Faraday Discuss. 1998 109 137»163 Current status of the H diÜuse interstellar bands theory 2 1 Introduction In a recently published article,1 a new theory was presented attributing the diÜuse optical interstellar bands (DIBs) (Fig. 1) to resonantly enhanced simultaneous twophoton (VUV]VIS) absorption of light from a bright star by H contained in a thin tenuous cloud located relatively near the illuminating star. While it was shown in ref. 1 that the wavelengths of over 70 narrow DIBs could be matched to within the obserconsensus of most astronomers (e.g. ref. 2) remained that these spectral matches were vational limits of error to calculated wavelengths of inter-Rydberg transitions in H2 the simply happenstance coincidences that did not provide any real credibility for the model.Within the past year additional investigations were made with the aim of further testing the viability of the H DIBs model. On the one hand laboratory spectra were acquired [at Vrije Universiteit (VU)] of H inter-Rydberg transitions that a priori would have been expected to correspond to DIBs according to the non-linear H DIBs model of ref. 1. On the other hand important changes in the structure of this model were proposed (at IBM) in an attempt to overcome some of the de–ciencies that had become apparent in the original model. In making such changes we have availed ourselves of a Assignments of the kk5780 6284 4428 4882 large-equivalent-width diÜuse interstellar bands P. P. Sorokin,a§ J. H. Glowniaa§ and W. Ubachsb a IBM Research Division T .J. W atson Research Center Y orktown Heights NY 10598-0218 USA b L aser Centre V rije Universiteit De Boelelaan 1081-1083 1081 HV Amsterdam Netherlands 2 2 2 2 2 Major changes recently incorporated into the structure of the non-linear H DIBs model (P. P. Sorokin and J. H. Glownia Astrophys J. 1996 473 900) are outlined. To account for observed relative intensities of narrow DIBs assigned in the original model to H inter-Rydberg transitions it has become necessary to postulate a form of lightwave coherence existing in the H -containing cloud of the model with numerous coherent 2n wave-mixing processes each initiated by broadband stimulated Raman scattering (SRS) occurring on various H transitions. By considering such wave-mixing processes it becomes possible both to interpret archived VUV spectra of B-type supergiants and to easily assign large-equivalent-width DIBs (e.g.kk5780 6284 4428 4882) whose origins cannot be understood using the original ìpassiveœ H two-photon absorption model. The wave-mixing schemes discussed also enable one to understand why DIB intensities in given lines-ofsight correlate well with the amount of reddening observed in the same lines-of-sight. 2 2 2 2 § E-mail addresses sorokin=watson.ibm.com; glownia=us.ibm.com; wimu=nat.vu.nl 137 138 Current status of the H DIBS theory 2 Fig. 1 ” (DIB) spectrum from 3800»8680 for a line-of-sight of unit reddening. Spectrum synthesized from data contained in Table 3 of ref. 4. variety of published spectral data that were not considered in ref.1. These range from recent high-resolution spectral measurements of the lineshapes of the k5797 and k6379 DIBs to vacuum ultraviolet (VUV) spectra of mid-/late-B supergiants recorded in the 1970s. In this paper we focus primarily on the changes that have been made in the past year in the original H DIBs model and on the reasons why such changes were required. 2 2 The H DIBs model1 2 Postulated in the model of ref. 1 was the existence of a thin H -containing cloud located ca. 0.01»10 pc from a bright early-type star and intersected by our line-of-sight to the 2 star. It was argued that in a collision-free medium (a good approximation for the cold cloud with density ca. 104 cm~3 assumed in the model) elastic (i.e.resonance Rayleigh) scattering of near-resonant VUV starlight should completely dominate inelastic scattering (i.e. ìabsorptionœ leading to real excitation of B- and C-state quantum levels) of the same light. (The theory of resonance —uorescence and light scattering is thoroughly discussed in ch. 8 of ref. 3 for example.) Consequently near-resonant VUV light coming from the nearby hot star diÜuses throughout the entire cloud resulting in the steadystate —ux column densities of this light along the line-of-sight to the star becoming greater than the values that would prevail in the total absence of the cloud. Conservation of energy dictates that ìabsorptionœ of near-resonant VUV photons whose freone-photon transitions. (For simplicity Doppler broadening in the cloud of the model is quencies lie outside the ca.0.003 cm~1 H2 natural linewidth cannot occur via singlet-gerade-state quantum levels involving both near-resonant VUV photons trapped assumed to be zero.) However simultaneous two-photon absorption transitions to H2 by elastic scattering within the cloud and visible photons directly coming from the star can exactly conserve energy and were assumed to occur in the model producing the DIBs. On the basis of the simple scheme described above it became immediately possible to assign several dozen narrow DIBs to H inter-Rydberg transitions. An example is the 2 narrow DIB shown in Fig. 2. According to Table 3 of ref. 4 the frequency of this (]) (i.e. ìcertainœ) DIB is 12 455.7^0.2 cm~1 (8026.21^0.15 ”) its linewidth is 1.2^0.1 cm~1, 139 P.P. Sorokin et al. Fig. 2 Diagram on right shows ref. 1 assignment of narrow DIB observed at ca. 12 456 cm~1. An expanded portion of the spectrum in Fig. 1 containing this DIB is shown on the left. In all synthesized DIB spectra shown in this paper DIBs with wavenumbers indicated were assigned in ref. 1. and its equivalent width (in HD 183143) is 52 m”. (Although the equivalent width is here relatively modest the sharpness of this DIB allows it to be clearly seen in Fig. 1.) The exact frequency of the H inter-Rydberg transition to which this DIB is assigned in Fig. 2 can be calculated from the H quantum level energies tabulated in ref. 5»7. The 2 2 value is 12 455.79 cm~1 well within the narrow error limits given in ref.4. In ref. 8 the frequency of this DIB is listed as 12 455.82^0.06 cm~1. Both the VUV and visible transitions shown in Fig. 2 have very large calculated radiative transition probabilities. For the C1»0R1 transition which originates (as required in the model of ref. 1) from the very lowest quantum level of orthohydrogen (JA\1 of X0) the value calculated9 is 0.14]9 s~1. The strength of the visible transition shown is indicated by its large ìadiabatic transition moment (ATM)œ. (ATM values are calculated and tabulated for a variety of H transitions in ref. 10.) At –rst glance the assignment in Fig. 2 seems quite compelling. However a serious difficulty is present here 2 that also occurs in most of the DIB assignments given in ref. 1. Brie—y stated no DIBs have thus far been observed that can be assigned to many other strong transitions originating from the same resonant intermediate-state quantum level J@\2(]) of C1.For example no DIB is observed at 12 518.54 cm~1 the calculated frequency of the GK37C1 R(2) transition. To us this strongly implied that a mechanism based entirely upon ìpassiveœ two-photon absorption by H molecules cannot adequately explain the origin of the DIBs. As will be explained in detail below we currently assume that some 2 form of coherent lightwave structure is present in the H -containing cloud of our model. In the case of Fig. 2 we would now suggest that broadband IR stimulated emission 2 spectrally centred on a transition connecting the GK3 J\1 quantum level with some lower-lying B- or C-state quantum level must be occurring.We would now additionally postulate that this IR stimulated emission occurs as a step in an existing parametric oscillation cascade that ìcomes from aboveœ i.e. that starts at a higher-lying quantum level. Absorption of ca. 12 456-cm~1 photons would then occur via a process that should 140 Current status of the H DIBS theory 2 probably be termed ìfour-photon inverse Raman absorptionœ a four-photon analogue of the inverse Raman eÜect.11 This mechanism should produce much stronger absorption of light at the DIB frequencies than passive two-photon absorption. Thus in our current view DIB selectivity can be the result of the operation of speci–c enhancement mechanisms. Another DIB which was assigned in ref.1 on the basis of a close frequency match is the narrow one (*lB2 cm~1) appearing in Fig. 3 at ca. 16 135 cm~1. In ref. 4 the frequency of this much studied DIB is given as 16 134.4^0.9 cm~1. In ref. 8 the value listed is 16 135.12^0.05 cm~1. The value calculated for the H transition to which the 2 DIB is assigned in Fig. 3 is 16 135.06 cm~1. In terms of a frequency match with existing observations the assignment is again seen to be a good one. However in trying to account for the observed DIB intensity simply on the basis of a passive two-photon absorption model one again encounters difficulty. The nature of this difficulty can be seen by comparing the two assignments shown in Fig. 2 and 3. For the B3»0P1 transition which also originates from the lowest level of orthohydrogen the calculated radiative transition probability12 is 0.10]9 s~1 about the same as for C1»0R1.However the ATM for the visible transition in Fig. 3 is seen to be more than ten times smaller than that for the visible transition in Fig. 2. Nonetheless the equivalent width of the DIB at 16 135 cm~1 is ca. 80 m” roughly 1.6 times greater than that of the DIB at 12 456 cm~1. ” one of the most widely studied of the DIBs was not actually 2 ”) H of the closest transition i.e. the By discussing together the cases of the strong but narrow k5797 and k6379 DIBs one can again illustrate both the strengths and the weaknesses of the H DIBs model of ref. 1. The DIB at 5797 assigned in ref. 1 since the air wavelength (5796.96 2 one originating from J@\2 of B0 and terminating on J\3 of EF12 appeared to lie outside the k5797 DIB wavelength measurement error limits (5797.11^0.05 ”) listed in ref.4. However subsequent very-high-resolution measurements of the k5797 DIB presented in ref. 13 show this DIB to be ca. 2.4 wavenumbers wide and to be roughly peaked at 5797.0 ” a point at which the DIB pro–le displays a distinct sharp ìnotchœ. Fig. 3 Ref. 1 assignment and expanded spectrum for the DIB at ca. 16 135 cm~1 141 P. P. Sorokin et al. This ìnotchœ is clearly seen in both lines-of-sight (i.e. towards l Sgr and towards f Oph) for which the k5797 DIB pro–le was recorded in ref. 13. The wavelength of this DIB is stated in ref. 8 to be 5796.98^0.04 ”. Thus the more recent k5797 DIB wavelength measurements lend strong support to the H2-based assignment.The k6379 DIB was assigned in ref. 1 to the transition (EF10 J\1)^(B0 J@\2) that is it was assigned to a transition having the same intermediate-state quantum level as in the above mentioned k5797 DIB assignment. The calculated (air) wavelength of this transition is 6379.23 ” within the error limits of ref. 4 (6379.27^0.08 ”) and very nearly within those of Ref. 8 (6379.20^0.02 ”). Some observations were recently made that lend more interest to the fact that our assignments of the k5797 and k6379 DIBs feature the same intermediate-state quantum level. In ref. 14 the pro–le of the sharp k6379 DIB was recorded at very high resolution in the line-of-sight to f Oph. After telluric correction this DIB showed a substructure described by the authors of ref.14 as consisting of two equal peaks. However the k6379 DIB pro–le shown in this work can equally well be described as having a distinct sharp notch near its peak. In a still more recent high-resolution study of DIBs,15 the presence of a clearcut notch at ” ca. 6379.25 on the k6379 DIB was con–rmed. An earlier study16 was evidently the –rst to suggest that the k6379 DIB possessed a two-peak structure. The serious difficulty appearing to discredit the H -based assignments of both of these DIBs is again the lack of an explanation for the observed DIB intensities. Both 2 k5797 and k6379 are among the strongest of the narrow DIBs. (In ref. 8 the equivalent widths in HD 183143 for k5797 and k6379 are listed as 238 and 123 m” respectively.) Yet the strengths of the simultaneous two-photon absorption transitions involved in the DIB assignments are in both cases relatively weak.The B0»0R1 transition is the weakest of all Bn»0R1 transitions lying below the Lyman limit being ca. 40 times weaker than C1»0R1 for example. In the simultaneous two-photon absorption model of ref. 1 the strength of the VUV transition in—uences both the intrinsic strength of the simultaneous two-photon absorption process and the density of near-resonant VUV photons trapped in the cloud by elastic scattering. In addition to the VUV transition being weak the ATMs for the transitions (EF12 J\3)^(B0 J@\2) and (EF10 J\1)^(B0 J@\2) are also comparatively modest being 0.04 and 0.15 respectively. The processes illustrated in Fig.4 represent a possible solution to the intensity anomaly problem discussed above. However several unusual features requiring considerable explanation are involved. To begin with as will be noted below there exists fairly compelling spectral evidence that broad-band coherent VUV Stokes-wave emission occurs on the transition B0»0P3 in H -containing clouds near B-type giants and 2 supergiants. This radiation would raise orthohydrogen molecules in JA\3 of X0 to ì virtual states œ lying near J@\2 of B0. From these virtual states the molecules could be induced to follow pathways similar to the ones shown in Fig. 4. In Fig. 4 it is assumed that both quantum levels EF12 J\3 and EF10 J\1 are already involved in parametric oscillation cascades proceeding downward from higher levels.[For simplicity in Fig. 4 we have speci–cally assumed a common IR cascade for the two levels proceeding through J@\2 of B15. If the transition from EF12 J\3 to EF10 J\1 happened to occur as a degenerate two-photon emission process the broad-band IR generated would be spectrally centred at 787 cm~1 the frequency of one of the ìunidenti–ed IR emission bands (UIBs)œ discovered in ref. 17.] With strong broad-band light waves present that are spectrally centred on the topmost two IR transitions in Fig. 4 and with strong broad-band VUV light around B0»0P3 also present one expects that light around 5797 ” will be absorbed through the same ìfour-photon inverse Raman absorptionœ process already brie—y mentioned above.A similar process would produce the k6379 DIB. From the unspecifed singlet-ungerade-state quantum level shown in Fig. 4 the downward parametric oscillation cascade would continue in some manner eventually returning the molecules to JA\3 of X0. 142 Current status of the H DIBS theory 2 Fig. 4 Wavemixing processes incorporating inverse Raman absorption steps proposed in text to explain selective enhancement of k5797 and k6379 DIB intensities On the basis of the scheme shown in Fig. 4 one can thus account for the relatively strong k5797 and k6379 DIB intensities that are observed for the fact that the intensities of these DIBs are strongly correlated with reddening in the line-of-sight (explanation to be given below) and for the fact that there here again must be some mechanism that restricts the number of DIBs.No DIBs are observed that correspond to the frequencies of the transitions (EF12 J\1)^(B0 J@\2) or (EF10 J\3)^(B0 J@\2) for example. In the present instance it is again seen that selectivity results from the presence of enhancement mechanisms. In global terms the model outlined in ref. 1 is far more inadequate than has thus far been represented. We have described the severe intensity anomalies present in some of the assignments of narrow DIBs. However on the basis of the model of ref. 1 most of the prominent large-equivalent-width DIBs appearing in Fig. 1 cannot be assigned at all. Several of the DIBs have very broad linewidths of the order of 50 wavenumbers or more. In ref. 1 only speculative arguments were oÜered to explain the origin of DIBs with such large linewidths.It was suggested that the cause of this width might be found in the rapid rates of predissociation and/or autoionization of singlet-gerade-state quantum levels lying higher in energy than 118 375.6 cm~1 the threshold for dissociation into H(1s)]H(2s 2p). The various double-resonance measurements described in the next section have generally dispelled both this notion and several others that were contained in ref. 1. 3 H double resonance measurements 2 In ref. 18 double resonance (VUV]VIS) ionization spectra of H were reported which showed a number of coincidences (i.e. frequency and linewidth matches) with modest- 2 equivalent-width DIBs (Fig. 5). The matching DIBs have only been reported in ref.4 however. Both C5 and C6 quantum levels were excited from X0 with the VUV laser 143 P. P. Sorokin et al. Fig. 5 Double-resonance ionization spectra probing singlet-gerade-state quantum levels lying above the ionization threshold. The VUV laser was tuned to C5 intermediate states (left) and C6 intermediate states (right). The bottom spectra show expanded portions of the DIB spectrum of Fig. 1 corresponding to the same wavelength ranges. separately tuned to each of the R(0) R(1) and Q(1) transitions. With the VUV laser frequency set to coincide with a given absorption line a tunable visible laser was then scanned in frequency and a photoionization spectrum was recorded. Singlet-geradestate quantum levels lying in a region just above the H2 autoionization threshold (124 418.4 cm~1) were probed.Somewhat remarkably it was found that in a spectral range spanning ca. 1000 cm~1 in an energy region where the H density-of-states might a priori be expected to be high only the strong resonances shown in Fig. 5 were seen. Four of these transitions termin- 2 ate on a singlet-gerade-state quantum level of orthohydrogen (con–guration unknown) located at 124 752.5 cm~1. The other two both terminate on a quantum level of parahydrogen (presumably a diÜerent rotational level belonging to the same con–guration as above) at 124 701.9 cm~1. The linewidths of all six resonances and of the –ve DIBs which seemed to match were all between 2 and 3 wavenumbers. These widths undoubtedly re—ect the rates of autoionization of these two quantum levels.One can attempt to discuss the resonances appearing in Fig. 5 in terms of the basic model of ref. 1. To begin with all three C5»0 transitions [i.e. R(0) R(1) and Q(1)] lie below the Lyman limit (91.2 nm). These transitions should therefore be potentially excitable in the H2-containing cloud assumed in the model of ref. 1. The equivalent widths (in HD 183143) of the two DIBs which seem to correspond to the top and bottom C5 resonances in Fig. 5 are stated in ref. 4 to be 24 and 12 m” respectively. Since the ratio of these equivalent widths is about the same as the ratio (1.82) of the C5»0Q1 and C5»0R1 transition probabilities it would seem at –rst glance that this particular pair of DIB assignments can be more-or-less understood on the basis of the original ìpassiveœ two-photon absorption model of ref.1. The middle C5 resonance is much too far oÜ resonance (ca. 9 cm~1 diÜerence) from the closest DIB appearing in Fig. 5 to be even remotely considered a frequency match. This DIB which has a frequency of 15 331.5 cm~1 and an equivalent width of 30 m” was reasonably assigned in ref. 1 as the R(2) transition of EF137B2. However one is now required to explain the absence of an observed DIB corresponding to the middle C5 resonance. At this point, 144 Current status of the H DIBS theory 2 from ref. 21.) Fig. 6 Double-resonance ionization spectrum probing singlet-gerade-state quantum levels lying below the ionization threshold. The VUV laser was here tuned to the C2»0R1 line.(Spectral data we can only postulate that broad-band stimulated Raman scattering (SRS) involving C5 J@\1([) as resonant intermediate state must be occurring in the H -containing clouds in which the DIBs originate. According to ref. 19 when the intermediate quantum level 2 in a resonant two-photon absorption process is radiatively coupled by a light wave to a fourth quantum level the probability of simultaneous two-photon absorption occurring from the ground level to the two-photon level may be reduced by many orders of magnitude. This eÜect is a two-photon analogue of ìelectromagnetically induced transparency (EIT)œ a topic of current theoretical interest. (See e.g. ref. 20.) It is thus seen that with the assumption of a coherent lightwave structure present in the H2-containing cloud there is the potential for both DIB-enhancing and DIB-attenuating mechanisms to exist.It is more awkward to try to explain the three apparent coincidences of DIBs with transitions involving C6 seen in Fig. 5. [The narrow DIB at ca. 13 718 cm~1 was assigned in ref. 1 to the strong (ATM\0.95) transition HH7C2 Q(2).] All three C6»0 transitions lie at shorter wavelengths than the VUV cut-oÜ imposed by the Lyman limit. We speculate that virtual states near the C6 levels are excited by VUV light existing in the cloud at certain wavelengths longer than 91.2 nm (vide infra). This VUV light promotes transitions of molecules existing in vibrationally excited levels of the X state. The latter are populated in primary VUV SRS processes of the type to be discussed in detail below.From the strong resonances seen in Fig. 5 one would guess that the potential curve for the unknown singlet gerade state is similar in shape to the C-state potential curve only vertically shifted from the latter to higher energies. This in turn would imply that strong transitions between the same two states could in principle occur from lower C-state vibronic levels to correspondingly lower vibronic levels of the singlet gerade state. However the energies of these lower singlet-gerade-state vibronic levels would lie below the threshold for H autoionization. One would therefore not expect signals to be generated at resonances using the experimental arrangement employed in ref. 18. 2 However by modifying the technique used in ref.18 to include an extra pulse for ionizing H(2s,2p) atoms produced in H(1s)]H(2s,2p) dissociation channels the group at VU has now shown21 that transitions from C-state vibronic levels to singlet-gerade-state 145 P. P. Sorokin et al. vibronic levels lying between the energy thresholds for dissociation into H(1s)]H(2s,2p) and autoionization into H2 `]e~ can easily be observed. (In unpublished earlier work,22 several H resonances in this same range were observed with use of a similar technique.) 2 Fig. 6 shows an example of an ionization spectrum obtained in this manner.21 Although striking resonances are seen here it turns out that there are no correspondences with DIBs. One can again reasonably propose that SRS involving C2 J@\2(]) as resonant intermediate state might be occurring and that consequently (again by the main result derived in ref.19) the intensity of two-photon absorption from JA\1 of X0 to any of the singlet-gerade-state quantum levels located by the resonances in Fig. 6 will be greatly diminished. However considering all the double-resonance experiments which have here been described one senses the futility of attempting to explain the origins of large-equivalent-width DIBs (especially the very broad ones) on the basis of rapidly dissociating and/or autoionizing singlet-gerade-state quantum levels existing in heretofore unexplored energy ranges. In the remainder of this paper we outline a promising new approach we have recently been following in seeking to provide an H -based answer to this question.2 4 Evidence for nonlinear generation of VUV light in H -containing clouds 2 near B-type supergiants If mechanisms involving coherent light generation are required to explain the observed DIB relative intensities it becomes a reasonable investigative step to examine archived VUV spectra of bright stars for some evidence of VUV light generation actually occurring in these stars. In a manuscript recently submitted for publication,23 we indicate that it is indeed possible to interpret some of the spectral data obtained by various VUV space probes (e.g. Copernicus and ORFEUS-124) to show that in clouds surrounding some B-type stars both SRS and a related process known as four-wave parametric oscillation (FWPO) ubiquitously occur on H transitions in a manner closely resembling some of the scenarios that were brie—y considered in ref.1 and that these 2 processes can actually represent ìmain eventsœ determining the spectral character of these objects in the VUV. We began outlining this evidence in ref. 23 by showing that for some stars located high above the galactic plane (ìhalo stars œ) whose lines-of-sight would thus be less likely to be intersected by interstellar H clouds that are far removed from the stars themselves the observed intensity ratios of individual Bn^X0 R(0) R(1) and P(1) transitions 2 cannot be comprehended on the basis of linear spectroscopy. This can be seen for example in the ORFEUS-1 spectrum of the B1 Ib halo star (d\1.7 kpc) HD 214080 (Fig. 7 and 8).Comparing these two –gures one observes that the B0»0 absorption components are clearly stronger than those of B4»0. Yet the calculated radiative transition probabilities12 of the latter are ca. 16 times those of the former. From this clear anomaly which is also apparent in the VUV spectra of several other B-type stars that were probed by ORFEUS-1 we infer that there exist ubiquitously in our galaxy spectrally accessible clouds of H for which paradigms based upon the Copernicus high- 2 resolution VUV spectrum of f Oph shown in ref. 25 are not relevant. The tentative explanation we oÜer for the strong enhancement of individual R(0) R(1) and P(1) Bn»0 absorption components that is observed for select low n in many B-type stars involves SRS processes occurring on some of these transitions.This will be discussed further in what follows. In ref. 26 Copernicus low-resolution (0.2 ”) observations of 16 O-type stars and 10 B-type stars (mostly supergiants) covering the range 1000 ” »1200 are presented in the form of a classical spectral atlas. In ref. 23 we focussed on what appeared to be a few 146 Current status of the H DIBS theory 2 Fig. 7 Expanded view of a section of the ORFEUS-1 HD 214080 spectrum. Absorptions marked ì s œ are of known stellar origin. Two interstellar N I absorption lines are indicated. dozen emission lines rising well above the background continuum in the mid-/late-B supergiant spectra shown in ref. 26 (Fig. 9). There seemed to exist no speci–c identi–cations or assignments of these apparent emission features in the scienti–c literature.However we have recently learned that it has long been the general opinion of the astrophysical community (see for example ref. 27) that (1) no emission lines are present in spectra such as those shown in Fig. 9; (2) the background VUV continuum level should always be placed at the level of the very highest peaks that are observed; and (3) the resulting large fraction of continuum light which is thus inferred to be missing is marked. Fig. 8 Expanded view of a section of the ORFEUS-1 HD 214080 spectrum adjacent to that shown in Fig. 7. Absorptions marked ì s œ are of known stellar origin. An interstellar O I line is 147 P. P. Sorokin et al. Fig. 9 Copernicus low-resolution VUV spectra of four mid-/late-B supergiants as shown in Fig.6 of ref. 26 Ref. 27 features a high-resolution (0.05 absorbed by over 1000 blended stellar photospheric absorption lines mostly due to ions of transition metals. Despite this interpretation we here proceed to describe some of the interesting consequences that follow if one assumes that emission peaks are indeed present in the spectra of Fig. 9. Fig. 10 shows a wavelength-expanded portion of Fig. 9 containing one of the most intense ìemissionœ peaks appearing in the latter. This peak appears in each spectrum of Fig. 10 at a wavelength that is very close to 1135.9 ”. Making the assumption that this peak must be nearly centred on the wavelength of an allowed transition of H2 and that low rotational quantum numbers must be involved one concludes from inspection of Table 61 of ref.28 that the most likely transition is B8»3R0 at 1135.90 ”. In ref. 23 it was assumed that this emission peak was generated as a Stokes wave in a resonantly enhanced stimulated Raman scattering process. This SRS process would result from broadband optical pumping of ground-state parahydrogen molecules by VUV photons in the H -containing cloud that are nearly resonant with B8»0R0. As has already been explained it is generally assumed in all of our DIB models that enhanced densities of 2 nearly-resonant VUV photons exist throughout the cloud as a result of elastic (i.e. Rayleigh) scattering. ” i.e. 5 cm~1 at ca. 1000 ”) Copernicus scan ” ” . In this scan the width of the 1135.9 peak appears to of b Ori A from 999 to 1561 be 50»60 cm~1.Since Doppler broadening of VUV —uorescent lines emitted by H2 molecules residing in the thin cloud of our model should be at least 10 to 100 times smaller than this one can conclude that if the 1135.9 ” emission band is indeed due to H2 it is generated not through normal —uorescence but through a mechanism such as broad-band SRS or FWPO. Another prominent emission peak in Fig. 10 is seen to occur ubiquitously at ca. 1116 ”. This emission band also appears strongly in all the ORFEUS-1 spectra of B-type giants and supergiants we have examined. (See e.g. Fig. 11.) From Table 58 of ref. 28 we assign this peak to B0»0P3 at 1115.9 ”. We speculated in Section 2 that generation of coherent light on this transition should play an important role in determining the absorption strengths of the k5797 and k6379 DIBs.In Fig. 11 the ORFEUS-1 spectrum of the (B1 Ib) star HD 214080 is compared with the Copernicus spectrum of b Ori A in the same wavelength range shown in Fig. 10. 148 Current status of the H DIBS theory 2 Fig. 10 Expanded view of a section of the Copernicus spectra shown in Fig. 9 While the (emission peak height/ background continuum level) ratio is clearly less in the case of the much hotter ORFEUS-1 star the major peaks are seen to occur at approximately the same wavelengths as in Fig. 10. One becomes more easily convinced of the existence of emission peaks viewing the b Ori A spectrum however. All other assignments of peaks shown in Fig. 11 result from analysing the higher-resolution b Ori A spectrum shown in ref.27 with the same method used above in assigning the 1135.9 ” peak. In Fig. 12 wavelength-expanded portions of two of the spectra appearing in Fig. 9 are shown in another spectral range. One sees again that the major peaks occur at exactly the same wavelengths in these two diÜerent temperature stars. Two of the emission peaks in this –gure (at ” ” ca. 1043.9 and ca. 1065.2 ) are assigned as Stokes waves in SRS processes having the same initial and –nal states as the SRS process proposed above as the generating mechanism for the 1135.9 ” emission peak. However in order for SRS to occur on a continuous basis some eÜective mechanism must exist to depopulate the terminal state and repopulate the ground state.A possible mechanism in this case would be that shown in Fig. 13. The essential idea here is that additional SRS and/or inverse Raman and/or parametric oscillation steps are required in order to deplete continuously the population of molecules pumped to JA\0 of X3 and to provide a return path for this population back to JA\0 of X0. With the incorporation of such additional steps the overall process can no longer be described as being simple broad-band SRS. It must instead be viewed as a type of hybrid wave-mixing process in which SRS pumping absorption resulting from inverse Raman scattering or parametric oscillation can each occur at more than one step. In ref. 23 we employed the term ìSRS»FWPOœ to describe such hybrid processes. The hybrid process may involve four 149 P.P. Sorokin et al. latter spectrum. Fig. 11 Expanded Copernicus b Ori A spectrum of Fig. 10 compared with the ORFEUS-1 spectrum of HD 214080 over the same spectral range. Two interstellar N I lines are indicated in the Fig. 12 Expanded view of a section of the Copernicus spectra of two of the stars shown in Fig. 9. A few emission bands discussed in the text are shown. 150 Current status of the H DIBS theory 2 Fig. 13 An SRS-FWPO wavemixing scheme that can account for continuous SRS Stokes-wave emission on B8»3R0 C4»3R0 and C3»3R0. waves six waves eight waves or more. In Fig. 13 it is assumed that a downward parametric oscillation cascade continues from an unspeci–ed singlet-gerade-state quantum level (the ì s.g. level œ in Fig.13) eventually terminating on JA\0 of X0. All waves participating in SRS»FWPO processes of the type shown in Fig. 13 must be colinear a basic requirement that follows from momentum conservation. In the thin H -containing cloud of our model this implies that all waves participating in SRS» FWPO processes must propagate in the plane of the cloud. This restriction will form the 2 basis for the explanation proposed in the next section for the universally observed dependence of DIB intensity upon reddening in the line-of-sight. In Fig. 13 it is assumed that intense pumping radiation in the vicinity of Ly-a exists in the cloud. A relatively high density of H atoms is assumed to exist in the cloud and elastic scattering of VUV radiation near Ly-a Ly-b . . . etc.by these atoms will result in there being present in the cloud greatly concentrated densities of photons that are nearly resonant with these transitions. Note that owing to the isotropic nature of the elastic scattering process there will always be Ly-a Ly-b Ly-c . . . etc. photons propagating in the plane of the cloud. These photons can therefore participate in SRS»FWPO processes. Let us restate the general hypothesis that has evolved from the discussion of Fig. 13 just presented. If there happens to exist a near-coincidence in frequency between either Ly-a Ly-b or a higher-lying H-atom resonance line and a strong transition to some higher-lying singlet-ungerade-state quantum level from the particular X-state quantum level that is populated by a given Stokes-wave emission an eÜective SRS»-FWPO pathway capable of depleting the X-state quantum level may exist allowing the VUV SRS to occur.On the basis of this general hypothesis it appears to be possible to justify most of the H2-based assignments we have thus far made. Consider for example the emission peak appearing at ” ca. 1126 in Fig. 11 which we have assigned as a broadband SRS Stokes-wave emission occurring on B16»5P1. (The exact wavelength of the B16»5P1 transition is 1126.085 ”.) The primary SRS process would here be pumped by VUV photons nearly resonant with the strong transition B16»0P1. According to our model the densities of such photons everywhere in the cloud should be greatly enhanced 151 P. P. Sorokin et al. Fig. 14 Expanded view of another section of the Copernicus spectra of two of the stars shown in Fig.9. Several emission bands assigned in the text are shown. through elastic scattering. There are several B16»nP1 transitions considerably stronger than B16»5P1 which should have correspondingly higher Stokes-wave gains but to which none of the emission peaks in the spectra of late-/mid-B supergiants actually seem to correspond. A plausible explanation can be oÜered for this unusual selectivity in terms of the general SRS»FWPO scheme here being proposed. If one adds the energy of a Ly-a photon (82 259 cm~1) to the energy29 of the X5 JA\1 quantum level (18 582 cm~1) the result is 100 841 cm~1. The energy of the B9 J@\0 quantum level is 100 843 cm~1 just two wavenumbers away. The B9 J@\0 level could thus eÜectively serve as the resonant intermediate state in a secondary SRS process originating from X5 JA\1.The secondary Stokes wave could be generated either in the IR for example on the (ATM\0.13) transition (B9 J@\0)](EF1 J\1) at ca. 1467 cm~1 or in the VUV on a transition that drops the molecules back to some vibronic level of the X state. Since Stokes-wave gain generally varies as o2l where o is the transition dipole moment and l is the frequency of the Stokes-wave transition VUV generation would a priori be heavily favoured except that once more some mechanism must exist that is capable of depopulating the terminal state of the secondary SRS process. Relaxation of the secondary SRS terminal state is not a problem in the case of IR Stokes-wave generation since EF vibronic levels can decay on a nanosecond timescale to lower-lying B- and C-state quantum levels.We are unable to specify with any accuracy an exact pathway for the SRS»FWPO process in the present instance. However a reasonable speculation would be that the secondary Stokes-wave emission occurs on B9»4P1 at 1169.6 ”. There is an emission peak seen at this wavelength in the spectra of the mid-/late-B supergiants. Moreover when one adds the energy of a Ly-a photon to the energy of the X4 J\1 quantum level (15 346 cm~1) one gets 97 605 cm~1 just 14 wavenumbers away from B6 J@\0 at 97 591 cm~1. The Stokes wave in a tertiary SRS process employing B6 J@\0 as resonant intermediate state would necessarily have to occur in the VUV since there 152 Current status of the H DIBS theory 2 are no EF vibronic levels below B6 J@\0.We speculate that the Stokes-wave emission might here occur on B6»11P1 at 1546.7 ”. This has a large calculated radiative transition probability and an emission peak is seen at this wavelength in ref. 27. Moreover from X11 J\1 a Ly-a photon reaches an energy of 115 197 cm~1 just 25 wavenumbers away from C9 J@\2(]) at 115 222 cm~1. This quaternary SRS process involving orthohydrogen molecules thus perhaps proceeds in a manner generally similar to the tertiary SRS process involving parahydrogen molecules shown in Fig. 13. In Fig. 14 wavelength-expanded portions of two of the spectra shown in Fig. 9 are presented in yet another spectral range. On the basis of the high-resolution b Ori A spectrum contained in ref.27 we have again assigned many of the most prominent peaks shown here. Four of the transitions assigned as Stokes-wave emissions in this –gure (B9»2R1 B8»2R1 B7»2R1 and B7»2P1) have the same SRS terminal state JA\1 of X2. Molecules brought to this terminal state by the primary SRS processes can be redirected back to the SRS ground state through the SRS»FWPO process shown in Fig. 15. In this case pumping light for the secondary SRS process is provided by the enhanced densities of photons in the cloud that are nearly resonant with Ly-b. An emission band whose frequency corresponds to the last leg (B10»0P1) of the SRS»FWPO process illustrated in Fig. 15 can be seen in ORFEUS-1 spectra of B-type stars (Fig. 16). In Fig.16 a notch can be discerned on the emission band at the exact frequency of the B10»0P1 line centre. Parametric oscillation normally develops in such a manner that gain is optimized and loss is minimized. Therefore to avoid loss associated with real absorption occurring within the natural linewidth or elastic scattering occurring at larger frequency oÜsets a notch in the VUV emission band forms at the exact position of the B10»0P1 line centre. In ref. 23 another SRS»FWPO pathway capable of depleting the population in X2 JA\1 was discussed. In this alternative scheme the secondary SRS Stokes-wave emission occurs in the VUV. The secondary SRS intermediate state is the same J@\1(]) of C3. The SRS process which produces the prominent Stokes-wave emission peak assigned as B16»4P4 in Fig.14 is somewhat unusual. In this case the molecules that are excited to undergo SRS are parahydrogen molecules occupying the X0 JA\2 quantum level. Fig. 15 A possible SRS»FWPO process discussed in the text capable of generating emission on the transitions B9»2R1 B8»2R1 B7»2R1 and B10»0P1 153 P. P. Sorokin et al. 2 Fig. 16 Expanded view of a section of the ORFEUS-1 spectrum of HD 214080. The marked emission peaks and absorption regions are assigned in the text to the H transitions indicated. The pumping transition is B16»0R2 at 933.2 ”. Some evidence of non-linear absorption occurring around this wavelength can be seen in the ORFEUS-1 spectra of B-type stars (Fig. 17). However adding the photon energies of either Ly-a Ly-b or Ly-c to the energy of the X4 JA\4 quantum level (16 191 cm~1) results in an energy that is far removed from that of any singlet-ungerade-state quantum level optically connected to JA\4 of X4.To achieve resonance one has to add the energy of a Ly-d photon 105 292 cm~1. The frequency of the strong D4»4Q4 transition is 105 289 cm~1.30 It is also possible to explain some of the absorption and emission features seen in the Copernicus and ORFEUS-1 spectra using FWPO processes of the simpler type that were considered in ref. 1. For example Fig. 18 shows a simple FWPO process characterized by high radiative transition probabilities which should lead to emission around 2 Fig. 17 Expanded view of a section of the ORFEUS-1 spectrum of HD 214080 extending to the Lyman limit (91.2 nm).The H transitions marked are discussed in the text. 154 Current status of the H DIBS theory 2 Fig. 18 A possible simple FWPO process that could generate VUV emission on B13»0R0 954.4” ” and absorption around 929.5 . In Fig. 19 a prominent emission band is seen corresponding to the B13»0R0 wavelength but the observed absence of any hint of a notch is somewhat puzzling. In Fig. 17 there appears to be a fairly well de–ned absorption region corresponding to C4»0R0 at 929.5 ”. There may also exist some evidence of C4 ” »0Q1 absorption at 930.6 in Fig. 17 but this is somewhat hard to discern in view of the H(7p) absorption occurring at 930.75 ”. Signi–cantly there appears to be no hint of absorption corresponding to C4»0R1 at 929.7 ” although the calculated radiative transition probabilities of C4»0R0 and C4»0R1 are roughly similar.We will refer again to this observation in discussing our assignment of the k4428 and k4882 DIBs in the next section. 2 Fig. 19 Expanded view of a section of the ORFEUS-1 spectrum of HD 214080. An emission peak and several regions of absorption are assigned in the text to the H transitions indicated. 155 P. P. Sorokin et al. 5 Assignments of the kk5780 6284 4428 4882 large-equivalent-width DIBs Two prominent emission bands appearing in all the low-resolution Copernicus mid-/ late-B supergiant spectra and in the high-resolution Copernicus spectrum of b Ori A occur at 1188.3” ” and at 1244.0 . In ref. 23 these bands were assigned as Stokes-wave emissions on the transitions C3»6R0 and B10»6R0 respectively.Following the same line of argument employed in Section 4 one can here again account for removal of molecules from the SRS terminal state JA\0 of X6 by a plausible SRS»FWPO scheme (Fig. 20). It will now be shown that by combining this particular SRS»FWPO scheme with another one to be shortly described it is possible to make an assignment for what is probably the most famous DIB of all the one at 5780 ”. ative transition probabilities that could be occurring in H2 The energy level diagram of Fig. 21 shows a speci–c H process having high radi- 2-containing clouds around B-type giant and supergiant stars. From (EF4 J\0) a downward parametric oscillation cascade terminating on JA\0 of X0 could occur which would deplete the EF4 J\0 quantum level.However such a parametric cascade is not required for the SRS process illustrated in Fig. 21 to occur since the EF4 J\0 quantum level could otherwise —uoresce to lower-lying B-state quantum levels in strongly allowed transitions. The X0 JA\0 quantum level could thus be repopulated through purely —uorescent channels. For the moment we assume the existence of the SRS process illustrated in Fig. 21 without further comment about possible optical pathways leading back to JA\0 of X0. The existence of a region of absorption near 972.0 ” in Fig. 16 should however be noted. The BA-state quantum level shown at the top left of Fig. 21 is the very same one appearing at the top right of Fig. 20. In the scheme shown in Fig.20 this quantum level is shown as the resonant intermediate state in a secondary broad-band SRS process driven by Ly-b photons trapped in the H -containing cloud by H atoms also present in the cloud. It now becomes apparent that the secondary SRS process shown in Fig. 20 2 also creates a new SRS»FWPO pathway for the population excited to EF4 J\0 by the SRS process shown in Fig. 21. V ia the ìinverse Raman eÜectœ (ref. 11) it now becomes possible for visible photons coming from the illuminating star to be absorbed in a band Fig. 20 SRS»FWPO processes explaining some observed strong emission peaks appearing in Copernicus VUV spectra of mid-/late-B supergiants 156 Current status of the H DIBS theory 2 Fig. 21 SRS»FWPO process (when combined with the process shown in Fig.20) proposed in text as origin of k5780 DIB centred at the wavelength of the BA17EF4 R(0) transition with H molecules that 2 have been excited to EF4 J\0 now being driven to the (unspeci–ed) singlet-geradestate quantum level shown in Fig. 20. In Fig. 21 we have indicated the exact energies of both the BA1 J@\1 and EF4 J\0 quantum levels as listed in ref. 31 and in ref. (6 and 7) respectively. When one converts the diÜerence in energies of these levels 17 294.92 cm~1 to air wavelengths one obtains 5780.45 ”. In Table A1 of his recent review article on the DIBs,8 Herbig states the rest frame air wavelength of the k5780 DIB to be 5780.45^0.02 ”. Jenniskens and Deç sert4 list the wavelength of this DIB as 5780.59^0.05 ”. An important point to note concerning the SRS»FWPO mechanisms invoked in the above proposed k5780 DIB assignment is the following.If the H population that is excited to the unspeci–ed singlet-gerade-state quantum level shown at the top right in 2 Fig. 20 makes its way back to JA\0 of X0 entirely via a downward parametric oscillation cascade the summed photon momenta of all the light waves comprising either the SRS»FWPO process pictured in Fig. 20 or the one just discussed that combines transitions shown in Fig. 21 and 20 must be conserved i.e. ; k ki\0 where is the wave- i vector of the ith wave. Hence all the light waves participating in such SRS»FWPO processes must be coplanar i.e. they must all lie in the ìplaneœ of the thin H cloud of our model. On the basis of this consideration an explanation can be oÜered for 2-containing the known strong dependence (see e.g.ref. 8) of DIB intensity upon reddening in the line-of-sight. Reddening is generally believed by astronomers to be caused by dust particles of some kind. The presence of dust in the thin H -containing cloud of our model would cause visible photons coming from the illuminating star to be scattered into the 2 plane of the cloud thereby allowing the photons to participate in SRS»FWPO processes. Without the presence of such dust in the cloud all visible photons would simply traverse the thin cloud along the line-of-sight since there are no H or H absorption lines in the visible region of the electromagnetic spectrum to produce elastic scattering at 2 these wavelengths.In the discussion presented above it was implied that generation of a broad-band Stokes wave in an SRS process pumped by an intense —ux of Ly-b photons results in absorption of ca. 5780 ” photons through the inverse Raman eÜect. That is it was 157 P. P. Sorokin et al. tacitly assumed that the photon —ux at ” ca. 5780 propagating in the plane of the cloud is not intense enough to produce SRS by itself. On general grounds one might expect the linewidth of an absorption resulting from the inverse Raman eÜect to be much narrower than the spectral linewidth of an SRS Stokes wave generated by broad-band pumping since the former is basically only sensitive to the dispersion in the Raman susceptibility s(3) whereas the latter depends both on s(3) being large and the linear dispersion being small.32 With this in view it is interesting to note that the linewidths of both the k5780 and k6284 DIBs are ca.6 cm~1 whereas the linewidth of the k4428 DIB is roughly ten times greater. In the k6284 DIB assignment to be given below absorption could again occur via a plausible inverse Raman eÜect process. However in the case of the k4428 DIB assignment that will also be oÜered absorption via the inverse Raman eÜect is not possible and one must assume that broad-band light propagating in the plane of the H -containing cloud at wavelengths near 4428 ” is sufficiently intense to reach the SRS threshold. If this speculation should turn out to be correct the linewidth 2 of a large-equivalent-width DIB should provide an indication of the mechanism through which the DIB is generated i.e.SRS or inverse Raman eÜect. Of all the DIBs k4428 has the largest equivalent width being almost four times that of k5780 for example. The ATMs calculated in ref. 10 in principle apply to J\0 singlet-gerade-state quantum levels only. In Fig. 21 the large value indicated (0.5) for the IR transition shown should therefore be reasonably accurate. In ref. 10 ATMs are listed for transitions occurring between EF and B@ quantum levels but not for transitions between EF and BA quantum levels. However the potential curve for BA is similar in shape to that for B@ being only vertically displaced from the latter to somewhat higher energies. Therefore ATMs listed for EF»B@ transitions may be used as a guide in obtaining relative ATMs of EF»BA transitions.The ATM listed for transitions between B@1 and EF3 is very large (2.4) but the ATM listed for transitions between B@1 and EF4 is 60 times smaller (0.04) implying a very small value for the 17 295-cm~1 transition in Fig. 21. At –rst glance this appears to damage seriously the credibility of the k5780 DIB assignment here being proposed. The EF4 J\0 quantum level is also known as the F2 J\0 quantum level. The wavefunction for this quantum level is primarily localized in the outer (ìFœ) well of the double-welled EF-state potential curve. The wavefunction for the EF3 J\0 quantum level also known as the E1 J\0 quantum level is primarily localized in the inner (ìEœ) well of the EF-state potential curve. While the energy of F2 J\0 exceeds that of E1 J\0 by 204 cm~1 the energies of the E1 quantum levels increase with J faster than the energies of the F2 quantum levels.A cross-over occurs and at J\3 the energy of the E1 quantum level exceeds that of F2 by 80 cm~1. It is well known that this near degeneracy in energies leads to tunnelling through the barrier existing between the E and F wells. According to ab initio calculations presented in ref. 33 the vibrational wave functions of the outer well show a small but signi–cant tunnelling into the inner well and thus into a region that has good Franck»Condon overlap with the vibrational wavefunctions of the B@1 and BA1 states. Experimental veri–cation of tunnelling occurring between E- and F-state quantum levels was reported in ref.34. The authors of ref. 34 excited various E,F-state quantum levels by two-photon absorption from thermally populated levels of X0. The non-linear absorption was detected by monitoring the subsequent photoionization of the excited E,F quantum levels. The ion signal amplitude for the Q(0) transition to F2 was observed to be 87 times less than that for the Q(0) transition to E1. In each case the ion signal should vary as the amplitude squared of the rovibronic transition dipole moment between the two-photon-state quantum level and some intermediate-state quantum level. Hence for the F2 J\0 quantum level this transition dipole moment should be about nine times smaller than for the E1 J\0 quantum level. Thus one can estimate the ATM value for the 17 295-cm~1 transition in Fig.21 to be ca. 0.3. 158 Current status of the H DIBS theory 2 In Fig. 22 an assignment is proposed for the k6284 DIB that bears some resemblance to the k5780 assignment just discussed. In this assignment parahydrogen molecules are again the ìDIB carriers œ. The EF4 J\4 quantum level can be equally well described as the E1 J\4 quantum level that is its wavefunction is primarily localized in the E well. (The cross-over between E1 and F2 occurs between J\2 and J\3.) Therefore in obtaining ATMs for transitions between EF4 J\4 and B- B@- and C-state quantum levels one uses the values calculated in ref. 10 for transitions involving EF3. Table 1 of ref. 10 indicates very strong coupling between EF3 and C1 (ATM\3.3) C2 (ATM\0.2) B@1 (ATM\2.4) and B@2 (ATM\1.3) so that a large ATM for EF37D2 can reasonably be assumed.Using the term energy values given in ref. 31 for D2 J@\5([) (117 989.67 cm~1) and in ref. 6 and 7 for EF4 J\4(]) (102 081.05 cm~1) one obtains 15 908.62 cm~1 for the diÜerence frequency. This corresponds to an air wavelength of 6284.17 ” well within the limits (6284.31^0.33 ”) for the k6284 DIB given in ref. 4 but somewhat outside the limits (6283.86^0.02 ”) given in ref. 8. In ref. 30 results of new measurements of the line positions of some B@7X and D7X tran- D2(1% sitions are presented. In Table 7 of ref. 30 the energy for the u `) J@\5([) quantum level is given as 117 990.25 cm~1. This would predict the wavelength of the k ” 6284 DIB to be 6283.93 much closer to the value listed in ref.8. In the scheme shown in Fig. 22 no indication is given of how the SRS process that generates a Stokes wave on the C27EF4 P(4) transition is actually pumped. A simple two-photon SRS process would obviously have to start from JA\2 of X0. At –rst glance it is reasonable to assume that a sizeable steady-state population of parahydrogen molecules might exist in this level and there is some evidence in the ORFEUS-1 spectra of absorptions occurring from this level for example on the transitions B8»0P2 (Fig. 16) and C3»0Q2 (Fig. 19). In Section 4 we also saw that SRS Stokes-wave emission on B16»4P4 resulted from optical pumping of molecules in JA\2 of X0. However no absorption is seen in Fig 19 at the critical wavelength (965.8 ”) of C2»0R2.One therefore concludes that excitation of the EF4 J\4 quantum level does not occur via a simple SRS process starting from JA\2 of X0. We propose that excitation of the EF4 J\4 quantum level occurs through the cascaded SRS process diagrammed in Fig. 23. There is abundant evidence in the Coper- Fig. 22 SRS»FWPO process (when combined with the process shown in Fig. 23) proposed in text as origin of k6284 DIB 159 P. P. Sorokin et al. Fig. 23 SRS»FWPO processes proposed in text as mechanisms for excitation of EF4 J\4 quantum level nicus and ORFEUS-1 spectra that a speci–c set of parallel SRS processes is occurring in the H2-containing clouds near the stars studied with each process starting from JA\0 of X0 and terminating on JA\2 of X6. One –nds in the Copernicus spectra emission bands at B2»6P2 (1406.8 ”) B4»6P2 (1359.8 ”) B5»6P2 (1338.4 ”) B8»6P2 (1281.1 ”) B11»6P2 (1232.7 ”) B14»6P2 (1191.4 ”) B15»6P2 (1179.2 ”) B17»6P2 (1156.5 ”) B18 ) ” ” »6P2 (1145.9 emission band may also be C0»3Q1) C4»6P2 (1165.2 C2»6P2 ”) (1221.4 C1»6P2 (1254.7 ”) and C0»6P2 (1292.1 ”).The strongest of these transitions are shown in Fig. 23. Regions of absorption corresponding to the R(0) Bn7X0 and Cn7X0 pumping transitions are easily identi–ed in the ORFEUS-1 spectra. One should keep in mind that in broad-band SRS it is the total pump power at all wavelengths that determines the Stokes-wave gain at any particular wavelength. Thus for example the pump power around B5»0R0 contributes to the gain of the Stokes wave around B14»6P2.The secondary SRS process shown in Fig. 23 could deplete the terminal state (JA\2 of X6) of the primary SRS process. One sees in this –gure that Ly-a is nearly resonant with the strong (0.13]9~1) transition C2»6R2. The secondary SRS Stokes wave is assumed to occur on the C27EF4 P(4) transition as shown in both Fig. 23 and 22. The sequence of two-photon transitions that begins as in Fig. 23 and that then proceeds to some other singlet-gerade-state quantum level via inverse Raman absorption of ca. 6284 ” photons with J@\5([) of D2 being the resonant intermediate state is assumed to be part of an overall SRS»FWPO process that returns molecules to JA\0 of X0. In the scheme shown in Fig. 22 absorption of photons near 6284 ” probably occurs via inverse Raman absorption.However unlike the case of the scheme shown in Fig. 20 it is here difficult to isolate an independent SRS process that can generate broad-band coherent radiation centred about the transition between J@\5 of D2 and a lower-lying singlet-gerade-state quantum level. The energies obtained by subtracting Ly-a Ly-b Ly-c or Ly-d from the energy of D2 J@\5 are nowhere close to those of X-state quantum levels except JA\4 of X13. However D27X13 transitions are extremely weak relatively speaking. This implies that broad-band coherent radiation centred on the transition from D2 J@\5 to a lower-lying singlet-gerade-state quantum level must 160 Current status of the H DIBS theory 2 ìcome from aboveœ that is it must represent a component of a parametric oscillation cascade that originates at some higher-lying level.The existence of such a higher-lying level emerges from our (combined) assignments of the k4428 and k4882 DIBs to be discussed next. Our assignments for both the k4428 and k4882 large-equivalent-width DIBs are shown in Fig. 24. From inspection of this –gure several unusual features are seen to be involved. (1) The uppermost quantum level shown in the –gure could be either D8(1%u `) J@\2(]) or BA6(1&u `) J@\2(]). According to ref. 31 both quantum levels have exactly the same energy 127 320.11 cm~1 and both are seen to be optically connected with the two EF-state quantum levels shown although none of the relevant ATMs were calculated in ref. 10. It is at this point impossible to say which of the two equi-energetic upper levels plays the dominant role in the case of each of the two DIBs.(2) In Fig. 24 excitation of the quantum level EF11 J\3 is shown occurring via an SRS process that starts from X0 JA\3. Strong supporting evidence that this process actually occurs can be seen from inspection of Fig. 17. We remarked at the end of Section 4 that no evidence of C4»0R1 absorption exists in this –gure. However the reader should now take note of the intense region of absorption appearing at the C4» 0P3 wavelength. In general absorptions originating from JA\3 of X0 appear quite prominently in the ORFEUS-1 spectra suggesting the existence of a relatively large population in this level perhaps fed by Stokes-wave emissions. In Section 4 a prominent emission band was assigned to B0»0P3.From Fig. 19 one sees that strong absorption on either C3»0R1 C3»0R0 or on both of these transitions could be occurring but it is hard to distinguish among these possibilities since the frequencies of C3»0R0 and C3»0R1 diÜer by only 4 cm~1. In principle the EF8 J\1 state could also be populated by an SRS process involving C3»0Q1 as the pumping transition. While there is no strong evidence of absorption occurring at C3»0Q1 in the case of HD 214080 the ORFEUS-1 spectrum of HD 149881 shown in Fig. 25 gives some indication that SRS excited via C3»0Q1 may be occurring in the H -containing cloud near this star. (The wavelength scale for the HD 149881 spectrum is less accurate than that for HD 214080.) The non-linear nature of the 2 H absorptions which appear in the ORFEUS-1 spectra of these two B-type halo stars is again illustrated by the fact that the radiative transition probability of C3»0Q1 is 3.5 2 times that of C3»0R1.Fig. 24 SRS»FWPO processes proposed in text as origins of j4428 and j4882 DIBs 161 P. P. Sorokin et al. Fig. 25 Expanded views of ORFEUS-1 spectra of two stars (HD 214080 and HD 149881) that include the wavelength region of the C3»0 transitions discussed in the text. All the pumping and Stokes-wave transitions shown in Fig. 24 have very large transition dipole moments making them very favourable for SRS processes. All the quantum level energies have been rounded oÜ in Fig. 24 since the DIBs here are very broad and the frequencies at their maxima are therefore much less accurately known than in the case of narrower DIBs.The exact frequencies and air wavelengths of the two transitions in Fig. 24 to which the two DIBs are assigned are 22 572.78 cm~1 (4428.89 ”) and 20 480.45 cm~1 (4881.36 ”). Ref. 4 lists the wavelengths linewidths and equivalent widths (in HD 183143) of the two DIBs as 4428.88^1.35 ” 12.33^2.06 ” and 2488 m”; 4881.83^0.65 ” 19.67^2.38 ” m and 810 ”. In ref. 8 the values of the same quantities are given as 4428^1 ” 18 ” m and 3400 ”; 4882 ” 25 ” m and 890 ”. In wavenumber units the linewidths of these two DIBs given in ref. 4 are 63^10 cm~1 for the k4428 DIB and 82^10 cm~1 for the k4882 DIB. Within the limits of error the linewidths could thus possibly be the same.We hypothesize that enough blue and blue-green light is scattered by dust into the plane of the H -containing cloud to pump the secondary SRS processes shown in Fig. 24 beyond threshold thereby opening up new hybrid SRS»FWPO optical pathways. 2 One should here bear in mind that the —ux emitted by a T \15 000 K radiator when expressed in units of power per unit area per unit frequency interval peaks somewhere near the blue region of the spectrum. It is also a feature of broad-band SRS that the Stokes-wave gain is remarkably —at even when the pump radiation spectrally spans a resonance line.32 The secondary SRS process shown in Fig. 24 is hypothesized to continue in a downward parametric oscillation cascade. If the optical pathway of this downward cascade were to involve for example the D2 J@\5([) quantum level in Fig.22 this would lead to absorption of photons near 6284 ” by the inverse Raman eÜect. 6 Conclusions In trying to account for major de–ciencies apparent in the H DIBs model of ref. 1 we have called attention to what we believe is VUV spectral evidence indicating that there 2 ubiquitously exist thin cold tenuous H -containing clouds located close enough to B-type giant and supergiant stars that the 2H molecules in these clouds are driven into a 2 162 Current status of the H DIBS theory 2 pattern of coherent oscillations by the VUV blackbody continua emitted by the illuminating stars. At present we are unable to estimate either the actual distances between the H -containing clouds and the nearby stars or the shapes of the clouds.Our overall conclusion regarding the generation of coherent light in these clouds mostly derives 2 from the following sequence of observations. (1) Emission bands seem to be clearly present in archived (900»1450 ”) spectra of B-type supergiants. (2) These bands appear at exactly the same wavelengths in the spectra of all the mid-/late-B supergiants examined. (3) On the basis of wavelength positions alone these bands appear to be readily assignable to low-JA H transitions on which one would expect SRS Stokes-wave emission to occur if viable mechanisms existed to deplete the populations of the terminal 2 states. We then proposed that such mechanisms are provided by the presence of greatly enhanced densities of Ly-a Ly-b Ly-c .. . etc. photons trapped in the H -containing cloud via elastic scattering by H atoms also assumed to be present at high densities in 2 the cloud. It was shown how pumping by the Ly-a Ly-b Ly-c . . . etc. —ux can initiate secondary SRS processes which deplete the primary SRS terminal states. It is assumed in our model that the secondary SRS processes then typically initiate downward parametric oscillation cascades which ultimately repopulate the ground state. The overall optical pathways in such schemes can best be described as SRS»FWPO mixing processes in which SRS inverse Raman absorption or parametric oscillation can occur at one or more of the 2n (nP2) steps. In such SRS»FWPO schemes conservation of photon momentum holds i.e. i\0 ; 2 n i/1 References k This necessitates that all the light waves participating in SRS»FWPO processes be coplanar.Assignments for several large-equivalent-width DIBs are shown to follow from consideration of speci–c hybrid SRS»FWPO processes. In order that visible photons emitted by the illuminating star can be absorbed in individual SRS or inverse Raman steps of a hybrid SRS»FWPO process the photons must be propagating in the ìplaneœ of the thin H2-containing cloud. 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