Formation of Brown Dwarfs - Stony Brook University · Apr 15, 2009 PHY 688, Lecture 30 19 Stars and Brown Dwarfs Are Homogeneously Mixed • e.g., Taurus molecular cloud – nearest

Formation of Brown Dwarfs

PHY 688, Lecture 30Apr 15, 2009

Apr 15, 2009 PHY 688, Lecture 30 2

Outline• Course administration

– final presentations reminder• see me for paper recommendations 2–3 weeks before talk:

Apr 27–May 1 talks– class re-scheduling reminder

• no class Apr 17, Fri (ASNY mtg)– attend Apr 15 (Wed) talk by Eric Jensen, 1pm ESS 450

• no class Apr 24, Fri (Astro2010 Town Hall mtg)– two 1.5-hour classes on Apr 27, 29 (Mon, Wed): 10:40–12:00pm

• Review of previous lecture– substellar populations: planets, brown dwarfs

• Formation of brown dwarfs– empirical evidence– theoretical scenarios

Apr 15, 2009 PHY 688, Lecture 30 3

Previously in PHY 688…

Apr 15, 2009 PHY 688, Lecture 30 4

Planet Mass and Period Distribution• dN = CMαPβ dlnM dlnP

α = –0.31 ± 0.2β = 0.26 ± 0.1N(M,P) – cumulative

number of planets withmasses up to M andperiods up to P

• i.e., dN/dM ∝ Mα–1;dN/dP ∝ Pβ–1

(Cummings et al. 2008)

Apr 15, 2009 PHY 688, Lecture 30 5

Planet Mass and Period Distribution


• dN = CMαPβ dlnM dlnPα = –0.31 ± 0.2β = 0.26 ± 0.1N(M,P) – cumulative

number of planets withmasses up to M andperiods up to P

• i.e., dN/dM ∝ Mα–1;dN/dP ∝ Pβ–1

• deficit of gas giantplanets in 10–100 dayperiods

Apr 15, 2009 PHY 688, Lecture 30 6

Exoplanet Frequency

• statistics and extrapolations are for Sun-like (spectral type FGK; ~1 MSun) stars• M dwarfs (<0.5 MSun) are 5–10 times less likely to have M sin i = 0.3–10 MJup

planets in P < 2000 days


Apr 15, 2009 PHY 688, Lecture 30 7

Precision Radial Velocity Planets• general trends:

– minimum massdistribution

– semi-major axisdistribution

– eccentricity vs. semi-major axis

(Marcy et al. 2008)

Apr 15, 2009 PHY 688, Lecture 30 8





– host massdistribution

(Marcy et al. 2008)

Apr 15, 2009 PHY 688, Lecture 30 9





– host mass distribution– host metallicity

dependence

(Santos et al. 2004;Valenti & Fischer 2008)

Apr 15, 2009 PHY 688, Lecture 30 10

Low-mass Star Formation• e.g., Taurus molecular

cloud– nearest star-forming

region– 1 Myr age– 140 pc away– 50 pc across

• brow dwarfs: SpT > M6– red crosses

• stars: SpT ≤ M6– blue circles

• formation of isolatedbrown dwarfs and starsis co-spatial

(Luhman et al. 2007)

Apr 15, 2009 PHY 688, Lecture 30 11

The (Sub)stellar Initial Mass Function

• The IMF is approximately consistent among various star-forming regions

(~1 Myr) (~2 Myr)

(~1 Myr) (~1 Myr)


Apr 15, 2009 PHY 688, Lecture 30 12

The Universal Mass Function

(Kroupa 2002; Kroupa & Bouvier 2003)

(traced by solid points infigure to the right)

ξ(m) = dN/dm ∝ m–α

α = 0.3 ± 0.70.01 ≤ m/MSun< 0.08

α = 1.3 ± 0.50.08 ≤ m/MSun< 0.50

α = 2.3 ± 0.30.50 ≤ m/MSun

BD: brown dwarfsMD/KD: M/K dwarfsIMS: intermediate-mass stars, etc

Apr 15, 2009 PHY 688, Lecture 30 13

Binaries: Separation Increases withTotal Mass

(Burgasser et al. 2007)

Apr 15, 2009 PHY 688, Lecture 30 14

Binaries:Period Distribution of FGK Stars

• log-normal100 1000 AU100.1 1

(Duquennoy & Mayor 1991)

!

f (logP)"exp# logP # logP( )

2

2$ logP

2

%

&

' '

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)

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logP = 4.8

$ logP

2 = 2.3 (P in days)

Apr 15, 2009 PHY 688, Lecture 30 15

(Sub)stellar Companions: Mass Functionand the R.V. Brown Dwarf “Desert”

planetsplanets

1010––15%15%

brownbrowndwarfsdwarfs<0.5%<0.5%

starsstars

~22%~22%

P < 8 yr(a < 4 AU)

(Mazeh et al. 2003)

Apr 15, 2009 PHY 688, Lecture 30 16

Binaries: Period Distribution

• log-normal

• r.v. brown dwarfdesert partly due to– fewer binaries

with short periods– fewer low-mass

ratio (q<0.1)systems

100 1000 AU100.1 1

radial velocity~0.5% BDs

direct imaging~3% BDs

(Duquennoy & Mayor 1991)

Apr 15, 2009 PHY 688, Lecture 30 17

Outline• Course administration

– final presentations reminder• see me for paper recommendations 2–3 weeks before talk:

Apr 27–May 1 talks– class re-scheduling reminder

• no class Apr 17, Fri (ASNY mtg)– attend Apr 15 (Wed) talk by Eric Jensen, 1pm ESS 450

• no class Apr 24, Fri (Astro2010 Town Hall mtg)– two 1.5-hour classes on Apr 27, 29 (Mon, Wed): 10:40–12:00pm

• Review of previous lecture– substellar populations: planets, brown dwarfs

• Formation of brown dwarfs– empirical evidence– theoretical scenarios

Apr 15, 2009 PHY 688, Lecture 30 18

Brown Dwarfs FormLike H-Burning Low-Mass Stars

• statistical properties of brown dwarfs form a continuumwith those of low-mass stars– homogeneously mixed in star-forming regions

Apr 15, 2009 PHY 688, Lecture 30 19

Stars and Brown Dwarfs AreHomogeneously Mixed

• e.g., Taurus molecular cloud– nearest star-forming region– 1 Myr age– 140 pc away– 50 pc across

• brow dwarfs: SpT > M6– red crosses

• stars: SpT ≤ M6– blue circles

• formation of isolated browndwarfs and stars is co-spatial

• star and brown dwarf spatialkinematics are indistinguishable

RV = 15.7 ± 0.9 km/s for BDs inChamaeleon I (~2 Myr old)

RV = 14.7 ± 1.3 km/s for stars


Apr 15, 2009 PHY 688, Lecture 30 20


• statistical properties of brown dwarfs form a continuumwith those of low-mass stars– homogeneously mixed in star-forming regions– initial mass function (IMF) continuity

Apr 15, 2009 PHY 688, Lecture 30 21

IMF Is Continuous acrossSubstellar Boundary

(~1 Myr) (~2 Myr)

(~1 Myr) (~1 Myr)


Apr 15, 2009 PHY 688, Lecture 30 22


• statistical properties of brown dwarfs form a continuumwith those of low-mass stars– homogeneously mixed in star-forming regions– initial mass function (IMF) continuity– continuity in binary properties

Apr 15, 2009 PHY 688, Lecture 30 23

Binaries Separations Vary Graduallyacross Substellar Boundary

(Burgasser et al. 2007)

Apr 15, 2009 PHY 688, Lecture 30 24

(Sub)stellar Companions: Mass Functionand the R.V. Brown Dwarf “Desert”

planetsplanets

1010––15%15%

brownbrowndwarfsdwarfs<0.5%<0.5%

starsstars

~22%~22%

P < 8 yr(a < 4 AU)

(Mazeh et al. 2003)

Apr 15, 2009 PHY 688, Lecture 30 25

Companion Mass Function Is Continuousacross Substellar Boundary

field MF (Chabrier 2003)CMF: a = 30–1600 AU

100-star Palomar AO survey (~1 M primaries)

brown dwarfs~3%

dN / dM ∝ M–0.4

(Kouwenhoven et al. 2005; Metchev & Hillenbrand 2009)

Apr 15, 2009 PHY 688, Lecture 30 26


• statistical properties of brown dwarfs form a continuumwith those of low-mass stars– homogeneously mixed in star-forming regions– initial mass function (IMF) continuity– continuity in binary properties– disks, accretion, and outflows

Apr 15, 2009 PHY 688, Lecture 30 27

Disk Accretion Rates Are Continuousacross Substellar Boundary

(Muzerolle et al. 2005)

Apr 15, 2009 PHY 688, Lecture 30 28


• statistical properties of brown dwarfs form a continuumwith those of low-mass stars– homogeneously mixed in star-forming regions– initial mass function (IMF) continuity– continuity in binary properties– disks, accretion, and outflows– rotation and x-rays

Apr 15, 2009 PHY 688, Lecture 30 29

X-ray Activity IsContinuous …

• … acrosssubstellarboundary

(Preibisch et al. 2005)

Apr 15, 2009 PHY 688, Lecture 30 30


• statistical properties of brown dwarfs form a continuumwith those of low-mass stars– homogeneously mixed in star-forming regions– initial mass function (IMF) continuity– continuity in binary properties– disks, accretion, and outflows– rotation and x-rays

• A single formation mechanism is likely responsible for~0.01–100 MSun “stars”– upper limit set by radiation pressure– lower limit set by gas opacity– possible overlap with planetary mass range (<0.015 MSun)

Apr 15, 2009 PHY 688, Lecture 30 31

From Lecture 6: Star FormationOccurs in Molecular Clouds

• Jeans mass– minimum mass / density for

gravitational collapse

• collapse occurs on free-fall(dynamical) time-scale

!

MJ

=" 5cs

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1 2

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sound speed

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tff " #R 2( )

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g cm%3

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%1 2

Apr 15, 2009 PHY 688, Lecture 30 32

Theories of Gravitational Collapseand Fragmentation

• 3-D collapse and hierarchical fragmentation– isothermal collapse of optically thin cloud → ρJ increases → parts of the

cloud start collapsing independently (fragmentation)– fragmentation continues until heat from collapsing fragments can no longer

be radiated away because of high rate of collapse or high (>1) optical depth:the opacity limit of fragmentation

• 2-D “one-shot” fragmentation of shock-compressed layers– star formation occurs where turbulent flows collide → produce a shock-

compressed layer or filament → filaments fragment directly into pre-stellarcores with masses down to opacity limit

• fragmentation of a circumstellar disk– gravitationally unstable (massive) disk fragments → fragments rapidly cool

and loose angular momentum, thus forming pre-stellar cores

Apr 15, 2009 PHY 688, Lecture 30 33

Thermodynamics of Collapse andFragmentation

• collapse occurs if M > MJ or ρ > ρJ• for fragment to continue collapsing, it must

radiate away PdV heat efficiently– medium must be optically thin– luminosity > heat ⇒ maximum critical density ρcrit

beyond which medium becomes optically thick– i.e., need ρJ < ρ < ρcrit

• minimum collapsing mass Mmin has ρJ ~ ρcrit at theopacity limitMmin ~ 0.003 MSun ~ 3MJup

Apr 15, 2009 PHY 688, Lecture 30 34

Problems with 3-D Fragmentation• no conclusive evidence that it operates in nature• not seen in numerical simulations• proto-fragments collapse more slowly than larger structure because

of being less Jeans unstable– likely to merge with other fragments before condensation becomes non-

linear

• proto-fragments increase their mass by a large factor throughaccretion– can not form low-mass stars

• individual fragments will be back-warmed by ambient radiationfield from other cooling fragments– increases Jeans mass, so again can not form low-mass stars

Apr 15, 2009 PHY 688, Lecture 30 35

2-D One-Shot Fragmentation ofShock-Compressed Layers

• 2-D ≡ fragment assembly motions are within plane of compressedlayer

• one-shot ≡ not hierarchical• fastest-growing fragments become Jeans unstable

– no larger structure that is even less stable against Jeans collapse– hence, unlike in 3-D hierarchical fragmentation, fragments do not merge

• condensation in a layer is very fast– limited accretion

• no back-warming from ambient fragments, since none exist outsideof 2-D layer

⇒ low-mass star formation pathways are preserved

• avoids all problems of 3-D fragmentation

Apr 15, 2009 PHY 688, Lecture 30 36

Fragmentation of a Circumstellar Disk

• fragmentation occurs in disks with sufficiently large surfacedensity (Toomre instability)– fragmentation must occur on dynamical time scale, or spiral arms are formed

that dissolve the over-density

• two critical conditions then need to be met to condense fragmentinto a pre-stellar core:– fragment needs to quickly radiate away thermal energy from compression

• also on dynamical time scale (~ days – years)– angular momentum needs to be efficiently removed

• by gravitational torques in the disk

• potentially a viable mechanism for forming low-mass stars andbrown dwarfs in disks around massive stars

Apr 15, 2009 PHY 688, Lecture 30 37

Numerical Simulations of StarFormation

Apr 15, 2009 PHY 688, Lecture 30 38

Star Formation: Low vs. HighInitial Density

Apr 15, 2009 PHY 688, Lecture 30 39

Star Formation: without vs. withRadiative Feedback

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Formation of Brown Dwarfs - Stony Brook University · Apr 15, 2009 PHY 688, Lecture 30 19 Stars and Brown Dwarfs Are Homogeneously Mixed • e.g., Taurus molecular cloud – nearest