Download Chapter 8 Formation of Stars

Chapter 8
Formation of Stars
Substantial direct and indirect information indicates that
stars are born in the clouds of gas and dust that we call
nebulae.
• Basics are well understood, many details are not.
• We shall have to gloss over various sticky points with
assumptions that will be justified by the observation
that stars exist and, therefore, something like our assumption must be correct.
• Much of this gloss is associated with the general observation that clouds that collapse to form stars have
too much kinetic energy and too much angular momentum to produce directly the stars that we see.
Since nature makes stars in abundance, this indicates that
there exist mechanisms for nascent stars to shed these excess quantities. It is the details of how this happens that
we shall circumvent with appeals to observations.
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CHAPTER 8. FORMATION OF STARS
8.1 O and B Associations and T-Tauri Stars
• Observation of many hot O and B spectral class stars
in and near nebulae is a rather strong indicator that
stars are being born there.
• These stars are so luminous that they must consume
their nuclear fuel at a prodigious rate.
• Their time on the main sequence is probably only a
million years or so, therefore they cannot be far from
their place of birth.
• We also see, usually in association with stellar O and
B complexes in dust clouds, T-Tauri variables.
• These are red irregular variables (spectral class F–
M), with a number of unusual characteristics. They
exhibit emission lines of hydrogen, Ca+ , and some
other metals.
8.1. O AND B ASSOCIATIONS AND T-TAURI STARS
269
Expanding
Shel l
Unshifted
Emission
Star
Blue-Shifted
Emission
Red-Shifted
Emission
Broad
Emission
Peak
To
Observer
Blue-Shifted
Absorption
Continuum
P Cygni Profile
λ
Absorption
Minimum
Figure 8.1: Origin of P Cygni profiles in Doppler shifts associated with expanding
gas shells.
• The spectral lines for T-Tauri stars often exhibit P
Cygni profiles, as illustrated in Fig. 8.1, which indicate the presence of expanding shells of low-density
gas around the stars.
• They are more luminous than corresponding mainsequence stars, implying that they are larger.
• They exhibit strong winds (T-Tauri winds), often
with bipolar jet outflows having velocities of 300–
400 km s−1.
CHAPTER 8. FORMATION OF STARS
270
Hidden Young Star
j et
j et
Hidden Young Star
Wobbling Jet
Figure 8.2: Jets and Herbig–Haro objects associated with outflow from young
stars near the Orion Nebula. In the top image, the star responsible for the jets is
hidden in the dark dust cloud lying in the center of the image. The entire width of
this image is about one light year. The Herbig–Haro objects are designated HH-1
and HH-2, and correspond to the nebulosity at the ends of the jets. In the bottom
image, a complex jet about a half light year long emerges from a star hidden in a
dust cloud near the left edge of the image. The twisted nature of the jet suggests that
the star emitting it is wobbling on its rotation axis, perhaps because of interaction
with another star. The Herbig-Haro object HH-47 is the nebulosity on the right of
the image. It is about 1500 light years away, lying at the edge of the Gum Nebula,
which may be an ancient supernova remnant.
• Herbig–Haro Objects are often found in the directions of these jets.
• Two examples of outflow from young stars and associated Herbig–Haro objects are shown in Fig. 8.2.
8.1. O AND B ASSOCIATIONS AND T-TAURI STARS
271
4
6
8
10
V
Giant
12
14
Main
Sequence
16
18
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
B-V
Figure 8.3: HR diagram for the young open cluster NGC2264. Horizontal bars
denote stars with Hα line emission; vertical bars denote variable stars.
These considerations indicate that T-Tauri stars are still in
the process of contracting to the main sequence.
• They are less massive than the O and B stars that
often accompany them, so they will have contracted
more slowly and many will not yet have had time
to reach the main sequence when the more rapidlyevolving O and B stars have done so.
• The HR diagram for a young cluster is illustrated in
Fig. 8.3, where we see many young stars that have
not yet reached the main sequence.
• Stars marked with horizontal and vertical bars in this
figure have observational properties of T-Tauri stars.
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CHAPTER 8. FORMATION OF STARS
• The bipolar outflows could in principle be explained
by an accretion disk around the young T-Tauri stars
that would form as a result of conservation of angular
momentum for the infalling matter.
• Then, if there are strong winds emanating from the
star, they would tend to be directed in bipolar flows
perpendicular to the plane of the accretion disk.
• However, it is difficult to explain the tight collimation
of the jets (as good as 10% over one parsec) by such a
mechanism, and the source of the energy driving the
winds is also not explained by such a simple model.
• The Herbig–Haro objects are likely the result of
shocks formed when the matter flowing out of the
T-Tauri star interacts with clumps of matter, or when
clumps of matter ejected from the star interact with
low density gas clouds.
These observations suggest that we must look to the nebulae to produce the stars. They also suggest that the life of
protostars contracting to the main sequence may be more
complex (and violent) than the following simple considerations would leave us to believe.)
8.2. CONDITIONS FOR GRAVITATIONAL COLLAPSE
8.2 Conditions for Gravitational Collapse
Let us investigate the general question of gravitational collapse to form stars by considering a spherical cloud
• composed primarily of hydrogen,
• that has a radius R, a mass M, and a uniform temperature T
• that consists of N particles of average mass µ .
We shall assume that the question of stability is one of competition between gravitation, which would collapse the cloud, and gas
pressure, which would expand the cloud.
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CHAPTER 8. FORMATION OF STARS
274
8.2.1 The Jeans Mass and Jeans Length
• The gravitational energy is of the form
Ω = −f
GM 2
,
R
where the factor f = 53 if the cloud is spherical and of uniform
density, and larger if the density increases toward the center.
• We take the thermal energy to be that of an ideal gas,
U = 23 NkT.
• From the virial theorem, which describes a gravitating gas in
equilibrium, we expect that the static condition for gravitational
instability is
2U < |Ω|,
implying that the system is unstable if it has a mass M with
3/2 3kT
3 1/2
3kT
,
R=
M > MJ ≡
f Gµ mH
f Gµ mH
4πρ
where
N = M/µ mH
R = (3M/4πρ )1/3
have been employed.
• The quantity
MJ =
3kT
f Gµ mH
3/2 3
4πρ
1/2
appearing in this condition is termed the Jeans mass.
8.2. CONDITIONS FOR GRAVITATIONAL COLLAPSE
275
• The Jeans mass
MJ =
3kT
f Gµ mH
3/2 3
4πρ
1/2
defines a critical mass beyond which the system becomes unstable to gravitational contraction.
• Since the Jeans mass is proportional to T 3/2 ρ −1/2 , it will be
smaller for colder, denser clouds.
This makes physical sense: it is easier to collapse a cloud
of a given mass gravitationally if the cloud is cold and
dense than if it warm and diffuse.
• We may also solve the preceding equation for the Jeans length,
MJ ≡
3kT
R
f Gµ mH
→
RJ =
f Gµ mH
MJ.
3kT
• This defines the characteristic length scale associated with the
Jeans mass and thus characterizes the minimum size of gravitationally unstable regions.
CHAPTER 8. FORMATION OF STARS
276
8.2.2 The Jeans Density
• It is often more useful to express the Jeans criterion in terms of
a critical density for gravitational collapse (the Jeans density)
3/2 3
3 1/2
3kT
3
3kT
→ ρJ =
.
MJ =
f Gµ mH
4πρ
4π M 2 f µ mH G
• Notice that the critical density is lowest (and thus more easily
achieved) if the mass is large and the temperature low, as we
would expect on intuitive grounds.
Example: Consider a cold cloud of molecular hydrogen at T = 20 K that has a mass of
1000 M⊙ ; the associated Jeans density is only
ρJ = 10−22 g cm−3.
On the other hand, a molecular hydrogen
cloud at the same temperature but containing
only 1 solar mass has a Jeans density that is 6
orders of magnitude larger.
• The Jeans criterion is simple because it is a static condition that
says nothing about gas dynamics and it neglects potentially important factors influencing stability such as magnetic fields, dust
formation and vaporization, and radiation transport.
• Nevertheless, the Jeans criterion is an extremely useful starting
point for understanding how stars form from clouds of gas and
dust that become gravitationally unstable.
8.3. FRAGMENTATION OF COLLAPSING CLOUDS
277
Figure 8.4: Fragmentation into gravitationally unstable subclouds.
8.3 Fragmentation of Collapsing Clouds
From the foregoing collapse of more massive clouds is favored, but
most stars contain less than 1M⊙ of material.
• The solution to this dilemma is thought to lie in fragmentation,
as illustrated in Fig. 8.4.
• As we shall see, the initial collapse is expected to occur at almost
constant temperature. Therefore, from
MJ =
3kT
f Gµ mH
3/2 3
4πρ
1/2
the Jeans mass decreases in the initial collapse
• We speak loosely: The Jeans criterion assumes a cloud near equilibrium, not one already collapsing.
• Hence as large clouds, which have the smallest Jeans density,
begin to collapse their average density increases;
• At some point subregions of the original cloud may exceed the
critical density and become unstable in their own right toward
collapse.
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CHAPTER 8. FORMATION OF STARS
• If there are sufficient perturbations present in the cloud, these
subregions may separate and pursue independent collapse.
• Within these subclouds the same sequence may be repeated: as
the density increases, subregions may themselves become gravitationally unstable and begin an independent collapse.
• By such a hierarchy of fragmentations, it is plausible that clusters of protostars might be formed that have individual masses
comparable to that of observed stars
8.4. STABILITY IN ADIABATIC APPROXIMATION
8.4 Stability in Adiabatic Approximation
To understand further the behavior of gravitationally unstable clouds, let us consider the adiabatic contraction (or
expansion) of a homogenous cloud.
• Real clouds will exchange energy with their surroundings and so are not completely adiabatic.
• However the results obtained in this limit will often
be instructive in understanding more realistic situations.
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CHAPTER 8. FORMATION OF STARS
280
(a)
(b)
T ~ ρ2/3 (γ = 5/3)
Expansion
Collapse
Halts
1 /3
T
~ρ
e
ps
la
l
o
C
log T
log T
Expansion
e
ps
olla
C
s
ou
nu
i
t
n
Co
1 /3
T
~ρ
Contraction
Contraction
T~
ρ1/3
(γ = 4/3)
log ρ
log ρ
Figure 8.5: Gravitational equilibrium in temperature–density space.
• From the Jeans density
3
ρJ =
4π M 2
3kT
f µ mH G
3
.
equilibration of gravity and pressure requires the
temperature T and density ρ be related by T ∝ ρ 1/3 .
• In Fig. 8.5, this divides the T –ρ plane into
– A region above the line T ∼ ρ 1/3 where the system is unstable toward expansion, and
– a region below the line where the system is unstable toward contraction.
8.4. STABILITY IN ADIABATIC APPROXIMATION
(a)
(b)
T ~ ρ2/3 (γ = 5/3)
Expansion
Collapse
Halts
1 /3
~ρ
e
ps
la
ol
C
log T
log T
Expansion
T
281
1 /3
T
~ρ
e
ps
olla
C
us
uo
tin
n
Co
Contraction
Contraction
T ~ ρ1/3 (γ = 4/3)
log ρ
log ρ
• For points above the stability line (in the unshaded
area), pressure forces are larger than gravitational
forces and the system is unstable to expansion.
• For points below the stability line (in the shaded
area), pressure forces are weaker than gravitational
forces and the system is unstable with respect to contraction.
CHAPTER 8. FORMATION OF STARS
282
(a)
(b)
T ~ ρ2/3 (γ = 5/3)
Expansion
Collapse
Halts
1 /3
T
log T
log T
Expansion
~ρ
e
ps
la
l
o
C
1 /3
T
~ρ
se
llap
o
sC
ou
nu
i
t
n
Co
Contraction
Contraction
T~
ρ1/3
log ρ
(γ = 4/3)
log ρ
8.4.1 Dependence on Adiabatic Exponents
• First consider a monatomic ideal gas, for which the
adiabatic exponent is γ = 35 .
• Since ρ ∝ V −1 and an adiabatic equation of state is
TV γ −1 = constant,
T ∝ ρ γ −1
→
T (γ = 35 ) ∼ ρ 2/3 .
• This corresponds to the dashed line in the left figure
above, which is steeper than the equilibrium line and
therefore crosses it.
8.4. STABILITY IN ADIABATIC APPROXIMATION
(a)
(b)
T ~ ρ2/3 (γ = 5/3)
Expansion
Collapse
Halts
1 /3
~ρ
e
ps
la
l
o
C
log T
log T
Expansion
T
283
1 /3
T
~ρ
se
llap
o
sC
ou
nu
i
t
n
Co
Contraction
Contraction
T ~ ρ1/3 (γ = 4/3)
log ρ
log ρ
• A cloud that is unstable to gravitational contraction
(corresponding to a point on the dashed line in the
shaded area of the left figure) will follow the dashed
line to the right as it collapses, as indicated by the
arrow (right is increasing density).
• But in this case the collapse will be halted at the point
where the dashed line reaches the stability line (point
labeled “Collapse Halts”).
• Likewise, a cloud unstable to expansion (corresponding to a point on the dashed line lying in the unshaded
area of the left figure) will follow the dashed line to
the left as it expands (left is decreasing density).
• This expansion halts at the stability line.
• Thus, γ = 35 is gravitationally stable.
CHAPTER 8. FORMATION OF STARS
284
(a)
(b)
T ~ ρ2/3 (γ = 5/3)
Expansion
Collapse
Halts
1 /3
T
~ρ
e
ps
la
l
o
C
log T
log T
Expansion
1 /3
T
~ρ
se
llap
o
sC
ou
nu
i
t
n
Co
Contraction
Contraction
T~
ρ1/3
log ρ
(γ = 4/3)
log ρ
• Now consider the right figure above, where we assume that the cloud has an adiabatic exponent γ = 34 .
• In this case, the contraction (or expansion) follows
an adiabat for which T ∝ ρ γ −1 ∝ ρ 1/3 .
• Since this adiabat is parallel to the stability line,
the two lines never cross and a system lying on the
dashed line collapses and continues to collapse adiabatically.
• This will also be the case if γ < 34 .
• Likewise, a system with γ = 43 that is above the stability line will continue to expand adiabatically as long
as γ = 43 .
• γ ≤ 34 is gravitationally unstable.
8.4. STABILITY IN ADIABATIC APPROXIMATION
8.4.2 Physical Interpretation
Physical meaning of the preceding discussion:
• A gas is less able to generate the pressure differences
required to resist gravity if the energy released by
gravitational contraction can be absorbed into internal degrees of freedom.
• This energy is not available to increase the kinetic
energy of the gas particles.
• The parameter γ is relevant because it is related to the
heat capacities for the gas (γ = CP /CV ).
• Typical sinks of energy that can siphon off energy
internally are
1. Rotations of molecules
2. Vibrations of molecules
3. Ionization
4. Molecular dissociation.
Such internal degrees of freedom are energy sinks that
lower the resistance of the gas to gravitational compression.
285
CHAPTER 8. FORMATION OF STARS
286
• In the large clouds of gas and dust that are candidates for stellar
birthplaces, γ can be reduced to a value of 43 = 1.33 or less by
1. The presence of polyatomic gases with more than five degrees of freedom, since
1 + s/2
s/2
γ=
→
γ (s = 5) =
1 + 5/2 7
= = 1.4,
5/2
5
2. By ionization of hydrogen around 10,000 K
3. By the dissociation of hydrogen molecules around 4,000 K.
• The large molecules required for the first situation are relatively
rare in the interstellar medium but their presence enhances the
chance of gravitational collapse for a cloud.
• In hydrogen ionization or molecular dissociation zones,
– Typically γ ≤ 43 and this causes an instability until the ionization or dissociation is complete.
– Then γ will return to normal values (γ ≃ 35 ) and collapse
on the corresponding adiabat will reach the equilibrium line
and stabilize the collapse (recall the following figure)
(a)
(b)
T ~ ρ2/3 (γ = 5/3)
Expansion
Collapse
Halts
1 /3
T
~ρ
e
ps
la
ol
C
log T
log T
Expansion
1 /3
T
~ρ
e
ps
olla
C
s
ou
nu
nti
o
C
Contraction
Contraction
T ~ ρ1/3 (γ = 4/3)
log ρ
log ρ
8.5. THE COLLAPSE OF A PROTOSTAR
8.5 The Collapse of a Protostar
The preceding introduction sweeps much under the rug,
but we shall assume that the existence of stars implies
that protostars form by some mechanism similar to the one
outlined above and follow the consequences of the gravitational collapse of such a protostar.
• Let us consider the collapse of a one solar mass protostar.
• From the Jeans criterion, ρJ ≃ 10−16 g cm−3 for T =
20 K and M = 1M⊙.
• Thus, we expect that a 1 M⊙ cloud can collapse if
this average density is exceeded.
• The size of this initial cloud may be estimated by
assuming the density to be constant and distributed
spherically, implying that R ∼ 1.6 × 1016 cm ∼
1000 AU.
• Thus, the initial protostar has a radius approximately
25 times that of the present Solar System.
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CHAPTER 8. FORMATION OF STARS
8.5.1 Initial Free-Fall Collapse
• We may assume that the initial collapse is free-fall and isothermal, as long as the gravitational energy released is not converted
into thermal motion of the gas and thereby into pressure.
• This will be the case as long as the energy not radiated away is
largely taken up by
1. dissociation of hydrogen molecules into hydrogen atoms
2. ionization of the hydrogen atoms.
• The dissociation energy for hydrogen molecules is εd = 4.5 eV
• The ionization energy for hydrogen atoms is εion = 13.6 eV.
• The energy required to dissociate and ionize all the hydrogen in
the original cloud is then
E = N(H2 )εd + N(H)εion
M
M
εd + εion ,
=
2mH
mH
where N denotes the number of the corresponding species and
mH is the mass of a hydrogen atom.
• For the case of a protostar of one solar mass, the requisite energy
is approximately 3 × 1046 erg.
8.5. THE COLLAPSE OF A PROTOSTAR
289
• If the dissociation and ionization energy
M
M
E=
εd + εion ,
2mH
mH
is supplied by gravitational contraction from radius R1 to R2,
GM 2 GM 2
−
R
2
|
{z R1 }
gravity
=
M
M
εd + εion
|2mH {z mH }
.
dissociation and ionization
• Solve for R2 assuming M = 1M⊙ and R1 = 1016 cm to give
R2 = 1013 cm ≃ 100R⊙ ≃ 21 AU.
• The corresponding timescale is (see Exercise 4.1)
p
tff = 3π /32Gρ ≃ 7000 yr.
• Therefore, a solar-mass protostar collapses from about 25 times
the radius of the Solar System to about half the radius of the
Earth’s orbit in near free-fall on a timescale of about 7,000 years.
• The collapse then slows because
1. All the hydrogen has been dissociated and ionized,
2. the photon mean free path becomes short and the cloud becomes opaque to its own radiation,
3. temperature increases as heat begins to be trapped, and
4. the resulting pressure gradients counteract the gravitational
force and bring the system into near hydrostatic equilibrium.
Thus, we may apply the virial theorem in near adiabatic
conditions from this point onward.
CHAPTER 8. FORMATION OF STARS
290
8.5.2 Homology
From the expressions for free-fall collapse we see that the
characteristic timescale for free fall is independent of the
radius of the collapsing mass distribution.
• This behavior is termed homologous collapse.
• One consequence of homologous collapse is that if
the initial density is uniform it remains uniform for
the entire collapse.
• Because successive configurations in homologous
processes are self-similar (related by a scale transformation), homologous systems are particularly simple
to deal with mathematically.
• Therefore, reasonably good approximate treatments
of the initial phases of gravitational collapse are often
possible by making homology assumptions.
8.5. THE COLLAPSE OF A PROTOSTAR
Adiabatic
log T
H ionization
H 2 dissociation
Thermonuclear ignition
Isothermal
291
Free fall
log ρ
Figure 8.6: Schematic track in density and temperature for the collapse of a gas
cloud to form a star.
8.5.3 A More Realistic Picture
The preceding picture is oversimplified but contains essential features
supported by more sophisticated considerations. A more realistic
variation of temperature and density for star formation is illustrated
in Fig. 8.6.
• In this more realistic picture the cloud begins to heat and deviate
from free-fall behavior once it traps significant heat.
• When the temperature is sufficient to dissociate and then ionize
hydrogen, the cloud again collapses ∼ isothermally for a time.
• Once all hydrogen has been dissociated and ionized, the collapse
returns to one governed by approximately adiabatic conditions in
near hydrostatic equilibrium.
CHAPTER 8. FORMATION OF STARS
292
8.6 Onset of Hydrostatic Equilibrium
The temperature at which hydrostatic equilibrium sets in may be estimated as follows.
• From the virial theorem we have that 2U + Ω = 0.
• The gravitational energy Ω is
M
M
GM 2
=−
Ω ≡ Ω(R2 ) = −
εd + εion ,
R2
2mH
mH
where Ω(R1 ) has been neglected compared with Ω(R2 ).
• From U = 23 NkT , the internal energy for the hydrogen ions and
electrons in the fully ionized gas is approximately
U ≃ 23 (NH + Ne)kT = 3NH kT =
3M
kT,
mH
where NH is the number of hydrogen ions and Ne ∼ NH is the
number of free electrons.
• Therefore, the virial theorem requires that
2U + Ω =
M
M
6M
kT −
εd − εion = 0,
mH
2mH
mH
and solving this for T gives
1 εd εion 2.6 eV
≃
+
≃ 30, 000 K
T=
k 12
6
k
for the onset of hydrostatic equilibrium.
8.6. ONSET OF HYDROSTATIC EQUILIBRIUM
10 3
10 4
10 6
293
10 2
100 M
Luminosity (Solar Units)
10
4
10
5
10 4
10 M
10 2
10
10 3
6
3M
10
5
10
10 0
10
ZAMS
10
5
10 5
6
1M
10
7
0.5 M
−2
0.1 M
63,000
25,000
10,000
4000
10
6
10 8
1600
Surface Temperature (K)
Figure 8.7: Evolutionary tracks for collapse to the main sequence. Numbers on
tracks are times in years.
• Subsequent contraction of the protostar is in near hydrostatic
equilibrium and is controlled by the opacities, which govern how
fast energy can be brought to the surface and radiated.
• As we have discussed in §4.6, this too is a consequence of the
virial theorem and leads to the Kelvin–Helmholtz timescale of
about 107 years for a star of one solar mass.
• The evolutionary tracks for protostars of various masses to collapse to the main sequence are shown in Fig. 8.7.
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CHAPTER 8. FORMATION OF STARS
8.7 Termination of Fragmentation
• Earlier we indicated that gravitational collapse of large clouds
is likely to fragment into a hierarchy of sub-collapses, and we
invoked this argument to explain why we observe many lowmass stars.
• However, this argument is incomplete (even leaving aside that
we gave no quantitative justification for it), because we must ask
the question of what stops the fragmentation in the vicinity of
0.1–1 solar masses.
• The most plausible answer is that the transition from isothermal to adiabatic collapse implies a modification of the Jeans
criterion and that this dictates a lower limit for the mass of the
fragments produced by a hierarchical collapse.
• Substitution of the condition T ∝ ρ γ −1 for adiabats in
3/2 3kT
3 1/2
MJ =
,
f Gµ mH
4πρ
implies that for adiabatic clouds
MJ ≃ ρ (3γ −4)/2 .
For γ = 5/3 then, the Jeans mass is proportional to ρ 1/2 and in
adiabatic collapse the Jeans mass increases.
• This implies that the transition from isothermal to adiabatic collapse sets a lower bound on possible Jeans masses.
Plausible calculations based on this idea show that the
fragmentation is likely to end in the vicinity of one solar
mass, in rough agreement with observations.
8.8. HYASHI TRACKS
295
Hyashi
Track
Log Luminosity
Star fully
convective
Radiative core
develops
Main
Sequence
Hydrogen
fusion begins
Region forbidden
to stars of mass M
and composition c
(M,c)
Log T
Figure 8.8: Evolution of protostars to the main sequence.
8.8 Hyashi Tracks
A more detailed understanding of the collapse to the main sequence
follows from a fundamental result first obtained by Hyashi:
A star generally cannot reach hydrostatic
equilibrium if its surface is too cool.
• This implies that there exists a region in the righthand portion
of the HR diagram that is forbidden to a given star while it is in
hydrostatic equilibrium.
• This region, the boundaries of which depend on the mass and
composition of the star, is called the Hyashi forbidden zone; it is
illustrated in Fig. 8.8 for a star of mass M and composition c.
CHAPTER 8. FORMATION OF STARS
296
8.8.1 Fully Convective Stars
Stars contracting to the main sequence
• Must have large surface areas and (relatively) high
surface temperatures, so they have large luminosities.
• Furthermore, once hydrogen is ionized they have
high opacities.
• The combination of high opacity with large luminosity ensures that the temperature gradients necessary
to transport the energy radiantly exceed the adiabatic one.
• Thus such collapsing stars are expected to be almost
completely convective .
• Recall from Ch. 3 that completely convective stars
are approximately described by a γ = 35 polytrope:
For a completely ionized star, fully mixed by
convection with negligible radiation pressure,
P = K ρ γ (r) = K ρ 1+1/n (r) = K ρ 5/3,
if γ = 35 , where the polytropic index n is parameterized by n = 1/(γ − 1), and where K is
constant for a given star.
8.8. HYASHI TRACKS
297
Hyashi
Track
Log Luminosity
Star fully
convective
Radiative core
develops
Main
Sequence
Hydrogen
fusion begins
Region forbidden
to stars of mass M
and composition c
(M,c)
Log T
By examining fully convective stars with a thin radiative
envelope, Hyashi showed that
• Contracting protostars follow an almost vertical HR
trajectory called the Hyashi track for the star.
• If the star is fully convective, the Hyashi track is essentially defined by the left boundary of the Hyashi
forbidden zone, as illustrated in the above figure.
• The forbidden zone can be understood simply:
– A star on its Hyashi track is fully convective and
radiates as a blackbody.
– Thus, no other configuration could lose energy
more efficiently in hydrodynamic equilibrium.
– Thus no such stars can exist to the right of the
Hyashi track in the HR diagram (which corresponds to lower surface temperatures).
298
CHAPTER 8. FORMATION OF STARS
8.8.2 Development of a Radiative Core
As the collapsing star descends the Hyashi track its central
temperature is increased by the gravitational contraction.
• This decreases the central opacity (recall that for the
representative Kramers opacity, κ ∼ ρ T −3.5 ).
• Eventually this lowers the temperature gradient in the
central region sufficiently that it drops below the critical value for convective stability.
• A radiative core develops.
• As contraction proceeds the radiative core begins to
grow at the expense of the convective regions, which
are eventually pushed out to the final subsurface regions characteristic of stars like the Sun.
• (In more massive stars the subsurface convective
zones are eliminated completely but the core may
become convective if the power generation is sufficiently large after the star enters the main sequence.)
8.8. HYASHI TRACKS
299
Hyashi
Track
Log Luminosity
Star fully
convective
Radiative core
develops
Main
Sequence
Hydrogen
fusion begins
Region forbidden
to stars of mass M
and composition c
(M,c)
Log T
• While the fully convective star is on the Hyashi track,
its luminosity decreases rapidly because of shrinking
surface area.
• However, as the opacity decreases over more and
more of the interior because of the increasing temperature, the luminosity begins to rise again because
more energy can flow out radiantly.
• Since at this point the star is shrinking as its luminosity increases, its surface temperature must increase
and the star begins to follow a track to the left and
somewhat upward in the HR diagram (above figure).
• Finally, the onset of hydrogen fusion causes the track
to bend over and enter the main sequence, as also
illustrated in the above figures.
CHAPTER 8. FORMATION OF STARS
300
Hyashi
Track
Log Luminosity
Star fully
convective
Radiative core
develops
Main
Sequence
Hydrogen
fusion begins
Region forbidden
to stars of mass M
and composition c
(M,c)
Log T
Thus, the contraction to the vicinity of the main sequence
is composed of two basic periods:
1. A vertical descent in the HR diagram for fully convective stars, followed by
2. a drift up and to the left as the interior of the star
becomes increasingly radiative at the expense of the
convective envelope.
8.8. HYASHI TRACKS
(b)
Reduced
metals
Increasing
mass
log L
(a)
301
1M
(c)
Ma
in s
Normal
log T
equ
enc
log T
0.1 M
20 M
e
log T
Figure 8.9: Dependence of Hyashi tracks on (a) composition and (b) mass. The
solid portions of each curve in (c) represent the descent on the Hyashi track.
8.8.3 Dependence of Track on Composition and Mass
Hyashi tracks depend weakly on the mass and composition, as illustrated in Fig. 8.9.
• For more massive stars of fixed composition the Hyashi tracks
are almost parallel to each other but increasingly shifted to the
left in the HR diagram (Fig. 8.9b).
• The Hyashi tracks also depend on stellar composition, because
this can influence the opacity.
• For example, a metal-poor star of a given mass will generally
have a Hyashi track to the left of an equivalent metal-rich star
because of lower opacity (Fig. 8.9a).
CHAPTER 8. FORMATION OF STARS
302
(b)
Reduced
metals
1M
(c)
Increasing
mass
Ma
in s
Normal
equ
enc
log T
0.1 M
20 M
log L
(a)
log T
e
log T
• Finally, the transition from convective to radiative interiors, and
the corresponding transition from downward motion to more
horizontal leftward drift on the HR diagram, is generally faster
in more massive stars because of more rapid interior heating.
• Therefore, as illustrated in Fig. (c) above and the following,
10
10 3
10 4
6
10 2
100 M
Luminosity (Solar Units)
10
4
10
5
10 4
10 M
10
2
10
0
10
10 3
6
3M
10
5
10
10
ZAMS
5
10 5
6
1M
10 7
0.5 M
10 −2
0.1 M
63,000
25,000
10,000
4000
10
6
10 8
1600
Surface Temperature (K)
massive stars leave the Hyashi track quickly and approach the
main sequence almost horizontally .
• Conversely, the least massive stars never leave the Hyashi track
as they collapse and drop almost vertically to the main sequence
They are thought to remain completely convective, even after
entering the main sequence.
8.9. LIMITING LOWER MASS FOR STARS
303
8.9 Limiting Lower Mass for Stars
A contracting protostar will become a star only if the temperature
increases sufficiently in the core to initiate thermonuclear reactions.
• The results of Exercise 4.7 show that, for an idealized star composed of a monatomic ideal gas having uniform temperature and
density, the temperature varies with the cube root of the density:
2/3
M
T = 4.09 × 106 µ
ρ 1/3 .
M⊙
• However, this behavior assumes an ideal classical gas; the temperature will no longer increase with contraction if the equation
of state becomes that of a degenerate gas.
• In Exercise 4.7, the critical temperature and density for onset
of electron degeneracy was estimated by setting kT equal to the
fermi energy; we found that the critical density is defined by
ρ ≃ 6 × 10−9 µeT 3/2 g cm−3.
• Inserting this into the preceding equation gives for the temperature at which the critical density is reached in the contracting
protostar,
M 2/3
1/3
7
.
T ≃ 5.6 × 10 µ µe
M⊙
CHAPTER 8. FORMATION OF STARS
304
• For M ∼ M⊙ and µ µe1/3 ∼ 1, we obtain from
2/3
M
.
T ≃ 5.6 × 107 µ µe1/3
M⊙
that T ∼ 107 K.
• Thus, a solar mass protostar can produce an average temperature
of 10 million K by contraction, which is more than enough to
ignite hydrogen fusion before the electrons in the core become
degenerate and stop the growth of temperature with pressure.
• On the other hand, as the mass of the protostar is decreased we
will eventually reach a mass where the core will become degenerate before the temperature rises to the required values to
support hydrogen fusion.
• Detailed calculations indicate that this limiting mass is approximately 0.08M⊙ − 0.10M⊙.
• What of collapsing clouds with less than this critical mass required to form stars?
• For them the growth in temperature is halted by electron degeneracy pressure before fusion reactions can begin and no star is
formed.
• It is speculated that many such brown dwarfs may exist in the
Universe, supported hydrostatically by electron degeneracy pressure and radiating energy left over from gravitational contraction.
8.9. LIMITING LOWER MASS FOR STARS
305
It is useful to tie together several threads of discussion involving hydrostatic equilibrium, the virial theorem, stellar
energy production, and gravitational collapse to form stars
by asking a simple question: “ Why are stars hot?”
• The popular perception is that stellar cores are hot because they
correspond to enormous thermonuclear furnaces.
• But the core of the Sun is in fact a very low density power source
(Exercise 5.18: a few hundred watts per cubic meter in the core).
• We have seen further in this chapter that it is the release of gravitational energy by contraction and the partial trapping of that
energy by high stellar opacity that raises the protostar interior to
the temperature (and density) required for hydrogen fusion.
• The role of hydrogen fusion is not to heat stars (gravity and the
virial theorem can do that nicely); it is to sustain the luminosity
over much longer periods than would be possible otherwise.
• Triggering thermonuclear reactions replaces the Kelvin–Helmholtz
timescale for sustained luminosity from gravitational contraction
with the much longer nuclear burning timescale.
• This enables the Sun to radiate its present power for billions of
years rather than millions of years.
• So the source of sustained luminosity and sustained high interior
temperatures for main sequence stars is indeed hydrogen fusion,
but the cores of those stars were heated by gravitational contraction, not fusion, to their present temperatures.
• They maintain those high temperatures and luminosities by slow
fusion reactions under conditions of hydrostatic equilibrium.
CHAPTER 8. FORMATION OF STARS
306
8.10 Brown Dwarfs
Brown dwarfs collapse out of hydrogen clouds, not out of
protoplanetary disks (like stars).
• But they radiate energy only by gravitational contraction, not from hydrogen fusion (like planets).
• Their masses are expected to range from several
times the mass of Jupiter to a few percent of the Sun’s
mass.
• The cooler brown dwarfs may resemble gas giant
planets in chemical composition,
• Hotter ones may begin to look chemically more like
stars.
• They are difficult to detect since they are small and
of very low luminosity.
8.10. BROWN DWARFS
8.10.1 Spectroscopic Signatures
The first brown dwarf discovered was Gliese 229B.
• Gliese 229B appears to be too hot and massive to be
a planet, but too small and cool to be a star.
• The IR spectrum of GL229B looks like the spectrum
of a gas giant planet.
• Most telling is evidence of methane gas, common in
gas giants but not found in stars because methane
can survive only in atmospheres having temperatures
lower than about 1500 K.
307
308
CHAPTER 8. FORMATION OF STARS
In addition to searching for gases like methane that should
not be present in stars, searches for brown dwarfs have
also looked for evidence of the element lithium.
• Hydrogen fusion destroys lithium in stars.
• At temperatures above about 2 × 106 K, a proton encountering a lithium nucleus has a high probability
to react with it, converting the lithium to helium.
• The amount of lithium that can survive is a function of how strongly the material of the star is mixed
down to the core fusion region by convection.
• Protostars are convective, so stars start off with a
strongly mixed interior, but the initial core temperature in the protostar is not high enough to burn
lithium.
• The lightest stars (red dwarfs) remain convective
once on the main sequence, so lithium is mixed down
to the fusion region and destroyed in red dwarfs.
• Because these stars are cool, it takes some time
to burn the lithium, but calculations indicate that
lithium could survive no longer than about 2 × 108
years in the lightest true star.
8.10. BROWN DWARFS
No Lithium
309
Molecular Hydrogen
and Helium
Lithium, Methane
Fully
c onvective
Solid
metallic core
Thermonuclear
reactions
Red Dwarf
No thermonuclear
reactions
Brown Dwarf
Gas Giant
Figure 8.10: Contrasting interiors of a red dwarf, a brown dwarf, and a gas giant
planet. Generally stars initiate thermonuclear reactions but brown dwarfs and planets do not. Thus, lithium is destroyed in stars. The presence of methane is also an
indication that the temperatures are too low for the object to be a star. Gas giant
planets can also contain lithium and methane, but their upper interiors tend to be
dominated by molecular hydrogen and helium.
The basic interior structures expected for stars, brown
dwarfs, and gas giant planets are summarized schematically in Fig. 8.10.
CHAPTER 8. FORMATION OF STARS
310
Sun
Gliese 229A
Teide 1
Gliese 229B
Jupiter
5800 K
3800 K
2700 K
900 K
180 K
G2 Star
Red Dwarf
Brown Dwarf
Planet
Figure 8.11: Size and surface temperature trends for stars, brown dwarfs, and gas
giant planets.
8.10.2 Stars, Brown Dwarfs, and Planets
Figure 8.11 summarizes the size and surface temperature trend from
middle main sequence stars like the Sun, through the lowest mass
stars (red dwarfs), through brown dwarfs, and finally to planets.
• Brown dwarfs can have surface temperatures comparable to that
of the lowest mass stars, but atmospheric compositions similar
to large planets.
• The challenge is to distinguish brown dwarfs from stars and gas
giants at interstellar distances.
• A number of brown dwarf candidates have now been identified
but in many cases there is uncertainty about whether they are
brown dwarf companions of stars, or giant planets orbiting stars.
8.11. LIMITING UPPER MASS FOR STARS
8.11 Limiting Upper Mass for Stars
As we have discussed in the preceding section, a limiting
lower mass for stars is set by the requirement that sufficient temperature be generated by gravitational collapse
to commence the fusion of hydrogen to helium in the core.
• An upper limiting mass for stars is thought to exist because of the opposite extreme: if the star is
too massive, the intensity of the energy production
makes the star unstable to disruption by the radiation
pressure.
• The pressure associated with the radiation grows as
the fourth power of the temperature and thus will be
most important for very hot stars.
• It is instructive to ask what photon luminosity is required such that the magnitude of the force associated with the radiation field is equivalent to the magnitude of the gravitational force.
• This critical luminosity, which defines limiting configurations that are stable gravitationally with respect
to the pressure of the photon flux, is termed the Eddington luminosity.
311
CHAPTER 8. FORMATION OF STARS
312
8.11.1 Eddington Luminosity
• As shown in Exercise 8.1, the force per unit volume
associated with a photon gas is given by the gradient
of the radiation pressure,
1
dPr 4 3 dT
Fr = −
= aT
.
V
dr
3
dr
• If the magnitude of this force is equated to the magnitude of the gravitational force, we obtain an expression for the Eddington luminosity
LEdd =
4π cGM
.
κ
• We may expect that stars exceeding this luminosity
can blow off surface layers by radiation pressure.
• The ejection of material may also be aided by stellar pulsations that result from pressure instabilities at
high luminosity, and may be influenced by the presence of stellar rotation and magnetic fields.
• Both the force from the radiation pressure and that
from the gravitational field are proportional to ρ /r2,
so the dependence on r and ρ cancels from the Eddington luminosity and the critical luminosity is determined completely by the mass of the star and an
appropriate opacity for regions near the surface.
8.11. LIMITING UPPER MASS FOR STARS
8.11.2 Estimate of Limiting Mass
The Eddington luminosity may be expressed as
M
LEdd
≃ 3.5 × 104
,
L⊙
M⊙
if we estimate the opacity κ by the Thomson formula.
• We may use this equation to estimate a radiationpressure mass limit by
– assuming that the most luminous stars observed
(L ∼ several × 106L⊙ ) are at the Eddington
limit, and
– approximating the relevant opacity by the
Thomson formula.
• As shown in Exercise 8.1, this suggests a maximum
stable mass of order 100M⊙.
This is a very crude estimate but calculations, and observations, suggest that the most massive stars indeed have
masses of this order.
313
314
CHAPTER 8. FORMATION OF STARS
8.11.3 Envelope Loss from Massive Young Stars
As we discuss in the next section, there is strong observational evidence that very massive stars eject large amounts
of material from their envelopes early in their lives. Radiation pressure and pulsational instabilities are thought to
play a leading role in these mass-loss processes.
8.11. LIMITING UPPER MASS FOR STARS
Massive stars may go through early stages where they expel large portions of their envelopes into space at velocities as large as 1000 km s−1.
• In such stars, the timescale for mass loss
τloss ∼ M/Ṁ,
where M is the mass and Ṁ the rate of mass loss, may
be shorter than their main sequence timescales.
• One class of stars exhibiting large mass loss while on
the main sequence is that of Wolf–Rayet stars, which
are main sequence stars characterized by
1. large luminosity,
2. envelopes strongly depleted in hydrogen, and
3. high rates of mass loss.
• Most Wolf–Rayet stars have masses of 5 − 10M⊙.
• They are thought to be the remains of stars initially
more massive than 30M⊙ that have ejected all or
most of their outer envelope, exposing the hot helium
core (as a result, they are very strong UV emitters).
• The envelopes of Wolf–Rayet stars typically contain
10% or less hydrogen by mass, with individual stars
exhibiting different levels of envelope stripping.
315
CHAPTER 8. FORMATION OF STARS
316
(a)
(b)
HD56925
η Carinae
Figure 8.12: (a) Wolf–Rayet star HD56925 surrounded by remnants of its former
envelope. (b) η Carinae, surrounded by ejected material.
• Figure 8.12a shows the nebula N2359, a wind-blown
shell of gas that has been expelled from the Wolf–
Rayet star HD56925 (marked by the arrow.)
• The nebula contains shock waves generated by interaction of the wind and interstellar medium, and is
glowing from excitation of expelled material.
• Figure 8.12b shows an extreme example of mass loss:
the supermassive, highly unstable star, η Carinae.
• Elemental abundances in the nebula around η Carinae are consistent with this being the supergiant
phase of a 120 M⊙ star that has evolved with very
large mass loss on the main sequence and afterwards.
• (Some evidence suggests that η Carinae may be a
binary star, which would complicate interpretation).
8.12. PROTOPLANETARY DISKS
317
Figure 8.13: Schematic model of an accretion disk and bipolar outflow.
8.12 Protoplanetary Disks
• In the final stages of protostar collapse, we may expect that because of conservation of angular momentum the matter from the
nebula will continue to accrete onto the star from an equatorial
accretion disk.
• There is also strong empirical evidence that young stars produce
very strong stellar winds that are focused perpendicular to the
equatorial accretion disk.
• Thus, accretion disks and strong bipolar outflow may be a rather
common feature of stars collapsing to the main sequence. Figure
8.13 illustrates.
• The strong wind blowing from young stars is not completely
understood. One idea is that it is caused by the matter drawing a
magnetic field inward as it falls into the accretion disk.
• The outward flowing wind is partially blocked by the accretion
disk around the equator of the forming star and so escapes along
the polar axis, thus producing bipolar outflows from the young
star.
CHAPTER 8. FORMATION OF STARS
318
Solar
System
Beta Pictoris
Vega
Fomalhaut
Solar
System
Solar
System
Figure 8.14: Radio frequency maps indicating the presence of dusk disks around
three young stars.
• However, this simple picture cannot explain the evidence for the
rather narrow width of the outflow observed in some cases. Presumably the full mechanism is more complex, perhaps involving
the effect of magnetic fields to focus the ejected material.
Figure 8.14 shows submillimeter radio frequency observations of three
nearby, young stars.
• The maps are false-color illustrations of the intensity of radio
emission, with the emission thought to originate primarily from
dust in the vicinity of the stars.
• The location of the star is indicated by the black star symbol.
• The size of our Solar System is illustrated by a vertical bar.
• In all three cases, there is strong evidence for dust disks around
these young stars.
8.13. EXTRASOLAR PLANETS
8.13 Extrasolar Planets
The dust disks observed around a number of young stars
suggests that planetary formation may be taking place in
these systems.
• Indeed, over the past few years impressive evidence
has accumulated for ∼1000 extrasolar planets.
• These planets are difficult to observe directly at their
great distance. They are detected primarily through
their gravitational influence on the parent star.
• In principle they could be detected by the wobble in
angular position on the celestial sphere of the parent
star caused by the gravitational tug of the planet as it
moves about its orbit.
• In practice, it has proven easier to instead detect the
wobble corresponding to the small periodic Doppler
shifts for the radial motion of the parent star induced
by this motion, and (in favorable cases) by small variations in light output caused by planetary transits of
the parent star.
319
CHAPTER 8. FORMATION OF STARS
320
Center of Mass
Period = P
Radial Velocity
Blueshift
Redshift
Full Amplitude = 2K
Observer
Time
Figure 8.15: The Doppler wobble method for detecting extrasolar planets.
8.13.1 The Doppler Wobble Method
The Doppler wobble method is illustrated in Fig. 8.15.
• It requires that changes in radial velocity for the parent star of
order 10 m s−1 be detected (see Exercise 8.4).
• The semiamplitude K of the stellar radial velocity caused by an
orbiting planet is given by
2π G 1/3
mp sin i
,
K=
P
(M∗ + mp )2/3 (1 − e2)1/2
where i is the tilt angle of the orbit, mp is the mass of the unseen
companion, M∗ is the mass of the star, the orbital eccentricity is
e, and the orbital period P is given by Kepler’s third law,
4π 2 a3
,
P =
G(M∗ + mp )
2
where a is the semimajor axis of the relative orbit.
8.13. EXTRASOLAR PLANETS
321
51 Pegasi
Radial Velocity (m/s)
+100
M = 2.11 x 1030 kg
+50
0
-50
0
20
40
60
80
100
120
140
160
Time (hours)
Figure 8.16: Doppler shift induced by planetary companion of 51 Pegasi.
• Generally, one does not know the tilt angle i, so masses are uncertain by a factor sin i in the absence of further information.
• Fits of the preceding equations to the 51 Pegasi data in Fig. 8.16
indicate that the wobble of the parent star is caused by a planetary companion of 0.44 Jupiter masses in an almost circular orbit
with only a 4.2 day period.
• Thus the planet would orbit well inside the orbit of Mercury in
our Solar System.
322
CHAPTER 8. FORMATION OF STARS
8.13.2 Precision of the Method
In the general case, the precision attainable with present
technology restricts the method to detection of massive
planets (Jupiters and Saturns), and is more sensitive for
planets relatively near their parent star.
• For example, with current precision a planet of one
Jupiter mass would be detectable for a = 1 AU but
not at Jupiter’s actual distance of 5.2 AU.
• Improvements in the Doppler technology are anticipated that would allow a Saturn-mass planet to be
detected for a < 1 AU and a Jupiter-mass planet at 5
AU.
• It is thought that the ultimate limits to the technique
correspond to a precision of about 3 m s−1 , dictated
by intrinsic stability limitations for the stellar photospheres that the method must observe.
• The only Earth-mass extrasolar planets detected so
far are for a special case of planets orbiting a pulsar, where one can exploit techniques depending on
the precise timing associated with pulsars to detect
lower-mass planets.
• In principle, the transit method discussed below
could also be used to detect Earth-mass planets.
Relative Flux (Brightness)
8.13. EXTRASOLAR PLANETS
323
1.01
1.00
0.99
HD209458
0.98
-0.1
0.0
0.1
Time (days)
Figure 8.17: Lightcurve for transit of HD209458 by an extrasolar planet.
8.13.3 Transits of Extrasolar Planets
In cases where the geometry is favorable for an eclipse as seen from
Earth, it is possible to detect the transit of extrasolar planets across the
face of their parent star through the periodic reduction in light output
for the system.
• In Fig. 8.17 we show data corresponding to the transit of the star
HD209458 by a planet.
• Such data allow the tilt angle i of the orbit to be constrained to
near π2 (since the geometry must lead to an eclipse), and from the
eclipse timing the radius of the planet can be estimated.
• This information, coupled with the information from Doppler
analysis of the system, allows a rather full picture to be constructed: a detailed orbit of the planet, its mass, its size, and its
density, and information about the atmosphere of the planet.
CHAPTER 8. FORMATION OF STARS
324
Relative Intensity
1.010
Secondary
eclipse
1.005
1.000
0.995
0.990
0.46
0.48
0.50
0.52
0.54
Phase
Figure 8.18: Lightcurve for Secondary IR eclipse of the extrasolar planet of
HD209458b.
8.13.4 Secondary Eclipses of Extrasolar Planets
Infrared measurements from above the atmosphere are sensitive enough
to detect the secondary eclipse of extrasolar planets (the eclipse of the
planet by the parent star).
• Such a secondary eclipse is illustrated in Fig. 8.18 for a planet
in an eclipsing orbit around the star HD209458b.
• These measurements permit the IR flux associated with the planet
to be deduced from the total flux decrease during the secondary
eclipse.
• By fitting such data to models of planetary atmospheres one
can begin to determine the properties of the planet from the IR
eclipse data.
• In this case it was concluded that the planet has an atmospheric
temperature of about 1100 K.
8.13. EXTRASOLAR PLANETS
325
Mercury Venus Earth
Mars
Inner Solar System
Tau Bootis
3.8 MJ
51 Peg
0.47 MJ
Upsilon Andromedae
0.68 MJ
0.84 MJ
55 Cancri
2.1 MJ
Gliese 876
1.1MJ
Rho Cr B
HD114762
10 MJ
6.6 MJ
70 Vir
16 Cyg B
1.7 MJ
47 UMa
2.4 MJ
4.0 MJ
Gleise 614
0
1
2
3
Orbital Semimajor Axis (AU)
Figure 8.19: Orbit radius and mass data for some extrasolar planets.
8.13.5 The Hot Jupiter Problem
• Around normal stars, the planets discovered so far tend to have
Jupiter-like masses and lie rather close to their parent star.
• Data for some extrasolar planets are compared with corresponding quantities for our Solar System in Fig. 8.19.
• There we see that many extrasolar planets of gas-giant mass have
orbital semimajor axes well inside 1 AU (implying orbital periods of only a few days).
• This is a situation very different from our Solar System, where
massive Jupiter-like planets are at large distances from the Sun.
CHAPTER 8. FORMATION OF STARS
326
Mercury Venus Earth
Mars
Inner Solar System
Tau Bootis
3.8 MJ
51 Peg
0.47 MJ
Upsilon Andromedae
0.68 MJ
0.84 MJ
55 Cancri
2.1 MJ
Gliese 876
1.1MJ
Rho Cr B
HD114762
10 MJ
6.6 MJ
70 Vir
16 Cyg B
1.7 MJ
47 UMa
2.4 MJ
4.0 MJ
Gleise 614
0
1
2
3
Orbital Semimajor Axis (AU)
• This anomaly has been called the hot Jupiter problem, since in
these extrasolar systems we see gas giants that are near their
parent star and therefore strongly heated.
• The hot Jupiter problem presents a challenge to our standard
ideas of how planets form.
• If this pattern remains in further study of extrasolar planets, it
may require us to revise our understanding of the history of gas
giants in our own Solar System.
• Observation of many massive planets very near their parent stars
has made popular various planetary migration theories.
• In these theories, planets formed originally in outer, colder regions of the solar nebula migrate inward over time because of
dynamical effects in the nebula.