MASERS IN SPACE* B. E. TURNER National Radio Astronomy Observatory! Green Bank, West Virginia. Received June 29,1970

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1 MASERS IN SPACE* B. E. TURNER National Radio Astronomy bservatory! re Bank, West Virginia Received June 29,197 f the sev molecules prestly detected at radio wavelgths in the interstellar medium, H and H2 display spectacular emission properties attributed to maser action. The H masers fall into three distinct classes, herein described, each of which is anomalously excited by a differt pumping mechanism. Far IR radiative pumping is applied to rect observations of anomalous H emission in dust clouds. The excitation of H by the collisional dissociation of water vapor is described next, and is shown to explain rect observations of microwave emission from excited states of H. It also explains why the type of H emission that it produces (Class I) is observed to occur in the same regions as anomalous H2 emission. A pumping mechanism for the H 2 is also described which is expected to operate in any regions in which Class I H emission occurs. I. Introduction At the time of writing, sev molecules have be detected in the interstellar medium at radio wavelgths: H, H 2, NH 3, H 2 C, C, CN, and HCN. f these, H and H 2 display spectacular emission properties attributed to masering. H 2 C has equally anom- alous excitation; the three transitions prestly observed have anti- inverted population distributions, resulting in anomalous absorption against ev the 3 K background. NH 3 is observed weakly in emission in only the alactic cter region, and its excitation also appears somewhat abnormal in the sse that the excitation temperatures for the inversion transitions increase with increasing rotational excitation. There is no prest evidce that C, CN, or HCN are anomalously excited, and neither is this expected on the basis of the very simple ergy level schemes in the vicinity of the observed transitions which include the ground states in each case. This simplicity does not apply to the ergy level schemes of H, H 2, H 2 C, and NH 3, and this, along with certain similarities ne of the invited symposia papers prested at the Pticton meeting of the Astronomical Society of the Pacific, June 18-2, 197. f perated by Associated Universities, Inc., under contract with the National Scice Foundation. 996

2 MASERS IN SPACE 997 in the structure of the first three of these molecules, probably has a bearing on their anomalous excitation. The observed states of H 2 C and NH 3 lie well above the ground state (~ 1 cm -1 and 15 cm -1 respectively) but are metastable against decay to the ground state. H 2 has a complicated ergy level scheme (see Fig. 3) which also relies on the metastability of certain IR transitions to establish anomalous population distributions under moderate collision rates. H and H 2 C have electron configurations which may, under special circumstances, be selectively orited by collisions leading to non-lte population distributions wh the collision rates do not exceed spontaneous emission rates in the IR wavelgth range. In this paper we will limit ourselves to a discussion of the anomalous excitation and emission of H and H 2, although at least one theory which we shall apply to the H case is probably also applicable to the excitation of H 2 C. We emphasize developmts made in the past 15 months, as the earlier work has be summarized elsewhere (Robinson and Mcee 1967; Turner 197h). During this period it has be established that anomalous H emission is associated primarily with Hii regions and infrared (IR) stars, but is also found in supernova remnants, close to IR nebulae, and in dust clouds. It has not be found in Wolf-Ray et stars, T Tauri stars, planetary nebulae, globules, and heavily redded stellar clusters. Anomalous H 2 emission has be found in H ii regions and IR stars. There is no prest alternative to the maser hypothesis of anomalous H/H 2 emission. n the contrary, observational evidce has be gathered which allows a quantitative test of one H excitation theory, and which provides strongly circumstantial support for another. Although progress has be made in understanding the nature of the pumping of H (and to a lesser extt, of H 2 ), there are three major obstacles to a complete picture of interstellar masers. 1. Are the masers saturated or unsaturated? Differt observations are still ambiguous on this question. 2. What is the solid angle of maser emission, and the geometry of the amplifying medium? These must be known to assess the efficicy of pumping theories and to understand whether background radiation or spontaneous emission is being amplified.

3 998 B. E. TURNER 3. What is the nature of the polarization? Currt ideas require a saturated maser to produce high degrees of polarization, so that the three problems just mtioned are not indepdt. Interstellar H 2 shows maser action in only one detected line as yet, the transition at Hz; since the hyperfine splitting of this transition is not resolved in the interstellar emission, the only constraint on a pumping theory for H 2 is that it invert the population distribution in the observed transition and that it involve sufficit ergy to significantly populate these levels, which lie 477 cm -1 above the ground state. These conditions do not distinguish betwe any of several possible theories, in particular those involving chemical or collisional pumping. Radiative pumping can probably be ruled out, since it appears inadequate to produce the 6 X 1 48 microwave photons/sec estimated to be radiated in the strongest source. By contrast, significant progress has be made in understanding the excitation of H interstellar masers, mainly because there are now nine differt detected transitions, including the four ground state ones, and 14 transitions searched without detection; these impose quite rigid constraints on any pumping theory. They also indicate, however, that several differt pumping mechanisms must be at work, singly or sometimes together, in the various H sources. These differt mechanisms manifest themselves in the fact that the relative strgths of emission among the four ground state lines, as well as their polarization properties, seem to fall into three distinct classes. These classes are also associated with differt types of objects, ranging from bright Hu regions for one class, to IR stars and Mira variables for another. We shall describe observationally the three-classes of H emission, two of which are also associated with H 2 emission, th review the two pumping theories (out of several proposed) that seem able to explain these classes. For the IR pumping theory a quantitative comparison with rectly discovered anomalous emission in dust clouds is carried out. Th we compare the theory of pumping of H by collisional dissociation of H 2 with the observations of those H sources found to be associated with H 2 emission; the predictions of this theory are also compared with rect observations of the excited states of H. Finally, we describe

4 MASERS IN SPACE 999 a pumping theory for interstellar H 2, and th compare the theory of coexisting H/H 2 masers with observations. II. Classes of H Emission Table I summarizes the properties of the three classes of anomalous H emission, as they apply to the four ground state lines. Significantly, this differce by class seems to be reflected in the differce in the origin of the emission. Most emission sources associated with H n regions are Class I, all emission sources associated with IR stars are Class 11(b); and most sources associated (in projection at least) with nonthermal sources are Class 11(a). As a measure of the gerality of this classification scheme, we note that the properties listed in Table I apply to all 39 well-studied H sources with minor exceptions in three cases. (In one of these cases, NC 7538, the properties are Class I except that 172 MHz emission is as strong as 1665 MHz emission; in the other two cases, which are Southern Hemisphere sources, properties are Class 11(b) except that the 1612 MHz emission is significantly circularly polar- ized.) Preliminary studies of 22 new H emission sources (Turner 197a) have uncovered no further discrepancies. In addition to the strange Tine ratios and peculiar polarization, it is well known that the third outstanding property of the H emission sources is their high brightness temperatures (T B ). Very long baseline (VLB) measuremts have established sizes of typically 1 14 cm, corresponding to T B as high as 1 13 K for the Class I emitters. More rectly, similar techniques have led to values of T b ~ 2 X 1 1 K for two Class 11(b) sources, NML Cygni and VY Canis Majoris. As in the Class I sources, these latter sources show a large number of small emission cters within a region of size ~ 2 seconds of arc. As yet, no definitive VLB results exist for Class 11(a) sources, but we may anticipate that they have values of T B within the range 1 1 and estimated distances to these sources. K to 1 13 K, based on the received fluxes It will be noted that we have not included the weak H emission from dust clouds in Table I. Rect measures of the satellite lines in these dust clouds (Turner and Heiles 197) show that they do not have LTE excitation. The anomaly is in the sse of the Class 11(a) sources in that the 172 MHz line is stronger, and the 1612 MHz line weaker, than would be the LTE ratios with the main

5 1 B. E. TURNER w J PP < H fc > < w S H ffi «S H < U W H H H a Ü a3 U U a; C o j-* C N X cq i-h C N ffi cq t> N 33 V5 f S M mh a; h ^ Sqy a cq ^ ^ ) N ffi s ca r I C rs l i-h (U»' a g: Z o S co Jh jg 3 S-H U r- S S Ci g* N g S g K - ^ ft -y î I î l ^ ai ai eg S 'go 2 g» "" j io ro rv> ofl co <*> *M S y S ^ C. *H PQ (J U 33 ph bud ph ph -M C/D ph C/D ph.s o C/D! C 4 1 s ) -M ai bjd S-H B*.g g S u in <! c2 5-1 o i-h 4-> ai N S JS ~ H o Ph * 4-> 5h «2 ph PP S ä S ( > ai 13 > g >* S ai I a'ï S g g g > ^ o) g æ * fi ai 2 o n. 4-» <4H 3^ co Z 4 i-h 1 l-h ai ai ^ S fi - Ifi ^ g: h 3 5 i I 33 6 Jh bj <3 J 13 > T3 -M jj 13 u P ; l 5 4-» i ( 13 PP bjd ai ^ N ÍME ph» i 13 > 5h cq r I C N - X bû S jh 2 io ^ 6 ai S u > ' bî) >N U VÍ Z N 3! 33 S 2 oo ^ cq V/ co C C U 1T S 4 > CN rf Vf D ph I 2 eu >-H æ g fi S g w w Ail but three of 26 known class 11(b) emitters have two distinct velocity ranges in the 1612 MHz emission; this suggests the emission is from an expanding, contracting, or rotating cloud. I Linewidths for Class I seem negatively correlated with line intsity. JLinewidths for Class 11(b) are usually intermediate betwe those of Class I and Class 11(a).

6 MASERS IN SPACE 11 lines. Later on, we shall indicate how the IR pumping theory for Class 11(a) sources explains the dust cloud emission. III. The Concept of an Interstellar Maser The high brightness temperature T B, anomalous line ratios, and high degree of polarization preclude any thermal explanation of H and H 2 interstellar emission. n a thermal basis die observed linewidths are also much narrower than is consistt with the observed values of Tß. It is now accepted that the populations of the ergy levels are inverted and that maser amplification is occurring, either of background radiation or of spontaneous emission from the H itself. For most purposes it is adequate to neglect time depdce in the equation of radiative transfer, which in the one-dimsional case is th dl dx od c + bl + (i) where a is the gain factor (negative absorption coefficit) for small stimulated rate and collision rate, al(c + bl) is the (reduced) gain factor wh these rates are not negligible, I is the specific intsity, and x is the path lgth, c = 14-2 SJS P where S c is the collision rate (per sec per molecule) which tries to thermalize the molecules and S p is the pump rate producing the population inversion. b = (2B/Sp) (il/47r) where B is the Einstein coefficit for stimulated emission and Í1 is the solid angle of the maser beam, e = Alwl4ir8v is the usual emissivity. If we neglect the depdce of e on I (through rifj) the solution at a giv frequcy is (a 4- eb)x b(i I ) c cebl(a 4- eb) ]- l} +/o. As a function of x, I lo grows expontially for small x, th decreases its rate of growth for larger x until in the limit of large x the growth is linearly depdt on x. The larger b is, the smaller is x at which the expontial growth goes over to linear growth, hce the smaller is I I at any giv x.

7 12 B. E. TURNER It has be customary to limit theoretical discussion to the two limiting cases of unsaturated and saturated maser amplification. In the unsaturated case, c>> bl, and the solution of (1) is simply /*= l e Mlc + (e *i c -1) (2) a where the first term is the amplified background and the second term the amplified spontaneous emission. The gain factor a = \ 2 AAn/87rô^, where An = n (g u /g ) with and n z re- ferring to the population dsities of the upper and lower levels of the transition in question, and A is the Einstein spontaneous emis- sion coefficit. Very large values of T B = A 2 / x /2k may result wh a x is large. Relatively small differces in a for the various transitions result in large corresponding differces in I x. A narrowing of the lines, by the factor (axlin2) v, is also accomplished by the expon- tial scaling of the frequcy depdce of a. In currt theories (see Litvak (197) for a summary) the anomalous polarization does not arise under conditions of unsaturated growth, but requires at least the onset of saturation. In the fully saturated limit (bl > > c) the solution is I x = Iq + (An S p hv/sv 4- e)x where for simplicity we again take all quantities in partheses as indepdt of path lgth x. Here, An is the population differ- ce calculated under unsaturated conditions, and we assume that the saturation is homogeous over the linewidth. Large values of Tb may still occur, but require much larger values of Anx than in the unsaturated case. No line narrowing occurs for a fully saturated maser; the narrow widths emerging from the unsaturated portion of a maser are broaded during the saturated part until they become equal in width to the unamplified lines. It is possible that the observed properties of narrow linewidths and high degree of polarization can occur in a maser which is only partially saturated, ough to produce the polarization if it indeed arises from the nonlinear suppression of one polarization mode by another, as currt theories indicate, but not ough to overcome appreciably the line-narrowing properties of the unsaturated growth. ne diffi- culty with this picture is that if a maser is ev partially saturated at the d we actually observe, as is expected from the very large

8 MASERS IN SPACE 13 values of bl that correspond to observed values of T B, th it must be at least partially saturated over the tire path lgth, assuming that a maser beam can propagate equally well in one direction as in the other. This situation is not altered by the fact that orthogonal polarization modes may be traveling in the opposite directions. Therefore if saturation is required to produce strong polarization, it is difficult to understand the very narrow observed linewidths, which correspond in Class I emitters to kinetic temperatures of typically 25 K to 4 K and as low as 7 K. Another difficult question is whether background radiation or spontaneous emission controls the number and direction of modes that are amplified. The answer depds among other things on the initial conditions in the maser. In a case in which the population inversion was established throughout a cloud in a time shorter than the light travel time through the cloud, the following possibilities occur. For large ough dsity and path lgth there will be an interior region in the cloud within which, after the onset of masering, the radiation fields built up by amplified spontaneous emission will be strong ough to cause saturation before the amplified back- ground has petrated this far. These modes, which are isotropically distributed, will td to persist under saturated conditions, rather than be overridd by the background modes. Hce the maser output will be into a large solid angle if it is not restricted by turbulce to narrow, filamtary paths. Such filamts would be expected to be continually varying, and hce appear somewhat unlikely for the H case, in which few instances of time-varying emission are observed. n the other hand, if the initial population inversions are established slowly and in a not-too-dse cloud, saturation might be induced by the background source modes if the source is sufficitiy strong, rather than by spontaneous emission modes, which would th be suppressed. The maser output in this case could be quite directional. In either case the back- ground radiation will not compete with spontaneous emission unless ToHo/47t ^ Iwriulk An.1 to 1 for typical H pumping models. This criterion probably would be satisfied only for continuum sources near the masering cloud which subtd a fairly large angle fio at the H cloud. Thus the background sources would not impose a high degree of directionality on the maser output, as would also be the case for amplification of the 3 K background.

9 14 B. E. TURNER IV. Far-Infrared Pumping of H An examination of the ergy level scheme for the three lowest rotational states of H is shown in Figure 1 (Litvak 1969); this indicates a simple explanation for the outstanding aspect of Class 11(a) emission in which the 172 MHz transition (F = 2» 1) is masering and the 1612 MHz transition (F = 1 >2) shows anoma- lously strong absorption relative to the two main-line transitions which have an LTE ratio. This situation will be achieved if pop- ulation can be transferred from the F = 1 to F = 2 level in both A doublet states. This transfer in turn is accomplished by far IR transitions connecting the ground state with the n 3/2, J = 5/2 state at 84 cm -1 and with the II1/2, / = 1/2 state at 126 cm -1. Either externally applied or internally gerated far IR continuum or F 1 Fig. 1 The ground 2 ri3/2, J = 3/2 and excited rotational states 2 n3/ 2, J = 5/2 and 2 i! 1/2 of H, which trap resonant far-ir photons and lead to a population transfer betwe the ground hyperfme-split states. Arrows indicate one possible direction of transfer.

10 MASERS IN SPACE 15 resonance line flux will cause the transfer, associated with the inter- locking far IR transitions whose line strgths are indicated as 4.86 and.2. These transitions connect the F = 1 and F = 2 hyperfine states of a giv parity in the ground state with a common excited hyperfine level, and a transfer can occur because of the unequal line strgths for the interlocking transitions. The transfer can be from F=ltoF=2, or F = 2 to F = 1 depding on the ratio of intsities of the interlocking transitions. This ratio in turn depds on the degree of resonant trapping of the far IR photons, hce on the optical thickness of the H cloud in the IR. Litvak (1969) has analyzed in detail the degree of population anomaly produced in the two satellite lines as a function of Hi, the fractional distance into the cloud? measured from the face upon which external far IR flux falls. Figure 2 is adapted from Litvak s results. Positive gain factors correspond to 172 MHz inversions (with corresponding anti-inversions at 1612 MHz). The reverse applies for negative gain factors. For all three values considered for To, the optical depth in the weakest IR transition, the back half of the cloud has an anomaly opposite to that of the front half. The three cases considered cover a range of dsities suitable for main- taining the necessary A doublet excitation via collisions with H atoms while allowing the IR to control the F-level populations. To interpret these results in the light of observations (of the strong Class 11(a) emitters), Litvak considers the IR pumping source to be a 1 K blackbody (similar to the IR nebula that exists in the rion nebula), which subtds it steradians at an H cloud whose dsity n H ~ 1 5 cm -3. Th for the case noh^ows*' ~ 1 22 (to 1 in Fig. 2) the cloud can produce ~ 3 X 1 1 pho- tons sec -1 cm -2, corresponding to approximately three perct efficicy for converting far IR photons to emitted microwave photons. The emission is assumed to arise in the back half of the cloud, since here there is inversion for a wider range of projected dsities than is the case for the front half. The H cloud is assumed to lie betwe the observer and IR source, to avoid att- uation which would occur in the front half. If the H cloud has a diameter of 1-3 parsecs, slightly larger than the VLB-established sizes for Class I emitters, th under saturated conditions the re- ceived flux (13 f.u.) from the strongest source in this category, W28, can be achieved if the maser solid angle is no larger than ~.1

11 16 B. E. TURNER Fig. 2 ain curves for an H cloud having the quantity nqn^qv/bp in the range 1 2 to 1 22, corresponding to an IR optical depth in the range ~.1 to 1, and pumped by far-ir radiation. Positive values of the gain correspond to inversions in the 172 MHz transition, while negative values correspond to 1612 MHz transitions. ster; for W44, a more typical Class 11(a) emitter, Í1 <.7 ster is required. Such beams could easily be produced by the requiremt of uniform velocity along the path lgth in the presce of turbulce, and do not make the probability of observing such sources excessively small. f course the 1612 MHz line would be strongly absorbed, as is observed, owing to the strong anti-inversion of this transition. While the far IR pumping model does not seem to counter any strong difficulties in explaining these Class 11(a) sources, neither can it be definitively checked since we do not know noh&o>

12 MASERS IN SPACE 17 Tb, or iî for the maser. The rect discovery of anomalous satellite line emission in dust clouds (Turner and Heiles 197), which appears to be a very weakly operating example of the Class 11(a) anomaly, serves us with a more definite test. In these clouds, the 172 MHz line is found to be anomalously strong, typically half as strong as the 1665 MHz line, while the 1612 MHz line is anomalously weak, being undetected in one case. Because the clouds are large relative to the observing beamwidth, we know T b ; and because the anomalies are observed to be the same over the tire extt of the clouds, we can safely assume Í1 = 47t. The ratio of line intsities 1667/1665 is observed to be slightly less than 1.8, the LTE ratio, and is attributed to the usual large optical depth effects; this allows a determination of both T K, the kinetic temperature (assumed equal to the excitation temperature of the main lines), and no H &o- Knowing n H^? we can select the particular set of curves in Figure 2 that must apply. ne quantity is unknown, the ratio r co i/r IR of collision rate to IR pump rate. To test the IR theory one th numerically integrates the appropriate curve in Figure 2 through the cloud in the presce of a 3 K background which may be either amplified or absorbed. The result is fitted to the observed intsity of the 1612 MHz line (say) by fixing the value of r co i/r IR, which incorporates the derived value of T k. ne th checks to see if the observed intsity of the 172 MHz line is predicted. The results of such calculations do fit the observations, but the solutions are not unique. If noh&ws*' 2 X 1 2 cm -2, the far IR pumping theory applies, in the case that the IR pump source is betwe the cloud and the observer. The result is quite inssitive to T k and to r co ilr m, although the larger T K is the smaller r col /r IR must be. However the result is critically depdt on the value of Woh^oWô*' and cannot fit the observations outside the range 1.4 X 1 2 < n H&*'/*' ^ 3 X 1 2 The value derived from the main lines lies within the acceptable range in each case except cloud 2, for which the data are rather uncertain. Litvak (1969) has also produced results analogous to those of Figure 2 for the case of near-ir pumping. Here, the 2.8/x transition betwe the v = and v = 1 vibrational states is excited, and on the suing cascade back to the ground state releases far IR photons at a large number of wavelgths corresponding to all of the rota-

13 18 B. E. TURNER tional transitions in the ground vibrational state. These far IR photons in turn are trapped within the thick cloud, and produce anomalous populations in the hyperfine levels in much the same way that direct far IR pumping does. The calculations apply to 2.8/a excitation applied uniformly within the cloud; such pumping radiation might arise from shock fronts within the cloud or from an imbedded IR nebula. ur calculations show that again a fit can be achieved with the observed ground-state line ratios, this time with n H&*'/*' 1.4 X 1 21 cm -2. The same sort of depdce is found on the various parameters as was the case for direct far IR pumping. The acceptable range for a fit is now very narrow, however, namely, 1.2 X 1 21 ^ noh^ow^ ^ 1.7 X The derived values of this quantity for clouds 4C and 1 definitely lie outside this range and within the range predicted by direct far IR pumping. The value of n H SL v l8v derived from the main lines for cloud 2 lies betwe that predicted by far IR and near IR pumping. What confidce can we place in far IR pumping as the source of excitation for the dust clouds? First, it is the only known model capable of reasonably correct quantitative predictions. (For example, UV pumping, which under some situations can hance the 172 MHz line relative to the others, was examined and found inadequate.) Second, the values of T K and r C oi/ r m required by the IR model also fit the observed values, for values of r IR which are consistt with the pump source being a few M5 stars, or the alactic cter IR source. But there are a few worrisome aspects of the IR model. Since the line ratios are found to be very nearly the same in all five positions observed in three differt clouds, we th require that noh^owôr' be almost exactly the same in all these cases. This is indeed implied by the values derived from the main lines. However this uniformity also implies that the IR pumping rate must be very uniform over a cloud, and the same for the three clouds observed. Both clouds 1 and 4 have some bright IR and UV stars around them, and cloud 2 has a bright IR star projected directly against the ctral portion. Presumably they cannot be responsible for the pumping, since they would not provide sufficitly uniform illumination over the cloud. The alactic cter IR source would suitably illuminate clouds 1 and 2, which lie beyond the solar circle so that the observer views

14 MASERS IN SPACE 19 the front face of the clouds. However a differt IR source may be required to pump cloud 4C since it lies inside the solar circle where the observer views the back face, a situation which may produce an hancemt of the 1612 MHz line. It is clear that a more definitive test of the far IR pumping model will emerge only from additional observations of many more clouds in both the 18-cm H lines and with IR techniques as well. V. Excitation of Class-I Emission Sources by Collisional Dissociation of Water ver the past four years there have be a number of attempts to explain the strongest and most prevalt type of H emission, Class I, by UV pumping (Litvak et al. 1966; Litvak 1968), preassociative formation of H (Solomon 1968), and pumping by anisotropic distributions of charged particles (Johnston 1968; Turner 1967). These models have all failed to predict the typical line ratios observed in Class I sources, or have lacked the necessary efficicy, or both. They have also failed completely to explain the observed emission from excited states. winn et al. (1968) have proposed a pumping mechanism which produces H in certain excited states by the collisional dissociation of water vapor. These excited H states, upon decay to the ground state, lead to a predominant inversion of the 1665 MHz transition as well as a very sizable inversion at 1667 MHz and small inversions of the satellite transitions. Besides producing the observed 18-cm line ratios of Class I sources, this mechanism has succeeded in predicting at least two other properties of Class I sources which have be observed only after the model was proposed: (a) Class I H sources are associated with powerful H 2 maser sources; and (b) it is consistt with all of the observations of excited state H lines. In addition, a pumping model based on a similar mechanism has rectly be applied to the anomalous excitation of interstellar H 2 C (Townes and Cheung 1969) and appears able to explain the observations of that molecule, which now include three differt states. The winn et al. mechanism involves the reaction

15 11 B. E. TURNER The most likely collisions involve a major interaction betwe the incidt H atom and one of the H atoms in the H 2. During rupture of the H-H bond by this collision, a force operates in the H--H plane to accelerate the atom relative to the cter of mass. This produces an angular momtum in the H fragmt which is perpdicular to the line betwe the and H atoms in the H. An additional process operates to orit the electron distribution in the H. The three PH electrons in the H 2 and H molecules are equivalt to a single PH electron hole. It is found that the P electron hole left on the oxyg will have the same orbital which exists in the H 2 before collision, since the collision is adiabitic. That is, only those electron distributions correlated with the original H 2 distributions will be formed. Calculation shows that these distributions have the PH electron hole perpdicular to the rotational angular momtum, and that this in turn corresponds to the upper A doublet levels in the n 3 /2 H states and in the ni/ 2, J ^ 9/2 states, but to the lower A doublet levels in the ni /2, J < 9/2 states. Because the collisions must be adiabatic, they also take place in a time short compared with the inverse hyperfine splittings. Thus there is no significant selection of one hyperfine state over another. (For those collisions that are not quite adiabatic, calculations show that the lower of the two hyperfine states in both levels of a A doublet will be selected, if the H 2 is initially in the ground oo state; this selection arises because the oo state is a singlet state both with respect to nuclear spin and to electron spin.) But a selection of the lower (F = 1) hyperfine levels in at least the ground state is also accomplished by trapping of the far IR photons released wh the H created in excited rotational states decays to the ground state. During the cascade the selection rules allow a sizable fraction of the molecules in ni/ 2 states to cross over to the n 3/2 states but not vice versa. Th, the effect of the far IR trapping is similar to that of near IR pumping, as described by Litvak (1969) in that it effects a transfer of populations from F = 2 to F = 1 states in the ground state. Together with the A doublet inversion produced by the collision process, there results a larger inversion of the MHz transition than of the others, as observed in Class I sources. In cases where the IR is ineffective (optically thin clouds) the 1667-MHz transition would be most strongly inverted. This is also the case in some Class I sources.

16 MASERS IN SPACE 111 The results of detailed calculations show that for r ÏR < 1, the 1665-MHz line dominates, while the 172-MHz line is not inverted at all. The 1612-MHz line is almost as strongly inverted as the 1667-MHz line. For r IR > 1, the 1667-MHz line becomes the strongest and the 172 line appears in emission also. These results apply to a wide range of collisional pumping rates. However if Tir becomes very large, IR pumping cycles which carry the ground state populations back up through higher states can transfer population from the upper to lower level of the ground-state A doublet, decreasing the gain factors. This already occurs slightly for r ÏR large ough to make the 1667-MHz transition the strongest, and explains why those Class I sources with strongest emission at 1667 MHz are in geral weaker than those for which the 1665-MHz line is strongest. The range of r IR for which the 1665-MHz line is strongest is ~.1 ^ r IR < 1, corresponding to 1.4 X 1 2 < noh^ow^ < 1.4 X 121, or 2.4 X 1 14 VT k ^ n^o ^ 2.4 X 1 15 V T Ky where T K is the kinetic temperature of the gas. Provided T K is large ough (~ 1, K) to allow a sufficit dissociation rate for the H 2, the only other condition required by the model is that the total particle dsity not exceed ~3X 1 6 cm -3, or the electron dsity ~ 1 3 cm -3, in order that IR radiation rather than collisions dominate the cascade to the ground state. ne problem which arises is that the observed narrow linewidths can only be produced by unsaturated masering and, for the overall gains implied by the observed intsities, only if T K < 3 K. Th the observed high degree of circular polarization might not occur if, as currt ideas suggest, it requires a region of saturated amplification. It is possible, however, that the kinetic temperature of the H and of the H 2, which is thought to be sputtered off grains, is considerably lower than that of the colliding particles. Certainly the grains, if prest, must be much cooler than 1, K to have survived; and since the H must, after creation, cascade to the ground state and give up its photon to the maser beam before being thermalized, its temperature might be low ough to allow a region of partially saturated masering without producing linewidths broader than those observed. VI. Excited States of H Two years ago the first excited state of H, the ni /2, J = 1/2 state, was observed in the Class I source W3 (Zuckerman et al. 1968).

17 112 B. E. TURNER nly the F = 1» transition at six-cm wavelgth was observed, and although this transition has since be se in several sources, all Class I, the F = 1» 1 line, which has twice the strgth of the F = 1» transition in LTE, has never be detected despite exhaustive searches. This means that the A doublet in the J = 1/2 state must be anti-inverted, as predicted by the winn et al. (1968) theory. The evidt inversion of the F = 1» transition can be produced of course by trapped far IR if the rate exceeds that of the anti-inversion process. That this is very likely follows from the fact that only approximately 2 perct of all H molecules created in excited rotational levels pass through the J = 1/2 state on their decay to the ground state. n the other hand the trapped IR intsity at 126 cm -1 can exceed that produced only by the photons released during the initial cascade through the J = 1/2 state, either because of externally produced IR, or because additional photons at 126 cm -1 can be produced by the cycle II3/2, J = 3/2 II 1/2, / = 3/2->n 1/2, J = 1/2-»Ila/a, /=3/2. Estimates based on the observed strgth of the six-cm line are that, by trapped IR processes, the magnetic sublevel populations of the J = 1/2 state are approximately t perct of the ground state population. Thus the IR can easily overcome the A doublet antiinversion for the 1 transition. Continuing with the n 1/2 states, exhaustive searches for the 3.8-cm lines from the J = 3/2 state have proved fruitless (Turner 1969; Schwartz and Barrett 1969a; Ball et al. 197). In addition, a rectly published detection of the 3.8-cm line from the F = 2 > 2 transition in the J = 5/2 state (Schwartz and Barrett 1969F) has proved to be erroneous (see Ball et al. 197). These two negative results are again consistt with the prediction of the winn et al. (1968) theory, that all A doublets in the IIi/ 2 ladder be anti-inverted for J ^ 7/2. In the n 3/2 ladder, Y et al. (1969) detected in W3 emission from both main lines in the J = 5/2 state, at five cm. The satellite transitions were not detected. More rectly (Zuckerman et al. 197) the main lines in this state have be found in the Class I objects NC 6334 and Sagittarius B2 although not in W49. In no case have the satellite lines be found. These lines are considerably stronger than the six-cm line by a factor of more than t. Strong emission from the main lines indicates that the A doublet

18 MASERS IN SPACE 113 is inverted, while failure to detect the satellite lines indicates that the IR trapping to this state is not sufficit to overcome the weak satellite line strgths relative to those of the main lines (1:1:14:2). Because the upper limit for the satellite lines is less than l/2th of the observed strgth of the F = 3» 3 line, the masering in this state is probably partially unsaturated. n the other hand, the emission seems to be circularly polarized (Y et al. 1969) indicating partial saturation. The velocity corresponds to one of the RH circularly polarized ground state features at 1665 MHz. Finally, the F = 4»4 transition at 2.2 cm from the J = 7/2 state of H was discovered rectly in W3 at the same velocity as the 5-cm and 6-cm lines (Turner, Palmer, and Zuckerman 197). None of the other transitions were found, although the upper limits on the satellite lines are greater than would be expected ev if the masering were fully saturated. Again a A doublet inversion is indicated. We note that the ratio of emission intsities of the F= 4»4 and F= 3»3 transitions is at least 13:1 while the LTE ratio is only 35:27. It is possible that the weak 3» 3 emission could be a result of unsaturated amplification of both transitions, but more likely it is the result of IR trapping betwe the J = 7/2 and J = 9/2 states. For temperatures betwe I o K and 14 K the hyperfine IR transitions are overlapped out of the lower, but not the upper, A doublet level. Th transfer of population occurs from F = 3 to F = 4 in only the upper half of the A doublet, favoring the F = 4» 4 transition over the F = 3» 3 transition. The excited state observations seem conclusively to tell us that the A doublets are inverted in the n3/2 ladder and anti-inverted in the n 1/2 ladder. Whether they will be found inverted for n 1/2, J > 7/2 states, as predicted by the winn et al. theory, awaits future ob- servations which may not be definitive owing to the expected small populations in these high-lying states with fast IR decay rates. Whether or not the winn et al. theory turns out to be operating in interstellar H masers, it appears quite certain at this time that the pumping mechanism is indeed oriting the electron orbitals in the H molecules relative to the rotational angular momtum direction. This effect can also be produced in a related theory due to winn and Townes (1968). In this similar theory, low-ergy incidt H atoms collide directly with

19 114 B. E. TURNER H and form transitory H-H bonds which serve to orit the electron orbitals as in the winn et al. theory. The same predictions are made regarding A doublet inversions in both theories except that the result for the n 1/2, J = 1/2 state is ambiguous in the winn and Townes theory. However since temperatures must be less than but comparable to 1 K in order that the winn and Townes theory have significant efficicy, the higher-lying excited states would not be populated ough to produce the rectly observed emission. Furthermore, the desire to avoid ergy requiremts of a few ev, and to avoid postulating the existce of large conctrations of interstellar water vapor which inspired the winn and Townes theory, is no longer relevant in view of the discovery of very powerful H 2 emission associated with H sources. VII. Interstellar H 2 Masers bservational Facts Relevant to Choosing a Theory Strong H 2 masering has at this time be observed in a total of 14 interstellar sources; nine associated with H n regions and Class I H emitters, and five with IR stars of which three are Class 11(b) H sources and the other two do not show H. Among the Class I H sources, the strongest usually correspond to the strongest H 2 emission. However both the radiated flux and the number of photons/sec gerated by the sources are much greater for the H 2 masers than for the H masers, typically by 1 times. W49 gerates 6 X 1 48 photons/sec in the H 2 line if the emission is isotropic. Since one microwave photon is gerated per pumping evt, it is very unlikely that radiative pumping can apply; for example the total IR emission from an M5 giant corresponds to a factor 1 5 less photons/sec than is gerated by the H 2 in W49. bserved linewidths are typically ~4 khz, corresponding to T k 12 K under pure Doppler broading with no line narrowing. Such a temperature is tirely inadequate for the excitation of the masering 6i transition which lies 477 cm -1 above ground. From a deduced total gain aio = 27.7 (see below), the lines would be narrowed by a factor of 6.3 in W49 if the amplification is unsaturated. Th T K can be as high as 45 K while producing the observed linewidths; such a temperature can also produce adequate rates of production of H from H 2 according to the winn et al. theory. Another indication that the H 2 masers are probably un-

20 MASERS IN SPACE 115 saturated is the rapid and large time variations observed in the emission, which have a time scale as short as a few days in some cases and produce a threefold or more change in intsity of some features. For an unsaturated maser of total gain a o = 27.7, a one perct change in a produces a 27.7 perct change in the output brightness T B, while for a saturated maser T B would only change by one perct. Rect VLB measuremts (Burke et al. 197) reveal angular sizes of less than.3 seconds of arc for several features in W49, rion A, W3 (H), and VY CM a. The corresponding linear sizes are less than 1.5 a.u. in ri A and 4 a.u. in W49. In W49, T B exceeds 1 13 K, which means that the microwave interaction rate W m 2 X 1 4 sec -1 for ft = 47t. Now in order that an anomalous population, rather than a Boltzmann distribution, can be set up betwe adjact rotational levels connected by far IR transitions, the IR spontaneous rate W IR must exceed the collision rate W c. Since in H 2, W IR ~ 1 sec -1 for the relevant levels, we have that W c << W m. This also means that the pump rate W p << W m so that the maser would seem to be saturated if a steady state applies, contrary to the above-mtioned requiremts on the line- widths and kinetic temperatures. The dilemma is resolved by assuming that some storage mechanism operates to store up the pumping action to a critical point at which a burst of unsaturated amplification occurs with corresponding sharp time variations and narrow linewidths. ne such storage process, involving trapped IR, is discussed below. The H 2 emission is se to be slightly linearly polarized (as high as 3 perct for one feature in ri A but much less in all other cases). Circular polarization has never be detected. Linear polarization can occur through resonant scattering; for example if IR photons pump the J = 5 level to the 6 16 level which th decays by microwave emission to the 5 23 level, the linear polarization can be as much as 3 perct, wh the microwave radiation is perpdicular to the IR radiation, which would need to be highly directed. In a more realistic case the degree of linear polarization can be produced by saturation effects, but would occur only for A F = ± 1 transitions, not A F =. Within the transition hyperfine transitions occur with both A F = ± 1 and A F =, and these transitions are virtually unresolved in the data since the in-

21 116 B. E. TURNER hert linewidths exceed the frequcy separation. Clearly the blded emission could be linearly polarized by this mechanism, especially since the three A F = ± 1 transitions have much larger (LTE) line strgths than the two A F = transitions. If a storage mechanism for the pump is operating, th during the depletion period after a burst of unsaturated microwave emission, the amplifier will momtarily saturate during which the radiation could become linearly polarized; if this polarized field can be partly preserved during the suing pumping period, it will be amplified in the next burst, and so on. However because of the requiremts on linewidths and kinetic temperatures, it seems more likely that the amplification is unsaturated, and that the observed linear polarization arises from the amplification of a very small degree of linear polarization arising from a nonspherical geometry and resonant scattering. Pumping Models for Interstellar H 2 We now describe a model, due to R. E. Hills (1969), which is both collisionally pumped, and which has a built-in storage mechanism, as required in the above discussion. The pumping requiremts are very geral; they need to insure only that the rotational levels above the 6 16 level be populated (by the collisions) at a rate which does not exceed the IR spontaneous emission rate (~ 1 sec"! ) of these levels. Figure 3 shows the ergy level scheme tak from Hills (1969). Downward radiative transitions can be via /»/,/»/ 1, or some of which are shown in Figure 3. Wh a cascade ds up in the lowest state of a giv angular momtum (bottom of a vertical column), the only possible path for IR transition is down the bottom edge of the array of levels, that is, through the lowest state for each /. Hce there is a tdcy for molecules to accumulate in these lower states, of which the 6 16 level is one. Conversely, the 5 23 level has many more exit routes into which to decay. Thus a population inversion is set up betwe the 6 16 and 5 23 levels. ther transitions are also likely to be inverted on this scheme, such as the 5 15» 4 22, 4 14 >3 21, and 3 13»2 2 (at Hz) to name a few. Hills has indicated how, in this model, trapped IR can lead to a build-up of pumping and a sudd release of this ergy into the amplified beam. At a time before the turn-on of the maser beam,

22 MASERS IN SPACE 117 J, TTAL ANULAR MMENTUM QUANTUM NUMBER Fig. 3 Energy, angular momtum diagram for the ground vibrational state of the water molecule. or wh it is very weak, the rotational de-excitation is along the diagonal 7o7» 6 16» 5o5» During this time the population inversion of the 6 16» 5 23 transition is increasing. Wh the maser turns on, many of the molecules take the route through 6 16» via stimulated transitions. The direct supply of molecules to the Sos, 4 14, and lower levels is th reduced. Whereas IR photons were being gerated from the o5 and 5o5~4 14 transitions wh the maser was off, they now become absorbed. The cycle down through the transition and back up again via these absorbed IR transitions can proceed at a high rate until these IR photons are used up. The largest effect is to pump back up to the 5 23 level, thus reducing the population inversion and evtually shutting off the maser. The original routes are th reestablished and pumping starts again. There is a delay betwe successive turning on and off

23 118 B. E. TURNER of the maser because the IR photons are trapped in an optically thick cloud during the time the maser was off; or, if the maser is operating in only a small part of the cloud, IR radiation can build up in other parts that are in the pumping-up part of the cycle. In all of this, the basic ergy source is still the collisional excitation, so that the total number of microwave photons produced never exceeds the total number of collisions which pump molecules into levels above the 5 23 level. The IR trapping effects simply able the conctration of the pumping in either time or space. H/H 2 Masering Sources It is instructive to compare the predictions of the winn et al. H theory and the Hills H 2 model with observations of those interstellar sources having emissions from both molecules. It is clear that the conditions for establishing a population inversion of the 1.35-cm transition of H 2 are more easily met than those required for producing excited H. In fact, since the proper excitation of both H and H 2 requires collision rates to be slower than IR rates, it might seem that conditions are always suitable for an H 2 maser if they are suitable for an H maser. If the H molecules are created predominantly in rotational states within a few hundred cm -1 of the ground state, th the required decay time to the ground state, ~15 s, is very similar to the IR pumping times required for the H 2. However if most H molecules start in much higher lying levels, th collisions could well destroy the inversions before they reached the ground state, while still having rates slow ough for the H 2 maser to work. bservationally, elev Class I H sources have be searched so far for H 2, with eight detections. However there are mitigating circumstances for the three cases not showing H 2 : for two of them (W33 and N-2) the H position was poorly known and may not have be included in the H 2 search; the other source, NC 6334S was observed at an excessively low elevation angle. In all eight Class I H/H 2 masers, the velocity range covered by the H 2 emission is as wide or wider than for the H. This is expected on the ground that the H 2 and H masers need not share the same volume, and hce velocity range, but that the H maser will only occur in those regions of a source where ~4.5 ev of ergy is available.

24 MASERS IN SPACE 119 ri A seems to be such a case, the indication being that there are three distinct H 2 sources but only one H source. By the same argumts, we would expect the angular sizes of H sources to be smaller than H 2 sources, assuming that the measured angular size is related to the actual size of the masering cloud. This will be the case if the emission is incohert across the output face, and if the beam is not narrowed by a differt degree for H 2 and H. In fact, VLB observations show that the H 2 sizes are oft smaller than the H sizes, as in W49 particularly. This may be explained by interstellar scintillations, which will broad the H image by a factor of ~ 18 more than the H 2 image. For W49, the expected H 2 size, wh scaled from the observed H size, would be about a factor of t smaller than the resolving power of the VLB observations. Hce the scintillation hypothesis is not tested. It is interesting that the smallest linear sizes established for H 2 sources (< 1.5 a.u. in ri A and VY CMa) are about t times smaller than the smallest known H source (W3 H). This suggests that ev the W3 H source may be broaded by scintillation, perhaps arising within the source itself. This would be expected if the electron dsities in the source are as large as are required by rect theories (Litvak 197) for the production of polarization by magnetoionic phoma. It is tempting to suggest that the observed correlation of H and H 2 emission sources not only tests the winn et al. theory for H, but also implies that both masers are emitting into a large solid angle, Í2 4tt; otherwise we would usually not be within the maser beam for one or the other of the masers. Unfortunately, several circumstances may constrain both masers to emit along the same direction. In this regard we can rule out alignmt of the molecules by magnetic fields because certain polarization patterns, not observed, would be required for both molecules. We can prob- ably also rule out background sources defining the direction of strongest emission, because foregoing argumts (see III) indicate that, especially for H 2, spontaneous emission will dominate the amplified modes, which are th isotropic. However the require- mt for amplification, that the velocity be constant to within roughly a linewidth over the path lgth, makes it very likely that, in the presce of turbulce, certain directions will be favored. If these directions were excessively restricted in angle we might expect