2. 2 M. E. Conrad et al.
Figure 1. The Canada - France - Hawaii Telescope (CFHT), equipped with
a 3.6 meter mirror and two mosaics of CCD detectors; MegaCam used for
all scales of structures, and WIRCam used for further wide-field infrared
observations. 7
Figure 2. The science case for MSE - The origin and diversity of stellar
systems (top left); Milky Way archaeology at the earliest times (top right);
galaxy evolution across cosmic time (bottom left); illuminating the dark
Universe (bottom right).5
In addition to these main themes, MSE could also achieve 5:
• An exceptional 3D map of galactic interstellar medium (ISM)
• The first panoramic, wide-field spectroscopic survey
• Measurement of gravitational masses and density profiles for a
complete sample of dark matter halos (to scales of dwarf galaxies)
• A comprehensive study of the relationship between stellar and
gravitational mass, baryon dynamics, and star formation efficiency
Figure 3. The Maunakea Spectroscopic Explorer. 5
in dark matter halos - this will consist of a baseline survey, gathering
spectra for half a million galaxies within a redshift of 0.15. This is
expected to cover an area four times larger than the GAMA survey
(see section 1.2), as well as reach to a extent of 2 magnitudes deeper.
The larger purpose of this specific project is to target the lowest
mass galaxies, and simulate the collection of their spectra via
fiber assignment. To do this, there are two proposed spectroscopic
surveys S1-W and S1-D to be conducted with MSE, both targeting
galaxies within z < 0.2; these will be modeled within this
simulation. The S1-W and S1-D surveys will be foundational for
later surveys, which will then be carried out at larger redshifts.
The wide area survey, S1-W, will aim to cover a cosmologi-
cally representative volume of 300 x 300 x 300 Mpc/h, with an
area of 3200 square degrees, and a depth of i < 23. The deeper
survey, S1-D, will target specific environments with 100 square
degree area, reaching i< 24.5.
Both of the said surveys will need to be spatially complete
(sample targets spanning entire field of view, not just local targets),
have a sufficiently large sample size, and include at least two
fiber configurations per field (to ensure both participants of a
close galaxy pair are sampled). The minimum integration time is
estimated to be an hour, yielding a minimum survey time of 5100
hours. Within this time, it is also estimated that 3000 spectra will
be collected per hour, resulting in 7 million spectra collected per
year.
1.2 Similar Surveys
In preparation for the construction of this algorithm, the GAMA
spectroscopic survey was researched because it also desired to ob-
tain spectra for nearly 100 percent of the magnitude - selected target
sample. The GAMA survey has been operating since February 2008
on the 3.9 meter Anglo - Australian Telescope (AAT) and is now
completed. The team had the following main scientific goals 1,3,6 :
(i) To test modified theories of gravity
(ii) To measure the connection between star formation fuelling,
stellar mass build-up and feedback processes.
(iii) To reveal the detailed mechanisms that govern the build-up
of the stellar content of galaxies.
(iv) To directly measure the recent galaxy merger rate as a
function of mass, mass ratio, local environment and galaxy type.
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3. Fiber Configuration Algorithm for the Maunakea Spectroscopic Explorer 3
Figure 4. Spatial redshift completeness of GAMA after first year of survey;
z approx 0.1. 6
The latter is loosely parallel to the interests of this algorithm.
The survey contains three similar 12 degree by 4 degree ar-
eas centered on 9h + 1◦; 12h + 0◦ and 14h30m + 0◦ 1,3 resulting
in just under 144 square degree area.
GAMA had the following requirements similar to that of
this algorithm (to be expanded on later in this paper) 6:
(i) Spatial completeness - require at least 99 percent of each
field to be ≥ 80 percent complete.
(ii) Pair completeness - require fiber assignments for galaxy
pairs within 40 arcseconds of each other - this is the range in which
fibers collide for this system
(iii) Reobservation of targets that failed to obtain spectra
The GAMA algorithm made use of prioritizing galactic targets;
this allowed for specific spectra to be obtained - perhaps the
“worst-offending" objects located in highly clustered regions. In
addition, the GAMA algorithm also manipulated the tiling of fields
on the survey area to optimize the run time while still achieving
high completeness.6
GAMA originally had two different strategies for their al-
gorithm - one greedy and the other dengreedy. The former dealt
with the number of redshifts obtained and involved a 2 degree
survey region with the greatest number of high priority targets. The
downfall of greedy was that in multiple tiles, more targets were
present than fibers - this would increase the total completeness,
but not exactly the spatial completeness. In addition, placing the
tile centers at the densest point might be too greedy. The latter,
more subtle algorithm, dengreedy, dealt with spatial completeness,
similar to the 1 year completeness modeled in Fig. 4. Tile centers
in this method were chosen based on the least spatially complete
Figure 5. Comparing greedy tiling mechanism for arranging tiles (top)
and dengreedy mechanism (bottom). It is seen that the former positions
tiles further inside the limits of the survey, thus causing more overlapping,
whereas the latter pushes the limits while positioning tiles. Dengreedy is
clearly more effective at producing optimal tile packing.6
location. This method reached angular completeness quicker than
the greedy approach, but typically returned fewer redshifts. A
comparison of the tiling strategies can be found in Fig. 5. 6
It was determined by GAMA that the dengreedy mecha-
nism was more advantageous; this was mostly apparent nearing
the end of the survey. Dengreedy reached high completeness faster
than greedy; for example, 46 tiles versus 48, respectively. The
former algorithm consequently returned consistently better total
and spatial completeness, thus becoming the chosen algorithm for
the remainder of the survey. 6
Once the strategy for tiling was determined, assigning prior-
ity to targets became the next step, particularly when focusing
on merging galaxy pairs and closely packed regions. For this
reason, reobservation, or re-running a configuration on the same
tile, occurred to ensure all participating targets were included.
The worst offending target, or a target lying in a dense region,
had priority increased by 1. Once a target was assigned a specific
priority level, the algorithm would assign fibers in the order of
priority. The targets too close to the galaxy-fiber pair were then
omitted from the list of potential galaxy targets for the tile. The
next worst offender was then found, and the previously mentioned
process was repeated until targets within a distance of 40” were
absent from the sample. If for any field, 5 or more fibers were not
assigned, the field position was moved, regardless of the number of
targets. The result of one year of survey using this process can be
seen again in Fig. 4. 6
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4. 4 M. E. Conrad et al.
While the main purposes of this paper’s algorithm don’t pre-
cisely align with that of GAMA, methods similar to GAMA’s
were kept in mind and sometimes employed during the code
construction.
2 METHODS
Python 2.7 was used to design an algorithm that assigns optical
fibers to galaxies based on conditions set forth by the structure
of the fiber-fed multi-object spectrograph. For testing purposes, a
Bolshoi dark matter simulation model of 451,000 galaxies with a
10 degree by 10 degree area was obtained from the Theoretical
Astrophysical Observatory.8
To remain as basic as possible, the algorithm gathers user-
supplied parameter input, generates hypothetical fiber locations,
loops over the supplied dataset of galaxies, and assigns fibers based
on whether they are available.
Due to the short duration of this project, the simplest fiber
assignment mechanism was used; the greedy algorithm was
originally considered, taking galactic target density into account
when assigning fibers. All TAO sample targets were initially
assigned a priority of 5; if the target was determined to have a
position located within a dense region, the priority was increased
to 4. If the location was not within a dense region, the priority
was lowered to 6. It was then realized that this method might
be too time consuming for the scope of this project. Instead, all
TAO sample targets were assigned the highest priority of 1. Upon
assignment of a fiber, the target’s priority was lowered to 2. This
priority was useful when indicating which targets to include in
each configuration.
2.1 Fiber Positioning Systems
For the purpose of this project the fiber positioner unit will be
assumed to be the Echidna due to the fact that a decision hasn’t yet
been made regarding the technology of the fiber positioning system2
To elaborate, the positioner is an array of 3200 actuators,
each securing the end of one of 3200 fibers. This device has the
ability to move each fiber end independently within a patrol field
of 174 arcsecond diameter, enabling precise placement of the fiber
on the image of the studied object. 2,4 The fiber machinery limits
the distance between two fibers to 12 arcseconds, as opposed to 40
as seen with the GAMA survey.
Since the fibers cannot be placed arbitrarily close together,
their positions were assigned in a radially uniform manner (Fig.6),
then masked over a selected field of view (Fig. 7), as seen in Fig.
8. A minimum initial separation of all fiber home positions was
calculated to be around 0.24 degrees for a field of view of 1.5
square degrees containing roughly 3200 fibers.
2.2 Algorithm Specifics
Initially for testing purposes, a field of view was chosen in the center
of the dataset at (RA,dec) of (5.0, 5.0) (Fig. 7). The inhomogeneous
distribution of galaxy position seen emphasizes the need for a
spatially complete survey. Therefore, it is imperative that objects
are sampled in both clustered areas as well as the spacious ones;
Figure 6. Fiber home positions assigned radially for a field of view centered
on (5,5)
Figure 7. A field of view located in the center of the TAO dataset. This plot
emphasizes the inhomogeneous nature of galaxy positions and the need for
a spatially complete survey.
closely packed regions of galaxies yield useful information for
many fields of study. That said, if two such galaxies are a distance
less than 12 arcseconds apart, only one is able to be measured due
to restrictions on fiber movement, also similar to GAMA. This is
one issue the algorithm aims to solve with reobservation of targets
that theoretically failed to obtain spectra.
From Fig. 8, it is seen that a number of galaxies could be
contained within one patrol field. The question then arises, "How
do you choose which galactic targets receive a fiber?". At the same
time, a single galaxy could fall within several different patrol fields,
as seen in Fig. 9, where there are 4 fiber assignment options in the
specific example. So the question must also be asked, "Which fiber
gets assigned to this specific galaxy?".
In order to properly simulate the placement of a fiber on a
galaxy, the limits of the fiber machinery need to be taken into
MNRAS 000, 1–7 (2016)
5. Fiber Configuration Algorithm for the Maunakea Spectroscopic Explorer 5
Figure 8. Determining if the locations of the fibers adequately cover the
field of view and the galaxies contained within
Figure 9. An example of determining the closest fibers for a single galaxy
(omitting surrounding galaxies)
account, as well as the user-defined parameters. This creates
conditions for the algorithm to include:
(i) The current galactic target the algorithm is inspecting must
not be within 12” of a previously successful assigned target - within
this distance fibers collide and will fail to obtain spectra
(ii) Each fiber must be assigned to only one galaxy - the
algorithm loops over the closest available fibers for each galaxy,
and chooses one that is available. If none are available, this
condition is not met
(iii) At least 10 percent of the fibers must be assigned to the
background to allow for background subtraction - if the number of
assigned fibers exceeds amount allotted for galaxy measurements,
the difference is randomly de-assigned.
Figure 10. Fiber configuration algorithm result for deep S1-D survey for
single tile centered on RA,dec = 5,5. Five configurations required to achieve
95 percent average completeness across magnitudes. Blue = first configura-
tion, red = second configuration, yellow = third configuration, green = fourth
configuration, pink = fifth configuration
If a galactic target fails to meet any of the requirements or be-
comes de-assigned after the third condition, additional configura-
tion rounds are conducted to assign fibers to the failures, simulating
reobservation. This process is repeated until the galaxy magnitude
completeness is satisfactory.
3 RESULTS
For the field of view seen in the previous plots, the designed algo-
rithm resulted in the plots seen in Figures 10 and 11. Magnitudes
corresponding to the S1-D survey were considered firstly; fainter
magnitudes were included in this run, thus increasing the number
of galaxies to be looped. For this reason, more configurations were
required to achieve a satisfactory completeness in all magnitudes
(Fig. 10). For each subsequent configuration, targets that were
assigned fibers in previous configurations were omitted to ensure
every target within the TAO sample received a fiber(in turn
also ensuring a high total completeness), and to highlight the
effectiveness of each configuration. Each configuration is modeled
in Fig 10. with different colours to demonstrate this effectiveness.
For the wide field S1-W survey (Fig. 11), fainter magni-
tudes were excluded, therefore lowering the amount of galaxies
looped. Consequently, the majority of targets received a fiber as-
signment in the first configuration, resulting in less configurations
required to achieve nearly 100 percent completeness. It is seen
in Fig. 11 that the third round assigned merely a few percent of
galaxies per magnitude, if at all.
Taking the above into consideration, it must be remembered
that this was just a simple simulation; the 300 Mpc volume
requirement of the S1-W survey, and the 100 square degree area
requirement of the S1-D survey was not included. In future work
on this algorithm, these would be included, but it is expected that
similar results and run times as the present simulation would be
seen.
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6. 6 M. E. Conrad et al.
Figure 11. Fiber configuration algorithm result for wide field S1-W survey
for single tile centered on RA,dec = 5,5. Two configurations required to
achieve 99 percent average completeness across magnitudes. Blue = first
configuration, red = second configuration, yellow = third configuration.
Figure 12. Average completeness in each magnitude for 100 tiles across
dataset
This simulation was repeated for 100 tiles linearly spaced
out across the 10 degree by 10 degree TAO dataset (see Fig. 15);
the average completeness results for each magnitude can be seen in
Figures 12 and 13, along with the respective standard deviations.
The higher magnitudes (i.e 14 < i < 15), and therefore the brighter
targets, resulted in the largest error. The remainder of the magnitude
bins saw consistent error alongside consistent completeness. Con-
sidering the target completeness for this algorithm was originally
80 percent, the results are quite satisfactory.
To summarize, the resulting number of configurations re-
quired for simulations of both the S1-D and the S1-W surveys
indicate that for a single field of view the user would require a
possible integration time of 5 hours and 3 hours, respectively, to
gather spectra. That said, it must be remembered that the simulation
configurations are non-cumulative; if this method is reproduced,
Figure 13. Average completeness in each magnitude for 100 tiles - including
standard deviation.
Figure 14. Legend for Figure 15; Range of Completeness
Figure 15. Comparing the tile completeness across the 100 field of views,
as well as the coverage of tiles and amount of overlapping
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7. Fiber Configuration Algorithm for the Maunakea Spectroscopic Explorer 7
the integration times would theoretically be less. By extending
the scope of the simulation algorithm to 100 tiles, the integration
time would overall be an average of 500 hours, and 300 hours
respectively. Thus, an estimated total of 800 surveying hours would
be required to gather spectra for a 10 degree by 10 degree area.
4 CONCLUSIONS
The resulting algorithm, although representing the simplest
configurations possible, produced optimistic results. The deep
S1-D survey required an average of 5 configurations to reach 95
percent completeness. The wide field S1-W survey required on
average 2 configurations to near 100 percent completeness.
In reference to MSE science objectives listed in Subsection
1.1, although this algorithm is mostly focused on low mass galaxies
and surveys S1-D and S1-W, it could also be applied to the other
science goals. The survey simulation results that contrast densely
packed galaxy regions with more sparse regions could theoretically
shed light on the diversity of stellar systems. By limiting the
simulation to nearby redshifts, the algorithm could be used to
survey the Milky Way; the new 10 meter mirror would allow for the
discovery of new pieces to galaxy’s archaeology puzzle. If instead
used to survey fainter redshifts between 0.5 and 1.5 (ranging from
5.05 billion years ago to 9.36 billion years ago),spectra could be
obtained for stepping-stone galaxies at the phase between that of
the younger, more irregular galaxies (z ∼ 3) and the older, more
ordered galaxies we see today (z < 0.1). These spectra could aid
in the study of galaxy evolution. Finally, the simulation could be
applied to illuminating the dark universe through the collection of
information pertaining to the expansion of the universe via fiber
placement at high redshift.
Next steps would involve making use of methods similar to
that in GAMA - perhaps applying dengreedy methods to the
existing algorithm as we wish to have high spatial completeness;
i.e, adding increased priorities to worst offenders located in densely
packed regions. This would ensure fibers were placed on a large
fraction of the galaxies in this region, and maximize the spectra
collected. In addition, priorities could be included that prioritize
to faint magnitudes; a large part of the studies surrounding MSE
require spectra from low mass galaxies.
Also with respect to low mass galaxies,specific fibers could
potentially be allotted to specific magnitude ranges to again
maximize on low magnitude spectra, on top of allotting fibers to
measure the background.
Further optimization of this algorithm could arise from us-
ing fiber permutations with the proposed algorithm conditions to
yield the best possible configuration. Of course, the definition of
"best possible" would depend on the desires of the user. Whether
the user wishes to maximize the total number of spectra collected,
or wishes to locally maximize spectra, these parameters could be
added to the original user-defined input.
The GAMA study indicated that their most serious concern
was that fewer targets might be present on a given tile, therefore
causing inability of using 100 percent of the available fibers.
That said, this algorithm does not maximize on the potential
spectra that could be obtained with each configuration - as stated
previously, each configuration omits the assigned galaxies from the
previous. If these assigned galaxies were to instead be included in
the subsequent configurations (if success in meeting subsequent
conditions), all available fibers would be potentially used. At the
same time, additional spectra for a target would be an advantage
due to the offering of a more precise measurement.
As stated in the results section, the respective volumes and
areas of the surveys should also be included as the algorithm
develops.
If the instrument design is modified instead, immediately it
would seem obvious to try to construct a fiber positioning
system with a collision distance less than 12 arcseconds; perhaps
decreasing the size of the actuators would allow for this to occur.
A decrease in the actuator size would allow for more room to
position additional actuators and therefore additional fibers. This
would lower the number of configurations required and therefore
the amount of time needed to conduct the surveys.
ACKNOWLEDGEMENTS
I would like to acknowledge all the support that Michael Balogh
has offered throughout the past 4 months. Without his support and
motivation, this project wouldn’t have been possible. I have learned
so much about the world of astrophysics research, from gaining
experience in Python, to gaining confidence presenting seminars.
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(4) Maunakea Spectroscopic Explorer. (n.d.). Retrieved January 10, 2016,
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(5) McConnachie, A.W., et al., SPIE 2014
(6) Robotham, Aaron, et al., 2009, PASA, 27, 76
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