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PHYS 3380 - Astronomy
Protostellar Disks and Jets – Herbig Haro Objects
Disks of matter accreted onto a protostar (“accretion disks”) often lead to the
formation of jets (directed outflows; bipolar outflows)
- originate from the star and the inner parts of the disk and become
confined to a narrow beam within a few billion miles of their source.
- not known how the jets are focused, or collimated. Suggested that
magnetic fields, generated by the star or disk, might constrain the jets.
When they strike interstellar medium/nebula - produce Herbig Haro Objects small nebulae that fluctuate in brightness
PHYS 3380 - Astronomy
Protostellar Disks and Jets – Herbig Haro Objects
HH34
Almost 50 years ago, George Herbig and Guillermo Haro independently
discovered a number of compact nebulae with peculiar spectra near dark
clouds.
- subsequently demonstrated that these objects were shockexcited nebulae.
- shown that the large range of excitation conditions requires bow
shocks and other complex morphologies.
By the early 1980s, several Herbig-Haro (HH) objects shown to be highly
collimated jets of partially ionized plasma moving away from young stars at
speeds of 100 to over 1000 km/s.
PHYS 3380 - Astronomy
Stellar Jets
Of the 56 proplyds observed in the Orion nebula, 23 had visible jets.
PHYS 3380 - Astronomy
Stellar Jets
Gases clumped - could provide insights into the nature
of the disk collapsing onto the star.
Beaded jet structure "ticker tape" recording of how
clumps of material have, episodically, fallen onto the
star.
• jets "wiggle" along their multi-trillion-mile long
paths, suggesting the gaseous fountains change
their position and direction.
- might be evidence for a stellar companion or
planetary system that pulls on the central star,
causing it to wobble, which in turn causes the jet
to change directions
• knots due to 'sputtering' of the central engine
Ubiquitous in the universe - occur over a vast range of
energies and physical scales, in a variety of
phenomena.
HH30
PHYS 3380 - Astronomy
Protostellar Disks and Jets – Herbig Haro Objects
Herbig Haro Object HH30
PHYS 3380 - Astronomy
XZ Tauri
XZ Tauri - young system with two stars orbiting each
other - separated by about 6 billion kilometers (about
the distance from the Sun to Pluto)
- shows bubble of hot, glowing gas extending
nearly 96 billion kilometers from this young star
system.
- appears much broader than the narrow jets
seen in other young stars, but it is caused by
the same process - the ejection of gas from a
star.
PHYS 3380 - Astronomy
Evidence of Star Formation
Fox Fur Nebula
Observe regions containing young stars
- must have formed recently
- lie between birth line and main
sequence
Nebula around S Monocerotis:
Regions of star formation rich
in dust and gas and contain IR
protostars and stars still
contracting toward the main
sequence
Contains many massive, very young
stars - O associations
Also includes T Tauri Stars – generally
low mass stars, strongly variable;
bright in the infrared - T associations
PHYS 3380 - Astronomy
Main Sequence
Low-mass star formation in upper Scorpius
- dashed lines evolutionary tracks of observed low-mass stars
- all the low-mass PMS (pre-main sequence) stars have a
mean age of about 5 Myr and show no evidence for a large
age dispersion.
- thin solid lines isochrones at 0.1, 0.3, 1, 3, 10, 30 Myr
PHYS 3380 - Astronomy
Evidence of Star Formation
Stellar formation itself triggers star evolutions - massive stars’ ionization
fronts compress nearby gasses - trigger
Smaller,
sunlike stars,
probably
formed under
the influence of
the massive
star
Young, very
massive star
Infrared
Optical
The Cone Nebula
PHYS 3380 - Astronomy
Evidence of Star Formation
Star Forming Region RCW 38
PHYS 3380 - Astronomy
Open Clusters of Stars
Large masses of
Giant Molecular
Clouds => Stars do
not form isolated, but
in large groups,
called Open Clusters
of Stars.
Open Cluster M7
PHYS 3380 - Astronomy
Open Clusters of Stars
Large, dense
cluster of (yellow
and red) stars in
the foreground; ~
50 million years old
Scattered individual
(bright, white) stars
in the background;
only ~ 4 million
years old
PHYS 3380 - Astronomy
Globules
Bok
Globules:
~ 10 to
1000 solar
masses;
Contracting to
form protostars
PHYS 3380 - Astronomy
Globules
Evaporating Gaseous Globules
(“EGGs”): Newly forming stars
exposed by the ionizing radiation
from nearby massive stars
The pillar is slowly
eroding away by the
ultraviolet light from
nearby hot stars "photoevaporation".
As it does, small
globules of especially
dense gas buried
within the cloud are
uncovered.
- Shadows of the EGGs protect gas behind them, resulting in the finger-like
structures at the top of the cloud.
- Forming inside at least some of the EGGs are embryonic stars -- abruptly stop
growing when the EGGs are uncovered - separated from the larger reservoir of gas
from which they were drawing mass. Eventually emerge as the EGGs themselves
succumb to photoevaporation.
PHYS 3380 - Astronomy
PHYS 3380 - Astronomy
Stellar Evolution
PHYS 3380 - Astronomy
Stellar Types by Mass
Brown dwarfs (and planets): estimated lower stellar mass limit is
0.08 M (or 80MJup). Lower mass objects have core T too low to
ignite H.
Red dwarfs: stars whose main-sequence lifetime exceeds the
present age of the Universe (13.7x109 yr). Models yield an upper
mass limit of stars that must still be on main-sequence, even if they
are as old as the Universe of 0.7M
Low-mass stars: stars in the region 0.7 ≤ M ≤ 2 M . After shedding
considerable amount of mass, they will end their lives as white dwarfs
and possibly planetary nebulae.
Intermediate mass stars: stars of mass 2 ≤ M ≤ 8-10 M. Similar
evolutionary paths to low-mass stars, but always at higher luminosity.
Give planetary nebula and higher mass white dwarfs.
High mass (or massive) stars: M >8-10 M. Distinctly different
lifetimes and evolutionary paths huge variation.
PHYS 3380 - Astronomy
Maximum Masses of Main-Sequence Stars
a) More massive clouds fragment into smaller pieces during star formation.
b) Very massive stars lose mass in strong stellar winds
Eddington limit - point where gravitational force can no longer balance
the continuum radiation force outwards. Exceeding the Eddington limit
- star initiates very intense driven stellar wind from its outer layers.
Mmax~ 100 solar masses
h Carinae
(Eta Carinae)
Example: h Carinae: Binary system of a 60 M and 70 M star.
Dramatic mass loss; major eruption in 1843 created double lobes.
The Eddington Limit or Eddington luminosity
The point at which the luminosity emitted by a star or active
galaxy is so extreme that it starts blowing off the outer
layers of the object. i.e., the greatest luminosity that can
pass through a gas in hydrostatic equilibrium, meaning that
greater luminosities destroy the equilibrium.
- named after the British astrophyicist Sir Arthur Stanley
Eddington - famous for confirming the general theory of
relativity using eclipse observations.
- Eddington limit is likely reached around 120 solar
masses, at which point a star starts ejecting its
envelope through intense solar wind.
- Wolf-Rayet stars are massive stars showing Eddington
limit effects, ejecting .001% of their mass through solar
wind per year.
PHYS 3380 - Astronomy
Minimum Mass of Main-Sequence Stars
Mmin = 0.08 M
Gliese 229B
At masses below 0.08 M,
stellar progenitors do not
get hot enough to ignite
thermonuclear fusion.
 Brown Dwarfs
PHYS 3380 - Astronomy
Brown Dwarfs
Hard to find because they are very faint and cool; emit mostly in the
infrared.
Many have been detected in star forming regions like the Orion
Nebula.
PHYS 3380 - Astronomy
Main Sequence Stars
The structure and evolution of a star is determined by the laws of
• Hydrostatic equilibrium - weight of each layer balanced by pressure
• Energy transport - energy moves from hot to cool
• Conservation of mass - total mass = sum of shell masses
• Conservation of energy - total luminosity = sum of shell energies
A star’s mass (and chemical composition) completely determines
its properties.
Stars initially all line up along the main sequence
- in hydrostatic equilibrium - outward pressure of gas
balanced by inward weight
PHYS 3380 - Astronomy
Stellar Model
For isolated, static, and spherically symmetric stars – these laws
lead to four basic equations to describe structure. All physical
quantities depend on the distance from the centre of the star
alone.
1) Equation of hydrostatic equilibrium: at each radius, forces
due to pressure differences balance gravity
2) Conservation of mass: Total mass equals sum of shell masses
- no gaps.
3) Conservation of energy : at each radius, the change in the
energy flux = local rate of energy release
4) Equation of energy transport : relation between the energy
flux and the local gradient of temperature
PHYS 3380 - Astronomy
Solving the Equations of Stellar Structure
We can derive four differential equations, which govern the structure of stars
- provide set of coupled equations for determining stellar model.
r = radius
 = density at r
dP(r)
GM(r)(r)
P = pressure at r

2
dr
r
M = mass of material within r
dM(r)
L = luminosity at r (rate of energy flow across
 4r 2 (r)
dr
sphere of radius r)

T = temperature at r
dL(r)
 4r 2(r)(r)
R = Rosseland mean opacity at r - opacity of gas of
dr

given composition, temperature, and density, averaged
over the various wavelengths of the radiation being
dT(r)
3(r) R (r)

L(r) absorbed and scattered.
dr
64 r 2T(r) 3
 = energy release per unit mass per unit time
P = P (, T, chemical composition)
R = R(, T, chemical composition)  =  (, T, chemical composition)
These quantities dependent on density, temperature, and chemical
composition
PHYS 3380 - Astronomy
Boundary Conditions
Two of the boundary conditions are fairly obvious, at the centre of the star
M=0, L=0 at r=0
At the surface of the star its not so clear, but we use approximations to
allow solution. There is no sharp edge to the star, but for the the Sun
(surface)~10-4 kg m-3. Much smaller than mean density (mean)~1.4103
kg m-3 (which we derived). We know the surface temperature (Teff=5780K)
is much smaller than its minimum mean temperature (2106 K).
Thus we make two approximations for the surface boundary
conditions:
= T = 0 at r=rs
i.e. that the star does have a sharp boundary with the surrounding
vacuum
PHYS 3380 - Astronomy
Use of Mass as the Independent Variable
The preceding formulae would (in principle) allow theoretical models of
stars with a given radius. However from a theoretical point of view it is the
mass of the star which is chosen, the stellar structure equations solved,
then the radius (and other parameters) are determined. We observe stellar
radii to change by orders of magnitude during stellar evolution, whereas
mass appears to remain constant. Hence it is much more useful to rewrite
the equations in terms of M rather than r.
If we divide the other three equations by the equation of mass conservation,
and invert the latter:
dr
1

dM 4 r 2 
dL

dM
dP
GM

dM
4r 4
dT
3 R L

dM
256 2r 4T 3
With boundary conditions:
r=0, L=0 at M=0
=0, T=0 at M=Ms
We specify Msand the chemical composition and now have a well
defined set of relations to solve. It is possible to do this analytically if
simplifying
 assumptions are made, but in general these need to be
solved numerically on a computer.
PHYS 3380 - Astronomy
Stellar Evolution
The equations are not time dependent - we must iterate with the calculation of
changing chemical composition to determine short steps in the lifetime of stars.
The crucial changing parameter is the H/He content of the stellar core.
The set of equations must be supplemented by equations describing the rate
of change of abundances of the different chemical elements. Let CX,Y,Z be the
chemical composition of stellar material in terms of mass fractions of
hydrogen (X), helium, (Y) and metals (Z) [e.g. for solar system
X=0.7,Y=0.28,Z=0.02]
(CX ,Y ,Z )M
 f (,T,CX ,Y ,Z )
t
So we can evolve a model using

(CX ,Y ,Z )M ,t0 t  (CX ,Y ,Z )M ,t0
(CX ,Y ,Z )M

t
PHYS 3380 - Astronomy
Theoretical Stellar Evolution Model
The outcome is a theoretical HRdiagram.
PHYS 3380 - Astronomy
The Main-Sequence Phase
Pressure increases steeply
in centre
- 50% of mass is within
radius 0.25R
- only 1% of total mass is
in the convection zone
and above
- no convective process
in 99% of star - does not
become fully mixed.
- core becomes He rich.
Fusion is most efficient in
the centre, where T is
highest.
PHYS 3380 - Astronomy
Hipparcos satellite measured
105 bright stars with
p>0.001"  confident
distances for stars with d<100
pc
Hertzsprung-Russell diagram
for the 41704 single stars
from the Hipparcos Catalogue
with relative distance
precision better than 20% and
 (B-V) less than or equal to
0.05 mag. Colors indicate
number of stars in a cell of
0.01 mag in (B-V) and 0.05
mag in absolute magnitude
(MV).
Notice the spread in stars on main sequence.
PHYS 3380 - Astronomy
Evolution on the Main Sequence
Main-Sequence stars live by fusing
H to He.
- finite supply of H => finite
life time.
As star evolves, H consumed,
chemical composition changes
(H/He ratio).
- total number of nuclei
becomes less - pressure
reduced
MS evolution
- gravity - pressure stability
Zero-Age
unbalanced
Main
- core contracts - temperature
Sequence
and density increase and
(ZAMS)
nuclear reaction rate increases
- star becomes more luminous
- additional energy flowing out
forces outer layers to expand
and cool
 Slow changes cause star to move up and to the
Star gradually becomes larger, right on HRD - main sequence not a line but a band
brighter, and cooler
- Sun about 30% brighter than when at ZAMS
PHYS 3380 - Astronomy
Lifetime on the Main Sequence
Dependent on mass
For the few main-sequence stars
for which masses are known, there
is a Mass-luminosity relation.
L  Mn
Where n=3-5. Slope changes at
extremes, less steep for low and
high mass stars.
This is why the main-sequence on
the HRD is a function of mass i.e.
from bottom to top of mainsequence, stars increase in mass
• The mass-luminosity relation flattens out at higher masses, due to the contribution of
radiation pressure in the central core. (This helps support the star, and decreases the
central temperature slightly.) The relation also flattens significantly at the very faint end
of the luminosity function. This is due to the increasing important of convection for
stellar structure.
• Main sequence stars also obey a mass-radius relation. This relation displays a
significant break around 1M; R /Mξ, with ξ≈0.57 for M > 1M, and ξ≈0.8 for M < 1M.
This division marks the onset of a convective envelope. Convection tends to increase
the flow of energy out of the star, which causes the star to contract slightly. As a result,
stars with convective envelopes lie below the mass-radius relation for non-convective
stars and also moves the star above the nominal mass-luminosity relation.
• The depth of the convective envelope increases with decreasing mass. Stars with
M≈1M have extremely thin convective envelopes, while stars with M < ~0.3M are
entirely convective. Nuclear burning ceases around M≈ 0.08M. The region of nuclear
energy generation is restricted to a very small mass range near the center of the star.
The rapid fall-off of εn (energy release per unit mass per unit time) with radius reflects
the extreme sensitivity of energy generation to temperature.
• Stars with masses below ~ 1M generate most of their energy via the proton-proton
chain. Stars with more mass than this create most of their energy via the CNO cycle.
This changeover causes a shift in the energy transport in stellar interiors.
PHYS 3380 - Astronomy
Lifetime on the Main Sequence
A star’s life time T ~ energy reservoir / luminosity
Energy reservoir ~
M
Luminosity: L ~ M3.5
T ~ M/L ~ 1/M2.5
Massive stars have
short lives.
Red dwarfs use fuel
so slowly, should
survive for 200 300 billion years all still in infancy
since age of
universe 10 - 20
billion years
PHYS 3380 - Astronomy
The Source of Stellar Energy
Recall from our discussion of the sun:
Stars produce energy by nuclear fusion of hydrogen into helium.
In the sun, this
happens primarily
through the
proton-proton
(PP) chain
PHYS 3380 - Astronomy
The CNO Cycle
In stars slightly more
massive than the sun,
a more powerful
energy generation
mechanism than the
PP chain takes over:
The CNO Cycle.
Highly temperature
dependent
PHYS 3380 - Astronomy
Energy Transport Structure
Inner convective,
outer radiative zone
Inner radiative,
outer convective
zone
CNO cycle dominant
PP chain dominant
PHYS 3380 - Astronomy
Summary: Stellar Structure
Convective Core, radiative
envelope;
Energy generation through
CNO Cycle
Sun
Radiative Core, convective
envelope;
Energy generation through PP
Cycle
• As a result of the extreme temperature dependence of CNO burning, those stars that
are dominated by CNO fusion have very large values of L/4πr2 in the core. This results
in convective instability and convective energy transport is extremely efficient.
• Because of the extreme temperature sensitivity of CNO burning, nuclear reactions in
high mass stars are generally confined to a very small region, much smaller than the
size of the convective core.
- conditions under which a region of a star is unstable to convection is expresses by
the Schwarzschild criterion:
dT
g


dZ C p
where g is the gravitational acceleration, and Cp is the heat capacity. A parcel of gas
that rises slightly will find itself in an environment of lower pressure than the one it
came from. As a result,
the parcel will expand and cool. If the rising parcel cools to a
lower temperature than its new surroundings, so that it has a higher density than the
surrounding gas, then its lack of buoyancy will cause it to sink back to where it came
from. However, if the temperature gradient is steep enough (i. e. the temperature
changes rapidly with distance from the center of the star), or if the gas has a very
high heat capacity (i. e. its temperature changes relatively slowly as it expands) then
the rising parcel of gas will remain warmer and less dense than its new surroundings
even after expanding and cooling. Its buoyancy will then cause it to continue to rise.
The region of the star in which this happens is the convection zone.