H. S. Liszt et al.: CO luminosity of diffuse gas6<strong>tel</strong>-<strong>00726959</strong>, version 1 - 31 Aug 2012T r* [Kelvin]e -τ -1543213 COx3112 CO(1-0)02HNC112 CO(1-0),13 COx20HCO +-1H Ix100-40 -20 0V LSR [km s -1 ]Fig. A.1. Line profi<strong>le</strong>s toward and near B0355+508 = NRAO150.Bottom: absorption line profi<strong>le</strong>s of H I, HCO + , 12 CO, 13 CO (multipliedby 2) and HNC; Hi absorption and emission are present over a muchbroader velocity range than shown here. Top: Emission from 12 CO,13 CO (sca<strong>le</strong>d upward by a factor 3) and HCO + (sca<strong>le</strong>d upward by afactor 100). The HCO + profi<strong>le</strong> is an average over a 3.5 ′ region aroundthe continuum (to avoid absorption). See Appendix A.is E B−V = 1.5 mag or A V ≈ 5 mag but it would be quiteopaque even if only the atomic gas were present. A lower limiton N Hi from the integrated 21 cm emission of the nearest profi<strong>le</strong>in the Leiden-Dwingeloo Survey (Hartmann & Burton 1997)in the optically thin limit is N Hi> ∼ 7.4 × 10 21 cm −2 , implyingE B−V> ∼ 1.27 mag. The H I column density derived by takingthe ratio of N Hi to Hi absorption as discussed in Sect. 3 here is,understandably, slightly larger, N Hi = 1.1 × 10 22 cm −2 .We show in Fig. A.1 various absorption and emission profi<strong>le</strong>salong and around the line of sight to NRAO150 akaB0355+508. We have published various analyses of this line ofsight in the references noted below, and most recently we synthesizedthe CO emission in a 90 ′′ region around NRAO150 at6 ′′ resolution (Pety et al. 2008). Hi absorption and emission extendwell outside the narrow kinematic interval shown here. Theweak HCO + absorption at −35 km s −1 is real, as is the broadwing extending up to −25 km s −1 .CO emission is fairly strong in this direction, W CO =17 K km s −1 , nominally implying 2N H2 ≈ 7 × 10 21 , comparab<strong>le</strong>to N Hi , but mo<strong>le</strong>cular absorption spectra of HCO + and CON(H I) tot [cm-2 ]10 2110 200.1 1 10⌡ ⌠ τ(H I) dv [km s -1 ]E BV >0.09E BV 36, >54 and >25 at the 2σ <strong>le</strong>velin these components (Liszt & Lucas 1998).In emission, the 12 CO/ 13 CO brightness ratios are 12 and 30for the two strong kinematic components, ref<strong>le</strong>cting both thefractionation and the fact that W CO ∝ N CO in the diffuse gasregime as discussed in the text here.HCO + emission is weak in Fig. A.1. The profi<strong>le</strong> shown (fromLucas & Liszt 1996) is an average of positions around the continuumsource to avoid contamination from absorption. The low<strong>le</strong>vels of HCO + emission seen toward our samp<strong>le</strong> of backgroundcontinuum sources can be understood as arising from relativelylow density gas (n H2< ∼ 100 cm −3 ) when the e<strong>le</strong>ctron fraction isas high as expected for diffuse gas, i.e. 2 × 10 −4 (Lucas & Liszt1994, 1996).Appendix B: The ratio of total to absorbing HIShowninFig.B.1 is a plot of the data from the tab<strong>le</strong>s of Hei<strong>le</strong>s &Troland (2003) that were used in Sect. 3 to convert the ∫ τ(Hi)dvmeasurements in Fig. 1 to a total quantity of Hi. The plot showsa regression line (power-law slope 0.84) fit to data points withE B−V > 0.09 mag (the range occupied by the HCO + detections inFig. 1) to point out a slight upturn at low ∫ τ(Hi)dv.Thesamp<strong>le</strong>means are largely unaffected by setting various samp<strong>le</strong> se<strong>le</strong>ctioncriteria.Appendix C: A chemistry-based determinationof N H2 /W COIt is also possib<strong>le</strong> to determine W CO /N H2 without the H I measureor formally estimating f H2 , although we preferred not toPage 7 of 10
A&A 518, A45 (2010)<strong>tel</strong>-<strong>00726959</strong>, version 1 - 31 Aug 2012W CO [K-km s -1 ]1010.11 10⌡⌠ τ(HCO + )dv [km s -1 ]Fig. C.1. Integrated CO J = 1–0 brightness plotted against theintegrated HCO + J = 1–0 optical depth. N HCO + = 1.12 ×10 12 cm −2 (∫ τ(HCO + )dv/1 kms −1) . See Appendix D.do this in the main discussion. In Fig. C.1 we show the variationof W CO with ∫ τ(HCO + )dv. CO appears reliably at detectab<strong>le</strong><strong>le</strong>vels W CO> ∼ 0.3Kkms −1 , N CO> ∼ 3 × 10 14 cm −2when N HCO + > ∼ 3 × 10 11 cm −2 or N H2> ∼ N HCO +/3 × 10 −9 =10 20 cm −2 .IfX HCO + = 3 × 10 −9 the ensemb<strong>le</strong> mean values〈W CO 〉 = 3.45 K km s −1 , 〈∫ τ(HCO + )dv 〉 = 2.38 km s −1 implyW CO = 1Kkms −1 per 2.6 × 10 20 H 2 cm −2 , just 30% above thatderived in Sect. 3.5.The near linearity of the N CO –N HCO + relationship in Fig. C.1results from bulk averaging over who<strong>le</strong> lines of sight: giventhe same general mix of conditions, an ensemb<strong>le</strong> of richer andpoorer or shorter and longer sightlines will show proportionalitiesbetween almost any two quantities in this way. As shownin Fig. A.1 there is no such proportionality on a per-componentbasis. In detail, and with much scatter, the overall chemical variationis approxima<strong>tel</strong>y N CO ∝ (N H2 ) 2 (Liszt 2007b; Sheffer et al.2008).Appendix D: Calculating the CO brightnessfrom galactic survey resultsThe statistics of observing the clumpy galactic mo<strong>le</strong>cular clouddistribution are Poisson (Gordon & Burton 1976; Burton &Gordon 1978) so the integrated CO brightness W CO (r) accumulatedwhen traversing a path of <strong>le</strong>ngth r in the galactic plane isW CO (r) = W CO0 (1 − exp (−r/λ))(D.1)where W CO0 is the characteristic brightness of a clump (GMC)and λ is the geometric mean free path between clumps.Although it is possib<strong>le</strong> to derive W CO0 and λ separa<strong>tel</strong>y, galacticsurvey results are given in terms of a hybrid quantity A CO whoseunits are K km s −1 per kpc corresponding to evaluating W CO (r)when r ≪ λ, i.e.W CO (r) = (W CO0 /λ) r = A CO r.ThecoefficientA CO is closely related to the mean density: just convertW CO to N H2 . For H I the integrated brightness per unit distanceis directly converted into a mean density n(H I), if it is assumedthat the gas is optically thin.The brightness of the CO cloud ensemb<strong>le</strong> viewed verticallythrough the galactic disk is then just A CO Δz, whereΔz is theequiva<strong>le</strong>nt thickness of the disk. For a Gaussian vertical distributionwith dispersion σ z , Δz = (2π) 1/2 σ z .ReferencesBigiel, F., Leroy, A., Walter, F., et al. 2008, AJ., 136, 2846Bohlin, R. C., Savage, B. D., & Drake, J. F. 1978, ApJ, 224, 132Bothwell, M. S., Kennicutt, R. C., & Lee, J. C. 2009, MNRAS, 400, 154Burgh, E. B., France, K., & McCandliss, S. R. 2007, ApJ, 658, 446Burton, W. B., & Gordon, M. A. 1978, A&A, 63, 7Cox, D. P. 2005, ARA&A, 43, 337Dickey, J. M., Kulkarni, S. R., Hei<strong>le</strong>s, C. E., & Van Gorkom, J. H. 1983, ApJSS,53, 591Draine, B. T., Da<strong>le</strong>, D. A., Bendo, G., et al. 2007, ApJ, 663, 866Falgarone, E., Pineau Des Forêts, G., Hily-Blant, P., & Schilke, P. 2006, A&A,452, 511Garwood, R. W., & Dickey, J. M. 1989, ApJ, 338, 841Goldreich, P., & Kwan, J. 1974, ApJ, 189, 441Goldsmith, P. F., Heyer, M., Narayanan, G., et al. 2008, ApJ, 680, 428Gordon, M. A., & Burton, W. B. 1976, ApJ, 208, 346Hartmann, D., & Burton, W. B. 1997, Atlas of galactic neutral hydrogen(Cambridge; New York: Cambridge University Press)Hei<strong>le</strong>s, C., & Troland, T. H. 2003, ApJ, 586, 1067Helfer, T. T., & Blitz, L. 1997, ApJ, 478, 233Leroy, A. K., Walter, F., Brinks, E., et al. 2008, AJ, 136, 2782Liszt, H. 1997a, A&ASS, 124, 183Liszt, H. S. 1982, ApJ, 262, 198Liszt, H. S. 1995, ApJ, 442, 163Liszt, H. S. 1997, A&A, 322, 962Liszt, H. S. 2007a, A&A, 476, 291Liszt, H. S. 2007b, A&A, 461, 205Liszt, H., & Lucas, R. 2002, A&A, 391, 693Liszt, H. S., & Lucas, R. 1994, ApJ, 431, L131Liszt, H. S., & Lucas, R. 1996, A&A, 314, 917Liszt, H. S., & Lucas, R. 1998, A&A, 339, 561Liszt, H. S., & Lucas, R. 2000, A&A, 355, 333Liszt, H. S., Burton, W. B., & Bania, T. M. 1981, ApJ, 246, 74Liszt, H. S., Pety, J., & Tachihara, K. 2009, A&A, 499, 503Lucas, R., & Liszt, H. S. 1994, A&A, 282, L5Lucas, R., & Liszt, H. S. 1996, A&A, 307, 237McCall, B. J., Hink<strong>le</strong>, K. H., Gebal<strong>le</strong>, T. R., et al. 2002, ApJ, 567, 391Morton, D. C. 1975, ApJ, 197, 85Münch, I. G. 1952, ApJ, 116, 575Pety, J., Lucas, R., & Liszt, H. S. 2008, A&A, 489, 217Rachford, B. L., Snow, T. P., Destree, J. D., et al. 2009, ApJSS, 180, 125Savage, B. D., Drake, J. F., Budich, W., & Bohlin, R. C. 1977, ApJ, 216, 291Sch<strong>le</strong>gel, D. J., Finkbeiner, D. P., & Davis, M. 1998, ApJ, 500, 525Sheffer, Y., Rogers, M., Federman, S. R., et al. 2008, ApJ, 687, 1075Sheffer, Y., Rogers, M., Federman, S. R., Lambert, D. L., & Gredel, R. 2007,ApJ, 667, 1002Sofia, U. J., Lauroesch, J. T., Meyer, D. M., & Cart<strong>le</strong>dge, S. I. 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