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A little astro art for today: as part of my analysis of stellar orbits of ultracool subdwarfs (presented at the 214th American Astronomical Society meeting in Pasadena, CA), I decided to try computing and visualizing the orbits of nearly 500 L-type dwarfs from the Sloan Digital Sky Survey (SDSS) based on kinematic data produced by Sarah Schmidt - you know, just for fun.
The orbits were generated by assuming that the gravitational potential of our Galaxy can be described by smooth, azimuthally symmetric functions (so-called “Plummer spheres“) that describe the thin disk, thick disk, halo and bulge populations of our Galaxy (see this link for good technical discussion of such models). I then use a simple numerical integrator (Runge-Kutta model) and the initial position and velocity vectors from Sarah’s work, to pre- and post-dict the orbits of these stars 500 million years into the past and future.
Each individual orbit is really a rough estimate of the star’s true path; uncertainties in the current distance and motion of the star, and the simplistic model used for the Galaxy, means that errors can creep up within a single Galactic orbit (about 200 million years for the Sun). However, a statistical picture of the entire population can be realized from this exercise. Stars are born from massive molecular clouds that typically have circular orbits in the plane of the Galactic disk. As stellar populations age, random encounters and secular disturbances can “puff” up their orbits to higher eccentricities and inclinations. This is visually apparent in an orbital plot.
This first figure shows the orbits as viewed from above. Note that the bulk of the stars fill an annulus, the outer edge of which is near the radius of the Sun’s Galactic orbit (our local neighborhood). Most of the stars in our area are coming from regions interior to this radius, rather than from the outer Galaxy, although a few L dwarfs do have pretty wide orbits (some off the projected area). At least one L dwarf gets within 1 kpc (3000 light years) of the center of the Galaxy.
This next image shows the same orbits, but now seen from the side along the edge of the Galactic plane. Again, we see that most of the orbits are bunched up into a band about 200 pc (600 light-years) in thickness – this is the “thin disk”. There is a loose skin of more inclined orbits that looks like a “thick” disk, and then a few L dwarfs that have crazy inclined orbits taking them thousands of light-years above or below the Galactic plane. A being standing on a planet around one of these stars 100 million years ago would have had a tremendous view of the Milky Way Galaxy!
This last image is my favorite, showing the same orbits but in a cylindrical projection: radial distance from the center of the Galaxy (at left) versus vertical distance below or above the plane. Families of orbits become quickly evident, occupying “boxes” in this diagram, the result of the symmetry of the gravitational potential used. The outer borders are defined by the total mechanical energy of the star, which is primarily set by the star’s local speed; the inner borders are defined by the angular momentum of the star. Thus, these two parameters – energy and angular momentum – are the two most important when working with symmetric potentials. These are the two quantities that best define planetary orbits around the Sun.
I found this to be a beautiful way of visualizing a fairly complex dataset, while illustrating the underlying orbital physics (as well as the assumptions made in the calculation). It’s also just beautiful, appearing as a dragonfly with meaty body and gossamer wings, a remarkably synergy between biological and astronomical systems.
This image was awarded 2nd prize in the 2011 Art in Science competition conducted by the UCSD Library (some of the other winners can be seen here). Who knew celestial mechanics can be both interesting and pleasing!
This week I received an IRex Iliad, an e-reader that has gotten increased scrutiny as a result of the Amazon Kindle launch (funny how Amazon’s launch has probably helped increase the sales of its rivals). My choice of the Iliad came after weighing the benefits of some of the the major e-readers now out there (see this Wired review and this MobileRead grid), and my personal desire to have something I can read research papers with while commuting or at home, without wasting paper and ink.
Welcome world, to my humble blog. I’ve finally gotten a chance to start this up while I wait….and wait….for Apple Support to help me fix my ailing MacBook. For the most part, this happy little machine has been working like a charm, with seemingly innocuous problems that software update doesn’t work (NSURLErrorDomain -1100, anyone?) and I can’t stream good live radio like Radiopio. I finally decided to do something about it today, googling my error message and reading the various blogs and lists with other having similar problems. When permission repair, file repair, and fsck’ing all failed to resolve the problem, I broke down and gave Apple Support a call. An excerpt of this experience post auto-responder (+15 minutes):
AS: Hello, my name is xxxxx, may I have your name, please?
Me: Adam Burgasser
AS: Hello, Adam, may I have the serial number of your computer?
Me: Yes, its XXXXX
AS: Thank you. Our records indicate we do not have your email address, may I have it?
Me: My email address? Do you really need that?
AS: Yes, it will allow us to send you information in case we are disconnected, or for future reference.
Me: Um, ok, its xxxxxxxx.
AS: Thank you. Can I please have a phone number that you may be reached by?
Me: My phone number? Don’t you know that already? It’s the one I’m calling from. Why do you need my phone number?
AS: Sorry sir, I do not have access to that information. If you can provide your phone number I can call you back in case our connection is lost.
Me: Oh, good idea. OK, its xxxxxxx.
AS: Thank you, Adam. Now what seems to be the problem?
I gave a long and thorough description of the seemingly minor problems I’m having and the efforts I made to reconcile it. My support person was reasonably impressed I had tried to solve it myself, gave me a few tests to try, and then instructed me to download an update of the operating system (10.4.11) from the Apple site to check if that would work, then do an Archive + Install from my install disks. It sounded like all would be well in a mere hour or so.
One hour later, I had my computer back running, but with an even more outdated operating system (10.4.6) which could no longer run half of my software (e.g., iTunes), and the same exact problem with software update. So I called support again.
AS: Hello, my name is xxxxx, can I get your name?
Me: Adam Burgasser, I have a case number, its xxxxxxx.
AS: Thank you, Adam, can I have the serial number of your computer?
Me: What? Isn’t that in my case?
AS: No, I don’t see it here, please if you could provide it.
Me: Um, fine, its xxxxx.
AS: Thank you. Our records indicate that we do not have your email address, may I have it please?
Me: What? You already sent me email from the last time I called, two in fact, how could you not have my email address in your system?
AS: Sorry sir, I don’t see it here. Could you please provide your email so we can follow up on the problem if we need to?
Me: (grr) Sure, its xxxxxx
AS: Thank you. May I please have a phone number that you may be reached by?
Me: Oy! Again, why isn’t that in my record? Are you actually storing this information?
AS: Please sir, you phone number will allow me to call you back if we get cut off.
Me. Fine, xxxxxxx.
AS: And what seems to be the problem?
Me: Umm, isn’t that at least in my case?
AS: Yes, uh, it says you’re not able to download files and your internet is not working?
Me: Did you actually read the case?
AS: I’m, uh, reading it now.
Me: Why don’t you ask me after you finish reading.
AS: [a pause] Ah, you are unable to use software download.
Me: Yes, and I followed the directions given to me and now I have an even older operating system running and that didn’t solve the problem at all and my software isn’t compatible.
AS: Do you have a portable harddrive nearby?
AS: Well, sir, you are going to have to do an erase and install, and that should fix the problem.
Me: What? I was told that this wouldn’t be necessary!
AS: Well, I don’t know what the problem is, sir, but an erase and install will definitely fix it.
Me: What about this NSURLErrorDomain -1100? Doesn’t that mean anything to you?
AS: I’ve never heard of such an error sir. I am sure this is a unique problem.
[Now would be a fun time to see the number of references to NSURLErrorDomain on the web. Only 5060 sites. Clearly an obscure error]
Me: [fuming] Please connect me with someone familiar with my system.
And here is where I am now, 30 minutes later, listening to bad music through my tinny cell phone speaker, expecting little to come of it. Sure, I am an inpatient, suspicious and quickly frustrated support customer, but if this is “support” who needs an enemy? However, when I see how the folks fail to carry my information from one call to the next, I have to admit I’m not as worried about them having my personal information as I was before…