Formation of Massive Stars

Question 1

The Stellar Birthline

Answer 1

• the line in the luminosity vs temperature (log-log space) below which young pre-main-sequence stars have become visible
• the birthline for massive stars seems to coincide with the main sequence
• massive stars are only observed already on the main sequence

Question 2

Kelvin-Helmholtz Timescale

Definition

Answer 2

• the cloud collapses into a protostar (hydrostatic core)
• before the protostar can begin hydrogen burning and join the main sequence it needs to contract further
• the protostar can only contract (second collapse phase) by radiating away the released gravitational energy
• the timescale for this contraction is called the Kelvin-Helmholtz timescale

Question 3

How do you derive the Kelvin-Helmholtz timescale?

Answer 3

t_kh = gravitational energy / luminosity

=> GM²/RL

Question 4

Mass-Luminosity Relation

Answer 4

• plot log(solar luminosity) against log(solar mass)

- straight line with positive gradient

Question 5

Kelvin-Helmholtz Timescale vs. Freefall Time

Answer 5

-for massive stars:
t_kh &laquo_space;tff
-therefore massive stars arrive on the main sequence while still embedded in their molecular clouds

Question 6

Kelvin-Helmholtz Timescale and Freefall Time

Low vs. High Mass Stars

Answer 6

• for low mass stars, the cloud collapses once to form the first hydrostatic core, the freefall time
• then the first hydrostatic core collapses to form a star, the Kelvin-Helmholtz timescale

-for high mass stars, the core collapses inside the cloud so the star is formed before the cloud finishes collapsing

Question 7

Why is it hard to identify massive stars?

Answer 7

• massive stars reach the main sequence while still accreting material so they don’t have birthlines
• this means that massive stars have an invisible pre-main-sequence phase

Question 8

How are massive stars identified?

Answer 8

• massive stars are luminous IR sources since they still have envelopes which absorb UV/optical radiation from the star and reemit at IR wavelengths
• HII regions (ionised H), very close to the star there is enough UV radiation to ionise hydrogen therefore there is a region of ionised hydrogen around the core

Question 9

Formation of HII Regions Around Massive Stars

Answer 9

-the salient characteristic of any massive star is its extreme energy output, much of which is at UV wavelengths, but only a finite number of photons with energy >=13.6eV
-energetic photons dissociate H2 and ionise atomic hydrogen, HI
H + h -> H+ + e-
-where h is a photon with >=13.6eV
-the electrons are deflected in the magnetic field of the star, as they are deflected they change energy state and emit radio photons of 6cm wavelength which are easily detected since radio is not easily absorbed by the ISM

Question 10

Stromgren Sphere

Definition

Answer 10

-as well as ionisation of atomic hydrogen:
H + h -> H+ + e-
-atomic hydrogen is recreated via the process of recombination with an electron:
H+ + e- -> H + h
-also stars are only emitting a finite number of photons with E>=13.6eV which are capable of ionisation
-thus a star with a fixed output in UV radiation can only ionise a limited region in the surrounding cloud
-if the surrounding medium is (relatively) uniform known as a Stromgren sphere

Question 11

Stromgren Sphere

Ionisation Balance

Answer 11

• the central star photo-ionises hydrogen atoms in the surroundings which results in a HII region
• in the ionised gas, free electrons can recombine with protons to form neutral hydrogen
• the photo-ionisation rate will be balanced by the recombination rate
• because there is a finite number of ionising (E>13.6eV) photons from the star, we can calculate the size of this region

Question 12

Calculating Stromgren Radius

Outline

Answer 12

-an estimated size of the Stromgren sphere can be found by considering the balance of forward and backwards reactions
-the ionisation balance holds at each locaton in the region:
volumetric ionisation rate = recombination rate (p+ + e-)
-integrating over the sphere:
total number of ionisation events per unit time = total recombination rate

Question 13

Calculating Stromgren Radius

Equations

Answer 13

-the volumetric rate at which free electrons and protons combine to produce atomic hydrogen can be written as:
ℛ = nenpαrec(T)
-can assume the cloud is charge neutral so, ne=np
ℛ = ne²αrec(T)
-the total rate of recombinations within the sphere follows by integrating ℛ over the volume:
𝐍 = 4π/3 * ne²αrec(T)Rs³
-where Rs is the Stromgren symbol

Question 14

What determines the size of the HII region?

Answer 14

-stellar temperature and luminosity on one hand and the density of the medium on the other hand determine the size of the HII region

Question 15

Calculating Stromgren Radius

ne and nh

Answer 15

-the ionisation spreads so quickly to the Stromgren radius that the original cloud density is not able to change appreciably, thus:
ne ~ nh
-that is the number density of electrons within the HII region is equal to the number density of H atoms external to Rs

Question 16

Relationship Between Rs and nh

Answer 16

Rs ∝ nh^(-2/3)
-the higher the density, reduces the size of the Stromgren sphere because the forward reaction depends only on nh but the backwards reaction depends on the density of both H+ and e- so recombination is less likely at higher density since collision is more likely in a smaller sphere

Question 17

Observing HII Regions

Answer 17

• stars with M>10M☉ and T>30000K can ionise their surrounding gas
• ionised gas emits radio continuum, free-free radiation
• this radiation is bright and is not absorbed by dust, can propagate unimpeded through the ISM
• massive stars eventually become visible in the optical

Question 18

Typical Stromgren Radius

Answer 18

-the HII region is very sharp-edged and has a radius of ~0.4pc for an O6 star and T=30000K

Question 19

What causes the ionisation front to expand?

Answer 19

• at the Stromgren radius, the ionisation fraction drops sharply
• at the boundary, there is a pressure difference (P=nkT):
• -ionised hydrogen has twice as many particles (H+ + e-)
• -the temperature is ~10000K (compared with 10K outside)
• the ionisation front expands due to overpressure
• the expansion speed ~ sound speed ~ 10km/s

Question 20

What are the main phases of a massive stars life embedded within their molecular clouds?

Answer 20

• infrared dark cloud (IRDC)
• hot core
• massive young stellar object
• hyper- then ultra-compact HII region
• compact then classical HII region

Question 21

Infrared Dark Clouds

Answer 21

• discovered by galactic surveys with infrared satellites, ISO and MSX
• defined as clouds that exhibit significant mid-infra-red opacity
• extreme properties:
• -cold (<20K)
• -dense (>10^4 cm^-3)
• -enormous column densities (>10^(23-25) cm^-2)
• -dark at 100 micron

Question 22

Massive Young Stellar Object

Answer 22

• bright at mid- and near-infrared wavelengths
• luminous: 10^4 L☉
• radio quiet as they are too young and accretion is still occurring so there are no UV photons
• can observe bipolar molecular outflow, evidence that accretion is still taking place

Question 23

Optically Visible / Classical HII Regions

Answer 23

L >= 10^18 cm

ne <= 10^4 cm^(-3)

Question 24

Ultra-Compact HII Regions

Answer 24

L <= 10^17 cm
ne >= 10^5 cm^(-3)
-in the far infra-red, they are the most luminous objects in the galaxy

Question 25

Are massive stars expected to form at all?

Answer 25

• need to consider:
• -mass accretion rate
• -luminosity as a function of mass
• a solar mass star is too faint by a factor of 10^6 to stop accretion

Question 26

What is the mass limit placed on massive stars by considering how radiation pressure impedes accreting material?

Answer 26

~30M☉

-but massive stars with M*>200M☉ have been observed

Question 27

Main Problems with Forming Massive Stars

Answer 27

• radiation pressure on dust considered a sever hindrance to accretion
• BUT previously assumed to occur spherically symmetrically
• problem may be fixed by accretion through a disk more likely accompanied by cavities carved by radiation / stellar wind in the polar directions

Question 28

Theoretical Models for Massive Stars

Answer 28

• monolithic collapse and disk accretion: isolated cores
• competitive accretion and runaway growth: strong clustering
• coalescence: stellar collisions and mergers, only in dense systems