Gas Flow in the Galaxy: Modeling the Bar and Spiral Patterns

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Gas Flow in the Galaxy Modeling the Bar and
Spiral Patterns

• Marco A. Martos (UNAM, Ciudad de México- U. of
  California, San Diego)
• Colaborators Miguel A. Yañez (UNAM, PhD thesis)
  Bárbara Pichardo (U. of Kentucky) Xavier
  Hernandez Edmundo Moreno (UNAM)
• Angra dos Reis, Brasil, December 2004

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• Published May 2004
• MNRAS 350, L47-L51
• A more synthetic abstract
• A spiral pattern speed of 20 km/s/kpc is
  predicted
• Starting with the 2-armed pattern of the K band,
  a 4-armed spiral is the hydro response

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The Comparison of near-infrared and optical
images of external galaxies reveal interesting
differences
Motivation
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..more examples

• It is common to observe a
• smooth, simple 2-armed
• K band pattern but a more
• structured pattern in the
• optical bands, often with
• more arms (bifurcations),
• and features people refer to
• as spurs, feathers, branches
• (images from Elmegreen D.
• 1981 Ap J) These features
• have been discussed,v.g by
• Shu, Milione Roberts (73)
• Block etal (94) Elmegreen,
• Patsis, Grosbol and group

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The Milky Way

• The conventional picture maps at least 4 arms,
  and features such as the Orion spur (where the
  Sun is placed)
• (Valleé 2002, review paper)

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..and the Milky Way as seen from
COBE/DIRBEDrimmel (2000) Drimmel and Spergel
(2001)
On the left, the 4 arms of HII regions the K
band (stars) the 2 arms model for J, K bands
(dashed) and the K-band fit (solid) surface
density of dust (right)
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Hypothesis

• The 4-armed structure is the gas response to the
  2-armed stellar pattern
• (the NIR data should be by far a better tracer of
  mass than the optically thin FIR is)
• To test that hypothesis, we start by first taking
  the locus and pitch angle of Drimmel and Spergel
  (2001) and study its dynamical self consistency

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Self-Consistency

• We model the spiral 2-armed pattern as a rigid,
  3D structure composed of many inhomogeneous
  oblate spheroids, with similar density laws
• Parameters Mass (local relative force)
  constrained by empirical correlation of Patsis,
  Contopulos Grosbol (1991) (PCG)
• From the value O 11 -13 km/s/kpc proposed by
  Lin, Yuan Shu (1969 ApJ), numbers in the range
  of 10-60 km/s/kpc have been used

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The Spiral Force Field
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Orbits in the Galactic model with spiral arms as
spheroidal structures
Bertin, Dynamics Of Galaxies
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Orbital support for ?19 km/s/kpc, spiral mass
0.0175 Mdisk)
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The Best Self-Consistent Model
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Is there another O that provides a self
consistent solution?
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Our best O and the extent of our best spiral
pattern

• Our axisymmetric model is that of Allen
  Santillán (1991), which assembles a bulge and a
  flattened disk (Miyamoto and Nagai 1975),
  together with a dark spherical halo
• We coupled to that our spiral, a superposition of
  inhomogeneous oblate spheroids along the K band
  locus with a pitch angle of 15.5? Each spheroid
  has a similar mass distribution
• The total spiral mass is fixed such that the
  local relative spiral force has a prescribed
  value, following the empirical relation of PCG
• In order to obtain the relative force (between 5
  and 10) corresponding to a Galaxy such as the
  Milky Way, the mass in the spiral is about 2 of
  the total mass in the disk
• We found that indeed the K band spiral terminates
  at the 41 resonance (confirmed observationally
  by Drimmel and Spergel 2001)
• The best self-consistency (a remarkable good
  merit function) was found at
• ?20 km/s/kpc

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What the stars and gas do (Martos et al MNRAS
2004)
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Testing our findings

• Theory recent simulations in full Galactic
  models are scarse
• Gomez-Reyes Cox (2003, ApJ) used too low a
  value for O
• But Bissantz, Englmeier and Gerhard (MNRAS 2003)
  coupled bar-spiral with a best fit model, using
  COBE DIRBE data, of 60 and 20 km/s/kpc
• Abundance Gradient in the Galaxy (Andrievsky etal
  2003) from Chepeids in R10,11 kpc, report
  abrupt change in metalicity (Iron) at corotation
  assuming O20 km/s/kpc

• Story of Star Formation in the Galaxy using
  Hypparcos data, Hernandez, Valls-Gabaud and
  Gilmore (MNRAS 2000) find an oscillatory
  component of 0.5
• Gyr over the last 3 Gyr
• De la Fuente Marcos(2) (2004) found, from age
  distribution of young globular clusters, a 0.4
  Gyr (both within 0.1 Gyr)

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Our prediction for star formation and Cosmic Ray
flux over past age
Density in g/cm3 vs azimuth along the Solar
circle
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Cosmic Ray flux and climate on Earth (Shaviv,
Phys Rev Lett 2003)
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Caveats

• No magnetic field was included (yet)
• The Galactic bar was not coupled however, see
  modeling in Pichardo, Martos and Moreno (ApJ
  2004)
• No self-gravity
• I. King (2004) ..we will not know the behavior
  of orbits..until we know the form of the bar much
  better than we know now

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What does the theory say?

• PCG in their self-consistency study of 12
  observed galaxies, in Sb and Sc types the best
  model is a nonlinear one ending at the 4/1
  resonance
• The 41 resonance generates a bifurcation of the
  arms and interarm features
• The central family of periodic orbits do not
  support a spiral pattern beyond the position of
  the 41 resonance
• Weak spirals can extend their pattern up to
  corotation
• The radial extent of 2-armed patterns is
  consistent with the
• location of, either 1. ILR 41 resonance
  OLR
• B. and D. Elmegreen (1990) optical structure
  linked to those and other resonances
• (61 11) related to outer edge of spiral
  pattern, rings, spurs, kinks
• Chernin (1999) spiral patterns with large
  scale-straight arm segments to be expected from
  shock fronts stability theory and, maybe,
  resonances
• S. Chakrabarti, Laughlin and Shu (2003) the role
  of ultraharmonic resonances, wave reflections,
  local gravitational instabilities in the
  formation of substructure akin to branches, spurs
  and feathers in a self-gravitating SID long
  before, Shu, Milione Roberts (1973) showed that
  substructure appears from ultraharmonic
  resonances

Contotopoulos and collaborators, in a series of
papers, (v.g. Patsis, Grosbol and Hiotelis 1997
and references therein)
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Optical features to be explained..Elmegreen,B.
and D. 1990 Chernin, A. 1999
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Interarm features (Patsis, Grosbol Hiotelis
1997) extraplanar features (Martos Cox 1998)
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The role of self-gravity, local gravitational
instabilities, ultraharmonics (Chakrabarti,
Laughlin Shu 2003) in branch, spur and feather
formation
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Termination at 41 Resonance
O 10 km/s/kpc
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Termination at 41 Resonance
O 20 km/s/kpc
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Termination at 41 Resonance
O 25 km/s/kpc
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Termination at 41 Resonance
O 30 km/s/kpc
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Termination at 41 Resonance
O 60 km/s/kpc
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Termination at Corotation
O 10 km/s/kpc
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Termination at CorotationO 20 km/s/kpc
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Termination at Corotation
O 30 km/s/kpc
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Termination at Corotation
O 60 km/s/kpc
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O 20 km/s/kpc Case High Mass, Termination at
Corotation
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MHD termination at Corotation O 20 km/s/kpc