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PH712: Advanced Cosmology and the Interstellar Medium L ECTURE 7 5. Massive Stars, H II Regions 5.1. Formation of Massive Stars We have so far considered the formation of low mass stars. Massive stars (OB), even if rare in numbers, have a profound impact on their environment. They are the fundamental producers of heavy elements, generate huge amounts of high energy radiation, trigger star formation. Their lifetime on the main sequence is rather short: τ MS ∼ 7 · 109 yrs · ( M/ M⊙ ) · ( L⊙ / L) (27) Hence for typical masses (above 10 M⊙ ) and luminosities (104 – 106 L⊙ ) their main sequence lifetimes range from 2 – 20 million years. Thus, those stars are always found very close to their birthplaces. Observations of forming massive stars are usually very difficult. They are deeply embedded within dust clouds, they are usually very distant, they exclusively form in multiple systems. Furthermore: their Kelvin-Helmholtz timescale (maximum time a star can produce its entire luminosity from contraction – this is the T-Tauri phase of low mass stars) is: tKH = GM2 RL (28) For a star like our Sun this is in the order of 3 · 107 yrs. For an O-star this is only about 104 yrs. This is much smaller than the time required to assemble the entire mass with an accretion rate found e.g. for low mass stars of at most 10−4 M⊙ yr−1 . Hence, contraction onto the main sequence will finish before accretion stops for stars of more than about 8 – 15 solar masses. Thus the evolutionary sequence for low mass stars cannot be applied here. There are in principle two main ideas how very massive stars for: 1) like low mass stars via the collapse of a very massive dense cloud; this implies very high mass accretion rates; observationally one should be able to observe massive discs and outflows from those objects; 2) by coalescence of lower mass stars in extremely dense cluster environments; – Observational evidence seems to favor scenario 1), at least for stars with masses of up to 40 M⊙ . Massive discs are found, as well as outflows from massive forming stars. These outflows are generally much more massive and less collimated than the low mass versions. Some even look like explosions. How the most massive stars (∼ 100M⊙ ) are formed is, however, still very much under debate today. 5.2. H II regions Once formed, massive stars produce large amounts of high energy radiation. Especially interesting is the ’extreme’ ultraviolet (EUV) or Lyman continuum. 46 PH712: Advanced Cosmology and the Interstellar Medium L ECTURE 8 Fig. 33. Left: Observations of a suspected disc shadow around a forming massive star in M17. Right: Massive outflow in Orion. Photons with such energies (E > 13.6eV) are able to ionise hydrogen. Absorption of the EUV radiation will be dominated by hydrogen atoms. The optical depth for photons above the Lyman limit ν0 can be derived from τν = σ0 ν ν0 −3.5 nH0 (29) where σ0 is the absorption cross-section at the Lyman limit for hydrogen (6.3 · 10−18 cm2 ). The HI gas density n H 0 in the mid-plane of the Galaxy is in the order of 0.6 cm−3 . Thus an EUV photon at the Lyman limit will get absorbed after it travels a distance corresponding to an optical depth of unity. This is reached after only 0.09 pc. Higher energy photons, e.g. at the threshold for the ionisation of Helium, can travel 0.6 pc before they get absorbed. We do however observe H II regions with very different sizes, radii ranging up to 100 pc, in the Galaxy and other galaxies. This requires that in the order of 99 % of the hydrogen is ionised in these regions. What determines the final size of the H II region? Let’s assume a thin shell of gas at a radius R and a thickness dR from a star with an ionising flux (inside all the material is ionised, outside it is neutral). The density of gas in the shell is n and the number of particles in the shell is 4π R2 ndR. If the star emits dN ionising photon each second, then the radius of the shell grows by dR, where 47 PH712: Advanced Cosmology and the Interstellar Medium dR dN = 4 · π · R2 · n · dt dt L ECTURE 8 (30) and assuming each photon ionises a hydrogen atom. However, if ions and electrons recombine in the entire sphere at a rate α , then this equation has to be modified to allow for the recombination. dN 4π R3 dR − · ni · n e · α = 4 · π · R 2 · n · dt 3 dt (31) In the final H II region the ionisation and recombination is in equilibrium and hence dR/dt = 0. Furthermore, we write the ionising flux from the star as S∗ = dN /dt and solve for the equilibrium (Stömgren) Radius Rs : Rs = 3 · S∗ 4 · π · ni · n e · α 1/3 (32) Since the number densities of neutrals in the neutral cloud equals the ion and electron density in the H II region one can replace ni · ne by n20 . In reality the final size of the H II region will be larger, since the ionisation process effectively doubles the number of particles in the sphere. This will create an extra internal pressure P = 2 · ni · k · Ti that has to be considered in comparison to the external pressure. The final radius of the H II region then is: R= 2Ti Tn 2/3 Rs (33) How does the ionisation front propagate? If one considers the number of Lyman photons I per unit area falling onto the ionisation front per second, then the front will move from R to R + dR in the time dt, hence I · dt = n · dR (34) Hence we obtain for the ionising flux S∗ (using Equ. 31): S∗ = 4 · π · R2 · I + 4 π R3 · ni · n e · α 3 and for the velocity of the shock front 48 (35) PH712: Advanced Cosmology and the Interstellar Medium S∗ dR R · n ·α = − 2 dt 3 4·π ·R ·n L ECTURE 8 (36) A very good practical approximation for the solution of this equation is: R3 = R3s · 1 − e−n·α ·t (37) Even if the final radius is reached eventually, the initial evolution of the H II region is very rapid, on timescales of ∼ 105 yrs. The radius is then growing initially with several kilometers per second. What is the ionisation fraction in the H II region? In ionisation balance the ionisation and recombination reactions are in balance. H I + photon ↔ H I I + e− (38) Hence the number of ionisations per unit volume per second Ni is equal to the number of recombinations per unit volume per second Nr . The number of recombinations can be expressed by: Nr = α · n( H + ) · n(e− ) = α · n2 ( H + ) (39) Using the flux of ionising photons φ and the ionisation cross-section σ (i.e. the probability that an atom of hydrogen will absorb an ionising photon) we also can express the rate of ionisation: Ni = n( H ) · φ · σ (40) The degree of ionisation defined as χ= n( H + ) n( H + ) = n n( H ) + n( H + ) (41) can then be calculated using the ionisation balance Nr = Ni and n = n( H ) + n( H + ). One obtains: χ2 σ ·φ = 1−χ α·n (42) With typical values for the above parameters 49 PH712: Advanced Cosmology and the Interstellar Medium L ECTURE 8 φ = 1015 s−1 m−2 σ = 7 · 10−22 m2 α = 2 · 10−19 m3 s−1 at T = 10000K n = 102 cm−3 one obtains χ = 0.99997. Hence only 0.003 % of the hydrogen is neutral, or in other words the gas is almost totally ionised. 5.3. Photo dissociation Regions (PDR) Besides the EUV radiation, capable of ionising hydrogen, massive stars generate a huge amount of FUV radiation in the range from 90 – 200 nm. Such radiation dissociates and ionises most molecules and a number of abundant atoms (e.g. C, Si, S, Fe). If clouds are exposed to FUV, they form zones were most of the gas is atomic or partially ionised. These include interfaces between H II regions and surrounding neutral cloud, neutral shells around planetary nebula. The size of these regions depend on the penetration depth of the FUV. Most efficiently the FUV is absorbed by dust and H2 . The extend of these regions is thus determined by the column density of material (τ ∼ a few – ∼ 1022 cm−2 ). Photoelectric heating and UV pumping are the most important gas heating mechanisms in PDRs. 5.4. (Ultra) Compact H II Regions Due to the lower densities H II Regions around established massive stars have sizes in the range 1 – 30 pc (the number of UV photons covers a wide range: B2: 4 · 1044 , T=20000 K; O8.5 2 · 1048 , T=35500 K; O4: 9 · 1049 , T=50000 K). There are however much more compact H II regions observed (We cannot observe the high energy radiation directly, but H II regions emit a large amount of free-free – radio continuum radiation). These compact H II regions have size of 0.005 – 0.5 pc and electron densities of 2 · 103 – 3 · 105 cm−3 . Ultra compact H II regions (UCH II) have sizes below 0.01 pc and electron densities above 105 cm−3 . They come in a variety of shapes: 20 % cometary, 16 % core-hale, 4 % shell like, 43 % spherical or unresolved, 17 % irregular or multiple peaked. These various shapes lead to several models for high mass star formation, each able to explain certain aspects of the observations, but non is able to capture them all. e.g. bow-shock models (ionising stars moving supersonic); champagne flow (ionising star formed close to cloud edge); mass loaded wind models (clumpy environment, winds pick up ablated material from the clumps); infall of material; photo evaporation of massive discs (wind replenished material in the H II region); Hence, high mass star are born in environments with a range of density, non-uniformity, disc masses, dynamical states. Each star might develop along its own evolutionary path. 50