General momentum equation

Transcription

1 PY4A4 Senio Sophiste Physics of the Intestella and Integalactic Medium Lectue 11: Collapsing Clouds D Gaham M. Hape School of Physics, TCD Geneal momentum equation Du u P Dt uu t 1 B 4 B 1 B 8 Lagangian Euleian time deivatives P - isotopic pessue = P(gas) + P(cosmic ays) + P(tubulence) ρ - gas density Φ - gavitation potential B magnetic field u flow velocity 1

2 Geneal momentum equation Du u P Dt uu t 1 B 4 B 1 B 8 Lagangian Euleian time deivatives P - isotopic pessue = P(gas) + P(cosmic ays) + P(tubulence) ρ - gas density Φ - gavitation potential B magnetic field u flow velocity Single Cloud Equilibia Conside an isolated, spheically symmetic in equlibium intenal pessue extenal pessue self-gavity Equation of hydodynamic flow Eqn hydostatic equilibium P P Poisson s Eqn 4G d G d dp d GM GM 4 d d d Mass in the shell thickness d d 4G d dm 4 d d

3 Single Cloud Equilibia dp d GM dm 4 d GM 4 dp dm V dp Integate fom the cente () of the to the edge whee the extenal GM dm pessue is P S Integate LHS by pats Ps V P Ps V P dp V P V dp S P M edge cente V GM PdV V dm PdV [1] P, d P S Enegy content of the Remaining integal on LHS can be witten in tems of the s themal enegy e Also V int P P dv V V RHS of Equation [1] is just the gavitational self-enegy Ω Combining tems we get s P dv c dv c M s V e dv T int V P T S

4 Spontaneous coe collapse Fist neglect extenal pessue, emaining tems ae intenal pessue acting against self-gavity, and the condition fo equilibium is T T T contaction equilibiu m expansion Afte petubation of the minimum enegy state esults NB we have also neglected magnetic and otational enegies, which can be included and ae impotant. Initiating contaction Assume that the molecula has unifom density (ρ c ), tempeatue, and pessue (P S ) then the gavitation self-enegy is given by M c R GM 16 4 GM dm cg d 5 R The total enegy equation in this simple case is GM 4R Ps cs M 5 R Neglecting the extenal pessue fo a moment, the condition fo collapse GM c 1 GM S cs M 5 R R 5 R 4

5 Time scale agument Intoducing the cossing time (sound wave cosses adius) RCloud S c The citeia fo initiation of collapse is theefoe S S 15 4G So what does this mean physically? Fee-fall time The fee-fall time (total collapse to a point) ff G c The citeia fo initiation of collapse is then that the fee-fall time is less than the sound cossing time ff s Collapsing shells of diffeent adii take the same time, and do not coss, all each the cente at the fee-fall time (neglecting bouncing) As long as density deceases outwads shells do not coss duing collapse - but aive at diffeent times This is highly idealized! 5

6 Whee do stas fom? Convet this to a citical mass (using R, density, sound speed) - Jean s Mass (see notes fom D. S. Jeffey s Stella Stuctue and Evolution couse) 5 cs M M cit 1 G Citical mass fo conditions in cold neutal (diffuse) T=7 K n H = cm - M cit ~ 1 4 M sola too big-sta fomation is not obseved on this scale Cool molecula s T= K n H ~5 cm - M cit ~ M sola (R ~. pc) What happens to citical mass when the collapses? Souces of petubations What can tun a stable to an unstable Souces of extenal pessue (which we have caefully neglected!) Ionization fonts Stella winds Cloud collisions Supenova shock waves Galactic spial density waves 6

7 Induced sta fomation Let us etun to ou oiginal equation and conside finite extenal pessue tems, i.e., (divide by 4πR ) A PS R B R 4 A and B ae constants of the. How does equilibium depend on pessue? Fo P S below theshold equilibium solutions P S ~ R 4 B A P R Bonne-Ebet Sphees Peviously we took an initial unifom (density=constant) Now conside an isothemal in equilibium, e-wite ou pevious equations 1 d d ln cs 4G d d Letting ln we get a special fom of the Lane-Emden Eqn With u c 1 d du e d d 4G c cs u 7

8 V I S I B L E A staless coe B68 ESO s VLT and ESO s NTT Find extinction towad 1s of stas in image N E A R - I R The inevitable futue of the staless coe Banad 68 Buket, A. & Alves, J. 9, ApJ, 695, 18 Numeical simulation of impact 8

9 Example of maginally stable B68 Vey good fit to Bonno-Ebet sphee max = (R/c S )(4 G c ) 1/ Coe on the vege of collapse ( max > 6.9±.) ( collapse > 6.5) Pediction B68 will collapse within, yeas to fom an isolated low mass sta The cold winte sky: T d ~ K IRAS 1 m 9

10 The Oion/Eidanus Bubble (Ha): d=18 to 5pc; Oion OB1 Association: ~4 > 8 M stas: ~ SN in 1 My λ Oi (< My) 1a (8-1 My; d ~ 5 pc)) 1b ( -6 My; d ~ 4 pc) 1c ( - 6 My; d ~ 4 pc) 1d (< My; d ~ 46 pc) Banads's Loop Eidanus Loop Globula Clustes Piotto et al, 7, ApJ, 661, L5 Exquisit photomety fom Hubble discoveed multiple mainsequences, tun-offs and RGBs in massive golubula clustes! [Oigin is not cuently esolved] 1

11 Hebig-Hao Objects HH 1 (McCaughean & Zinnecke) VLT (image) HH HH 1 HST

12 HST HH HST

13 HH HST