Polar Rings in Galaxies
Joe Wolf, April 2007
1. Introduction to Polar Ring Galaxies
Polar ring galaxies are S0 galaxies that have a ring of stars (usually young and blue) and HI
gas that rotates perpendicular to the plane of the disk. Observationally they comprise approximately
0.5% of the S0 population, although some believe this to be an underestimate due to biases selecting
these galaxies based on their orientation. (1,2,3)
Hubble Classification Diagram:
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2. Motivation to study Polar Ring Galaxies
The obvious motivation to study polar ring galaxies is to better understand them! Some
questions that exist: Why are nearly all of the host galaxies S0? Why are polar ring galaxies so rare?
Why do some polar rings have a narrow ring while others have more circular rings? Why are the
mass and angular momentum of the ring comparable, or sometimes larger, than those of the host
galaxy? Why are rings so “polar”? Why do some polar rings have even more peculiar morphologies,
such as helical and double-ringed shapes? Why is there a large amount of interstellar gas in the polar
ring rather than in the host? (1) I will attempt to bring light to some of these questions, but many are
still open.
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These exists another form of motivation to study these objects: because the gas and stars in
the perpendicular rings seem to be in equilibrium, studying polar ring galaxies can help us probe a
more pressing problem in astronomy: the three-dimensional shapes of dark matter halos of the host
galaxy. Dark matter halos are assumed to be spherical, but little empirical evidence exists to support
this claim as a generalization. Getting better constraints on the shape of dark matter halos will help
us better understand the nature of dark matter.
To determine these properties the perpendicular ring must not strongly influence the host
galaxy. We need to be able to derive back the initial shape of the host galaxy with a given
assumption about the formation history of the perpendicular ring. (3, 4)
3. Observational Results & Challenges
The Hubble Space Telescope (HST) has allowed for a more detailed
study of the inner regions of polar rings and their host. In 2002, Iodice et. al.
analyzed NGC 4650A from a 1999 observation with the HST and found
that the polar ring in this galaxy is more extended in the optical bands (B, V,
I) than in the near infrared. The HST data shows young blue star clusters
extending from the main polar ring plane, as expected. There was an
acceptable 13% error on declaring the color. (5)
When attempting to retrieve models for the light distribution, Iodice
et. al used measurements made in the Kn and I bands to reduce dust
absorption from the polar ring. This challenge forced the group to ignore
some regions of the galaxy when fitting the model to the data. (5)
The group modeled the light distribution of the host galaxy with a
combination of an exponential disk and a spheroidal center:
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Spheroidal
k = 2.17n – 0.355, rb =
x2 
Exponential Disk
2
y
, where
qb2
qb = 1 - spheroidal ellipticity, μe = effective surface
brightness, re = effective radius (half-light)
rd =
x2 
y2
, where qd = 1 - disk ellipticity,
q d2
μd = central surface brightness, rh = scale
length of the disk
As can be seen below, the model fits well with the Kn band on the left, but a dip in I band
(right) occurs at r ≈ 5 arcseconds. This effect is caused by the previously mentioned dust absorption
in the optical spectrum, which is not as prevalent in the infrared. One can also verify the claim of the
polar ring being more extended in the optical light than in the infrared by noticing that the noise in
Kn band increases at a smaller radii than it does in the I band. This claim leads to the conclusion that
an older stellar population exists closer in the S0 host, but star formation is occurring in the outer
edges of the polar ring. (5)
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4. Formation Theories
Before discussing the results of analyzing these galaxies to determine whether or not
researchers have been successful in obtaining the shape of dark matter halos, I will present several
theories on the formation of these rare objects. As mentioned earlier, open questions still linger,
which are interesting in their own right.
4.1 Resonant capture
Until 2000, the only formation theories of polar ring galaxies, which are discussed below,
required external mass to be acquired to form their rings. In 2000, Tremaine & Yu published a
theory of resonant capture of stars and gas from the host to form the younger ring. (2) The
mathematics becomes a bit involved, as this model is purely theory driven. I will do my best to
qualitatively describe the theory.
Tremaine & Yu begin their argument discussing how inclinations of disk-star orbits can be
excited by resonant coupling to a triaxial (non-spherical) halo potential, with the locations of these
resonances given by the Binney resonance:
, where
and
and azimuthal frequencies, respectively. If
slowly settles to 0, implying that
are the vertical
=
, then an
outer polar ring is formed from the stars in the host. The justification for this is highly quantitative
in nature, and the authors show from their numerical simulations that stars can be captured by the
Binney resonance without large changes in energy or total angular momentum. (2)
One of the concerns mentioned by the authors is the required timescale for this process to
actually occur. Some of their results require more than 1010 years to form. Hope is not lost, as they
describe that some of their model parameters were over-simplified, and they don’t believe they
searched enough into how they can alter the parameters to retrieve results to resolve these issues. (2)
The authors’ numerical simulations represented stars as point particles to achieve their
results, and it is unclear whether or not the host’s gas could be captured by the Binney resonance as
well. A concern is that rising gas clouds might interact at high velocities, leading to energy
dissipation by radiation and increased temperature, while their velocities decrease. Numerical
simulations will be the best way to determine the outcome of this problem. (2)
As of 2005, F. Combes states that this mechanism has not been confirmed in observation.
She offers an example of the previously mention galaxy, NGC 4650A, whose stellar dynamics do
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not show the characteristic of counter-rotation, one of the predictions of this theory. (3) It is evident
that more data needs to be taken and more analysis needs to be completed of velocity fields of the
rings to see if the empirical results agree or rule out this resonance theory.
4.2 Merger
In 1998 K. Bekki proposed an extended description of a 1997 version of his own work to
propose that merger events give rise to polar ring galaxies. He was motivated by the popular belief
that polar ring galaxies were formed from an existing S0 galaxy, which would later undergo some
method of acquisition and/or transformation by another object. That is, most do not believe these
rings are part of the initial formation stage of the galaxy. (1)
The proposed merger requires gas-rich galaxies and late-type disk/spiral galaxies. Bekki
doesn’t go into depth about star formation, but incorporates the mechanism into his model because
of the observational result of the polar rings comprising many young stars. His initial conditions are
shown below, where the intruder will eventually become the S0 host and the victim is the gas-rich
galaxy:
Bekki’s time-evolution simulations show that the intruder, initially a thin disk, gets
gravitationally pulled back to piece through the victim again, creating a S0 shape. Consequently, the
simulations also show that narrow polar rings tend to be formed through his method. These results
answer two of the original posed questions in the motivation section. The proposed answer to why
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the rings are so “polar” is due to the approximate interaction angle. Similarly, the chance of the
initial conditions being just right, which includes having the correct types of gas distribution in each
progenitor, gives rise to the explanation of why polar ring galaxies are so rare and why. (1)
As convincing as Bekki’s model sounds, he was the first to admit that his method need not
be unique in describing the formation of polar ring galaxies. In addition, one of the criticisms is an
inability to reproduce examples of current polar ring galaxies, such as NCG 4650A (above), whose
rings have more of a circular feature.
4.3 Gradual Gas Accretion
In 2003, B. Bournaud & F. Combes explored the stability of Bekki’s simulation, and they
concluded that although his method forms the polar rings well, the majority of polar ring galaxies
are formed through gas accretion and not through mergers. (3) Their motivation to study this
stemmed from the careful geometric initial conditions that must be present, and how accretion
models are more robust.
A. Macciò et. al. (2006) show that cold gas accretion usually comes in filaments on the order
of 1 Mpc. This formation theory proposes that when one of these filaments comes in close contact
with a S0 galaxy, the host can strip some of the gas and form a ring. (6) This is the least violent of all
formation theories and seems plausible as long as the cross section of interaction is large enough to
account for a portion of the observed polar ring galaxies.
4.4 Tidal Gas Accretion
F. Schweizer et. al. (1983) proposes a tidal accretion scenario, in which a donor galaxy comes
close to the host galaxy, where it deposits some gas and stars as it departs They claim this method to
be preferred over a galaxy merger, as they believe mergers to be disruptive. (4) However, note that
this paper came out 15 years before Bekki’s simulations were published.
The first numerical simulation of tidal accretion was performed by V. Reshetnikov & N.
Sotnikova in 1997. Their first goal was to explain why bulge-dominated S0 galaxies possess only
short narrow rings, while the disk-dominated galaxies host wider polar rings. They examined 8 polar
ring galaxies, so the information given about masses and distances scale to this small sample. (8)
During the tidal encounter, as the host galaxy strips the outer regions of the visitor/donor, a
ring rotating in the direction of the visitor’s orbital motion eventually forms perpendicular to the
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host. Approximately 10% of the donor’s gas is required for this process to work, which is on the
order of 109 M. Because this is a tidal interaction, most of the exchange is happening on the outer
edges; about 1/10th of this gas fell into the center. This helps account for the question of why most
the gas is in the polar ring. The time scale is on the order of 109 years, leaving plenty of time for the
visitor to depart. (5)
The authors’ simulations also produced the observable phenomenon they were trying to test:
the ring size for a bulge-dominated system was ~7kpc and ~13 kpc for a disk-dominated system.
They also found that some polar ring galaxies had much further extended rings, up to 30 kpc. To
account for this a spherical dark matter halo was introduced, and the authors conclude that it is
impossible to get such extended objects by only including luminous matter. (8) Remember, this
result is 10 years old, and the authors make no claim to the shape being spherical. Merely, they state
that you need more mass than can be directly observed to account for the extended rings.
Taking this analysis a step further, V. Reshetnikov & N. Sotnikova make the claim that
bulge-dominated polar ring galaxies may not have as greatly pronounced dark matter halos as diskdominated polar ring galaxies, because of the difference in the extension of the perpendicular rings
from the host. (8)
These results make the tidal gas accretion scenario appear very favorably, which is further
supported by F. Combes’ claim that from initial conditions, this formation theory is approximately
four times as likely to form polar rings than other non-accretion models. (3) I will not go into the
details of this claim, and therefore I ask the reader to accept this statement with a grain of salt.
5. Halo Shapes
There are two different views on the shapes of the dark matter halos: one group thinks they
are round, and the other flatter. Recalling the second half of the motivation, finding the shape of
dark matter halos will help researchers better understand dark matter. It seems we are still not at
agreement.
5.1 Tully-Fisher Relation: Flattened Dark Matter Halo
The Tully-Fisher relation is an empirically derived relation between disk rotation velocity and
4
absolute luminosity of a galaxy: L  Vrot
. Although a popular use for the Tully-Fisher relation is to
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measure distances to galaxies, researchers use the relation to better understand the relationship
between dark halo properties and the quantity of luminous matter in galaxies. (4)
In order to retrieve these velocities, astronomers try to find polar rings which are aligned as
the figure on the left shows. By observing the rings edge on, one can take a measurement of the HI
spectrum, and very accurately derive from the Doppler Shift the difference in velocity between the
top and bottom of the ring. (4)
The above graph shows many dots and a few more defined shapes. The 16 circles, squares,
stars, etc are polar ring galaxies, while the 100+ dots are disk/spiral galaxies taken from a previous
survey. 81% of the disk galaxies fall between the two dotted lines centered on the solid line. This line
represents the Tully-Fisher Relation between the absolute magnitude in B band and the log of the
line width at 20% of the peak line flux density. This line width is used to obtain the difference in
velocity, as described above. (4) Recall that B band observations of polar ring galaxies are strongly
biased to only include the structure of the polar rings- which is what we’re looking for!
These polar ring galaxies were obtained from a catalog with a bias of trying to find galaxies
with a nearly edge-on view of the ring, to best obtain their HI spectra. Notice how nine of the polar
ring galaxies fall below the bottom dotted line, but only two are above the upper dotted line. The
other five fall between the solid line and the lower dotted line. (4)
The group argues that this observation will have consequences for determining the shapes of
dark matter halos. If no dark matter was present and if the gravitational potential was oblate just as it
would be for a flattened host galaxy, polar rings would have an eccentric shape. Viewing this shape
edge on would result in lower-than-expected velocities. (4)
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However, the graph above shows that most of the polar ring galaxies have larger velocities
than expected. If we did observe lower velocities the argument that polar ring galaxies can be used
to constrain properties of these dark matter halos would be weakened.
To strengthen the existence of a dark matter halo, the model predicts that the velocities
should be larger than expected for a disk galaxy if the halo is flattened toward the polar ring. If the
halo is spherical, the authors claim that the ring will still be eccentric, where the observed velocities
would fall low of the expected values, once again contradicting the empirical observations. They
source a more detailed previous work (9) to state that a spherical halo cannot account for the higherthan-expected velocities. This work also states that a flattened halo requires less dark matter to
explain the higher velocities. (4) There seems to be the potential for a possible correlation between
this statement and V. Reshetnikov & N. Sotnikova’s results where they introduce a spherical dark
matter halo to account for the extended ring structures.
5.2 Gas Cooling: Rounder: Rounded Dark Matter Halo
In 2004, Kazantzdis et. al. produced N-body simulations that showed when dark matter
halos formed in situations where gas was being cooled, they were significantly more spherical than
the halos mentioned above, which formed under adiabatic conditions. The difference in shape
surprisingly decreased slowly with radius, despite the fact that further out the halo is not thought to
be affected by this local thermodynamic process. (10)
The authors use an argument that after a few crossing times/rotations, the central halo
should grow and influence the rest of the halo to become more spherical. However, they
diplomatically leave open the possibility that mergers can produce elongated remnants further out in
radius. (10) The question then becomes, what is the average time scale between mergers in
comparison to the average time scale for the central gas to cool, and influence the rest of the dark
matter halo?
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6. Conclusions
Polar ring galaxies, a peculiar type of S0 galaxy, have gained interest from a subset of
determined astronomers who wish to solve two problems. 1. What is the formation history of these
objects? 2. How can we use polar ring galaxies to constrain the shapes of dark matter halos in
galaxies?
A number of questions were posed, and most were answered throughout this paper.
However, members of the community continue to (seemingly) amiably disagree on their answers.
Instead of trying to fill this last page by repeating these questions and possible answers, I will offer a
brief overview of this paper.
Polar ring galaxies have extended rings filled with HI and young blue stars, while their host is
older and not filled with as much gas. Groups have been able to model the light curves after
accounting for dust absorption, and find that superimposing a spherical bulge and exponential disk
model works reasonably well.
The popular formation theories seem to be gas accretion and merger situations. The merger
scenario seemed to answer a lot of the originally posed questions, but other analyses challenged the
rate at which mergers could successfully explain a majority of the polar ring galaxies. The accretion
models, although not an overwhelming success, seem to perform better than the merger or
resonance models. This may have been partly due to a bias of papers I read with similar authors, so I
am keeping an open mind.
Lastly, by using empirical evidence (of which I know the reader trusts over theory) and by
invoking the Tully-Fisher relation, one can follow the detailed work to find a strong case for
flattened dark matter halos. There was also a group that, by using N-body simulations produced a
good argument as to why they believe the halos should be rounder. Hopefully these groups can
review each other’s work and author papers together that find a way for theory and observation to
mesh. Not only will we understand polar ring galaxies better, but we will (hopefully) be one step
closer to understanding the nature of dark matter.
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References
1
Bekki, K. 1998, ApJ, 499, 635
2
Tremaine, S., Yu, Q. 2000, MNRAS 319, 1
3
Combes, F. 2006, EAS 20, 9
4
Iodice, E., Arnaboldi, M., Bournaud, F. et al, 2003, ApJ 585, 730
5
Iodice, E., Arnaboldi M., De Lucia, G., et.al, 2002, ApJ 123, 195
6
Macciò, A., Moore, B., Stadel, J. 2006, ApJ 636, L25
7
Schweizer, F., Whitmore, B. C., Rubin, V. C. 1983, AJ, 88, 909
8
Reshetnikov, V., Sotnikova, N. 1997, A&A, 325, 933
9
Combes, F., Arnaboldi, M. 1996, A&A 305, 763
10
Kazantzidis, S., et. al. 2004, ApJ, 611 L73
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