A Possible Pumping Mechanism for Interstellar Class Ⅱ107 GHz Methanol Masers

Chin. J. Astro. Astrophys. Vol. 2 (2002), No.1, 51-58Chinesc Journal ofAstrooiny andAstrophvsicsA Possible Pumping Mechanism for Interstellar Class HI107 GHz Methanol MasersHan- Ping Liu' * and Jin Sun2.3P| A1 Department of P hysics, Beijing Normal University. Beijing 1008752 Department of Astronomy, Bejjing Normal University. Beijing 1008753 CAS-PKU Joint Beijing Astrophysics Center, Pcking University, Beijing 100871Received 2001 July 8; accepted 2001 November 28Abstract It is recognized that the interstellar methanol 107 GHz masers andOH-4.765 GHz mnasers towards Class I1 sources are associated with each other andcoexist towards ultracompact HII regions. Therefore we suggest a new plumpingmnechanismmethanol masers withont population inversion. It can explain theformation of 107 GHz methanol masers, with the 4.765 GHz OH masers acting asa driving coh rent microwave field. It is argued that this imechanism is compatiblewith the astronomnical conditions.Key words: H Il regions 一masersradiation mechanisms: non-thermal 一ISM: moleculs- line: formation1 INTRODUCTIONOver more thar. thirty years dozens of transitions of interstellar methanol masers have beenfound in directions of star-forming regions, especially massive star-forming regions. All suchmasers can be divided into two distinct classes (Batrla et al. 1987; Menten 1991): in no casedoes a Class I methanol maser cmit in a Class II maser line, and vice versa. While Class Isources show enhanced absorption at frequencies of 6.7, 12.2 and 107GHz. Class ll sourcesshow prominent enission at those frequencies. Class I sources are usually situated away fromcompact continuur sources, while Class II masers are usually found close tu ultraconpacl HIIregions, or near tht ir edges.In addition, a new methanol masers - the 3)→4oA' transition at 107 GHz has beendiscovered in sever l galactic sources recently (Val'tts ct al. 1995). In general these sourcesare in the same re.ions as the Class II 6.7 and 12.2 GHz masers enitters and all of them areassociated with H L regions and OH masers. Therefore Caswell et al. (1995) suggested that theOH and methanol nasers are commonly in very close association. Towards Class I nethanolmaser sources. however, the 107GHz line is found in absorption or in weak. quasi-thermal★E-mail: gaozm@ :mail bnu ecdu.cn中国煤化工MYHCNMHG52HI.P.Liu&J.Sunenmission. These findings make the purnping mechanisrn of the 107 GHz maser still a matter ofdebate.One of the major goals of rescarchers on astrophysical masers is to understand 1naser pump-ing mechanisns in interstellar clouds. Extensive surveys have shown that the Class II methanolmaser phenonenon is very widespread. This result adds to the inuporlance of understandingthe nature of Class II mcthanol llaser sources, which Inay be done through detailed studies ofparticular mas ers in various transitioms. In this paper we will follow the hints above and arguefor a new pumping nechanisin for the interstellar Class 1I 107 GHz methanol masers. which canbe used to explain the formation and behavior of the Class II sources. The proposed mechanisinis complementary to other mechanisrns. We shall also demonstrate thal this new mechanism iscompatible wi:h the astronomnical conditions.2 THE PUMPING OF CLASS II METHANOL 31→40A+ MASERS2.1 The Relevant Level Structure of the Methanol MoleculeMethanol is one of the sinplest molecules displaying hindered internal rotation, and it isa slightly asyr armetric top, as the OH group does not lie on the principal molecular axis. loliet al. (1955) >roposed that the energy levels of the methanol molecule sharing all the sarnequantum numlers except J can be expanded into a Taylor serics in J(J + l);E(q.J)= Sam(9)J(J + 1)]"土[(J + K)/2(J -k)1|S(q)+ J(J + 1)T(g)|，(1)where q stand: for the common quantum numbers of a given sequence, i.e., v.n,T. and K. Forthe vibrationa quantum nunber rt; because the frequencics corresponding l pure vibrationalmodes are of the order of 1000 cm-I, ouly the ground level (u= 0) is of interest here; n is thetorsional vibra tion quautur number; T may have thc values 1, 2 and 3, and arises from thethreefold nature of the hindering potential; J is the lolal angular momentum quantum number;and K is the projection of J along internal axis. It is worth pointing out that the transitionsmay only occur between states belonging to the saune syunetry species - A or E'. The terns .including S ard T describe the asynmetry doubling. designated by + or一，and are presentonly for levels belonging to A symmetry with snall bul nonzero K values. The summnation inEq. (1) can be truncated at m = 4. but in a few cases m = 3 is suficient while in other casesm=5 is requi ed. .At the mo nent we are only interested in the transition of3|→1oA+: u=0,n=0. Thelatest relevant parameters, according to Moruzzi (1998), are as fllows (all values are in cm-'，and the energv of J =0, K = 0 has been set equal to zero):KIoaa2(x106)S(x102)T(x107)( 00001.0.806777-4.9564410. 105200.806825- 3.26136- 1.391521.40647Thus we can calculate the separation (The experimental value has been confirmed to be 5005.321(6)MHz (X11 et. al. 1997a).Some relevant levels are shown in Fig. 1. The relative selection rules are:+←→+and-←→一, for△J =+1, On= 0;+←-and-←+.forOJ-0,On=0.中国煤化工MYHCNMHGA Possiblc 'urmping Mechanism for Interstellar Class II 107 GHz .Mlcthanol Masers53- 3厂I Rabi osr.时MaserFig.I Relevant encrgy levels of the methanol molecule.2.2Equations of Motion and Masers w ithout InversionThere has been considerable interest in the study of lasing without population inversion.Many schemes have been proposed. One of them is the ladder system with coherent punpingproposed by Prasad (1991). Consider a threc-level systcn with non-cqtidistant, non-degeneratclevels |a), |b> and ) and with energies 0, hwab and hwar. respectively. as shown in Fig. 2. Here?1 (72) are the sportaneous decay rates, and λ (入2), the incoherently pumping rates by thermalradiation. There is no dircct dipole coupling between states |a) and |c). The transition |b) - |c}of frequency wbe is driven by a strong coherent field of frequency山with Rabi frequency 2G.A1=Wbe-山,andlG = Eulpoel/2h.(2)where Eru is the aumplitude of the strong coherent field, Phe is the dipole transition matrixelement.A probe field cf frequency w2 with Rabi frequency 2g is applied to the transition |a) - |b}of frequency wiab, 4以2 = wub -公G and g may Ee assurned to be real and positive for simplicity, and we let Og= O: + O2.wibe7wab入2山2lascra)Fig.2 Ladder system with coherent punping.中国煤化工MYHCNMHG5H. P. Liu& J. SunThe equations of motion for the particle density matrix in the rotating frame can be witenas:Pun = 72Pb6 - λ2Puu + ig(Pba - Pab).Pib = T1Poe- (72-入1)Pbh + λ2Pan + iG(Pcb - Pbe) + ig(Pab - Pua).Prc =一1Pee + λIPbb + iG(Pve - Pt).(3)phb = -(712 + i△l)Pcb + iG(Pb - Pcr) - igPca;ρa = -(713 + i△3)Pca + iGpba - igpcb.Pra = -(723 + iO2)PUa + iGpea + ig(Pa - Pbb);along with the cquations of their cornplex conjugates, where7:2=(m +2 +入1)/2: 7YI3=(ru +入2)/2, 723=(n2+λ +入2)/2.(4)The density Ilatrix Eqs. (3) can be solved for the steady state, though the solving is cuber-some:Puau = [2r12G2 + rn(732 + O})r2/W,Pub - {2r:2G2 + n(7品+ o号)X2/W,Pec = |2r12G2 +入(r名z + o})|X2/W.Pha = g/(W?2 + W)x:|G2(ri2W2 + OIWi)(Pbb - Per)/(i + 0}) + (Y:3W2z - O:W;)(Paa - pu川]+i{G(ri2Wi - A:W2)(06 - Pec)/(r32 +△}) + (71sWi - O3W2)(Paa - Pow)I}. (6) .whereW = [2:12G2+入(啦+ O})入z + [2712G2 + 71(72 + 0})](~2 +入2).W= G2+ 7137238 -△2O3, .(7)W2 = 713Oz + 7r23A; .The equation of motion for the probe field amplitude E20 can be written as:E20= -k:E2n + 2πiw2Npub x Pbu，(8)where的is thε loss rate of propagation, N the nunber density of molecules, and Pab the ma-trix element cf dipole trausition. Therefore, if the loss rate k is so small as can be ignored,amplification of the probe field is obtained withIm(Pba)< 0.(9That is, due to quantum coherence effect, the spontaneous enission fror the upper state |b;to the lower sti:tc |a) will be restrained, while the stimulated emission is not affected significantly.Therefore even when there is no population inversion between the upper and lower levels, therewill still be net coherent light amplification - laser (or maser). As a matler of fact, the strongcoherent field acts as a trigger or a stirmulant.Of coursc, it should be noted that Eq. (9) is only a necessary condit ion for amplification ofcoherent radiation. In order to explain the observed maser intensities in detail, large enough中国煤化工MYHCNMHGA I'ossible 'umping Mechanism for Interstelar ( "lass II 107 (;Hz Methanol Mlasers55gain coeficients are needed. Thus besides Pbua. the interstellar conditiors. such心the gns densityand coherent path length of mnaser region must also be right. In the next section we will showthat. in principle, the energy levels 47. 3十and 37 in Fig. 1. as the cnergy levels |a). |b) and |c)in Fig. 2. make up a ladder system with coberent pumping for gain without inversion.2.3 The Pumping of Interstellar Class 1I 107 GHz Methanol MasersWW'e argue in this section that the 107 GHz methanol masers are masers without inversiondriven by the inte:stellar OH 4.765 GIz masers. neglecting the origin of the latter temporarily.As mentioned in Subsection 2.1, the levels 3j. 31 and 45 are pure n-dlegeneratc. nonequidistant levels. They constitute the three-level ladder system as in the model proposed byPrasad et al. (1991). Astronomical observations and statistics show that the Class I sourres ofinterstellar metha:nol maser are always associated with HII regions, but Class I sources are not.The VLBI observations indicated that (Menten 1992a) Class I masers are located at distanccsof at least 0.1 - : pc from ultracompact HII centers. but Class II masers are located in thedense envelopes ol ultracompact HIII regions. Hartquist (1995) has also pointed out that ClassII met hanol masers occur in the immediate vicinity of ultracompact H II regions and sen: to beclosely related to hydroxyl masers. Virtually all known Class Il methanol maser sources showmaser action in 0H coincidently, with the emissions of both specics alway's covering sirnilarvelocity ranges. Ispecially, 107 GHz methanol masers are always projected on ultrncompactHII regions (Mehringer ct al. 1997). Therefore, following his measurements. Caswell (1995)suuggecsted that the: OH and methanol masers are cononly in very close association.He evensuggested that a global model is required to incorporate both masers and their associationwith ultracompact H II regions. A similar proposal for Class II 6.7 CHz and 157 GHz methanolmasers was made in Liu et al. (1997, 1998, 2002).In regard to th e methanol- 107 GHz masers. Valtts et al. (1995) pointcd out that while tlereare strong methan)-6.7 GHz masers toward the sourccs G9.62 +0.19, W33(A) and G23.01 - 0.41.there are no methanol-107 GHz masers in these directions. Wo also noticed that there are noOH-4.765 CHz masers found in the three strong methanol-6.7 GHz naser sources. It seerms thatthere is something connection between the methanol- 107 GHz and OH-4.765 GHz masers.The W3(OH) region, one of compact HII regions and the prototype of Class II methanolmasers, can be sclected as an cxample. Menten (1992b) showed from VL.BI data that Ianymethanol masers and OI1 masers observed toward W3(OH) appear to be spat illy coincident.As a matter of fa:t, the position coordinate of methauol-107 GHz maser source in W3(OH) isa= 023*"17.3*, δ= +61938'58" at the VisR = -43.3kms- 1 with a 3" rmns pointing accuracyand half-power be amwidth 35" (Val'ts et al. 1995), and that of OH-4.765 GHz maser sourceat the similar -43.21kms-1 is a = 02l"23*16.45*, δ = +61938'57.51" from high resolutionVLBI observations (Baudry 1988; Baudry & Diamond 1991). Despite the large difference ofresolution and pointing accuracy, we consider both masers in W3(OH) to be spatially relatcd.Following the above hints, we propose a picture in which the 107 GHz methanol masersand 4.765 GHz OIl masers co emit in the W3(OH) region around an O-type star which excitesthe compact HII region. The 4.765 GlHz masers can drive the local inethanol molecules asa coherent field. In W3(OH) the associated infrared source is W3- IRS8, its total infraredluminosity is ≈2x 105 L。 (Schaifers et al. 1982). We estimate the tempcrature of centralstar is≈1.5 x 104 K, on assuming the infrared source is a zero-age main sequence (ZAMIS)star. Because of the strong thermal radiation, the excitation levels of methanol molecule willbe populated moc erately. The separation of K-doublet of level 31 is 5005.321 M1Hz (Xu et al.中国煤化工MYHCNMHG50H.P. Liu& J. Sun1997a), therefnre the doublet of level 31 can produce Rabi uscillation driven by the 4765.562 \MIHzOH maser, wi.h A| = 5005.321 - 4765.562 = 239.759 MHz. The relative frequency deviation is .only 01/5005 321≈4%.Observations of the 4.765 GHz OH irnasers toward W3(OH) show a terrestrial antenna peakflux density of≈3.69Jy at - 43.21km s-1 (Baudry 1988). The spectrum bandwidth of themaser spot OV = 43.58 一42.84 = 0.74 kn s-1, corresponding to 12 kHz. Tbe distance frounW3(OH) to tte Earth, D, is 2.2 kpc (Migenes et al 1999). The angular size of the source spotis < 10mas, su its linear size is d≈1014 cm. Hence the energy fAux density of the source regionwill be:S=(3.6)x 10-26W m-2IHz-')x 1.2x 10*Hzx (D/d)2 = 2.04101 x 10~6W m- 2.Thus the enensy density in the maser source region will at least beu:= S/c= 6.80336x 10-15J m-3,where c is the light speed. Since the relationship of w and electric field E is:w=eo(E2)/2 = eoBRo/4,where E1n is aunplitude of clectric strength, ε0 is dielectric constant,Eo=8.85x 10-12C2N-'m-2,we haveE1o= (4w/eo)/2 = 5.54524x 10-2NC-,also, Pbr of CE.3OH≈1 Debye (Xu et al. 1997b). Substituting these values into Eq. (2). weobt ain:G= 2.64059 x 10*s-1.In general, the sizc of the central star r≈10'3 cm, and, according to quantum mcchanics.the incoherentlv punping ratc by thermal radiation isλ= Brc(w) = A/exp(hw/kT) - 1(r/d)*.(10)where w(w) is the radiative energy density at frequency w. The methanol molecules are irra-diated by re-radiated starlight, the radiation temperature can be estimated as 100K (Sobolevet al. 1994). From Pei et al. (1988), the Einstein Ceofficient A of transition 37- -3i is9.765 x 10-11s-1, transition frequency 5.005 GHz, thosc of3t -4t are 5.811 X 10-6 s-1 and107 GHz. Thus we obtain:入I= 4.05613x 10-10s-',入z= 1.1016x 10-6s-'.The theore ical value of wab = 107.01377GHz (De Lucia et al. 1989), the observationalvalue of w2 = 107.01382 GHz (Sobolev et al. 1997). thus △z = - 0.05 MHz. As before. O!-239.759MHz, Cn3 = 239.709 MHz.Substitutin., all the above values into Eqs. (4), we obtain~12= 2.90575x 10-°s-',n3= 5.50846x 10-7s-1.723= 3.4565x 10-°s-1.中国煤化工MYHCNMHGA Possible Punping Mechanism for Intcrstellar Class II 107 (;Hz Mcthanol MasprsSubstituting then: into Eqs. (7)、 we haveW°i = 1.19855x 10*s-2， W2 = 8.28572x 1025-2， W" = 64.48845- 4.Substituting the same into Eqs. (5) and (6), we obtainIm(Pna)= -8.14116x 10"0 xg/(W? + W谷).(11)There is always g/(W2 + W2) > 0, thus we have verified finally lm(Pba) < 0, and Eq. (9) .is satisfied. As nuentioned above, it will cause coherent amplification between states |a} and|b). Therefore levels of 37, 3十and 4古together constitute a typical three-level systcm withcoherently pumping. It can result in masers without the requirenent of inversion. That is ;ust the mechanisu of3 →4oA+ 107 GHz masers associated with astronomical 4.765 GHz OHmasers.3 DISCUSSIONMaser emission from interstellar Iechanol is a widespread phenomenon; observed towardmany dense molccular cloud cores in regions of massive star formation. The search for newmethanol maser tranusitions is still in progress. Methanol masers are observed in transitions be-tween energy levels in diferent K ladders. The pumping mcchanisms of two classes of methanolmasers are not yet well understood, though the collision mechanisin is more successful in Class1 sources (Walmslcy et al. 1988). We note thal for A-species levels of mct hanol, the lowestlevel has quantur1 nunbers of J = 1,K = 0. A strong preferential process is OK = 0 for col-lision excitation {Lees et al. 1974). That can becorme the population inversion mechanism forJo→(J- 1)1A+ masers, such as the 7o→61A+,8o→7A+ ,and9o→8A+ masers at 44, 95.and 146 GHz, res pectively. This mechanism also produces enhanced absorption in the 107 GHzof 31→4oA+ transition and 6.7GHz of the 51→6gA+ transition which is characteristic ofthe Class 1 sourcs. Whereas in Class II masers the situation is reversed; the3y →41A+ and5→6oA t transitions present strong maser emissions toward Class II methanol sources. Thatcannot be explained at all by collision mechanism.We propose that the two classes of interstellar methanol masers may have difcrent pumpingmnechanisms and physical conditions. In conpact H I regions, radiative processes are likcly tobe a main sourcs of pumping up Class II mcthanol masers. We suppose that the Class IImasers should be radiatively pumped, so it is seen toward the W3(OH) region. In that region,the strong thernal emnission of central star populates the excitation levels of the methanolmolecule and, the 107 GHz and 4.765 GHz masers are well associated with cach other. The40 level and 3jA doubling co _form a typical thre-level, non equidistant, ladder system withcoherent pumping. The 4.765 GHz nascrs drive strongly the 31 doubling. It acts as a trigger.Those create the 31-→ 40A+ masers without inversion.The mechanism we argued for here is associated with astrophysical conditions. The physicalenvironments of maser. forming regions are various. Perhaps, there are diferent Inechanismsfor diferent mnasers and, there are several mnechanisms which co-operate on one mascr: theydo not contradic , but complement each other. Following this reasoning. we ran obtain a trueunderstanding of astrononical masers.Acknowledgen ents The authors gratefully acknow ledge the financial support of Nat ionalNatural Science Foundation of China (Nos. 19873003 and 20073005).中国煤化工MYHCNMHG58H. I”. Liu&: J. SulReferencesBatrla w. Mattlews II. F.. Menten K. M. et al.. 1987. .Nalure. 326. 49Baudry A.. Diam md P. J.. Booth R. S. e al, 1988. A&A.201. 105Baudry A.. Diam,nd P.J.. 1991, A&A, 247, 551Caswell J. L., Vaile R. A.. Forster J. R. ct al, 1995. MNRAS.277. 210Chang T. Y. Bridges TJ, 1970, Optics Comm.. I, 423De Lucia F. C.. Herbst E, Anderson T. ct al., 1989. J. Mol. Spectrosc 134, 395Hartquist T. W. Menten K. M.. Lcpp S. el al., 1995. MINRAS.272, 184loli N.. Moruzzi C.. Riminucci P. et al.. 1995, J. Mol. Spectrosc.. 171. 130Lees R. 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