1. Σπειροειδείς γαλαξίες

2. Spiral Galaxies
Compared to ellipticals, the spirals cover a distinctly
smaller range in absolute magnitude (and mass). They
are limited to −16 > MB > −23 and 109Mסּ < M < 1012Mסּ
Looking at the sequence of early-type spirals (i.e., Sa’s
or SBa’s) to late-type spirals, we find a number of differences
that can be used for classification
• a decreasing luminosity ratio of bulge and disk, with
Lbulge/Ldisk ~ 0.3 for Sa’s and ~ 0.05 for Sc’s
• an increasing opening angle of the spiral arms, from
~ 6◦ for Sa’s to ~18◦ for Sc’s;
• an increasing brightness structure along the spiral
arms: Sa’s have a “smooth” distribution of stars along
the spiral arms, whereas the light distribution in the
spiral arms of Sc’s is resolved into bright knots of
stars and HII regions.

4. Spiral galaxies Brightness Profiles
The light profile of the bulge of spirals is described by a de Vaucouleurs profile to a good approximation
the disk follows an exponential brightness profile, as is the case for our Milky Way
μe is the surface brightness at the effective radius Re
The central surface brightness and the scale-length of the disk are denoted by μ0 and hr , respectively.
μ0 is not directly measurable since μ0 is not the central surface brightness of the galaxy, only that of its disk component. To determineμ0, the exponentialis extrapolated from large R inwards to R = 0.

5. The brightness profile of the haloes of spirals
Difficult to study due to low surface brightness
A stellar halo of red giant branch stars was detected n M31
It extends out to more than 150 kpc from its center.
The brightness profile of this stellar distribution indicates that for radii r <20 kpc it follows the extrapolation from the brightness profile of the bulge,
i.e., a de Vaucouleurs profile.
for larger radii it exceeds this extrapolation, showing a power-law profile which corresponds to a radial density profile of approximately
ρ ~ r−3, not unlike that observed in our Milky Way.

6. Low surface brightness spirals (LSB)
the central surface brightness of disks has a very low spread, i.e., it is very similar for different galaxies (Freeman’s law, 1970). For
Sa’s to Sc’s
μ0 = 21.52±0.39 B-mag/arcsec2 is observed,
Sd spirals and later types,
μ0 = 22.61±0.47 B-mag/arcsec2.
Galaxies exist which have a significantly lower surface brightness, the low surface brightness galaxies (LSBs). They seem to form a separate class of galaxies whose study is substantially more difficult compared to normal spirals because of their low surface brightness.

7. Rotation curves and Dark matter
the rotation curves measured from the 21-cm line typically extend to much larger radii than those from optical stellar spectroscopy
The rotation curves of spirals do not decrease for R ≥ hr , as one would expect from the light distribution, but are basically flat.
We therefore conclude that spirals are surrounded by a halo of dark matter.
The density distribution of this dark halo can be derived from the rotation curves.
The force balance between gravitation and centrifugal acceleration yields the Kepler rotation law
from which one directly obtains the mass M(R) within a radius R.
The rotation curve expected from the visible matter distribution is
can be determined assuming a reasonable value for M/L

8. M/L can be obtained
The spectral light distribution of the stars, together with knowledge of the properties of stellar populations,
or by fitting the innermost part of the rotation curve (where the mass contribution of dark matter can presumably be neglected) assuming that M/L is independent of radius for the stellar population.
From this estimate of the mass-to-light ratio, the discrepancy between υ2lum and υ2 yields the distribution of the dark matter,

9. Schneider 2007

10. Correlations of Rotation Curves with Galaxy Properties
The form and amplitude of the rotation curves of spirals are correlated with their luminosity and their Hubble type.
The larger the luminosity of a spiral, the steeper the rise of v(R) in the central region, and the larger the maximum rotation velocity vmax.
For the characteristic values of the various Hubble types, one finds
vmax ~300 km/s for Sa’s
vmax ~175 km/s for Sc’s,
vmax < 70 km/s for Irr’s.
For equal luminosity, vmax is higher for earlier types of spirals.
The shape (not the amplitude) of the rotation curvesof different Hubble types is similar, despite the fact that they have a different brightness profile as seen, for instance, from the varying bulge-to-disk ratio.
This point is another indicator that the rotation curves cannot be explained by visible matter alone.

11. The Tully–Fisher Relation
Using 21-cm observations of spiral galaxies, in 1977 Tully & Fisher found that the maximum rotation velocity of spirals is closely related to their luminosity, following the relation
Schneider 2007