nuclear fusion in substellar objects - stony brook university · –rebolo et al. (1995)...
TRANSCRIPT
Mar 4, 2009 PHY 688, Lecture 16 2
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 4(Burrows & Liebert 1993)
T
Hydrogen phase diagram
Evolution is towards:• lower entropy S• higher degeneracy η
H+
Mar 4, 2009 PHY 688, Lecture 16 6
Evolution of Effective Temperature
13 MJup10 M
Jup
5 MJup
1 MJup
starsbrown dwarfs“planets”
M
(Burrows et al. 2001)
Gl 229B
2MASS 0535–0546 A/B
Jupiter
Mar 4, 2009 PHY 688, Lecture 16 7
Evolution of Luminosity
(Burrows et al. 2001)
starsbrown dwarfs“planets”
Mar 4, 2009 PHY 688, Lecture 16 8
Evolution of Nuclear (Fusion) vs.Total Luminosity
0.060 MSun
0.070 MSun
0.075 MSun
0.080 MSun
(Burrows & Liebert 1993)
Mar 4, 2009 PHY 688, Lecture 16 9
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 10
The Minimum Main-Sequence Mass
• Derive by equating nuclear energy generation toenergy loss through cooling.
• Have expression for L(M, κR, η)• Find expression for!
dE
dt+ P
dV
dt= T
dS
dt= ˙ " #
$L
$M= 0
!
˙ " (M,#)
Mar 4, 2009 PHY 688, Lecture 16 11
From Lecture 14: Energy Generation isEnhanced in Electron Degenerate Dwarfs
• unscreened energy generation rates for 1H + 1H (p + p) and 1H + 2H (p + d):
Yd is 2H mass fraction (primordial value is 2 × 10–5)• but recall that H is in a state of strongly coupled plasma
– proton and deuteron screening decreases Coulomb barrier– p + p and p + d rates enhanced by factor of
– at main sequence edge S ~ 2; can be higher at lower masses
!
˙ " pp = 2.5 #106 $X 2 /T6
2 3( )e%33.8 T6
1 3
ergs gm%1cm%1
˙ " pd =1.4 #1024 $XYd /T6
2 3( )e%37.2 T6
1 3
ergs gm%1cm%1
!
(" = Z2e2rskT >1)
!
S " eH (0)
, where H(0) "min(0.977#1.29
, 1.06#)
!
˙ " pp #T6.31$1.28 in core of transition mass object
˙ " pp #T4$ in core of the Sun
Mar 4, 2009 PHY 688, Lecture 16 13
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 14
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 16
Lithium and Deuterium Burningstarsbrown dwarfs“planets”
Li and H burning: at > 2.7 × 106 K
D burning: at > 4 × 105 K
(Burrows et al. 2001)
LiH
Mar 4, 2009 PHY 688, Lecture 16 17
Deuterium Depletion
starsbrown dwarfs“planets”
(Burrows et al. 2001)
Mar 4, 2009 PHY 688, Lecture 16 19
starsbrown dwarfs“planets”
(Burrows et al. 2001)
Li and D: Depleted within Few 100Myr
50% Li depletion50% D depletion
Mar 4, 2009 PHY 688, Lecture 16 20
Lithium is Observable in the Photosphere
(Kirkpatrick et al. 1999)
Mar 4, 2009 PHY 688, Lecture 16 21
The Lithium Test for Age/Substellarity
starsbrown dwarfs“planets”
(Burrows et al. 2001)
Mar 4, 2009 PHY 688, Lecture 16 22
The Lithium Test for Age/Substellarity
(Basri 1997)
presence of Li:
• youth
and / or
• substellarmass
Mar 4, 2009 PHY 688, Lecture 16 23
1995: Teide 1 –First Bona-Fide Brown Dwarf
• member of 100 Myr-oldPleiades open cluster– Rebolo et al. (1995)
• spectroscopic signature oflithium 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
(Rebolo et al. 1995)