Ay20: What I Thought of the Class:

Ay20 has been the most enjoyable class I've taken at Caltech thus far, and I highly recommend it to anyone at Caltech, regardless of major.  Perhaps the best aspect of the class has been the format, which is unique among all of the other courses available.  All class time has been spent actually solving worksheet problems on the board with my peers.  There were no formal lectures.  This may seem strange at first to those who are more familiar with traditional teaching methods, but without a doubt, I have learned a lot from this class.

We started off with pretty basic material covering flux and luminosity, and slowly built up from there to problems involving the equations for stellar structure and virial theorem.  Working in groups of 2-4 students, we were immersed in the material from the start and took a very hands-on approach to solving the problems on the worksheets.  Needless to say, the step-by-step format of the worksheets allowed us to get to the answers mostly on our own.  Throughout the process, though, our professor and TA asked us questions that would lead us in the proper direction.  Students who solved problems faster than others could also provide assistance to other groups.  This is one of the advantages of replacing lecture time with work time - it allows the professor and TA to take advantage of Caltech's great student-faculty ratio and work directly with the students in a very collaborative manner.  In addition, the class format allowed us to cover more material than we could have through lectures.  Typically, we had one to two worksheets per week which each introduced a new topic.  Without devoting class time to solving the worksheets, we would have been working at a much slower pace.

Professor Johnson also had a number of astronomers who worked in Cahill visit to discuss their research, allowing us to ask questions about their career.  This was another great part of the class.  In addition to keeping the class fun and interesting, it provided us with a number of contacts and potential research projects for the summer.  In addition, it provided me with further insight into the career path I am following.

Overall, Ay20 has been a blast.  The class was immersive and collaborative, and I gained a lot out of the unique format.  I have no doubt that I am enthusiastic and well prepared for my future astronomy classes at Caltech.

Using Scaling Relations to Compare Quantities

Second Authors:  Eric and Lauren


Compare the transit probabilities of a 3 Earth-mass planet in the habitable zone of a solar analogue and a 3 Earth-mass planet in the habitable zone of a 0.25 solar-mass red dwarf.

From problem 2, we know that the probability of transit is the radius of the star divided by the orbit distance of the exoplanet.  Because of the relationship between a star's mass and radius, this scales with the ratio between the star's mass and the exoplanet's distance.  We also know from the habitable zone problem that the distance of the habitable zone scales with the square of the star's mass.  This means that the probability of transit scales inversely with the mass of the star.  From this, we can determine that the exoplanet around the red dwarf is four times as likely to transit as the planet around the solar analogue.

Compare the transit depth and duration for the same two planets.

By comparing the area of an exoplanet and its star, we get that the transit depth scales with the planet's radius squared divided by the star's radius squared.  Since the star's radius scales with its mass, we get that the depth scales with the planet's radius squared divided by the star's mass squared.  This means that the depth of the planet transiting around the red dwarf is 4 times greater than that of the planet around the solar analogue.

Using our formula for radial velocity, we can get that the transit time scales with the radius of the star, the cube root of the orbit period, and the inverse cube root of the star's mass.  Using the handy-dandy relation between the star's mass and radius again, we get that the transit time scales with P^(1/3) * M^(2/3).  From Kepler's third law, P^2 scales with a^3.  This scales with M^6 given that both planets are in the habitable zone.  This means that P scales with M^3, and the transit time t scales with M^(5/3), and that the transit time is 10 times longer for the planet around the solar analogue.

An Interview with an Astronomer

Over the past few weeks, Daniel, Monica, Eric, and myself have collected questions to ask a number of astronomers at different stages in the career. I had the opportunity to ask my SURF co-mentor, Dr. Kieran Cleary, these questions. The following are his responses:

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

Practically very little, I would say. However I think that the term 'astronomer' still carries with it an emphasis on the practicalities of observation. For this reason I would describe myself as an astronomer as I am quite interested in the observational/experimental aspects but in practice I try to get involved in all parts of my field, from the instrumentation development, through observation to the science itself.

What are your primary areas of research as an astronomer/astrophysicist?  How did you get interested in them?
My primary area of research is observational cosmology. I spend most of my time working on a project to measure the B-mode polarization of the cosmic microwave background. Right now, this is focussed on instrumentation - trying to develop more sensitive detectors. If we are successful in securing funding, then I will be involved in developing the receiver, commissioning it at the observing site (Atacama, Chile), troubleshooting the data and helping with the analysis.  

I entered astronomy with the aim of getting involved in observational cosmology as I have always been interested in the origin of the universe. The chance to obtain data from the early universe attracted me to my thesis project, which was on the Very Small Array - a CMB interferometer. I am also interested in infrared properties of active galaxies as I spent two years working on this area as a postdoc. I am interested in the problem of the "anomalous" microwave emission. This is an unexpected component of Galactic emission thought to come from spinning dust grains, peaking in the 10-100 GHz region. This is interesting in its own right, but is also important as it could be a contaminant of CMB polarization measurements. 

How did you get into astronomy/astrophysics?  What did you study as an undergrad?  Where did you go to graduate school and why?
My route to astronomy was slightly convoluted. I was quite sure that I wanted to study physics and astronomy at university, but this was considered an unrealistically exotic pursuit (there was a severe economic recession at the time). Instead, my parents convinced me to take engineering (which was considered to have better employment prospects). I spent 6 years getting a Bachelors and then a Masters in electronic engineering, then worked in industry for another 6 years. At that point I decided to return to university to do a PhD in radio astronomy at the University of Manchester (Jodrell Bank Observatory) in the UK. The CMB group at Jodrell Bank was involved in the "Very Small Array". This was a 30 GHz CMB interferometer which was competing with other experiments to measure the large-scale acoustic peaks of the CMB temperature fluctuations. This was a perfect fit for me as it combined radio astronomy (which overlapped well with my engineering training) and my interest in the early universe.

What precisely is a postdoctoral fellowship?  How does it fit in to a career in astronomy/astrophysics?
I'm not sure I can precisely define a postdoctoral fellowship. The term seems have different meanings in the US and the UK, for example. In the US context, it can refer to a prize postdoc position, or a kind of long-term postdoc position. In terms of one's career, the latter kind of fellowship can smooth out the bumps of the postdoc cycle in which one might otherwise have to jump from position to position before getting longer-term employment.

How has your career played out?  Is it what you expected?  What is the typical career arc of an astronomer/astrophysicist?
I've been fortunate to be able to still work in the area that first attracted me to astronomy. I didn't expect to get so involved in instrumentation - I was surprised how much I liked the process of helping to build, then observe with, an instrument. Because I didn't do my undergraduate studies in astronomy, I didn't develop a well-defined set of preconceptions from having observed astronomy faculty at work. I think that has been an advantage and has made me more flexible, but it is also good to have well-defined goals. 

How have your goals evolved over the course of your career, if they have at all?
My scientific goals are still the same: to work on observational cosmology.

If you hadn't gone into academia, what would you be doing with your education in astronomy/astrophysics?
I'm not sure what practical use I would make of my astronomy education (besides volunteering to teach pre-college students) in those circumstances.

What is the best part of being an astronomer/astrophysicist?  The worst?
For me, the best part is observing with an instrument you have helped to build. I have been lucky enough to have spent time observing in Atacama, Chile. For me there is nothing quite like fielding an instrument in a remote, beautiful location and using it to wrest information from the early universe. The worst is enduring the years of uncertainty it can take to secure funding for a project (and writing the proposals!).

What can aspiring astronomers/astrophysicists do to make things easier for themselves?  i.e., what do you wish you'd known as an undergrad?
I wish I'd known the importance of getting involved in real research projects. This is something which is available to Caltech undergrads through the SURF program. It's absolutely essential to dive into a project and use the opportunity to learn from and observe the experienced researchers around you, in a friendly setting.

What has been the most difficult stage of your career so far?  What have been some notable inspirations along the way?
The most difficult part was my first postdoc - making the transition from working on a project with many other people (i.e. the Very Small Array, my grad school project), to working on my own isolated project in a location which had few others working in the same area.

Any final thoughts for the undergraduate astronomy student?
In research, if you're not making mistakes, you're not doing it properly! (I'm quoting someone, but can't remember who).

Becoming an Astronomer: The Academic Journey Thus Far

I've written a lot in previous blogs about what initially inspired me to pursue astronomy, but I haven't blogged about what I have actually experienced thus far in the academic process.  How have my views changed in the first year of my undergraduate career and how do I view the road ahead?

The Academic Process Thus Far:

One of my main findings from the first four terms at Caltech was the sheer difficulty of the academics. The classes I have taken thus far (physics classes and non-physics classes)  have definitely pushed me to the limit.  I have certainly realized that becoming a professional astrophysicist, at least at Caltech, is not an easy process.  At the same time, however, I have immersed myself in an environment of brilliant minds and countless resources.  Challenging myself now will prepare me for what lies ahead in an astronomy graduate program, and as a budding astronomer, now is the time to make the vital connections with the professionals around me.

My first four terms as an undergraduate have also presented me with a number of potential alternatives to astronomy.  Entering Caltech, I was absolutely certain that I wanted to pursue cutting edge astrophysics.  I had no real grasp of what such a career would require of me, and I had not considered other career paths.  During the second and third terms of freshman year, however, I took two geology classes which I found really interesting.  Perhaps, I thought, doing a geophysics or planetary science program would be just as interesting as astrophysics, and maybe the classes would be less stressful than some of the intense physics courses in the Ph and Ay options.

Ultimately, I have decided to stick with astrophysics, but examining the alternative options has opened my mind and widened my understanding of what I would have to do in the future to become a professional astronomer.  In addition, my experience as SURF student over the summer has given me a taste of real scientific research.

The Summer - SURF:

Over the summer, I got the opportunity to work in the Cahill Radio Astronomy Laboratory with a number of astronomy postdocs.  One of these postdocs, Kieran Cleary, has offered to answer a number of career questions compiled by Monica, Eric, Daniel, and myself.  His responses will be posted in a blog at some point later this week.

The SURF had been my first opportunity to work in a research laboratory, and I was really excited.  The project I worked on in particular involved creating low noise amplifiers for QUIET, an experiment under development to detect the B-mode polarization of the cosmic microwave background.  Over the three or so months I spent working in the lab, I characterized the gain and noise of twenty or so of these amplifiers.  During the process, I was introduced to the methods of scientific research and to the equipment that I may very well be using as a professional in the future.  The experience was very interesting, and certainly eye-opening.  For the first time, I felt like an actual astrophysicist as opposed to just a student, which secured my decision to go for the astronomy option as opposed to geophysics or planetary science.

The Road Ahead:

My experiences in the past year have lead me to the realization that becoming an astronomer is a long, and definitely difficult, process.  Nevertheless, I am eager to move forward and to gain even more knowledge and experience as a graduate student, a post-doc, and hopefully as an educator.  Ultimately, I am confident that a career as an astronomer is exciting and rewarding, and I am more than willing to put in the work to get to where I want to be.

Radial Velocities

Second Authors:  Eric, Lauren


The Problem:

Use Kepler's Third Law and constancy of momentum to express the time variation of the line-of-sight velocity of the star in terms of the orbital period P , the mass of the star M and the mass of the planet m<<M.


The Solution:

Step 1: By definition, the frequency of the planet's orbit is 2π/P.


Step 2: The velocity is given by the product of this frequency and the distance from the center.


Step 3: Since the period for the star and the planet are the same, the velocity of the star can be expressed as shown.


Step 4: Constancy of momentum.


Step 5: Express velocity in terms of angular velocity and distance a.


Step 6: Express the distance of the star from the center of mass in terms of the desired quantities.  First, we begin with equation 5, and rearranging the equation to get a_star.  By definition, a_planet is given by a - a_star.  We ultimately get the expression shown with the help of Kepler's third law:

Step 7:  The amplitude of the star's line-of-sight velocity, K, is obtained by substituting our value of a from equation 6 into equation 3.


Step 8:  The line-of-sight velocity as a function of time is given by the amplitude K multiplied by cosine of the frequency/time product.


Evaluating our Results:
Using only our intuition, it is not difficult to see how the velocity K will scale directly with the mass of the planet and inversely with the mass of the star.  It is also simple to grasp that a larger period will mean a smaller velocity.  In our calculations, we have confirmed this.  We have shown that the K and m are directly proportional, while K scales inversely with M by a factor of 2/3 and with P by a factor of 1/3.

The Spatial Scale of Star Formation

How big are stars relative to the clouds in which they form?  Let's examine the relative scale of star formation.  A smaller star forming cloud such as the Taurus region is about 30 parsecs across.  A typical star is more or less the same size as the sun (to an order of magnitude).  If we were to shrink the molecular cloud to the size of a human body, how big would the stars be?  To find out, we set up a proportion.  The ratio of the sun's volume (4/3 * pi * (7e10 cm)^3) to the approximate volume of the cloud (4/3 * pi * (15 pc)^3) is equal to the ratio of the value we're looking for to the volume of a human body (let's estimate it as a block of 1' by 2' by 6').  Using these numbers, we discover that, if the star forming cloud were the size of a person, the forming stars would be on the order of 10^-21 cm^3 in volume.  That would mean that the radius of the star would be comparable to the radius of a DNA helix!

Now let us evaluate the relative densities.  The Taurus complex contains roughly 3e4 solar masses of gas.  This gives the region a density on the order of 10^-22 g/cm^3.  The density of a typical star like our Sun is on the order of 1 g/cm^3.  That is a difference of 22 orders of magnitude!  In comparison, lead is only 4 orders of magnitude denser than air.

Second Authors:  Eric, Lauren

Here Comes the Sun

Second Author:  Eric

Anonymous argues that the Sun is undergoing, and is powered by, free-fall collapse, claiming that a contracting body heats up.  They claim that this accounts for the Sun's heat, and that the timescale for collapse is long enough for us to not notice.  Let's prove this argument wrong with some basic physics.

Let's first calculate the total potential energy contained in the Sun, given its mass and radius.
We begin with our formula for gravitational potential energy:

Now let us examine how this potential energy is related to the velocity of a free-falling element of mass near the surface of the Sun.  Setting our potential energy equal to kinetic energy, we get the following relation:

As an order of magnitude calculation, let's replace our velocity with the solar radius divided by the free-fall time.  Anonymous objects to this substitution on the grounds that friction and interactions between the particles will slow this velocity down.  However, it likely won't be slower by more than an order of magnitude, and the answer we will get will still be way too small.  Making the substitution and solving for the free-fall time, we get:

Given that we calculated the free-fall time to be on the order of 24 minutes, our "questionable" substitution would have to be off by many orders of magnitude to make the collapse slow enough.