Observational Astronomy, fall 2013
Galaxy radii
Galaxy radius NGC-7331 late-type spiral galaxy
Folkert Nobels1 *, Bas Roelenga1† , Tobias Vos1‡
Abstract
The purpose of this project is to determine characteristics of the galaxy NGC-7331. There will be looked at the surface
brightness of NGC-7331, whether a de Vaucouleurs a1/4 profile or an exponential profile fits the surface brightness profile of
NGC-7331 best, the scale length of NGC-7331, if the position angle changes as a function of semi-major axis and if the
ellipticity of the isophotes changes as a function of semi-major axis. To answer these questions the Gratama telescoop at
the Blaauw observatory in Groningen was used, to observe NGC-7331. After observing the data obtained at the telescoop
was reduced and extracted. Using these data plots of the Surface brightness profile of NGC-7331 were made. This plot
concluded NGC-7331’s surface brightness resembles an exponential profile. So the scale length of NGC-7331 could be
determined. The determined values for the scale length are 32, 42 and 37 pixels for the B, V and R band. Then plots of the
Position angle and the Ellipticity as a function of the semi-major axis were made. It can be concluded that the position angle
of the isophotes of NGC 7331 does not change as a function of semi-major axis, whereas the ellipticity does.
Keywords
NGC-7331 — Late-type spiral galaxy — Galaxy radius – Spiral galaxy – surface brightness profile – Scale length – Position
angle – Ellipticity – isophotes
1 Faculty of mathematics and natural sciences, University of Groningen, Groningen, The Netherlands
*Corresponding author: [email protected]
† Corresponding author: [email protected]
‡ Corresponding author: [email protected]
Contents
Introduction
1
1
Data
1
2
Results
2
2.1 Surface brightness profile of NGC-7331 . . . . . . . . . 2
2.2 Scale lengths of NGC-7331 . . . . . . . . . . . . . . . . . 2
2.3 Position angle of NGC-7331 . . . . . . . . . . . . . . . . . 3
2.4 Ellipticity of NGC-7331 . . . . . . . . . . . . . . . . . . . . . 3
3
Discussion
4
4
Conclusion and summary
4
5
Appendix
4
Acknowledgments
4
References
4
Figure 1. NGC-7331 in the V-band
1. Data
Introduction
In this article there is looked at different characteristics of
the galaxy NGC-7331. There will be looked at the surface
brightness profile, the scale length and if the position angle
and ellipticity of the isophotes change as a function of semimajor axis. first there will be explained how the data was
collected, Then we will discuss these properties one by one.
Which lead us to our conclusions.
Data that was used for the determining of the surface brightness profile, scale lenghts, ellipticity and position angle was
taken at the Blaauw observatory on top of the Bernoulliborg
on the first of october 2013. The images were taken in the B,
V and R band with exposure times of 5 minutes. In total there
were 41 images taken that were used for determining these
properties. Besides these images, there were also 15 flat fields
taken for the data reduction.
Data reduction was used on the data that was taken that
Galaxy radius NGC-7331 late-type spiral galaxy — 2/4
day (correction for instrumental artifacts). The Bias and dark
frames were however taken a few days earlier, but because of
bad weather these were the only pictures taken that day. The
data reduction was done by using the commands zerocombine,
darkcom, flatcom and ccproc. These commands removed the
instrumental artifacts using the bias, dark and flatfields. Then
there was also compensated for the gain and the readnoice
by adjusting the parameters of the command ccdproc (epar
ccdproc). [1]
Now the data was ready for processing. Using the program
IRAF we extracted the properties from the .fits files. Command like imexamine and imcombine were used for to shift
the images together in order to combine the images from each
band. Then the command imstat and imarith were used to
determine the skylevel and compensate our data for this. Then
as last the edited the size of the semi-major axis using the command ”epar geompar” and used ellipse and tdump to get the
data files with all the properties we needed. These properties
are discussed more in depth in the following sections.[1]
away from the center, than the lines in figure 3, which are less
linear lines in all bands. This means the exponential profile
fits the best and not the de Vaucouleurs a1/4 profile. This
means our surface brightness profile obeys equation 1, the
equation for an exponential profile. Moreover it is important
to note that our galaxy is brightest in the R band, which means
there are a lot of old stars in the center, this is very normal for
spiral galaxies like NGC-7331. [1]
2. Results
Using the obtained data from IRAF, the required plots were
made for answering the questions. For plotting the obtained
data we wrote a python script which used the module matplotlib.
Figure 3. Surface brightness profile 2
2.1 Surface brightness profile of NGC-7331
R
I(R) = I0 exp −
hR
(1)
Using the fact that our graph is an exponential profile, we
now can calculate the scale length. [1]
2.2 Scale lengths of NGC-7331
Equation 1 can be written in magnitude, see equation 2. Using
algebra it can be derived that the scale length can be expressed
as equation 6.
− hR
−2.5·log10 (I(R)) = −2.5·log10 e
Figure 2. Surface brightness profile 1
After extracting the information using IRAF, plots of the
surface brightness profile where made. First a plot of the
surface brightness in mag · arcsec−2 against the semi-major
axis in pixels was made, see figure 2 for this plot. After this
plot, a plot of the surface brightness in mag · arcsec−2 against
the semi-major axis in pixels1/4 was made, see figure 3. After
plotting the surface brightness, there was determined that the
surface brightness profile of figure 2 fits the best. This is
because in figure 2 The lines of the bands are more linear far
R
−2.5 log10 (I(0)) (2)
R
µ(R) = −2.5 · log10 e × −
+ µ0
hR
1.086
µ(R) =
R + µ0
hR
µ(R) = aR + b
a=
1.086
hR
(3)
(4)
(5)
hR =
1.086
slope figure 2
(6)
In equation 3 it is clear that a straight-line fits the surface
brightness. This straight line is a function of R, see equation
Galaxy radius NGC-7331 late-type spiral galaxy — 3/4
Figure 4. Scale length of NGC-7331
Figure 5. Position angle of NGC-7331
5. From this equality of µ(R) it can be derived that hR can be
written as the slope of graph 2, see equation 6.
Using equation 6 all of the scale lengths were calculated
and they are displayed in figure 4. The scale length is the
length in pixels (in this case) at which the brightness of the
galaxy has fallen of by a factor of the number e. In figure 4 we
can see that the brightness in the B-band falls off a lot faster
than the brightness in the other bands. This is because a spiral
galaxy contains a lot of interstellar matter which absorbs the
light in the B-band more than the other 2 bands, so naturally
the scale lengths for the other 2 bands are higher, which is the
case here.[1]
most plausible one is that NGC 7331 is not an elliptical galaxy
to begin with and is likely a spiral galaxy. The literature
confirms this assumption.[1, 4]
2.3 Position angle of NGC-7331
The 2D surface brightness profile of NGC 7331 was measured for all three bands. Here map contours of constant
surface brightness are called isophotes. Isophotes are not exact ellipses, but with deviations of only a few percent, fitting
ellipses to these isophotes works well for most cases. These
ellipses can be described by two variables i.e. position angle
and ellipticity. The (projected) position angle θ is defined as
the orientation of the ellipse’s semi major axis a, measured
in degrees counterclockwise from north. The ellipticity ε is
defined as one minus the semi minor axis a divided by the
semi major axis b. In other words: its value shows how much
the ellipse deviates from being circular (With ε = 0 being a
perfect circle).[1, 2, 3]
Figure 5 shows a R band plot of the position angle of the
isophotes as a function of semi-major axis a. Apart from a
few values close to the centre – which have large error bars –
the position angle doesn’t seem to change at all. This means
no isophote twisting occurs, a process common in triaxial
elliptical galaxies. If it did the change in apparent position
angle would be larger for isophotes which are more nearly
round, so isophotes with different ellipticities would end up
having different position angles. The fact that this doesn’t
happen could have a number of reasons, but in this case the
2.4 Ellipticity of NGC-7331
Figure 6. Ellipticity of NGC-7331
Figure 6 shows a B band plot of the ellipticity of the
isophotes as a function of semi-major axis a. It is clear that
the ellipticity does change as a function of a. The graph shows
a curved line. The isophotes are circular at the centre and then
get more and more elliptic until about a = 40 pixels. This is
explained by the fact that NGC 7331 is a spiral galaxy which
consists of a flat, rotating disk and a central concentration
of stars known as the bulge. The bulge is roughly shaped
as a sphere and therefore projects circular isophotes. The
flat circular disk projects elliptical isophotes when viewed
at skew orientations. Far away from the bulge the shape of
the isophotes is only influenced by the disk which causes the
ellipticity to stabilise. In general, isophotes have also been
Galaxy radius NGC-7331 late-type spiral galaxy — 4/4
found to become more circular near the centre of the brightest
galaxies in clusters and groups.[1, 5]
It can be concluded that the position angle of the isophotes
of NGC 7331 does not change as a function of semi-major
axis, whereas the ellipticity does. This implies that it is a
spiral galaxy viewed at a skew angle and that it might be the
brightest of its group.
3. Discussion
Briefly said, we are quite satisfied with our results. The graphs
clearly show us what is happening with properties of the
galaxy and how these match with the literature. Besides that
we learned a great deal about how to use the software at
the telescope, data reduction and the program IRAF. It also
sharpened our python programming skills.
4. Conclusion and summary
An exponential profile fits best for the surface brightness
profile of NGC-7331. The scale length for the R-band is 37
pixels, for the B-band 32 pixels and for the V-band 42 pixels.
The ellipticity of the isophotes changes with the semi-major
axis and the position angle of the isophotes stays approximatly
the same. All this leads to the conclusion that NGC-7331 is
certainly a spiral galaxy.
5. Appendix
On pages 5 till 7 the appendix will show an example of our
used programs and the galBsub.dat file which was used as a
data file for the plotting of the properties in the B-band.
Acknowledgments
Advice given by prof. dr. Scott Trager has been a great help in
finishing our project. Also Assistance provided by Anastasia
Ponomareva and Nadine Giese was greatly appreciated.
References
[1]
S.C. Trager.
Various presentations and articles.
www.astro.rug.nl/∼sctrager/*, October 2013.
[2]
M Whittle. Astr 553 5: Spiral galaxies: Extragalactic
astronomy. www.astro.virginia.edu, June 2011. web. October 2013.
[3]
Melott A. L. Chambers, S. W. and Miller C. J. The nearest neighbor alignment of cluster x-ray isophotes. iopscience.iop.org, February 2002. web. October 2013.
[4]
Kormendy J. Elliptical and cd galaxies:observations of
galaxy structure and dynamics. California Institute of
Technology,, March 2002. web. October 2013.
[5]
Binney J.
Observations of nonspherical structure:dynamics of elliptical galaxies and other spheroidal
components. Ann. Rev. Astron. Astrophys., 20:399–429,
1982. web. October 2013.