Cardiff University

School of Physics and Astronomy

Student number: C1005749

Star formation studies with Herschel spaceobservatory

Author:Pawala Ariyathilaka

Supervisor:Dr. Pete Hargrave

May 8, 2015

Contents

1 Abstract 2

2 Introduction 32.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32.2 Initial mass function (IMF) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2.2.1 Core mass function (CMF) . . . . . . . . . . . . . . . . . . . . . . . . . 4

3 Background theory 53.1 Molecular clouds and Dust . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53.2 Jeans Mass . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53.3 Pre Stellar Core . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53.4 From gas cloud to Protostar . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63.5 The Herschel space observatory . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

4 Data collection and discussion 74.1 The images . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74.2 Tools developed and used . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

4.2.1 GAIA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84.2.2 Photometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94.2.3 Greybody curve fitting . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

4.3 Core Mass Function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144.3.1 Mass estimation function . . . . . . . . . . . . . . . . . . . . . . . . . . 144.3.2 CMF plot . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154.3.3 Error discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

5 Conclusion 18

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1 Abstract

Pre stellar cores (PSCs) within the Aquila rift were studied. A PSC is a starless gravitationallybound core within a cloud of gas and dust. The aim was to measure the mass of the cores andto construct a core mass function (CMF), to see whether there is a relationship between theCMF and the initial mass function (IMF). An IMF is the mass distribution of stars at thetime they enter the main sequence, and the CMF is the mass distribution of the cores.

Using a written photometry python script, the flux of selected sources were calculated. Theflux was plotted and a greybody function was fitted to the data. With the greybody function,the temperatures of the cores were estimated. The temperatures were used in a mass equationto calculate the core mass.

Comparing the outcome with the Konyves CMF (which was used as a base for comparison),the calculated CMF was five orders of magnitudes smaller. Reasons for discrepancies are theerror caused by the mass calculation python script, along with the shape of the aperture andthe aperture size used.

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2 Introduction

2.1 Overview

The main objective of the project was to locate pre stellar cores within the Aquila rift, thento produce a core mass function (CMF), which demonstrates the distribution of mass of thesedense cores. These dense pre stellar cores are one of the first stages of star formation. Datacollected from the Herschel space observatory was used to look for pre stellar cores within theAquila region. Two maps from the PACS and three maps from the SPIRE instrument wereused. The wavelength range was from 70µm to 500µm.

2.2 Initial mass function (IMF)

IMF is the mass distribution of stars, at the time they enter the main sequence. Throughobservations, it is concluded that the shape of the IMF is universal, through many observationsof star clusters. Yet it is not understood where the shape comes from. One widely used IMFis the Salpeter IMF[1] which was the first IMF to be derived in 1955. Salpeter fitted availableobservational data at the time with a power law between 0.4M and 10M and found,

φ(M)dM ' KM−2.35dM (1)

Where K is a constant of proportionality and φ(M)dM is number fraction of stars betweenM and M + dM . The available data was main-sequence star luminosities within the solarneighbourhood. The formulation of the above function involves looking at the different lumi-nosities, splitting them in to intervals and counting how many stars fall within each intervalusing equation (2),

L

L=

(M

M

)ν(2)

Where M and L are the mass and luminosity of the star being observed, and M and Lare the mass and luminosity of the Sun. The value for ν has a range from 3 to 5 (Prialnik -Theory of stellar evolution). A value of 3.5 is commonly used for main sequence stars.

The IMFs have developed over the years with more observations been taken such as Chabrier(2003), Kroupa (2001). However it has not changed much from the Salpeter form. AnotherIMF is the Kroupa IMF that was published in 2001. This was derived from a sample of youngstar cluster observations[2]. He introduced the following,

φ(M)dM ' KM−2.3dM : 0 > M > 0.5M (3a)

φ(M)dM ' KM−1.3dM : 0.5M > M > 0.08M (3b)

φ(M)dM ' KM−0.3dM : 0.08M > M > 0.01M (3c)

Where M is the solar mass and the other symbols are same as of (1). The Kroupa IMFis a more universal IMF unlike Salpeter given by (1), which is mainly for much larger starsthan the Sun.

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2.2.1 Core mass function (CMF)

The CMF was only observed recently and derived, when sub-mm astronomy helped observethe cold cores hidden with gas and dust clouds. Both the IMF and CMF have a similar shape,but the CMF peak is shifted to higher mass as evident from figure 1.

Figure 1:Figure showing CMF plotted alongside the Kroupa and Chabrier IMFs. The CMF is shiftedto the right in comparison with the IMF, but when the cores end up as main sequence starson the IMF, the peak moves to the left. This shows the inefficiency when moving from the

CMF to the IMF[3].

This suggests the star forming inefficiency within the pre stellar cores. Normally, onlyabout 1

3 of mass from CMF makes it to the IMF. The reasons behind this is still not clearlyunderstood. However, the relationship between the efficiency is thought to be related to thebipolar flow of a newly formed protostar. The outflow is thought to be limiting the accretedmass on to the protostar. Theoretical work has shown that outflows can give star formingefficiencies of about 30% which matches the observations[4].

The core mass function is defined by Ward-Thompson and Whitworth in the textbook, An intro-

duction to star formation as follows,

φ(Mcl)dMcl ∝M−2.3cl : Mcl ≥ 2.4M (4a)

φ(Mcl)dMcl ∝M−1.3cl : 2.4M ≥Mcl ≥ 1.3M (4b)

φ(Mcl)dMcl ∝M−0.3cl : 1.3M ≥Mcl ≥ 0.4M (4c)

Where φ(Mcl)dMcl is the number fraction of cores between (Mcl) and (Mcl) + dMcl[5]. Thesimilarity between the two curves suggest that the IMF for stars are predetermined by theCMF. If the CMF follows a universal appearance, this can give clues to why the IMF havethis particular shape.

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3 Background theory

3.1 Molecular clouds and Dust

Star formation takes place in clouds of gas and dust. The matter in the clouds is constantlymoving, acted on by gravity and being influenced by pressure. These gas clouds are vast, andeven though they have a lower density than the Sun, an average mass of a cloud exceeds themass of the Sun by many magnitudes.

The universe is full of dust. When doing astronomy, the effect dust imposes on an obser-vation needs to be taken in to account. Most the visible light emitted by stars are absorbedby dust and re-emitted at longer wavelengths, specifically at sub-mm and far infra-red. Dustradiates away energy like a greybody (an adjusted blackbody), with temperatures between10K and 100K. Dust particles can capture atoms, molecules to form new molecular speciesand grains can lump together to form larger grains.

3.2 Jeans Mass

The densest part of molecular clouds need to be observed when looking for new stars and starnurseries. These dense areas within the clouds are created through stellar winds, magneticfields and supernova shock waves which disrupts the ISM. These create perturbations, whichcreate areas of high density within parts of the giant cloud. Now the gravitational potentialenergy within that region, will increase along with the gas pressure. However, the changein pressure will not be enough to maintain hydrostatic equilibrium. So the result will bea gravitational collapse of the cloud. We define Jeans mass as the mass upper limit, thatcan be contained in hydrostatic equilibrium within a region of a given volume. If the cloudmass exceeds the Jeans mass, the cloud will gravitational collapse. Jeans mass is defined byPrialnik as,

MJ =

[(3

4π

) 12(

3

α

) 32](

RT

µG

) 32

1√ρ

(5)

Where α is a constant of the order of unity, R is the ideal gas constant, G is the gravitationalconstant, T is the temperature, ρ is the density and µ is the sum of the mean atomic mass ofstellar material which has a value of 0.61 for the solar composition.

3.3 Pre Stellar Core

Prior to having a protostar, a pre stellar core(PSC) is formed. The proper definition ofa pre stellar core, as defined by Ward-Thompson and Whitworth (2011) is, a phase in which

a gravitationally bound core has formed in a molecular cloud, and moves towards higher degrees of

central condensation, but no protostar exists within the core. The material in the pre stellar coreis sufficient for an individual star or a small solar system. With temperatures ranging from7K-15K these are some of the coldest regions in the universe. They emit radiation in the farinfrared and sub-mm bandwidth region. Typical size of PSCs are around 0.05pc in diameterand a density of 105cm−3[7].

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3.4 From gas cloud to Protostar

Once the pre stellar core becomes gravitationally unstable, it collapses. The initial releasedgravitational energy, is radiated away thus keeping the temperature relatively constant. Be-cause of the large radius, there is high luminosity and a relatively low temperature.

The collapse will create a central matter concentration. This will turn in to a protostarwhen hydrostatic equilibrium is reached. As the matter at the center reaches hydrostaticphase, due to contraction and expansion of the collapsing cloud, an opaque gaseous envelopewill form. As this envelope becomes more dense, it becomes harder for gravitational potentialenergy to radiate away. This reduces the luminosity. This evolutionary path is called theHayashi track as shown in figure 2. The Hayashi track is followed by cores that have a mass< 3M.

Figure 2: Different paths protostars take as they join the Main sequence [8]

The object at the center of the protostellar core starts to gather in-falling material fromthe accretion disk, that is now formed around the protostar. Most mass of the protostar isattained at this stage, whilst constantly warming up.

Whilst material is being accreted towards the central mass, there is also an ejection ofmaterial through opposite directions of the protostar, called bipolar flow as shown in figure 3.It is thought that this process takes place in order to carry away excess angular momentum ofthe in falling matter. The protostar is called a pre main sequence star when it has gatheredmost of its final main sequence mass.

Eventually the interior of the protostar becomes hot enough for radiative energy to dom-

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Figure 3: Figure showing the accretion disk and bipolar flow of a protostar [9]

inate. Still supplying most of its luminosity through contracting and releasing gravitationalpotential energy. But both temperature and luminosity are now increasing and the protostarmoves down the Henyey track shown in figure 2 until the main sequence phase. When at themain sequence phase the central density and temperature are high enough for nuclear fusion.Thus the star stops contracting and reaches its more stable years[10].

3.5 The Herschel space observatory

The five images used in this project, were imaged by the Herschel space observatory. Herschelis one of European Space Agency’s (ESA) cornerstone missions, launched in 2009 to studythe ’cold’ universe.

Herschel operates at the far infra-red and sub-millimetre (submm) wavelength region. Thiswas the largest infra-red telescope in space as of the launch date with a mirror diameter of3.5 meters. Herschel will mainly observe dust and cold objects in the universe, which emitsradiation in the spectrum Herschel operates in.

Herschel has 3 instruments, PACS (a camera and medium resolution spectrometer), SPIRE(a camera and a spectrometer) and lastly HIFI (high resolution heterodyne spectrometer).PACS is centred on 70µm and 160µm with the broad bandwidth (∆λ

λ )<0.5 (Poglitsch 2010)[11].For SPIRE, the central wavelengths are 250µm, 350µm and 500µm. SPIRE has broad band-width (∆λ

λ ) of ≈ 3 (M.Griffin et al 2010)[12]. The instruments work in different bandwidthsfrom 60µm all the way to 670µm.

4 Data collection and discussion

4.1 The images

The data used in this report were from the Gould belt survey[13], which allows the studyof different aspects of star formation, from pre stellar cores all the way to protostars. Theimages used were of the Aquila rift, part of the Aquila constellation.

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Each map is 2314× 2314 pixels, with each pixel representing six arcseconds. In total therewere five maps, two from PACS instrument and three from SPIRE.

Figure 4 represents a multi-wavelength image of the Aquila rift. The Herschel maps are inunits of MJy/Sr (MegaJanskys/steradian) which will need to be converted to Janskys whenthe flux values are found.

Figure 4: Figure showing the Aquila rift. This image has all the different wavelengthssuper-imposed.[14]

4.2 Tools developed and used

The main aim of the project was to construct a core mass function for the Aquila rift. In orderto achieve this, 250 sources were selected and their flux were measured. This was done usinga photometry script written in python. The flux calculated was plotted against frequency.Then a greybody function was fitted amongst these points to calculate the temperature ofthe source. Then the temperature was used to calculate the dust mass, which allowed thecalculation of the mass of the source. These steps were repeated for all the sources within thestudy. The first step was to use GAIA to select sources.

4.2.1 GAIA

The acronym stands for Graphical Astronomy and Image Analysis tool. This is an imagedisplay tool that has the capabilities to carry out photometry[15].

The Herschel images were loaded on to GAIA, and source selection was carried out onthe Herschel maps, one at a time. By changing the ’cut’ level within the maps one can findrelatively faint sources.

To do photometry, select a circular (only available one on GAIA) aperture of any radius(given in pixels), and place around a source. This then calculates the total flux within thataperture, given in counts along with the position. The sky background aperture is drawn at

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the same time the main aperture is defined. When GAIA presents the final counts values, ithas taken to account of the sky background.

Even though it can perform its own photometry, the main purpose of GAIA was to selectthe sources. The source positions are selected when the apertures are placed on the maps.Since the aperture radius was kept constant throughout the project, care was taken to choosesources that had a diameter similar to that of the aperture. A total of 250 sources wereselected. All the data is saved in to a table that can be loaded on to python. Data includesthe flux, X and the Y positions of the selected sources.

4.2.2 Photometry

A major part of the project was to develop a piece of python code to effectively measure theflux of the selected sources. This was the first step towards obtaining a CMF.

It simply works the following way. The pre selected X and Y positions are loaded on topython. Then, a square aperture of diameter 12 pixels (72 arcseconds) is placed around eachselected source to calculate the count rate. The photometry script is written such that, itmeasures the flux for each source from all five Herschel maps. This output flux (which is inMJy/sr) is then converted to Jy. Figure 5 shows the 250 selected sources mapped out on oneof the Herschel maps.

Figure 5: Figure showing the positions of the selected sources next to a multi-wavelengthimage of the same area.

Two methods were used to measure the sky background count rate. Again, these countrates also have to be converted to Janskys.

The first method was to have a sky background aperture, that was 0.5 larger than thesource aperture. This sky background aperture was placed around each source. The area ofthe sky background aperture and the main source aperture were the same. When the finalcounts were calculated, the sky background will be deducted from the counts within the source

9

aperture. This way, the sky background count varies from one source to another. So the 250different sources had 250 different sky background apertures.

The second method was to have a sky background aperture in a quiet part of the mapthat do not have any sources. Having a background aperture of such, it is possible to get atrue value of the background, one that has not been affected by any filaments. Then usingthis, the average sky background Janskys per pixel was calculated. This calculated value, wasdeducted from each pixel within the source aperture. This way a constant background value,that is deducted from each source was obtained.

Figure 6 shows the two different sky background selecting methods along with the GAIAsdefault aperture.

Figure 6: Figure showing the two different sky background selecting methods and the GAIAaperture for comparison. (A)shows the first method and it is similar to the approach GAIAtakes. A source aperture in the center, and a background apertures around it. The onlydifference between this method and GAIA is the shape of the aperture. (B) shows the defaultGAIA circular aperture. Sub figure (C) shows just the source aperture, the sky backgroundis obtained from a separate part of the sky, as shown in (D)

Converting the map units of MJy/sr to Janskys is important. Janskys are normally used todescribe point sources, since PSCs are assumed spherical, working with Janskys is required.The conversion is done as below,

Area in steradians =

(2π

360

)2

(2r)2 (6)

Where r, the radius is in degrees and is given by,

r =

(Pixel radius

3600

)(7)

Where Pixel radius is in arc seconds.

Use (6) and (7) to calculate the area of the aperture in steradians. Then multiply the countsby 106 in order to convert to Jy/sr. Finally multiply by steradians to get an output of countsin Janskys.

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The counts from GAIA were used to check the accuracy of the photometry script. Figure7 shows the difference in counts between the photometry script and GAIA. This is when thefirst method for sky background reduction was used.

Figure 7: Figure showing the difference in counts for method one, of sky background reduc-tion. The average counts for all the sources using the photometry script is 3357.5, the averagewith GAIA is 3363.3 counts. The average difference in counts between the two photometrymethods is 5.8 counts, which suggests that the photometry code does a good job of whatGAIA does, since the method of measuring the counts is exactly the same as GAIA. The onlydifference is GAIA uses a circular aperture.

Figure 8 shows the same concept as figure 7 but for the second sky background reductionmethod.

The first method is exactly what GAIA implements, with a central source aperture andsurrounding larger background aperture. So it is expected that most the data points agreewith the written python script. A potential for errors is having a square aperture whereasGAIA uses a circle. The area difference between the two mean, more sky background thanthe circle. Also the very high flux count values are unlikely to be from a pre stellar core (morelikely to be a protostar).

In the second method, an aperture was placed around a quiet part of the sky. From this,an average flux value was found per pixel. This was always likely to be a small value, sincethe background aperture will be placed in an area with no sources, so little flux. This wasthen used as the sky background value. So this value was subtracted from the flux calculatedfor all 250 sources on this project. So when this small sky background value deducted from abright source (that we will expect from the main sub-field of this map), the expected outcome

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Figure 8: Figure showing the difference in counts for method two of the sky backgroundreduction. GAIA and photometry do not agree with each other here. Doing the backgroundin this method has the advantage that an average background noise from each pixel is takenout, means the background noise value will be a constant for each source. By using this methodwe could eliminate the errors that could arise from having lots of background emission (suchas a filament that do not belong to the source). Also having a sky background aperture inan area with no sources will give a proper value for the background, one that has not beenaffected by emission from a source.

should represent something of the sort shown in figure 8. Again, having the square aperturemight have some implications on the outcome, in terms of more background.

In order to produce the CMF presented in this report, the second method was used asthe sky background reduction method. The greybody fitting function was implemented withboth sky background methods initially. Through this test, the second method came out asthe more reliable one to obtain the core temperatures. Even with the discrepancy betweenGAIA and the photometry python script, when the output flux values were used within thecurve fit function code, more than 97 percent of the sources gave out an expected greybodyfunction fit and a temperature. Out of the 250 selected sources, only on 7 sources the curvefit function failed. The comparison between the two is shown in figure 9,

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Figure 9: Left hand side image shows method one, and the right side shows method two.When method one was implemented, there were 20 graphs that didn’t produce a well fitgreybody function. When looked closer, it was not entirely clear the exact cause for thediscrepancies. But the most likely scenario is that the sky background aperture had more fluxthan the source aperture, the presence of a filament that goes through the sky backgroundaperture could cause these discrepancies. Towards the most active part of the cloud, therewere sources that clearly had filaments through the apertures. This is evident if a closer lookis taken at the first image on figure 6. A filament that goes through the sky backgroundaperture is visible. These are very difficult to avoid. There was also one instance that twoapertures were overlapping which was corrected.

4.2.3 Greybody curve fitting

The final output from the photometry code is an array of 250× 5 which contains all the fluxvalues, for all the sources, from the five maps in Janskys. Afterwards, this data was plottedagainst frequency, along with a modified greybody function using (8). The curve fit functionon python is used in this instance.

Sν = Ω

(c

ν

)βB(ν, T ) (8)

Where Sν is the flux density at frequency ν, Ω is the dust constant, β is the dust emissivityindex (fixed at 2 for purposes of this report, Hildebrand 1983[16]) and B(ν, T ) is the Planckblackbody function in terms of frequency given by (9),

B(ν, T ) =2hν3

c2× 1

ehνkBT − 1

(9)

Where h is the Plancks constant, c is the speed of light, ν is the frequency, T is thetemperature and kB is the Boltzmann constant.

In order to plot equation (8), some initial guess values for Ω, β and T had to be estimated.These estimates were used within the curve fit function on python. The initial estimates were0, 2 and 20K in that order. The outcome of this piece of code is shown in figure 10, the five

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flux values plotted with a modified greybody curve. A graph was produced for each one ofthe 250 sources. The greybody functions gives out a calculated temperature of the source andsaves the values to an array.

Figure 10 shows the plotted flux and the modified greybody curve. This is one examplefrom a list of 250. The calculated temperature from figure 10 was 9.64K which lies in therange we expect for a pre stellar core.

Figure 10: Figure showing the flux values obtained from GAIA plotted with the modifiedgreybody function. The second sky background reduction has been used. This greybodyfunction gives out an accurate temperature of the source its looking at.

The average temperature for all the sources were about 15.049 Kelvins. The expectedtemperature range for PSCs are between 7 and 20 Kelvins. Within the sources selected, therecould be protostars. When the flux is plotted against frequency, if the source is a protostar,the flux is expected to increase at low wavelengths, rather than drop. If such plots were found,the data was removed from the final set.

4.3 Core Mass Function

4.3.1 Mass estimation function

With the temperatures obtained, the mass of these cores can be determined. Using equation(10) (Hildebrand 1983) which is shown below, the mass of the dust between Earth and thepre stellar core can be figured out. Since only 1% of ISM is dust, to find the mass of the core,the calculated dust mass is multiplied by 100.

Md =SνD

2

kνB(ν, T )(10)

Here Sν is the adjusted blackbody curve, D is the distance, B(ν, T ) is the Planck blackbodyfunction and kν is the dust absorption coefficient(Konyves 2010[17]) given by,

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kν = 0.1

(ν

1000GHz

)β(11)

where ν is the frequency and β is the dust emissivity index.There is extreme uncertainty in the value for kν since it is difficult to measure and the value

changes with the physical environment as well. Values between 0.1-1.5 are used. The valueKonyves used which this paper adopted was 0.5 for kν . That value is mostly accepted for 350

and 500µm since these were the wavelengths previous studies took place in.

4.3.2 CMF plot

Using (10), the dust mass was calculated. By multiplying this by 100, the mass of the corewas attained since the core is a gravitationally held gas. The CMF was obtained by plottingthe core mass, against the number of cores in each of these mass intervals. The expectedgraph should be similar to the shape of the IMF but shifted to a higher mass.

A python script was used to obtain the mass values of the selected sources. The mass wascalculated using (10), using an initial value of 0.5(Konyves 2010) for kν . However with thisvalue the CMF obtained was five magnitudes out, when compared with Konyves. This CMFis presented in figure 11. The error could be credited to a problem in the mass calculation,thus a problem with the written python code. Attempts should be made to rectify this if timeallows.

Figure 11:The photometry gives the expected shape of the CMF, even though it is shifted to much

lower mass than expected. A value of 0.5 was used for the kν constant (konyves2010).Method two was used as the background subtraction method.

If the value of kν is adjusted to 10−5, a Konyves CMF is obtained. Here, the KonyvesCMF is assumed to be a base CMF. This is not completely incorrect since kν is an unknown

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constant, however suggesting such a small value is similar to saying there is no dust in spaceand implying that dust has a very small effect, which is not the case. With this new value forkν , a CMF for the Aquilla rift is obtained. This shown in figure12

Figure 12:The figure shows the obtained CMF for the Aquilla rift. A value of 10−5 for kν was used.

The second method has been used for background reduction.

This CMF looks similar to the Konyves CMF. However due to a smaller sample numberfigure 11 has a lower number of cores per bin.

4.3.3 Error discussion

When the Konyves CMF is compared with the calculated CMF, the difference between thetwo is evident, with the calculated CMF being 5 magnitudes smaller.

The main source of error in the project was a problem with the code that was used tocalculate the mass. However, there are also a other sources of error that will lead to thediscrepancies between the two CMFs. After adjusting the mass function, these are the othersources of error that needs to be corrected.

Error arising from the positioning of the apertures. In order to record the X and Y positions,250 separate sources had to be placed within the Herschel maps using GAIA. If the apertureis not central on the source initially, it will be reflected in the photometry script. So if theGAIA apertures were off center, when python places its own square aperture, those aperturesit will be off center from the source too. This mean the counts output is different. The countsoutput could be larger, or smaller than the real source counts.

The main error in this project (after the mass calculation) arises from the kν constant. Thevalue of this is not known well at all, and a slight change in the value can cause big differencesin the outcome. Values from 0.1 to 0.7 have been used previously ( Hildebrand 1983, Kramer

16

et al 2003) and even 1.5. This is a hard constant to validate since the value also depends onthe environment the dust is in.

By changing from the current square aperture to a circular one as shown in figure 13 willhave a big impact on the flux, thus the core mass.

Figure 13: Figure showing the current square aperture and the potential circular one. Asevident, the background that the circular aperture measures will be less. The source is shownin red.

This way, the source will be covered without having extra background being involved, sincewe are assuming a spherical shape for the sources. The reason for not using circular aperturesin this project was because, the difficulty of programming a circular aperture. With moretime available, this should be possible and should yield better results.

Another factor that could change the outcome is having different radius values for differentsources. In this project the radius was fixed at 6 pixels. However, what this means is thatone would get more flux sometimes, and less flux at other times as shown by figure 14.

Figure 14: Figure showing the problems that arise from having a constant aperture. Witha changing aperture size for each source, a more accurate flux value can be calculated. Thesource is shown in red

Applying the above method will change the flux obtained from the cores. This also meanthat the list of sources that can be looked at will increase since sources of all sizes can be

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observed. In this project, on purpose, the sources were chosen such that they were as closeto a diameter of 12 pixels as possible. But when we can work with multi radii levels moresources can be looked at. This will increase the data sample, which will give more PSCs toanalyse.

Another option to try out would be a follow the Konyves paper as an example and concen-trate mostly on the main sub-field. This is the brightest part of Aquila rift where most theactivity is happening. The main sub-field is the blue area shown on figure 5.

5 Conclusion

The CMF obtained using a kν value within the accepted range, does not reflect the CMFobtained by Konyves. Since this project closely followed that paper, it is safe to place theKonyves CMF as a base to compare the outcome with.

The CMF obtained was five magnitudes smaller than the Konyves CMF. A typical IMFdrops off at small masses. This is because stars with a small mass are less luminous, thusit is difficult to observe these faint main sequence stars. Since the CMF is presumed as theprogenitor for the IMF, it is expected that the CMF will also drop at lower mass values.

However according to the CMF obtained in this project, most the observed cores were faint.But this is an extremely unlikely scenario due to observation difficulties, and therefore mostlikely false. Bearing this fact in mind it is safe to assume that there is likely to be some errorin the mass calculation that caused this discrepancy.

This would be the first error to be corrected with more time. It is assumed that the errororiginated at the mass calculation python script. After this correction, there are some othererror sources to study further and improve on.

One of them is to change the aperture size and and shape. Changing from a square apertureto a circle will reduce the background signal that will be recorded. This means the flux valueswill be different, thus resulting in different mass estimates which will lead to an improvedCMF. Having a variable aperture radius for different sources will allow the use of a largerdata set. Also with this in place, the maximum possible flux can be measured accurately.The aperture will be as close to the radius of the source as possible, thus most the source fluxcan be recorded.

With these errors rectified, a CMF that can be compared with the Konyves CMF could beachieved.

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References

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[3] From filamentary clouds to prestellar cores to the stellar IMF. Initial highlights fromthe Herschel Gould belt survey, Author: Ph Andre et al, Publisher: Astronomy andAstrophysics, Date: 04/05/2010

[4] University of Victoria - Physics and Astronomy department notes, Viewed on:04/04/2015,Available on: http://www.astro.uvic.ca/ venn/A404/JKeown-IMF.pdf

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[8] Stellar Evolution:Stages in the life cycle of stars, Viewed on: 01/12/2014, Available on:http://hubpages.com/hub/Stellar-Evolution-Stages in the Life Cycle of Stars

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[17] The Aquila prestellar core population revealed by Herschel, Author: V.Konyves et al,Publisher: Astronomy and Astrophysics, Date: 02/05/2010

[18] From filamentary clouds to prestellar cores to the stellar IMF. Initial highlights fromthe Herschel Gould belt survey, Author: Ph Andre et al, Publisher: Astronomy andAstrophysics, Date: 04/05/2010

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