Nuclear Fusion in Substellar Objects

PHY 688, Lecture 16Mar 4, 2009

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 3

Previously in PHY 688…

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 5

Evolution of L and Teff

(Burrows & Liebert 1993)

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 12

p-p Chain Reaction Rate is Decidedby the First Step (p+p)

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 15

Lithium and Deuterium Burning:the Fastest Fusion Reactions

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 18

Lithium Depletion

(Burrows et al. 2001)

starsbrown dwarfs

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)

Mar 4, 2009 PHY 688, Lecture 16 24

Teide 1 spectrum

(Rebolo et al. 1996)

Mar 4, 2009 PHY 688, Lecture 16 25

The Lithium Test for Age/Substellarity

(Basri 1997)

presence of Li:

• youth

and / or

• substellarmass

Teide 1,Calar 3