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1
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Today: Reminders/Assignments
- Longair, Ch. 3,4-Galaxies
- Unless noted, all figs and
eqs from Longair.
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2
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- Astro-ph preprints:
- Galaxy Spectra/Modeling Assignment
- Reading Bennett et al. 2003 (MAP) paper
- WIRO still pending…
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3
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- The textbook is rather weak when it comes to observational properties
like spectra – as budding young observers you need to know more!
- Find and download the galaxy spectra templates of Kinney et al. (1996)
– and read the paper!
- Find and download the spectral synthesis population models of Bruzual
and Charlot.
- “Fit” the elliptical template and one spiral galaxy.
- Show some plots indicating how broad-band colors change with redshift
assuming not evolution (up to z=2).
- Write up your results like you would for publication with clarity,
citations, etc.
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4
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- Virial Theorem: A relationship between gravitational potential energy
and velocities for a dynamically relaxed and bound system.
- T = ½ |U|, where T is the total kinetic energy and U is the
potential energy.
- So, for a cluster of stars or a cluster of galaxies, measuring T (by
measuring velocities) can give U and therefore M.
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5
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- Light Distribution, 1st Hubble’s law:
- Much better is the de Vaucouleur’s (1948) r1/4 law:
- re is the radius within which half the total light has been
emitted.
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6
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- Then the total luminosity of an elliptical galaxy can be parameterized:
- Ie is a surface brightness, and b/a is the apparent axis
ratio of the galaxy.
- Van der Kruit (1989)
- Will discuss models and mass distribution in context of galaxy clusters
in section 4.3.2.
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7
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- Luminosities, surface brightness, central velocity distribution, (and
others), are correlated, hence the term “fundamental
plane.” Ellipticals
populate a plane in parameter space. BIG area of research – very
useful tool and helps us understand galaxies.
- Faber & Jackson (1976) is a classic in this area (you might want to
look up and read this one):
- L ~ σx where x ≈4
- So, get dispersion from spectrum, get luminosity, and with magnitude get
distance!
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8
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- Dressler et al. (1987) include all three of the plane parameters and
find a tight relationship:
- Can also substitute in a new variable Dn (a diameter chosen to match a
surface brightness) which incorporates L and Σ.
- Can get distances then to various accuracies.
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9
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- So, are ellipticals simple to understand dynamically? Not so clear. We’re seeing a 2D picture
of a 3D object.
- Elliptical galaxies rotate too slowly for this to account for the
flattening observed. In
other words, their ratios of rotational to random kinetic energy is too
low.
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10
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11
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- Light Distribution
- Two components, spheroid + disk
- Spheroid is like a mini-elliptical right down to a de
Vaucouleur’s law distribution
- Exponential disk component:
- Where h is the disk scale length (3 kpc for the Milky Way), so total L
is then 4πh2Io.
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12
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- Analogous relationship to the ellipticals’ Faber-Jackson relation
is the Tully-Fisher relation:
- The width of 21cm H I line, corrected for inclination, correlates with
luminosity.
- Again, can make a spectral measurement plus a magnitude to estimate a
distance.
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13
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- Tully-Fisher relation:
- Original exponent = 2.5, later steeper, 3.5, and even steeper for
near-IR H-band. Very tight
near-IR correlation so great distance indicator (recall the Hubble
assignment!).
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14
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- Tully-Fisher relation interpretation:
- Assuming mass follows light, then
- Then most mass within r ~ h and the maximum of the rotation curve goes
as the Keplerian velocity at radius h. Then making the same
Newton/Kepler argument:
- Combine the equations to eliminate h and you get that mass goes as Vmax4,
and for spirals M/L is roughly constant in the disk, so expect L ~ Vmax4
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15
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16
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- Roberts & Haynes 1994:
- Masses from S0 to Scd roughly constant, then decrease, and M/L roughly
the same (recall these are all primarily luminous massive galaxies
– why?)
- H I not significant in ellipticals (< 1 in 10000), but is in spirals
(0.01 to 0.15 from Sa to Sm)
- Total surface density decreases, H I surface density increases
- Ellipticals are red, spirals are blue…
- H II regions frequency increases monotonically along the sequence
(Kennicutt et al. 1989)
- Star formation rates appear key to these relations
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17
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18
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- Large Scale Distribution of Clusters
- Galaxy Distribution in Clusters
- Dark Matter in Clusters
- Forms of Dark Matter
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19
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- Palomar Sky Survey using 48 inch Schmidt telescope (1950s)
- Abell (1958) cataloged “rich” clusters – a famous work
and worth a look
- Abell, Corwin, & Olowin (1989) did the same for the south using
similar plates
- All original work was by visual inspection
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20
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21
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- Richness Criterion: 50 members brighter than 2 magnitudes fainter than
the third brightest member. Richness
classes are defined by the number in this range:
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22
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- Compactness Criterion: Only
galaxies within an angular radius of 1.7/z arcmin get counted. That corresponds to a physical
radius of 1.5 h-1 Mpc.
The redshifts are (were) estimated based on the apparent
magnitude of the 10th brightest cluster member.
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23
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- Distance Criteria: Lower
redshift limit (z = 0.02) to force clusters onto 1 plate. Upper limit due to mag limit of
POSS, which matches z of about 0.2.
Distance classes based on magnitude of 10th member:
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24
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- Complete Northern Sample:
- 1682 Clusters of richness 1-5, distance 1-6.
- Counts in Table 4.2 follow:
- This is consistent with a uniform distribution*.
- Space Density of Abell Clusters richer than 1:
- For uniform distribution, cluster centers would be 50 h-1
Mpc apart, a factor of ten larger than that of mean galaxies.
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25
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- Based on Abell’s Northern Sample:
- Spatial 2-point correlation function (Bahcall):
- Scale at which cluster-cluster correlation function has a value of
unity is 5 times greater than that for the galaxy-galaxy correlation
function.
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26
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- Peebles (1980) schematic picture:
- Cloud of galaxies is basic unit, scale of 50 h-1 Mpc
- About 25% of galaxies in these clouds
- All Abell Clusters are members of clouds (with about 2 per cloud), and
contain about 25% of the galaxies in a cloud are in Abell Clusters
(superclusters occur when several AC combine)
- Remaining 75% follow galaxy-galaxy function
- In terms of larger structures, galaxies hug the walls of the voids,
clusters at the intersections of the cell walls.
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27
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- A range of structural types (Abell)
- Regular indicates cluster is circular, centrally concentrated (cf.
Globular clusters), and has mostly elliptical and S0 galaxies. Can be very rich with > 1000
galaxies. Coma is regular.
- All others are irregular (e.g., Virgo).
- I don’t know why he didn’t just call them type 1 and type
2…!
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28
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- A range of structural types (Oemler 1974)
- cD clusters have 1 or 2 central dominant cD galaxies, and no more than
about 20% spirals, with a E: S0: S ratio of 3: 4: 2.
- Spiral-rich clusters have E : S0 : S ratios more like 1: 2: 3 –
about half spirals.
- Remainder are spiral-poor clusters. No dominant cD galaxy and
typical ratio of 1: 2: 1.
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29
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- Galaxies differ in these types (Abell)
- In cD clusters galaxy distribution is very similar to star distribution
in globular clusters.
- Spiral-rich clusters and irregular clusters tend not to be symmetric or
concentrated.
- Spiral-poor clusters are intermediate cf. above.
- In spiral rich clusters, all galaxy types similarly distributed and no
mass segregation, but in cD and spiral-poor clusters, you don’t
see spirals in the central regions where the most massive galaxies
reside.
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30
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- Kormendy (1982) distinguishes these from being merely giant ellipticals.
- Extensive stellar envelope up to 100 kpc
- Only in regions of enhanced galaxy density (a factor of 100 denser than
the average)
- Mutiple nuclei in 25-50% of cDs (a very rare thing)
- Regular cD clusters are systems that have relaxed into dynamical
equilibirum.
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Notes