PS700
Case for Support
Stephen
Hamer
Identification of Star Forming Regions in the Galactic Plane
I. Overview of Project
The dense cocoons of dust and molecular gas in which new stars are formed often obscure them from view at visible
wavelengths. However at near to mid infrared wavelengths the radiation can pass though giving a glimpse of new born stars.
Spitzers IRAC camera can observe this radiation allowing the observation of young and newly formed stellar objects. This is
ideal for observing YSO’s (young stellar objects) because at these wave lengths each class of YSO has very distinct features.
I have recently conducted a study of some of the data collected by spitzer (Stephen Hamer, 2007, Classification and
distribution of young stars in the galactic plane, PH600, submitting). This study found that the ratio of T Tauri’s to protostars
was around 23:1. This was much higher than the value calculated previously. This previous result obtains a ratio of 10:1,
less than half of that observed in my study. The report put the anomalous result down to a selection process early on which
removed all objects which did not have all four data points. This was done because the standard definitions for a colourcolour diagram (Allen et al. (2004)) requiring all 4 data points. Time constraints did not allow these definitions to be
redefined for different colours.
Further to this the study also concluded that the definitions of YSO,s according to the gradient of their spectral
energy distribution was not the same as predicted over a larger data range (Lada (1887)) and that its was in fact not possible
to resolve T Tauris from main sequence stars by this method. How ever this part of the study was only done over a very
small data set. I would like to take the same data set as previously used and complete the analysis to identify all objects
within the region. With this done a more comprehensive study of the gradients of their spectral energy distributions can be
done. From here a complete analysis of objects throughout the galactic plane will be conducted leading to the identification o
star forming regions and the conditions present there.
II. Track Record of Applicants
It is my belief that it is past research that has given us a general understanding of the physics that forms the basis for
the strong interest in astronomical research within this country. From the work I have done previously[1], under the
supervision of members of the CAPS[2] group (Centre for Astrophysics and Planetary Science) at the University of Kent I
have developed some expertise in the various procedures and techniques that will be needed in the proposed work. I have
had the opportunity to work and learn from the members of the CAPS group through both a research project [1] and through
undergraduate studies at the University of Kent. As such I have developed a productive working relationship with members
of this group.
Stephen L. Hamer (Undergraduate Masters Student, University of Kent, SLH). Since 2004 I have been studying
Astronomy, Space Science and Astrophysics at the University of Kent, under taking such modules as Stars, Galaxies and the
universe (PH607), the Multiwavelength Universe and Exoplanets (PH507) and Multimedia for Astronomy, Astrophysics and
Planetary Science (PH512) which are relevant to the branch of research that I am proposing here.
During the my third year of study at the University of Kent, I undertook a research project under the supervision of Dr Dirk
Froebrich, a member of the CAPS group with a particular interest in related research fields, which introduced me to the
concepts, methods and results that are obtained when dealing with Young stellar objects [1]. This project was my main
inspiration for the proposed work as it left some very open ended questions wish I wish to answer with the proposed work
CAPS Group (Professor M. D. Smith, Dr J. Miao, Dr M. J. Burchell and Dr D. Froebrich, University of Kent). This
group covers a range of Astrophysics and planetary science research topics. The most relevant of these to the proposed work
is the study of dynamical collapse modelling of induced star formation. Recent publications[3][4][5][6][7] from this group such as
“The origin of stars: simply explaining Complex Systems” (Smith, M.D. 2006,)[3] and “Triggered star formation in
bright-rimmed clouds: the Eagle nebula revisited” (Miao, J et Al. 2006)[4] have particular relevance to the proposed
work. The members of this group also find time to lecture at the University of Kent and run some of the 3rd and 4th
year projects such as the one I undertook under the supervision of Dr Dirk Froebrich[1].
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Case for Support
Stephen
Hamer
Track Record References
[1] Stephen Hamer, 2007, Classification and distribution of Young Stars in the Galactic Plane, PH600, submitting.
[2] http://astro.kent.ac.uk
[3] Smith, M.D. 2006, The origin of stars: simply explaining Complex Systems, in proc.; Teaching and
Communicating Astronomy (EDP Sciences), eds. A. Ortiz-Gil, V.J. Martìnez,pp 125-127
[4] Miao, J. ; White, Glenn J. ; Nelson, R.; Thompson, M.; Morgan, L. 2006, Triggered star formation in brightrimmed clouds: the Eagle nebula revisited, Monthly Notices of the Royal Astronomical Society, Volume 369, Issue
1, pp. 143-155
[5] Stanke T., Smith M.D., Gredel R., Khanzadyan T. 2006, An unbiased search for the signatures of protostars in
the ¦ÑOphiuchi A Molecular Cloud: II. Millimetre continuum observations, A&A, 447, 609
[6] Kumar, M. S. N.; Davis, C. J.; Grave, J. M. C.; Ferreira, B.; Froebrich, D. 2007, ``WFCAM, Spitzer/IRAC and
SCUBA observations of the massive star-forming region DR21/W75 - II. Stellar content and star formation'',
2007MNRAS.374...54K
[7] Davis, C. J.; Kumar, M. S. N.; Sandell, G.; Froebrich, D.; Smith, M. D. ; Currie, M. J. 2007, WFCAM, SpitzerIRAC and SCUBA observations of the massive star forming region DR21/W75: I. The collimated molecular jets,
2007MNRAS.374...29D
III. Scientific Background
III.1 Introduction
Star forming region or SFR is a term which describes a particular region of space in which stars for, through the collapse of
gas and dust. Since such regions are undergoing star formation the age of stellar object in these regions is generally lower
than the age of Stellar objects in the rest of the galactic plane. Since stellar objects are formed from the collapse of Gas and
dust SFR are generally associated with regions of high density of the Inter stellar medium (ISM) and in particular with giant
molecular clouds (GMC's) and the sub structure within them. It is these clouds which collapse to form the dense cores which
eventually become stars. This collapse of gas is currently the focus of intense academic interest. Understanding this process
and the subsequent process of star formation from dense core to main sequence star is vital for understanding the origins of
our own solar system and stars and galaxies in general.
Young Stellar object or YSO is a phrase used to describe pre-main sequence stars. These are objects which are
currently evolving from dense cores of gas and dust into stars. The objects undergoing this process are split into several
distinct classes which based generally on their basic properties. Of particular interest in this project are Protostars and T
Tauri's. Protostars or Class I YSO's have a dense object at the centre which has reached temperatures hot enough to radiate at
infrared wavelengths. Such objects are characterised by bi-polar jets and extensive discs around them. T Tauri's or Class II
YSO's are the next stage of evolution of stars. The disc is still present but has been greatly reduced by accretion of it into the
core. The bi-polar jets remain but are diminished as well. It is believed that it is at this stage of evolution that planets are
created. As such objects of this class are of particular interest in understanding the evolution of solar systems. Since these
objects form from gas and dust clouds they are often obscured from view at visibly wavelengths by the very clouds from
which they form.
The other classes of object are Class 0 or sub millimetre protostars and Evolved T Tauri's or class III YSO's. These
are not relevant here as Class 0 objects do not emit at the wavelengths studied and Class III objects are virtually
indistinguishable from main sequence stars. The IRAC camera aboard the SPITZER space telescope allows us to observe the
infrared radiation which can pass though this gas and dust. It is such observations which I intend to use in this project.
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Case for Support
Stephen
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III.2 Current Knowledge
At this point it is necessary to discuss what is known about the classes of YSO's of interest. T Tauri's have a very
distinctive spectral energy distribution which is caused by the disc surrounding the central object. These features are caused
by the disc emitting radiation as well as the central body. The disc emits at longer wavelengths than the peak emission of the
central body. This causes the Spectral energy distribution to have relatively flat line to the right of the peak rather than the
usual Boltzmann distribution. It can also be determined from observations of the spectra of T Tauri's that YSO's exist in this
Class for approximately 1,000,000 years.
Similarly Protostars also have distinctive features in their spectral energy distributions. However since in the case of
Protostars the disc is more extensive than that in T Tauri's the effect its emission has is also more extensive. Again the
emission from the disc affects the shape of the spectral energy distribution after the peak. However in this case it causes the
distribution to rise further from the peak emission by the central black body rather than fall of as would be expected for a
simple Boltzmann distribution. The life time of protostars has been predicted at approximately 100,000 years by counting the
numbers of them relative to the number of T Tauri's. This found a ratio of T Tauris to protostars of approximately 10:1
suggesting that protostars have a lifetime of approximately 1/10th that of T Tauri's.
Due to the distinctive spectral features of T Tauri's and protostars at the wavelengths observed the class of any object
can be easily identified simply by comparing spectral features calculated from observations to models of each class. There
are two standard ways of doing this, an analysis of the gradient of each objects spectral energy distribution after the peak of
the black body emission and analysis of each objects position on a colour-colour diagram. The gradient analysis is described
in Lada (1987) which states the gradient range into which each class of object will fall. As such by identifying an objects
spectral energy gradient and comparing it to the standard models stated in Lada (1987) it is possibly to identify its class.
Since the Spectral energy distribution is a curve rather than a straight line the gradient after the peak must be calculated by
assuming a straight line of best fit through the points of the curve. A linear regression is best used to achieve this. The
colour-colour analysis is described in Allen et al. (2004) which identifies regions on a colour-colour diagram which would be
occupied by a particular class of object. As such by calculating the relevant astronomical colours and plotting them n a
colour-colour diagram objects in each of the regions can be identified and as such the class of the objects determined. The
necessary colours can easily be calculated directly from the data obtained by SPITZER by simply subtracting the magnitude
at one wavelength from the magnitude at the other wavelength.
III.3 Issues
During my previous work using data from SPITZER to analysis the class of objects in one regions of the galactic
plane several issues became apparent with the methods of analysis and the findings of the work. It is necessary to discuss
these now. The first Issue found during the previous work was that around 80% of the objects identified by SPITZER were
missing one or more of the data points necessary for analysis by the colour-colour method using the standard model of it
described in Allen et al. (2004). Since it was later determined that the gradient analysis method did not work over the
wavelength range used this meant that 80% of the data obtained by SPITZER could not be analysed using the standard
models. As has already been stated the gradient analysis method would not work for the wavelength range observed by
SPITZER's IRAC camera. This was because the gradient ranges described in Lada (1987) did not correctly identify an
objects class to any correlation with the Colour-colour method (in fact it identified almost 90% of the objects to be T Tauri's).
As such it was attempted to redefine the gradient ranges over the wavelength range used however this showed that the
gradients of main sequence stars and T Tauri's were un-resolvable over the sample used (Hamer et al. (2007)).
In my previous work it was also found that the ratio of T Tauri's to protostars was 23:1 rather than the expected value
of 10:1. This suggests that there are less protostars relative to T Tauri's than previously though and as such their predicted
lifetime would be correspondingly different. However due to removing 80% of the objects early in the analysis this cannot be
accurately confirmed and may simply be the results of a selection effect. Finally one of the major topics of academic interest
today on the topic of star formation is the idea of rapid collapse of gas caused by turbulence in the ISM. This process of star
formation suggests a rapid collapse from gas cloud to dense core which contests the classical view of star formation as a slow
quasi-static process. However for rapid star formation to occur the turbulence within the clouds would have to be constantly
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Case for Support
Stephen
Hamer
driven by some external mechanism. No such mechanism has yet been identified preventing rapid star formation from being
fully understood. In order to identify potential driving mechanisms behind the turbulence it is first necessary to identify
similar conditions and objects in star forming regions.
III.4 Scientific Motivation
A detailed understanding of the process of star formation is necessary if we are to understand the origins of stars, solar
systems and galaxies. However before we can attain this it is first necessary to be able to accurately identify the class of
objects so regions in which Star formation is occurring can be identified for study. To this end it is necessary to have
standard models which allow the class of any object to be identified quickly and accurately. It is a further requirement that
these methods can identify objects with less than perfect observations to ensure that false results are not obtained due to
studying only a fraction of the data available. Further more it is important to obtain accurate readings of information such as
the relative abundance of T Tauri's and protostars so that important deductions made from these findings are as accurate as
possible. Of Particular note in this instance is the life time of protostars which is crucial for fully understanding this stage of
development. Finally it is also necessary to know where Stars are forming so that conditions in these regions can be
identified and their role in the process determined. Further more by knowing where stars are forming it will be possibly to
identify potential candidates for the driving mechanism behind the turbulence responsible for rapid star formation.
IV. Aims and Objectives
The project will primarily focus on two main problems. Firstly Completion of the analysis done in my previous project by
analysing all objects in the region and accurately determining the Ratio of T Tauri's to protostars. This will require the
development f new analysis methods enabling most of the data to be used. Secondly Analysis of objects throughout the
galactic plane will be done using the new methods. These identified objects will then be used to find clusters of YSO's which
are potential star forming regions With this conditions in these regions can be identified and compared. Information on
known objects in these regions will then be used to identify potential driving mechanisms behind the turbulence necessary for
rapid star formation.
The aims of this project can be summerised as follows:(a)
The development of standard methods which will allow the class of most young stellar objects to be determined
quickly and accurately using information over the wavelength range of 3.5 - 8 micrometers
(b)
Obtain an accurate reading of the ratio of T Tauri's to protostars in the galaxy and use this as a means to estimate
the lifetime of Protostars if different from the currently expected value of 10:1.
(c)
Identification of conditions in Star forming regions and the identification of potential candidates for the driving
mechanism of turbulence in molecular clouds.
The specific objectives of the project will be data analysis that will yield:(i)
A set of standard methods to allow the determination of a YSO's class without the necessity that the object have
readings at all four wavelengths obtained by SPITZERS IRAC camera
(ii)
Identification of the class of YSO's throughout the galactic plane.
(iii) Identification of potential Star forming regions throughout the galactic plane.
(iv)
Understanding of the conditions in star forming regions and the identification of potential driving mechanisms of
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Case for Support
Stephen
Hamer
Turbulence in the ISM
V. Program of Work and Detailed Methodology
The program of work will begin with the selection of Good example of main sequence star, T Tauri’s and protostars
from those already identified. Once selected these object will have all possibly astronomical colours calculated for them.
These objects will then be plotted on various colour-colour diagrams and the regions on the diagram which they inhabit will
be identified. This will be done for several sections already studied to ensure correlation between the regions identified.
Once these regions have been identified they will be used to analyse the data missed in the previous project. Once all objects
(with three or more readings) have been classified this way their gradients will be calculated and each class will have a curve
of gradient against number of object with that gradient plotted. This will enable the gradient ranges for each class of object to
be identified and with this all object with more than two data points can be classified. With these standard analysis methods
objects throughout the galactic plane will be identified and plotted on a position plot so that clusters of YSO’s can be
identified as potential star forming regions. Once these regions have been identified they can be compared to knowledge
about each region and possible conditions necessary for star formation can be identified. This methodology is summarised
below and in the diagrammatic project plan, which is in the next section.
1. Development of
new standard
analysis methods.
- Sample selection
- Regions on the
colour-colour
diagrams
- Gradient Ranges
2. Full analysis of the galactic
plane.
- Including Ratio of T Tauri’s to
protostars
3. Position plot of objects in the
galactic plane.
- Used to identify potential star
forming regions
4. Identification of similar
conditions between SFR’s
- Including potential driving
mechanisms of turbulance
Improved ability to
determine class of YSO’s,
Improved knowledge of
the distribution of star
formation, identification
of potential conditions
needed for star formation
and potential candidates
for the driving mechanism
behind turbulence in
molecular clouds.
V.1 Development of new standard analysis methods
This particular Stage of the project will focus on developing the techniques needed for the analysis of the rest of the
galactic plane in later stages. The development of these methods are fundamental to the completion of this project and will
take up a large amount of the total time spent working on the project. This section of the project will be completed in three
separate steps each of which will be described individually.
Sample selection involves the selection of the initial objects used to redefine the regions on different colour-colour
diagrams. Because the objects are scattered across all regions of he colour-colour diagrams it is necessary to select only those
object which best fit the descriptions of each class of object, this should avoid spill over on other colour-colour which would
make the identification of regions representative of that class of object very difficult. Object well within the limits of each
original region will be selected to ensure good examples. For the main sequence stars a region close to the origin is selected,
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Case for Support
Stephen
Hamer
the region of 0.2 either side of the origin (0, 0) on both axis will be used. For T Tauris a region of 0.2 either side of the centre
of their election region (0.75, 0.4) on both axis was used and finally for Protostars a region greater than (1.3, 1.0) on both axis
was used.
Regions of the colour-colour diagrams have to be identified next. This first requires every colour possible to be
calculated for the objects selected in the previous step. Since an astronomical colour is the brightness at one wavelength
minus the brightness at a higher wavelength and SPITZER’s IRAC camera measures at four wavelengths there are a total of
six potential colours for each object, two of which are already known. These six colours mean there are a total of 15 different
colour-colour combinations however not all are necessary, only five are needed (one using all four readings, and another 4
using a different combination of three readings) one of which has already been used (the one using all four readings).
However all 14 unused combinations need to be investigated to determine which is the most suitable for identifying an
objects class for each combination of wavelengths. The regions on each colour-colour combination are identified by plotting
the positions of each class of object separately on the diagram and then visually identifying the region on the diagram which
they inhabit.
Gradient ranges will be identified by plotting each type of object separately on a scatter plot of gradient against
number of objects with that gradient. Before his can be done however it is necessary to identify the class of more objects
using the colour-colour ranges obtained in the step above. Once the class of all objects in one region of the galactic plane
have been identified using the methods above their gradients will be calculated and this will be the sample data for the
gradient scatter plot. This will give a good sample and will allow the gradient ranges to be resolved more accurately. Once
these gradient ranges have been identified any object with two or more of the readings taken by SPITZER’s IRAC camera
can have its class determined.
V.2 Full analysis of the galactic plane
Once the methods developed in section V.1 are found I will begin to analyse all the objects identified by SPITZER
across the whole of the galactic plane. This will be done by performing each different analysis technique separately until all
objects with two or more of the data points have been classified. After each analysis the objects analysed by that method will
be removed from the data set so that objects are not analysed more than once. Objects identified as either T Tauri’s or
protostars will be recorded separately along with their galactic coordinates. The total number of each class of object will then
be compared to each other to find the ratio of T Tauri’ to protostars throughout the whole of the galactic plane. This ratio can
then be used to estimate the lifetime of protostars since the lifetime of T Tauri’s is known.
V.3 Position plot of objects in the galactic plane
Once all of the objects throughout the galactic plane have been identified their positions, in terms of galactic
coordinates, will be plotted. This will be done separately for each region of the galactic plane so that the spread of objects
can be more easily seen. These plots will be used to identify clusters of YSO’s which are potential star forming regions.
V.4 Identification of similar Conditions between SFR’s
Once these regions have been identified the conditions in each of the regions can be looked at and compared. This
will be done by comparison of different wavelength observations of the regions (obtained from already conducted surveys).
This comparison will allow similarities between the regions to be identified some of which may be necessary for star
formation to occur. Further to this analysis the positions of these SFR’s will be compared to positions of known objects
(using catalog’s) to determine which are present in star forming regions. Any which are identified to be present in multiple
SFR’s will be identified as potential driving mechanisms behind turbulence in molecular clouds, further investigation will be
necessary to confirm which have the potential to be this driving mechanism.
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VI. Timetable and Milestones
Year 1
Task
Q1
Q2
(1) Initial object selection
(2) Calculation of colours
(3) Transposing of objects
(4) Comparison of regions
(5) Analysis of missed objects
(6) Calculation of gradients
(7) Complete analysis of region
one
(8) Identify T Tauri’s
(9) Identify Protostars
(10) Plot positions of identified
objects
(11) Gather information on regions
(12) Comparison of conditions
(13) Identify known objects
(14) Identify potential cause of
Turbulence
(15) Plot positions of SFR’s
X
X
X
X
(D) Project management meetings
(C) Literature Review
(B) Skills Training
(A) Report Preparation
X
X
X
Q3
Year 2
Q4
Q1
Q2
Q3
X
X
X
X
X
X
X
X
Year 3
Q4
Q1
Q2
Q3
X
X
X
X
X
X
X
X
X
X
X
X
X
Q4
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
Below is a more detailed description of what each of these steps involves.
Initial object selection – Selection of good examples of Evolved T Tauri’s, T Tauri’s and protostars from those
already identified.
(2) Calculation of colours – Calculate every possible colour for the objects selected in step 1.
(3) Transposing these objects onto different colour-colour diagrams and identifying the regions on the new plot which
correspond to Objects of one particular type.
(4) Comparison of these new regions across different sections of the galactic plane – for the sections already studied.
(5) Analysis of objects by the colour-colour method – Analysing the objects missed due to a lack of data points from the
regions already studied.
(6)
Calculation of gradients and analysis of gradient histograms – displayed as scatter plots and used to identify gradient
ranges that correspond to an object of one particular class.
(7) Use the gradient ranges to complete a full analysis of every object in the sector of the galactic plane already studied.
(8) Identification of all T Tauri’s across the galactic plane using the methods developed during year 1.
(9) Identification of all protostars across the galactic plane using the methods developed during year 1.
(10) Plot the positions of all identified objects and use these plots to identify clusters of YSO’s – Potential star forming
regions.
(11) Gather information about the regions identified as potential star forming regions – Observations at different
wavelengths and known objects.
(1)
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Stephen
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(12) Compare the conditions in each region and identify those with similarities as well as those with known indicators of
star formation. – Using the observations at different wavelengths.
(13) Identify any known objects which are present in the regions and compare these to objects known of in other regions –
identify correlations.
(14) Identify which known objects have the potential of being the cause on turbulence in GMC’s.
(15) Plot the positions of all believe star forming regions in the galactic plane.
(A)
(B)
(C)
(D)
Report preparation – Prepare and write the report on the study.
Skills Training – Acquire any new skills which may be necessary for the completion of the project.
Literature review – Review previous work on similar topics.
Project management meetings – Meetings to discuss the progress of the project.
VII. Project Management
The project will be coordinated by myself as the principle investigator with support from the CAPS group. This is a
very hands on project which will require 100% of my time to be spent working on it. All the raw data was collected by
NASA using the SPITZER space telescope1 and stored at the GLIMPSE data archive2 and the analysis will now be carried
out at the University of Kent by myself under the guidance of the CAPS group. Myself and a member of the CAPS group
will meet Quarterly to discuss the progress of the work and any issues that may have arisen.
VIII. Relevance to Beneficiaries
The major beneficiaries will primarily be the academic community working on Star formation, Giant molecular cloud
processes and the ISM (inter stellar medium). This is strong community in the UK with groups
IX. Dissemination of Results
The results of this research will be published in internationally-leading high impact journals, which make contact
with the star formation and astronomy communities. Presentations at conferences will make the work known to both the
direct peer community and the more general astronomy community. ~The progress of the work will be regularly updated on
the CAPS group web site. Any processes or discoveries that have commercial value will be discussed with the university
office so I can be advised on patent protection and commercial exploitation.
X. Resource Requirements
This project proposal is for a three year PhD project. As such fees for the three years will be required, these fees will
pay the costs incurred by the department during the time this project is undertaken. These fees are preset by the institution
and cover office space, cleaners, lighting etc. Skills’ training is a required part of any PhD and the level of funding required
has been advised to me by the SPS departmental administrator. This level of training is required by the university in the form
of a departmental post graduate training program which aims to give post graduates the skills necessary to work
independently in scientific fields. The level of stipend is required to cover my living costs during the duration of this project.
This total takes into account both inflation and income tax, the values stated per year are net amounts.
The travel and subsistence covers the costs of a number of conferences necessary for my career development as well
as gaining insight into the field of astronomical research. Although the university does supply standard computing equipment
1
2
http://www.spitzer.caltech.edu/spitzer/index.shtml
http://www.astro.wisc.edu/sirtf/glimpsedata.html
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Stephen
Hamer
as a part of the fees paid this equipment is not suitable for the analysis necessary for the competition of this project. As such
a high specification computer is needed to handle the data analysis, all software used for this is freely avalible.
Full costing analysis
Purpose
STAFF : Stipend
Fee Level
Skills Training
TRAVEL AND SUBSISTENCE :NAM Conferences (2008,2009,2010)
The MPA/ESO/MPE/USM 2007
Joint Astronomy Conference
IAU XXVIIth General Assembly
JENAM (Joint European and
National Astronomy Meeting)
EQUIPMENT:High specification computer
Totals
Amount
in year 1
Amount
in year 2
Amount
in year 3
Lump sum
Total
Total
after tax
£12,600
£3,200
£0
£12,900
£3,200
£0
£13,200
£3,200
£0
£0
£0
£4,500
£38,700
£9,600
£4,500
£47,214
£9,600
£4,500
£500
£500
£500
£0
£1,500
£1,500
£360
£0
£0
£1,800
£0
£0
£0
£0
£360
£1,800
£360
£1,800
£0
£600
£0
£0
£600
£600
£0
£0
£0
£3,000
£3,000
£3,525
£16,660
£19,000
£16,900
£7,500
£60,060
£69,099
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