Many spiral galaxies, including our own, show an "integral sign" twist
in their outer disc. This feature is a characteristic of a warp in a
galaxy. Galactic warps can be observed in the neutral hydrogen layer as
well as in the stellar disc of a galaxy, although they are more
pronounced in the extended neutral hydrogen layer of a galaxy (deGrijjs 1997).
Warp in a galaxy can be conceived as a discrete mode of bending of the disc,
when the disc is subjected to an aspherical potential of an oblate halo (Sparke
& Casertano 1988). They can also arise from when the galaxy disc, embedded
in a rotating halo, has its angular momentum axes misaligned with respect to
that of the halo (Debattista & Selwood 1999). Other models suggest that
they could be the result of cosmic infall and outer gas accretion or could
arise from an intergalactic magnetic field (Reshetnikov & Combes 1998).
Some observations suggest that presence of a warp in a galaxy is strongly
related to its environment. Thus, a galaxy in a rich environment is likely to
have a warp as compared to an isolated one <(Reshetnikov & Combes 1998).
But, on the other hand, there have been evidences of warps in isolated galaxies
as well (deGrijs 1997). A common outcome of all these models
and observations is that the analysis of warps in galaxies can provide
important information on the distribution of dark matter around these galaxies,
which has been the driving force to study the optical warp in NGC 5529.
This galaxy was chosen for this study because previous work on this
galaxy by R. de Grijs and P.C. van der Kruit in 1995 (deGrijs & Kruit, 1995)
indicated the presence of a warp in its stellar disc. Another reason
for choosing this galaxy was that it is nearly an edge-on galaxy with
an inclination angle of 86 degrees as determined by R. de Grijs in his paper
mentioned above. This makes it a good candidate to study its vertical
structures as unknown inclination effects can be avoided. Moreover, the galaxy
resides in an isolated environment, thereby meaning that it is not interacting
with other galaxies or undergoing the process of merging. Thus, it makes an
ideal candidate to verify the claim that the environment of a galaxy doesn't
play a crucial role in making its disc warped.
A warp is defined as the deviation of outer disc of a galaxy with
respect to the plane in the inner region of that galaxy and the amount
of deviation gives the warp angle. Thus, it becomes important to have
well-resolved data as one goes further out towards the outer disc of a
galaxy. Hence, it is very important to choose the right filter and
signal-to-noise ratio that could give the best results. For, this
purpose I band was ideal as it is not sensitive to dust, which
is very prominent in the outer disc of this galaxy. In order to obtain a warp
curve from the observed data, which is essentially the observed intensity from
the galaxy, vertical bins of certain sizes need to be extracted from the data,
along the major axis of the galaxy, to get a high signal-to-noise ratio.
Intensity-weighted mean algorithm is then applied to each bin and the loci of
these centroids as a function of radius along the major axis of the galaxy
would produce the required warp curve. The warp curve can then be used to
obtain warp angle as a function of radius. A plot of warp angle as a function
of radius can be used to distinguish between the nature of the warp of a galaxy.
This distinction has been discussed in a paper by Linda S. Sparke and Stefano
Casertano (Sparke & Casertano). According to this paper, if a galaxy is
embedded in an aspherical potential of an oblate halo, two types of bending
modes for the disc are possible, either the outer parts of the disc deviate
away from the midplane of the halo or bend towards it. These two families of
bending modes are referred to as Type I or Type II respectively. However, the
difference between these two classes is not observable as the halo plane
cannot be seen. But, indirectly they can be distinguished on the basis of the
nature of the two types of warps. Type I warps change abruptly near the
outer edge of the disc whereas, Type II warps generally start around 3
or 4 scale lengths where the disc rotation curve falls and extend over
half the disc.
NGC 5529 was observed in
I band on 2004 May 17 (UT) and
2004 May 23 (UT), with the ST8 CCD detector mounted on the 0.25 meter
Great Ohio Telescope (GOT). Both nights were non photometric and the
last set of observations was taken through a thin layer of fog. Also,
both nights became slightly windy towards the end, which affected the
images obtained for NGC 5529 although this did not affect the results
significantly. For the first night, nine evening flats were taken, 3 in
V, 3 in
I and 3
in
R filters at exposure times ranging from 10 to 180
seconds. The
V filter was
used by another observer, observing a different object on the same
night however the evening flats in
R
filter were discarded later as no other observers, observing on the
same night, needed it for their science.
The evening flats were followed by recording seven zeroes of exposure
time 0.11 second each and then two darks were taken for 600 seconds
each. After that one more zero of exposure time 0.11 seconds was
recored before starting with the actual observations. After first set
of observations was completed by the first observer, three more zeroes
were taken for 0.11 seconds and again the actual observations were
carried out by the second observer. One more dark, 600 seconds long was
recorded after the second set of observations was over. NGC 5529 was
observed later in the night. It was observed in 5 frames, each 600
seconds long until it moved above 2 airmasses. The galaxy was not
positioned in the center of the CCD field of view, in order to have the
guiding star in the guiding frame of the CCD. After this last set of
observations was complete, one more dark for 600 seconds was recorded
and then 11 zeroes were taken for 0.11 seconds each. Then, ten morning
flats were taken, 4 in
I band
and 6 in
V with time ranging
from 120 seconds to 10 seconds.
For the second night, total eight evening flats were taken, 3 in
V, 4 in
I and then one exposure again in
V ranging in time from 10
seconds to 200 seconds. They were followed by nine zeroes with each
exposure being 0.11 seconds long. Then two darks were taken each of 600
seconds before starting with the actual observations by the first
observer. NGC 5529 was observed later in the night, about at the same
time as that for the first night. It was observed in the
I band in 6 frames for 600 seconds
per frame. The last observation was followed by two darks of 600
seconds each and then 11 zeroes of 0.11 seconds each. Finally, a total
of 11 morning flats were taken, 5 in
I and 6 in
V ranging
in time from 150 seconds to 10 seconds. For this project, only flats in
I were used from both the nights.
3. Reductions
The basic image
reduction of frames from two nights was carried out in
IRAF. For the first night, all the
22 zeroes were combined after visually examining each of them
separately. Then, all the 4 darks were also visually examined
individually before combining them together. These combined darks were
then zero corrected and inspected. These combined zeroes and
zero-corrected darks were then used to dark- and zero-correct the flat
fields. From, the first night only 3 out of the 4 morning flats in the
I band were used as they resulted
in a much better flat-corrected object frames. Once the chosen flat
frames were corrected, then individual object frames from the first
night were examined visually. These 5 object frames were then dark and
zero corrected, which resulted in less noisier object frames. The next
step was to combine the chosen corrected flat frames and then
flat-correct all the 5 object frames. The final flat-corrected object
frames were very flat with a cleaner image of the galaxy without any
noticeable bright ring, which was present in the uncorrected frames.
This completed the basic reduction process for the images from the
first night. The second night's images were also reduced in the same way by
using all the zeroes and darks taken on that night, however, only 4 out
of 5 morning flats were chosen to do the flat field-correction on the
object frames for the same reason as mentioned above. The final flat
field and dark- and zero-corrected object frames were much more cleaner
than the uncorrected frames and also very flat to look at without the
presence of any noticeable bright ring in the images. However,
presence of some bad pixels with extremely large negative values were
noticed in all the images from the second night. This problem was fixed
by using a code, which filled up these pixels with the Poisson
distributed noise pixels.
After the basic reduction of images, the next step was to remove any
cosmic rays present in the images. The cosmic ray removal process was
carried out using a code in
C -
language available on the internet (Wjotek, 2004). The cleaning threshold
parameter was set to a value of 4 in
C code. The images from both the nights were individually cosmic ray
cleaned and then carefully examined to see if cosmic ray cleaning over cleaned
the images. It was then decided to use only 1 cosmic ray cleaned image out of
5 cleaned images from the first night and 4 cosmic cleaned images out of 6
cleaned images from the second night. This was followed by registering and
coadding the images. For registering, 4 non-cosmic cleaned and 1 cosmic cleaned
images were used from the first night and were registered using
'xregister' task in
IRAF under the package
ccdred. After registering the
images, the next step was to coadd the images for each night. This was
carried out by using the task
'imexpr'
under
ccdred and then
the output image from each night was trimmed using
'imcopy'. This procedure resulted
in two images as the final outputs from each night. Hence, the next
important task was to combine those final output images from each night
before doing any kind of data analysis. In order to do this, few steps
in astrometry were followed and then the two images were first
registered using the task
'wregister'
and then coadded using
'imexpr'.
This resulted in one final image as an output of adding two final images
from each night. The final step, before going to data anaylysis, was to
perform sky subtraction on the final image. For sky subtraction, three
regions from the final image were chosen and
'imstat' task was used to obtain
the average brightness level, in counts/pixel, for those three regions
and the average of those three mean values was used to subtract from
the final image using
imexpr'.
The sky subtracted image was then used to extract the information
needed to get the warp curve of the galaxy. The final coadded, trimmed and sky
subtracted image of NGC 5529 is shown in figure 1. This image was used to
finally extract the data and get the warp curve out of it.
|
Figure 1: I band image of NGC 5529 in the final coadded, trimmed and
skysubtracted frame. The colors shown here are not the true colors of the
object.
|
4. Results
The final coadded, trimmed and sky
subtracted image was rotated by a trial-and-error method, which
invloved a few iterations of rotation angles and checking contour
profiles for the rotated image until the plane of the galaxy looked
parallel to the horizontal axis. This rotated image was again trimmed
in a way that would extract the galaxy out of the whole image and give
enough area to even include the last contour for data analysis. Figure 2 shows
the final rotated image of the galaxy with contour profiles fitted onto it.
|
Figure 2: Rotated and trimmed image of the galaxy with contour profiles
fitted onto the image.
|
The first step in this direction involved reading the image into
IDL, which generated a two dimensional array. This
array was then further trimmed in order to get vertical bins of sizes 12
arcsecond x 56 arcsecond. The trimmed image of NGC 5529 of size 636 arcsecond x
56 arcsecond is shown in figure 3. In this figure the image is divided by its
total intensity integrated over
z.
|
Figure3:Trimmed image of NGC 5529 of size 636 arcsecond x 56 arcsecond.
This image is normalized with respect to its total intensity.
|
The bin size was decided in such a way so as to have a good signal-to-noise
ratio and resolution of data points in the outer parts of the galaxy, where the
signal is noise dominated. Also, this bin size gave a relative error of around
2% in each bin. After deciding on the bin size, intensity-weighted mean was
calculated for each bin along the radius of the galaxy, let's call it vertical
centroid (vertical height), and similarly intensity-weighted mean was calculated
for each bin along the vertical height of the galaxy, let's call it horizontal
centroid (radius). 1 sigma errors were calculated for vertical centroids of
each bin. The errors become larger in going further out in the galaxy along its
radius. Finally, the warp curve was obtained by plotting the vertical centroids
against horizontal centroids as shown in figure 4. The curve obtained is not
centered around the center of the galaxy. The curve indicates a definite
presence of one-sided warp in NGC 5529.
|
Figure 4:Vertical centroids (in arcseconds) are plotted against
horizontal centroids (in arcseconds) to produce a warp for NGC 5529. 1 sigma
errors on the vertical centroids become larger as one moves from center towards
the outer disc of the galaxy.
|
From this graph, angles between vertical centroids and the center of
the galaxy were calculated and plotted against the horizontal centroids
to get a graph between warp angle and horizontal centroid (radius).
Vertical and horizontal brightness profiles were also examined for the galaxy.
The surface brightness was obtained by converting photon counts to uncalibrated
magnitudes. As shown in figure 5, the profile closely follows an exponential
profile but does not show presence of any sharp edge to the disc as one moves
away from the center of the galaxy towards its outer disc along the radius.
Errors were not calculated for these profiles.
|
Figure 5: Horizontal Surface Brightness profile for NGC 5529. The profile
does not show the presence of a sharp edge to the disc.
|
Exponential scaleheight as a function of radius was also calculated independently.
1 sigma errors were calculated approximately for scaleheights using a program
in
IDL available on the internet (Craig). Figure 6 shows scaleheight
as a function of radius in arcseconds.
|
Figure 6: Exponential scale height distribution for NGC 5529 as a
function of radius along the major axis. Errors become larger in the outer
parts of the galaxy.
|
5. Discussion
The warp curve for NGC 5529 indicates
a definite presence of a one-sided warp in this galaxy in the NW
direction. The reason for the curve not being centered around the
center of the galaxy is the way the final rotated image was trimmed.
This was done in order to focus more on the side which clearly shows a
twist as one goes further out along the radius of the galaxy. The other side
of the galaxy was more dominated by foreground stars, which could have
severely contaminated the warp curve on that side and hence the final
rotated and trimmed image is not equally extended on both sides. Figure 6 shows
that the exponential scale height begins to increase with radius at around
radius of 80 arcseconds or 1.33 arcminutes. This value is consistent with that
of de Grijs (de Grijs, 1996) according to which the radius at which the scale height begins to increase is at around 1.2
arcminutes. Using the published exponential scalelength value for this galaxy
(de Grijs, 1996), and, knowing that for most of the galaxies warp generally
begins at radii of about 3 to 5 times the exponential scalength of that galaxy
(Sparke, 1988), the radius around which the warp in the galaxy sets in was
estimated to be around 1.44 arcminutes, which is consistent with the experimental
value of approximately 1.26 arcminutes (the center of the galaxy is approximately shifted by -0.63
arcminutes from the center of the graph). Thus, it can be concluded that for this galaxy, the warp approximately sets in where
the exponential scale height begins to increase with radius along the major
axis. The plot between warp angle and radius was highly inconclusive and
hence has not been included here. This could be possible because the midplane
of the galaxy was not determined very accurately as rotation of the galaxy was
a trial-and-error method. Thus, with this information it was difficult to
conclude if the galaxy exhibits a Type I or Type II warp (Sparke, 1988). Also,
because of lack of time, theoretical modelling of the warp curve for this galaxy
could not be done and hence a quantitative estimate of the core radius
of the halo, in which the galaxy is embedded, could not be obtained.
Acknowledgments
I would like to thank Dr. Thomas Statler for helping me throughout my
project. Without his guidance, it would not have been possible to
materialize this project. I would also like to thank Dr. Joseph C.
Shields, Dr. Mangala Sharma, Dr. Brian Mc Namara and Dr. Markus
Boettcher for helping me at various stages of my project. I am highly
thankful to all my colleagues for their useful discussions , especially
to Steven Diehl and James Steiner for helping me in understanding many
things and giving me useful advice at the right time.
References
Debattista Victor P. & Selwood J.A., 1999, ApJ, 513, L107
de Grijs R., 1997, www.ub.rug.nl/eldoc/dis/science/r.de.grijs/c9.pdf
de Grijs R. & van der Kruit P.C., 1996, Astron. Astrophys, 117, 19
Craig B. Markwardt, http://cow.physics.wisc.edu/~craigm/idl/idl.html
Reshetnikov Vladimir & Combes Francoise, 1998, Astron. Astrophys.,
337, 9
Sparke Linda S. & Casertano Stefano, 1988, Mon. Not. R. astr. Soc.,
234, 873
Wojtek Pych, 2004, PASP, 116, 148
