Study of nucleosynthesis in accretion disks around black holes was initiated
by Chakrabarti et al. (1987). In the present work we do the similar analysis
using the state-of-the-art disk model, namely, Advective Accretion Disks.
During the infall, matter temperature and density are generally increased which
are first computed. These quantities are used to obtain local changes in
composition, amount of nuclear energy released or absorbed, etc. under various
inflow conditions. In the cases where the magnetic viscosity is dominant
neutron torus may be formed. We also talk about the fate of Li^7 and D during
the accretion. The outflowing winds from the disk could carry the new isotopes
produced by nucleosynthesis and contaminate the surroundings. From the degree
of contamination, one could pinpoint the inflow parameters.Comment: 9 Latex pages and 2 Figures. crckapb.st

Mukhopadhyay, Banibrata

English

arXiv

IACS Institutional Repository

Indian J. Phys. 73B  (6 ), 9 17 -924  (1999)U P  B— an international journalN u cleo sy n th esis  around black holesBanibrata MukhopadhyayTheoretical Astrophysics Group,S. N. Bose National Centre For Basic Sciences JD Block, Salt Lake, Sector-Ill, Calcutta-700091, Indiae-mail: bm@boson.bose.res.inA b s t r a c t .  Study of nucleosynthesis in accretion disks around black holes was ini­tiated by C hakrabarti et al. (1987). In the present work we do the similar analysis using the state-of-the-art disk model, namely, Advective Accretion Disks. During the infall, m atter tem perature and density are generally increased which are first com­puted. These quantities are used to obtain local changes in composition, amount of nuclear energy released or absorbed, etc. under various inflow conditions. In the cases where the magnetic viscosity is dominant neutron torus may be formed. We also talk about the fate of Li7 and D during the accretion. The outflowing winds from the disk could carry the new isotopes produced by nucleosynthesis and contaminate the surroundings. From the degree of contamination, one could pinpoint the inflow parameters.K ey w o rd s  : Accretion, black holes, nuclear astrophysics, origin and abundance of elementsPA C S N os. : 97.10.Gz, 04.70.-s, 98.80.Ft, #8.01. IntroductionT here a re  m any  observational evidences where the incoming m atte r has the p o ten tia l to  becom e as ho t as its virial tem perature  Tviriai ~  1013 h  [1]. T hrough  various cooling effects, th is incoming m atter is usually cooled down to  p roduce  h a rd  an d  soft s ta te s  [2]. In the accretion disk, m atter in the sub- K eplerian region generally  rem ains ho tte r than  Keplerian disks. 1 he m atter is so h o t th a t  a f te r  b ig-bang nucleosynthesis this is the most fevourable tem ­p e ra tu re  to  p roduce  significant nuclear reactions. The energy generation due to  nucleosynthesis could be high enough to  destabilize the flow and the mod­ified com position  m ay  com e o u t through winds to  affect the inetallicity of the galaxy [3-7}. P rev io u s w orks on nucleosynthesis in disk was done for cooler© 1999I A C S918 Banibrata Mukhopadhyaythick accretion disks. Since the sub-Keplerian region is much hotter than of Keplerian region and also than the central temperature (~  107K) of stars, presently we are interested to study nucleosynthesis in hot sub-Keplerian re­gion of accretion disks.2. Basic equations and physical system sIn 1981 Paczynski &, Bisnovatyi-Kogan [8] initiated the study of viscous tran­sonic flow although the global solutions of advective accretion disks were obtained much later [9] which we use here. In the advective disks, matter must have radial motion which is transonic. The supersonic flow must be sub- Keplerian and therefore must deviate from a Keplerian disk away from the black hole. The basic equations which matter obeys while falling towards the black hole from the boundary between Keplerian and sub-Keplerian region are given below (for details, see, [9]):(a) The radial momentum equation:M  \d P  A2Kep -  A2 dx p dx x3 =  0,(b) The continuity equation:(la)=  0, (16)(c) The azimuthal momentum equation:0d \ ( x )dx(d) The entropy equation:_ L _ 1Ea; dx (z2WW) =  0, (lc)2napdh(x)da a2,dh(x) dp _  f/vf.j  d i  7  { ’where the equation of state is chosen as a2 =  Here, A is the specific angular momentum of the infalling matter, AKcp is that in the Keplerian region is defined as A^ep =  [l®]i £  is vertically integrated density, Wa+ is thestress tensor, a is the sound speed and h(x) is the half thickness of the disk (~  axl^2(x — 1)), n =  js the polytropic index, /  is the cooling factor which is kept constant throughout our study, Q+ is the heat generation due to the viscous effect of the disk. For the time being we are neglecting the magnetic heating term.During infall different nuclear reactions take place and nuclear energy is released. Here, our study is exploratory so in the heating term Q+, we do not include the-heating due to nuclear reactions. (Work including nuclear energyNucleosynthesis around black holes919release term is in [6].) Another parameter [i is defined as ratio of gas pressure to total pressure, which is assumed to be a constant value throughout a particular case. Actually, the factor @ is used to take into account the cooling due to Comptonization. To compute the temperature of the Comptonized flow in the advective region which may or may not have shocks, we follow Chakrabarti k  Titarchuk [2] and Chakrabarti’s [11] works and method. The temperature is computed from.r  =  ~ w ~ -  (2)It is seen that due to hotter nature of the advective disk especially when accre­tion rate is low, Compton cooling is negligible, the major process of hydrogen burning is the rapid proton capture process, which operates at T £  0.5 X 109K which is much higher than the operating temperature of PP chain (operates at T  ~  0.01 -  0.2 x 109K) and CNO cycle (operates at T ~  0.02 -  0.5 x 109K) which take place in the case of stellar nucleosynthesis where temperature is much lower. Also in stellar case, in different radii same sets of reaction take place but in the case of disk, in different radii different reactions (or different sets of reaction) can take place simultaneously. These are the basic diiferences between the nucleosynthesis in stars and disks.For simplicity, we take the solar abundance as the initial abundance of the disk and our computation starts where matter leaves a Keplerian disk. According to [2] and [11], the black hole remains in hard states when viscosity and accretion rate are smaller. In this case, xk (at radius xr matter deviates from Keplerian to sub-Keplerian region) is large. In this parameter range the protons remain hot ( Tp ~  1 -  10 X 109K). The corresponding factor / ( =  1 — Q+/Q~) is not low enough to cool down the disk, (in [1], it is indicated that, m /a 2 is a good indication of the cooling efficiency of the hot flow), where Q+ and Q~ are the heat gain and heat loss due to viscosity of the disk.We have studied a large region of parameter space with 0.0001 £  cv 1, 0.001 < m < 100, 0.01 < fi < 1, 4/3 £  7  & 5/3. We study a case with a stand­ing shock as well. In selecting the reactibn network we kept in mind the fact that hotter flows may produce heavier elements through triple-o and rapid proton and o capture processes. Furthermore due to photo-dissociation sig­nificant neutrons may be produced and there is a possibility of production of neutron rich isotopes. Thus, we consider sufficient number of isotopes on either side of the stability line. The network thus contains protons, neutrons, till ” Ge - altogether 255 nuclear species. The standard reaction rates were taken [6].3. R esultsHere we p re sen t a  typ ica l case containing a shock wave in the advective region[6]. We express the length in the unit of one Schwarzschild radius which is920 Banibrata Mukhopadhyay1 where M is the mass of the black hole, velocity is expressed in the unit of velocity of light c and the unit of time is 2GJt* ■ We use the mass of the black hole M/M@ =  10 (Mq =  solar mass), II-stress viscosity parameter an =  0.05, the location of the inner sonic point x,n =  2.8695, the value of the specific angular momentum at the inner edge of the black hole A,n =  1.6, the polytropic index 7  =  4/3  as free parameters. The net accretion rate rh — 1 in the unit of Eddington rate, cooling factor due to Comptonization ft = 0.03, xk — 481. The proton temperature (in the unit of 109), velocity distribution (in the units of 10 10 cm sec-1 ), density distribution (in the unit of 2 x 10 -8  gm cm-3 ) are shown in Fig. 1 (a).In Fig. lb, we show composition changes close to the black hole both for the shock-free branch (dotted curves) and the shocked branch of the solution (solid curves). Only prominent elements are plotted. The difference between the shocked and the shock-free cases is that, in the shock case the similar burning takes place farther away from the black hole because of much higher temperature in the post-shock region. A significant amount of the neutron (with a final abundance of Yn ~  10-3) is produced due to photo-dissociation process. Note that closer to the black hole, X2C, l^O, i4Mg and 28Si are all destroyed completely. Among the new species which are formed closer to the black hole are :i0S i , 4eT i ,  59f,V. Note that the final abundance of 20N e  is sig­nificantly higher than the initial value. Thus a significant, metallicity could be supplied by winds from the centrifugal barrier. In Fig. lc we show the change of abundance of neutron (n), deuterium (D) and lithium {7Li ) .  It is noted that near black hole a significant amount of neutron is formed although initially neutron abundance was almost zero. Also D and 7Li are totally burnt out near black hole which is against the major claim of Yi & Narayan [13] which found significant lithium in the disk. It is true that due to spallation reaction, i.e.,4He +4 He ->7Li +  p7Li may be formed in the disk but due to photo-dissociation in high temper­ature all 4He are burnt out before forming 7Li i.e. the formation rate of 4He from D is much slower than the burning rate of it. Yi & Narayan [13] do not include the possibility of photo-dissociation in the hot disk.In Fig. Id, we show nuclear energy release/absorption for the flow in in units of erg sec- 1  gm-1 . Solid curve represents the nuclear energy re­lease/absorption for the shocked flow and the dotted curve is that for unstable shock-free flow. As matter leaves the Keplerian region, the rapid proton cap­ture such as, p+l80  - * 18 N+4He etc., burn hydrogen and releases energy to the disk. At around x =  50, D —► n+p dissociates D and the endothermic reaction causes the nuclear energy release to become ‘negative’, i.e., a huge amount of energy is absorbed from the disk. At around x =  15 the energy release is again dominated by the original processes because no deuterium is left to burn. Due to excessive temperature, immediately 3Hc breaks down into deuterium andNucleosynthesis around black holes9210 . 5  1 1 .5  2  2 .5lo g (x )-2 0- 2 5J“T i' | l i i i | r-1 1 ■ j » r i i | i i i i npr■ f\ ~/ Xi j y i i v  :r \X/ (c)J111111111..1 l j j t 1-1 i 1 ■ i i i 17L in0 .5  1 1 .5  2  2 .5lo g (x )lo g (x ) lo « (x )Figure 1. Variation of (a) proton temperature (7s), radial velocity vJ0 and density distribution p-s (b) matter abundance Y  in logarithmic scale (c) neutron, deuterium and lithium abundance Y  in logarithmic scale and (d) nuclear energy release and absorption as a functions of logarithmic radial distance x. See text for parameters. Solutions in the stable branch with shocks are solid curves and those without the shock are dotted in (a-d). At the shock, temperature and density rise and velocity lower significantly and cause a significant change in abundance even farther out. Shock induced winds may cause substantial contamination of the galactic composition when parameters are chosen from these regions [6].through dissociation of D again a huge amount of energy is absorbed from the disk. It is noted that energy absorption due to photo-dissociation as well as the magnitude of the energy release due to proton capture process and that due to922 Banibrata Mukhopadhyayl o g ( x )Figure 2. The convergence of the neutron abundance through successive iterations in a very hot advective disk. From bottom to top curves 1st, 4th, 7th and 11th iteration results are shown. A neutroi* torus with a significant afc -Jidance is formed in this case [15].viscous dissipation (Q+) are very similar (save the region where endothermic reactions dominate). This suggests that even with nuclear reactions, at least some part of the advective disk may be perfectly stable.We now present another interesting case where lower accretion rate (m =0.01) but higher viscosity (0.2) were used and the efficiency of cooling is not 100% ( /  =  0.1). That means that the temperature of the flow is high (/3 =  0.1, maximum temperature T™*1 =  11). In this case xk — 8.8, if the high viscosity is due to stochastic magnetic field, protons would be drifted towards the black hole due to magnetic viscosity, but the neutrons will not be drifted [13] till they decay. This principle has been used to do the simulation in this case. The modified composition in one sweep is allowed to interact with freshly accreting matter with the understanding that the accumulated neutrons do not drift radially. After few iterations or sweeps the steady distribution of the composition may be achieved. Figure 2 shows the neutron distributions in iteration numbers 1, 4, 7 & 11 respectively (from bottom to top curves) in the advective region. The formation of a ‘neutron torus’ is very apparent in this result and generally in all the hot advective flows. In 1987 Hogan &Nucleosynthesis around black holes 923Applegate [14] showed that formation of neutron torus is possible with high accretion rate. But high accretion rate means high rate of photon to dump into sub-Keplerian region and high rate of inverse Compton process through which matter cool down, that is why photo-dissociation will be less prominent. Also formation of neutron is possible through the photo-dissociation of deuterium in the hot disk which is physically possible prominently in our parameter region, where neutron torus is formed. Details are in Chakrabarti k  Mukhopadhyay4. D iscussions and conclusionsIn this paper, we have explored the possibility of nuclear reactions in advective accretion flows around black holes. Temperature in this region is controlled by the efficiencies of bremsstrahlung and Comptonization processes [2, 7]. For a higher Keplerian rate and higher viscosity, the inner edge of the Keplerian component comes closer to the black hole and the advective region becomes cooler [2, 9]. However, as the viscosity is decreased, the inner edge of the Kep­lerian component moves away and the Compton cooling becomes less efficient.The composition changes especially in the centrifugal pressure supported denser region, where matter is hotter and slowly moving. Since centrifugal pressure supported region ran be treated as an effective surface of the black hole which may generate winds and outflows in the same way as the stellar surface, one could envisage that the winds produced in this region would carry away modified composition [16-18]. In very hot disks, a significant amount of free neutrons are produced which, while coming out through winds may re­combine with outflowing protons at a cooler environment to possibly form deuteriums. A few related questions have been asked lately: Can lithium in the universe be produced in black hole accretion [12,19]? We believe that this is not possible. When the full network is used we find that the hotter disks where spallation would have been important also heliums photo-dissociate into deuteriums and then to protons and neutrons before any significant produc­tion of lithiums. Another question is: Could the metallicity of the galaxy be explained, at least partially, by nuclear reactions? We believe that this is quite possible. Details are in [6].Another important, thing which we find that in the case of hot inflows for­mation of neutron tori is a very distinct possibility [15]. Presence of a neutron torus around a black hole would help the formation of neutron rich species as well, a process hitherto attributed to the supernovae explosions only. It can also help production of Li on the companion star surface (see [6] and references therein).The advective disks as we know today do not perfectly match with a Ke­plerian disk. The shear, i.e., dQ/dx is always very small m the advective flow compared to that of a Keplerian disk near the outer boundary of the advective924 Banibrata Mukhopadhyayregion. T hus som e im provem ents o f th e  disk model a t  the  tran sition  region is needed. Since m ajo r reactions are closer to  the  black hole, we believe th a t  such m odifications o f th e  m odel would no t change our conclusions. T he  neutrino  lum inosity in a  steady  disk is generally very sm all com pared to  the  photon lum inosity [6], b u t occasionally, i t  is seen to  be very high. In these cases, we predict th a t  the  disk would be unstab le. N eutrino lum inosity from a  cool advective disk is low.In all th e  cases, even when the nuclear com position changes are no t very significant, we no te  th a t  th e  nuclear energy release due to  exotherm ic reactions or absorp tion  o f energy due to  endotherm ic reactions is o f the  sam e order as th e  g rav ita tio n a l binding energy release. Like the energy release due to  viscous processes, nuclear energy release strongly  depends on tem pera tu res . This add itional energy source o r sink may destabilize the  flow [6].A cknow ledgm entsI would like to  th an k  Prof. Sandip K. C h ak rab a rti for in troducing  me to  th is  su b jec t and helpful discussion th ro u g h o u t the  work.R eferences1. M J Rees Ann. Rev. Astron. Astrophys. 22 471 (1984)2. S K Chakrabarti and L G Titarchuk Astrophys J. 455 623 (1995)3. S K Chakrabarti, L Jin and W D Arnett Astrophys. J . 313 674 (1987)4. L Jin, W D Arnett and S K Chakrabarti Astrophys. J. 336 572 (1989)5. S K Chakrabarti Astrophys. J .  324  391 (1988)6. B Mukhopadhyay and S K Chakrabarti Astron. Astrophys. (1999) in press7. B Mukhopadhyay in Observational Evidences for Black Holts tn the lhuverse, (Ed.) S K Chakrabarti (Dordrecht: Kluwer Academic Publishers) 105 (1998)8. B Paczynski and G Bisnovatyi-Kogan Acta Astron. 3 1 283 (1981)9. S K Chakrabarti Astrophys. J. 464 664 (1996)10. B Paczynski and P J Wiita Astron. Astrophys. 88 23 (1980)11. S K Chakrabarti Astrophys. J. 484 313 (1997)12. I Yi and R Narayan Astrophys. J. 486 383 (1997)13. M J Rees et al., Nat, 295, 17 (1982)14. C J Hogan and J H Applegate Nat 390 236 (1987)15. S K Chakrabarti and B Mukhopadhyay Astron. Astrophys. 344 105 (1999)16. S K Chakrabarti Astron. Astrophys. (1999) in press17. T K Das and S K Chakrabarti Class. Quant. Grav. (1999) in press18. T K Das in Observational Evidences for Black Holes in the Universe (Ed.) S. K. Chakrabarti (Dordrecht: Kluwer Academic Publishers) 113 (1998)19. L Jin Astrophys. J. 356 501 (1990)

Nucleosynthesis Around Black Holes

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