Nuclear Fusion in Substellar Objects
PHY 688, Lecture 16
Mar 4, 2009
Outline
• Review of previous lecture
– substellar evolution
– analytical solution for L(t) and Teff(t)
• The hydrogen burning limit
• Lithium and deuterium burning
Mar 4, 2009
PHY 688, Lecture 16
2
Previously in PHY 688…
Mar 4, 2009
PHY 688, Lecture 16
3
Hydrogen phase diagram
Evolution is towards:
• lower entropy S
• higher degeneracy η
T
H+
Mar 4, 2009
PHY 688, Lecture 16
(Burrows & Liebert 1993)
4
Evolution of L and Teff
Mar 4, 2009
PHY 688, Lecture 16
(Burrows & Liebert 1993)
5
Evolution of Effective Temperature
stars
brown dwarfs
“planets”
2MASS 0535–0546 A/B
M
13
10
M
Ju
p
M
Ju
p
5M
Jup
Gl 229B
1M
Jup
Jupiter
(Burrows et al. 2001)
Mar 4, 2009
PHY 688, Lecture 16
6
Evolution of Luminosity
stars
brown dwarfs
“planets”
Mar 4, 2009
PHY 688, Lecture 16
(Burrows et al. 2001)
7
Evolution of Nuclear (Fusion) vs.
Total Luminosity
0.080 MSun
0.075 MSun
0.070 MSun
0.060 MSun
Mar 4, 2009
PHY 688, Lecture 16
(Burrows & Liebert 1993) 8
Outline
• Review of previous lecture
– substellar evolution
– analytical solution for L(t) and Teff(t)
• The hydrogen burning limit
• Lithium and deuterium burning
Mar 4, 2009
PHY 688, Lecture 16
9
The Minimum Main-Sequence Mass
• Derive by equating nuclear energy generation to
energy loss through cooling.
dE
dV
dS
$L
+P
=T
= "˙ #
=0
dt
dt
dt
$M
• Have expression for L(M, κR, η)
• Find expression for "˙(M,#)
!
Mar 4, 2009
!
PHY 688, Lecture 16
10
From Lecture 14: Energy Generation is
Enhanced in Electron Degenerate Dwarfs
•
unscreened energy generation rates for 1H + 1H (p + p) and 1H + 2H (p + d):
"˙ pp = 2.5 #10 ( $X /T
6
"˙ pd = 1.4 #10
24
2
23
6
($XYd /T
)e
23
6
%33.8 T61 3
)e
ergs gm%1cm%1
%37.2 T61 3
ergs gm%1cm%1
Yd is 2H mass fraction (primordial value is 2 × 10–5)
•
2 2
but recall that H is in a state of strongly coupled plasma (" = Z e rskT > 1)
! – proton and deuteron screening decreases Coulomb barrier
– p + p and p + d rates enhanced by factor of
! 1.29 , 1.06#)
S " e H (0), where H(0) " min(0.977#
– at main sequence edge S ~ 2; can be higher at lower masses
!
Mar 4, 2009
"˙ pp # T 6.31$1.28 in core of transition mass object
"˙ pp # T 4 $ in core of the Sun
PHY 688, Lecture 16
11
p-p Chain Reaction Rate is Decided
by the First Step (p+p)
Mar 4, 2009
PHY 688, Lecture 16
12
The Minimum Main Sequence Mass
• Depends slightly on metallicity
– He content
– atmospheric opacity
• At [m/H] = 0.0 (solar metallicity):
– MMMSM ≈ 0.075 MSun
– LMMSM ≈ 6 × 10–5 LSun
– Teff, MMSM ~ 1600–1750 K
• At [m/H] → –∞ (zero metallicity)
– MMMSM ≈ 0.092 MSun
– LMMSM ≈ 1.3 × 10–3 LSun
– Teff, MMSM ~ 3600 K
Mar 4, 2009
PHY 688, Lecture 16
13
Outline
• Review of previous lecture
– substellar evolution
– analytical solution for L(t) and Teff(t)
• The hydrogen burning limit
• Lithium and deuterium burning
Mar 4, 2009
PHY 688, Lecture 16
14
Lithium and Deuterium Burning:
the Fastest Fusion Reactions
Mar 4, 2009
PHY 688, Lecture 16
15
Lithium and Deuterium Burning
stars
brown dwarfs
“planets”
Li and H burning: at > 2.7 × 106 K
H
Li
D burning: at > 4 × 105 K
Mar 4, 2009
PHY 688, Lecture 16
(Burrows et al. 2001)
16
Deuterium Depletion
stars
brown dwarfs
“planets”
Mar 4, 2009
PHY 688, Lecture 16
(Burrows et al. 2001)
17
Lithium Depletion
stars
brown dwarfs
Mar 4, 2009
PHY 688, Lecture 16
(Burrows et al. 2001)
18
Li and D: Depleted within Few 100Myr
50% D depletion
50% Li depletion
stars
brown dwarfs
“planets”
Mar 4, 2009
PHY 688, Lecture 16
(Burrows et al. 2001)
19
Lithium is Observable in the Photosphere
Mar 4, 2009
PHY 688, Lecture 16
(Kirkpatrick et al. 1999)
20
The Lithium Test for Age/Substellarity
stars
brown dwarfs
“planets”
Mar 4, 2009
PHY 688, Lecture 16
(Burrows et al. 2001)
21
The Lithium Test for Age/Substellarity
presence of Li:
• youth
and / or
• substellar
mass
Mar 4, 2009
PHY 688, Lecture 16
(Basri 1997)
22
1995: Teide 1 –
First Bona-Fide Brown Dwarf
• member of 100 Myr-old
Pleiades open cluster
– Rebolo et al. (1995)
• spectroscopic signature of
lithium in absorption
– Rebolo et al. (1996)
– destroyed in the convective
interiors of low-mass stars
• …but initially
– insufficient sensitivity to
detect Li (at 6708 Å)
– skepticism about age
Mar 4, 2009
PHY 688, Lecture 16
(Rebolo et al. 1995) 23
Teide 1 spectrum
Mar 4, 2009
PHY 688, Lecture 16
(Rebolo et al. 1996) 24
The Lithium Test for Age/Substellarity
presence of Li:
• youth
and / or
• substellar
mass
Mar 4, 2009
Teide 1,
Calar 3
PHY 688, Lecture 16
(Basri 1997)
25