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Home , Teide 1

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

brown dwarfs “” 2MASS 0535–0546 A/B M

13 M J 10 up M J up

5 M J up Gl 229B

1 M Jup Jupiter

(Burrows et al. 2001) Mar 4, 2009 PHY 688, Lecture 16 6 Evolution of

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): 33.8 T 1 3 ˙ 6 2 2 3 % 6 %1 %1 " pp = 2.5 #10 ($X /T6 )e ergs gm cm 37.2 T 1 3 ˙ 24 2 3 % 6 %1 %1 " pd =1.4 #10 ($XYd /T6 )e ergs gm cm 2 –5 Yd is H mass fraction (primordial value is 2 × 10 ) 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 S " e H(0), where H(0) " min(0.977!# 1.29, 1.06#)

– at main sequence edge S ~ 2; can be higher at lower masses 6.31 1.28 "˙ pp #T $ in core of transition mass object ! 4 "˙ pp #T $ in core of the

Mar 4, 2009 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 –5 – LMMSM ≈ 6 × 10 LSun

– Teff, MMSM ~ 1600–1750 K • At [m/H] → –∞ (zero metallicity)

– MMMSM ≈ 0.092 MSun –3 – LMMSM ≈ 1.3 × 10 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: 1 – First Bona-Fide • member of 100 Myr-old – 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 Teide 1, Calar 3 mass

Mar 4, 2009 PHY 688, Lecture 16 (Basri 1997) 25