Advective disk paradigm of black hole accretion includes self-consistent
formation of shocks and outflows from post-shock region. We apply this paradigm
to understand rich variation of the light curve of the black hole candidate
GRS1915+105. We propose that out of five possible {\it fundamental states} the
black hole candidate GRS1915+105 moves around among three of them creating all
possible observed light curves.Comment: Latex file and four figures. Indian Journal of Physics (in press

Chakrabarti, Sandip K

Nandi, Anuj

arXiv

IACS Institutional Repository

Indian J. Phys. 75B (1), 1 -4  (2001)U P  Ban intemational journalFundamental states of accretion/jet configuration and the black holecandidate GRS1915+105Sandip K Chakrabarti'* and Anuj NandiS N Bose National Centre for Basic Sciences, JD Block, Salt l^ke, Sector-Ill, Calcutta-700 09H, India E-mail . chakraba@boson.bose.ress.in, anuj @ boson bose.res.inReceived 24 October 2000, accepted 30 November 2000Abstract ' Advective disk paradigm of black hole accretion includes self-consistent formation of shocks and outtlows from posUshock region We apply this paradigm to understand rich variation of the light curve of the black hole candidate GRS191S+105. We propose that out of five possible fundamental staiex tlie black hole candidate GRS1915i'105 moves around among three of them creating all possible observed lightcur\'esKeywords ; Black holes, X~ray sources, stars : individual (ORS19IS 1 1 OS)PAf'S Nos. 04.70 -s, 97 OO.U, 9K 70.Qy1. IntroductionChakrabarti [1,2] pointed oul that considerable amount of oultlow could be generated from the centrifugal pressure supported boundary layer (CENBOL) of a black hole. Indeed, it was shown that when the shock is weak (compression ratio R ^ the outflow must be negligible and when the shock is strong {R ~ 4 -  7), the outflow is small but non-negligiblc. However, for the intermediate shock strength (R ~ 2 -  3), the outflow rate is very large—close fo thirty percent of the inflow rate. Subsequently, Chakrabarti |3] showed that the slope of the hard-tail of the spectrum of a black hole must become larger in presence of outflows from the CENBOL region and conversely, if external matter IS added to CENBOL for the same intensity of soft photons (from the Kcplcnan disk), the spcaral slope must become smaller. In other words, hard-state spectrum should be softened and soft-state spectrum should be hardened. This has also been observed to be the case [4].Another important phenomenon involving outflow is its periodic cooling by Compton scattering. When the outflow rate is large, the slowly moving subsonic region could be catastrophically cooled down by soft photons from theKeplerian disk |3,51, The sonic surface of the cooler outflow conics closer to the black hole horizon and the flow separates into two parts. Matter from the region above the new sonic sphere separates supersonically as blobs, and matter below the new sonic sphere returns back to the accretion disk. This causes enhancement of accretion rates of the disk temporarily in a very short time-scale and could produce interesting temporal variation of the photon flux.Meanwhile, Bclloni et al (6] (hereafter B2000) and Nandi et al [7] (herciiftcr N 2000) classified all possible types of light curves of a very e.xciting black hole candidate GRS1915+105. B2000 divided the light curves in twelve types (termed as A ® P)N2000 divided the light curves in four fundamental classes (Hard, Soft, Semi-Soft and Intermediate). B2000 mentioned that from the spectral point of view, however, one could imagine that there arc three types of States \ A. B and C combining which these light curves could be generated. In the present Rapid Communication, wc claim that existence of these fundamental states cannot be understood by a standard Keplerian disk model and can be easily understood from the advective disk paradigm. In the next Section, we^Corresponding Author' Also, Honorary Scientist at Centre for Space Physics, 114/V/lA, Raja S. C. MulUck Road, K.olkaU-700 047, IndiaO 2001 lACSSandip K Chakrabarti and Anuj Nandip resen t the b ack b o n e  so lu tions o f  the  ad v ectiv e  d isk . In §3, w e d iscuss five fundam en tal sta tes w hich  are  fo rm ed  ou t o f  these  back b o n e  so lu tion  and  show  tha t the sta tes A, B and  C o f  the  b lack  ho le  can d id a te  G R S I 9 1 5 4 105 [6 ] co m p rise  th ree  o f  them  F inally  in §4, w e draw  ou r co n c lu s io n s.2. B a c k b o n e  so lu tio n s  o f  a d v e c tiv e  a c c re t io nE qu atio n s g o v ern in g  ad v ectiv e  accre tio n  d isks in p seu d o - N ew ton ian  g eo m etry  and in K err g eo m etry  w ere  p resen ted  e lsew here  and w ill no t be rep ea led  here [8 ,9]. It is o b se rv ed  tha t there are a to ta l o f  e igh t d iffcrerlt types o f  .solutions [9] w hich are d en o ted  as0  : F low  p ass in g  th ro u g h  the o u te r son ic  po in t only .1 : F low  p ass in g  th rough  the inner son ic  p o in t only.SA : f low has tw o sadd le  type son ic  po in ts, and a .steadyshock  f o r m s jn  accre tio n .NSA Sam e as SA but no s tead y  shocks can  form . S hocks are o sc illa lo iySW  . Sam e as SA but s tead y  sh o ck s form  on ly  in w inds. N S W  . Sam e as SW  but o sc illa to ry  sho ck s Ib m i in w inds. /* Incom ple te  so lu tion  w ith in n er .sonic po in t.()* : In co m p le te  so lu tio n  w ith ou ter son ic  po in t.In F igure  I, one so lu tion  (in  K err g eo m etry ) from  each  type is show n in M ach n u m b er fv -ax is) v.v lo g ( r)  (x-axi.s)Figure 1. All possible rcprcsciUative solutions of an inviscid advective flow (A ll) and Uic nelure ol ihc disk-jcl syMcm (a-h) In the solutions, Mach numbers fv a\is) are plotted agamsi logaiilhinic radial distance (a- axis)plane. Vectical equilibrium and axi-symmetry have been assumed. For each of lha solutions, we also present the schematic diagram of the nature of the flow. Transverse thickness is estimated from the assumption of vertical equilibrium h -  ar^ \^r -  1), where r is the radial distance in units of Schwarzschild radius (A/j§ is theblack hole mass and G and c are the gravitational constant and velocity of light respectively.). One notes that close to the black hole, matter is puffed up since its temperature is higher. Non-steady solutions have been represented by turbulence [in (^) and (A)].When viscosity is added, closed topology of the solutions shown above open up [8J and the flow can join with a Keplerian disk. The specific energy of a Keplerian flow is :I , . 12(r-1)’ (')w h ere  n is th e  p o ly tro p ic  c o n s tan t, v is th e  ra d ia l v e lo c ity , a is the  so u n d  v e lo c ity  an d  A is th e  sp e c if ic  angujiar m o m en tu m  re sp ec tiv e ly . F o r a c o o le r  flow , £ is n e g a tiv e , But fo r a h o tte r flow , p a rtic u la rly  aw ay  fro m  th e  e q u a to r ia l plaice (so  th a t the last te rm  in eq. ( I )  is sm all), th e  e n e rg y  c o u ld  be p o sitiv e  In case  m a tte r  b rin g s  in m a g n e tic  fie ld , it^  d is s ip a tio n  w o u ld  ra ise  th e  en e rg y  to  a  p o s itiv e  v a lu e  so  th a t sh o ck s m ay  fo rm  in a s tead y  flow . In a n o n -s te a d y  flo w , su ch  re s tr ic tio n s  do  n o t ap p ly  an d  o sc illa tin g  sh o c k s  m ay  fo rm  ev en  w ith b o u n d  flo w s [ 1 0 , 1 1 1 .M1.0MJ^01(a)Optically thick Winds i  Shocke^  OpIlMlIythin'X  ' 0 ) Optically thin (b) Optically thicklog(r)Figure 2. Same as Figure 1 bul for a viscou.s flow (a) Viscosity smaller than ihe critical value and (b) larger than the critical valueFigure 2 shows representative solutions in a viscous flow and how a realistic disk looks like. In (a), flow viscosity is smaller than the critical value [8] and shocks can form and outflows are produced from CENBOL as in Figure 1. In (b), flow viscosity is higher than the critical value [8] and there are two solutions : one is mostly Keplerian (optically thick) till it passes through the inner sonic point, and the other is Keplerian farther out iind pas^s through the outer sonic point. This is the optically thiif branch of the solution.Fundamental states o f accretion/jet configuration etc3. Fundamental states of a realistic accretion flowO ne co u ld  c o m b in e  so lu tio n s  in  l ( a - h )  an d  2 ( a - b )  to  o b ta in  realistic  acc re tio n -w in d  sy s tem s a ro u n d  a  b lack  h o le . V isco sity  is c o n s id e re d  to  b e  h ig h  in th e  e q u a to r ia l p la n e  a n d  sm a lle r  aw ay  fro m  th e  p la n e . F ro m  F ig u re  2 (b )  e q u a to r ia l flo w  w ill be K ep le rian  c lo s e r  to  th e  b la c k  h o le , an d  so lu tio n s  o f  F ig u re  2 (a ) w o u ld  c o v e r  a b o v e  a n d  b e lo w . T h e re  a re  sev era l p o ss ib ilitie s  fo r  re a s o n a b le  p a ra m e te rs  o f  a b lack  ho le  acc re tio n . W e n a m e  th e se  s ta te s  a c c o rd in g  to  th e  w a y  th ey  are c o m m o n ly  p e rc e iv e d  in th e  lite ra tu re .(i) Hard state :1 l i e  a c c re tio n  ra te  (in  u n its  o f  E d d in g to n  ra te )  in th e  K ep lerian  c o m p o n e n t is low  -  0 .0 0 1 -  0.1 an d  th a t  o f  the  su b -K e p le r ia n  c o m p o n e n t is h ig h  aV, --1 - T h e  c o m b in e d  su b -K ep le rian  f lo w  en te rs  in to  th e  b la c k  h o le  w ith o u t fo rm in g  a sh o ck . F ig u re  3 (a )  sh o w s th e  sc h e m a tic  d iag ram  o f  th e  a cc rc tio n -w in d  sy s tem . Spectral signature; H ard  stale  w ith o u t q u a s i-p c rio d ic  o sc illa tio n  o f  X -ray s . I f  sh o ck s  fo rm  an d  o sc illa te . Q u as i P e rio d ic  O sc il la t io n s  (Q P O s) c o u ld  be o b se rv ed . ’wrtnda •nd W Uiif up u< Muic ^ phai«Fif^ure 3 . Fundamental States of the black hole accretion-jct system obtained by combining backbone solutions of Figure 1 and Figure 2 (a)I liird State, (b) Off State, (c) Dip State, (d) On State and (e) Soft State(^ 0 Off stateT he a c c re tio n  ra te s  a re  s im ila r  a s  a b o v e , b u t v isco sity  is lo w er th a n  th e  c r itic a l a  < 0 .01  ( a  is  th e  S h a k u ra -S u n y a e v  [ 12] v isc o s ity  p a ra m e te r )  so  th a t  sh o c k s  m a y  fo rm . I f  c o o lin g  rale in th e  p o s t-s h o c k  re g io n  ro u g h ly  a g re e s  w ith  th e  in flow  rate, q u a s i-p e r io d ic  o sc i lla tio n  o f  X -ra y s  c o u ld  b e  seen .O u tflo w  is p ro d u c e d  w h ich  in te rc e p ts  so f t p h o to n s  fro m  K ep le rian  d isk . F ig u re  3 (b ) sh o w s th a t sc h e m a tic  d ia g ra m . Spectral signature . h a rd  s ta te  w ith  Q P O . W ith  tim e , th e  sp ec tru m  can  g e t so f te r  i f  th e  so n ic  sp h e re  (re g io n  till th e  so n ic  p o in t in th e  o u tf lo w ) g e ts  filled  u p  g ra d u a lly .(Hi) Dip state :K ep le rian  acc re tio n  ra tes  a re  h ig h e r  X/., -  O.I -  0 .3  a n d  v isco sity  IS a lso  h ig h e r a  > 0 . 0 1  o r  m o re  so  th a t sh o c k s  a re  w e a k e r .  P o s t - s h o c k  f lo w  is p a r t ly  c o o le d  d u e  to  C o m p to n iz a tio n . O u tflo w  till th e  so n ic  sp h e re  h a s  su ff ic ie n t o p tica l d ep th  th a t it is c o o le d  by  C o m p to n iz a tio n . T h e  so n ic  p o in t co m es d o w n  as so u n d  sp eed  g o e s  d o w n  in th is  reg io n . F low  w h ich  rem a in s  su b -so n ic  w ith  re sp e c t to  th is  so n ic  sp h ere  lo ses o u tw ard  d riv e  a n d  re tu rn s  b ack  to  th e  d isk , w h ile  th e  su p e rso n ic  flow  se p a ra te s  as b lo b s  in th e  je ts . F igure 3 (c) show s the schem atic  d iagram . Spectral signature : te n d e n c y  to w a rd s  so f te r  sta te  an d  la rg e  sp e c tra l s lo p e . Q P O  m ay  n o t be v is ib le  ^s th e  sh o ck  is c o o le r  (w ith  lo n g e r  c o o lin g  tim e  sca le ) w h ile  in fa ll tim e  is sh o r te r  s in ce  th e  K ep le rian  d isk  m o v es  in w ard  d u e  to  la rg e r v isco s ity .(iv) On state :O rig in a l flow  m ay  re m a in  s im ila r  to  a b o v e , b u t th e  re tu rn  flow  en h a n c e s  bo th  K ep le rian  an d  su b -K e p le r ia n  d isk  ra tes  last few  h u n d red  S c h w a rz sc h ild  rad ii. F ig u re  3 (d )  sh o w s th e  sch em a tic  d iag ram . D u ra tio n  o f  th is  s ta te  is th e  d u ra tio n  o f  d ra in ag e  o f  th e  e x cess  ac c re tio n  from  re tu rn  f lo w . Spectral signature : so f te r  s ta te  w ith  h ig h  p h o to n  flux . Q P O  is ab sen t.(v) Soft state .A c c re tio n  ra te  o f  th e  K ep le rian  c o m p o n e n t is h ig h  -0 .3 and  th e  v isco sity  is h ig h  en o u g h  so  th a t K e p le ria n  d isk  m o v e s  in all th e  w ay  to  th e  in n e r ed g e  o f  the  d isk  (F ig u re  2b). M a tte r m o v es a lm o st rad ia lly  a n d  tran sfe rs  its m o m e n tu m  to  so ft p h o to n s  (bu lk  m o tio n  C o m p to n iz a tio n  [1 3 ]). F ig u re  3 (e ) sh o w s th e  sch em a tic  d iag ram . Spectral signature : so ft sta te  sp ec tru m  w ith o u t Q P O  w ith  a  w e a k  p o w e r- la w  h a rd - tailC o lo r-C o lo r  d ia g ra m s [H R I vs H R 2  d ia g ra m s  w h e re  H R l == h/a an d  H R 2 = cla {a \ 2 -  5 k eV , h : 5 -  ]3 k eV , c : 1 3 - 6 0  k eV )] sh o w ed  v e ry  in tr ic a te  s tru c tu re s  (s h a p e s  o f  a to ll, b an an a , etc.) [6 ]. F rom  th ese , B 2 0 0 0  c o n c lu d e  th a t th e re  a re  th ree  d is tin c t S ta le s  o f  G R S  1915 +  105 : A ( lo w  ra te  an d  low  H R  I , H R 2 ), B (h ig h  ra te , h ig h  H R  1) an d  C  (lo w  ra te , low  H R  I, v a ria b le  H R 2  d e p e n d in g  on  len g th  o f  th e  ev en t) . A c c o rd in g  to  c la s s if ic a tio n s  o f  N a n d i et al [7 ], th is  w o u ld  co rre sp o n d  to  d if fe re n t re g io n s  in th e  so f tn e ss  ra tio  d iag ram . It seem s th a t th e  S ta te  C  e x h ib its  Q P O . S ta te  A an d  S ta te  B d o  n o t ex l\ib it Q P O . M o re  in te re s tin g ly , e x c e p t fo r  C ->  B tran s itio n , a l l  o th e r  tra n s it io n s  o f  s ta te s  a re  a llo w ed . N a n d i et a l[\4 ]  fo u n d  e v id e n c e  o f  Q P O  in in te rm itta n t s ta te  C  w h ich  are  e m b e d d e d  in sta te  B.Sandip K Chakrabarti and Antf/ NandiA co m p ariso n  o f  th e  d e sc r ip tio n  o f  th e  S ta tes  g iv en  a b o v e  an d  th e  d esc r ip tio n  o f  th e  fu n d am en ta l S ta tes  ( 1 - 5 ) ,  it seem s that, fo r G R S I 9 I 5 + I 0 5 ,  d a ta  o b ta in ed  so fa r  su g g es ts  th a t th e  fu n d am en ta l s ta tes  I an d  5 are m issin g , S ta tes  2 - 4  can  be  iden tified  w ith  S ta tes C\ A an d  B o f  B 20 0 0  re sp ec tiv e ly . O n e  can  u n d e rs tan d  a  ty p ica l ev o lu tio n  o f  S ta tes  in th e  fo llo w in g  w ay  S u p p o se  w e sta rt w ith  th e  S ta te  2 d e sc r ib e d  above . I f  th e  acc re tio n  ra te  is g en e ra lly  in c reased , sh o ck  is w eak en ed  (c o m p re ss io n  ra tio  g o es  d o w n ). T h e re  c o u ld  b e  tw o  ty p es o f  h ig h  c o u n t s ta tes (S ta te  3 [D ip ] an d  S ta te  4 [O n]), A fte r th e  w in d s  o f  S ta te  2 fills  in th e  so n ic  sp h e re  and  co o ls  it d o w n  b y  C o m p to n iz a tio n , C E N B O L  an d  th e  reg io n  till th e  so n ic  sp h ere  co llap se . T h is  is th e  S ta te  3. N o w  th e re  a rc  tw o  p o ss ib ilitie s  [5 ] :  c ith e r th e  flo w  se p a ra te s  c o m p le te ly  as a b lo b  an d  re tu rn s  to S ta te  2 o r  th e  flo w  m o s tly  re tu rn s  back  to  the acc re tio n  d isk  and  en h a n c e s  th e  ac c re tio n . T h is  w o u ld  be th e  S ta te  4 T h is  m ay  in tu rn  in c rease  th e  o u tf lo w[1,2]. B ut sh o ck  b eco m e s w e a k e r b ecau se  o f  p o s t-sh o c k  co o lin g , hen ce  th e  o u tf lo w  is v e ry  m ild , b u t m ay  re m a in  a t th e  th re sh o ld  so  th a t a b it m o te  o u tf lo w  can  cau se  th e  so n ic  sp h ere  to  c o llap se  ag a in . T h u s, o c c a s io n a l tr ip s  to  S ta te  3 from  S ta te  4 is p o ss ib le . T h is  is reg u la rly  o b se rv e d  [6 ]. O n c e  th e  en h an ced  m a tte r is d ra in ed  o u t an d  th e  sh o ck  b o u n c e s  back  to  ro u g h ly  th e  o rig in a l lo ca tio n  (c o m p a tib le  w ith  its sp ec ific  en erg y  an d  a n g u la r  m o m en tu m ), S ta te  2 fo rm s ag a in . S in ce  S ta te  2 p ro d u ce  few er so ft p h o to n s . S ta te  4 is no t d irec tly  p o ss ib le  from  S ta te  2 w ith o u t firs t p ro d u c in g  re tu rn  flow  an d  e n h an ced  acc re tio n . T h is  m ay  ex p la in  w h y  a d irec t tran s itio n  from  S ta te  2 to  S ta te  4 is no t seen  [6 ].It is c le a r  th a t th e  c o m p le x  b e h a v io u r  o f  G R S I 9 1 5 + 1 0 5  n ecessa rily  re q u ire s  b o th  K ep le rian  an d  su b -K e p le ria n  d isk s  fo r a p ro p e r ex p la n a tio n  o f  th e  ligh t cu rv e . T h e  re tu rn -f lo w  from  th e  c o o le r  w in d  ac ts  as  a n o n lin e a r  fe e d b a c k  w h ich  can  be rep re sen ted  sc h e m a tic a lly  in F ig u re  4. H ere ,M n ’ H u ll M/ih '■epresents K ep le rian  ac c re tio n  ra te , su b -K ep le rian  acc re tio n  ra te , to ta l a cc re tio n  ra te , ra teof return flow outflow rate and the rate of actual accretion to the black hole respectively. The soft photon intensity Sy intercepted by the sonic sphere and the CENBOL is a function of the Keplerian rate.4. Concluding remarksWe have presented the fundamental states of a viscous advective disk which includes radiative transfer. We identify that trips through States 2-4 cause the variable light curves in GRS 1915+105. Outflow seems to be a determining factor in switching these states. Numerical simulations showed existence of such outflows [15]. We already noted that the spectral states are related to the outflow rates [5]. Observations also suggest such a possibility [16,17]. We believe that non­linear feed-back from the outflowing wind is essential to understand the variable light curves observed in this black hole candidate. Detailed modeling of these light curves would be presented elsewhere.AcknowledgmentThis project is partly supported by a DST grant No. SP/S2/ K - 14/98.References^ipure 4. 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Fundamental States of Accretion/Jet Configuration and the Black Hole Candidate GRS1915+105

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Fundamental States of Accretion/Jet Configuration and the Black Hole Candidate GRS1915+105

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