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Physics International 5 (1): 36-44, 2014 ISSN: 1948-9803 ©2014 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 on the CO by accreting from a companion 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 limit) can detonate due to tidal heating, leading to a . Material falling on to the at relativistic velocities can cause its collapse to a or or 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 (NS) and Black Holes (BH), are stellar 2.1. White Dwarfs remnants and at the end-point of , 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 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 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 HWD (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 ∼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 disks around black holes. The temperature of g the disk corresponding to the Eddington 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 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  MHNS(4 Rh) 2 10 g ~ 10 M sun (10)  

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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. This mass is releasing at least 10 42 -10 43 J in the optical band. These ~0.05 solar mass. To detonate carbon, the temperature × 8 models (Kasen et al ., 2009; Mazzali et al ., 2007) required is 7 10 K. The required energy to heat the generally explain the observed properties, with notable WD to this temperature is Equation 16: exceptions like the sub-luminous 1991 bg type of SN MR T≈7 × 10 49 ergs (16) (Leibundgut et al ., 1993). g It has also been debated whether all progenitors of SN Ia are single white dwarfs pushed over the limit. Mergers The helium layer which forms on the WD must be 8 of WDs (in a binary, for e.g., white dwarf binaries with 5 heated to a temperature of 2×10 K to trigger helium min orbital periods are known) could give rise to SN Ia burning. The height of the layer (on the WD) required to (Webbink, 1984; Iben and Tutukov, 1984). heat the helium to this Temperature (THe ) can be However some calculations did not result in an obtained from Equation 1 as h∼3×10 7cm . The mass of explosion (Stritzinger et al ., 2006; Saio and Nomoto, the He layer is Equation 17: 1985). More recently it was suggested that merger of =π2 ρ ≈ × 31 equal mass WDs could lead to sub-luminous explosions M4 Rh 210 g ~0.01 M sun (17) (Pakmor et al ., 2010). Again in such sub-luminous explosions, the C-O nuclei would not be expected to be As the helium nuclear reaction releases completely converted to mostly Ni-56. For instance ∼3×10 18 ergs/g , the detonation of the helium layer (on isotopes like Ti-50, are supposed to be primarily reaching its reaction temperature) would release an produced in such so called sub-Chandrasekhar SN Ia energy of ∼6×10 49 ergs , which is sufficient to heat the C- (Hughes et al ., 2008). In such collapses electron captures WD, to the required temperature for carbon burning. So may dominate to produce neutron rich nuclei like Ti-50. this double detonation mechanism, first of the helium

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C. Sivaram et al . / Physics International 5 (1): 36-44, 2014 layer accumulating on the WD and followed by energy (this is equivalent to one Hiroshima bomb going detonation of the sub-Chandrasekhar C-O WD, could off every second continuously for 10 years). result in a sub-luminous type Ia SN. If a of ’s mass collides with A lower mass He layer could detonate an even lower (Zhang and Sigurdsson, 2003), we can observe extreme mass C-O WD and a heavier mass He-shell can UV-soft X-ray flash for several hours and bright IR glow detonate a heavier WD. For 1.3 solar mass WD, we lasting for several thousand years. In dense stellar clusters, need a 0.1 solar mass layer, since the gravitational like , star collisions are not uncommon. 7 binding energy scales as M 3 . The origin of the blue stragglers in old stellar populations The collapse time scale for the WD is about a second is due to merging of 2 or maybe 3 MS stars of 0.8 solar but as the reactions have much shorter time scales, the mass. Perhaps about half the stars in central regions of explosions of the WD is inevitable. Our analytical results some GC’s underwent one or two collisions, over a period are in agreement with numerical calculations of other of 10 10 years (Zwart et al ., 2010). authors. (Fink et al ., 2010) In R136 cluster of Tarantula nebula, there are more 7 3.2. Collapse of ‘Super Chandrasekhar’ White than 10 stars in a region less than a . There are Dwarf many examples of celestial bodies colliding. The collision of has been studied for long. The One can also consider a situation when a white dwarf and Andromeda galaxies are approaching close to the acquires such a helium each other at ~300 km/s. They are due for collision in layer or debris from an accretion disc (or tidal disruption another 3 billion years. of a low mass object), falls onto the WD (Sivaram, White Dwarf binary with less than 5 min period 2006). The WD, in this case, which may be ‘Super merges in a few thousand years. Neutron star-white Chandrasekhar’, would collapse, but the temperature to dwarf binaries with periods, 11 and 10.8 min are also which it would be heated up (as the energy released observed which will undergo merger (Tamm and Spruit, 7 scales as M 3 ) would be substantially higher than the 2001; Chen and Li, 2006). required 7×10 8K for carbon detonation. There would also be now losses due to the photo- 4.1. Head-on Collisions neutrino process which scales at least as T8. So even if If a white dwarf smashes into a Main-Sequence (MS) the WD mass is 10% higher than the limit, the neutrino star like the Sun, we need to know the signatures. The energy loss would increase by a factor of three or more incoming velocity is ≥700 km/s . The massive 4 (T would go up by M 3 , so the loss rate would increase would compress and heat the sun. The time taken for the 11 as M ) (Sivaram, 1993). So rather than the detonated ‘smash up’ is about 5000 s (about an hour). The tidal disintegration of the WD, we would have the collapse of energy released is given by Equation 18: the WD, followed by e-capture by the heavier nuclei, leading to a neutron star. 3GM M R 8 WD sun sun ~ 10 K (18) Moreover, there is a general relativistic induced d 2 instability in the collapse of WD’s (above the mass limit). This sets in at about 250 times the Schwarzschild Due to the impact the nuclear reactions will become radius (Shapiro and Teukolsky, 1982) (i.e., at <1000 much faster. In about an hour, Sun would release 49 km). This would inevitably lead to collapse to a NS for a thermonuclear energy of about 10 ergs , as much energy 8 super-Chandrasekhar WD (rather than a nuclear as it would release in 2×10 years. On an average it will detonation induced fragmentation). be about 3×10 45 ergs/s . The instabilities would blow the sun apart in a few hours. The white dwarf being much 4. SMASHNOVA denser would continue on its way. If a white dwarf impacts a (RG), it would The phenomenon of one celestial body smashing into take about 2 months to penetrate the bloated RG. The another is quite common. This process on all scales can RG would collapse, becoming another WD. If the white be very energetic. Recent example in the is dwarfs merge, it can form a neutron star. This will that of the shoemaker-levy, that slammed into release about 10 53 ergs of binding energy. NS impacting a Jupiter (Molina and Moreno, 2000). The fragments RG or Red Super-Giant (RSG) can cause a SN outburst measuring 3 km across released 6 million megatons of first followed by collapse of NS and the in-falling

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C. Sivaram et al . / Physics International 5 (1): 36-44, 2014 material into a black hole and hence leading to GRB. NS 12C+→ 12 C 20 Ne +α ( OrC) 12 +→ 12 C 24 Mg colliding with a WR star will result in SN followed by • ρ 25 12   (21) GRB, as the core collapses to a BH. ε nuc ≈105 × × n() C frergsgs // 9  es 12 c Black holes in a certain mass range can tidally disrupt 10  a neutron star (Sivaram, 1986), leading to a 1053ergs

GRB. In the case of WD and NS close binary, the WD Where: can be tidally stretched or broken up when the separation 30 −16 T  is about RWD . CO white dwarf (close to Nch ) can detonate ≈ × r12 7 10 8  (22) due to heating. Tidal energy of the order of 10 50 ergs can C 7× 10  heat WD to about 10 9K. ρ 2.4− 7 This is enough to detonate C and this can hence lead 3  T  f ≈ 10    (23) to a SN. Enough material falls on NS at velocities greater es 109  710× 8  than about 10% the . About 5×1032 g of matter falling in has a kinetic energy of ∼10 52 ergs . On Therefore, we have Equation 24: impact, gamma rays of nuclei energy ≥1MeV is released 52 • 23ρ 3.3 with more than 10 ergs in γ-ray photons. 13 T   ε nuc ≈310 ×    ergs // g s (24) Neutron stars can be spun up and the flux squeezing 7× 108  10 9  can increase the magnetic field. When NS slows down due to dipole radiation (Magnetar), in-falling matter The nuclear specific energy due to the reaction is of can make it collapse to a BH releasing more than × 17 12 12 53 the order of 5 10 n ( C) ergs/g , where, n( C) is the 10 ergs , with the acceleration of particles due to the fraction of 12 C. The specific heat is due to ions, electrons magnetic field. Tidal stretching and heating can and radiation. It is given by, (Alastuey and Jancovici, considerably increase thermonuclear (detonation) rates, 1978; Porter and Woodward, 2000; Kraichnan, 1962) especially carbon burning. This process is strongly Equation 25: dependent on the temperature. The Zeldovich number is given by Equation 19: 3Nkπ 2 k 2 4 aT 3 C=A B +ρ NYT + (25) P ρ A e 2A f  2 ρ T T− T    me c Z = crit b u  (19) mc  e T T b b  The temperature and density are given by Equation 26: where, Tcrit is the triggering temperature. Tb and Tu are the burnt and un-burnt material temperatures respectively. For a T=×7108 K ,ρ =× 210 9 g / cc (26) ze≈10, we have peaked energy generation rates. The flame speed is related to Markstein number, Therefore the specific heat is given by, which is given by Equation 20: CP ≈10 15 ergs/g 10 8K. For T = 7 ×10 8K Equation 27:

22 3.3 σ 2 -T crit  C T 7× 108  10 9  baX Fu T τ =P ≈ = b  nuc • 10    s (27) VF e (20) ρ 2 T  ε T   (Cp ) crit  24 nuc where, σ , σ are the conduction and specific heat. The pressure is given by Equation 28 to 34: b p When convecting WD reaches density of 3×10 9g/cm 3 8 4 × 4 ρ 3 and temperature of T = 7 10 K, the ignition turns critical 27   2 P= kρ3 =10  dyne / cm η = r (28) (Kuhlen et al ., 2003; Niemeyer, 1999). Nuclear energy 2× 10 9  a generation time scale is comparable to convective 1 turnover time (100 s) and order of sound travel time ~10   2 where, =k ≈ . s (over a scale height of about 500 km). Flame has a a2 3  400 km πG ρ  laminar speed and buoyancy (Khokhlov et al ., 1997); the 0 2 convection speed is of the order of 10 km/s. The material   is accelerated due to the off centre ignition. One solar () ≈4π3 ρ − 3 η 2 M r r 0 1  (29) mass can become convective Equation 21 to 23: 3 10 

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3ρ 2 ∆ ∆ 1 2  gl C PT ρ()r = ρ1 − η  () Polytropic index (30) Ra ≈P ≈ 10 24 (42) 0 2  Tησ

( ) Ql 12 dP GM r Nu = ≈ 10 (43) = − ρ ()r (31) σ∆ dr r 2 T

−3 Kolmogorov length is given by: lRe4 ≈ 10 −3 cm . dT1  T dP =1 −  (32) Effect due to tidal stretching (change of area) is drΓ  Pdr quantified by the Karlovitz number, which is given by Equation 44: 2 3 2  − ρ   () = −2 r − 1 η 2  T r T 0 1 10  1  (33) dA Ax()− Ax () 1 dA 2× 109  10 7 15   k= =u b ≅ t (44)   a f A Ax(u ) Adx

• ρ 4.3 where, t is the flame thickness Equation 45: =π ε ρ 2 = 45   f L4∫ r dr 10 ergs / s 9  nuc 2× 10  (34)   23 2 =o +1 − Ze (45) T  r VF V F 1 ( 1) ka  ()− () t l L 2  8 ∫ 7 1 f n e 7× 10  10

where, L e is the Lewis number Equation 46: The size of the region (Timmes, 2000) is about 150 ρ × 9 =0 ( + ) (46) km with density = 2 10 g/cc . For a recent review of VFl VFl 1Mk a a the parameters see Hillebrandt and Niemeyer (2000). The heat flux is Equation 35 to 37: Change in the flame speed causes several flame instabilities (Reinecke et al., 2002). The Landau- C( r ) ρ Darrieus instability gives us a mechanism for the Qr() = = vCT ∆ (35) 4π r 2 2 conv P accelerating burning rate of detonation in a white ρ dwarf. For a density ratio r = u , the growth rate is ρ 1 1 3 b 2g∆ρ  2 1  4 ε rPL  =2 ≈ (36) vconv   t   given by Equation 47: ρ  3C T P   rkV0 r 2 + r − 1   exp Fl  +kt M() kt Ma +−+ 2α 1 kt M   (47) 1 1 1 + faf fa 2Q2 T  3  710× 8  3  L  3  r1  r   ∆T ≈  ≈ 50 km / s   (37) ρ 2 2 ∆ 45  CglPP   T  10  Consider the reaction 12 C+12 C (Clayton, 1984;

Caughlan and Fowler, 1988; Niemeyer et al., 1996) The conduction Equation 38 to 43: Equation (48 and 49):

3 4acT dX 1 σ = (38) C = − X2ρ N λ (48) ρk dt 12 C A

5 9 ρ   10   9 6 η = ≈ 10g / cm / s (39) λ T9 crit −85 −  9  =×26 1 × −× 3 3 (49) Z 10  N A 5103 exp 1 2.210 T 9  T 2T 3  9 91crit  ρv l Re≈conv = 10 14 (40) η T 12 where, T = and XC is the mass fraction of C. 9 10 9 24 C η − For each Mg nucleus created, 13.9 MeV is released. Pr≈P ≈ 10 2 (41) σ The reactions would proceed further as:

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24Mg(α , γ ) 28 Si ,... GRB. We can classify the various scenarios as arising 28Si+ 28 Si → Ni 56 from the following impact possibilities or impact 28Si+ 28 Si → Ni 56 types in Table 1 . There are 28 different possibilities. 4.2. Possible Formation of Quark Star Let the of the colliding bodies are M 1 and M 2 such that, M 1>>> M 2, with radii, R 1 and R 2. The glancing The NS can also shrink to a Quark Star (QS) by R event problem ≈ 2 accretion of impacting white dwarf fragments. Accretion R rate of the corresponding fall back material is given by, 1 The energy is given by Equation 55: (Priceand Rosswog, 2006) Equation 50:

GM M 3 1 E ≈ 1 2 (55) ρ  R  2  M  2 R ≈ 29 acc (50) 1 m& 10 g / s 7      10g / cc   10 km   1.4 M sun  And the velocity Equation 56 to 58: where, ρacc is the density of accreted matter. The rotational period of a newly formed NS (or QS) is 1 M  2 of the order of 1-2ms. The magnetic field is of the order of v≈ 600km / s sun  (56) R  10 13 -10 15 . Light cylinder Radius is given by Equation 51: sun c≈10 − 50 km / s s c P  R= = 95 km   (51) R L Ω 2ms  The shock crossing time is given by: 2 ≈ t c s s

Magnetospheric radius (R mag ) is obtained from the dEE Mr   relation, Ram pressure of infalling matter ≅ magnetic field ≈ ≈ 1048 erg / sec sun  sun  (57) dtt rc pressure. The slow down due to the magnetic dipole s sun  s  emission causes collapse of NS to BH. During this process 1 jets are emitted along the rotational axes Equation 52: ηL  4 T = Edd  (58) PK π2 σ 4 R L  2   7 4 B2 R 6   B  7 R = = mag 1  15  Table 1. Various scenarios arising from different impact   10 G  (52) 2m& (2 GM ) 2  possibilities 2 12 1 29 Impact possibilities Result 10gs /  7  R 7 1.5 M  7    sun  60 km WD hits Red Giant (RSG) WD + WD m10 km  M  &  WD + Disk +WD NS or BH + Disk + WD The co-rotation radius RCO is Equation 53: RSG → SN NS hits RG NS 1 2   3 3 NS or BH + Disk+ = M P  (53) RCO 30 km     → 1.4Msun   2 ms  NS hits RSG RSG SN NS or BH + Disk + WD 4.3. Propeller Regime NS hits NS NS or BH + Disk NS hits WD NS or BH + Disk In falling material may be accelerated and hence Canonical → NS hits NS NS or BH + Disk carries away angular momentum (10 30 grams carrying WD hits WD NS away 10 50 ergs in ten seconds) (Lattimer and Prakash, WD hits MS WD 2004) Equation 54: MS hits MS (Depending on mass) WD + WD NS + NS 2 BH       47 m& Rmag 2 ms 52 J& =10 erg      ≈ 10 ergs (54) MS hits RSG WD + WD prop 1029 g / s 60 ρ     0  MS hits RG NS + NS SG hits SG The rotational energy carried away in jets is of the SG hits RG order of 10 52 ergs, sufficient to power a short duration RG hits RG

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The mass of material ejected on impact is given by Hillebrandt, W. and J.C. Niemeyer, 2000. Type IA (Sills, 2001; Hurley and Shar, 2002) Equation 59 and 60: supernova explosion models. Annual Rev. Astrophys., 38: 191-230. DOI: 1  0.48 m V 2 ρ  3  10.1146/annurev.astro.38.1.191 ej≅ imp tar  (59) 0.1    Hoyle, F. and W.A. Fowler, 1960. Nucleosynthesis in m0 8 m imp     supernovae. Astrophysical J., 132: 565-590. DOI: 10.1086/146963 0.2 1.2 m(V)> ρ  V  esc ≈ 0.1 imp   (60) Hughes, G.L., B.K. Gibson1, L. Carigi1, P. Sanchez- mρ V imp tar  esc  Blazquez and J.M. Chavez, 2008. The evolution of carbon, sulphur and titanium isotopes from high The above equations follow from Impact theory (to redshift to the local . Monthly Notices obtain this the Hertz theory of impact may be used). Royal Astronomical Society, 390: 1710-1718. DOI: 10.1111/j.1365-2966.2008.13870.x 5. CONCLUSION Hurley, J.R. and M.M. Shara, 2002. The promiscuous In this study we have looked at the possibilities of of stars in clusters. Astrophys. J., 570: 184- nuclear detonation around stellar remnants and its 189. DOI: 10.1086/339495 consequences. We have considered the possibility of Iben, I.J. and A.V. Tutukov, 1984. Supernovae of type I being produced by sub-Chandrasekhar as end products of the evolution of binaries with and super-Chandrasekhar WD’s, rather than only the components of moderate initial mass (M not greater canonical limiting mass white dwarf. The energetics than about 9 solar masses). Astrophys. J. involved that could make such scenarios plausible agrees Supplement Series, 54: 335-372. DOI: with the numerical analysis. We also propose a new 10.1086/190932 model (Smashnova model), where a supernova is Kasen, D., F.K. Ropke and S.E. Woosley, 2009. The followed by a gamma ray burst. The material falling on diversity of type Ia supernovae from broken to the neutron star at relativistic velocities cause its symmetries. Nature, 460: 869-872. DOI: collapse to a magnetar or quark star or black hole leading 10.1038/nature08256 to a gamma ray burst. Also other variations of possible ‘smash-ups’ and their dynamics are analysed. Khokhlov, A.M, E.S. Oran and J.C. Wheeler, 1997. Deflagration-to-detonation transition in 6. REFERENCES thermonuclear supernovae. Astrophysical J., 478: 678-688. DOI: 10.1086/303815 Alastuey, A. and B. Jancovici, 1978. Nuclear reaction Kraichnan, R.H., 1962. Turbulent thermal convection at rate enhancement in dense stellar matter. Astrophys. arbitrary prandtl number. Physics Fluids, 5: 1374- J., 226: 1034-1040. DOI: 10.1086/156681 1389. DOI: 10.1063/1.1706533 Caughlan, G.R. and W.A. Fowler. 1988. Thermonuclear Kuhlen, M., W.E. Woosley and G.A. Glatzmaier, 2003. reaction rates V. Atomic Data Nuclear Data Tables, 3D Anelastic Simulations of Convection in Massive 40: 283-334. DOI: 10.1016/0092-640X(88)90009-5 Stars. 3D Stellar Evolution; Astronomical Society Chen, W.C. and X.D. Li, 2006. Why the braking indices Pacific Conference Series, 293: 147-156. of young are less than 3? Astronomy Lattimer, J.M. and M. Prakash, 2004. The physics of Astrophys., 450: L1-L4. DOI: 10.1051/0004- neutron stars. Science J., 304: 536-542. DOI: 6361:200600019 10.1126/science.1090720 Clayton, D.D., 1968.1984. Principles of Stellar Evolution and Nucleosynthesis. 2 Edn., University of Chicago Leibundgut, B., K.P. Robert, Phillips, M. Mark and Press, Chicago. ISBN-10: 0226109526, pp: 612. Wells et al ., 1993. SN 1991bg: A type Ia supernova Fink, M., F.K. Ropke, W. Hillebrandt, I.R. Seitenzahl with a difference. Astronomical J., 105: 301-313. and S.A. Sim et al ., 2010. Double-detonation sub- DOI: 10.1086/116427 Chandrasekhar supernovae: Can minimum helium Mazzali, P.A., F.K. Ropke, S. Benetti and W. shell masses detonate the core? Astronomy Hillebrandt, 2007. A common explosion mechanism Astrophys., 514: A53-A62. DOI: 10.1051/0004- for type Ia supernovae. Science, 315: 825-828. DOI: 6361/200913892 10.1126/science.1136259

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C. Sivaram et al . / Physics International 5 (1): 36-44, 2014

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