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dynamical regulation of star formation Sharon E. Meidt (MPIA) A. Hughes, E. Schinnerer, S. Garcia-Burillo, D. Colombo, C. Dobbs, A. Leroy, C. Kramer, K. Schuster, G. Dumas, T. Thompson Saturday, July 19, 14 Global Star Formation Relation =

  1. Garcia-Burillo et al. Present-day gravitational Torques (2005, 2009); NUGA Meidt et al. (2013) outflow inflow inertial torques stellar mass distribution - + + CO M51 - - + + - R ×∇Φ ring pile-up bar end < Γ > (R) M sol pc -2 azimuthal bins inflow to Meidt et al. (2012a) center! R(arcsec) Querjeta, Meidt et al (2014) spiral corotation Meidt et al. (2014) S. E. Meidt--Q&Q July 2014 Saturday, July 19, 14

  2. gas kinematics non-circular streaming motions V azimuthal motions directed along and through spiral arm (see Roberts & Stewart 1987; V radial Wong, Blitz & Bosma 2004) S. E. Meidt--Q&Q July 2014 Saturday, July 19, 14

  3. gas kinematics non-circular streaming motions V azimuthal motions directed along and through spiral arm (see Roberts & Stewart 1987; V radial Wong, Blitz & Bosma 2004) S. E. Meidt--Q&Q July 2014 Saturday, July 19, 14

  4. gas kinematics non-circular streaming motions V azimuthal motions directed along and through spiral arm (see Roberts & Stewart 1987; V radial Wong, Blitz & Bosma 2004) view depends on choice of tracer! S. E. Meidt--Q&Q July 2014 Saturday, July 19, 14

  5. gas kinematics non-circular streaming motions 50 different distributions CO (1”) 40 == CO (6”) 30 different kinematics (Colombo, SEM et al. 2014b) 20 HI (6”) 10 in M51 0 S. E. Meidt--Q&Q July 2014 Saturday, July 19, 14

  6. gas kinematics non-circular streaming motions 50 different distributions CO (1”) 40 == CO (6”) 30 different kinematics (Colombo, SEM et al. 2014b) 20 HI (6”) 10 in M51 0 • molecular gas is • clumpier (Leroy et al. 2013) • denser, confined more to mid-plane • in spiral potential well minimum (HI typically offset; e.g. Rand & Kulkarni 1990) S. E. Meidt--Q&Q July 2014 Saturday, July 19, 14

  7. Molecular Gas disk of M51 single dish (~ 500 pc) Schuster et al. (2007) Saturday, July 19, 14

  8. Molecular Gas disk of M51 single dish (~ 500 pc) Schuster et al. (2007) Saturday, July 19, 14

  9. PAWS view (Pety et al. 2013; Schinnerer et al. 2013) CO(1-­‑0) ¡in ¡central ¡9kpc ¡at (PI:Schinnerer) GMC ¡resolution ¡(40pc, ¡10 5 M sun ) IRAM ¡ Colombo et al. (2014a): 30m: ¡40 ¡hr CPROPS catalog of over 1900 Molecular Clouds PdBI: ¡170 ¡hr S. E. Meidt--Q&Q July 2014 Saturday, July 19, 14

  10. Molecular Gas kinematics in M51 Colombo ¡et ¡al. ¡(2014b) bar twist ~40 km s -1 non- circular streaming motions! Saturday, July 19, 14

  11. Molecular Gas kinematics in M51 Colombo ¡et ¡al. ¡(2014b) bar twist ~40 km s -1 non- circular streaming motions! Saturday, July 19, 14

  12. Molecular Gas kinematics in M51 Colombo ¡et ¡al. ¡(2014b) bar twist ~40 km s -1 non- circular streaming motions! Saturday, July 19, 14

  13. the role of spiral arms M51 HST ACS & ORGANIZATION STRUCTURE • streaming motions funnel gas through/along spiral arms star • build up high densities formation • + reduce shear (always?) S. E. Meidt--Q&Q July 2014 Saturday, July 19, 14

  14. the role of spiral arms M51 HST ACS ORGANIZATION • streaming motions funnel gas through/along spiral arms star • build up high densities formation • + reduce shear (always?) STRUCTURE S. E. Meidt--Q&Q July 2014 Saturday, July 19, 14

  15. the role of spiral arms M51 HST ACS ORGANIZATION • streaming motions funnel gas through/along spiral arms star • build up high densities formation • + reduce shear (always?) STRUCTURE • large-scale down to scale of Giant Molecular Clouds , the star-forming unit !! S. E. Meidt--Q&Q July 2014 Saturday, July 19, 14

  16. the role of spiral arms M51 HST ACS ORGANIZATION • streaming motions funnel gas through/along spiral arms star • build up high densities formation • + reduce shear (always?) STRUCTURE • large-scale down to scale of Giant Molecular Clouds , the star-forming unit !! • massive clouds build/form in spiral arms via convergent flows, collisions & self-gravity (M51, IC 342; Hirota et al. 2011; Koda et al. 2009; Egusa, Koda & Scoville 2010) S. E. Meidt--Q&Q July 2014 Saturday, July 19, 14

  17. the role of spiral arms • Colombo et al. - cloud Cumulative Mass Spectra (2014a): PAWS Columbo et al. GMC catalog of (2014a) over 1900 clouds across central 9 kpc in M51 log N cl [(m>M)/kpc 2 ] spiral arms help build more and larger clouds dispersal in inter- arm due to shear, feedback log M lum [M sun ] S. E. Meidt--Q&Q July 2014 Saturday, July 19, 14

  18. the role of spiral arms • Colombo et al. - cloud Cumulative Mass Spectra (2014a): PAWS Columbo et al. GMC catalog of (2014a) over 1900 clouds across central 9 kpc in M51 log N cl [(m>M)/kpc 2 ] spiral arms help build more and larger clouds dispersal in inter- center arm due to shear, spiral feedback interarm log M lum [M sun ] S. E. Meidt--Q&Q July 2014 Saturday, July 19, 14

  19. the role of spiral arms • Colombo et al. - cloud Cumulative Mass Spectra (2014a): PAWS Columbo et al. GMC catalog of (2014a) over 1900 clouds across central 9 kpc in M51 log N cl [(m>M)/kpc 2 ] spiral arms help build more and larger clouds dispersal in inter- center arm due to shear, spiral feedback interarm log M lum [M sun ] S. E. Meidt--Q&Q July 2014 Saturday, July 19, 14

  20. the role of spiral arms • Colombo et al. - cloud Cumulative Mass Spectra (2014a): PAWS more Columbo et al. GMC catalog of (2014a) over 1900 clouds across central 9 kpc in M51 log N cl [(m>M)/kpc 2 ] spiral arms help build more and larger clouds dispersal in inter- center arm due to shear, spiral feedback larger interarm log M lum [M sun ] S. E. Meidt--Q&Q July 2014 Saturday, July 19, 14

  21. the role of spiral arms - cloud properties, scaling relations Hughes et al. (2013b) log (velocity dispersion) log (CO Luminosity) M51 ) 7 8 S c -­‑2 ( ¡ p W M33 M M sun ¡ 4 LMC 4 exgal. ¡(B08) 4 ¡ B08 Σ H2 = ¡4 ¡M sun pc -­‑2 log (radius) log (radius) large range of gas surface densities no size-line width relation ➱ ➱ GMC properties are not universal clouds are not (always) virialized no universal free-fall time! scatter in KS relation S. E. Meidt--Q&Q July 2014 Saturday, July 19, 14 completely unexpected:

  22. the role of spiral arms - cloud properties, scaling relations Hughes et al. (2013b) log (velocity dispersion) log (CO Luminosity) M51 ) 7 8 S c -­‑2 ( ¡ p W M33 M M sun ¡ 4 LMC 4 exgal. ¡(B08) 4 ¡ clouds in ARM are B08 Σ H2 = ¡4 ¡M sun pc -­‑2 • brighter, • more massive, log (radius) • higher gas surface density log (radius) large range of gas surface densities no size-line width relation ➱ ➱ compared to inter-ARM GMC properties are not universal clouds are not (always) virialized no universal free-fall time! scatter in KS relation S. E. Meidt--Q&Q July 2014 Saturday, July 19, 14 completely unexpected:

  23. varying properties with dynamical environment the role of external pressure S. E. Meidt--Q&Q July 2014 Saturday, July 19, 14

  24. varying properties with dynamical environment the role of external pressure • how do clouds inherit from environment? • Pint~Pext (Hughes, SEM et al. 2013a) S. E. Meidt--Q&Q July 2014 Saturday, July 19, 14

  25. varying properties with dynamical environment the role of external pressure Hughes, Meidt et al. • how do clouds inherit from (2013a) environment? • Pint~Pext (Hughes, SEM et al. 2013a) S. E. Meidt--Q&Q July 2014 Saturday, July 19, 14

  26. varying properties with dynamical environment the role of external pressure Hughes, Meidt et al. • how do clouds inherit from (2013a) environment? • Pint~Pext (Hughes, SEM et al. 2013a) clouds coupled to surroundings S. E. Meidt--Q&Q July 2014 Saturday, July 19, 14

  27. varying properties with dynamical environment the role of external pressure Hughes, Meidt et al. • how do clouds inherit from (2013a) environment? • Pint~Pext (Hughes, SEM et al. 2013a) clouds coupled to surroundings • changes in pressure-balance (due to non-circ motions) alter cloud stability (Meidt et al. 2013) KEY: surface pressure important! S. E. Meidt--Q&Q July 2014 Saturday, July 19, 14

  28. dynamical pressure Meidt et al. (2013) cf. Jog (2013a,b) S. E. Meidt--Q&Q July 2014 Saturday, July 19, 14

  29. dynamical pressure Meidt et al. (2013) cf. Jog (2013a,b) ` S. E. Meidt--Q&Q July 2014 Saturday, July 19, 14

  30. dynamical pressure Meidt et al. (2013) cf. Jog (2013a,b) ` • Bernoulli: gas in motion, reduced pressure within gas, on clouds S. E. Meidt--Q&Q July 2014 Saturday, July 19, 14

  31. dynamical pressure Meidt et al. (2013) cf. Jog (2013a,b) ` • Bernoulli: gas in motion, reduced pressure within gas, on clouds • increased cloud stable mass (bigger before collapse) • fewer collapse-unstable clouds • lower star formation, longer τ dep S. E. Meidt--Q&Q July 2014 Saturday, July 19, 14

  32. dynamical pressure Meidt et al. (2013) cf. Jog (2013a,b) ` • Bernoulli: gas in motion, reduced pressure within gas, on clouds cloud mass spectrum • increased cloud stable mass log ¡N cl ¡[(m>M)/kpc 2 ] ¡ (bigger before collapse) • fewer collapse-unstable clouds • lower star formation, longer τ dep log ¡M lum ¡[M sun ] ¡ S. E. Meidt--Q&Q July 2014 Saturday, July 19, 14

  33. dynamical pressure Meidt et al. (2013) cf. Jog (2013a,b) ` • Bernoulli: gas in motion, reduced pressure within gas, on clouds cloud mass spectrum • increased cloud stable mass log ¡N cl ¡[(m>M)/kpc 2 ] ¡ unstable stable (bigger before collapse) • fewer collapse-unstable clouds • lower star formation, longer τ dep log ¡M lum ¡[M sun ] ¡ S. E. Meidt--Q&Q July 2014 Saturday, July 19, 14

  34. dynamical pressure Meidt et al. (2013) cf. Jog (2013a,b) ` • Bernoulli: gas in motion, reduced pressure within gas, on clouds cloud mass spectrum • increased cloud stable mass log ¡N cl ¡[(m>M)/kpc 2 ] ¡ unstable stable (bigger before collapse) • fewer collapse-unstable clouds • lower star formation, longer τ dep log ¡M lum ¡[M sun ] ¡ S. E. Meidt--Q&Q July 2014 Saturday, July 19, 14

  35. depletion time variation due to dynamics depletion time M51 0.5 τ dep = Σ H2 / Σ SFR lines of constant τ dep Ê velocity ) . s 10 8.5 Gyr log 10 S SFR H Msol pc - 2 yr - 1 L Ha + 24 micron n 0.0 e Ê d Ê Ê . Ê Ê f r 10 9 Gyr u Ê Ê - 0.5 Ê s Ê Ê Ê Ê Ê Ê Ê Ê Ê Ê Ê Ê R Ê Ê Ê Ê Ê Ê F Ê Ê S Ê Ê Ê ( Ê Ê Ê Ê Ê 10 9.5 Gyr Ê Ê Ê Ê Ê Ê g Ê - 1.0 Ê Ê Ê o Ê Ê Ê Ê l Ê Ê Ê Ê - 1.5 1.9 2.0 2.1 2.2 2.3 2.4 2.5 PAWS CO log (molecular surface density) log 10 S H2 H Msol kpc - 2 L S. E. Meidt--Q&Q July 2014 Saturday, July 19, 14

  36. Molecular Gas disk of M51 ¡ CO(1-0) in central 9kpc at cloud resolution (40pc, 10 5 M sun ) ? ? Saturday, July 19, 14

  37. Spatial Relation b/n Gas and Star Formation white contours: CO Saturday, July 19, 14

  38. Spatial Relation b/n Gas and Star Formation white contours: CO Saturday, July 19, 14

  39. Spatial Relation b/n Gas and Star Formation white contours: CO ln gas depletion time ‘universal’ time (Bigiel et al. 2008) Saturday, July 19, 14

  40. depletion time variation due to dynamics depletion time M51 0.5 τ dep = Σ H2 / Σ SFR lines of constant τ dep Ê velocity ) . s 10 8.5 Gyr log 10 S SFR H Msol pc - 2 yr - 1 L Ha + 24 micron n 0.0 e Ê d Ê Ê . Ê Ê f r 10 9 Gyr u Ê Ê - 0.5 Ê s Ê Ê Ê Ê Ê Ê Ê Ê Ê Ê Ê Ê R Ê Ê Ê Ê Ê Ê F Ê Ê S Ê Ê Ê ( Ê Ê Ê Ê Ê 10 9.5 Gyr Ê Ê Ê Ê Ê Ê g Ê - 1.0 Ê Ê Ê o Ê Ê Ê Ê l Ê Ê Ê Ê - 1.5 1.9 2.0 2.1 2.2 2.3 2.4 2.5 PAWS CO log (molecular surface density) log 10 S H2 H Msol kpc - 2 L S. E. Meidt--Q&Q July 2014 Saturday, July 19, 14

  41. depletion time variation due to dynamics depletion time M51 0.5 τ dep = Σ H2 / Σ SFR lines of constant τ dep Ê velocity ) . s 10 8.5 Gyr log 10 S SFR H Msol pc - 2 yr - 1 L Ha + 24 micron n 0.0 e Ê d Ê Ê . Ê Ê f r 10 9 Gyr star formation still occurs near spiral arms, u Ê Ê - 0.5 Ê s Ê Ê Ê Ê Ê Ê Ê Ê Ê Ê Ê Ê R Ê Ê Ê Ê but not as efficiently as it ‘could’ Ê Ê F Ê Ê S Ê Ê Ê ( Ê Ê Ê Ê Ê 10 9.5 Gyr Ê Ê Ê Ê Ê Ê g Ê - 1.0 Ê Ê Ê o Ê Ê Ê Ê l Ê Ê Ê Ê - 1.5 1.9 2.0 2.1 2.2 2.3 2.4 2.5 PAWS CO log (molecular surface density) log 10 S H2 H Msol kpc - 2 L S. E. Meidt--Q&Q July 2014 Saturday, July 19, 14

  42. depletion time variation due to dynamics depletion time M51 0.5 τ dep = Σ H2 / Σ SFR lines of constant τ dep Ê velocity ) . s 10 8.5 Gyr log 10 S SFR H Msol pc - 2 yr - 1 L Ha + 24 micron n 0.0 e Ê d Ê Ê . Ê Ê f r 10 9 Gyr star formation still occurs near spiral arms, u stronger spiral (stronger streaming), Ê Ê - 0.5 Ê s Ê Ê Ê Ê Ê Ê Ê Ê Ê Ê Ê Ê R Ê Ê Ê Ê but not as efficiently as it ‘could’ Ê more suppression Ê F Ê Ê S Ê Ê Ê ( Ê Ê Ê Ê Ê 10 9.5 Gyr Ê Ê Ê Ê Ê Ê g Ê - 1.0 Ê Ê Ê o Ê Ê Ê Ê l Ê Ê Ê Ê - 1.5 1.9 2.0 2.1 2.2 2.3 2.4 2.5 PAWS CO log (molecular surface density) log 10 S H2 H Msol kpc - 2 L S. E. Meidt--Q&Q July 2014 Saturday, July 19, 14

  43. depletion time variation due to dynamics depletion time M51 0.5 τ dep = Σ H2 / Σ SFR lines of constant τ dep Ê velocity ) . s 10 8.5 Gyr log 10 S SFR H Msol pc - 2 yr - 1 L Ha + 24 micron n 0.0 e Ê d Ê Ê . Ê Ê f r 10 9 Gyr star formation still occurs near spiral arms, u stronger spiral (stronger streaming), Ê Ê - 0.5 Ê s Ê Ê Ê Ê Ê Ê Ê Ê Ê Ê Ê Ê R Ê Ê Ê Ê but not as efficiently as it ‘could’ Ê more suppression Ê F Ê Ê S Ê Ê Ê ( Ê Ê Ê Ê Ê 10 9.5 Gyr Ê Ê Ê Ê Ê Ê g Ê - 1.0 Ê Ê Ê o Ê Ê Ê Ê l Ê Ê Ê Ê - 1.5 1.9 2.0 2.1 2.2 2.3 2.4 2.5 NGC 4303 PAWS CO log (molecular surface density) log 10 S H2 H Msol kpc - 2 L S. E. Meidt--Q&Q July 2014 Saturday, July 19, 14

  44. depletion time variation due to dynamics since spirals stronger in more massive disks, τ dep larger in (well-defined dispersion relation) S. E. Meidt--Q&Q July 2014 Saturday, July 19, 14

  45. depletion time variation due to dynamics mass since spirals stronger in more massive disks, Leroy et al. 2013 τ dep larger in (well-defined dispersion relation) ‘starburst’ what if we also limit cloud lifetimes? weak streaming strong streaming S. E. Meidt--Q&Q July 2014 Saturday, July 19, 14

  46. COLD GASS global measurements Saintonge et al. (2013) S. E. Meidt--Q&Q July 2014 Saturday, July 19, 14

  47. depletion time variation due to dynamics in massive Early-type galaxies S. E. Meidt--Q&Q July 2014 Saturday, July 19, 14

  48. depletion time variation due to dynamics in massive shear Early-type Davis et al. (2014) galaxies fast rising slow rising = rotation curve shape (flat) (solid-body=1) S. E. Meidt--Q&Q July 2014 Saturday, July 19, 14

  49. depletion time variation due to dynamics in massive shear Early-type Davis et al. (2014) galaxies (but β =0 in fast rising slow rising = rotation curve shape disks) (flat) (solid-body=1) S. E. Meidt--Q&Q July 2014 Saturday, July 19, 14

  50. Shear limits cloud lifetimes • cloud lifetime in M51 ~ shear timescale Oort A -1 (Meidt & PAWS in prep.) • also found in numerical simulations (Dobbs & Pringle 2013) t orb 1 A -1 = π (1- β ) in disks, in the centers, β =0 and t orb very long! β =0 but t orb short! • short cloud lifetimes<t ff , perhaps not long enough for star formation S. E. Meidt--Q&Q July 2014 Saturday, July 19, 14

  51. Take Away • not all cold, dense (molecular) clouds form stars..... S. E. Meidt--Q&Q July 2014 Saturday, July 19, 14

  52. Take Away • not all cold, dense (molecular) clouds form stars..... ➡ dynamics regulates organization, structure and stability of molecular gas S. E. Meidt--Q&Q July 2014 Saturday, July 19, 14

  53. Take Away • not all cold, dense (molecular) clouds form stars..... ➡ dynamics regulates organization, structure and stability of molecular gas ➡ same large-scale processes that fuel centers also suppress star formation S. E. Meidt--Q&Q July 2014 Saturday, July 19, 14

  54. S. E. Meidt--Q&Q July 2014 Saturday, July 19, 14

  55. short gmc lifetimes: an observational estimate with PAWS! S. E. Meidt--Q&Q July 2014 Saturday, July 19, 14

  56. short gmc lifetimes: an observational estimate with PAWS! ‘upstream’ dynamical environments zone II ‘downstream’ zone I ARM center S. E. Meidt--Q&Q July 2014 Saturday, July 19, 14

  57. short gmc lifetimes: an observational estimate with PAWS! ‘upstream’ dynamical environments • mostly only destruction zone II ‘downstream’ zone I ARM • interarm easy to dynamically characterize • clouds follow circular paths (very little center radial excursion) S. E. Meidt--Q&Q July 2014 Saturday, July 19, 14

  58. short gmc lifetimes: an observational estimate with PAWS! ‘upstream’ dynamical environments • mostly only destruction zone II ‘downstream’ zone I ARM • interarm easy to dynamically characterize • clouds follow circular paths (very little center radial excursion) S. E. Meidt--Q&Q July 2014 Saturday, July 19, 14

  59. short gmc lifetimes: an observational estimate with PAWS! ‘upstream’ dynamical environments • mostly only destruction zone II ‘downstream’ zone I ARM • interarm easy to dynamically zone II characterize zone I • clouds follow circular paths (very little center phase radial excursion) S. E. Meidt--Q&Q July 2014 Saturday, July 19, 14

  60. short gmc lifetimes: an observational estimate with PAWS! ‘upstream’ dynamical environments zone II ‘downstream’ zone I • cloud numbers decreases from zone I to ARM zone II (Colombo et al. 2013) zone II • mass spectrum evolution: shear and star zone I center formation feedback destroy clouds, phase limit lifetimes S. E. Meidt--Q&Q July 2014 Saturday, July 19, 14

  61. short gmc lifetimes: an observational estimate with PAWS! ‘upstream’ dynamical environments zone II ‘downstream’ zone I • cloud numbers decreases from zone I to ARM zone II (Colombo et al. 2013) zone II • mass spectrum evolution: shear and star zone I center formation feedback destroy clouds, phase limit lifetimes S. E. Meidt--Q&Q July 2014 Saturday, July 19, 14

  62. short gmc lifetimes: an observational estimate with PAWS! ‘upstream’ dynamical environments zone II ‘downstream’ zone I • cloud numbers decreases from zone I to ARM zone II (Colombo et al. 2013) zone II • mass spectrum evolution: shear and star zone I center formation feedback destroy clouds, phase limit lifetimes shear Oort A feedback = Ω -B = Ω /2 (for V flat) S. E. Meidt--Q&Q July 2014 Saturday, July 19, 14

  63. short gmc lifetimes: an observational estimate with PAWS! ‘upstream’ dynamical environments zone II ‘downstream’ zone I • cloud numbers decreases from zone I to ARM zone II (Colombo et al. 2013) zone II • mass spectrum evolution: shear and star zone I center formation feedback destroy clouds, phase limit lifetimes mass loss and dispersal shear Oort A feedback = Ω -B = Ω /2 (for V flat) S. E. Meidt--Q&Q July 2014 Saturday, July 19, 14

  64. short gmc lifetimes: an observational estimate with PAWS! ‘upstream’ dynamical environments zone II ‘downstream’ zone I • cloud numbers decreases from zone I to ARM zone II (Colombo et al. 2013) zone II • mass spectrum evolution: shear and star zone I center formation feedback destroy clouds, phase limit lifetimes mass loss and dispersal shear Oort A feedback = Ω -B transformation = Ω /2 (for V flat) S. E. Meidt--Q&Q July 2014 Saturday, July 19, 14

  65. a (simple) framework if cloud numbers decrease from zone I to zone II then lifetime < travel time from arm to arm S. E. Meidt--Q&Q July 2014 Saturday, July 19, 14

  66. a (simple) framework if cloud numbers decrease from zone I to zone II then Eulerian vs. lifetime < travel time from arm to arm Lagrangian arm time II I arm S. E. Meidt--Q&Q July 2014 Saturday, July 19, 14

  67. a (simple) framework if cloud numbers decrease from zone I to zone II then Eulerian vs. lifetime < travel time from arm to arm Lagrangian arm time split interarm in half, II I count N I and N II original arm lost half arm-to-arm travel time; measure from t orb S. E. Meidt--Q&Q July 2014 Saturday, July 19, 14

  68. a (simple) framework if cloud numbers decrease from zone I to zone II then Eulerian vs. lifetime < travel time from arm to arm Lagrangian arm time split interarm in half, II I count N I and N II original arm lost half arm-to-arm travel time; measure from t orb • still sources + sinks (feedback cloud splitting, etc.) and when i.e. mostly losses S. E. Meidt--Q&Q July 2014 Saturday, July 19, 14

  69. a (simple) framework if cloud numbers decrease from zone I to zone II then Eulerian vs. lifetime < travel time from arm to arm Lagrangian arm time split interarm in half, II I count N I and N II original high F lost small F lost arm long τ short τ pop. growth lost (transformation) half arm-to-arm travel ≈ time; measure from t orb • still sources + sinks (feedback cloud splitting, etc.) and when i.e. mostly losses S. E. Meidt--Q&Q July 2014 Saturday, July 19, 14

  70. GMC lifetimes S. E. Meidt--Q&Q July 2014 Saturday, July 19, 14

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