Adaptive Optics

Why do we need adaptive optics?

There are two places for optical telescopes: on the surface of the earth and in space. The effort to put a telescope in space and maintain it is much greater than that required for a ground-based telescope, so why would this avenue of observation have ever been pursued? The answer to this question is, simply, the atmosphere. Earth has an atmosphere, which affects light traveling through it.

The variances in the atmosphere consist mainly of differences in temperature from one region to another. The pockets of differing temperatures mean that a path straight from a distant source to a telescope located on the surface of the earth would include regions of higher and lower temperatures? Why does this matter for light?

Photons propagate as waves. The speed of a propagating wave is dependent upon the medium through which it is propagating. For photons from distant stars, the majority of the medium they propagate through is the interstellar medium, which can be approximated as a vacuum (this is what I have been taught, but the fact that Caltech has a whole class on the interstellar medium –Ay 101, which I will take next year – makes me wonder if this is merely a simplistic approximation... anyway, for now I consider space to be roughly a vacuum). Once the photon reaches the atmosphere, however, it is propagating through much denser air. Even this air is not uniformly dense, however: regions of hotter and colder air change the index of refraction for different air pockets, creating what are essentially different mediums.

If you consider the wavefront of light emitted from a distant star, you can see why this would be a problem. When the wavefront reaches the atmosphere, each individual part of the wave front has propagated at the same speed (since the entire wave front has been propagating through the same medium). However, this is no longer true once the photons pass through the atmosphere. Photons that pass through hotter packets of air will propagate at a greater speed than those traveling through cooler air.

You can imagine what happens to the poor wavefront when each photon travels through different temperature air pockets – the poor thing is in disarray by the time it reaches an earth-based telescope! Some areas of the wavefront have travelled faster while other bits have travelled more slowly – what used to be a smooth wavefront is altered by the atmosphere into a much more “squiggly” form.

This is a problem! One solution to this problem is to place your telescope in space, where the wavefronts don’t have to make the perilous journey through the atmosphere. However, in recent years a much more amazing method of avoiding atmospheric distortion has come into being… and this method is adaptive optics!

What does adaptive optics (AO) do?

Adaptive optics corrects for distortions due to the atmosphere in the wavefront. The way that is does is REALLY COOL – I hardly believed it was real the first time I heard about it!

AO uses a deformable mirror. The mirror itself is deformed!!! Now, this mirror is not the mirror that first receives the image. You aren’t deforming the 5 meter mirror at Palomar, for example. Adaptive optics are not a part of the main mirror, but instead an instrument that you can add onto a telescope. The photons are first received by the ‘big mirror,’ as you might expect, but then refracted to the smaller, deformable mirror, which can correct the image.

Basically, AO corrects the image for atmospheric distortion. The goal is that the image received from a ground based telescope using AO would be as good as an image from a space-based telescope.

How do you calibrate AO (find out how air pockets affect the wavefronts)?

The distortions by the atmosphere on the wavefronts are not random. They are very directly caused by the varying temperatures in the atmosphere. So, theoretically, if you could map the air pockets of different temperatures, you could write program to subtract the “noise” caused by said air pockets.

To measure how much correction is needed, AO systems use mainly two methods: a guide star or a laser. Guide stars are those used as references. We already know what we SHOULD get by observing these stars, so if the observed image differs from the expected image, the difference is the interference due to the atmosphere, and can be corrected in subsequent observations.

Lasers are even cooler! The laser used with AO is a sodium laser, which works by emitting a wavelength of light that will excite sodium atoms, which then emit light back to the telescope. This is sort of a fake guide star – it is used in the same way that a real guide star is, but it is much more versatile!

The laser/guide star calibration method is used simultaneously with the observation of whatever source the telescope is studying. That way, corrections are as accurate as possible. As the air pockets change and the wavefront’s “squiggles” change, the corrections to the entire image can be altered (based on whatever the light from the guide star says the change should be) so the image is as accurate as possible.

How does a deformable mirror correct the image?

Firstly – how is a mirror deformed? The method of deformation is pretty cool! I looked at documentation about the PALM-3000, which is an AO system for Palomar, as a case study of how the method works.

Mirrors are deformed by needle-looking things called actuators. The actuators actually push the surface of the mirror into a pattern that counteracts the effects of the atmosphere. If you don’t think about it too much, the idea that you can just physically counteract the distortions in the wavefront makes sense. Where the wave travelled too slow, push the mirror up so it receives the lagging photons sooner. Where the wave travelled too fast, leave the actuator unpushed so the photons must travel farther and thus all photons arrive at the mirror at the same time. If you start thinking more deeply about this, you will realize how complicated writing the code for this algorithm would be! (Image to the left from 4)

Another remarkable fact is the rate of correction – that is, how often AO reads in data from its guide star and adjusts the actuators to counteract the distortions due to the atmosphere. The whole process sounds computationally arduous – can you believe that AO is corrected 2000 times a second (5)?!? This frequency seems CRAZY to me! Imagine the engineering that went into allowing the fast and precise movements of all those actuators – which, on the PALM 3000, is 4356 actuators (4)!

Why is AO useful?

As they say, a picture is worth one thousand words. This Palomar image shows the difference between an observation with adaptive optics (right) and an observation without (left) (image from 2).

Useful links:
1. http://www.mtwilson.edu/ao/ - tells about the AO system used at Mt. Wilson; good explanation about AO more generally as well
2. http://www.astro.caltech.edu/palomar/AO/ - cool images – AO is important at Palomar!
3. http://amazing-space.stsci.edu/resources/explorations/groundup/lesson/basics/g18a/ - good image on what the air pockets do
4. http://spie.org/x39226.xml?ArticleID=x39226 – specifically about the PALM-3000, good explanation on how the actuators work and some cool images!
5. http://www.oir.caltech.edu/twiki_oir/bin/view/Palomar/Palm3000/WebHome - more on PALM-3000

Fixing my mistakes… [lab 3]

When I said “by Wednesday”… I guess I didn’t specifically say WHICH Wednesday I would fix it by…
New information:
• the “ marks in the image are arcseconds, not degrees - I should have converted units to account for this!
• Keep values in radians
• Recheck what K-band really means!

SO! Now, I have 0.009 arcseconds as the value for the separation of the binaries, which I can covert to degrees:

Proceeding with this value, I know that the distance to the first airy ring should be 0.1 arcseconds, not 0.1 degrees. With this knowledge, I can convert again to degrees and then radians (for radians, see summary table way below).

Now, I also need to check the values for the wavelengths of K-band. According to Wikipeida: http://en.wikipedia.org/wiki/Photometric_system
The values of K-band in this system of measurement have a center of around 2190 nm. Using these new values, I can use the same methodology as last time, except my value for theta will be different. Theta in the equation below refers to not the distance from the center to the airy ring, but the entire distance across the diameter of the airy ring. So,



Using small angle approximation, and the fact that 2190 nm = 2.19*10^-6 meters,



This suggests that the aperture is 2.76 meters – not the 10ish meters I previously found.
NOW – which telescope could this be? …. I notice that depending on the measurement for the width of the airy ring, I get different results. This is frustrating because depending on from where I measure (the innermost and smallest distance, or from the center of the outer pixel) I get different values for the minimum angular resolution. I can get what look like equally valid measurements varying from 0.09 to 0.23 arcseconds. These correspond to apertures between roughly 2.5 and 6.5 meters. See graph below, which graphs D as a function of the diameter of the smallest airy ring, measured in arcseconds.

Choosing what telescope this image is from is difficult because of the uncertainty in my original measurement of the diameter of an airy ring. However, based on considerations of where in the sky this source would be visible (see the uncorrected post) I can say that it would be visible from Hawaii, California, or equivalent areas. Combined with my knowledge that this image came from a Caltech-affiliated source, who likely has most easy access to Palomar and Keck, I can hypothesize that the image was taken using the Hale telescope at Palomar, which has an approximately 5 meter aperture, within my error bounds.
Trying to confirm or disprove my hypothesis, I combed through the publications of the two observers listed in the FITS header and found this abstract:
http://adsabs.harvard.edu/abs/2010DPS....42.3930L
So, K-band observing was going on at Palomar April 25-26…. Looks promising! Unfortunately I can’t seem to find a copy of the entire paper – maybe because I am not on the Caltech network?
Also, I found:
http://www.palomar.caltech.edu:8000/calendar.tcl?cal_date=2010%2d04%2d25+00%3a00%3a00%2b00
Which shows that April 27 was used by a different astronomer… but the nights of the 25th and 26th were used by a consistent observer to the file. I would say that the day had just changed and this observation was from the night of the 27th, but the observation time says 11:28. This does not mean that my hypothesis was wrong; I’m not sure which time zones /sidereal time/PST time were used to mark the file; so although the observation was marked 11:29, April 27th it could possibly have been from the 26th.
Also – Knowing that Justin Crepp was the observer, (I feel like such a stalker…) how likely is it that he would, having observed all night on April 26th, then proceed to fly somewhere else and observe AGAIN the next night? I don’t think that would be very likely, and it is always possible that the nights got switched or something else unreported on the observation time website happened. Therefore I will not reject the hypothesis that this image was taken at Palomar on the Hale 200-inch telescope.


Fixing my errors: a summary

Airy ring distance from center: I used to think this was 0.09 degrees.
Now I know it's 0.000025 degrees, or 4.36332 × 10^-7 radians
K-band wavelengths: I used to think it was 7.5*10^-1 to 1.5 cm,
Now I know that it's centered at 2190 nm
Aperture: my first value was 10.48 meters,
My new value was 2.9 meters but I also realized that this number comes with some sizeable error bounds!
Telescope: I used to think it was the Keck2, NIRC2
Now I think the Hale 200 inch at Palomar was used

Becoming a professional astronomer, the final post

So, before I explain how my opinion has changed since the start of this project (affected by the interviews my group and I did – see Iryna and Tommy's blogs for our other posts – as well as the various conversations I have had with post-docs throughout the term), I wanted to post some interesting posts I found while perusing resources online, along with just a couple thoughts I had on each one. Most of the most interesting things online are blog posts. I have never read so many blogs before this class, but they are fun and useful!

http://science-professor.blogspot.com/2011/09/dealing-with-it.html - Just what is the relationship between an advisor and a grad student? If you’ve ever seen the PhD comics, then it appears that grad students are like slaves to uncaring, busy advisors. From my SURF, I thought that grad students and professors were more like friends (both of whom too busy for an undergrad like me!). This article implies that the relationship doesn’t have to be chummy, but merely professional.

http://www.astrobetter.com/valuing-all-kinds-of-astronomy-smarts/ - This is interesting because it discusses the idea of the gap between school skills and practical skills. The people who can do problem sets really well might not be the best scientists…

http://astrobites.com/2011/11/16/for-your-perusing-pleasure-some-preliminary-results-from-the-social-perceptions-of-astronomy-survey/ - on a side note, I tried out Professor Johnson’s idea that telling people on a plane you were an astronomer, as opposed to an astrophysicist, is more conducive to conversation. I had a two-hour conversation with a telephone tech about astronomy on the way home for Thanksgiving… maybe I’ll write one last blog post on this! It was actually pretty cool.

http://astrobites.com/2011/10/02/applying-for-the-nsf-our-own-experiences/ - Oh gosh! I don’t even want to think about this. One of my cross country teammates, a senior, just applied for NSF, and it sounds nerve-wracking.

Now – my own thoughts. I have realized over the course of the semester, after talking to various grad students, that for astronomy there are many different directions you can go. You can be more instrumentation, or theory, but each discipline is different. Also, I have gotten over my hesitation to say the word “astronomy”. I was always worried that “astronomy” was not a real career path. This is what my parents and high school teachers led me to believe; there was always the joke about the student going off to college to pursue something useless like philosophy or astronomy. For that reason, I always answered “astrophysics” when people asked my major.

This term, I have realized that many of the actually parts of astronomy are exciting. Actually observing data is exciting, because of the years of work that lie behind every single observation. It’s not as easy as just looking at the sky; adaptive optics and other modern aspects of telescopes show the field is not static and involves far more than simply looking at stars.

One other contrast that this term has brought to my mind is the difference between astronomy and other fields of science. The research process of biology or chemistry has always seemed a little scary to me; you could spend years working on a project only to see it fail or another group scoop you before you publish. In astronomy, there seem to be far more data than astronomers. I like that idea that even someone like me could comb through public data and find something publishable that simply hasn’t been studied by anyone yet.

The process for becoming a professional astronomer seems less daunting. I have also realized, because of what Jackie said last week, that there is nothing wrong with verbalizing my goal of being a professor, even if I think it might be presumptuous of me to suppose that I “deserve” to have this as a goal. There is no reason to pretend to pursue a career in industry when I know my dream job is to be a professor.

Pursuing this goal, I have learned from this project and the rest of term, will involve facing rejection many times. Not only do I have to apply to grad school and perhaps fellowships, but I will eventually apply to postdocs and eventually faculty positions. I have also realized how important other people are. I would never have learned any of the things I learned this term if I had been in a regular class, because I would have spent my time doing problem sets instead of meeting interesting people and going interesting places (Palomar, the Solar laboratory here, seeing the adaptive optics in the basement). There is nothing wrong with asking questions and there is nothing wrong with having fun.

From the interview with Annelia Sargent, I learned that it is possible to have a family and pursue a career in astronomy simultaneously. She also spoke to us about all the different committees and projects she has been on. It was cool when I read an article of Science a few days later and saw her mention in concert with yet another project that she works on, but the fact that she considers all the extra things she does as “community service” made me realize that it is very difficult to put limits on what a professor does, as every position is different and a lot of what they do is what they choose to do.

Reading posts online, I am struck by the sheer volume of posts by older people in the field giving advice to younger ones seeking to attain their positions. Grad students advise undergrads with seeking guidance from postdocs, and professors offer advice to all. Everyone in the field seems to realize that it is a tough path, and they want to make it easier for those attempting the arduous journey. Astronomy seems, at least as seen through the eyes of the blogosphere, as a cooperative and friendly field. This certainly corroborates my experience this term here at Caltech.

There is also a lot of discussion online about the problems with the current system. Many people lament that the ‘problem set/test/grade’ status quo is alienating to some minds that would be great in astronomy, and theorists have an easier time than people who could be great coders or instrumentationists. I would agree with this – although here at Caltech, we have theory pounded into our brains until it is all we can think, qualities that make a great astronomer cannot necessarily be measured by checking someone’s ability to do a physics problem.

This semester has given me a lot to think about, and changed my habits forever. I really do enjoy talking to others in the field, and now I know how to approach them. One of the goals Professor Johnson gave at the beginning of term was to be able to talk to an astronomer, be it a professor or someone else. He wanted us to see someone that we think is way “above” us, and just be able to talk to them. The me of a year ago could not have done this, and the me of this summer didn’t know to try, but ever since the day I met up with Dr. Kirby on Professor Johnson’s suggestion, I have realized that approaching other people isn’t so scary as it seems. I look forward to continuing the habits of this class, and pursuing the career path of being a professional astronomer.

Habitable Zone

The so-called “habitable zone” around a star is the range of semimajor axes corresponding to
planetary surface temperatures warm enough for liquid water. How does the location of the
center of the habitable zone scale with stellar mass? (Recall the scaling relationships from our activities on stellar structure.
We will have liquid water from 0 degrees Celsius to 100 degrees Celsius. This is equivalent to 273K to 373K.
We know from our activities on stellar structure that mass scales with radius. We also know relationships for luminosity, flux, temperature and radius:




Note that Ta is NOT the value of the temperature on the planet. It is the effective temperature, due to the sun, at a distance (a) from the sun. Luminosity remains constant, thus the further away from the star you get, the smaller the flux is and the smaller temperature is.

MORE!!! After Professor Johnson's comment... I didn't go quite far enough!!

I want an expression for a in terms of M. This means that if I use the current expression but find scaling relations for R, T* and Tp in terms of a and M, I should have a better answer.

M scales with R.

This is the energy due to pressure. Balance this with thermal energy:

For temperature, we can just use flux, since we have a direct relationship between flux and temperature. flux is dependent on the distance from the star.

(more coming!!! sorry!!)

Aladin Lab #3

Aladin is a visual FITS file viewer software. It is available online: http://aladin.u-strasbg.fr/ It is easy to install – no Cygwin necessary for Windows computers (phew!). In this blog post, I will show step-by-step what I did… not all of which was right! I headed down dead ends at some points! But hopefully seeing my mistakes will make it easier for everyone else to learn how to use this software J

With this software, you can analyze fits images, found online or stored locally on your computer. For this lab, I used the file found on Professor Johnson’s website with a binary system. Loaded into the Aladin viewer, a FITS file is represented visually as a field of stars:

What is a FITS file? A FITS file is a format of storing data specific to astronomy. A FITS file is not simply an image, but it also comes with information about the image (such as ascension and declination of the targets, field of view, photon counts for each pixel, etc).

From this specific FITS file, we can determine the location of the targets: from Aladin, I found the following for each source:

Source	RA	DEC	RA (degrees)	DEC (degrees)
A	18:05:27.73	+2:29:48.0	270.5455	2.4967
B	18:05:27.18	+2:29:44.4	270.5363	2.4956

We have found the angular separation of the binaries to be 0.009 degrees. This distance was found using the distance tool on Aladin (just click on your two sources, and the program computes the exact distance between them!). Also, it can be found manually using the source positions.

Given that the angular resolution is based on the ‘airy’ pattern – it would be useful to know, what is an airy pattern? The airy pattern refers to the lighter and darker regions, where different strengths of intensities of light are visible.

[I start to go down the wrong road here… skip ahead if you want!]

The sinc function, which is the Fourier transform of the box function, is defined by:

http://www.codecogs.com/eqnedit.php?latex=\bg_black\textup{sinc}(x)=\textup{sin}(πx)/(πx) \textup{ if } x ≠0, \textup{and sinc}(0) = 1" target="_blank">http://latex.codecogs.com/gif.latex?\bg_black \textup{sinc}(x) =\textup{sin}(πx)/(πx) \textup{ if } x ≠ 0, \textup{and sinc}(0) = 1" title="\bg_black \textup{sinc}(x) =\textup{sin}(πx)/(πx) \textup{ if } x ≠ 0, \textup{and sinc}(0) = 1 "/>

You can load the Simbad database into Aladin as well. Also, you can select individual sources and see an image of each source. If you do this with this data file, you get what looks like a giant region of exposure.

What I wanted to do next was to find the sinc function of the light from these images. Theoretically, you could do this by extracting a spectrum of the region containing the point source, and plotting how intensity oscillates as you move further away from the center (maximum). I played around with Aladin for a ridiculously long amount of time until I found a feature that gives you the full width at half maximum in each direction. To find this, I used the “Phot”[ometry] command to select a circular region containing the point source, then examined the table of values to find the full width values. This was harder for me than it should have been, because I wasn’t sure exactly what I was looking for. I only vaguely remembered that “full width at half maximum” can refer to a sinc function.

The values I found for full width at half maximum for each source were:

Source	FWHM (appx)
A	13
B	11

We want to see how the full width at half maximum (FWHM) relates to other qualities of the telescope.

WAIT! At this point, I asked Professor Johnson if I was going about this project the right way, and he suggested a much easier way to do it. Instead of using the FWHM (which I am still unclear if this would actually work), he suggested I change the display range and measure the airy rings.

I was having some trouble finding the way to change the display range (sad, I know) until I found that there is an undergraduate mode for the Aladin software! It looks like the undergraduate mode if just the regular version with a bunch of features locked out, but it’s a little less overwhelming to start with.

If you zoom in, you can see what look like airy rings. These are the distances at which there appears to be a dark spot. We can see the cause of these if we look at the function of light reflected on a screen. The airy ring, therefore, occurs at this first node. On the image, we can measure how far it is between the center (max) and this first mode (min). The image gives a value of approximately 0.1 degrees.

How can we use this to find the angular resolution of the image? It is given that the image is in K-band. This means that the frequency of light is between 20 and 40 GHz. This corresponds to 7.5*10^-1 to 1.5 cm for the wavelength. Using the average-ish value, we can say that lamba equals 1.15 cm. Using the formula:

Substituting theta with the value found by the airy ring method. Note that these values are in radians and nanometers. Also, the small angle approximation is used here.

So,

This implies that the diameter of the telescope is roughly 10 meters. Which telescopes do we know of that have an aperture of 10 meters? The first one that springs to mind for me is Keck. However, how could this be? The K-band is infrared. Now, there are two ways to figure out from which telescope this file was observed. One way is to look at the declination of the pair.

The source is at about +2:30. This means that the object is just slightly north of the celestial equator. Also, I found the observation date in the image – 4/27/2010, at 11:28 – so we can check if the pair would have been visible from Keck at that time. I will assume the time given is PM, rather than military time (though it is possible there is some mix-up with times zones)? 11:30 pm is probably an acceptable approximation, however). The right ascension of the image is around 18 hours. At the vernal equinox, the RA is 0 hours at noon. So, we must calculate how much that changes in a month.

Each sidereal day is four minutes shorter than a solar day. So, the sidereal time will be at about 3:00 at noon on April 27 (this is a rough estimation). At 18:00, sidereal time, it will be roughly be 3:00 AM April 28. This is the time that the source would be directly overhead. It would totally be possible to see this source from Keck at 11:28 PM, April 27.

If you look at this paper: http://www.astro.cornell.edu/academics/courses/astro233/symp06/symp06.pdf, you will see that there is actually a way for Keck to observe in infrared! The NIRC is a near-infrared camera that was on Keck at one point. NIRC2 would have been operational on April 27, 2010, when this data was taken.

The second way to figure out from which telescope the image came involves some marginally sketchy stalking… I looked up the observers, who were named in the FITS header, and saw that the file mentioned Cornell IR. NIRC is associated with Cornell, as well. Also, I looked at a paper published by these observers, using data taken over the nights centered around April 27, 2010, and the paper said that Keck was used. Although none of these people were actually named in the list of people who were allocated that night at Keck, it does say on the telescope time allocation site that that night, NIRC 2 was being used. (http://www2.keck.hawaii.edu/observing/schedule/index.php?sched=Both+Tels&year=2010&month=4&go=GO#) I am a little skeptical, since the people listed in the FITS file as observers were not listed as observing at Keck that night, but I would say that it is likely that this image was taken with NIRC2 at Keck2.

The Exoplanet App. Also... the floodgates lift

Thus begins my backlog of posts, all of which have been in the “almost done” stage of being for varying amounts of time (2 weeks-today).

First, I wanted to draw everyone’s attention to this cool Iphone app that Professor Johnson showed me! It’s called “Exoplanet,” Hanno Rein, and it is basically a visual catalog of exoplanets! You can zoom in on systems, see the orbit, see light curves and other cool stuff! There were a few systems that I have found that are particularly cool:

HD 98649 – Gas giant, 7 Jupiter masses, orbital period of 10400 days (which is around 30 years!)

This planet is so big it makes the sun move! It is worth looking at on the Exoplanet app because not only are its light curves interestingly-shaped, but the animation shows the sun moving! Both planet and sun are orbiting around their mutual center of mass. The eccentricity of this sun’s sole planet is 0.860 (a highly elliptical orbit). It is surprising that not all parameters for this system are posted - maybe the system is so new that no papers have been published on it yet? I want to study this system, but its HUGE period probably makes it impractical to study.

HD 20794 system: b, c and d – each around 2-4 Earth masses, orbital periods of 18, 40, and 90 days, respectively.

This system exists unfortunately right inside the habitable zone of their star. The star is 0.7 times the mass of our sun, and the orbits are nearly circular. I love systems with many planets – three may not be “many,” but it’s more than usual for sure!

PSR 1257 12 b – 0.02 Earth masses, orbital period of 25 days.

How is this possible? How can a planet be so tiny? This seems more like an asteroid than a planet… it is roughly ten times smaller than Mercury. Other planets in this system are 3 and 4 times earth mass, but all the planets orbit too close to be in the habitable zone.

Honestly, there is no limit to cool systems. Each one has something new and interesting – “how is a planet that big orbiting so fast?” – “how did such a skewed system form?” – “why hasn’t that planet collapsed into the sun?”. This app is a good diving board for new research projects!

And again...

http://inspirehep.net/record/928153/files/arXiv:1109.4897.pdf?version=2

I'm still skeptical....

What does it mean to be a professional astronomer?

When I think of being a professional astronomer, I can’t help but keep thinking about how amazingly awesome it would be to go observing! After our class trip to Palomar, I want nothing more than to have a project where I can go observing. Which, of course, requires that I think up a project and get telescope time. But after that…… J

The process to become a professional astronomer, as far as I know, is basically constrained to academia. Professors and staff scientists of universities/ organizations such as CfA are the only people who can actually participate in this process, as it helps tremendously to be associated with a telescope-owning institution to study the sky. In this vein, to become a professional astronomer, one would need to follow the path of being an undergraduate -> grad student -> postdoc -> assistant professor -> professor. Each step of this transition needs something new. To become a grad student, I need to do research as an undergrad to learn research skills, and get good grades and test scores so I can get into a grad school. To become a postdoc, I would need to win a fellowship. I am unclear if this is the only way to become a postdoc. I’m also unsure how one goes about becoming a professor – I assume that if you are a really good postdoc, then you can apply for jobs and if you’re lucky, you’ll get one?

Also, your job can limit the science you can do. As a undergrad, I cannot apply for telescope time, unless someone qualified submits the proposal for me and I am listed only as a coauthor. Something I have learned in that last few months is how extremely important knowing people is. Who you know is almost more important than what you know. Working with people (or, in my case, learning from people) is one of the most important ways to grow as scientist. No matter how many papers on adaptive optics I read, I could never have gotten the same emotional fascination with them nor rough understanding of them that I did from listening to people explain it.

There also seems to be a lot of luck in becoming a professor – if the system you are studying happens to contain some crazy new structure, it could boost your career hugely. However, this also requires you have enough skill to recognize an opportunity when you see it. I have met a few postdocs who are doing such interesting projects, and being so successful with them, that I can’t believe they aren’t professors yet. This shows how high the standards are in the field. I think that rather than it always being the researcher who is the BEST who become a professor, there is an element of luck to it. There is not a definite measurement of being the “best” researcher, after all.

Like any field, I think the most important things to becoming a professional astronomer are connections and luck, with a necessary amount of skill to take advantage of the luck you have. More skill can offset a lack of luck, but luck cannot offset a lack of skill.

The Formation of Stars

Introduction

Here we consider the time scale of star formation and stability. We do this by considering the time it would take a cloud of particles to collapse into a star, and in this process derive an approximation for the Jean’s Length.

This is the system we must consider. The grey cloud is all the dust orbiting the point mass. The test particle is at the far right edge of the red line. The red line is the semimajor axis of the ellipse. The test particle must travel along the red line to reach the center. The time it takes to travel this distance is the free fall time.

Solution

a. Consider a test particle in an e=1 “orbit” around a point mass.

An orbit with an eccentricity of 1 would be a straight line. That is, it would mean that that the planet would orbit back and forth straight across the point mass:

If the test particle starts at the edge of the orbit - that is, r away from the point mass, then the distance it will have to fall is equal to r (the semimajor axis of the whole clous - see image above!)

Kepler’s third law, from memory, is:

The expression for mass of a sphere, in terms of its density, is:

Combining these two expressions, we can solve for the free fall time by considering the period. Since the period, p, is the time it would take the test particle to “cross” over the point mass twice and return to its initial position, one half of the period will equal the free-fall time. Also, we can substitute 2a for r (see the diagram above).

Solve for p (period. Note that this is different from the symbol for density, which is p-bar):

We know the relationships between t_ff and p, as well as r and a:

This expression describes the free fall time of a particle on the edge of the cloud, and this the time it would take the cloud of dust to collapse into a star. We are assuming that the test particle experiences exactly one half a period of motion.

b. Determine the dynamical time for a sound wave to cross this same distance.

Defining the speed of sound as c_s, we can define the time it would take a sound wave to cross the same distance as a test particle as;

We can solve for the length variable – that is, a.

Which is equivalent to:

This length signifies the distance at which the forces of gravity and pressure are at an equilibrium. The gas cloud will neither expand nor contract at this size.

c. What is the significance of Jean’s Length?

Jean’s Length shows the distance at which a cloud of dust would not be stable, and thus susceptible to collapse. The force of gravity attempts to pull the dust into the center, while the force of pressure tries to push it back out. If a sound wave takes longer to cross the distance than the actual particle of dust, then the force of pressure won’t be strong enough to prevent the dust cloud from collapsing. So, if a dust cloud is larger than Jean’s Length, that means that it cannot sustain itself, and will collapse into its center, resulting in stars!

d. Consider a collapsing cloud with a radius equal to Jean’s Length: when the cloud reaches a radius equal to one half of its initial radius, by what fractional amount had R_J changed?

To see the ratio of the Jeans’ Length for a cloud of equal mass but different radii, we must consider how the density changes from one size to another. So, first, we can find the densities of the two clouds, assuming a constant mass.

So:

We can plug in 0.5R_O and see how R_J changes. As R_o shrinks, the density p must grow by a balancing amount.

So the density increases by a factor of 8 if the radius decreases by a factor of 2.

Thus,

If R becomes 0.5R_o then the density becomes 8p:

So, R_j decreases by a factor of 0.35. This is fractional change of about 65%; the new value of R_J will be around 65% of the old one.

Conclusion

Jeans’ Length, the point of balance between the forces of pressure and gravity, can help you determine the behavior of a cloud of dust. By knowing the radius and mass, or by knowing just the density, you can calculate whether the cloud will expand or contract. If the cloud contracts, then it will likely become a star. Decreasing the radius of a cloud by 50% decreasing the Jeans’ Length by 35%, so the new length is 65% of the old one.

Acknowledgements

Thanks to Iryna and Monica! We had a lot of fun with this problem :)