Download 4. Massive Stars and HII Regions

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