Paper - Magnetic Fields in Star Formation

Magnetic Fields in Star Formation

A star’s evolution begins and ends in the interstellar medium, the dust and gas that exists between the stars. At the beginning of this cyclic process of star formation where dust and gas collapse and compress together due to gravity. However, if gravity always draws things together, why isn’t everything a star? Why isn’t the universe mostly stars and planets rather than dust and empty space? This is because on average the distance between two particles in the interstellar medium is too far, and so on average the dust is too diffuse for star formation to occur. Only through turbulence and random chance can the dust group up enough to begin coagulating into a star.

The first requirement for star formation is if there is enough mass in a given area to form a star. This minimum mass over an area is called Jean’s criterion, which models the interstellar medium as a uniform, stationary cloud of gas that acts under only gravity and ideal gas pressure. Given these assumptions we can use the Virial theorem to model the collapse of the gas. The virial theorem tells us that for a closed system in equilibrium, the following is true.

So we can see that on average the total potential energy of every single particle in the system is equal to twice the kinetic energy in the system. So from this stability assumption we can assume that if the potential energy of the system exceeds twice the kinetic energy, it will begin to collapse in on itself as gravity links more and more mass together. With a bit of substitution we get the equations

M is the minimum mass to trigger collapse, and R is the minimum radius for that this mass must be contained in. Now we can envision a new process that has to occur just from thinking about this equation. As the density increases the jean’s mass decreases, which means as the object collapses less mass is needed to collapse, and greater density increases the potential energy of gravity. This gives rise to the process of fragmentation where, the collapse of a dust cloud is a runaway process in which denser areas of gas will collapse faster. This means that not all the material in an area gets used, the more dense and massive a cloud, the smaller fragments and thus smaller stars are formed from the gas cloud.

Another property we can deduce from the above equations is the average velocities of the particles in the cloud. <T> represents average kinetic energy which is equal to ½ m <v>2. This gives us

Which is the root mean squared speed of the particle, which gives us an average speed of a collapsible gas cloud of about 500 m/s. So just by making the simplest of assumptions we already have a lot of information and approximations for star formation. We have a rough idea of the density and size necessary to form a star, and we have some idea of the structure of it by knowing the velocity of the particles within it. However, it obviously lacks many other important aspects which contribute significantly and change the criteria of this basic model including: the initial velocity of the the cloud, radiation transport through the cloud, ionization, rotation, and magnetic effects. In particular the magnetic field plays a very important effect in preventing or triggering collapses.

Troland and Heiles in 1986, found that the magnetic field strength in the beginning stages of collapse is on the same order as the gravitational and kinetic energy of the molecular cloud. Although we might be able to guess that it has a strong effect because em fields are stronger than gravitational ones, we have to realize that electromagnetic field strength goes down as r2 which should be extremely significant due to the large distances we deal with in molecular clouds. So its not inherently obvious that em fields can play such a huge role. However, it does, and we know this because of the Zeeman effect, which allows us to detect the strength of magnetic fields from a distance.

The Zeeman effect is the splitting of electron energy levels in an atom due to the presence of a magnetic field. This separates a solid emission line into 3 distinct lines, and the distance between these lines is proportional to the strength of the field. In particular the 21 cm line produced by hydrogen, and the 18 cm line produced by OH are often measured because their wavelengths are large enough to penetrate out through the clouds of interstellar dust. Troland and Heiles measured these lines using a method called stellar spectropolarimetry, which takes advantage of the polarization of e-m fields in order to measure the strength of the electric field. These measurements led to the discovery of the magnetic field strength in molecular clouds.

Now that we know the strength of the field, we can now try to characterize what they do. It serves two main functions, the first aids in supporting or collapsing the cloud, the second is changing the distribution of mass in a cloud. Lets start by analyzing the first function. We can think of the magnetic field lines as distributed among the particles in the gas. Since the fields are linked to the particles, when the gas tries to collapse in on itself, the field lines come together. We know from lenz’s law that in e-m fields resist changes, so this increases the magnetic pressure in the system which resists compression due to gravity. If we include this to the Jean’s mass criterion it rises to

Where cB is 380 N1/2m-1T-1. We call clouds that are above this new Jean’s mass magnetically supercritical, and clouds that are below this mass magnetically subcritical.

However, this idea has some issues. If we use this to predict star formation, the initial mass function would be much higher than it is observed to be. The initial mass function is the distribution of masses of newly formed stars since, and since the magnetic field here is treated in a way where it only resists collapse, the mass function rises.This means we most likely have a problem with our assumption that the magnetic field lines are linked to the position of the particles in the clouds. This is supported by the fact that newly formed stars would contain a very high magnetic field as the contributions add up. However, recent theories indicate that there is a way to account for this magnetic field loss, so the assumption may not be entirely untrue.

One of these theories is ambipolar diffusion. The logic behind this is that although the interstellar medium is mostly neutral, there are still ions. These ions must travel along the path of the magnetic field lines in the ISM. So the ions can be thought of as a stationary grid which slows down the neutral particles that collide into it, letting the magnetic field absorb the energy transferred to the ionic particles instead of acting as an elastic collision. This means that more mass will coagulate around magnetic field lines.

In addition since the position of the ions are fixed in space, even though the neutral mass is collapsing down, the ions star relatively close to where they are and are linked to the magnetic field. This means that the magnetic field doesn’t get drawn in nearly as much as we thought in the original model where the field can gets dragged in uniformly with the collapse of the dust cloud. And accounts for the weaker magnetic fields of new stars, since the density can increase without drastically increasing magnetic flux. This effect also helps explain the high field strength in the interstellar medium because its a function of all the ions left over after star formation, so star formation doesn’t reduce the magnetic field strength in the surrounding area.

So now we have a good explanation right? Unfortunately it still has some issues, one of the major problems is that the effectiveness of this process would be dependent on the metallicity of the medium, since the process is dependent on the number of ions that can link up to the magnetic field. This does not match observations, which seem to be independent of metallicity. It was also shown by Troland and Heiles in 1986 that ambipolar diffusion is too slow of a process to remove the magnetic field from a gas if the gas is diffuse, and Shu et. al 2006 showed that ambipolar diffusion was too slow for dense gases, so it doesn’t account for either extreme, only mid range cases.

However, since the results match for many general cases, ambipolar diffusion is still a reasonable theory to follow. It could mean that it is a main process for mid range molecular clouds, and that we only need to change the model for fringe cases, or the data could be matching out of chance and we require a different explanation.

Another explanation that has become more popular recently is magnetic reconnection. In this model, we take into account that the gas is turbulent. So the magnetic field lines are not stationary but are warping and twisting. The field lines are simply an indication of flux, but it is a good idea to think about them as actual lines in this case because magnetic reconnection occurs when field lines “touch”. This means that huge amounts of magnetic flux are passing through the same area which results in a huge release of energy. This is the same process that happens in a more familiar event, the solar flare. In either case, magnetic reconnection that happens in a short time frame is capable of quickly releasing a lot of energy from the magnetic field associated with those field lines, which can account for the field loss rate depending on the rate of reconnections or touches that occur due to turbulence.

Lazarian and Vishniac were the ones who calculated the timescale for this process by solving the incompressible magnetohydrodynamic equations using fourier methods. They got the solution for the magnetic field by solving for the field in a box sized to the fundamental wavelength of the B-field, then repeat that over all space, while meeting boundary conditions. The equations are listed as follows.

∂v/∂t= (∇ × v) × v − (∇ × B) × B + ν∇2v + f + ∇P′ (1)

∂B/∂t= ∇ × (v × B) + η∇2B (2)

∇ · v = ∇ · B = 0 (3)

where f is the driving force, P′ ≡ P/ρ + v · v/2, v is the velocity over r.m.s. velocity, and B is the Alfven speed over the r.m.s. velocity. The real space components of time t is in units of the large eddy turnover time (∼ L/v) and the length in units of L, the inverse wavenumber of the fundamental box mode.

The magnetic reconnection model better accounts for the loss of magnetic field in a molecular cloud mainly because its much faster in those fringe cases of high and low density, and is not dependent on metallicity, rather on turbulence, and there is enough random motion in the ISM to account for the number of reconnections necessary. This gives us a more accurate inital mass function. However, this model has a major problem in that it predicts tangled field lines in the cores of molecular clouds, which contradicts observations that show that the B field in molecular clouds are regular, thats how we were able to polarize and observer the additive effect.

There now exists research into models that try to combine the two effects together, in which both ambipolar diffusion and magnetic reconnection are accounted for. However, these models are difficult to create because magnetic reconnection by itself already accounts for the reduction rate of the magnetic field in this stage of stellar evolution. Also by definition these two processes counteract one another since the stronger the ambipolar diffusion effect, the less turbulence can occur since the ionic grid slows down the particles, which makes it difficult to model due to feedback loops.

In conclusion, more research into this field is necessary in order to create a model that matches observations. Ambipolar diffusion explains many cases, and matches observations of regular field lines. Magnetic reconnection models match initial mass functions more accurately and over a wider range of star formation scenarios. Some new formulation, either involving both processes or a new process altogether must be found in order to accurately match all the data gathered.

Paper - Pulsar Formation and Structure

Pulsar Formation and Structure

            Even a star cannot live forever. Over time, the fuel of the hydrogen core fuses into helium, the helium can be fused into carbon, and even heavier elements. These changes in the fuel of the star, causes drastic changes in the star’s structure and is called the process of stellar evolution. The most common end stage of this process is the white dwarf, a low mass, high density star that emits very little radiation. These stars no longer undergo nuclear fusion and are supported by electron degeneracy and will eventually radiate away its energy and cool down until it can no longer be detected, vanishing into the darkness of space.

How does degeneracy support a white dwarf from collapsing under its own mass? Degeneracy pressure is caused by the Pauli exclusion principle which says that two fermions cannot occupy the same quantum state, meaning they can’t have the same quantum number. Some examples of fermions include protons, neutrons and electrons which have antisymmetric wavefunctions. This property limits the number of particles you can stuff into a given volume because they cannot share an energy state, imposing a limit to the proximity of the particles. This means that white dwarfs and other objects in a degenerate state cannot be compacted down any farther.

This paper will describe the formation of another type of degenerate object, pulsars, which are a type of neutron star. As the name suggests neutron stars are neutron degenerate objects, so instead of being packed so tightly that the electrons can’t be packed any closer they are limited by the proximity of their neutrons. These stars can be formed by certain types of supernova.

The first way a supernova can form neutron stars is by having a white dwarf find a companion star that’s less dense than itself, such as a main sequence star. Due to its greater density, it can draw mass away from the less dense companion star. We can explain this ability to remove mass from another object by both Newtonian and Relativistic physics. Overall it boils down to the greater density more sharply curving spacetime around the white dwarf, or by fringe material on the companion star escaping its original gravitational pull.

However, despite giving us an acceptable reason Newtonian physics fails to give us the appropriate rate of mass loss and gain from the companion star to the white dwarf. This process is called mass accretion and allows a white dwarf to destabilize itself by exceeding the Chandrasekhar mass limit set by:

where ω03 is a constant derived from a from the lame-emden equation, µe is the average molecular weight of the star, mH is the mass of hydrogen, and mp is the planck mass. This formula gives us a maximum weight of approximately 1.4 times the mass of the sun, which is the upper stability limit for a white dwarf. Normally the white dwarf doesn’t have an ongoing process that increases its mass and can destabilize itself. However, if a companion star is present, this cannot occur, and the white dwarf will collapse. Electron degeneracy pressure will no longer be able to support it and so the star pretty much implodes as gravity wins out over its outward pressure. This happens so fast that the mass gets superheated and undergoes runaway nuclear fusion resulting in a supernova.

Another way a supernova could occur is if the star was simply extremely massive. High mass stars burn hotter and can progress through enough cycles of stellar evolution that it can fuse much heavier elements. This allows them to naturally exceed the Chandrasekhar limit at the end of their stellar lifetimes instead of reaching a proper white dwarf phase and undergo a supernova without the aid of a companion star.

Either way, a supernova has the potential to form a new celestial body. The leftover matter at the center of these explosions is extremely condensed, which can form a neutron star. It can reach this only if the mass lies between the Chandrasekhar mass and the Tolman - Oppenheimer - Volkoff mass limit, the upper bound of a white dwarf and the lower bound of a black hole.

Now we shall delve into the structure of these interesting stars, starting with the equation of state. These tell us the pressure, the density, and the temperature of the star as a function of radius. Currently, there aren’t consistent formulations for the equations of states. Some models include APR EOS, UU, EOS FPS, and L, all of which come up with different mass predictions. An example of one of the possible equations of state for pressure is

The integral over the mass is a volume integral adjusted by the central density rho to give the mass as a function of radius. The factor nabla shows that this is a general relativity equation as the factor 2Gm/c2 factor is known as the Schwarzschild radius, the radius of a black hole.

This term is commonly used in general relativity, and we can use the Schwarzschild metric here to show us some interesting properties that occur on the surface of a neutron star.The Schwarzschild metric is

By taking some average values for a neutron star, 1.5 solar masses for its mass, and 10 km for its radius, we get the Schwarzschild radius to be roughly 4.4 km. This makes the factor 1-rs/r roughly .66 which we can see will have a significant factor in warping the space around the neutron star. This means that at the surface of the neutron star, the actual distance is ~1.2 times the coordinate distance! This means that if you were able to walk on the surface of a neutron star, in order to walk 10 meters from an observer’s reference frame, such as a scientist floating in a spaceship, the walker would need to walk 12 meters in his own frame!

The exact way in which to incorporate this spacetime curvature into an equations of state for a neutron star is currently unknown and warrants further research. The main contention between the different models, is on the application of general relativistic corrections, so its clear that we can gain a greater understanding of quantum gravity from the creation of more accurate neutron star models through data gathering and analysis.

Another structural feature to look at is the neutron star’s temperature. In particular it is important to model the cooling process. Immediately after a supernova, a neutron star must be immensely hot, on the order of 10^11 kelvins. We know from observation that it can’t dissipate this heat simply through simple radiation of heat, so there needs to be explanations on methods to quicken this rate of heat loss. In addition, neutron stars often undergo periods of quiescence where it turns on/off its x-ray emission spectrum. The speed at which it turns off also requires explanation, and one of the most common explanations is the Direct URCA process. This is when the star emits neutrinos via the processes:

This cools the star because neutrinos don’t interact very strongly with matter, they can simply pass through and leave the core of the neutron star, carrying away with it large amounts of energy very quickly. This process occurs at a rate many orders of magnitude quicker than cooling by radiation. This means that a neutron star actually cools from the inside out rather than from outside in, which is a very interesting side effect of this process. Another cooling method is the modified URCA process in which 

helps to explain the timeframe of long term changes in temperature of a neutron star, its overall cooling and eventual darkening. It was shown by Lattimer et. al in 1991 that both of these methods matched up with gathered data and so these processes are heavily looked at in neutron star research. However, the strength of the contribution depends on the possible temperatures at the core of the neutron star during formation. The direct urca process predicts a cooler core than external temperature which is a very odd process to have happen and goes against the typical star structure in any sequence of stellar evolution. In addition not only do we not know about the temperature, we don’t even know for certain what kinds of matter exists at the core of a neutron star.

For now the most accepted structure of a neutron star is as follows. The surface of the star is a solid lattice formed of degenerate electrons and heavy nuclei such as iron. Below this is an inner crust that contains a lattice of heavier nuclei such as krypton, and superfluid neutrons and electrons. It is around here that neutron drip occurs. Neutron drip is when a neutrons tunnel out of the nuclei to become free neutrons. Normally a free neutron would decay into a proton, however, since the star is neutron degenerate, there is no lower energy state to occupy, so instead of decaying into a proton and its antiparticle, it stays a neutron and tunnels out of the energy well, becoming a free floating neutron, then undergoes its decay. This forms a layer in the star of free neutrons and protons located below the inner crust, and below this is the unknown core.

That fermi sea though, causes many of the interesting properties associated with neutron stars, including the ability for it to become a pulsar. Not only are the particles in that area a superfluid they are also superconductors. Superfluidity is a state of matter where a liquid behaves as though it has no viscosity, and has infinite thermal conductivity. Due to the property of infinity thermal conductivity a superfluid is also isothermal. What this means is that since it has an infinite ability to distribute heat, its not possible to locally heat a superfluid, so it always has the same temperature throughout the entire liquid. Superfluidity also allows a liquid to maintain equilibrium in containers regardless of gravity, allowing for fluids to crawl up or down the outside surfaces of its container. Also turbulence that is self contained, like a vortex last indefinitely inside a superfluid since it has no friction.

The neutron star’s sea of protons, neutrons and electrons eventually behave like a superfluid because the degenerate neutrons can pair together to form a boson. Boson’s do not have to obey the pauli exclusion principle and can be in the same state at the same time, which allows them to pass freely through one another. This gives it even more freedom than a gas as it has a viscosity of 0, but is still considered a liquid due to the distance and bonds between the particles as a whole.

In addition a neutron star’s sea of particles is also superconductive which means that it has no electrical resistance, and can maintain currents indefinitely. Only lenz’s law can slow down the current in a superconductive material.

These properties heavily affect the structure of the neutron star. Since the sea of particles has some charge due to protons and electrons, once the movement of this sea becomes uniform, the magnetic field lines they form will become constant, making the surface which is also charged solid. The particles on the surface are degenerate electrons and heavy nuclei, which means it is purely ionic and its position is heavily fixed due to the magnetic field lines created by the rotating superfluid.

This effect seems to be akin to the effect of ambipolar diffusion in star formation. In that case, the dust of the Interstellar medium has ionic particles that couple to the magnetic field lines of a molecular cloud, which slow down the movement and helps in the accretion of mass around those field lines. This lends credence to the idea of a solid surface on a neutron star because the effect of the superfluid causes a magnetic field many times stronger than that of ambipolar diffusion so the increasing of density and slowing of movement should also increase.

When these fields are strong enough, they can force the electromagnetic radiation of the star to exit only at the poles of the star resulting in a pulsar. The only way for them to get this strong is if the superfluid has enough angular momentum through formation, but where does it come from?

It relates all the way back to the formation of the original star. In the giant molecular clouds that formed the original star. In order to shrink some of that gas down gravitationally, assuming there was some initial rotation, or turbulence in that cloud, angular momentum has to be conserved. This is why stars rotate, such as our sun, and why they have a magnetic field. The ambipolar diffusion previously mentioned is a process that explains how the rotation can be slowed by clumping of material and removal of momentum through magnetic fields. Though again ambipolar diffusion is its own topic with its own controversies.

However what holds true is that as you decrease the size of the object and pull in more particles together, the rate at which it spins has to go up. Once the rest of the star is blown away and only the compacted matter is left, the speed at which it rotates is enormous because it went from a huge cloud of dust to a few kilometers compounded with the moment of inertia calculated as r2. Neutron stars have been recorded to have a period of rotation on the order of a millisecond. Not only that it will maintain this rotation very accurately due to the superfluid nature underneath the crust, no friction to slow down the process.

However there are some strange events that can disrupt this regularity. Sometimes a pulsar will “ glitch” or “kick”. Some speculate that this is caused by asymmetric supernova, others think that there are starquakes in which the solid crust compacts, as deformities caused by landing meteorites or crust compacting as pressure towards the surface goes down, causing quakes on the surface of the star. That quake can then severely disrupt the period of rotation for that star as the motion will remain in  the superfluid. Forces continue endlessly as there is no friction disrupting its motion, so even the smallest events could have major consequences.

In conclusion there are still a lot of unknowns pertaining to the pulsar. In particular we don’t know the composition of the core, or have a definitive explanation for anomalies or “kicks” in the pulsar, or a reliable equation of state for a neutron star, which makes it very difficult to model. However, further research into this area will help further our understanding of both general relativity and quantum mechanics and possibly how to reconcile the two.

Medicine - Pseudoephedrine Study Draft 2010

BACKGROUND
Pseudoephedrine (PSE) is a readily available over-the-counter nasal decongestant which is a sympathomimetic amine. Specifically PSE activates adrenergic receptors in presynaptic neurons causing muscle contraction in blood vessels, also known as vasoconstriction. This results in decreased inflammation and mucous production which relieves the symptoms of the common cold. This study in particular considers one of its alternative uses as an ergogenic aid.

As an ergogenic aid it was banned from use in sports competition as doping is illegal in most realms of professional sports. However, it is debatable whether or not PSE is capable of generating any ergogenic effect, and so there was a period from 2004-2010 where PSE was not on the banned substances list due to WADA’s list replacing the IOC’s list of banned substances.

Despite potential risks, and uncertainty on the ergogenic effects of PSE, athletes have still been known to abuse the use of pseudoephedrine in hopes of gaining an edge on their competitors. Data generated and recorded in the doping control laboratory of Cologne between 1996 and 2003 that included a total of 52,347 in-competition analyses yielded 33 AAFs for pseudoephedrine, which amounts to an average of 4.1 positive controls per year. In 2007 and 2008, that is, 3 years after pseudoephedrine was removed from the prohibited list, the prevalence of pseudoephedrine and ephedrine was determined in 16,335 in competition doping control samples. The analyses resulted in 102 cases of pseudoephedrine use or misuse. In particular there have been a high number of cyclists who have abused this drug in hopes of an edge in competition, out of those 102 cases of pseudoephedrine use, 44 came from cyclists (Thevis et. al).

The potential ergogenic effects that athletes believe PSE can provide is as a stimulant and to increase muscle performance. This is one of the points of controversy between studies, as a boost to muscle performance has yet to be confirmed. PSE’s use as a stimulant is also controversial as its effect on the nervous system is relatively minor and will probably only affect sensitive individuals. This use of PSE is likely due to its association with ephedrine and methamphetamine both of which do have significant effects on the nervous system to increase concentration. The association from ephedrine is due to the plant Ephedra sinica which contains both and is used as a traditional herbal remedy in Chinese medicine. The association with methamphetamine is because pseudoephedrine is used as a chemical precursor in the illicit creation of methamphetamine.

The purpose of this systematic review is to quantitatively consolidate the results of studies relating to the ergogenic effect of Pseudoephedrine in order to determine the validity of its ban from competition. Previous studies have yet to resolve these conflicting results even when using the same testing methods. Chu et. al 2002 found no ergogenic effect while performing a 30 second Wingate test, and yet Gill et. al found that there was an ergogenic effect with the very same Wingate test.

METHODS
In consultation with 2 research librarians, we developed search strategies to identify potentially relevant studies from the MEDLINE, and EMBASE databases. We sought reports of randomized control trials, including crossover trials, in relation to pseudoephedrine use for its ergogenic effect. From medline, our first search strategy retrieved 100 articles between the time period 1950-2010. Our second search strategy retrieved 42 articles between 1950-2010. From embase, our first search strategy retrieved 159 articles between the time period 1980-2010. Our second search strategy retrieved 80 articles between the 1980-2010.

One author and a peer then reviewed the titles and abstracts through our search and retrieved potentially relevant studies. Studies that were excluded in this process included those with co-interventions with other drugs. In particular, for the purposes of data abstraction, articles that related to Ephedra, ma huang were excluded due to it containing ephedrine. Out of those possibly relevant articles we retrieved 16 but were unable to retrieve two. However, as will be explained later, from reading the abstracts those studies just verified what is already established about PSE’s ergogenic effect. Also, out of those two, one of the articles studied the effects of PSE with the additional variable of diving, which is not as relevant to this study. Out of those 16 articles, only 8 were found to be relevant trials devoted solely to studying the ergogenic effects of PSE.

The same author and peer then independently abstracted data into abstraction forms. We resolved abstraction differences by repeated review and consensus. Similarly the same author and peer assessed risk of bias through the use of both the Jadad scale and the Cochrane collaboration’s tool for assessing risk of bias, once again resolving differences by repeated review and consensus. It was determined that articles with a jaded scale of less than 3 would be removed from the study, however all 8 studies were found to have a passing score.

RESULTS
Table 1 summarizes the results gathered from the 8 relevant retrieved articles. Displayed are the results of main tests of each trial, the significance of their results, as well as the quality of the studies. As these studies did not have results in which PSE produced a significant decrease in performance, significant outcomes signify that the study was able to find some kind of ergogenic effect while testing their subjects.

The participants in these studies were primarily male, females accounted for only 9.7% out of the total pool of subjects. Participants were on average 24.38 years of age, and in general good health. In total, the studies examined 93 individuals. 7 out of the 8 studies examined the ergogenic effect of a single dose of pseudoephedrine; the remaining study was a multiple dose trial.

Contrary to the apparent controversy over whether or not PSE can generate an ergogenic effect, the results of these studies seem fairly consistent. There appears to be a threshold value at which it becomes possible to detect the ergogenic effect of pseudoephedrine. The studies considered here can be separated into a relatively low dosage group and a high dosage group. Those below 120 mg, including the trial run by Swain et. al, as well as the sole multiple dose trial run by Chester et. al, fall into the low dosage group, which report no ergogenic effect of any sort. As was mentioned in the methods section there were articles found that were unable to be retrieved, however the abstracts of those articles only confirm this result. Below this dosage, it is definitive that no ergogenic effect can be found, and this range is well above that needed for a therapeutic dose.

Those trials with dosages above this value report finding some sort of ergogenic effect. The trial run by Gill et. al was able to find a significant increase in anaerobic performance while running a 30 second Wingate test, as well as an increase in isometric leg extension. The PSE group in this study had a mean +- SD of 1262.5+-48.5 over the placebo group which had a mean+-SD of 1228.4+-47.1 in peak power measured in watts for the Wingate test. The values in the leg extension test were 321.1+-62.0 in the PSE group over 295.7+-72.4 in the placebo group. However, they were unable to find any benefit in the bench press test, which showed that the possible ergogenic effects would be limited to the lower portion of the body. It’s important to note that while ingestion of PSE resulted in an increase in peak power that did not correspond to a significant increase in total work performed, which corresponds to a higher average power as the time was kept constant in these 30 second Wingate tests. However, there was a trend towards this result, so this study verifies an anaerobic ergogenic effect produced by PSE in high dosage.

The next two studies evaluated the possibility of an aerobic ergogenic effect produced by PSE. Hodges’ 2006 study noted a 5.8 second/2.1% decrease in time to completion in a 1500 m trial. This was noted as significant decrease in time, which would correlate to an increase in average power, which somewhat contradicts Gill’s result should anaerobic vs aerobic comparison be deemed valid. This report was odd in that 8 people were included in study 1 to determine the efficacy of the 1500m test, but only 7 people participated in the study 2 which was the RCT crossover with placebo study. It was not mentioned whether or not participants in study 2 overlapped with those in study 1 which would result in a baseline that nulls the results of the crossover study as the baseline time to completion was lower than either the placebo or PSE group by .3% with significance set at .5%. It is also important to note that all participants showed some sort of improvement when dosed with PSE.

The study done by Pritchard-Peschek et. al in 2010 confirms the trial run by Hodges in 2006. In this study a 180 mg dose of PSE was shown to provide a 5.1% decrease in cycling time set at the same significance level of .5%. Once again all participants showed some sort of improvement when dosed with PSE, as in the trial done by Hodges. In light of the study done by Hodges and Gill, it is confirmed that both an anaerobic and aerobic ergogenic effect is produced by the ingestion of high doses of PSE in the lower portion of the body.

Table 1

Study	Design	Subject description	Pseudoephedrine dosage	Main Outcomes	Outcome results
Gillies et. al 1996	RCT crossover, single dose	10 male cyclists	120 mg 90 minutes prior to testing	Time to completion, Isometric muscle test	Not significant, Not significant
Swain et. al 1997	RCT crossover, single dose	20 male cyclists, 10 relevant to pse	1mg/kg, 2mg/kg 60 minutes prior to testing	Time to exhaustion	Not significant
Gill et. al 2000	RCT crossover, Single dose	22 male athletes	180 mg 45 minutes prior to testing	Wingate test, Isometric leg extension, bench press	Significant, Significant, Not significant
Chester et. al 2002	RCT crossover, multiple dose	8 male endurance runners	60 mg,6 doses over 36 hours, 4 hours prior to testing	5000m time trial, steady state exercise Statistical data not reported	Not significant, Not significant
Chu et. al 2002	RCT crossover, single dose	10 male, 9 female healthy university students	120 mg, 2 hours prior to testing	Wingate test, MVC grip test, dorsi-flexion test	Not significant, Not significant, Not significant
Hodges et. al 2003	RCT crossover, single dose	11 male athletes	60 mg, 90 minutes prior to testing	40% submaximal cycling, 60% submaximal cycling, Wingate test	Not significant, Not significant, Not significant
Hodges et. al 2006	RCT crossover, single dose	7 male athletes from a university’s athlete club	2.5 mg/kg, 90 minutes prior to testing	1500 m time trial	Reported as significant
Pritchard-Peschek et. al 2010	RCT crossover, single dose	6 male cyclists or triathletes	180 mg, 60 minutes prior to testing	70kJ/kg standardized work time trial	Significant

Table 1 cont.

Study	# of Subjects recruited	# of Subjects completed	Jadad scale	Cochrane risk of bias
Gillies et. al 1996	10	10	4 randomization sequence not described	Acceptable
Swain et. al 1997	20	20	5	Acceptable
Gill et. al 2000	22	22	4 randomization sequence not described	Acceptable
Chester et. al 2002	12	8	4/ randomization sequence not described, reason for drop outs acceptable	Acceptable
Chu et. al 2002	19	19	4 randomization sequence not described	Acceptable
Hodges et. al 2003	11	11	4 randomization sequence not described	Acceptable
Hodges et. al 2006	8 or 15 or 7	7	3 randomization sequence not described, dropouts not made clear	Assuming subjects recruited is 7, Acceptable
Pritchard-Peschek et. al 2010	6	6	4 randomization sequence not described	Acceptable

DISCUSSION
Perhaps one of the most confusing aspects in studying the ergogenic effect of PSE is attempting to explain just how it could possibly produce an ergogenic effect. As mentioned in Prtichard-Pescheck et al.’s paper there is speculation (Chester et al., 2003; Gill et al., 2000; Gillies et al., 1996; Hodges et al., 2006; Swain et al., 1997) that PSE exerts an effect through “central” pathways and that the potential mechanisms of action may be related to one of the many sympathetic actions of NE, including increased fuel mobilization or stimulation of the central nervous system.
Hodges et al. (2006) alluded to the possibility that dopamine is involved in PSE’s mechanism of action. However, studies have yet to be done to confirm or deny these possibilities. In relation to its ban from use in competition, as was shown in the sole multiple dose study, no ergogenic effect was found even at the maximal therapeutic dose. The only effects were shown in single dose studies with at least triple that amount. In a study done by Chester et. al in 2004, it was shown that the maximal therapeutic dose done in a 36 hour time period had urine tests results of 149+-72 mg/L. This ranks above the current limits of testing which is 125 mg/L. Considering that there seems to be a threshold value at which ergogenic effect can be made possible, which is far above that of the maximal therapeutic dose, it is recommended that there is once again a raise in the limit of testing for PSE. It is also recommended that further studies be done to evaluate the potential mechanisms of action of PSE in relation to its ergogenic effect for the lower portion of the body.

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