1. A Simple Model
o The Interstellar Medium
o Observations and Predictions
o Fragmentation and Rotation
o Magnetic fields and Outflows
o Galactic links: Shockwaves and Self-sustaining formation
3. Recent theories
1. Definition of the Problem
2. The Software
3. The Model
As we lead our busy day-to-day lives on this planet – attending to a multitude of everyday endeavours – it would be fair to say that we give very little consideration to our astronomical origins. As absurd it may seem, our origins lie in a sequence of cosmological processes that began billions of years ago. They finally allow for our ability to contemplate this notion (and our very existence).
These particular ‘cosmological processes’ range in scale and expression, and are on the whole not well understood despite the substantial advances made in the last few decades. For a moment let us view the big, big picture. Apart from the Big Bang – the moment our universe came into existence (which we should take for granted here so as to avoid the headache of the quantum ‘froth’) – these processes have transpired with what appears to be mechanical precision. The Strong and Weak Anthropic Principles find their foundation in this notion: whether the chances of ‘everything going right’ from the outset was a mere fluke of ‘astronomical’ proportions, or that our awareness of our home in the cosmos is a direct result of the fact that everything did go right anyway. The question of whether the universe is guided by any supernatural phenomena presents an entirely different ballgame, but for the time being the project will attempt to examine issues from within a framework provided by known physical laws and natural phenomena.
Let us consider snapshots of the cosmological processes as a series of universal events. One of the common phrases heard at someone’s burial is “ashes to ashes, dust to dust”. Although it is a time of mourning and sadness, and not a good opportunity to take a reductionist line of thinking, it is nevertheless reassuring to realise that this ‘dust’ of which a person is made – the protons, neutrons and electrons (and perhaps other exotic matter) originated in the Big Bang, our first snapshot. During the cosmological processes that have occurred over the past 8-15 billion years, matter and energy have combined in just the right proportions with just the right forces to construct what we see and feel at this moment.
The more complex particles – which have been formed from the primary constituents of the early universe following the Big Bang, hydrogen and helium – were (and still are) being fused together inside the infernal factories of billions of billions of stars scattered throughout the cosmos. The super-massive stars quickly run out of hydrogen as their main source of fuel and resort to ‘burning’ increasingly heavier elements in other fusion reactions. Once a star begins to collapse (being unable to sustain the inward gravitational pull with its radiation pressure) it rapidly implodes, then explodes into a brilliant supernova, lighting up the sky and more importantly spewing vast amounts of the heavier elements back into the universe that may be re-processed by other smaller stars, such as our Sun.
Now let us imagine a snapshot of the birth of our Sun: the flash of the triggered fusion reaction helps blast away the surrounding gas and dust revealing the sparkling new orb. We can see much circumstellar dust and some largish chunks of matter floating around the core. This is the birth of our solar system. The largish ‘planetesimals’ are the foundation of proto-planet formation and have appeared because heavier particles and dust grains have been coagulating for some time around the ‘proto-Sun’. The particles eventually build up in size, like a snowball, after incessantly bombarding each other, slowly becoming more massive objects orbiting the Sun in roughly the same plane. As the planetesimals collide to form proto-planets and the proto-planets collide in enormous explosions, our planets take shape – their composition is not of hydrogen and helium, but of the heavier elements originally formed inside stars and simple compounds. As the system evolves and the planets cool off from the heat of their forging, the conditions on one planet just happen to be ideal for the formation of simple life forms, evolving from complex molecular structures. Then, moving our snapshot forward again several billion years, we arrive in the present day. When put in the perspective of the universe, life on planet Earth seems utterly amazing. However, life as we know it only orbits one star. There are billions of billions of other stars ‘out there’ – might not life be too?
It is this project’s aim to examine stars, in particular their formation. In recent times much emphasis has been placed on larger and larger scale structures, rather than their building blocks. Although we can look into the night sky and see a multitude of stars, little of the precise details are actually well understood about stellar formation. In the more recent past, there has been much debate and conjecture about stellar formation, with many theories and ideas being advanced that suggest interactions of dark matter and changes in the development of stars now, in the visible universe, compared to early times.
This project will review the theories regarding the conditions and processes that lead to star birth, how formation impacts on other ‘stellar nurseries’ and on the formation of galaxies (a topic which is even less soundly understood), and will discuss the creation of a basic model that investigates the possibilities of stellar formation, based on altering initial conditions and physical forces.
The star cluster of M13 – a product of grouped
stellar formation from the same massive matter cloud.
As we have observed that stars have long life times (in the range of a few million to several billion years) and we believe the universe to be approximately 10 billion years old, it is safe to assume that not only did stars form in the very early stages of the universe (as astronomers think old Population II stars did) but that stellar nurseries have existed ever since these early stages and star formation is still active in the visible universe.
Today’s closest centres of star formation have been captured in vivid (false) colour by optical telescopes, such as the Hubble Space Telescope and radio arrays, such as the Very Large Array in the United States. Perhaps the most notable area of star formation is the Orion Nebula. The image to the right is a portion of the nebula (also known by its Messier Catalogue code: M42) photographed by the HST – several optically ‘reddened’ stars, colourful dust and ionised gas regions are visible. Both optical and radio images reveal such vast clouds of gas and dust inside nebulae – clouds that are host to the birth of new protostars.
But how do stars actually form? How does a system evolve to the stage of producing a protostar? Although little has been understood about the subtleties of stellar formation, there is one ‘overarching’ theory that is generally accepted as the most plausible process. In its simplest form, it is the collapse of clouds of matter that contract until a point is reached where enough heat is generated to ignite fusion reactions. However even this simple model has its own complexities.
These matter clouds are the essential constituents of the InterStellar Medium (ISM) and require a close study to fully understand stellar formation. The majority of the ISM is showered with primary cosmic rays and is threaded with magnetic fields. The component gas and dust clouds are found distributed out over vast areas in clumps. The larger clouds tend to become the stellar nurseries that are home to new stars (some of which are binary systems, super-massive stars and others that will develop planetary systems).
It is important to note the nature of this ‘simplistic’ theory. The processes to be described here are those that seem to apply to stellar formation occurring in the visible universe – formation whose building blocks are the matter clouds of the ISM, a product of continual evolution, processing, recycling and condensation over extended time periods. The processes that gas and dust clouds underwent in the early “Dark Ages” of the universe might have been somewhat different. Wondering what the building blocks of stellar formation were during that era can raise the question of uncertainty in the current model’s applicability: if there was no ISM as we observe today, what exactly were the building blocks and formation processes of the early stars that formed along side galaxies? A detailed answer still remains a mystery, although a short discussion will ensue toward the end of Part A of the project.
Considering only the gas found in the ISM for the moment, the element of highest abundance is neutral hydrogen (H I) that tends to mass into large clouds. Other components of the gas such as ionised atoms, free electrons and molecules, are also present in varying smaller concentrations depending on their location. The neutral hydrogen gas is cold (10-100 K) and extremely tenuous: at some points the ratio of the distance between two atoms to their size is estimated12 to be 100 million to 1. For a hydrogen atom that is about 10-10 metres in diameter, such a ratio would mean its nearest neighbour would be around 1 centimetre away. Despite these comparatively large average distances between atoms of the gas, the sheer volume and total mass of a cloud is enough to make it ‘clump’ and sometimes develop stars.
The gases between the H I clouds are also dilute but composed of mainly ionised hydrogen (H II). They are hot and luminous as they interact with radiation being emitted from nearby young O- and B-class stars. A typical H II gas region is thought to surround these stars to a diameter of a few light years. The hot stars (with a surface temperature of about 30 000 K) at the centre of the cloud emit radiation at high enough energies (ultraviolet photons) to ionise H I to H II increasing its temperature to about 10 000 K. The basic equation for this reaction is:
H + UV Photon à H+ + e-
As the ionised H II heats up it expands back into the cooler H I clouds while forcing some more H I into its place. It is thought this process can influence such clouds out to a distance of a few tens of light years. The image to the right represents this phenomenon.
The ionised H II regions are clearly visible as ‘fuzzy patches’ in many diffuse (bright) nebulae in the night sky. As previously mentioned, the Orion Nebula (about 20 light years in diameter) shows perhaps the best example of these properties of the interstellar gas at optical and radio wavelengths. H I has a characteristic 21-cm emission line (know as the Hydrogen-a line) that can be received by radio telescopes. The emission spectrum of H II on the other hand, is continuous (has a constant intensity over a range of wavelengths, as opposed to the discrete peak or trough in emission or absorption line spectra). It is continuous because an electron in an ionised atom, which will emit a photon, can fall to any number of energy levels inside an atom – not just the ground state – thus the photon has a wider set of possible frequencies (although the individual wavelengths are quantised). This is known as the free-free emission process and it enables radio astronomers to estimate the total mass of ionised hydrogen atoms in an H II region (for example Orion which has about 300 solar masses of H II gas).
The existence of the H I clouds in the ISM was predicted by astronomers but not observed until 1951 when radio telescopes picked up the 21-cm emission line of neutral hydrogen. Surveys of nebulae, such as Orion, provided direct evidence to show that the vast majority of the gas in most bright nebulae is infact H I. Initially though, the H I regions could not be directly observed as they are cold and not optically visible: the electrons in neutral hydrogen would barely ever have enough energy to be promoted from the ground state to higher energy levels – except when an atom would absorb ultraviolet light. However these UV absorption patterns are not visible from ground-based telescopes as UV light is hindered from penetrating the Earth’s atmosphere. It was with the advent of satellite observatories, which could be situated outside the Earth’s atmosphere, that the UV absorption spectra of H I clouds could be clearly discerned.
The UV images showed that the H I distribution in clouds of the ISM was ‘patchy’ ranging in diameters of about tenths of light years to tens of light years. The average concentration of H I atoms in these clouds is thought to be approximately 106/m3. Some regions have been shown to have around ten times less per cubic metre. For comparison there are about 1025 particles per cubic metre in the air at the Earth’s surface. When looking at our own Milky Way, H II is found to be concentrated in the plane of the galaxy. Here an estimated concentration of 3x105/m3 is found to have a temperature of about 70 K. Again, for comparison there are about 1023 times more hydrogen atoms in one human body than there would be from this H II concentration for the same volume. In total, H I clouds are supposed to make up 40% of ISM’s mass (each individual cloud being approximately 50 solar masses) while H II clouds contribute very little.
The elemental composition of interstellar gas does not only include neutral and ionised hydrogen, but also to a lesser degree oxygen, nitrogen, sodium, potassium, ionised calcium and iron. These elements have been found through optical spectroscopy and have been confirmed as definite components of the gas, not of the atmospheres whose stars emit the original photons. Interestingly, strong evidence was provided for this claim while observing binary star systems. As the stars orbit around one-another, their changing velocities shift the absorption spectra of their atmospheres according to the Doppler effect (hence they are called “spectroscopic binaries”). However the spectra of the other elemental components of the interstellar gas were seen to remain still, indicating they were not part of the stars.
There exist cold molecular clouds in the ISM as well. They are found in close proximity to active H II regions and exhibit a very wide range in total size. The molecular clouds too contain mostly hydrogen, although it is in diatomic form. Matter in these clouds is on the whole cold and easily observable at only millimetre wavelengths. A search, started in the 1960s with the wide-scale advent of radio telescopes, has revealed that there are over 60 different types of molecules in the normal ISM: the majority are of an organic nature (contain carbon atoms). The most common organic molecule is carbon monoxide (CO) and it is accompanied by water, ethanol, ammonia, formaldehyde and free radicals of hydrocarbons. The conglomerations of these molecules tend to form clouds near the H II regions and sometimes result in several ‘cloud complexes’. These complexes contain on average a few hundred molecules per cubic metre, are a couple of tens of light years across and internally contain multiple molecular clouds of different compositions, sizes and densities. The internal clouds have a density of a few billion molecules per cubic metre and are held together by their own gravity (for example those observed in Orion). Molecular clouds are estimated to contribute a few billion solar masses (40%) to the ISM. An individual cloud may have a mass of 103 solar masses while a cloud complex may be about 104-107 solar masses. The cores of sub-clouds in cloud complexes are vital to stellar formation as shall be seen shortly. The temperatures inside sit around 10 K due to radiative cooling from their ‘shells’. It is these self-gravitating cores that inevitably begin collapsing and become the progenitors for new stars.
Apart from interstellar gas clouds there are also inter-cloud regions. Ultraviolet observations have provided direct evidence showing this gas to be very hot and thin. The absorption spectrum of ionised oxygen atoms (O VI) has been found in such regions, signifying that temperatures must be at about 106 K (the temperature of the Sun’s corona – hence the inter-cloud gas is named the ‘coronal interstellar gas’). The gas is speculated to occupy 0.1% of ISM by mass.
In addition to all of these gases, the ISM contains dust (though it is incredibly scattered). On average there is one dust particle for every million cubic metre volume of space, yet the ‘grains’ contribute as much as several hundred solar masses (1%) to the total mass of the ISM. Dust clouds can vary in size from some 200 light years to a fraction of a light year. Some ultra-small clouds, known as Bok globules measure one light year across and are so dense their mass can reach 20 times the Sun15.
Dust clouds provide stunning images of light extinction (the dimming of starlight, for example the Horsehead Nebula) and reddening (the scattering of wavelengths – most noticeable when increasing from the blue end of the spectrum). Starlight in the Milky Way is dimmed by a factor of 2 roughly every 3000 light years. Dust clouds can also simulate the appearance of H II regions in bright nebulae by simply reflecting the light from its host nebulae’s stars. Such reflection nebulae do not exhibit the characteristic emission lines of an active H II region, only an absorption spectrum of the stars whose light the dust clouds reflect. The stars appear to be redder than the standard colour that would be obtained from their spectral class analysis, as red light penetrates dust clouds to a greater extent than blue light. This is because their blue light is being preferentially scattered and absorbed (the principle behind the reddening of the sun and moon as they sit on the horizon). The blue light that is not absorbed is reflected inside the dust cloud until the photons leave in any other direction. Thus the entire dust cloud itself takes on a bluish appearance (as the sky here on the Earth does for the same reason). Dust leaves its signature on background starlight as well: grains tend to be aligned along extensive magnetic fields so that certain wavelengths of light are absorbed depending on the orientation. By measuring the change in polarisation and thus the alignment of the dust, it may even be possible to plot the directions of the influential (though weak) Galactic magnetic fields.
Despite dust’s curious nature, it provides endless hassle to optical astronomers when it essentially blocks out the visible light emitted from objects lying behind a dust cloud. Apart from regions where extinction due to dust clouds is obvious as they form a defined silhouette over a much brighter background (such as a large H II region), it is nearly impossible to tell areas that are ‘clothed’, rendering that patch of sky optically dark. However in this case, Infra Red astronomy comes into its own: not only do IR photons penetrate dust clouds, the dust grains themselves can act as tiny blackbody radiators re-emitting any absorbed radiation in the far IR range of the spectrum when their temperature reaches about 100 K. So although the optical peak from bright nebulae might lie in an active H II region, the IR peak may lie elsewhere: in an IR cluster of cool dust near a molecular cloud that is being heated by an external source. Such a difference in peaks of separate spectral ranges is most apparent between the optically strong source of the dense H II region in the Trapezium Cluster (the four stars seen in the image on the right) and the strong IR core of the Becklin-Neugebauer object behind it (thought to be powered by a massive developing star), both in the Orion Nebula.
In spite of the breakthrough in IR observations providing this new ‘visibility’ of dust clouds, the accurate makeup of the individual dust grains eludes astronomers. At first it is easy to select the most probable candidates from the elements common to the ISM. Based on observations of light extinction and reddening caused by dust, astronomers have formed a well-founded model that suggests the grains have a small core about 0.05mm in radius and a surrounding mantle layer about 1.0mm wide. The core is thought to be made from silicates (supported by some recognised absorption patterns), iron or graphite, and the mantle from a mixture of ‘icy’ materials (for example: water, carbon dioxide or methane, which are solids below 100 K). It has been put forward that the organic compounds of the mantle may have been ‘processed’ in reactions offset by the ultraviolet light that permeates the ISM, forming more complex molecules (much like in hydrocarbon substitution reactions). Their precise composition is unknown too, though one theory proposes they are a form of ‘tar’ that adds a considerable mass to each grain. The organic processing of these molecules plays a crucial role in the formation of molecules in molecular clouds. These two cloud types are closely linked: they are usually found to inhabit each other’s space. The grains form a surface on which molecules can build. For example: it is suggested that hydrogen atoms readily ‘stick’ to a grain’s mantle in waiting for a collision with another hydrogen atom. As they meet on the grain, a molecule of hydrogen will form. Molecules cannot remain on the grain as easily, so it departs back into the molecular cloud. The formation of larger molecules on dust presents a problem with their ‘departure’ from the grain: they can easily split back up into their component atoms. This has lead astrochemists to believe that although some molecules may indeed form on mantles, molecules of up to around four atoms could simply build up inside the gases of a molecular cloud by way of UV catalysis and collision (not on a dust grain). Even though UV radiation effortlessly breaks apart simple organic molecules, the construction of them from single atoms is supposed to be ‘shielded’ from UV photons in the cores of molecular clouds by other larger and more stable molecules.
The formation of cosmic dust has been a puzzling phenomenon too. Cool giant and M-class supergiant stars blow large amounts of mass into the surrounding space. Denser dust grain cores are thought to form in the atmospheres of supergiants, which are subsequently blown into the ISM. Their atmospheres would typically peak at 2 500 K, allowing for hotter gases rising from within the star to condense into small solid grains. The rate of total mass released is estimated to climb as high as 10-5 solar masses per year. The smaller giants release less: 10-6 solar masses per year. Observational evidence has been found that supports this formation method by highlighting the unique spectral characteristics of carbon and silicates in some stars’ atmospheres and circumstellar clouds. The M-class stars that do have such circumstellar clouds loose mass at the greatest rate of all: 10-4 solar masses per year – they are thought to be the largest contributors to the ISM.
As for the dust’s mantle, it is thought to condense inside dense, low temperature molecular clouds. As a grain’s mantle only exists at low temperatures, when it is heated to a couple of hundred kelvins, its mantle will evaporate. However, it will ‘grow’ another every 108 years or so (the sheer number of dust grains make this a regular occurrence).
The application of infrared astronomy in the study of dust clouds has begun to break down the optical barrier that obscures our view not only of other galaxies and clusters, but also of areas of stellar formation. Since dust contributes significantly to overall cloud volumes in the ISM, they partially draw a curtain over the processes leading to the birth of new stars – in the optical range. With past infrared observations (primarily using the Infrared Astronomy Satellite, IRAS) dust cloud distribution and dynamics in the Milky Way have been better comprehended. This knowledge can then be applied to understand stellar formation processes. With the future launch (scheduled for December 2001) of NASA’s fourth edition to the Great Observatories: the Space Infrared Telescope Facility, SIRTIF, astronomers can begin to uncover further mysteries of current stellar nurseries using more sophisticated equipment to probe through these dusty ‘cocoons’.
It is essential to realise that all models of stellar formation are in part based on theory and there has yet been no compelling direct evidence to support any definite sequence of events. Even a simple model founded on basic collapse may well be missing critical undiscovered physical effects that play a part in governing the evolution of protostars. This consideration of a “simple model” here will discuss the overarching ideas of basic theoretical models: cloud collapse, protostar development, and the accretion and dispersion of matter.
The process begins with the vast structures of matter clouds in the ISM. As a cloud progressively builds in size and maintains a low temperature, these self-gravitating regions will fall under the influence of gravity and begin to collapse on themselves (not necessarily in the positional centre of each cloud). It was Sir Isaac Newton who created the first mathematical description of the force responsible for this very action – although now it had been clarified as the curvature of space-time (Albert Einstein’s revolutionary perspective of the universe). The cloud must be sufficiently cold so the radiation pressure exerted by energetic particles does not counteract the gravitational forces in the early stages. As the collapse starts to accelerate, the rate of collapse at different points changes so the cloud density should be dramatically different at various points. The central regions of the cloud contract faster than the outer layers, which effectively form an envelope around a condensing core. Once the core has formed and become sufficiently hot it begins accreting the in-falling envelope. At this stage the process may take either of two slightly different paths depending on the initial mass of the collapsing cloud:
If the original cloud was a ‘solar-mass cloud’ (i.e.: its total mass was around that of one solar mass) and a few light years in diameter, it will form one primary core that will develop into a protostar about twice the size of the Sun typically in about 1 million years. While the central region is contracting faster than the external layers, the pressure and density increase as gravitational potential energy is converted into the kinetic energy of particle collisions. The hydrogen molecules become the most active particles, and as they collide with dust grains, the dust takes away some of the energy and radiates it away at infrared wavelengths. This helps prevent – for a period – the core from reaching excessive temperatures (a very high density and pressure) that would slow down the inward pull of gravity with the opposite push of radiation pressure. However given enough time the core will reach critical density and become opaque to the radiation. This state is exacerbated by the continual shower of in falling matter from the cloud’s external envelope. As the temperature reaches about 2 000 K, hydrogen molecules split into single atoms and serve to absorb enough radiation so that gravity may continue with its inward haul – the increase in radiation pressure is too slow to counteract gravity for the entire duration of this development. The semblance of a protostar begins to contract again until the internal pressure stabilises the gravitational force once more. Thus a protostar is born. Although its luminosity is a few times that of our Sun, it is still shrouded in the in-falling envelope and so blinded from the view of the optical astronomer. The intense temperature does in fact heat the envelope up so much that it emits strong infrared radiation. Such a compact source is thought to be the telltale signature of stellar formation, especially when it comes from dense regions in the ISM. The envelope will slowly dissipate leaving a shining cool pre-main sequence star. The dissipation is though to occur not so much because the majority of the envelope fall has fallen onto the protostar, rather that the accretion flow has been reversed by strong solar winds generated by the star. The envelope is blown away from the core as the star recycles the remaining portion of its share of the ISM for other future stars to use. Until its ‘star-hood’, the majority of emitted radiant energy will come from the release of gravitational energy. An estimated 50 million years passes before a protostar properly matures and joins the main sequence. At this moment the concentrated bombardment of particles inside the protostar’s core gives way to ignition of nuclear fusion reactions while the accretion of the envelope draws to a close.
If the mass of the original cloud was not in the order of solar masses but much greater, a massive protostar forms in a similar sequence of events. The main difference is that after an estimated 300 000 years, the core becomes hot and dense enough to initiate fusion reactions before accretion of the envelope reaches an end. At this point, around half of the original cloud mass found in the envelope is blown back into the ISM, a great proportion more than solar mass protostars. The new massive protostars are also more luminous and thus stronger infrared sources. In addition, the fusion reactions produce copious amounts of ultraviolet photons that ionise the circumstellar gas transforming it into another H II region, which helps in the dissipation of the remaining envelope too. The high output of UV and IR radiation makes massive protostars more easily identifiable in space. Understandably many more massive protostar candidates have been found in the sky than solar mass ones. The quicker evolution of massive protostars allows them to reach the main sequence long before their solar-mass counterparts, even though they appear to still be shrouded in the remnants of their dusty molecular host cloud.
An active stellar nursery
Much speculation still exists over the formation of solar-mass stars, as they are so much smaller than massive protostars. On the other hand the birth of massive stars seems to appear with a possible set of known radiation emissions in different spectral bands dependant on the protostar’s progress. The following is a prediction of the likely sequence of events based on observational evidence:
After about 300 000 years as young massive protostars begin shinning from the gravitational contraction of a massive molecular cloud, they should appear as a compact far-infrared sources linked to their parent cloud. Some theory suggests massive stars that finish accreting matter early should be metal poor. Throughout the next 50 000 years as their surface temperatures increase while fusion burning ignites in their cores, the protostars are now observed as near-infrared sources. During the following 30 000 years as nuclear reactions proceed, emitted ultraviolet photons create a new H II region around the stars, enabling their detection as a strong radio emission source. The H II regions expands in size at about 5-10km/s for 500 000 years while infrared emission strength decreases (while the protostars’ envelopes begins to dissipate). At this point the H II regions are optically visible and emit radiation of centimetre-radio wavelengths. For the next 2 million years both the H II regions and parent cloud dissipate. Infrared emissions drop off and radio signals become diffuse. By now, several new O- and B-class stars have materialised from the once massive molecular clouds. The important fact to realise here is the preceding section, describing the collapse of matter clouds, dealt with single stars; stellar formation is thought typically to occur in associated clusters. After a subsequent 6 million years, H II regions surrounding the stars are thought to have spread entirely back into the ISM, pushed by the H II regions’ expansion and the strong solar winds, leaving naked OB-stars. Despite these extended time periods, some ultra-massive protostars can form in around 100 000 years if conditions are right. The maturing of these stars in clusters and the act of ‘pushing away’ the molecular cloud has fundamental repercussions on further stellar formation – this will be investigated in a later section.
Solar-mass protostars begin their adolescent ‘star-hood’ as pre-main sequence stars, astronomers believe. They are thought to often form in association with the massive OB-stars, but mostly in their own clustered ‘T’ associations, within giant molecular clouds. The majority of these solar-mass stars are known as ‘T’-Tauri stars (known after the prototypical star found in regions of young stars). These stars have been observed to have low masses of 0.2-2 solar masses and ages from 100 000 to 100 millions years. They are almost always found in dark clouds of the ISM, which contain so much dust they are completely opaque to optical wavelengths. The grouping of these stars in one cluster is the most common result of their formation from small, dense, loosely aggregated cloud cores about a tenth of a light year wide, inside the same molecular cloud complex. These clusters are estimated to make up only 1-10% of all stellar births. Once they appear as optically visible objects, they are actually several times larger than they will be in their future stable positions on the main sequence, and will contract slowly until they reach the line. Other ideas have also been put forward that suggest solar-mass stars do not form in giant clouds along side massive protostars, but develop in their own smaller isolated molecular clouds. The general consensus is that is process may occur less frequently than the original type in massive complexes.
One piece of observational support for the stages of these two types of star formation comes from analysis of Hertzsprung-Russel diagrams of stellar clusters. One such open cluster, NGC 2264 (on H-R diagram to the right), exhibits a pattern where the young massive OB-stars already lie on the main sequence line, yet much of the smaller A-M class stars sit above the line. The normal interpretation of this configuration would suggest the stars formed at the same time, and the more massive OB-stars evolved quicker (as predicted above). The pre-main sequence protostars are still developing and could be grouping in loose T-Tauri associations. More general observational clues have been found in the Orion Nebula and M17 (another bright H II region) that support the basic signposts of massive protostar formation, such as incredibly wide H II regions being heated by young OB-class stars, near which lie intense sources of infrared radiation in dark molecular clouds.
The stellar formation stages depicted so far have appeared as somewhat rudimentary systems – there has not been any particle dynamics on the large scale apart from intra-cloud contraction. Two connected processes, recognised as being potentially some of the most important, are the initial fragmentation of massive clouds into smaller denser ones and the rotational rate of a cloud core. These processes go hand-in-hand, as one usually leads to another.
The case of major fragmentation occurring first before any significant rotational forces come into play will be investigated in the section dealing with stellar formation in the context of galactic dynamics. However natural fragmentation to a slightly smaller degree is expected in massive matter clouds as they begin to unevenly contract. Although the different rates of contraction in cloud cores are responsible for generating a protostar’s envelope, the large-scale collapse of a cloud complex should cause its sub-cloud matter to concentrate around the multiple cloud cores themselves. This effect is brought about by instabilities in the massive cloud being amplified by contraction. For this reason, the majority of very young stars, especially of OB-class, are found in the gravitationally associated clusters because they formed from the same massive cloud complex (as mentioned in the previous section). The same thinking applies to the similarity of stellar ages in a cluster (also seen previously in the H-R distribution mentioned for NGC 2264). As for the number of different star types, the variation depends on the overall size of the initial gas cloud. A comparison of open and globular clusters, and their relative positions in galaxies will be briefly looked at later.
Within a cloud complex it is proposed that solar-mass protostars form in other locations than do massive protostars, even though they often materialise from the same matter cloud. Massive protostars are believed to form on the edges of clouds while solar-mass ones form inside, among the breakaway fragments of the main cloud. There may be several reasons for this, including the mentioned instabilities of fragmentation and rotational factors. The process that dictates much of the clouds extent of fragmentation is each core’s ability to radiate away its gravitational potential energy. Once the cloud becomes opaque to the radiation, the fragmentation of that region stops and star formation processes continue as described.
Rotation of matter clouds both on large and small scales has a profound impact on the outcome of the system. If there is even a slight amount of initial rotation in a cloud, it will be magnified as the cloud contracts due the laws of the Conservation of Angular Momentum. This is a crucial physical influence because as the cloud begins to rotate more quickly (each particle’s velocity is increased as it rotates about the system), further instabilities will cause ‘blobs’ or condensations to form. These blobs are infact separate concentrations of the one cloud’s matter. The processes here will lead to the creation of multiple stars from the one collapsing cloud. This is how, it is thought, binary and other multiple star systems are typically formed. The frequency in observation of multiples, particularly binary systems, supports this notion very well.
The time it takes for separations to occur in such gas clouds is not well known. Once again it must be reiterated that all these theories are idealistic scenarios and have been investigated only in computer simulations – there is no conclusive proof. The actual formation of the blobs is surrounded by some uncertainty too: simulations have shown ‘strings’ and ‘bars’ forming across the cloud, which are meant to gradually merge and form the multiple concentrations. Some predict that these structures become apparent after about 25 000 years.
Another consequence of rotation and angular momentum is the flattening of clouds into a single plane that sit perpendicular to the axis of primary rotation. This process is also believed to be the method for flattening galaxies (as seen to the right). When particles in the system come closer together as the cloud contracts, the conservation of angular momentum will give each particle more kinetic energy as it swings about the centre of mass (just as ice skaters increase in rotational velocity as they retract their extended arms). The particle’s rotation is really only pronounced about the one primary axis. Thus the particles in the plane central to the axis will move faster, but their high tangential velocities will prevent them from being sucked into the centre of mass because their centripetal acceleration will be relatively small. The particles above and below this plane will be drawn more in toward the centre, feeling the pull increasing out to the poles of the system. They experience a greater force that will more easily overcome their slower tangential velocities (their rotational momentum about the axis will decrease). The result is the concentration of the cloud (whether it be of multiple system or not) into a planar formation.
The ‘squashing’ of clouds into such planes has no effect on the development of the star. In fact, the process seems inevitable. The envelope will continue to bear down on the protostar’s core while it accretes matter. The planar alignment of the accretion disk is important in understanding the reversal of the accretion flow as the star ignites and blows the remaining matter cloud back into the ISM. This process is known as the outflow and will be looked at in the next section.
The one hindrance angular momentum does have on a collapsing system is its increase of the total kinetic energy in the system. If the total KE becomes too high, the cloud will naturally withstand any more collapse by exerting pressure against the gravitational forces. This is why the radiative cooling (releasing the gravitational potential energy) of molecular clouds to low temperatures is crucial in the early time of protostar development.
Taking into account this slightly more complicated picture of stellar formation, one of several question remains to be asked: what is the critical mass of a cloud that will allow gravitational attraction to over come the forces of the gases trying to expand it? An estimate for this critical mass, known as Jean’s Mass (MJ), in a matter cloud can be calculated with the equation below:
where ‘T’ is the cloud temperature, ‘r’ is the density, ‘mH’ is the mass of a hydrogen atom and ‘m’ is the mean atomic weight of the cloud relative to hydrogen.
This equation concerns the entire massive cloud, not the individual molecular clouds. A cloud above Jean’s Mass should eventually fragment into smaller concentrations, which should ultimately develop new protostars.
As the extent of fragmentation can vary considerably across one massive cloud, certain experimental calculations have shown that the lowest possible mass of one collapsed sub-cloud region is about 10MJ. The instabilities in the massive cloud’s collapse can result in a whole range of different stars and multiple systems. It is believed that those stars that have a chance of forming a planetary system would have masses up to 15MJ. There has been discussion over the importance of low mass brown dwarf stars (considered as failures of star formation) and their relevance to stellar formation theories. It is suggested that any object of a mass less than 10 MJ, accompanied by other stars in a single cluster, would probably be some of sort planet. Brown dwarfs are thought to have approximately the same mass, so the discovery of such a star isolated in a collapsed cloud could present serious implication for formation theory: it is not conceivable that contraction of molecular clouds, of greater mass than their future protostars, could create anything less than a single very low solar-mass star. If isolated brown dwarfs are found, their presence begs the question of how they were able to form in the first place, or more precisely: how nuclear fusion did not start given a quantity of matter more than sufficient to cause collapse and heating to ultra-high temperatures.
What is the duration now of the entire process of formation, with the latest forces added? With multiple fragmentations, which could fragment themselves, the length of time still depends of the amount of mass that accumulates in the collapsing cores. If a massive protostar accretes enough matter, it will enter the main sequence in as little as several hundred thousand years. If a cloud has enough rotation, it will fragment normally (the condensation forming a low mass protostar that may take several billion years to mature).
Magnetic fields that thread through the ISM are proposed to play a significant role in protostar formation just as angular momentum does. Although angular momentum does accentuate rotational motion of a cloud core, cores typically do still turn quite slowly due to their considerable size and to, as it is suggested, magnetic fields, which provide a ‘braking action’.
The magnetic fields of developing protostars would form from the core and extend out through the envelope. They are important in the two phases of matter accretion and cloud dispersal. During accretion, the braking effect would ensure that the core is rotating with nearly the same angular velocity as the envelope, ensuring that there exists a sufficient quantity of matter that can easily be accreted about the protostar. If the envelope rotated with greater angular velocity, the accretion disk would evolve at a much slower rate and the protostar’s core would not be able to take in as much in-falling matter. The same concept applies to the formation of planetary systems around the future star: the magnetic fields would slow the circumstellar matter down allowing it to coagulate into sizable protoplanets12.
Magnetic fields may also be a factor in the apparent overall inefficiency of star formation. Such a proposal involves the ‘slippage’ of the neutral atoms and molecules of a protostar’s circumstellar cloud and envelope through the slightly ionised components of the same cloud, which are being held in place by a background magnetic field23. The rationale is that such slippage in molecular clouds around developing protostars pushes much of the matter back into the ISM – matter that could have contributed to core collapse. It is possible that this might be a solution to the brown dwarf problem if ever it is encountered: perhaps too much mass is lots through slippage to sufficient densities cannot build up in the protostar’s core to trigger nuclear fusion.
In a similar fashion, magnetic fields seem to aid in the dispersion of the remaining envelope once the protostar is nearing the main sequence. Observations of molecules around candidate developing protostars reveal a fast bipolar flow away from the core and envelope. This means that particles travelling at about 100km/s are being pushed away from the protostar in two opposite directions, collimating out of the plane of rotation (up along the poles). The directions of the flows have been inferred from bipolar Doppler shifts (both blue and red shifting) of the high-speed particles moving with ‘forward’ and ‘reverse’ velocities. These particle flows, which extend to a few light years, are estimated to carry a considerable mass of ambient matter away from the protostar (see above image). For such a distance, an enormous amount of energy must drive the lobes: they are thought to be associated with the birth of a massive star, though the exact source is unknown. It is worth noting that the bipolar flows have attracted much interest, as it is such a process (though of a much larger scale) that is observed around extragalactic compact radio sources. Mystery still surrounds the identity of the energetic sources driving those clouds too. Promising scenarios for massive protostars involve using the rotational energy stored in either the newly formed protostar or its disk-like envelope, and strong magnetic fields to effectively act as a giant fan that forces out the circumstellar gases. This picture might also be coupled with the strong solar winds that would be channelled toward the poles by the circumstellar disk (which is much more dense in the rotational plane). The initial stages of this process probably would be hidden from view by the surrounding gas and dust – but once enough matter has been pushed out and lobes begin to form, they show up most brilliantly in the radio range of the electromagnetic spectrum.
The final outflow component is thought to be a jet of ionised particles that shoot straight up and down from the protostar to a length of perhaps 1010 kilometres at speeds reaching 300km/s (seen in image on the next page). The strong magnetic field lines flow up through the accretion disk in the same direction (though it bends in, then away, as it approaches, and leaves, the envelope). The magnetic fields push along a molecular outflow at perhaps 50km/s that surrounds the ionised ‘lane’ through its centre. Essentially the toroidal gas volume around the protostar has two warped molecular cones coming off either side.
If the influence of rotation and magnetic fields is set out as ‘realistically’ as possible, being correctly accounted for, the radiative spectra emitted from many candidate protostars may provide verifiable support for this extended model.
The next series of questions lie in the formation of planetary systems. The presence of the vast outflows strongly alludes to the large circumstellar disks containing solid matter (the disks have never been directly observed as they as blanketed with dust). Once the majority of the envelope has dissipated, this leftover debris may end up becoming the building blocks of protoplanets and eventually an entire solar system. For example: a star in our galaxy, known as Beta Pictoris, appears to be encircled by a disk of dusty material extending 6x1010km from the star – planets may have already formed here. Another star, the famous Vega that is around one-fifth of the Sun’s age, has once been the focus of a study with IRAS. The results showed that there is a nearby cool cloud
170 AU wide of about 90 K, whose dust grains are about a thousand times larger than those typically of the ISM. In total, these grains would be equivalent to 1% of the Earth’s mass. Considering the star’s young age, the cloud might be a possible site of planetary formation.
So far, the models have centred on individual stars and clusters. Star formation in matter clouds is very much a collective occurrence. This is where the models enlarge in scope and incorporate processes of galactic proportions.
Firstly, the contraction of molecular clouds is thought to be offset not only by gravitational collapse, but also shock waves (‘density-wave patterns’) that spread through the ISM. As a shock wave passes through matter clouds that are significantly dense, the sudden pushing together of the cloud from the side of the propagated compression wave can induce the gravitational collapse of the cloud. If the conditions are right, an immediate shock front will cause the cloud to contract and events to proceed as previously considered. The triggering of these shock waves is attributable to a few known events: the expansion of H II regions around young, especially massive stars (as in image below) and supernovae explosions.
As young OB-class stars ionise the circumstellar gas and form an H II region, the heated gas expands back into the neutral H I area. This ‘ripple effect’ creates a density-wave pattern that moves outward through the ISM and develops the forceful shock fronts in dense molecular clouds.
The same wave process applies to supernovae explosions. The sheer magnitude of such an event is sufficient to propagate similar waves and tilt the gravitational balance for molecular clouds. They may even trigger other supernovae explosions in super-massive stars that are nearing the end of their shorter lifetimes and are situated along the wave front.
The ‘chain reaction’ of a star formation can be regarded as the ‘sequential feedback model’ and is prominent in massive cloud complexes. Cloud complexes are usually in the shape of spheres, quite elongated along one axis. As star formation sends out shock waves from one end of the cloud, a sequence of formation events should follow in the shock front’s wake. New OB-class stars in small sub-groups are born approximately
1 millions years after each density-wave pattern passes their dense molecular cloud.
Now, in taking the viewpoint from an entire galaxy, the representation of collapsing molecular clouds forming protostars seems to have much in common with the way galaxies probably formed in the past (for example: they form in one massive disk and have an axis of rotation). During these times, star formation would have been much more efficient and widespread. Today, the greatest amount of star formation seems to take place along the each spiral arm’s boundary in spiral-armed galaxies (as can be seen in the image to the left), especially if they are rotating at a considerable rate. The ISM throughout the spirals arms of such galaxies looks as if it is the densest compared to all other parts. As spiral arms rotate, gases will be compressed in ‘spiral density waves’ and star formation will be stimulated. Self-perpetuating stellar formation occurs when massive clouds in the ISM are dense enough and shock fronts are in abundance.
The frequent development of stars in the past is suggested to influence the formation of galaxies. Stars would form during the creation of a galaxy, and any stars finding themselves outside the galactic plane would probably form globular clusters as we observe them today. All other stars would normally form open clusters inside the main disk and be carried in it as it rotates. Some numerical simulations have proposed galaxies that did not have any spiral bars to begin with, would eventually form some through the interaction of stellar orbits18 – quite a claim indeed, something that may never be verified.
Other simulations have caused revision of theories involving the formation of elliptical galaxies. The traditional notion was these galaxies formed from gas clouds that did not have much initial rotation. Recent models say they could have formed through collision with other galaxies. What is intriguing about this model is the explosion in star formation, triggered by the unbelievable shock waves created by such a catastrophic event. This would most likely use up the vast majority of available gas too. As elliptical galaxies do not have much gas at all or any spirals that could encourage the formation of new generations of stars, stagnation would occur (as presented in the graphs of Star Formation Rate – SFR – versus time in the image above). This idea corroborates with the observations that such galaxies are very old. Also, in dense super-clusters of galaxies, the average counts of ellipticals are higher than spirals. The simulation regarding the collision of galaxies to form ellipticals is supported by this observation, as the era of galaxy formation would have been slightly lacking in empty space with protogalaxies flying about in every direction (so the chances of collision and hence elliptical galaxy formation would have been much higher).
Lastly, what of the question concerning changes in formation processes of the first stars during the universe’s Dark Ages, compared with the ones we model today?
The simplest remedy to this mystery is a slightly altered initial sequence of events that lead up to the same processes of the current model. During the era of galaxy formation, there obviously would not have been any galaxies in which stellar formation could have been stimulated by shock waves in the ISM. The simple remedy is to assume that after a certain period of time, a number of gas clouds had already coagulated, were self-gravitating and moved about in space. When two gas clouds would collide and form one, they would produce their own shock front (as shown in the diagram above). This compression would act in the same manner as the current model suggests: it would trigger star formation in the new larger cloud by offsetting the gravitational collapse of denser cloud cores.
These new stars would then form the building blocks of protogalaxies, which would inturn create new stars, leading to the evolution of large-scale structures in the observable universe and the current model of stellar formation.
An extraordinary amount of new theory is being generated that somehow, or another, incorporates stellar formation. Whether it is a theory on the nature and effects of dark matter or super-massive black holes inside galaxies, star formation seems to play a part, either in theory or in practise. This reaffirms the notion that the stars are fundamental to all structures in the universe. In this section, a few of the prominent theories that deal with more recently extended stellar formation models will be visited.
Low-surface-brightness (LSB) galaxies have been the focus of studies that suggest they collapsed and formed at a later stage than the majority of conventional galaxies. Their blue colour, a typical indicator of active star formation and relative galactic youth, is difficult to understand. Measurements performed with radio telescopes show they have rather low densities of neutral hydrogen gas. This and other data support the idea that the surface gas density in a developing galaxy’s disk must be greater than a certain threshold for widespread star formation to occur. The Schmidt Law states that the SFR of a spiral galaxy depends on the disk’s gas surface density. LSB galaxies, it seems, might somehow stay below the threshold value for a much longer time than conventional galaxies.
Another theory proposes that the formation of galaxies and quasars is heavily influenced by super-massive black holes. It has run into some trouble because of the historical evidence showing a distinct time difference between stellar formation and the beginnings of quasar activity. The black hole theory proposes that the formation of the first ‘bludge’ in a galactic disk, which would already contain developing stars, coincides with the ‘quasar phase’, which is, by its reasoning, the appearance of a black-hole surrounded by a galactic bludge in the centre of the galactic disk. The historical evidence contradicts this by saying that these two stages could not have occurred simultaneously. This scenario is still “sketchy” and more observations are required to make revisions. The theory’s main failing point is its inability to explain what caused the ‘seed’ black holes to initiate the whole process in the first place.
The influence of dark matter on stellar formation has also received considerable attention. Many different theories exist that propose stellar formation in strange circumstances, in many ways unlike what the standard model of stellar formation predicts.
One of the chief reasons behind dark matter’s ‘existence’ is to explain gravitational effects manifested in the motions of disks in galaxies, for example. The problem is that luminous baryonic matter alone cannot be held accountable for the observed effects. Regardless of whether dark matter is cold or hot, is made up of Weakly Interacting Massive Particles (neutrinos, axions, etc) or Massive Astronomical Compact Halo Objects (black holes, white and brown dwarfs, etc), one of its fundamental features is to interact with normal matter through gravity. Yet gravity is the very force that causes molecular clouds to collapse and form protostars. So in the broader sense, it might be possible to claim that the SFR is infact higher than what it would be without the universal presence of dark matter, because dark matter (if it really does exist) would be adding to the forces promoting cloud contraction and thus more stellar formation.
Other more detailed theories have been created involving the increase of the SFR in protogalaxies due to non-baryonic dark matter acting as a ‘quantum fluid’, which could condense in the absence of gravity. As an over-dense region of ordinary baryonic matter and non-baryonic dark matter would begin to collapse in the development of a protogalaxy, the dark matter would condense into this quantum fluid. Tidal interactions with other protogalaxies cause vortices to form in the quantum fluid, which itself does not rotate about the protogalaxy’s centre of mass, as it does not directly interact with the baryonic matter. The vortices create wells into which ordinary matter falls. Once in these wells, the baryonic matter loses its angular momentum, so in effect, it rapidly accumulates. This sudden increase in density throughout the vortices will trigger large counts of stellar formation events across the protogalaxy.
The discovery of specific types of baryonic dark matter (the large number of white dwarfs in the halo of our galaxy, for example) seems to have serious implications, again, on theories of stellar formation processes in the early universe. Current estimates show that in the visible universe, stellar formation produces much more stars of lower mass than of higher mass. However, the existence of a number of ancient white dwarfs (with many more predicted to exist) suggests that in the early stages of galaxy and star formation, the trend was reversed: many more massive stars were created and than solar-mass stars. The reasons for this are unclear at present – it is one of stellar formation theory’s main mysteries.
Many computer simulations have been run with varying initial conditions and distributions of normal and dark matter to investigate galaxy formation. Recently, increasing attention has been paid to the effects of star formation and supernova feedback in such simulations. The aim of one simulation performed in 2001, which incorporated all of these effects, was to resolve the “Angular Momentum (AM) problem” found in previous simulations. The problem arose from excessive transport of angular momentum from baryonic gases to dark matter in the disk of the modelled galaxy, especially during ‘mergers’ with other galaxies. This simulation was found not to suffer a devastating loss of angular momentum and the results reproduced many of the fundamental properties for observed galaxies. The article addressing the simulation results raises several pertinent issues associated with computational modelling of CDM systems. It mentions another group of researchers who argue, “that the inclusion of star formation can help stabilise disks against bar formation and subsequent AM loss”. These bars are those discussed previously, occurring in the earlier fragmentation simulations. However, it seems with the inclusion of dark matter into the system, these anomalies are largely overcome. Another issue raised states “it is not currently possible to model individual star formation and feedback events in cosmological simulations of disk formation”. The basis for this impossibility depends on the modelling software and simulation parameters. In this case, there was too greater difference between the timescales of supernova feedback and the minimum time step of the simulation. These events were approximated so that “each gas particle carries an associated star mass and can spawn two star particles, each half the mass of the original gas particle”. This manner of effectively approximating physical processes to one quantity or body is the key in creating a successful simulation that can run efficiently on simulation software – this will be reiterated in the project’s next part.
Unfortunately, due to our position on Earth and the current capabilities of observational equipment, directly viewing a small snapshot of a star formation event is practically impossible. As has been shown while discussing the observational clues that we can gather from massive protostar development, the radio, ultraviolet and infrared emissions associated with stages in stellar formation are only vague signposts and do not provide astronomers with the detailed evidence required for significant advances in formation models. Thus theories of possible models are developed using mainly inferences from observations. Once they seem reasonably within the limits of a system, they are ‘put to the test’ in computer simulations to investigate the extent to which they agree with predictions. Simulations on computers are helpful because modelling software today is highly flexible and can take into several different effects that may have a crucial impact on formation theory (even though it may end up being a step in the wrong direction).
Despite the fact that computers are still limited in speed, processing power and storage space, professional simulations are run with highly optimised algorithms on parallel-processor supercomputers. One of the most common algorithms incorporates complex ‘Smoothed Particle Hydrodynamics’, or SPH, equations, which provide an efficient way of calculating particle dynamics in a many-bodied system. The actual modelling of individual particles in a molecular cloud, for example, is far from an achievable reality because the sheer number of bodies is too great for any configuration of computers to handle. Therefore, single particles can be approximated to exist in larger bunches: a group of particles is treated as one ‘quantity’ so that calculations may proceed at an optimal rate without incurring severe mathematical errors on the properties of imagined individual particles. The calculations are performed so that the effect of a single quantity of particles is taken into account throughout the entire system. This is part of a typical scenario in simulating an “N-body” system (known this way because the system contains any number of particles). The need for an analytical approach in calculating system dynamics results from the “N-body problem” encountered in continuous analysis. The problem states it is impossible to take into account the effect (the forces, etc) of more than one particle on another single particle simultaneously (in one instant of time of the system itself). This constraint arises because in the moment that the effect one body has on another is calculated, the third body would respond to those same forces and change position (if the focus was on each body’s displacement). That is to say: if a system contains only two bodies, calculation of both bodies’ effect on the other in one mathematical function, for one instance of time, is easy. On the other hand, if there are three or more bodies, it is not possible to do this because as the mathematical calculation is performed for two particles, the others will alter in their properties. To overcome this, the analytical approach is necessary. It involves stepping through each body and applying its effect to every other body. In this way, it is not necessary to consider performing continuous integration of the mathematical functions governing each body’s dynamics in sequence. The valid option in this analytical approach is to make the system perform as a function of an independent variable (usually time). With time, its value is incremented for each frame (or ‘snapshot’ of the system) and the simulation calculates each body’s effect on every other body as a function of the last time increment. This is fundamental analytical procedure used in the vast majority of N-body simulations, and although it does not match the real world’s ability to overcome the N-body problem, it provides a sufficiently accurate representation of physical events, based on a system’s constants and initial conditions.
Many N-body simulations have been performed for the collapse of galaxies, now especially inclusive of the Cold Dark Matter theories. As mentioned previously, such modelling has attempted to incorporate the influence of stellar formation and supernovae explosions in developing galaxies. Fewer simulations have been performed on star formation events themselves. The second part of this project deals with putting the simpler ideas of stellar formation theory through simulations in order to investigate the changes in development caused by altering initial conditions, the numbers and types of particles, distributions, initial velocities and rotation, and selecting different combinations of effects (for example angular momentum and radiation pressure). By comparing the outcome of each simulation, it is possible to obtain a better understanding of the influence each effect and condition has on a system, and hopefully promote further thinking to extend the current models in the right direction.
Naturally, to perform any calculations of particle dynamics on a computer, modelling software must be written to handle such simulations. Some of the hallmarks of any good multipurpose modelling package is its ability to live up to increasing computational demands, incorporate relatively hassle-free extension including more procedures and physical effects, and scalability and compatibility on newer, more sophisticated software and hardware platforms. As part of this project’s investigation of very simple stellar formation models, I have attempted to write my own modelling software to perform the simulations. The irony is, considering the current state of the software and my own relatively basic mathematical, physical and programming knowledge (compared to those scientists who design SPH modelling software for parallel-processing super-computers), the software does not exactly measure up to any of those hallmarks. Not only this, but the relatively late fruition of my ideas inspiring me to attempt such a task, has not left enough time to fully complete all components of the software. It is operational, however experiences very limited functionality.
The purpose of my software and rudimentary model inclusion into the project is two-fold. On one hand, to look briefly at the scaled-down process of creating modelling software and writing the physics and mathematical calculation procedures. On the other hand, to discuss ways of approximating known stellar formation theory and choosing the model’s crucial assumptions in order to perform some simulations.
Firstly, I shall give a concise overview of the modelling software. It is designed to operate on workstations running the Intel hardware and Microsoft Windows software platform (compatible versions are Windows 98, Me and 2000). Although the software can run on one computer alone, its primary feature is the distribution of the computational workload. To take advantage of this, the software can be loaded onto as many computers as there are connected to a network. It is even possible to extend this configuration from a simple Local Area Network, to a Wide Area Network – the software communicates in the same manner, though speed factors may come into play on WANs such as the Internet. The software does not support multi-processor systems as yet – it will be a future improvement: calculations will be spilt and allocated to different ‘threads’ running on separate processors, increasing the speed by a factor roughly of the number of CPUs.
The modelling software consists of several components, each contributing varying degrees to it’s functionality. The main components are the ‘Marshaller’ and ‘Worker’. The Marshaller is used to set the initial conditions, effects and parameters of the simulation. The Worker software is installed on each of the networked workstations and performs the actual simulation calculations. Other components are the ‘Plugin Host’ (this is a Windows NT ‘Service’ that runs as a Dynamic Link Library housing for ‘plugins’, such as the Worker software, that have been created with conventions I have specified) and ‘Plugin Host Configuration Utility’ (which enables the remote installation and control of the Plugin Host on each workstation – for example, it overcomes the problem of manually installing the software onto each workstation, by automatically connecting to each one and configuring them remotely). The final component is the extension for both the Marshaller and Worker: the “Effects”. Effects are also plugins that are used to apply any sort of force or effect to bodies in the simulation – this will be discussed again shortly.
Once the workstations are running the Worker software, a new simulation can be created in the Marshaller. The available Workers can be added to the Marshaller’s Worker selection list – the selected workers will handle the calculation of the simulation. The next step is to specify the initial conditions and parameters of the simulation. At the moment, the set parameters that can be controlled are: initial velocity, initial distribution, system lifetime and particle types. Each of these parameters has extended settings. For example, the initial velocity can be set to zero, random directions, rotation about a point along an axis, toward or away from a point or it can be based on an ‘expression’ that is written using pseudo-algebraic terms (setting the velocity for each particle as a function of its displacement is one possibility). Similar options exist for the initial distribution (random displacement in a sphere or box, functional distribution dictated by an expression, filling a 3D object, even spacing or slight perturbation off even spacing) and system lifetime (not fixed – so it stops on command, fixed: the simulation finishes once a system is a specified age, or completion on the satisfaction of certain criteria, such as attaining a critical particle density and confinement for ignition of nuclear fusion). Multiple particle types can be specified. Each particle has a unique count (or percentage of the total), mass and radius. Particles can also have separate rules governing them as opposed to the global initial conditions and parameters already listed. For example: it is possible to have a total of 3 particle types and to specify that the global initial conditions should govern 2 of them, but have a separate distribution pattern for the third. The global conditions can also be applied to these particle-specific settings, so that a combination of the two governs a particle type’s behaviour (not just one or the other). If the user is satisfied with the initial conditions and parameters, he or she can connect to each selected worker and automatically transfer the initial conditions to each one. In doing so, the Marshaller benchmarks each Worker to gain an idea of its processor rating (how many calculations it can perform relative to the other Workers). Once it has obtained a processor rating, the Marshaller then divides the total number of particles up into sizable chunks, relative to a Worker’s processor rating, for each Worker to handle (chunks that each Worker should finish at the same time). When the user clicks on the ‘Start simulation’ button, the Marshaller will send a ‘save, prepare and start’ sequence to each Worker. When a Worker receives such a set of commands, it saves the current simulation configuration (in case the user would like to resume a simulation later on or continue one based on the conditions and state of another), prepares its allocated section of the system and starts working.
As can be gathered from the networked Worker approach, this is a distributed style of computing. Therefore, the most important aspect of such distributed simulations is to split the simulation up effectively and fairly, and then to make sure each Worker has the correct information of the whole system through the entire duration of its lifetime. The other consideration lies in the analytical modelling method. In the end, the goal of the simulation is to calculate the new displacements of each particle after taking into account any forces acting upon them. To do this and overcome the N-Body problem, these calculations must be done in sequenced ‘frames’ or ‘snapshots’, each with its own system time. Thus the other factor set in the Marshaller’s initial conditions it the frame time: the time increment between each frame of the simulation. The options for this are: fixed increments, adaptive increments (if there is no significant motion in the majority of particles then the increment is increased until particles start moving at least a little – complex statistical analysis must be implemented here to ensure mathematical errors do not occur in pushing the increment value too high) and linear and accelerating increments. The consequence of frame times in the distribution of calculations is that each Worker must synchronise its particle system ‘snapshot’ (the properties, for example: position and velocity, of every particle in the system) with every other Worker so that the calculations may proceed correctly while every Worker is calculating the same data. The issue of synchronisation comes into play in the preparation and at the conclusion of calculation for each frame of the simulation. When each Worker has finished creating its allocated section of the entire particle system, it communicates this allocation to every other Worker in exchange for their allocations. When synchronisation has completed, every Worker will have the same snapshot of the entire particle system on which to work. Once the Workers have finished calculating each subsequent frame of the simulation, the synchronisation process starts again until the simulation can continue. The future design of the software should re-allocate the particle system across each Worker in the event that one or more go ‘offline’ and disconnect from the simulation, which otherwise would cause the simulation to abort.
The one point that has not been mentioned so far is that in this developing example of the simulation, nothing would actually happen to any particles because no Effects have been configured to run with the simulation. As briefly stated, an Effect serves as a force on each particle in the system and also conforms to the modelling software’s modular architecture, making the software fully extensible in this way.
An example of an Effect follows: the first one created was ‘Newtonian Gravity’ – it calculates the attractive force in newtons between two particles and adds the force vector to the particles’ resultant force vectors. The Effects are initially configured on the Marshaller and each Effect’s custom configuration data is sent to each Worker (which must have the same Effect installed too). As each Worker calculates a frame of the simulation, it ‘realises’ the selected effects on the specified particles. As with the global and particle type-specific initial conditions parameters, so to can Effects be configured globally and per particle (interesting results can come from changing the Universal Gravitational Constant, especially on one type of particles among other groups). Once each Effect has been realised on every particle, the Worker cycles through each particle and applies the resultant force, which accumulated for that one frame, to the particle: the force is multiplied by the particle’s mass to give acceleration – this is then multiplied by the time increment for that frame to give a velocity vector that is added to the particle’s current velocity vector. The new velocity vector of the particle is multiplied by time increment again to obtain a displacement vector that is added to the particle’s current displacement, in the end moving the particle. Any number of Effects can be created to calculate any number of physical forces on a particle system, such radiation pressure, collision handling and angular momentum.
In terms of each Worker’s load, one Worker will only calculate the new displacement for the particles that have been originally allocated to it. The calculations do still take into account all other particles, but the distribution of calculations is achieved by having each worker only process its own particles in the context of the system.
The distribution of calculations gives rise to any increase in overall computational power of the Worker ‘collective’. The only concern for a simulation is network speed and traffic conditions. The total size, in bytes, of each Worker’s particle allocation is relatively small if there are quite a few Workers and a moderate total particle count. So on a high-speed network, the synchronisation stage of the Workers, following each calculated frame of the simulation, should not take very long compared with the time to calculate one frame itself. If there is excessive traffic on a large scale network and a large number of Workers, the time difference between the two functions may not be all that large, so the positive effect of decreased total calculation time of the distributed approach is lost. Thus, care must be taken to configure the network correctly, ensuring traffic is kept to a minimum and that a sufficient amount of particles is chosen so that the benefits of distributed computing may be realised (if too few particles are selected, the synchronisation time over a large number of workers will again outweigh the calculation time, rending that simulation inefficient).
At the end of the simulation (regardless of whether is it ended, or the lifetime criteria are met), frame data from each Worker is sent back to the Marshaller to be reassembled into one continuous sequence. There exists a specific viewer incorporated into the Marshaller that enables the user to view each frame of the simulation in both 2D and 3D space. Density maps can also be created in specific dimensions to demonstrate the desired dynamics of a system (for example several images might be created to show the planar distribution of particles in a system that had initial rotation and collapsed into a disk).
Unfortunately due to time pressures, the software has not been finished. The only Effect that exists is gravity and the synchronisation functions have not been completed (so the simulation can only run on one computer). Also, as to be expected with any software-under-development, the Marshaller and Worker need more debugging to fix current problems and to prevent future ones from occurring. A test simulation has been run to check if the basics of the Marshaller and Worker run. Indeed the simulation frames’ viewer displays the image sequence and the pictured particles do move due to the Effect of gravity – the software’s functional prospects are ‘looking good’. Although the Worker’s calculation algorithms are heavily dependent on that of each installed Effect, and do not incorporate any advanced functions like those of SPH (in part because they are out of my league at the moment), the software itself really only serves as a little experiment in distributed computing and an easy-to-use tool for simulating simple N-body systems and investigating the influence a combination of physical forces (Effects) will have on a system’s development. This was the philosophy behind its creation for this project, but because there has not enough time to complete the software, design some more effects and actually run the simulations, the original idea has not yet been fulfilled. It stands at the moment as ‘work in progress’ and will be completed hopefully in the upcoming months. I hope that this software package will have some sort of future as I have spent much time and effort creating it and I would like to see some good use out of it – even if it is only on small and simple scales.
The entire software package has been created over the last 3 weeks. It has been written in Microsoft Visual C++ 6.0 and requires MFC 4.2 and newer ATL DLLs than those found in NT 4. A count of the number of lines of code (of every sub-project in the package: Marshaller, Worker, Plugin Host, Plugin Host Configuration Utility and Effect prototype) yields a sum of about 13 000 (my biggest project so far). It will continue to grow later in the year. Once it is fully operational, I will perform the original simulations I intended for this project and post the results, images and density maps on my website at http://homepages.tig.com.au/~balint
Despite the fact that I am unable to put any simplistic models through my software in its current state, the possible models for the early part of a stellar formation event deserves a short discussion.
The object of testing different models is to discover what effect the differences between them has on the overall system. As this project has gradually built up the understanding of stellar formation, and in doing so has listed more and more forces that, as it is perceived, come into play, it is the same rationale behind gradually building up this simulation model.
The goal of the models here would be to simulate an approximated molecular cloud and add forces to investigate how its collapse is affected and whether a protostar could have the chance of forming, and maybe later seeing whether fusion ignition could be reached (through satisfaction of the Lawson criterion governing the minimum density-containment time of particles in plasma, required to start self-sustaining fusion reactions).
The first step is to identify to what extent molecular clouds should be approximated to make the simulation’s calculations efficient, while still retaining physical accuracy to the real physical event as much as possible. This means, instead of accounting for every single particle in a molecular cloud (which is huge), a group of several particles would be treated as one big ‘particle’ by the simulation. Thus one ‘particle’ would have the many, many times mass and radius of one dust grain or hydrocarbon. The collisions of particles (an Effect that would be activated at a later stage) would have to randomised too, as just because one ‘particle’ overlaps another’s space, the bodies inside them may not be touching. However another consideration is radiation pressure and the extent to which it will counteract the force of gravity. Collisions are necessary to convert kinetic energy into radiation, which inturn would increases the radiation pressure as the system heats up. So a balance between the two must be struck, and several simulation test runs might be dedicated to investigating this.
Yet another Effect that would have a significant influence is angular momentum. This would be another crucial step in understanding what influence is has on such a collapsing system. If the parameters are realistic and the Effects’ influence proceeds as planned, it would be very rewarding to see clouds both fragment, form increased concentrations of mass, which would inturn collapse and form an envelope. If these series of events were to occur, it would show that the model was reasonable correct. If not, the model may require some ‘tweaking’ or be completely incorrect (with a bit of luck it is not the simulation software itself). This very process reflects the ordeal professional astronomers and cosmologists go through in taking observational evidence, analysing probable models tested in simulations, and then attempting to create newer, more accurate models that fit all available knowledge. This is the very core of the scientific method itself.
Once a model has been simulated here and different combinations of Effects have been tested, analysing exactly what each Effect has, and what the general results were, would be satisfying and enlightening, while also reaffirming of the theory. Although improvements to the simple model here may be necessary anyway, but are too complex to be handled by the simulation, it would still give a sense of the process of reviewing models and suggesting well-founded theories that could be the solution to a more accurate and improved model for the future.
This picture is taken from the analysis of simulation results of galaxy
formation with star formation feedback and is the kind of output
the Marshaller will give. The software used here was GADGET.
Stellar formation is one of the most essential, yet primal, events of the cosmos’ construction and evolution. Stars are the main component of galaxies; stars process lighter elements and create heavier ones that form the dust and gas of the interstellar medium; stars create planetary systems and provide energy to life that may inhibit such homes; stars form in different configurations and have lifetimes with alternative endings: some die and cool slowly, others explode in spectacular flashes – all this from a ball of plasma. The formation of stars was crucial to the evolution of the universe. In humanity’s yearning to understand the universe, astronomers have made several key observations and used computer simulations to at least try and predict how these sparkling orbs come about. Its complexities are still another mystery, intertwined with galaxy formation and dark matter. With the progress that has been made in current stellar formation models, it would be pleasing to see the theory mature alongside new observational evidence provided from radio and infrared telescopes – a great deal is in store for SIRTIF. So much attention has been drawn to developments in the evolution of large-scale structures in the universe – if good progress is made in the future, awareness of such a key area as in-depth star formation will increase. A better understanding of the processes involved in star formation, and the effect on its surroundings, promises to have consequences, not only for other theories, especially regarding galaxy formation, but also perhaps for the very fundamentals that we perceive to dictate the physical universe.
Creating a simple model of the early stages of stellar formation seemed like an interesting application of the knowledge I have gained from researching this project. Despite the forward push of time and the looming HSC, I was unable to test the with my incomplete simulation software. However, all things considered, I believe this has been a fulfilling, beneficial and fun experience. I would like to continue this project once I finish school: I plan to finish the simulation software and write a wide variety of Effects to combine. I guess I shall taste the world of professional astronomers and programmers who attempt to perform these miracles on a regular basis. I will be able to put the many forces governing stellar formation to the test, to really see and exemplify what effect they have on protostar development – what really might be going on in the intangible interstellar medium.
· Encyclopaedia Britannica, Multimedia Edition 1999 (CD-ROM):
o The Interstellar Medium (Article)
o Galaxies: Dust clouds
o Galaxies: The general interstellar medium
o The Cosmos – Star and Chemical Elements: Star Formation
· Scientific American (http://www.sciam.com):
o Bothun, G.D., The Ghostliest Galaxies”, March 1998
o Musser, G., “The Whole Shebang”, October 2000
· Parker, B., “Creation”, Chapter 4, Plenum Press, New York, 1988
· Harrison, R., “Cosmology”
· Zeilik, Michael, “Astronomy: The Evolving Universe”, John Wiley & Sons, 1988
· Meadows, A. J., “Stellar Evolution”, 2nd Edition, Pergamon Press, 1978
· Lightman, A. and Brawer, R., “An Introduction to Modern Cosmology”, Chapter 1, “Origins, The Lives and Worlds of Modern Cosmologists”, Harvard University Press, Cambridge, Mass, 1990
· Thickett, Geoffrey, “Pathways to Chemistry”, Macmillan Education Australia, 1996
· Rickey, Tom, “The Rochester Review”, University of Rochester, New York, 1999, “The Last Great Eye in the Sky” (http://www.rochester.edu/pr/Review/V61N3/feature4.html)
· Thinkquest, “Life Cycle of Stars”, 1998 (http://library.thinkquest.org/17940/texts/star/star.html)
Matter, and the Formation of Galaxies”
- Studies of the stars - Studies of the Universe, “Stars”,
· Leicester University Astronomy Group, “Brown Dwarfs & Stellar Formation”, 1998. (http://www.star.le.ac.uk/astron/brown/contents.html)
· “Galaxy Formation” (http://zebu.uoregon.edu/~js/ast123/lectures/lec28.html)
Criteria for Nuclear Fusion”
formation and feedback in isolated disk galaxies”
· “Cosmological Dark Matter: An Overview” (http://www.astro.ucla.edu/~agm/darkmtr.html)
· The Astrophysical Journal, 555:L17-L20, 2001 July 1: Thacker, R.J., Couchman, H.M.P., “Star Formation, Supernova Feedback and the Angular Momentum Problem in Numerical Cold Dark Matter Cosmogony: Halfway There?”
· Science: Onaga, L., “Astronomers detect elusive dark matter in Galaxy” (http://www.usatoday.com/news/science/aaas/2001-03-22-dark-matter.htm)
· Berkeley Campus News: Sanders, R. “Astronomers at UC Berkeley, Edinburgh, Cambridge, Vanderbilt report first direct detection of dark matter in galactic halo, part of universe's missing mass”, 22 March 2001 (http://www.berkeley.edu/news/media/releases/2001/03/22_halo.html)
· Peoria Astronomical Society: Ware, D., “PAS General Articles: Why Do Stars Form?” (http://www.astronomical.org/astbook/starform.htm)
· ‘Our Sun’ (Title sheet): [Unknown] H II spectra photographed by SOHO
Star Cluster of M13’ (p. 6), ‘An Active Stellar Nursery’ (p. 18), ‘Initial Star
Formation Rates’ (p. 31), ‘Star Formation’ (p. 32),
‘Globular Cluster of M80’ (p. 32):
“Galaxy Formation” (http://zebu.uoregon.edu/~js/ast123/lectures/lec28.html)
· ‘The Orion Nebula’ (p. 7): Encyclopaedia Britannica Online (http://search.ebi.eb.com/ebi/binary/0,6103,30589,00.gif)
· ‘Trapezium cluster’ (p. 13): “Images of the Universe” (http://www.mv.cc.il.us/alternativelearning/starimages.htm)
· ‘Pleides cluster’ (p. 21): [Unknown]
· ‘Gas cloud collapse’ (p. 23), ‘Spiral Galaxy’ (p. 30): “Dark Matter, and the Formation of Galaxies”
Graphic Output’ (p. 46):
“Star formation and feedback in isolated disk galaxies”
 Two books that raise this issue are: Gribbin, John and Rees, Martin, “Cosmic Coincidences”, [Date and publisher unknown] and Rees, Martin, “Just Six Numbers”, Phoenix Press, 1999
 Lightman, A. and Brawer, R., “An Introduction to Modern Cosmology”, Chapter 1, “Origins, The Lives and Worlds of Modern Cosmologists”, Harvard University Press, Cambridge, Mass, 1990. Pp 46-47.
 This time range seems to be coherent within more recent frameworks, even though it is still relatively wide.
 Parker, B., “Creation”, Chapter 4, Plenum Press, New York, 1988. Pp 57-74
 Harrison, R., “Cosmology”, Chapter 2, “Stars”. Pp 36-37.
 Harrison, R., “Cosmology”, Chapter 2, “Stars”. Pp 42-43.
 One famous piece of evidence of a supernova clearly visible from Earth during the night comes from old Chinese manuscripts, discovered during World War II, that describe what we now know as the Crab Nebula. When it exploded in the 14th century, it was bright enough to write by at night, the manuscript says.
 Harrison, R., “Cosmology”, Chapter 2, “Stars”. Pp 38-39.
 This is one of the very convincing propositions of many who believe in ‘E.T.’ – especially people who support the ‘Search for Extra-Terrestrial Intelligence’, a world-wide, distributed analysis of radio signals, received mainly at the Arecibo dish in Puerto Rico, for ‘signatures’ of other civilisations. ‘(Frank) Drake’s equation’ (created by one of SETI’s founder) is supposed to ‘approximate’ the number of intelligent civilisations in the universe based on several variables – the result is considerable based on this thinking. For more detail, see http://setiathome.berkeley.edu and http://www.seti-inst.edu/science/drake-calc.html
 Harrison, R., “Cosmology”, Chapter 3, “Galaxies”. Pp 49-50.
 Encyclopaedia Britannica: “Interstellar Medium” (Article)
 Zeilik, Michael, “Astronomy: The Evolving Universe”, Chapter 15, “Star birth and interstellar matter”, John Wiley & Sons, 1988. Pp 306-323
 Thickett, Geoffrey, “Pathways to Chemistry”, Macmillan Education Australia, 1996
 The ‘scattering function’ [s(f)] is proportional to the frequency to the fourth power. So the higher frequencies toward the blue end of the spectrum are preferentially scattered over the lower ‘redder’ frequencies. If we take the ratio of the two frequencies to be roughly 2, blue photons are scattered 16 times more than red ones.
 Encyclopaedia Britannica: “Galaxies – Major Components: Dust Clouds”
 Encyclopaedia Britannica: “Galaxies – Major Components: The general interstellar medium”
 Hydrocarbon substitution reactions of alkanes require UV radiation to break strong covalent bonds between atoms.
 For more information, visit: http://sirtf.caltech.edu
 Rickey, Tom, “The Rochester Review”, University of Rochester, New York, 1999, “The Last Great Eye in the Sky” (http://www.rochester.edu/pr/Review/V61N3/feature4.html)
Newtonian Law of Universal Gravitation:
(as used programmatically in modelling – see Part B of the project)
 Thinkquest, “Life Cycle of Stars”, 1998 (http://library.thinkquest.org/17940/texts/star/star.html)
 “Dark Matter, and the Formation of Galaxies”
 Encyclopaedia Britannica: “The Cosmos – Stars and the Chemical Elements: Star formation”
 If the system is not being acted upon by any external forces, its total angular momentum will remain constant. Angular momentum will also be conserved if the system’s centre of mass changes.
 Astronomy - Studies of the stars - Studies of the Universe, “Stars”,
 These are the fundamental relationships of physical body dynamics in Uniform Circular Motion.
 Leicester University Astronomy Group, “Brown Dwarfs & Stellar Formation”, 1998. (http://www.star.le.ac.uk/astron/brown/contents.html)
 Brown dwarfs are failures of star formation because their cores were not dense and hot enough to begin nuclear fusion reactions. They are usually 0.08 times one solar mass.
 An Earthly example of the braking of envelope rotation is eddy current braking: as eddy currents are induced in a rotating metallic disk by surrounding magnets, the ‘eddies’ circle in such a way to oppose the disc’s motion, thus slowing it down.
 Density-wave patterns are large-scale compressions and rarefactions of gas clouds and look like waves travelling through the ISM.
 Sumner, T.J., “Astrophysics Course”, 1997/8, “Galaxies - 4.4 Other galactic components”
 “Galaxy Formation” (http://zebu.uoregon.edu/~js/ast123/lectures/lec28.html)
 Scientific American: Bothun, G.D., The Ghostliest Galaxies”, March 1998
 Scientific American: Musser, G., “The Whole Shebang”, October 2000
 “Cosmological Dark Matter: An Overview” (http://www.astro.ucla.edu/~agm/darkmtr.html)
 Berkeley Campus News: Sanders, R. “Astronomers at UC Berkeley, Edinburgh, Cambridge, Vanderbilt report first direct detection of dark matter in galactic halo, part of universe's missing mass”, 22 March 2001 (http://www.berkeley.edu/news/media/releases/2001/03/22_halo.html)
 Science: Onaga, L., “Astronomers detect elusive dark matter in Galaxy” (http://www.usatoday.com/news/science/aaas/2001-03-22-dark-matter.htm)
 The Astrophysical Journal, 555:L17-L20, 2001 July 1: Thacker, R.J., Couchman, H.M.P., “Star Formation, Supernova Feedback and the Angular Momentum Problem in Numerical Cold Dark Matter Cosmogony: Halfway There?”
 “Lawson Criteria for Nuclear Fusion” (http://hyperphysics.phy-astr.gsu.edu/hbase/nucene/lawson.html)