Sec$on 6.
Low mass stars and white dwarfs
6.1 Evolu$on of low mass stars
6.2 White dwarfs

MESA codeh>p://mesa.sourceforge.net/index.html

1 Msun (ρ-T)

1 Msun (HR diagram)20 Msun (ρ-T)

20 Msun (HR diagram)

Contrac$on of the core
= Expansion of the envelope

Shell burning => energy genera$on(more than required to support the envelope )(A color version of this figure is available in the online journal.)(A color version of this figure is available in the online journal.)

Figureblack23. line)
2 M⊙and, Z MESA
= 0.01
tracksupgrayto thefirsi(solidstar(thickline)(solid black line) and MESA star (thick gray line

Low/intermediate
mass stars

Figure 22. Top: MESA star H-R diagram for 2–10 M⊙ models from the PMS
to the end of the first thermal pulse (2–7 M⊙ ) or into C-burning (8 and 10 M⊙ ).

mass, and hence luminosity, in the EVO
mass, andhenceenvelope
luminosity,
the EV
maintainsimilarmassinevolution
maintainsimilarmass evolutio
theparameter
ηBlenvelopein the mass-loss
formu
the parameter
mass-loss
MESA
star andηBl
0.1ininthe
EVOL.
Everyform
eff
MESA thestar
andstar
0.1 inmodel
EVOL.
etailorMESA
to Everythe EVO
tailorthe evolution
MESA starmodel
to the toEV
theAGBis very
sensitive
the AGBevolutionvery sensitivetowhich
depends
on theismixing
assumption
which depends onthe mixing
assumptio
implementation
duringthe precedingHe
implementation
duringthe preceding
H
Consequently,
small
differenceson the TPConsequently,
small
differences
the TP
when
comparing
tracksfrom twoon
codes.
Core
when
comparing
tracks23,
fromcodes.
Ascontrac$on
shown
in FigurethetwoEVOLan
As shown
Figure23,
the EVOL
well ininofthetheH-R
diagram.
Tabla=>compare
Expansionenvelope
properties
differinbythelessthan5%. MESA
compare well
H-R
diagram.
Ta=>toproperties
Redgiant
imposeadifferminimumsizethanon convectio
by less
5%. MESA
overshootis ignored.
EVOL
does
to imposemixing
a minimum
size onconvecti
leading
to moremixingof He into
the coreovershootmixingis ignored.
EVOL
doelargerage
the mixing
EVOL sequence
thecorfileading
to ofmoreof He intoatthe
The age
TP-AGBcharacterized
reclargerof the is
EVOL
sequence byat theinstabilitiesof theisHe-shell,leading
The TP-AGB
characterized
bytorenucleosynthesis.
Theseprocesses
are prto
instabilities of theHe-shell,leading
MESA
star calculations,as revealedare
in pF
nucleosynthesis.
These processes
ofMESAstarstar
to calculateastherevealed
evolution
MESA
calculations,ininsmoothandtocontinuous
evenof aMESA
star
calculate manner
the evolutio
thermalpulseandphasesand beyond
is demoin a smooth
continuous
mannereve
The
top panel
evolution
thermalpulseshowsphasestheand
beyond inis thedemH
thepanelshows
evolutionofThebottom
top panelshows
the theevolution
in theC/Ocore. The
adiabaticin the othe bottompanel
shows coolingthe evolution
duringthe Heflash(duethe pressuredPaxton
etal.to2011
C/O core.
Theadiabaticcoolingin theof the C/O core) is evident in the down

TheAstrophysicalAstrophysical Journal
Journal Supplement(35pp),
2011
January
The
SupplementSeries,Series,192:3
192:3(35pp),
2011
January

Massive stars(un$l He-burning)

Core contrac$on=> Expansion of the envelope=> Red super giant

Figure 29. Top: H-R diagram for 10–100 M⊙ models from the PMS to the end ofcore Helium burning for Z = 0.02 but with zero mass loss. Bottom: trajectories

Figure 30. Evolution of the central temperature andmetallicity Mi = 25 M⊙ models from different stella
Figure30. Evolutionof thecentral
temperatur
locationsof corehelium, carbon,neon,oxygen,and sili
1/3
as ismetallicity
the relationM
Tci ∝=ρc25 .M⊙ models from differen
locations of core helium, carbon, neon, oxygen, a(A color version of this figure1/3
is available in the online

ρc al.
. 2011
as is the relationTc ∝ etPaxton(A color version of this figure is available in theContrac$on of the core
= Expansion of the envelope

Evolu&on in the rho-T plane is determinedby the proper&es of the core
T ~ M2/3 ρ1/3
M decreases => Lower part of the ρ-T plane

Massive stars（un$l Si burning）

Finally degeneracy pressure
becomes importantdege
ne

ratee

lectrons

relativistic electrons

textbook by PolsWhat about lower mass stars?
What is the minimum mass of the stars?
What is the fate of low mass stars?

BrowndwarfPlanetDeuterium
burning
0.001

1 Jupiter
mass

0.01

H-burning

0.1

1He
WDC+O
WD~0.5
Origin of He WD?
(too long life &me)

10 (Msun)
MassFecore
8-10?

Sec$on 6.
Low mass stars and white dwarfs
6.1 Evolu$on of low mass stars
6.2 White dwarfs

Sirius A(シリウス)

Sirius B
白色矮星

hLps://kids.yahoo.co.jp/zukan/astro/winter/0001.html

Cat’s eye nebula(J.P. Harrington and K.J. Borkowski, and NASA)Helix nebula(NASA, ESA, and C.R. O'Dell)Mass-radius rela$on for white dwarfs
764

PROVENCAL ETHe
40 Eri B.014

.012

.01

Procyon B

R ~ M-0.3.008

FeSirius B

Mg

C.006

.004
.3.4.5.6.7.8.9

1

1.1

FIG. 2.ÈObservational support for the white dwarf mass-radius relaProvencal
et al.Hipparcos,
1998
tion after
showing revised positions for the visual binaries andincluding results from the common proper-motion systems.

ProsigniÐ
carbo
on theter ofshows
threeThe
core mradii
we obwell-sevidenmyste
a comthat G
EG 5from

More massive white dwarfs are smaller
Opposite to the main sequence stars

Why??

Summary: Low mass stars and white dwarfs• Low mass stars• Maximum temperature to reach• M < 0.08 Msun: cannot reach H burning => brown dwarfs• White dwarfs• Supported by electron degeneracy pressure=> Stellar equa&ons become independent on temperature• More massive stars have smaller radius
R ~ M-1/3 (non-rela&vis&c)• Limit of rela&vis&c electrons

M = constant (Chandrasekhar limit) ~ 1.4 Msun