Influence of radiative pumping on the HD rotational level populations in diffuse molecular clouds of the interstellar medium
PPublished in Astronomy Letters, 2020, Vol. 46, Iss. 4, pp. 224-234.
Influence of Radiative Pumping on the HD RotationalLevel Populations in Diffuse Molecular Clouds of theInterstellar Medium
V.V. Klimenko (cid:63) , A.V. Ivanchik Ioffe Institute, Russian Academy of Sciences,ul. Politekhnicheskaya 26, St. Petersburg, 194021 Russia
Received March 14, 2020; revised March 14, 2020; accepted March 24, 2020
Abstract
We present a theoretical calculation of the influence of ultraviolet radiative pumping on the excitation of therotational levels of the ground vibrational state for HD molecules under conditions of the cold diffuse interstellarmedium (ISM). Two main excitation mechanisms have been taken into account in our analysis: (i) collisionswith atoms and molecules and (ii) radiative pumping by the interstellar ultraviolet (UV) radiation field. Thecalculation of the radiative pumping rate coefficients Γ ij corresponding to Drane’s model of the field of interstellarUV radiation, taking into account the self-shielding of HD molecules, is performed. We found that the populationof the first HD rotational level ( J = 1) is determined mainly by radiative pumping rather than by collisions ifthe thermal gas pressure p th ≤ (cid:16) I UV (cid:17) K cm − and the column density of HD is lower than log N (HD) < i ∗ /C i and C i ∗∗ /C i ). We suggestthat taking into account radiative pumping of HD rotational levels may be important for the problem of thecooling of primordial gas at high redshift: ultraviolet radiation from first stars can increase the rate of HD coolingof the primordial gas in the early Universe. Key words. interstellar medium, molecular clouds, early galaxies, quasar spectra.
1. Introduction
HD are the next most abundant molecules in theUniverse after H . Their number density in the coldphase of the neutral interstellar medium (ISM) of ourGalaxy is lower than the number density of molecularhydrogen approximately by 5 − z , λ obs = λ em (1 + z ), and can bedetected by optical ground-based telescopes. HD ab-sorption lines were first detected in the spectrum of thequasar Q 1232+0815 in 2001 (Varshalovich et al. 2001).At present, about 20 HD absorption systems have beenidentified in damped Lyman-alpha (DLA) systems with (cid:63) E-mail: [email protected] The abundance of CO is approximately the same as thatof HD. z > . abundance was investigated byLe Petit et al. (2002), Liszt (2015), Ivanchik et al.(2015), and Balashev and Kosenko (2020). These au-thors pointed out that the HD/H ratio my be usedas an indicator of the physical conditions in the coldISM phase (the number density, ionization rate by ofthe cosmic-ray background, intensity of UV radiation,the dust content). An analysis of the populations of theHD rotational levels of the ground vibrational state canprovide additional information about the physical condi-tions in the ISM. Like H , HD has a system of rotational-vibrational levels that are populated by collisions withatoms and molecules (mostly H, He, H , and e − ) andby radiative pumping (through the upper electronic lev-els). At the same time, there is a significant difference inrelaxation dynamics between HD and H : owing to thehigher symmetry of H , the lifetime of its excited statesis greater than ones in HD by several orders of magni-tude. Therefore, the molecular hydrogen transitions inthe spectra of quasars are reliably detected for higher ro-tational levels, J = 3 − z abs = 2 .
626 (Balashev et al.2010) and J 0843+0221 at z abs = 2 .
786 (Balashev et al.2017). Transitions from the upper levels J ≥ a r X i v : . [ a s t r o - ph . GA ] J a n Klimenko et al.: Radiative Pumping on the HD
HD level population N ( J = 1) /N ( J = 0) allowed thegas number density to be determined, n = 240 cm − in J 0812+3208 A (Balashev et al. 2010; Liszt 2015)and n = 260 −
380 cm − in J 0843+0221 (Balashev etal. 2017). The authors neglected the effect of radiationpumping due to self-shielding of HD molecules from UVradiation, since these systems have a high HD columndensity.In this paper we present the results of our calculationof the radiative pumping rate coefficients for the HD ro-tational levels. We determine the range of physical con-ditions in the ISM and HD column densities whereby ra-diative pumping contributes significantly to the excita-tion of HD rotational levels. Our calculation of the radia-tive pumping rate coefficients is described in Section 2.In Section 3 we analyze the effect of self-shielding. InSection 4 we compare the relative population of the HDlevel J = 1 with other indicators of the physical con-ditions and present our analysis of the physical condi-tions in two molecular clouds towards J 0812+3208 andJ 0843+0221.
2. Radiative pumping calculation
The structure of the HD levels is similar to that ofthe H ones, but there is also a significant difference:since the HD molecule has a dipole moment, the tran-sitions between its levels with ∆ J = ± radiative pumping calculation (Black andDolgarno 1976), we calculated the radiative pumping ofHD rotational levels. HD molecules absorb UV radia-tion and populate excited electronic states (B Σ u andC Π u ), and then relax to the rotational-vibrational lev-els of the ground state X Σ +g (subsequently producinga rotational-vibrational cascade). The main parameters describing the distribution of levelpopulations during relaxation to the ground electronicstate are the cascade efficiency factors a ( ν , J ; J ),which describe the probabilities to occupy a rotationallevel J of the ground vibrational state ν = 0 througha series of spontaneous transitions from an excitedvibrational-rotational state ( ν , J ). The scheme de-scribed by Black and Dolgarno (1976) was used to cal-culate a ( ν , J ; J ).Suppose that some level ( ν , J ) is populated at aconstant rate Q ( ν , J ) (cm − s − ). Then, the equilib-rium population of the level ( ν , J ) is defined as follows: n ( ν , J ) = Q ( ν , J ) /A ( ν , J ) , (1)where A ( ν , J ) = ν (cid:88) ν (cid:48)(cid:48) =0 J max (cid:88) J (cid:48)(cid:48) =0 A ( ν , J ; ν (cid:48)(cid:48) , J (cid:48)(cid:48) ) [s − ] (2)denotes the total probability of spontaneous transitionsfrom the level ( ν , J ) to various levels of the groundelectronic state. The probabilities of spontaneous dipole and quadrupole transitions A ( ν , J ; ν (cid:48)(cid:48) , J (cid:48)(cid:48) ) for therotational-vibrational levels of the HD ground electronicstate were calculated by Abgrall et al. (1982) for vibra-tional levels ν ≤
17 and rotational levels J ≤ J max = 13.In this paper we took into account the levels with J ≤ J max = 13 and ν ≤
13. This is justified by thefact that in molecular clouds, under typical physicalconditions, the populations of the overlying levels arenegligible and their subsequent inclusion does not affectthe radiative pumping rate coefficients. The equilibriumpopulations of the underlying levels ( ν, J ) < ( ν , J ) aredetermined from the system of equations: n ( ν, J ) A ( ν, J ) = ν (cid:88) ν (cid:48)(cid:48) = ν J max (cid:88) J (cid:48)(cid:48) =0 n ( ν (cid:48)(cid:48) , J (cid:48)(cid:48) ) A ( ν (cid:48)(cid:48) , J (cid:48)(cid:48) ; ν, J ) . (3)Assuming Q ( ν , J ) = 1 cm − s − we can calculate thecascade efficiency factors a ( ν , J ; J ) a ( ν , J ; J ) = ν (cid:88) ν (cid:48)(cid:48) =1 J max (cid:88) J (cid:48)(cid:48) =0 n ( ν (cid:48)(cid:48) , J (cid:48)(cid:48) ) A ( ν (cid:48)(cid:48) , J (cid:48)(cid:48) ; 0 , J ) . (4)Since the population rate is constant, the normalizationcondition must be fulfilled: the number of molecules ap-pearing per unit time at the excited level ( ν , J ) is equalto the number of molecules arriving at the levels of theground vibrational state: J max (cid:88) J =0 a ( ν , J ; J ) = Q = 1 cm − s − . (5)The values of a ( ν , J ; J ) were calculated for each pair( ν , J ) of the ground electronic state ( ν = 1 .. J = 0 ..J max ) and are given in Table 1 (for the firstfour vibrational levels). Γ( J i , J j )To describe the fraction of the molecules at the groundvibrational level ν = 0 passed from a state ( ν = 0 , J i )to a state ( ν = 0 , J j ) during radiative pumping, let usintroduce the rate coefficients Γ( J i , J j ):Γ( J i , J j ) = (cid:88) ν =1 J max (cid:88) J =0 Q J i ( ν , J ) a ( ν , J ; J j )+ Q J i ( ν = 0 , J j ) , (6)where Q J i ( ν , J ) describes the excitation rate of thelevels of the ground electronic state ( ν , J ) throughspontaneous transitions from the levels of excited HDelectronic states and is defined as follows: Q J i ( ν , J ) = (cid:88) B,C (cid:88) ν (cid:48) =0 J (cid:48) max (cid:88) J (cid:48) =0 R (0 , J i ; ν (cid:48) , J (cid:48) ) A tot ( ν (cid:48) , J (cid:48) ) A ( ν (cid:48) , J (cid:48) ; ν , J ) , (7)where R (0 ,J i ; ν (cid:48) ,J (cid:48) ) A tot ( ν (cid:48) ,J (cid:48) ) = n ( ν (cid:48) ,J (cid:48) ) n (0 ,J i ) are the relative equilibriumpopulations of the rotational-vibrational levels ( ν (cid:48) , J (cid:48) )of states ( B and C ) when excited from the level of the The rate of the induced transitions is much lower thanthe rate of the spontaneous ones, and their contribution maybe neglected.limenko et al.: Radiative Pumping on the HD 3 ground electronic state (0 , J i ), R (0 , J i ; ν (cid:48) , J (cid:48) ) is the ex-citation rate through the absorption of UV radiation, A tot ( ν (cid:48) , J (cid:48) ) = A c ( ν (cid:48) , J (cid:48) ) + (cid:80) ν ,J A ( ν (cid:48) , J (cid:48) ; ν , J ) is the to-tal probability of radiative transitions from level ( ν (cid:48) , J (cid:48) )of the excited electronic states to the continuum andthe rotational-vibrational levels ( ν , J ) of the groundelectronic state (see data in Abgrall and Roueff 2006).Here and below, the superscript (cid:48) denotes the popu-lations of the excited HD electronic states and the sub-script 0 denotes the levels of the ground electronic state.The photoabsorption rate is defined by the followingexpression: R ( ν (cid:48)(cid:48) , J (cid:48)(cid:48) ; ν (cid:48) , J (cid:48) ) = (cid:90) ∞ σ ik ( ν ) cu ν ( ν ) dν == f ik √ πe mc (cid:90) ∞ H ( a, x ) cu ν ( ν ) dν (cid:39) f ik πe m u ν ( ν ik ) , (8)where f ik is the oscillator strength of the transi-tion between states ( ν (cid:48)(cid:48) , J (cid:48)(cid:48) ) ) and ( ν (cid:48) , J (cid:48) ), u ν ( ν ik ) isthe spectral UV radiation density inside the cloudat the transition wavelength (cid:104) photonscm Hz (cid:105) , H ( a, x ) = aπ (cid:82) + ∞−∞ exp( − y )( x − y ) + a dy is the Voigt function with parame-ters a = ∆ ν R / ∆ ν D and x = cb (cid:16) ν − ν ik ν ik (cid:17) . In the opticallythin case, the value of the integral is equal to the valueof the function at the transition frequency. Thus, thephotoabsorption rate is proportional to the UV photondensity. The influence of shielding effect is considered inthe next section.To calculate the photoabsorption rate, we usethe standard model of an interstellar UV radia-tion field (Draine 1978). In the wavelength range < (cid:2) photons / s cm Hz sr (cid:3) is described by the following ex-pression from Sternberg and Dalgarno (1995): φ ( ν ) = I UV × π × (cid:20) . × − (cid:18) λ (cid:19) −− . (cid:18) λ (cid:19) + 54 . (cid:18) λ (cid:19) (cid:35) (9)In the case of an isotropic radiation, the spectral den-sity is related to the intensity as u ν = 4 π I ν /c ; the to-tal radiation density in the range (912-1108 ˚A) is then6 . × − cm − . We introduce the scale factor I UV totake into account the stronger radiation fields, then I ν = I UV I Draine ν ( ν ). The scale factor I UV appears lin-early in Eqs. (6-9) and, therefore, the radiative pumpingrate coefficients Γ( J i , J j ) depend linearly on I UV . Thevalues of Γ( J i , J j ) calculated for the standard galacticbackground radiation ( I UV = 1) are given in Table 2. HD and H molecules, along with atomic hydrogenH i , in molecular clouds are known to absorb UV ra-diation in lines, thereby shielding the interior of thecloud from radiation at the frequencies of the cor-responding transitions (see, e.g., Draine and Bertoldi 1996; Wolcott-Green and Haiman 2011). In these worksthe self-shielding factor is calculated as the ratio ofthe total dissociation rates of molecules deep in thecloud and at the cloud boundary, f shield ( N HD ) = ξ diss ( N HD ) /ξ diss ( N HD = 0) . The dissociation ofmolecules occurs as a process accompanying radiativepumping, so that some of the excited molecules re-lax to the continuum (about 15%) and are destroyed,while the other ones (about 85%) pass to the excitedlevels of the ground electronic state. Thus, as a re-sult of self-shielding, the dissociation rate of molecules( ξ diss ), along with the excitation rate of the groundstate levels Q J i ( ν , J ), weaken in the same way. Weused the expression for the shielding factor from Draineand Bertoldi (1996). It gives zero shielding at the cloudboundary, in contrast to the approximation proposed byWolcott-Green and Haiman (2011): f shield ( x, D ) = 0 . x/D ) + 0 . √ x ×× exp( − . × − √ x ) , (10)where x = N (HD) / . × cm − is the normalizedcolumn density and D = b/ cm s − is the Dopplerparameter.In our model the molecular cloud is described bya plane-parallel slab irradiated by a uniform interstel-lar radiation background on both sides. We assume theradiation flux to be uniform and incident normally tothe cloud surface. The flux density on each of the cloudsides is F ν = 2 πI ν I UV . The cloud is divided into parallellayers, in each layer the UV radiation density u ν ( x ) iscalculated by taking into account the shielding of theradiation coming from both sides: u ν ( x ) = 2 πI ν I UV c ( f shield [ N HD ( x )] + f shield [ N HD ( l c − x )]) , (11)where l c is the cloud size, x is the coordinate alongthe line of sight (normally to the layer), and N HD ( x )is the column density of molecules on the line of sightbetween the cloud edge and the depth x . In the absenceof shielding, the radiation density u ν ( x ) = 4 πI ν I UV /c isconstant and does not depend on x . Thus, the radiativepumping rate coefficients Γ( J i , J j ) for molecules deepthe cloud decrease by a factor f sh ( x ) = 12 ( f shield [ N HD ( x )] + f shield [ N HD ( l c − x )])(12)compared to the unshielded case.
3. Excitation of HD levels
In equilibrium the populations of the HD rotational lev-els in the ground vibrational state are described by asystem of linear equations: (cid:88) i (cid:54) = j N i (cid:32)(cid:88) q n q k qij + A ij + Γ ij (cid:33) == N j (cid:88) i (cid:54) = j (cid:32)(cid:88) q n q k qji + A ji + Γ ji (cid:33) (13) Here (and below) N is the column density expressed in cm − . Klimenko et al.: Radiative Pumping on the HD Table 1: Cascade efficiency factors a ( ν , J ; J ) for the population of rotational levels J of the HD ground vibrationalstate ν = 0. The data for the first four vibrational levels are given. ν J ν = 0 , J where the indices i and j are the HD rotational levelnumbers, q are the particles involved in the collisions(H i , pH , oH , He, and electrons), n q are the particlenumber densities, and k qij are the collisional rate coef-ficients that are functions of the kinetic temperature.The collisional rate coefficients were taken from Floweret al. (2000) and Dickinson and Richards (1975). Theparticle number densities with respect to the total hy-drogen number density n tot H = n H + n H + n H + wereassumed to be equal to their typical values measuredin diffuse molecular clouds of our Galaxy: n He /n tot H =0 .
085 (Asplund et al. 2009), the electron number den-sity n e /n tot H = 10 − (in molecular clouds, as a rule,it corresponds to the abundance of ionized carbon,n C / n totH ∼ × − × Z , where Z is the metallicity), n H /n tot H = 0 . N H >
19 (see, e.g., Balashev et al. 2019), theortho-to-para hydrogen ratio was assumed to be equalto the equilibrium one 9 × exp( − E /kT kin )).The populations of the first and second HD rota-tional levels as functions of the number density, tem-perature, and UV background intensity are shown inFig. 1. We find that radiative pumping increases (bymore than 10%) the population of the first HD rota-tional level J = 1 in molecular clouds with a thermalgas pressure lower than p th = nT kin < (cid:18) I UV (cid:19) K cm − . (14)This pressure is higher than the typical pressure indiffuse molecular clouds measured in the Milky-Way(log p = 3 . ± . p = 3 . − . limenko et al.: Radiative Pumping on the HD 5 Energy of HD levels, E(J) [K] − − − − − − l og [ N ( J ) / J + / N ( ) ] T=100 Kn=100 cm − I UV = 0 I UV = 10 I UV = 0 , , , ,
10 10 − n [cm − ] − − − n / n T=100 KCollisions I UV = 1 , , ,
10 10 − n [cm − ] − − − − n / n T=100 KCollisions I UV = 1 , , , Figure 1: Left panel represents populations of the HD rotational levels as a function of the energy of HD levels.The populations calculated for different intensities of the UV field I UV = 0, 1, 2, 5 and 10, and coded in differentcolors: black, blue, green, violet, and orange. Right panel: the populations of HD rotational levels J = 1 and J = 2relative to the ground level n J /n = n ( J ) /n ( J = 0) are shown as a function of the number density.2016), and galaxies at high redshifts observed in ab-sorption as DLA systems in the spectra of quasars with z = 2 − p th = 4 . ± . The self-shielding of HD molecules reduces the radia-tive pumping rate by the factor f sh ( x ). We have calcu-lated the ratio of the HD column densities at J = 1and J = 0 rotational levels for various gas numberdensities and UV background intensities in clouds withlog N HD = 14 , ,
16. The gas temperature was assumedto be 100 K, corresponding to a typical kinetic temper-ature in diffuse molecular clouds (see, e.g., Balashev etal. 2019). The results are shown in Fig. 2. The colorgradient encodes the ratio N HD ( J = 1) /N HD ( J = 0)as a function of the number density and UV intensity.Contours indicate the isolines corresponding to 1 / /
30, 1 /
10. Thus, we conclude that at column densitieslog N HD <
15 pumping by UV radiation can contributesignificantly to the HD rotational level populations evenif the self-shielding of molecules is taken into account.
4. Physical conditions in a molecular gas
The population of the first HD rotational level is de-termined by collisions and radiative pumping, thus theratio N ( J = 1) /N ( J = 0) can be used to probe physicalconditions (number density and intensity of UV radia-tion). These parameters can also be measured using theanalysis of fine-structure levels of atoms and ions (Silvaand Viegas 2002). The most useful indicator is neutralcarbon C i (for example, see study of C i absorptions inthe Milky-Way by Jenkins and Tripp 2011).In Fig. 3 we compare sensitivity of the excitationof C i fine-structure and HD rotational levels to ratesof collisional and radiation pumping. We calculate the populations of C i ∗ and HD (J=1) rotational levelsfor the range of physical conditions: 0 < log n < − < log I UV < T kin = 100 K .It is usually believed that self-shielding strongly sup-presses the radiative pumping of HD molecules. Tocheck this assumption, we calculate the excitation ofHD levels for three clouds with the total HD columndensity log N (HD) = 14 , ,
16. Due to a typicallylow C i column density, the self-shielding of C i atomsis usually neglected. We find that at a column densitylog N (HD) ≤
14 the excitation of HD(J = 1) level isseveral times more sensitive to the UV intensity thanthe excitation of the C i ∗ (see left and second pan-els). As N HD increases, the shielding suppresses theradiative pumping efficiency. At HD column densitieslog N (HD) ∼
15 the radiative pumping of HD ( J = 1)and C i ∗ levels gives similar excitation. In case of highercolumn density log N (HD) >
15 the radiative pumpingof the HD (J = 1) is suppressed.At the same time, as it was shown in Section 3, theupper HD rotational levels J ≥ J = 1 andcould be a good indicator of the UV radiation inten-sity. However, at present, the these transitions have notyet been detected in absorption in our Galaxy (see, e.g.,Snow et al. 2008) and high-redshift galaxies (see, e.g.,Ivanchik et al. 2015). Detection and analysis of high Jrotational HD levels will measure the UV intensity inmolecular clouds. This problem may become possible innearest future, such as the Extremely Large Telescope(ELT) with the HIRES spectrograph (Oliva et al. 2018)or Spectrum-UV (Shustov et al. 2018) are put in oper-ation.As an example, we constrain physical conditions us-ing excitation of the HD rotational and C i fine-structurelevels in two DLA systems with high redshifts z > Excitation of the second C i ∗∗ level shows approximatelythe same sensitivity as C i ∗ Klimenko et al.: Radiative Pumping on the HD
12 13 14 15 16log N (HD) tot − − l og f s h i e l d [ N ( H D ) ] n [cm − ] − l og I UV [ D r a i n e un i t s ] log N HD ( J = 1) /N HD ( J = 0) as a function of N (HD) tot log N (HD) tot =14 n [cm − ] − N (HD) tot =15 n [cm − ] − N (HD) tot =16 − − − l og N J = H D / N J = H D Figure 2: Left panel: the self-shielding function of HD. Right panels: the ratio N HD ( J = 1) /N HD ( J = 0) as afunction of the gas number density and intensity of UV radiation calculated for different total column densityof HD cloud log N ( HD tot ) = 14 , ,
16. Color indicates the logarithm of the ratio. The dashed lines indicate theisolines, corresponding to N HD ( J = 1) /N HD ( J = 0) = 1 / /
30, 1 / J i , J j ) (cid:2) − s − (cid:3) calculated for the stan-dard interstellar UV radiation field in Draine model with I UV = 1. J i J j J = 0) 15 . +0 . − . . +0 . − . HD ( J = 1) 13 . +0 . − . . +0 . − . Table 3: Column densities of HD molecules at theground and first rotational levels in the DLA systemstowards the quasars J 0812+3208 (Balashev et al. 2010)and J 0843+0221 (Balashev et al. 2017).HD and C i give similar constraints. The kinetic tem-perature was equal to the excitation temperature H .If we assume that the UV intensity does not exceed10 units of Draine field, we can estimate the numberdensity, n ∼
240 cm − . On the other hand, we can setan upper limit on the UV intensity I UV <
60 units ofDraine field. Therefore, even in case of high column den-sity ( N HD = 15 . J = 1 and C i fine-structure levels. Wealso show the constraint on the UV intensity with HD,when we neglect the self-shielding effect. The constrainon I UV with HD could be about two orders of magni-tude stronger than ones with C i . In case of J 0843+0221constraints on n H and I UV obtained with HD are weakerthan with C i due to high uncertainty in the column den-sities of J=0 and J=1 HD levels.
5. Conclusions
We consider the influence of radiative pumping by UVradiation on the excitation of lower rotational levelsof the ground electronic state of HD molecules underphysical conditions of the diffuse cold ISM. We calcu-late the rate coefficients for radiative pumping of HDmolecules by background UV radiation in Draine model.The radiative pumping rate coefficients for the first 11( J = 0 −
10) rotational levels of the ground HD vibra-tional state are given in Table 2.We show that at the edge of a molecular cloud, whenthe self-shielding of HD molecules may be neglected, thepopulation of the first HD rotational level ( J = 1) is de-termined mainly by radiative pumping rather than bycollisions if the thermal gas pressure satisfies the con-dition p th ≤ (cid:0) I UV (cid:1) K cm − . Such conditions corre-spond to typical physical conditions of the cold phase ofthe diffuse ISM in local (Jenkins and Tripp 2011) andhigh redshift galaxies (Balashev et al. 2019, Klimenko& Balashev 2020). The populations of the upper HDrotational levels with J ≥ limenko et al.: Radiative Pumping on the HD 7 n [cm − ] − l og I UV [ D r a i n e un i t s ] CI(J=1) . . CI excitation n [cm − ] − HD(J=1) . . log N (HD) tot = 14 0 1 2 3log n [cm − ] − HD(J=1) . . log N (HD) tot = 15 0 1 2 3log n [cm − ] − HD(J=1) . . log N (HD) tot = 16 . . . . . . l og N J = H D , C I / N J = H D , C I ( I UV = ) Figure 3: Calculation of the excitation of the C i ∗ fine-structure level (left panel) and HD J = 1 level (right panels)performed for the range of UV intensity and number density and three column densities of HD: log N (HD) =14 , ,
16 (from left to right). The column density of HD is shown at the top of the panel. The color gradientindicates the logarithm of the ratio of (C i ∗ or HD J = 1) level populations excited by radiative pumping andcollisions and only by collisions ( I UV=0 ). The dashed and solid lines indicate the isolines corresponding to anincrease of level populations by 10 and 100% (or 0.04 and 0.3 dex). Black dashed lines correspond to C i ∗ , green,blue and black thick dashed lines in right panels correspond to HD J = 1. log( n ), [cm − ] l og ( I UV ) ,[ D r a i n e un i t ] HD J1/J0 CIHD J1/J0 with self-shielding % % % % % % % J0812+3208 log( n ), [cm − ] l og ( I UV ) ,[ D r a i n e un i t ] HD J1/J0 CIHD J1/J0 with self-shileding % % % % % % % % % J0843+0221
Figure 4: The constraint on the gas number density and UV radiation intensity obtained by analysis of the relativepopulation of the HD J = 1 level (with and without self-shielding) and the fine-structure levels of C i in the DLAsystem with z = 2 .
626 in the spectrum of the quasar Q 0812+3208 (a) and in the DLA system with z = 2 .
786 inthe spectrum of the quasar J 0843+0221 (b). The contours indicate the probability density corresponding to 30%and 68% confidence levels. Even if the self-shielding effect is taken into account (log N (HD) = 15 . N ( J = 1) /N ( J = 0) for HD turns outto be comparable to the constraint obtained from the excitation of fine-structure levels of C i .We consider the influence of self-shielding effect onthe radiative pumping efficiency of the excitation of J=1HD rotational level. We show that at log N (HD) < I UV = 1 Draine unit) significantly ex-cite the first HD level (J = 1), if the number density n <
50 cm − and temperature ∼
100 K. The additionalmechanism of excitation of HD molecules can be im-portant in calculating the cooling of primordial plasmabehind the shock fronts at the galaxy formation epoch.For example, the ionizing radiation of the first stars can increase populations of HD rotational levels, that in-creases the HD cooling rate.We suggest that the population of HD rotational lev-els N ( J = 1) /N ( J = 0) can be used to estimate theintensity of UV radiation and number density in dif-fuse molecular clouds of the ISM. At a column densitylog N (HD) <
15 the ratio of column densities J1/J0turns out to be more sensitive to the UV intensity andless sensitive to the number density than the the pop-ulations of C i fine-structure levels. As an example, weestimated the physical conditions in two DLA systems Klimenko et al.: Radiative Pumping on the HD at high redshifts towards the quasars Q 0812+3208A(log N (HD) = 15 .
7) and Q 0843+0221 (log N (HD) =17 . ∼
240 cm − and constrained theUV radiation intensity, I UV <
60 Draine field units.
6. ACKNOWLEDGMENTS
This work was supported by the Russian ScienceFoundation (project no. 18-12-00301).
References
H. Abgrall, E. Roueff, and Y. Viala, Astron. Astrophys.Suppl. Ser. , 505 (1982).H. Abgrall and E. Roueff, Astron. Astrophys. , 361(2006).M. Asplund, N. Grevesse, A.J. Sauval, P. Scott,ARA&A, , 481 (2009).S.A. Balashev, A.V. Ivanchik, D.A. Varshalovich,Astron. Lett. , 761 (2010).S.A. Balashev and D.N. Kosenko, MNRAS , L45(2020).S.A. Balashev, V.V. Klimenko, P. Noterdaeme, J.-K. Krogager, D.A. Varshalovich, A.V. Ivanchik, P.Petitjean, R. Srianand et al., MNRAS , 2668(2019).S.A. Balashev, P. Noterdaeme, H. Rahmani, V.V.Klimenko, C. Ledoux, P. Petitjean, R. Srianand, A.V.Ivanchik et al., MNRAS , 2809 (2017).J.H. Black and A. Dolgarno, Astrophys. J. , 132(1976).Varshalovich D.A., Ivanchik A.V., Petitjean P.,Srianand R., Ledoux C. Astron. Lett. , 683 (2001).D.E. Welty, J.T. Lauroesch, T. Wong, D.G. York,Astrophys. J. , 118 (2016).A.M. Wolfe, E. Gawiser, and J.X. Prochaska, Astrophys.J. , 215 (2003).J. Wolcott-Green and Z. Haiman, MNRAS , 2603(2011).A.S. Dickinson and D. Richards, J. Phys. B: At. Mol.Phys. , 2846 (1975).E.B. Jenkins and T.M. Tripp, Astrophys. J. , 32(2011).B.T. Draine, Astrophys. J. Suppl. Ser. , 595 (1978).B.T. Draine and F. Bertoldi, Astrophys. J. , 269(1996).A.V. Ivanchik, S.A. Balashev, D.A. Varshalovich,Klimenko V.V., Astron. Rep. , 100 (2015).V. Klimenko, S.A. Balashev, A.V. Ivanchik, D.A.Varshalovich, Astron. Lett. , 137 (2016).D.N. Kosenko and S.A. Balashev, J. Phys. Conf. Ser.012009 (2018), doi:10.1088/1742-6596/1135/1/012009.S. Lacour, M.K. Andre, P. Sonnentrucker, F. Le Petit,D.E. Welty, J.-M. Desert, R. Ferlet, E. Roueff et al.,Astron. Astrophys. , 967 (2005).F. Le Petit, E. Roueff, and J. Le Bourlot, Astron.Astrophys. , 369 (2002).H.S. Liszt, Astrophys. J. , 11 (2015).P. Noterdaeme, C. Ledoux, P. Petitjean, F. Le Petit,R. Srianand, and A. Smette, Astron. Astrophys. ,393 (2007).P. Noterdaeme, R. Srianand, H. Rahmani, P. Petitjean,I. Paris, C. Ledoux, N. Gupta, S. Lopez, Astron.Astrophys. , 24 (2015).E. Oliva, A. Tozzi, D. Ferruzzi, M. Riva, M. Genoni,A. Marconi, R. Maiolino, L. Origlia, Proceed. SPIE , 18 (2018).T.P. Snow, T.L. Ross, J.D. Destree, M.M. Drosback,A.G. Jensen, B.L. Rachford, P. Sonnentrucker, R.Ferlet, Astrophys. J. , 1124 (2008).A. Sternberg and A. Dalgarno, Astrophys. J. Supp. Ser. , 565 (1995).A.I. Silva and S.M. Viegas, MNRAS , 135 (2002).L. Spitzer, J.F. Drake, E.B. Jenkins, D.C. Morton, J.B.Rogerson, D.G. York, Astrophys. J. , L116 (1973). limenko et al.: Radiative Pumping on the HD 9 L. Spitzer, W.D. Cochran, and A. Hirshfeld, Astrophys.J. Suppl. Ser. , 373 (1974).D.R. Flower, J. Le Bourlot, G. Pineau des Forets, E.Roueff, MNRAS , 753 (2000).B. Shustov, A.I. Gomez de Castro, M. Sachkov, J.C.Vallejo, P. Marcos-Arenal, E. Kanev, I. Savanov, A.Shugarov, et al., Astrophys. Sp. Sci.363