Pre-main sequence evolution of low-mass stars:
Effects of planet formation on stellar composition
Masanobu Kunitomo (Nagoya Univ.)
collaborators
Tristan Guillot (Observatoire de la Côte d'Azur),
Taku Takeuchi and Shigeru Ida (Tokyo Tech.)

6/1/2015
DTA Symposium@NAOJ

Classical picture of pre-main sequence evolution
large radius (~10R⊙)

1.2log LL*[L[Lsun]
log]⊙1M⊙ star’s
1 evolutionary track
0.8
radiative
core

0.6
0.4

Main
0.2 Sequence
0-0.2~4×107yre.g., Stahler+80

Hayashitrack“forbidden region”
Henyey track

Hayashi61

due to the opacity of H−~107yr-0.4
3.78 3.76 3.74 3.72 3.7 3.68 3.66 3.64 3.62
log log
TeffT[K]eff [K]
star shrinks→central temperature increases→opacity decreases→radiative core develops

Classical picture of pre-main sequence evolution
large radius (~10R⊙)

1.2

log LL*[L[Lsun]
log]⊙1M⊙ star’s
1 evolutionary track
0.8
radiativecore

0.6
0.4

Main
0.2 Sequence
0-0.2~4×107yre.g., Stahler+80

Hayashitrack“forbidden region”
Henyey track

Hayashi61

due to the opacity of H−~107yr-0.4
3.78 3.76 3.74 3.72 3.7 3.68 3.66 3.64 3.62
log log
TeffT[K]eff [K]

stellar age and mass are estimated by comparing
observed Teﬀ and L with theoretical evolutionary tracks

Classical PMS evolution may not be accurate
the classical PMS evolution has been called into question
by recent observations:mass anomaly of PMS stars

Stassun+14

PMS stars’ masses estimated with the classical evolutionary tracks
are inaccurate up to 50-100% using eclipsing binary systems

luminosity (age) spread problem“model mass”

Hillenbrand09“dynamical mass”

Luminosity (age) spread problem
1log LL[Lsun]
log[L⊙]0PMS stars’ ages in the samecluster widely spread (~10Myr)
if the classical PMS evolution is used

1Myr

0.5

1Myr

10Myr

-0.5 10Myr-1-1.5

if stars in a cluster are almost coeval,this is a big problem-2-2.5-3
5000 4500 4000 3500 3000 2500 2000 1500
Teff [K]Teff [K]▲Tauras and Chamaeleon I■ρ Ophiucus●σ Orionis— classical isochrone(Muzerolle+05; Gatti+06,08;Baraffe+98)

possible solutions:

1. observational error2. long-lasting star formation in a cluster(Inutsuka+15)

3. classical isochrones are not accurate

Standard picture of star formation
molecular
cloud corefirst coresecond core(protostar)~MJupmain massaccretion
phase

(MS)
(PMS)
main
pre-mainsequence sequence

~M⊙
~10R⊙

(c) NASA(c) NASA

Configuration of accretion■Classical picture

e.g., Stahler+80

shock front

gravitational energy (GMṀ/R)↓supersonic (free-fall) velocity↓
thermalized at stellar surface↓
ineﬃcient radiative coolingsphericalaccretion
protostar

ineﬃcient radiative cooling→a large amount of entropy is injected→star is formed with large radius↓large entropy is carriedConfiguration of accretion■Classical picture

e.g., Stahler+80

shock front

Machida+10,■Recent picture e.g.,
Tsukamoto+11,e.g., Baraffe+09

protostar

Kratter+10

radiative coolingdiskspherical
accretion
protostar

ineﬃcient radiative cooling→a large amount of entropy is injected→star is formed with large radiuseﬃcient radiative coolingfrom disk’s and/or stellar surface→low-entropy accretion

we revisit the PMS evolution
with the low-entropy accretion

Computational method■Stellar evolution code MESA Paxton+11,13■Stellar structure equations (1D)
1. continuity@r
1=@Mr4⇡r2 ⇢2. momentum@P=@Mr

3. energy@l= "nuc@Mr@T
4. temp. gradient @M =r

5. composition✓@Xi@Mr◆

accretion is included
Mr: mass coordinate

GMr(hydrostatic equilibrium)4⇡r4

mixing-length theory,
αMLT=1.905@sT+ "add@t0
mi @X 0=rji⇢
Mrj(Cox & Giuli68;Henyey+65)

d ln T
r=d ln P

GMr Tr
44⇡r PXk11 @0 A
rik+ 2r @r

nuclear reaction✓@Xi
r2 D@r

◆diﬀusioncomposition
X=0.70, Z=0.02

Computational method■Eﬀect of the low-entropy accretion@l= "nuc@Mr@sT+ "addheat injection@tby accretion

Ladd= ξGM★Ṁ/R★
●heating efficiency ξ (=0-1)
ξ is poorly constrained
by RHD simulations

εadd=Ladd/M★
●distribute the injected heat
uniformly in the entire staraccreting materials’ gravitationalenergy from infinity to star:GM?
Lacc =ṀR?

Ladd= ξLacc

Lrad= (1−ξ)Lacc

injectedto the starradiated away(+rotation)

PMS evolution with low-entropy accretion
0.01

M★ [M⊙]

accreting phase

51110

101 102 103 104 105 106 107 108
t [yr]

Ṁ=10-5M⊙/yr
Mass [M⊙]MS

10.5
0-0.5

0.10.01
100 101 102 103 104 105 106 107 108
Time [yr]1M⊙-1-1.50.5 0Mass [M⊙]1.5log LL
log[Lsun⊙]]* [LR [Rsun]
Radius[R⊙]100.1 1

Mini=0.01M⊙
Mfin=1M⊙
Ṁ=10-5M⊙/yr
ξ=0, XD=2.0×10-5-20.01M⊙
accretion stops
3.8

3.7

3.6

3.5
3.4
log TlogTeffeff[K]
[K]

3.3

3.2

Mini=0.01M⊙
Mfin=1M⊙
Ṁ=10-5M⊙/yr
ξ=0, XD=2.0×10-5

Comparison with classical evolution■Evolutionary track■Radius evolution
accreting phase

51.5classicalevolution

no acc.

110101 102 103 104 105 106 107 108
t [yr]

Time [yr]Hayashi track

0.5
0-0.5

1M⊙

-1-1.50.5 0no-acc.

1log LLlog[Lsun⊙]]* [L

R [Rsun]Radius[R⊙]10-20.01M⊙
accretion stops
3.8

3.7

3.6

3.5
3.4
log Tlog
Teffeff[K]
[K]

3.3

3.2

●below 1R⊙●about one order ofmagnitude smaller radius●small luminosity

low-entropy accretion →significantly diﬀerent fromthe classical evolution

diﬀerent evolutionary track
results in diﬀerent estimation of
M★ and age●no Hayashi track

PMS evolution with low-entropy accretion
0.01

R [Rsun]Radius[R⊙]

100.1 1

M★ [M⊙]

accreting phaseMS5①②10③

101 102 103 104 105 106 107 108
t [yr]

Time [yr]stellar radius is determinedby mass and entropy
R/M

1/3



2Rexp
(s3µ①: adiabatic contraction●constant entropy because ξ=0●shrink due to the mass accretion②: deuterium burning●D+p→3He+5.5MeV→entropy supply

10.5 0Mini=0.01M⊙
Mfin=1M⊙
Ṁ=10-5M⊙/yr
ξ=0, XD=2.0×10-5s0 )(fully convective, hydrostaticequilibrium, monoatomic ideal gas)
Chandrasekhar67(T>106K)③: depletion of deuterium●mass accretion overcomes
D-burningaccreting material’s entropy
and deuterium content
are importantDependence on the heating eﬃciency ξ

Mini=0.01M⊙
Mfin=1M⊙
Ṁ=10-5M⊙/yr
XD=2.0×10-5

Ladd= ξGMṀ/R■Radius evolution
accretion stops

ξ=0.5classicalevolution

1.50.1
ξ=0.5
0.05
0.10.01
cold5 0.05
no acc.
0.01
01log
logLL* [L[Lsun⊙]]R [Rsun]Radius [R⊙]10

■Evolutionary track

10.5
0-0.5
-1-1.5 ●:

101

102

103

104 105t [yr]

Time [yr]
R/M

1/3

exp



2R
(s3µs0 )

106

107

108-2

accretion stops

3.8

3.7

3.6
3.5log Teff [K]3.4

log Teff [K]●high entropy injection rate→expansion●ξ largely aﬀects the PMS evolution

3.3

Mini=0.01M⊙
Mfin=1M⊙
Ṁ=10-5M⊙/yr
D ξ=0

Dependence on the deuterium content X

Deuterium content decreases with time after the Big-Bang
It can be diﬀerent in each star even in the same age
0.5[D]=40ppm
30200]

10.50101

no acc.
-5 (Big-Bang)
X
=4×10
D
[D]=4e-5-5[D]=3e-5
3×10[D]=2e-5[D]=02×10-500log L [L1.5

accretion stops

log L* [Lsun⊙]R [Rsun]Radius [R⊙]2-0.5-1-1.5

10210

310

451010t [yr] [yr]Time6107

108-2
3.8

3.7

3.6

3.5
3.4
log TTefflog[K]eff [K]

3.3

3.2

deuterium burning starts●large deuterium content→lots of entropy is generated→expansion●diﬀerent evolutionary tracks in the high temperature region

Impact on the luminosity spread problem
11Myr
1Myr

0.5
log L [Lsun]

0-0.5

10Myr

10Myr

-1-1.5-2-2.5-35000 4500 4000 3500 3000 2500 2000 1500
Teff [K]▲Tauras and Chamaeleon I■ρ Ophiucus●σ Orionis— classical isochrone(Muzerolle+05; Gatti+06,08;
Baraffe+98)

Mini=0.01M⊙
Ṁ=10-5M⊙/yr
XD=2.0×10-5

Impact on the luminosity spread problem

Mini=0.01M⊙
Ṁ=10-5M⊙/yr
XD=2.0×10-5

1Myr isochrones with different ξ
10.5

log L [Lsun]

0-0.5-1

ξ=0.5
0.1
0.05
0

●isochrones spread widely→isochrones of diﬀerent ξ
can explain the observed
luminosity spread-1.5-2-2.5-35000 4500 4000 3500 3000 2500 2000 1500
Teff [K]Estimation of stellar ages andmasses using the classicalisochrones is no longer valid

Anomaly of the solar surface composition
Our Sun is a peculiar starΔ[X/Fe](abundant volatilein the Sun)
0.06refractory●the Sun is-abundant in volatile and-scarce in refractory elements
compared to the solar-twins

0.04
0-0.04(scarce0in the Sun)

Δ[X/Fe] = [X/Fe]⊙ - [X/Fe]solar-twins: difference between the Sun and solar-twins●diﬀerence: ~0.04dex ~10%500 1000 1500

Condensation temperature [K]Melendez+09*solar-twins: stars with the similar age,
metallicity, luminosity and mass to the Sun

Internal structure evolution■Classical 1M⊙ evolution

Relative m/Mmass* [M★]

1

0.9 convective zone
0.8 (CZ)
0.6

radiativezoneclassical evolution:
surface CZ shrinks
after ~20 Myr
convectivezone

0.4
0.20104

105

106

107
Timet [yr][yr]Hayashi track

108

109

MS

radiativecore1010

Internal structure evolution
with low-entropy accretion■low-entropy accretionclassical evolution:
surface CZ shrinks
after ~20 Myr

10.9 CZ
Relative m/Mmass* [M★]

Mini=0.01M⊙
Mfin=1M⊙
Ṁ=10-5M⊙/yr
ξ=0, XD=2.0×10-5

0.8
0.6
0.4
0.20104base of CZ
in classicalevolution
105

106

107
Timet [yr][yr]radiative
108

1091010low-entropy accretion:
CZ shrinks much faster●smaller radius→higher internal temperature→smaller opacity→radiative zone can be developed
more easily

Mini=0.01M⊙
Mfin=1M⊙
Ṁ=10-5M⊙/yr
ξ=0, XD=2.0×10-5

Internal structure evolution
with low-entropy accretion■low-entropy accretion■ age when mass in CZ
becomes 0.1M⊙
low-entropy acc.: 2.7Myr

1

Relative m/Mmass* [M★]

0.9 CZ
0.8

2.7Myr

0.624Myr•~10 times faster than theclassical evolution•shorter than the typicaldisk lifetime (~6Myr)

0.4
0.20104base of CZin classicalevolution
105

106

107
Timet [yr][yr]radiative
108

109

1010

Pollution of stellar surface by planet formation•thin CZ within the disk lifetime•metal-poor accretion due to formation of rocky planets→stellar surface can be polluted to be metal-poor composition
accreting materials are mixed only in CZ

thinsurface
CZ

rad.
core

(e.g., Chambers10,Ramirez+14)

rockyobjects

metal-poor gas(e.g.,Guillot, Ida+Ormel 14)classical evolution: tdisk ≪ tCZ→pollution to the fully convective staris negligible

Planet formation can affect the host star’s surface composition
This process may be the solution of•the solar/stellar anomaly of composition•the solar metallicity problem

We derive the conditionin which this mechanism
occurs (tdisk>tcz)

Mini=0.01M⊙
Mfin=1M⊙
Ṁ=10-5M⊙/yr

0.1
0.08
0.06

10Myr

126Myr103Myr

80.04

60.02 3Myr
01405 10 15 20 25 30 35 40
deuterium[ppm]
DD
Deuterium
masscontent
fractionXX
in ppm

420

when
MCZ
=0.1M⊙⊙[Myr][Myr]
AgeAgewhen
MCZ=0.1M

Heat
injectionefficiency
efficiencyξ ξheat injection

Age of CZ shrinkage

estimated XD ofprotosolar nebula

terrestrial planet
formation can be
imprinted to thestellar surface• CZ shrinks before disk lifetime in low ξ and XD• given low entropy accreted (ξ=0-0.02), the solar surface
composition anomaly can be made by planet formation processSummary
We calculated PMS evolutions with the low-entropy accretion and found(1) stars formed by the low-entropy accretion evolve with the much lower
radius and luminosity than the classical evolution→aﬀects the estimation of stellar mass and age,disk evolution, and planet formation(2) the PMS evolution strongly depends on the heat injection efficiency anddeuterium content(3) the luminosity spread problem and the solar composition anomaly can be
explained by the low-entropy accretion(4) multidimensional RHD simulations are needed to determine the accreting
materials’ entropy

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