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Today in Astronomy 142

! The epicyclic frequency ! Summary of spiral structure, density waves

! Elliptical, lenticular and irregular galaxies ! Distribution of mass and light in normal galaxies

Background: warped spiral galaxy ESO 510-G13, by the Hubble Heritage Team (HST/STScI/NASA).

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The epicyclic frequency

Same procedure can be used to estimate the vertical oscillation frequency

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For different rotation curves

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The eccentric disk in M31

HST image of M31’s nucleus shows two peaks separated by about a pc. The brighter one is at the location of the Black hole. Lauer et al. 1994

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Spiral structure summary ! Spiral arms generally trail

rotation; there are only a couple of possible exceptions (one shown below).

! Spiral arms seldom wind more than once or twice around a galaxy.

! Concentration of H II regions and young blue stars is higher in the arms than elsewhere in a galaxy: the star formation rate is higher.

! Dust lanes lie on the trailing edges of arms. ! Molecular cloud complexes tend to be more massive in

the arms than elsewhere in a galaxy. Most stars are formed in clusters in spiral arms. Bias in our local study of Star formation

M100 (Sc), by David Malin

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trailing

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An exception: spiral structure in

NGC 4622

Note that the direction in which the spiral arms wind is different inside and outside the complete ring. One set of arms must lead rotation, and one must trail. Composite color image by Byrd et al., with the WFPC2 camera on HST (NASA).

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Spiral structure summary (continued)

! The central bulges in spirals usually (2/3 at present) look at least slightly oval or elliptical, rather than perfectly axisymmetrical.

! Less commonly (but not rarely) the bulge is strongly barred: the SB galaxies. More than one bar is is frequently visible in these.

! This is in harmony with computer simulations of rotating clusters of stars: initially symmetrical clusters always develop quickly (within a few rotation periods) into stable, oval/elliptical or barred shapes (see, e.g., Hohl 1971).

NGC 1365 (SBc), by David Malin

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The “bar instability”

In this simulation by Frank Hohl (1971, Ap.J. 168, 343), 100000 stars start off as a uniformly rotating, axisymmetric disk, but soon erupt spontaneously into a spiral pattern before settling down into an ellipsoidal distribution (i.e. a bar) that appears to be stable. The time unit is the rotation period of the disk, 1.5×108 years.

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Spiral structure interpretation

! Differential rotation must be important but cannot itself produce the spiral structure: there are too many spirals seen, and the arms never wrap around very many times.

! The high star formation rate observed in most spiral arms would exhaust the associated interstellar gas in a time very short compared to the age of the Universe. However, we see lots of spiral galaxies in the sky, so the arms are not material arms: matter must constantly be flowing into and out of them.

! The masses of spiral-arm molecular cloud complexes and the high star formation rate both imply that the interstellar matter in spiral arms is compressed, compared to ISM elsewhere in a galaxy’s disk.

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Spiral density waves

Lin and Shu, 1963: arms are due to spiral density waves. ! Analogy to road work and traffic jams (in 1-D):

Imagine a road crew painting lane stripes on a freeway. They move along at a couple of mph. A traffic jam forms behind them and moves along with them. Cars before and behind the jam move at 65 mph and are much further apart than in the jam. Cars enter the jam from behind, slow as they move through it, and resume speed as they leave. From a helicopter it appears that a dense concentration of cars moves along with the road work, but it is composed of different cars at different times.

Normal traffic speed <==> normal stellar orbit speed; traffic jam <==> density wave <==> spiral arm

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Spiral density waves (continued)

What plays the role of the road crew in a spiral galaxy disk? Gravity from the rotating, non-axisymmetric stellar distribution: ! Force on orbiting objects

larger than average when the ends of the oval or bar make their closest approach; smaller than average in between.

! Other things equal, this alternately speeds up and slows down the orbital speeds.

For more details, take AST 242.

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Stability to bars or spiral modes

When the velocity dispersion is high then spiral modes cannot form. There is a stability criterion

Kinetic vs potential energy, hot disks are stable.

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Other normal galaxies (besides spirals)

Elliptical (Eq) ! Rotation often not evident: random motions dominate the

stellar velocity distribution. ! Very little interstellar matter, compared to mass in stars.

Consequently there isn’t much star formation. ! Variety of shapes, ranging from round (E0) to an

ellipticity of 0.7 (E7). •  In terms of the major and minor axes a and b the

ellipticity is given by The notation Eq, where q = 10ε, is used to denote the shape.

! May be prolate (football-shaped) or oblate (pancake-shaped) in 3-D; in general, they could be triaxial (principal axes all different lengths, like a bar of soap).

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M87 (NGC4486), an E0 galaxy

Photograph by David Malin (AAO), with the Anglo-Australian Telescope (3.8 m).

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NGC 1332, an E7 galaxy

...with a smaller or more distant E1 to the southeast.

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Other normal galaxies (continued)

Lenticular (S0, SB0) ! Like ellipticals, they have very little interstellar matter,

and very little star formation in consequence. ! Like spirals, they have disks, in which rotation dominates

the stellar velocity distribution. ! The central bulges tend to dominate the mass in

lenticulars; no spiral structure is seen in the disks. ! In attempts to explain spiral and elliptical galaxies as

forming an evolutionary sequence, lenticulars represent the transition between the other two classes. (Note that such attempts are no longer taken very seriously.)

! Lenticulars are components of polar ring galaxies, an important class of “interacted” galaxies. (More later.)

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NGC 4526, an S0 galaxy

This galaxy is seen edge on. Note the bulge-disk contrast, in comparison to the E7 galaxy NGC 1332, which would otherwise look similar.

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NGC 1201 (left), an S0 galaxy, and NGC 2859 (right), an SB0 galaxy. (From Chaisson and McMillan, Astronomy Today).

Lenticular galaxies

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Other normal galaxies (continued)

Irregular (Irr I, Irr II) ! As the name implies, these galaxies are supposed to be

amorphous. Wide range of masses and luminosities, though they are usually small compared to typical spirals.

! They tend to be rich in ISM and have respectable star formation rates, though most have very small abundances of heavy elements.

! Irr I: hints of regular structure; e.g. the “bar” in the Large Magellanic Cloud.

! Irr II: no regular structure at all. (Note, though: the archetype Irr II, M82, looks amorphous just because of extinction; underneath it’s just a spiral galaxy.)

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LMC IRAS view

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Photograph by Weihao Wang (NRAO).

The Large Magellanic Cloud (LMC, Irr I)

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Photograph by Weihao Wang (NRAO). The big globular cluster – part of our galaxy, of course, not part of the SMC – is 47 Tucanae.

The Small Magellanic Cloud (SMC; Irr I)

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Photograph by David Malin (AAO), with the Anglo-Australian telescope (3.8 m).

NGC 1313 (Irr I)

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M82 (NGC 3034), archetype of Irr II, but not irregular at all

B,V,R and Hα composite photograph by S. Kohle and T. Kredner, with the Calar Alto 1.2 m telescope.

Its rotation curve reveals that M82 is an edge-on spiral with heavy fore-ground extinction by material stripped from nearby M81.

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M82: Purple represents emission in ionized hydrogen (H-alpha) and ionized nitrogen, and the green is ionized sulfur in the WIYN data. In the HST image, these colors refer to H-alpha and nitrogen separately. Note the varying angular resolution of the dust lanes in the central part of the superwind on either side

of the stellar disk. NOAO

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The Hubble sequence of normal galaxy shapes

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“Late type” “Early type”

Hubble originally thought that the shape of a galaxy indicates evolution-ary status, and proposed this arrangement of shapes as the corresponding evo-lutionary sequence. (We know now that this isn’t right, but the scheme still has utility.)

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Distribution of mass and light in normal galaxies

Elliptical galaxies are found to fit very well the following distribution of luminosity:

where L, the surface brightness, is the luminosity per unit area projected onto the plane of the sky, and r0 is the core radius. Mass can be deduced from random motions and the virial theorem:

rather like the way it is inferred from rotation curves in spirals.

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Distribution of mass and light in normal galaxies (continued)

The bulges of spiral galaxies usually fit the luminosity-radius relation that applies to ellipticals pretty well. The disks fit

But, as we have noted before, the rotation curves are flat as far away from the nuclei as lines can be detected, and well past the visible extent of the stellar distribution. ! Thus the M/L ratio increases with increasing radius. ! Recall our example rotation curves (lecture, 21 March): flat

curves obtained for a spherical halo with

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Vertical structure as seen from edge-on galaxies

Exponentials in both radial and vertical directions turn out to be a pretty good approximation.

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Dark matter II: spiral galaxy rotation curves and surface brightness

! All spiral-galaxy rotation curves are essentially flat outside the nuclear region, indicating that enclosed mass increases linearly with increasing radius.

! Surface brightness decreases exponentially with increasing radius for all spiral galaxies.

! Thus the mass-to-light ratio in the outer parts of spiral galaxies is very large, maybe too large to be due to stars.

All this can be understood if each galaxy is embedded in a large, spherical, halo of dark matter, with density proportional to 1/r2. Other configurations are possible too.

From Chaisson and McMillan, Astronomy Today.

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Distribution of mass and light in normal galaxies (continued)

Polar ring galaxies are S0 galaxies with rings or disks of stars and gas clouds in polar orbits (i.e. in a plane perpendicular to the galaxy’s disk), acquired during an interaction with another galaxy. Rotation curves of galaxy disk and polar ring give both the horizontal and vertical distribution of mass in the S0, allowing a determination of the shape of that galaxy’s (dark) halo. Interesting results so far: ! A0136-0801 might have a spherical halo (Schweitzer,

Whitmore and Rubin 1983). ! NGC 4650A seems to have a flattened halo, with shape

about E7 (Sackett et al. 1994).

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Tully Fisher relation

Empirical relation between galaxy luminosity and rotation velocity as seen in HI line width. Correct for inclination when using the HI line width. Can be choosy about the band.

Independent of surface brightness!

Either dark matter distribution is related to light distribution or dark matter dominates everywhere.

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Polar-ring galaxy NGC 4650A

S0 galaxy

Polar ring

Rotation axes of galaxy and ring are perpendicular.

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A0136-0801 Schweizer, Whitmore and

Rubin 1983: E0 halo

NGC 4650A Sackett, Rix, Jarvis and Freeman 1994: E7 halo

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Warped galaxies IRAC SIRTF image (J. Keene)

Optical image

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Warped galaxies- continued IRAC SIRTF image My simulation!