Second Authors: Nathan, Lauren


Introduction
We know how stars are formed to a certain extent and that while they are on the main sequence, they are supported by hydrostatic equilibrium. However, when a star moves off the main sequence and can no longer support itself, what happens? We assume that at this point, the core of the sun has converted all of its mass to energy and is now undergoing gravitational collapse.

Methods
We know that the Sun generates energy throughout its lifetime at a rate of:

   

 

 

It is easy to tell that we have one molecule per cubic lambda.  So we have:

The actual value is 8 times this, for reasons I can't remember, but Nathan tells me Professor Johnson said the factor of 8 was okay to include in our calculations.  So multiplying this by the mass of a hydrogen atom and using T = the temperature of the sun's core, we get density

Which is more than twice the current maximum density of the sun's core.

Conclusions
We find that by converting 0.7% of the mass of the sun's core into energy, the sun's lifetime is roughly 10 billion years, which agrees with what scientists have predicted.  The density of the core after collapse will also be far greater than the current density of the sun's core, which is reasonable or it would not be able to support the sun post-collapse.

As some readers may know, this past summer I had the privilege of being able to work for Dr. Andy Goulding at the Smithsonian Astrophysical Observatory.  Dr. Goulding is a first year Smithsonian Research Fellow in the High Energy Astrophysics division.  He did his PhD work in AGN activity at the University of Durham, UK in the fall of 2010 before moving to Boston as a postdoc.  Working with him was a wonderful educational experience that I'd happily do over if I had the chance.  He gave me a look into the life of a researcher and how much research differs from course work.

We've vaguely kept in touch since September and he generously agreed to answer a few questions on his career for me.  Of course, given the title of this blog, the first question was obvious.  He took a lot of time in answering these questions, and I definitely learned some new things.  For example, I had no idea that there was a difference between a postdoctoral research associate and a fellow.


What is the difference between an astronomer and an astrophysicist at this point in time?  Which, if you have a preference, are you?

From a professional point of view, this is really semantics. People have degrees/PhDs in astronomy and/or astrophysics - it depends on institution. However, it is more likely that someone who is an amateur (non-PhD) is considered to be an astronomer. Classically, an astrophysicist attempts to understand and interpret the astronomical observations through application of physics. My PhD is in astrophysics, so in the strictest sense, I am an astrophysicist.

Black hole growth and galaxy evolution. Black hole physics was considered a "popular science" in the 1990s, so when I was younger it was very easy to pick up a book in the local store, and this naturally progressed from a hobby into a profession.

As an undergrad I studied Theoretical Physics - this involved particle theory, supersymmetry, advanced quantum theory and general relativity - this had little to do with astronomy, so it does not necessarily follow that your undergrad major must be your graduate major. Despite offers from several graduate schools in the UK, I decided to stay at my undergrad institution, Durham University, as it has a fantastic worldwide reputation as well as the largest astrophysics/cosmology department in the UK.

Once a predoc has completed their PhD, they will generally look for a Post-doctoral position at a different institution - these come in 2 flavors: (1) research associate and (2) fellowship. A research associate position is when a group/faculty has money available to employ a post-doc to carry out their specific research and help pre-doc students within the research group. A fellowship is generally a highly sort-after monetary prize which may or may not be linked with a specific institution and allows the holder to carry out the research of their choice - this is often predicated by the research proposal which is submitted in order to win the fellowship.

At this stage, I am not really in a position to answer this question. I completed my PhD in late 2010, and moved to Harvard shortly after to begin my fellowship which I had been accepted for earlier in the year. As I have only been here for a little over 12 months, it is not really possible to answer this question. 'Typically', an astrophysicist will expect to go from grad student (3-6 years) -> post-doc associate (2-3 years) -> [post-doc associate (2-3 years) ->] post-doc fellow (2-3 years) -> [post-doc fellow (2-3 years) ->] associate professor (3-10 years) -> tenured professor (indefinite). N.b., I added the other post-doc positions as some people prefer to stay as post-docs for longer periods of time to help with their publication records to move to the next stage and/or keep their teaching duties lower.

As I said above, my career is still becoming established. As I skipped the post-doc associate stage, and gained a fellowship on my first position, my current goal (for next year) will be to win a second prize fellowship to further expand my publication record.

My Masters degree is in theoretical physics, many people with this degree become statistical analysts and/or military defense specialists.

This is quite an interesting question as I'm pretty sure that you will get a different answer from every person. Being an astrophysicist is all about 'puzzle solving', we all have some intrinsic desire to answer the questions which are the most difficult to answer, so when we answer them, or move a step closer to answering them, this is the 'best part of being an astronomer'. However, it can be worst, you can find yourself working on one project for 6 months and then finding out that you have gone down completely the wrong avenue, and you have to start over. Of course, there are certainly perks too - for example, we travel to very exotic places (a lot), telescopes ares not generally in well-populated areas so you get to travel to places like Hawaii, the Canary Islands, Australia, the Atacama desert (Chile).

Of course, get very high grades and after that, you need something on your cv that will get you noticed (e.g., a summer studentship in a department)

At this point in time, astrophysics is struggling for funding from the government due to certain projects costing significantly more than was originally budgeted for, as such further funding money which would be relatively easy to propose for 5 years ago is not forth-coming. Hence, much more time must be put into proposing for the next year's projects, and this slows down the current research. This is not necessarily 'difficult' but it is certainly frustrating.

Astronomy as an undergraduate student and astronomy research are nothing alike (as you have already seen, Eric).

Introduction
Star formation is governed by the collapse of a cloud of particles into a gravitationally bound sphere which we call a star.  The radius of the could at which this occurs is called the Jeans Length, where the gravitational force of the cloud overcomes the thermal energy causing it to expand.  Here we examine the time scale of such a collapse and also calculate the Jeans Length.

Methods
In order to determine the time it takes for this collapse to occur in terms of the mass and size of the cloud, we consider a cloud of mass M and a test particle a distance away from it.  We assume the cloud has a mass given by

 

We were recently, or not so recently—I'm very good at procrastinating—assigned a multi-part blogging to find out what it truly means to be an astronomer.  I realise as a sophomore astrophysics major that I still don't understand the specifics of what being an astronomer entails or means to me.  To quote my friend Alexa,

I just want to be one. So much. “Space” is, if you think about it, everything but Earth. When we study it, we’re pausing our narcissistic tendencies for just a moment. We’re not everything; we’re part of everything. Ignoring that is shameful.

She stated in the best way possible what attracts me to astronomy, but that still doesn't mean I know what astronomy is.  Right now I just think of astronomy as some nebulous loosely defined field of Things I Would Like To Do Because They Are Amazing, but that's not an acceptable answer to the question.  So without further delay I shall attempt to synthesise my thoughts on the topic.

The point of being a professional astronomer, in my experience, is to contribute understanding of what the universe is, how it is structured, how it came to be, and what its future might hold.  Most likely this is because the first astronomer I ever met was a professor of cosmology.  I've come to accept that he's probably the reason my main research interest tends to observational cosmology.  Of course, this is a very broad and relatively unhelpful answer to the astronomer question.  Sure, that's the intention, but how do we get there?

I think it's safe to assume that the journey to becoming a professional astronomer begins as an undergrad, or if you're very lucky, as a high school student.  I think mine was a bit of both, as I did get the opportunity as a junior to do some busy work for he of blog title fame.  But that was a week long, and although it was some exposure I doubt it's how careers in astronomy start.  Careers in astronomy, at least for a Caltech student, probably start with a SURF fellowship.  I know SURF was my first real look at what an astronomer does.  I sat alone in an office 8-9 hours a day, writing code in a language I'd never seen before to analyse data I didn't understand, and I had fun doing it.  I think that enjoyment that's what sets the astronomer apart from the average person.

Then the natural course of things is to go to graduate school.  This is where you decide What You Want To Do With Your Life.  As far as I know, you don't have to decide right away.  Unless you're in the UK in which case you need to know what you want to study before you've learnt anything about it.  At least, that is what my SURF mentor who is English tells me.  Being a grad student requires doing semi-independent research under the guidance of a faculty member who works on a similar topic.  You'll probably start to hate your field at some point during this process, but hopefully you'll get over it soon.  Next is the postdoctoral fellow.  I have no idea what a postdoc does.  Don't tell my SURF mentor that because he is one.

I believe your career options then become a) professor at an academic institution, b) research scientist some place like the SAO, or c) finance.  I'm sure there are more options, I'm just uneducated in that side of things.  The first two options strike me as pretty similar except the professor track astronomer will probably have to teach at some point or another.  This part is where you get to move on to independent research in topics that interest you.  You might find out something that only you know about, and that's a rewarding experience.  Although any work in astronomy is rewarding if it's what's truly exciting and inspirational to you.

I have given my impression of what it takes to become an astronomer.  So once again, we're back to the question of what does it mean to me to be an astronomer?  It's going to take a lot of work.  Astronomy, as it turns out, is hard.  But the work will be worthwhile because I'll be learning how the universe works, or how we think the universe works.  Maybe I'll end up amending some of that knowledge.  Who knows?  Being an astronomer means getting excited about the mysteries of space and our tiny place in it.  It means realising how small we really are in the grand scheme of things, accepting that, and moving on to understand why.  Most of all, it means that when your friend starts talking about M83 and means the band, this is all you can see.

Abstract
We would like to know how the sun is being "supported".  We assume that this mechanism is hydrostatic equilibrium, but to be sure we work through the derivation.

Introduction
We know that the sun is somehow being prevented from gravitational contraction.  Our theory is that it is supported by hydrostatic equilibrium, which means that the internal pressure provides an opposing support force.  We calculate the gravitational force on a mass shell, the pressure required to balance it, and then derive the force equation for hydrostatic equilibrium.

Methods and Results
We first assume the Sun to be a spherical gas cloud with density ρ(r).  We consider a differential mass shell of this sphere with radius r.  We recall that the volume of a sphere is ⁴/₃πr³ and that the differential volume is its derivative. Then we get a differential mass dM:

We know the equation for universal gravitation:

Here we let M be the total mass enclosed by the mass shell and m be the differential mass element.  As a result, we get the differential gravitational force to be:

We know that pressure is equal to force divided by area.  So we can say:

Now dividing by dr on both sides of the equation we arrive at the equation of hydrostatic equilibrium:

Conclusions

We have derived from simple physical laws that the equation for hydrostatic equilibrium is a plausible explanation for the way the sun is supported.  A quick search shows that we are indeed correct.  Hooray!