Prog. Theor. Phys., 1995). Composition of the explosively burned Si-rich layer is similar to the pre-sn composition of the He-rich layer (Hashimoto, Prog. Theor. Phys., 1995).