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Today: Reminders/Assignments
- Longair, Ch. 3-Galaxies
- Unless noted, all figs and
eqs from Longair.
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2
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- On Friday Astro-ph preprints:
- Galaxy Spectra/Modeling Assignment
- Reading Bennett et al. 2003 (MAP) paper
- Debrief Spacegrant proposals?
- History of the Hubble Constant:
- http://cfa-www.harvard.edu/~huchra/
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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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- Virial Theorem: T = ½ |U|
- You do need to worry about the conditions of the theorem in an
astrophysical context. For
instance, comparing crossing times with the relevant timescale. Text examples are the sun’s
orbital period and galaxies in Coma.
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6
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7
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- Astronomical context more complex.
Cannot in general get all the 3D velocities. In exgal context, uncertain
cosmology can translate into uncertain spatial dimensions. Usually only have position on sky
plus radial velocities. Must
make assumptions about velocity distribution to apply virial theorem.
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8
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- Isotropic case: <v2> = 3<vr2> (why?)
- If velocity dispersion independent of masses:
- T = 3/2 M <vr2>, where M is total mass
- More complex if the above is not true. Assuming spherical symmetry and
an observed surface distribution, get a weighted mean separation Rcl:
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- More complex if the above is not true. Assuming spherical symmetry and
an observed surface distribution, get a weighted mean separation Rcl:
- Works for elliptical galaxies and yields mass to light ratios of 10-20
in solar units.
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10
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- Rotation Curves of Spiral Galaxies:
- This just comes from Newton, by equating gravity to centripetal
acceleration. This produces
Kepler’s third law, and Keplerian orbital velocities around point
sources fall off as r-1/2.
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- Keplerian fall-off near center indicates compact mass at center
- Flat curve throughout disk indicates much distributed mass
- Lack of fall-off beyond visible “edge” indicates “dark
matter”
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12
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13
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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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- 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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- 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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- 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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- 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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- 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 4πr2Io.
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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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- 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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22
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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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23
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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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Notes