... born.^1.1

Note that although the moment of nuclear ignition might be considered a logical point to define the change from a protostar to a star, it is presently not entirely clear at what stage this ignition takes place and thus many objects that are today classed as protostars may in fact, under this definition, already be stars.

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...^1.2

Both the picture and the diagram were taken from the HST web site, the reference is as included on the figure.

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...$10^7$K)^1.3

ie. the kinetic energy (which depends on temperature) of some of the hydrogen nuclei must become high enough to overcome the electrical repulsion of the nuclei, thus enabling the strong nuclear force to bind the two nuclei together, thereby releasing binding energy and hence heating the core still more so that more such reactions take place.

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... ^1.4

Source for this section is André, Ward-Thompson & Barsony [1]

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...^1.5

This figure is taken from Hartmann [12]

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... program^1.6

See section 4.2.

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... be^2.1

The sources for this section are the two books Townes & Schawlow [32] and Gordy & Cook [9].

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... Earth^2.2

For example by measuring the changing resistance with temperature of a piece of metal or the expansion of a liquid.

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... dish^2.3

Most receivers are not sensitive enough to actually count individual photons and will only be able to count to a certain accuracy.

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... (JCMT)^2.4

The source for most of the statistics listed in this section is the JCMT web page and the JCMT user manual (a copy of which can be found on the JCMT web page).

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... effect^2.5

eg. Lead which is one possible material that can be used in SIS junctions becomes superconducting at 7 K.

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... Digital^2.6

Some times the word 'Digital' is replaced by the word 'Dutch' here as the DAS was made in the Netherlands.

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... logarithms^2.7

The type of logarithm that is taken is not important, the natural logarithm is used here but log$_{10}$ is also commonly used.

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...[16,24,25]^3.1

Much of the information in this section is taken from these papers (ie. sources [5,16,24,25]).

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... method^3.2

After Feautrier [8] who first applied the method to the radiative transfer equation.

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...[30]^3.3

Which is also the source for much of this section.

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... co-moving^3.4

ie. co-moving because the frame moves with the program as the program deals with each shell in turn.

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... STENHOLM^4.1

This is often referred to as the STEN program.

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... test^4.2

See section 4.7.5 for a description of the convergence test.

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... solids^4.3

The 5 platonic solids are the regular tetrahedron (4 sides), cube (6 sides), regular octahedron (8 sides), regular dodecahedron (12 sides) and the regular icosahedron (20 sides).

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... degrees^4.4

$\Omega=2\pi(1-\cos \frac{\theta}{2})$, where $\Omega$ is the solid angle of the apex of a right circular cone and $\theta$ is angle between the two sides on a cross-section of the cone that includes the centre line. If $\Omega=\frac{4\pi}{20}$then $\theta=52^\circ$.

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...${\bf x_2}$^4.5

This would be $\vert{\bf x_2}\vert=b\sqrt{r_{los}^2+z_{los}^2}$ but recall $r_{los}$ was chosen to be 1.

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... in^4.6

`in' here means the line of sight is getting closer to the centre line of the cloud (ie. the z axis).

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... as^4.7

Note the standard convention that $[x]$ means 'the integer part of $x$'.

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... defined^4.8

The idea for this program improvement was taken from Henry Buckley's 1-D version of STEN - this will be described in more detail in chapter 5.

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... centre^4.9

This number should really be a variable. Provision for making it a variable has been made by including the variable velsteps in the MODELDATA.DAT file, however it has not yet been implemented in the main ASTRA program.

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... give^4.10

Note that the numbers used here are due to there being 11 velocity steps, if the number of steps were to become a variable, say $n$, then the top line of the fraction on the exponent would become $\frac{2}{[\frac{n}{2}]}(l-[\frac{n}{2}]-1) \Delta V_i-v_m$ where $n$ is odd and the $[]$ brackets mean 'the integer part of'.

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... segment^4.11

Effectively the requirement here is to take the largest value of $x$ such that the line joining the two points $y(0)=e^{0}=1$ and $y(x)=e^{-x}$ has a gradient acceptably close to -1 (the smaller the value of $x$ the closer to -1 the gradient will be but the longer the program will take to run as a small $x$ implies a large number of subsegments). For $x=0.2$ the gradient is -0.906, for $x=0.1$ it is 0.952, the program uses 0.2 as this seems to reduce the error to an acceptably small amount.

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... into^4.12

Note again the standard convention that $[x]$ means 'the integer part of $x$'.

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... coefficients^4.13

For an explanation of the Einstein coefficients see section 2.1.1.

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... properties^4.14

'properties' in this case includes such things as still getting the correct answer at the end! For a proper description of how elementary operations affect a matrix see for example [11].

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... so^4.15

The exact definition of when the program accepts convergence is easily changed if other problems arise - it turns out that when simulating a 1-D cloud with the 2-D version of the program (see section 5.2) that it is sometimes necessary to relax the convergence criteria as the rings outside the spherical area of interest have problems converging due to them having been assigned very low H$_2$ densities.

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...tex2html_comment_mark^4.16

Note that this matrix in fact consists just of the individual elements in ${\bf x_2}$, ${\bf y_2}$ and ${\bf z_2}$ stacked on top of each other. The entries in the i$^{th}$ column in the matrix are the components of the basis vectors for $B_1$ in $B_2$.

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...$y$-axis^4.17

This is only approximately true but as long as the cloud diameter is small compared to the distance of the cloud from the telescope (which for molecular clouds is definitely true) it will be a very good approximation.

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... system^4.18

Note that $\vert{\bf X_2}\vert=\sqrt{\sin^2 \theta_r \sin^2 \theta_e + \cos^2 \theta_e + \cos^2 \theta_r \sin^2 \theta_e}=1$ as expected since the transformation shouldn't change the magnitude of the original ${\bf X_1}=(0,1,0)$.

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... round^4.19

There is no good reason for this rather unfortunate circumstance.

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... rings^4.20

Recall that if the velocity steps or optical depth steps between two rings was too large then the segment was split into sub-segments as described in the text near figure 4.14.

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...$outpts$^4.21

As defined in the input file MODELDATA.DAT.

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... ASTRA^4.22

Note the labeling convention used in this document is that "ASTRA" refers to the executable produced by the "astra.f" source code, which is different to the "astra.tcl" executable for the Tcl/Tk frontend.

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... used^4.23

Note that as presently written the program cannot cope with transition numbers greater than 99. This may need changing in order to be able to model molecules with a large number of levels.

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... models^5.1

On a 400MHz Pentium II with sufficient RAM that no disk swapping takes place. For comparison on a SUN Sparc Ultra I the $18\times36$ model took 121 minutes of CPU time.

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... respectively^5.2

The formula given on the JCMT web page is $B=19.52\frac{245}{\nu ({\rm GHz})}+0.47 \cos (0.2428 \times \nu ({\rm GHz})+3.6064)$ where $\nu$ is the frequency and $B$ is the beamwidth in arcseconds for A band lines. $B=14.3 \frac{340.0}{\nu ({\rm GHz})}$ for B band lines.

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... axis^5.3

To convert AU to pc divide by 206265.

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... rotation^6.1

As has been explained previously to avoid problems with the lines of sight running parallel to the cylinders the angle of $90^{\circ }$ is not used but rather something very close to $90^{\circ }$ - in this case $89.9^\circ$.

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... galaxy^6.2

This ignores problems with resolving out 'large' structures for such a sparse configuration - the true maximum distance where it can be used may be considerably less but would definitely cover all nearby star formation regions.

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