Physics International 5 (1): 36-44, 2014 ISSN: 1948-9803 ©2014 Science Publication doi:10.3844/pisp.2014.36.44 Published Online 5 (1) 2014 (http://www.thescipub.com/pi.toc) NUCLEAR DETONATION AROUND COMPACT OBJECTS 1C. Sivaram, 2Kenath Arun and 2 O.V. Kiren 1Indian Institute of Astrophysics, Bangalore-560 034, India 2Department of Physics, Christ Junior College, Bangalore-560 029, India Received 2014-02-05; Revised 2014-03-17; Accepted 2014-03-24 ABSTRACT In this study we explore the various aspects involved in nuclear detonations occurring around compact objects and the energetics involved. We discuss the possibility of sub-Chandrasekhar white dwarfs detonating due to the buildup of a layer of hydrogen on the CO white dwarf by accreting from a companion star to explain observed deviations such as subluminous type Ia. We also detail some of the energetics involved that will make such scenarios plausible. Also an alternate model for gamma ray bursts is suggested. For a very close binary system, the white dwarf (close to Chandrasekhar mass limit) can detonate due to tidal heating, leading to a supernova. Material falling on to the neutron star at relativistic velocities can cause its collapse to a magnetar or quark star or black hole leading to a gamma ray burst. As the material smashes on to the neutron star, it is dubbed the Smashnova model. Here the supernova is followed by a gamma ray burst. Keywords: Nuclear Detonation, Compact Objects, Subluminous Type Ia SN, GRB, Smashnova 1. INTRODUCTION 2. ASPECTS OF NUCLEAR BURNING AROUND COMPACT OBJECTS Compact objects, such as White Dwarfs (WD), Neutron Stars (NS) and Black Holes (BH), are stellar 2.1. White Dwarfs remnants and at the end-point of stellar evolution, when The height of the layer (on the WD) required to heat most of their nuclear fuel is exhausted. White dwarfs no hydrogen to this temperature ( TH) is: longer burn nuclear fuel; they are slowly cooling as they radiate away their residual thermal energy, R T h≈ g H ~ 25 km (1) balancing gravitational pressure with electron gWD degeneracy pressure. If the white dwarf accretes mass, 2 then temperature increases due to increase in the where, gWD ≈109 cm/s is the acceleration due to gravity increase in the gravitational pressure. This could result on the WD. (where R ≈108≈ergs/g is the gas constant) g in igniting hydrogen or carbon thermonuclear reaction. The mass of the H layer is given by Equation 2 The ignition may occur if the reaction time is shorter M=(4π Rh2) ρ ≈ 210 × 30 g ~10 − 3 M than the time of cooling process (such as neutrino loss H WD sun (2) ρ 5× 8 or convection). The time of the thermonuclear reaction ()where, ~10 gccR / , WD ~6 10 cm at the white dwarf centre becomes shorter than the typical convection time when the temperature exceed The energy released during this process is ∼ × 7 ∼ × 8 18 3 10 K for hydrogen burning, 2 10 K for helium ∼6×10 ergs/g . The velocity with which this mass is ∼ × 8 burning and 7 10 K for carbon burning. ejected is given by Equation 3: © 2014 C. Sivaram, Kenath Arun and O.V. Kiren. This open access article is distributed under a Creative Commons Attribution (CC-BY) 3.0 license which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly credited. DOI: 10.3844/pisp.2014.36.44 C. Sivaram et al . / Physics International 5 (1): 36-44, 2014 13 6 181 2 (where, ρ × ) M()6× 10 = M v ~10gccR / , NS ~2 10 cm H H (3) 2 The energy released during this process is ≈ × 9 v310 cm / s ∼ × 17 9 10 ergs/g . The velocity with which this mass is ejected is given by Equation 11: And the corresponding energy released is given by Equation 4: ()×17 = 1 2 MH 910 M H v 2 (11) 1 2≈ 49 ≈ 9 MH v 10 ergs (4) v10 cm / s 2 And the corresponding energy released is given by White dwarfs cannot attain the temperature required Equation 12: to initiate carbon burning. But once the reaction starts, it can sustain and even increase the temperature which 1 Mv2≈ 10 45 ergs (12) could be high enough to ignite helium and carbon. If ε is 2 H the energy released per unit mass then Equation 5: 2.3. Black Holes = ε MRg T M ε (5) High temperatures can also be produced in the T = R accretion disks around black holes. The temperature of g the disk corresponding to the Eddington luminosity can be obtained as Equation 13: In the case of H burning, even if a fraction (say 1%) of the energy goes into increasing the temperature, this 4πGMm c 4πR2 σ T 4 = P (13) works out to be Equation 6: D σ T ε =0.01 × 8 (6) T~7 10 K = = 2GM Rg where, R fRS; R S 2 is the Schwarzschild radius c and typically f∼3, below which there will be This is high enough to ignite carbon. relativistic instabilities. This gives the disk 2.2. Neutron Stars temperature as Equation 14: In the case of the neutron stars, since the surface 1 c5 m 1 1 4 15 2 = P (14) gravity on them (g ≈10 cm/s ) is higher, the carbon TD 2 NS G M σσ 4 f burning temperature can be attained. The height of the T layer on the neutron star required to heat hydrogen, The disk temperature depends inversely with black helium and carbon to their respective burning hole mass, hence nuclear burning can be achieved only temperature is Equation 7 to 9: around lighter black holes. For a 3.8 solar mass black hole (J1650, the smallest observed black hole), this temperature R T h≈ g H ~ 2 cm (7) corresponds to that of hydrogen burning (∼3×10 7K). g NS Once this reaction starts, it can sustain and increase the temperature which could be high enough to ignite R T h≈ g He ~ 20 cm (8) helium and carbon as given by Equation 5 and 6. g NS Another possible way by which higher temperatures can be achieved is when tidal break up of compact R T h≈ g C ~ 60 cm (9) objects like white dwarfs or neutron stars occur around gNS the black hole. The mass of the black hole required for the tidal break up (at about a distance of ten times the The mass of the C layer on the neutron star is given Schwarzschild radius) is given by Equation 15: by Equation 10: − 1 3 2 = 20 G M (15) M BH =π2 ρ ≈ × 27− 6 Rc 2 4 MH(4 Rh NS ) 2 10 g ~ 10 M sun (10) Science Publications 37 PI C. Sivaram et al . / Physics International 5 (1): 36-44, 2014 For a typical white dwarf, this works out to We also have the recent example of SN2005E, which 3 ∼5×10 Msun . The corresponding binding energy released showed presence of about 0.3 solar mass of Calcium 3 GM 2 (most Calcium rich SN), which is an intermediate stage is given by: ~1051 ergs . 5 R in the production of Ni. So this is an example of In the case of a neutron star the black hole mass incomplete silicon burning occurring in low density C-O required for its tidal break up ∼10 Msun . The corresponding fuel for a range of temperatures. The density of a WD binding energy released ∼10 54 ergs . This could be a scales as the mass, M squared, i.e., ρ∝M2. possible scenario for short duration gamma ray bursts. A very large number of white dwarfs are known to have a mass substantially lower than a solar mass 3. SUBLUMINOUS TYPE IA (Sivaram, 2006). Is there any way these sub- SUPERNOVAE Chandrasekhar WDs could detonate? 3.1. Double Detonation of Sub-Chandrasekhar Type Ia supernovae form the highest luminosity class of supernovae and are consequently used as distance White Dwarfs indicators over vast expanses of space-time, i.e., over One way could be to build up a layer of helium on the cosmological scales. They are used commonly as the C-O WD by accreting from a helium rich companion brightest standard candles as they are thought to result star, i.e., a hydrogen deficient star with an extensive He from thermonuclear explosions of carbon-oxygen white atmosphere. The helium layer would first detonate at dwarf stars (Hoyle and Fowler, 1960). These explosions ∼ × 8 2 10 K releasing enough energy to heat the C-O nuclei arise when the C-O WD accretes material from a × 8 to 7 10 K to initiate C-burning, which would incinerate companion star and is pushed over the Chandrasekhar a sub-Chandrasekhar WD. The lower progenitor mass limit causing it to collapse gravitationally and heat up to would then give rise to a sub luminous SN type Ia. carbon detonation temperature. Here we detail some energetic of the phenomena The degeneracy (i.e., high density of C and O nuclei) which would make such scenarios plausible. For accelerate the reaction rate so that the entire white dwarf instance, a 0.6 solar mass WD would have a can be incinerated and disintegrated resulting in about gravitational binding energy of ∼7×10 49 ergs . As one 0.5-1.0 solar mass of Ni-56, which subsequently gram of carbon, undergoing nuclear detonation releases undergoes two consecutive beta decays (6 days to Co-56 ∼ × 17 32 and 77 days to Fe-56), the exponential decay of these 9 10 ergs , 10 g of carbon must detonate to form isotopes then powering the light curve for a few months Ni-56 to disintegrate the white dwarf.