Chandra, Suresh

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/,* « /W y * -’™TO-6n-620(2003)/IJPB \Radiative excitation of CS molecules in atmosphere of a star*Suresh ChandraSchool of Physical Sciences, S RTM. Uiiivcrsiiy, Nandecl-431 606, Maharashtra, IndiaE-mail . surcsh492000@yahoo co inReceived 25 March 2005. a u  epied 5 September 2003Ahslracl We have invesligated radiative excitation of CS molecules in atmosphere of a cartion star Hcsidcs those of the observed lines of CSmolecule, intensities of some other lines, in the ground v = 0 as well as vibrationally excited v = I slates, are computed. Intensities of other lines arc louiul comparable to those of the observed ones, in the corresponding vibrational state, and therefore, those lines are probable candidates for their ilcictiion The lines in the vibrationally excited state, as well as between higher rotational levels in the ground vibrational slate, arc found to have a luiideiuy of their formation in the regions close to the photosphere of the star, whereas the reverse has been found for the lines between lower loiaiional levels in the ground vibrational stale|i IS tound that lines in the vibrationally excited stale cannot be generated, even in a high density and high temperature region, unless external i;ilr.iiccl r.uliation field is presentKeywords . CS molecule, radiative excitation, sleller atmosphere VM S No.s. 33 20.Vq, 33.20 Ea. 33 20.Bx, 31 20 -p1. introductionInlet .stellar C S  was discovered by Penzias e t  a l  \ \ ]  through its iransitiony = 3 —>2 in the ground vibrational state (v = 0), inO ri A, W 51, DR 21 and IR C  + 10216 astronomical objects. Since ihen, various rotational transitions of C S  have been observed Ilia number of astronomical objects. Some rotational transitions have been observed in the vibrationally excited (v = 1) state also The observed transitions of C S  are marked by putting an asterisk on the frequency in Table 1. Molecules arc found in Vibrationally excited states either near the regions of star lormaiion or in the atmosphere of an evolved star. Hence, vibrationally excited molecules may play an important role for f^ inding out physical conditions near star forming regions and in the atmosphere of an evolved star.In the present investigation, we are interested in the C S  molecules observed in the atmosphere of a carbon star. Carbon t^ars show a substantial mass-loss rate, and thus, their envelopes ‘ire expanding. Since the details of pumping processes of the 'inc.s depend on the velocity difference between the photosphereI c^Uicaied to Professor A W Joshi on the occasion of his sixtieth birth-day.of the star and the emitting volume element, intensities of the observed lines may be used as a useful tool to study the velocity field in the envelope of the star. We, in particular, have investigated the influence of the photospheric spectrum of the star on the pumping mechanism.Thbic 1. Frequency (in (iHz) of transitions of CS molecule in the ground (V = 0) and vibrationally excited (v = I) states, The observed lines arc marked by putting an asterisk on the frequency.Transition V = 0 v = 1J = 1 0 48.991* 48.636J = 2 --> 1 97.981* 97 271*J = 3 2 146 969* 145 904*J = 4 3 195.954 194.534J = 5 - > 4 244.035* 243.161*J = 6 -> 5 293.912* 291.782*J = 7 - > 6 342 883* 340.398*J = 8 7 391.847 389.007J = 9 -> 8 440.803 437.608J = 10-> 9 489 751* 486.201*© 20031A C S618 Suresh ChandraT o th e  b e s t  o u r  k n o w le d g e ,  th e r e  is  n o  th e o r e t ic a l  th c-sp o ta p p ro x im a tio n , by usin g  the e sca p e  probability methodinvestigation for the C S  molecule in atmosphere of an evolved (see, c.g., Rausch e t a l  [7]), where the external radiation field /star. However, studies for the molecules in interstellar molecular impinging on the volume element emitting the lines, has twoclouds have been done by Turner e t  a l  [2], Liszt and Linke [3] components : (i) the cosmic 2.7 K  background, and (ii) theand Marlin and Barrett [4J, Turner [5] and Highberger e t  a l  [6J. radiation coming from the photosphere of the star. Hence,2. Basic formulation and input parameters lv ,b , = (1 - / )  B , ( 2 . 1 K )  + f  (V, d v , ),Non-Local Thermal Equilibrium (N LTE) occupation numbers of where n  is the Doppler shifted photospheric flux a n d / i s  C S  molecules in atmosphere of the star arc calculated in an on- the dilution factor.f » 10-^-.1'62-7i :ItTDI "f -= 10-^1 «  1 — 0  (V  =  0 )lu ^i = (v = 0)I«3 -^2(v = 0)6-6 J 5 — 4  (V  «  0 )7-M-5- f t2 -7I -■l!-’t :H-3i = 7 - .6 < v  = n■TsCs-ILL1=*6—5(v = 0) LL—TiTn II =  7 (V  »  OJ __________ 10^-liL1 ^  1 0 — 9  (V' H i -f = 10-*i = 2 —  I (V:^ I)1 a  5 (V  =  1) in'10-in'f icr« f = 0log (n„j/cm-*)log (n„/cnv^)Figure 1. Iso-lines for the intensity in the units of Planck's function al kinetic temperature of 100 K, of some lines, for various values for the dilution factor/. The dilution factor/ =  0 corresponds to the case (li).Radiative excitation of CS molecules in atmosphere of a star 619In our investigation, wc have considered a carbon star IR C  + 1 0 2 1 6  (the source of infrared (IR) radiation field) having a photosphcric temperature of 2300 K  reported by Keady e t  £i/[ 8 ]. ] he star is considered to behave like a black*body. Temperature the atmosphere of the star varies, and we considered a kinetic remperature of 1(X) K  for the volume element, which may exist „,nic where at a distance in between from 15/?* to 500 /?* {R^  being the radius of the star). Therefore in our calculations, the jiluiion factor/has been varied from ICT  ^ to lO"* in order to ^ o v e r  a  wide range. Molecular clouds are dust-rich and the r a d i a t i o n  from the star are reprocessed by the dust grains. The ftfeci o f  the dust grains would be cared through the dilution txior/  Moreover, the on-the-spot approximation being rather , r i i d c  one, present results show qualitative behaviour.In order to limit the numerical efforts in the investigation, we ja'ounied for three vibrational states, v = 0, 1 and 2 of the C,Smolecule. In these states, we considered those rotational levels which lie below the next higher vibrational state, and hence, we accounted for the rotational levels up to 7 =  39,38. and 38, in the vibrational states, v = 0, I and 2, respectively. Thus, in all, our system consists of 118  energy levels, which are connected through 345 radiative transitions. For these 345 radiative transitions, wc used the Einstein A-coefficients, calculated by Chandra e t  n/ [9]. Collisional rate coefficients between all the levels are computed by using standard formulae discussed by Chandra and Sharma 1 1 Of Though the validity of these formulae at 10 0  K  is questionable, to some extent, we have no other options due to absence of other data.3. Results and discussionWe performed calculations for two situations : (i) when there is radiation field from the star having photosphcric temperature ofFiBurc 2. Iso-lines for Ihc intensity in the units of Planck's function at kinetic temperalure of 100 K. of other lines, for various values for the dilution factor/. The dilution factor/ = 0 corresponds to the case (n).620 Suresh Chandra2 3 0 0  K ,  b e s id e s  th e  c o s m ic  2 .7  K  b a c k g r o u n d ,  a n d  ( i i )  w h e n  o n ly  th e  c o s m ic  2 .7  K  b a c k g r o u n d  is  p re se n t . E f f e c t  o f  th e  a tm o s p h e re  in  b e tw e e n  p h o to s p h e re  o f  th e  s ta r  a n d  th e  v o lu m e  e le m e n t  in c lu d in g  d u s t  is  a c c o u n te d  fo r , th ro u g h  th e  d i lu t io n  f a c t o r / .  C a s e  ( i i )  o b v io u s ly ,  c o r r e s p o n d s  to  th e  s itu a t io n  w h e n  th e  d i lu t io n  f a c lo r / i s  z e ro  in  th e  c a se  ( i) . T h e  m o le c u la r  h y d ro g e n  d e n s it y  is  v a r ie d  o v e r  th e  ra n g e  f r o m  10^ c m " ’  to  10® cm"^T h e  fre e  p a ra m e te rs  in  o u r  in v e s t ig a t io n  a re  th e  m o le c u la r  h y d ro g e n  d e n s it y  a n d  / (d v ^ /d r ) ,  w h e re  is  d e n s it y  o f  C S  m o le c u le s ,  an d  ( d v jd r )  th e  v e lo c i t y  g ra d ie n t .  I n te n s it ie s  in  th e  u n it  o f  P la n c k ’s f u n c t io n  a t k in e t ic  te m p e ra tu re  o f  1 00  K ,  o f  th e  l in e s  g iv e n  in  T a b le  1, a re  c a lc u la te d .  I s o - l in e s  o f  in te s it ie s  fo r  th e  l in e s  a re  g iv e n  in  F ig u r e s  1 a n d  2. V a r io u s  l in e s  s h o w  d if fe r e n t  b e h a v io u r  f o r  v a r ia t io n  o f  in t e n s it y  w it h  m o le c u la r  h y d r o g e n  d e n s it y  a n d  w it h  th e  p a r a m e te r  { d v ^ /  dr) .  I n te n s it ie s  o f  th e  l in e s  in  th e  g ro u n d  v ib r a t io n a l s ta te  a re  a b o u t th re e  o rd e r s  o f  m a g n itu d e  la rg e r  th a n  th o s e  in  th e  v ib r a t io n a l ly  e x c i t e d  s ta te ,  s h o w in g  th a t  o b s e r v a t i o n  o f  l in e s  in  th e  v ib r a t io n a l ly  e x c it e d  s ta te  is  a r a th e r  d i f f i c u l t  ta sk .In te re s t in g  to  n o te  th a t in t e n s it ie s  o f  th e  u n o b s e r v e d  l in e s  a r c  c o m p a r a b le  to  t h o s e  o f  th e  o b s e r v e d  o n e s ,  in  th e  c o r r e s p o n d in g  v ib r a t io n a l s ta te , a n d  th e re fo re ,  th e se  l in e s  m a y  a ls o  b e  o b s e rv e d . T h e  l in e s  in  th e  v ib r a t io n a l ly  e x c it e d  sta te , as w e l l  as b e tw e en  h ig h e r  ro ta t io n a l le v e ls  m  th e  g ro u n d  v ib r a t io n a l s ta te , a re  fo u n d  to  h a v e  a te n d e n c y  o f  th e ir  fo rm a t io n  in  th e  r e g io n s  c lo s e  to  th e  p h o to s p h e re  o f  th e  s ta r, w h e re a s  th e  re v e rs e  is  fo u n d  fo r  th e  l in e s  b e tw e e n  lo w e r  r o t a t io n a l le v e ls  in  th e  g ro u n d  v ib r a t io n a l state. S in c e  th e  n a tu re  o f  v a r ia t io n  o f  in te n s it y  IS d if f e r e n t  f o r  v a r io u s  l in e s ,  r a t io  o f  in t e n s it ie s  o f  tw o  l in e s  o b s e r v e d  in  a  c o m m o n  r e g io n  m a y  p r o v id e  in f o rm a t io n  a b o u t m o le c u la r  h y d ro g e n  d e n s it y  in  th e  r e g io n  a n d /o r  a b o u t d e n s it y  o f  th e  m o le c u le  o f  C S  fo r  th e  k n o w n  v e lo c i t y  g ra d ie n t .W h e n  th e  e x te rn a l I R  f ie ld  is  a b s e n t  { f  -  0 ) , in te n s it y  o f  th e  l in e s  in  th e  v ib r a t io n a l ly  e x c it e d  s ta te  (v  = 1) is  p r a c t ic a l ly  z e ro . T h u s ,  fo r  a  m o le c u le  to  be  in  a  v ib r a t io n a l ly  e x c ite d  sta te , e x te rn a l I R  f ie ld  is  e s se n t ia l. F u r th e r , in  a b se n c e  o f  th e  I R  f ie ld ,  m o le c u la rh y d ro g e n  d e n s it y  d o e s  n o t  h e lp  in  fo rm a t io n  o f  l in e s  in  the v ib r a t i o n a l ly  e x c i t e d  s ta te .  C o l l i s i o n a l  r a te s  a re  the only p a ra m e te rs  w h e re  k in e t ic  te m p e ra tu re  is  u t i l iz e d .  W e  repeated th e  c a lc u la t io n s  f o r  a  k in e t ic  te m p e ra tu re  o f  K X X )  K  in  the region fo r  th e  c a s e  w h e n  e x te rn a l I R  f ie ld  is  a b se n t i f  = 0 ). In tensitie s of th e  l in e s  in  th e  v ib r a t io n a l ly  e x c it e d  s ta te  w e re  s t i l l  found p r a c t ic a l ly  z e ro , s h o w in g  th a t in  a b s e n c e  o f  th e  e x te rn a l IR  f id d  h ig h  d e n s it y  a n d  h ig h  te m p e ra tu re  o f  th e  r e g io n ,  c a n n o t support th e  fo rm a t io n  o f  th e  l in e s  in  th e  v ib r a t io n a l ly  e x c ite d  state. Ji m a y  th e re fo re ,  b e  c o n c lu d e d  th a t l in e s  in  v ib r a t io n a l ly  excited s ta te s  c a n n o t  b e  fo u n d ,  e v e n  in  th e  r e g io n s  h a v in g  h ig h  densiiv an d  h ig h  k in e t ic  te m p e ra tu re , u n le s s  e x te rn a l I R  f ie ld  is  presentF in a l ly ,  w e  w o u ld  l ik e  to  sta te  tha t o n -th e -sp o t approx im ation  is  ra th e r  c r u d e  o n e , a n d  th e re fo re ,  th e  p re s e n t  in v e s t ig a t io n  is q u a l i t a t iv e  in  n a tu re .Acknow ledgm entsW e  a re  g ra te fu l to  P r o f  J  V  N a r h k a r ,  P r o f  S  A  Su ryaw an .sh i and P r o f  D r .  W  H  K e g e l  f o r  e n c o u ra g e m e n t .  S p e c ia l  th a n k s  are due to  m y  w i f e  M r s .  P u r n im a  S h a rm a  fo r  h e r  v a lu a b le  coopera tion .R eferences[1] A A Penzias, P M Solomon, R W Wilson and K B JelTnts Auropliys J 168 L53 (1971)(21 B E  Turner, B Zuckerman. P Palmer and M Morris Asimphw J 186 123 (1973)[3] H S Liszt and R A Linkc Astrophys J 196 709 (1975)[4] R N Martin and A H Barrett Astrophys J 202 L83 (1975)[5] B E Turner As iron Astrophys. 182 L15 (1987)[6] J L Highbcrger, A J Apponi, J H Bieging, L M Ziurys and J (i Mangum Astrophys J. 544 881 (2000)[7] E Rausch, W H Kegel, T Tsuji and G Piehler Asiron Asimphw Suppl. 315 533 (1996)[8] J J Ready, D N B Hall and S T Ridgway A.strophys J 326 K32 (1988)[9] S Chandra. W H Kegel, R J Le Roy and T Herlen.stein Asiwn Astrophys. Suppl. 114 175 (1995)[10] S Chandra and A K Sharma Astron Astrophys 376 356 (2IX)1)

Radiative Excitation of CS Molecules in Atmosphere of a Star

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Radiative Excitation of CS Molecules in Atmosphere of a Star

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