Formation of Brown Dwarfs
PHY 688, Lecture 30
Apr 15, 2009
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
2
Previously in PHY 688…
Apr 15, 2009
PHY 688, Lecture 30
3
Planet Mass and Period Distribution
• dN = CMαPβ dlnM dlnP
α = –0.31 ± 0.2
β = 0.26 ± 0.1
N(M,P) – cumulative
number of planets with
masses up to M and
periods up to P
• i.e., dN/dM ∝ Mα–1;
dN/dP ∝ Pβ–1
(Cummings
Apr 15, 2009 et al. 2008)
PHY 688, Lecture 30
4
Planet Mass and Period Distribution
• dN = CMαPβ dlnM dlnP
α = –0.31 ± 0.2
β = 0.26 ± 0.1
N(M,P) – cumulative
number of planets with
masses up to M and
periods up to P
• i.e., dN/dM ∝ Mα–1;
dN/dP ∝ Pβ–1
• deficit of gas giant
planets in 10–100 day
periods
Apr 15, 2009
PHY 688, Lecture 30
(Cummings et al. 2008)
5
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
(Cummings et al. 2008) 6
Precision Radial Velocity Planets
• general trends:
– minimum mass
distribution
– semi-major axis
distribution
– eccentricity vs. semimajor axis
Apr 15, 2009
PHY 688, Lecture 30
(Marcy et al. 2008)
7
Precision Radial Velocity Planets
• general trends:
– minimum mass
distribution
– semi-major axis
distribution
– eccentricity vs. semimajor axis
– host mass
distribution
Apr 15, 2009
PHY 688, Lecture 30
(Marcy et al. 2008)
8
Precision Radial Velocity Planets
• general trends:
– minimum mass
distribution
– semi-major axis
distribution
– eccentricity vs. semimajor axis
– host mass distribution
– host metallicity
dependence
Apr 15, 2009
(Santos et al. 2004;
PHY 688, Lecture 30
Valenti & Fischer 2008)
9
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 isolated
brown dwarfs and stars
is co-spatial
(Luhman
Apr 15, 2009et al. 2007)
PHY 688, Lecture 30
10
The (Sub)stellar Initial Mass Function
(~1 Myr)
(~2 Myr)
(~1 Myr)
•
(~1 Myr)
The IMF is approximately consistent among various star-forming regions
Apr 15, 2009
PHY 688, Lecture 30
(Luhman et al. 2007)
11
The Universal Mass Function
(traced by solid points in
figure to the right)
ξ(m) = dN/dm ∝ m–α
α = 0.3 ± 0.7
0.01 ≤ m/MSun< 0.08
α = 1.3 ± 0.5
0.08 ≤ m/MSun< 0.50
α = 2.3 ± 0.3
0.50 ≤ m/MSun
BD: brown dwarfs
MD/KD: M/K dwarfs
IMS:
intermediate-mass stars, etc
Apr
15, 2009
PHY 688, Lecture 30 (Kroupa 2002; Kroupa & Bouvier 2003)12
Binaries: Separation Increases with
Total Mass
Apr 15, 2009
PHY 688, Lecture 30
(Burgasser et al. 2007)
13
Binaries:
Period Distribution of FGK Stars
• log-normal
%# log P # log P
(
f (log P) " exp'
2
2$ log
'&
P
0.1
)
2
1
10
100 1000 AU
(
*
*)
log P = 4.8
2
$ log
(P in days)
P = 2.3
Apr 15, 2009
PHY 688, Lecture 30
(Duquennoy & Mayor 1991)
14
(Sub)stellar Companions: Mass Function
and the R.V. Brown Dwarf “Desert”
P < 8 yr
(a < 4 AU)
Apr 15, 2009
planets
brown
dwarfs
10–15% <0.5%
PHY 688, Lecture 30
stars
~22%
(Mazeh et al. 2003)
15
Binaries: Period Distribution
• log-normal
• r.v. brown dwarf
desert partly due to
0.1
radial velocity
~0.5% BDs
1
10
100 1000 AU
direct imaging
~3% BDs
– fewer binaries
with short periods
– fewer low-mass
ratio (q<0.1)
systems
(Duquennoy & Mayor 1991)
Apr 15, 2009
PHY 688, Lecture 30
16
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
17
Brown Dwarfs Form
Like H-Burning Low-Mass Stars
• statistical properties of brown dwarfs form a continuum
with those of low-mass stars
– homogeneously mixed in star-forming regions
Apr 15, 2009
PHY 688, Lecture 30
18
Stars and Brown Dwarfs Are
Homogeneously 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 brown
dwarfs and stars is co-spatial
star and brown dwarf spatial
kinematics are indistinguishable
RV = 15.7 ± 0.9 km/s for BDs in
Chamaeleon I (~2 Myr old)
RV = 14.7 ± 1.3 km/s for stars
(Luhman
Apr 15, 2009et al. 2007)
PHY 688, Lecture 30
19
Brown Dwarfs Form
Like H-Burning Low-Mass Stars
• statistical properties of brown dwarfs form a continuum
with those of low-mass stars
– homogeneously mixed in star-forming regions
– initial mass function (IMF) continuity
Apr 15, 2009
PHY 688, Lecture 30
20
IMF Is Continuous across
Substellar Boundary
(~1 Myr)
(~2 Myr)
(~1 Myr)
Apr 15, 2009
(~1 Myr)
PHY 688, Lecture 30
(Luhman et al. 2007)
21
Brown Dwarfs Form
Like H-Burning Low-Mass Stars
• statistical properties of brown dwarfs form a continuum
with 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
22
Binaries Separations Vary Gradually
across Substellar Boundary
Apr 15, 2009
PHY 688, Lecture 30
(Burgasser et al. 2007)
23
(Sub)stellar Companions: Mass Function
and the R.V. Brown Dwarf “Desert”
P < 8 yr
(a < 4 AU)
Apr 15, 2009
planets
brown
dwarfs
10–15% <0.5%
PHY 688, Lecture 30
stars
~22%
(Mazeh et al. 2003)
24
Companion Mass Function Is Continuous
across Substellar Boundary
100-star Palomar AO survey (~1 M primaries)
CMF: a = 30–1600 AU
field MF (Chabrier 2003)
dN / dM ∝ M–0.4
brown dwarfs
~3%
Apr 15, 2009
(Kouwenhoven
et al.
PHY 688, Lecture
30 2005; Metchev & Hillenbrand 2009)
25
Brown Dwarfs Form
Like H-Burning Low-Mass Stars
• statistical properties of brown dwarfs form a continuum
with 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
26
Disk Accretion Rates Are Continuous
across Substellar Boundary
(Muzerolle et al. 2005)
Apr 15, 2009
PHY 688, Lecture 30
27
Brown Dwarfs Form
Like H-Burning Low-Mass Stars
• statistical properties of brown dwarfs form a continuum
with 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
28
X-ray Activity Is
Continuous …
• … across
substellar
boundary
(Preibisch et al. 2005)
Apr 15, 2009
PHY 688, Lecture 30
29
Brown Dwarfs Form
Like H-Burning Low-Mass Stars
• statistical properties of brown dwarfs form a continuum
with 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
30
From Lecture 6: Star Formation
Occurs in Molecular Clouds
• Jeans mass
– minimum mass / density for
gravitational collapse
$ " 5c s6 '1 2
MJ = &
3 )
% 36G # (
sound speed
$
' 3 $ n '+1 2
cs
* (2MSun )&
+1 ) &
3
+3 )
% 0.2kms ( % 10 cm (
or
" 5c s6
#J ,
36G 3 M J2
• collapse occurs on free-fall
(dynamical) time-scale
!
t ff " #
Apr 15, 2009
PHY 688, Lecture 30
!
( R 2)
32
12
(GM )
& $ )%1 2
" 35min (
%3 +
' g cm *
31
Theories of Gravitational Collapse
and 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 shockcompressed layer or filament → filaments fragment directly into pre-stellar
cores 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
32
Thermodynamics of Collapse and
Fragmentation
• 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 the
opacity limit
Mmin ~ 0.003 MSun ~ 3MJup
Apr 15, 2009
PHY 688, Lecture 30
33
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 nonlinear
• proto-fragments increase their mass by a large factor through
accretion
– can not form low-mass stars
• individual fragments will be back-warmed by ambient radiation
field from other cooling fragments
– increases Jeans mass, so again can not form low-mass stars
Apr 15, 2009
PHY 688, Lecture 30
34
2-D One-Shot Fragmentation of
Shock-Compressed Layers
• 2-D ≡ fragment assembly motions are within plane of compressed
layer
• 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 outside
of 2-D layer
⇒ low-mass star formation pathways are preserved
• avoids all problems of 3-D fragmentation
Apr 15, 2009
PHY 688, Lecture 30
35
Fragmentation of a Circumstellar Disk
• fragmentation occurs in disks with sufficiently large surface
density (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 fragment
into 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 and
brown dwarfs in disks around massive stars
Apr 15, 2009
PHY 688, Lecture 30
36
Numerical Simulations of Star
Formation
Apr 15, 2009
PHY 688, Lecture 30
37
Star Formation: Low vs. High
Initial Density
Apr 15, 2009
PHY 688, Lecture 30
38
Star Formation: without vs. with
Radiative Feedback
Apr 15, 2009
PHY 688, Lecture 30
39