The Local Galactic Escape Velocity: Bootstrap Analysis

1
The Local Galactic Escape Velocity Bootstrap
Analysis

• Gregory Ruchti
• Advisor Rosie Wyse
• (Johns Hopkins University)
• In collaboration with M. Smith, A. Helmi, M.
  Williams, J. Navarro, K. Freeman

2
Short-comings of method for finding escape
velocity

• Our method, as described by Martin Smith in his
  talk, assumes the sample of stellar velocities is
  representative of an underlying equilibrium
  distribution which may not be the case
• And that the underlying stellar halo distribution
  function is isotropic

3
Short-comings of method for finding escape
velocity

• Assumes sample of stellar velocities is
  representative of an underlying equilibrium
  distribution which may not be the case
• Binary Systems
• Center-of-mass velocity has not been measured
  accurately.
• Radial velocity from one observation may be
  inflated by orbital motion typical amplitudes of
  30km/s (Latham et al. 2002) but may be higher
• ltVorbgt 30 km/s X 2-2/3 X M (M?) /P (yrs)1/3

4
Short-comings of method for finding escape
velocity

• Assumes sample of stellar velocities is
  representative of an underlying equilibrium
  distribution which may not be the case
• Binary systems
• Populating the High-velocity Tail
• Ejected stars from binary systems.
• Hypervelocity stars ejected from super-massive BH
  at the Galactic center
• 6 extreme velocity (vgalacto,los gt 500 km/s)
  stars are known, plausibly on orbits consistent
  with SMBH interaction (Brown et al. 2006)

5
Short-comings of method for finding escape
velocity

• Assumes sample of stellar velocities is
  representative of an underlying equilibrium
  distribution which may not be the case
• Binary systems
• Populating the High-velocity Tail
• Hierarchical clustering and merging model
• Continually changing velocity distribution
• function.

6
Short-comings of method for finding escape
velocity

• Assumes distribution of stellar velocities is in
  equilibrium which may not be the case
• Binary systems
• Populating the High-velocity Tail
• Hierarchical clustering and merging model
• Disruption of globular clusters to streams
• Must be careful to reduce sensitivity to such
  non-equilibrium velocities.

7
The Bootstrap

• Performs resampling on original data set to
  reduce sensitivity to extreme velocities.
• Allows us to evaluate the likelihood for both ve
  and k simultaneously.
• Not possible (for samples lt 200 stars) using
  straight likelihood method.

8
The Bootstrap Analysis

• DF
• ? kr k 1
• Maximize for ve and kr
• Choice of a priori probability distributions for
  ve and kr less clear for the bootstrap technique.
• Derived many priors to apply to analysis for
  improved statistical analysis.

9
Tests of the Bootstrap

• Random samples drawn from velocity distribution
  function assuming
• ? ve600 km/s, kr2.0, vmin260 km/s
• 20 star sample
• Does not return input values for every prior.
• Clear variation in results from different priors.
• Confidence intervals must be studied carefully.

10
Tests of the Bootstrap

• Random samples drawn from velocity distribution
  function assuming
• ? ve600 km/s, kr2.0, vmin260 km/s
• 50 star sample
• Returns assumed input values within error
• Slight variation in confidence interval endpoints
  from different priors.

11
Tests of the Bootstrap

• Random samples drawn from velocity distribution
  function assuming
• ? ve600 km/s, kr2.0, vmin260 km/s
• 200 star sample
• Returns input values.
• Results identical for all priors
• Choice of prior not important for large
• number statistics.

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Tests of the Bootstrap

• Sensitivity to kinematic streams
• 20 of sample with constant velocity,
• vgalacto 300 km/s
• Stellar samples of lt 50 stars
• Clear shift in estimated values for original data
  set
• However, confidence intervals still contain
  assumed values of ve and kr
• 200 stars or more
• Shift is negligible
• Bootstrap good for reducing sensitivity to streams

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The RAVE Data

• Galactocentric Radial Velocities
• Converted from Heliocentric assuming
• vLSR 220 km/s
• solar peculiar motion (10.00,5.25,7.17) km/s.
• Chose correlation function R gt 15 cut-off.
• Chose vmin cuts of 270 km/s and 300 km/s.
• RAVE samples
• 25 stars, vgalacto gt 270 km/s
• 14 stars, vgalacto gt 300 km/s

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The RAVE Data

• Most high-velocity stars only have 1 observation
  within RAVE database.
• Follow-up observations
• 2.3m ATT, Australia (Mary Williams and Ken
  Freeman)
• 3.5m at Apache Point Observatory, NM (with Jon
  Fulbright)

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APO Data

• Data obtained using single-slit echelle
  spectrograph (spectral resolution 37,000).
• Observed 5 high-velocity stars.
• Radial velocity measurements agreed with RAVE
  velocities within 2.5 0.5 km/s. (Even one
  binary! Really need more than two observations.)
• Gravities were derived from spectra
• discussed later

16
Reduced Proper Motion

• RPM diagram of entire high velocity (gt 270 km/s)
  sample.
• Isochrones from Bonatto et al. (2004)
• Significant fraction of stars are most likely
  halo giants.
• Good!
• At these magnitudes and inferred metallicities,
  stars are few kpc distant
• Need to model v_escape from non-local sample

Thin Solid (thin disk) vtan20 km/s, Z0.019,
age2.5 Gyr Dashed (thick disk) vtan46 km/s,
Z0.004, age10 Gyr Thick Solid (halo) vtan200
km/s, Z0.001, age10 Gyr
17
Reduced Proper Motion

• Red Triangles represent those stars with
  velocities gt 300 km/s.
• Clearly these stars can be considered halo
  giants.
• One star may be a blue horizontal branch star.
  (shown as blue triangle.)

Thin Solid (thin disk) vtan20 km/s, Z0.019,
age2.5 Gyr Dashed (thick disk) vtan46 km/s,
Z0.004, age10 Gyr Thick Solid (halo) vtan200
km/s, Z0.001, age10 Gyr
18
Reduced Proper Motion

• Stars of which APO gravities were derived are
  shown as blue diamonds.
• Computed gravities match with being halo giants
  consistent with RPMD
• Derived gravity consistent with the bluest star
  being a BHB star but uncertain

Thin Solid (thin disk) vtan20 km/s, Z0.019,
age2.5 Gyr Dashed (thick disk) vtan46 km/s,
Z0.004, age10 Gyr Thick Solid (halo) vtan200
km/s, Z0.001, age10 Gyr
19
Isotropy Around Zero

• Most samples have halo anisotropic (e.g. Chiba
  Beers 2000).
• Positive vs. Negative velocities appear to have
  same distribution.
• However, small number statistics.

Squares Positive Velocity Diamonds Negative
Velocity
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Complementary Data

• Included high-velocity stars from Nordstrom et
  al. (2004) (10 stars)
• Magnitude-limited sample of F/G stars (like RAVE,
  no kinematics or metallicity bias)
• Increases sample size for better statistics.
• Has metallicity information and full space
  motions for stars use only line-of-sight
  velocities

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Bootstrap Results

• RAVE only
• Vmin270 km/s (25 stars)
• ve520 km/s, 90 conf.430,615
• kr2.5, 90 conf.1.0,5.0
• Vmin300 km/s (14 stars)
• ve560 km/s, 90 conf.430,710
• kr3.5, 90 conf.1.0,7.0

22
Bootstrap Results

• RAVE plus Nordstrom
• Vmin270 km/s (35 stars)
• ve550 km/s, 90 conf.450,642
• kr3.0, 90 conf.1.0,5.0
• Vmin300 km/s (16 stars)
• ve550 km/s, 90 conf.450,700
• kr3.5, 90 conf.1.0,7.2

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Concluding Remarks

• Bootstrap holds promise our sample of
  high-velocity stars.
• Although, clearly need more data and repeat
  observations.

24
APO Data

• Gravities were derived from spectra
• C0953535-083919, log g 1.89
• C1100242-024226, log g 4.5
• C2041305-113156, log g 1.75
• T4931-00266-1 , log g 1.45
• First pass to check velocities, will follow-up to
  get elemental abundances

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L,B of Stars
Circles 250,270) Squares 270,300) Diamonds 3
00,)