Michael Solway J A Sellwood and Ralph Schönrich Michael Solway

T ti R
Testing
Radial
di l Mi
Migration
ti iin Thi
Thickk Disks
Di k
Michael Solway1, JJ. A
A. Sellwood1, and Ralph Schönrich2
1Rutgers,
R
Th
The SState U
University
i
i off N
New Jersey
J
2Max-Planck-Institut
M Pl k I i
fü
für A
Astrophysik
h ik
R di l Migration
Radial
Mi ti
S
Summary
• Stars that corotate* with a steadily rotating spiral undergo large
changes
h
i angular
in
l momentum
t
and
d move to
t new radii
dii while
hil
remaining on nearly circular orbits by riding the spiral
spiral’ss potential.
potential
•We
W have
h
extended
d d Sellwood
S ll
d & Binney’s
Bi
’ (2002) workk on radial
di l migration
i
i in
i 2D razor-thin
hi disks
di k
to 3D thickened disks using two-component (thin and thick disks) N-body simulations.
simulations
•We
We have shown that the mechanism persists in thickened disks:
• Its extent decreases with increasing disk thickness
• But remains strong for disks as thick as that of the Milky Way
• It is weaker for disks with greater radial velocity dispersion
• Multiple
l i l spirals
i l accumulate
l the
h effect
ff to a stronger net radial
di l migration
i
i
• The presence of a bar strengthens it slightly further
•This
This reinforces the key assumption made by Schönrich & Binney (2009) that radial migration
occurs in the thick disk of their Galaxy
y chemical evolution model,, which reproduces
p
various
observed properties of the metallicity gradients in both stars and gas.
•We found that vertical action is conserved, not vertical energy as assumed by Schönrich &
Bi
Binney
(2009) when
(2009),
h stars
t gain
i or lose
l
angular
l momentum
t
d i radial
during
di l migration.
i ti
∗ Move
M
with
ith the
th wave.
• Multiple spiral activity, over time, causes radial diffusion of stars.
• Stars can migrate
g
far from their birth radii.
• A single
g stellar age
g bin ends upp containing
g a wide range
g of
angular momenta and formation environments that are not
correlated together.
• This explains why the metallicity gradient is shallower for
older
ld stars.
t
Si l T
Single
Two-Armed
A
dS
Spiral
i l
Simulation Setup
p
• Controlled simulation with a single seeded spiral
in order to measure angular momentum changes
d to
due
t one spiral
i l only.
l
• Two
T o active
acti e 3D components: thin & thick disks
Evolution of the thin and thick disks,
disks showing the growth and decay of a spiral,
spiral which makes a full rotation every 45.5
45 5 time units.
units
rms Changes in Angular Momentum
Varying Disk Thickness and Radial Velocity Dispersion of the Thick Disk
The filled symbols show rms ΔLz as a function of
scale height
g z0 ((bottom axis)) of different thick disk
particle populations that only vary in z0. The black
squares are for all the particles in the angular
momentum range 2.5 < Lz(t = 0) < 10.0, while the
red triangles are for only those particles having
vertical extents greater than z0.
Th green plus
The
l symbols
b l show
h
th variation
the
i ti off rms
ΔLz with initial radial velocityy dispersion
p
σR ((top
p
axis) of all the particles in the same Lz(t = 0) range
from thick disks that vary only in σR. The blue
crosses are for only those with vertical extents
greater than z0, which is fixed at 1.2.
12
Thin: 〈(ΔLz)2〉1/2 = 1.59
Thick: 〈(ΔLz)2〉1/2 = 0.97
ΔLz is measured by subtracting the specific angular
momentum
t
off a particle
ti l att the
th initial
i iti l time
ti t = 0.0
0 0 from
f
that at the final time t = 387.2.
Radial migration occurs in thick disks,
disks
is weaker than in the thin,
b t its
but
it extent
t t is
i only
l slightly
li htl smaller.
ll
Radial
R
di l migration
i ti
weakens
k
with
ith increasing
i
i
disk thickness, because the potential of the
spiral
decreases
about
exponentially
vertically
ti ll away from
f
th midplane.
the
id l
S more
So
vertically-energetic
y
g
pparticles gget affected less.
Conserved Quantity of Vertical Motion
Schönrich & Binneyy ((2009),
), in their chemical model of
Galaxy evolution, assumed that the vertical energy is
conserved as stars undergo radial migration,
migration making
their vertical and radial motions decoupled.
It iss aalso
so wea
weaker
e for
o increasing
c eas g radial
ad a ve
velocity
oc y
dispersion, because more eccentric stars
cannot hold station with the steadily rotating
spiral
p
as well,, since their angular
g
velocities
vary more as they oscillate radially.
We tested this assumption by measuring changes of
various estimates of vertical energy and vertical action
in the single two-armed spiral simulation.
We found that vertical action,
action not vertical energy,
energy
is conserved:
For all the estimates of the action, the mean and
median ΔJz are zero no matter what ΔLz is.
is
Whereas the mean and median ΔEz correlate with
Whereas,
ΔLz for all the estimates of the energy:
Negative for outwards migrating particles and
positive
iti for
f inwards
i
d migrating
i ti particles.
ti l
Multiple
p Transient Spirals
p
with and without a Bar
Choice of Units
Our simplified units can be scaled to physical units
b making
by
ki
• 0.75 kpc
p the unit of distance
• 3.0 Myr the unit of time
〈(ΔLz)2〉1/2 = 2.65
2 65
〈(ΔLz)2〉1/2 = 3.15
3 15
This choice makes
• 244 km⋅s-1 the unit of velocity
• 183 kpc⋅km⋅s-1 the unit of specific angular momentum
• 1.04×1010 MŸ the unit of mass
to
Multiple
p
spirals
p
yyield a net radial
migration that is stronger than in the single
spiral case.
case
Kregel
g M.,, van der Kruit P. C.,, de Grijs
j R.,, 2002,, MNRAS,, 334,, 646
Sellwood J. A., Binney J., 2002, MNRAS, 336, 785
ΔLz versus initial
i iti l Lz for
f the
th particles
ti l off the
th thin
thi
(top) and thick (bottom) disks of a simulation
with multiple transient spirals without (left) and
with ((right)
g ) a bar.
The horizontal red line denotes zero change. The
vertical blue line marks the approximate
corotation resonance of the bar. And the dashed
red line has a slope of -11 and shows the the
ΔLz = -Lz(t = 0) locus below which particles end
up on retrograde
t
d orbits.
bit
Root mean square
q
changes
g are noted in the
bottom left corners.
E h simulation
Each
i l ti
contains
t i
about
b t 20 transient
t
i t
spirals, which significantly scatter the particles
during ~ 7 Gyr. The bar contributes during the
last ~ 4.5 Gyr.
y
The slanted features correspond
scattering
g due to the latest spirals.
p
References
Schönrich R., Binney J., 2009, MNRAS, 396, 203
• Half the mass is active.
active The other half resides in
a rigid
g spherical
p
halo.
• Both disks have the same radial scale length.
• The thick disk contains 10% as much mass as the
thin, and is 3 times as thick.
• The
Th scale
l height
h i h off the
h thin
hi disk
di k is
i 1/10th its
i
radial scale length.
length This ratio agrees with the
average ratio found by Kregel, van der Kruit &
de Grijs (2002) for 34 nearby galaxies.
• The thick disk’s radial and vertical velocity
dispersions are twice as great as those of the thin.
thin
〈(ΔLz)2〉1/2
= 1.95
〈(ΔLz)2〉1/2
= 2.34
The presence of a bar yields slightly
stronger
g radial migration,
g
but the transient
spirals still dominate its extent.