Monday, December 31, 2012

Music for the Eve of a New Year

The Local Natives with Wide Eyes

Monday, December 24, 2012

Galactic storm

My New Year's resolution #1: Take the boys to a dark site. We might not see something exactly like this, but I gotta give the boys a chance to see the night sky before its all lost to light pollution.

"The photo above showing the Milky Way stretching across the desert sky and a distant monsoon thunderstorm on the horizon was captured just outside of Dead Horse Point State Park in Utah."

Sunday, December 23, 2012

On the number of guns and planets out there, Part 2

(Note: It might take a while for the math symbols to load.)

In my previous post I set up the problem of gun statistics and planet statistics (where I mean math-problem, rather than trouble-problem). There's a question of the number of guns per capita, versus the fraction of the population with a gun (fraction of citizenry that are gun-owners). Also in there is the number of guns per gun-owner.

Similarly, there's the question of the number of planets per star throughout the galaxy, the fraction of stars with a planetary system, and the number of planets per system.

To illustrate this mathematically (and this involves nothing but multiplication and division, so stay with me!), let's set up two scenarios. Both scenarios have five stars and five planets:

Now let's introduce some mathematical terms. The first is the total number of stars in our sample, $N_\star$. Next is the number of planets, $n_p$. In both of the cases in the figure above, $n_p = 5$ and $N_\star = 5$. These two terms allow us to assess the number of planets per star:

$f_p = n_p/N_\star = 5/5 = 1$

So both cases give 1 planet per star. In terms of bulk numbers this is interesting. But it doesn't really give you a lay of the land. If you are searching for planets, the two cases pose very different situations with very different problems to solve. In Case 1, it's a hunter's bonanza: every target star has a planet to detect! In Case 2, it's 4 misses and one hit, but the one hit has a very complicated signal to decipher.

For planet-hunting, we want the fraction of stars with a planetary system $f_S$, where a system is one or more planets. Clearly the two example cases in the figure have very different values of $f_S$. This number is given by the number of systems $N_S$ divided by the number of stars $N_\star$. By inspection, Case 1 has $N_S = 5$ and $f_S=5/5=1$. Case 2 has $N_S = 1$ and $f_S = 1/5 = 0.2$.

A little more thought should reveal that $f_p$ and $f_S$ are related to one another. They're related by the average number of planets per system, given by $R$ (I'm running out of symbols!). To find the relation, let's figure out how one would use the various symbols above to come up with the number of planets in the sample. The number of planets is given by the number of stars, times the number of systems per star, times the number of planets per system:

$n_p = [{\rm Stars}] \times \left[\frac{{\rm Systems}}{\rm{Star}}\right]\times \left[\frac{{\rm Planets}}{\rm{System}}\right] = N_\star f_S R$
$\frac{n_p}{N_\star} = f_S R$
$f_p = R f_S$

Notice that if $R=1$, then $f_p = f_S$ because there is only one type of planetary system: those with a single planet. Of course, this isn't a likely scenario for planetary systems (just look at ours!), and it certainly isn't the case with most gun-owners. I'd hazard a guess that once you get to the point that you like guns enough to own one, you'll probably own several.

Also, note that $f_S$, or equivalently the fraction of gun-owners, must be less than or equal to one ($f_S \leq 1$). However, $f_p$ can be more than one, but for that to be the case, $R$ has to be bigger than one.

Anyway, the upshot is that the math is fairly simple, but the statistics of gun ownership and planet occurrence are somewhat subtle and you can get tied into knots unless your question is well-phrased. For the answer to the number of planets per star, stay tuned for our press release and final publication of our paper. For gun ownership, let's check out the numbers.

In the U.S. there are 89 guns per 100 civilians, or 0.89 per capita. We're number 1 in the world based on that statistic. (U-S-A! U-S-A! Suck it Serbia!). Thus $f_p = 0.89$.

But only 40-45% of adults own a gun (only!), or $f_S = 0.43$ to pick the average. This means that the number of guns per gun-owner is:

$R = f_p / f_s = 0.89/0.43 \approx 2$

This means that there are about 2 guns per gun-owner, on average.

So this is probably why Ta-Nehisi Coates had such a hard time squaring the various numbers for gun ownership. On the one hand, there are 0.89 guns per citizen. But only 45% of people own a gun, and when they do, they tend to have 2 guns.

In orbit around 1 Mjup at 1 AU

What if Jupiter were at 1 AU and we were its moon? This is what it'd look like:
Art by jb2386 on Reddit
The NASA Kepler mission might help us find a situation like this. David Kipping at the Harvard Center for Astrophysics is on the case.

Saturday, December 22, 2012

On the number of guns and planets out there, Part 1

Ta-Nehisi Coates recently asked his readership to "talk to him like he's stupid" about gun ownership rates in the US and in other countries. I really like it when he makes these requests. It's how I often feel about stories in the news, which make me feel like I'm walking in on the middle of a grown-up conversation. I need someone to talk to me like I'm stupid about Benghazi or the fiscal cliff. Fortunately, Slate and Salon are good sources for this sort of information, as is Andrew Sullivan.

Anyway, regarding gun ownership rates, the discussion that Ta-Nehisi sparked got a bit muddled over the question of guns per capita (number of guns per person) versus the number of guns per gun-owner. This is an important distinction. There are two ways to get 1 gun per person in a hypothetical town of 100 people. One way is to give a gun to every person in town. The other is to have one person in town with 100 guns.

Of course this whole discussion goes back to the most recent mass shooting. But when I read it, my mind drifted into a much nerdier direction, as it is wont to do. Call it a coping mechanism. Or just call me a nerd.

What I immediately thought about was the question of the number of planets in the Galaxy, which Jon Swift, myself and our collaborators touch on in a soon-to-be posted paper about planets around red dwarf stars in the Galaxy. Long story short, we come to the conclusion that there is one planet per star throughout the Galaxy. Given that the Galaxy has 200 billion stars, and that 70-80% of those stars are red dwarfs, that's a whole lot of planets! Of order 100 billion planets in our an order-of-magnitude estimate...of the lower limit.

This many: 100,000,000,000+

But the way in which those planets are distributed throughout the Galaxy matters. Is that literally one planet per star, or no planets for most stars with dozens of planets around a few stars? The number we quote in our paper and in our upcoming press release makes for good press: billions and billions of planets! It's also good fodder for Drake Equation discussions (for what those conversations are worth). But from the standpoint of planet-hunting, we're more interested in the fraction of stars with at least one planet (think of it as the fraction of stars with planetary systems), and the number of planets per system.

In analogy to the gun discussion, it's the number of guns per capita, versus the number of gun-owners, versus the number of guns per gun-owner. The correct statistics depends on what question you want to answer. I'll get to the math of the matter in my next post.

Friday, December 21, 2012

Happy Winter Solstice!

The days only get longer from here! (at least until June 21st).

Photo from Astronomy Picture of the Day

Monday, December 17, 2012

Me and my sisters

Via Facebook, this picture from earlier this year of me, and my sisters (from left to right, youngest to most experienced) Erin, Rachel and Christina. I'm often amazed that I came from the same beautiful gene pool. Fun facts: They are all artists and singers. I'm a scientist who can't carry a tune. We also all live along the same 20-mile stretch of the 210 freeway north of LA. We all have two kids each: 6 boys and 2 girls, and all 8 kids were born within a 10-year interval. Finally, our kids have skin tones that span Kenya to Sweden. Fun with genetics!

Sisters: Sorry we missed each other at Thanksgiving while I was out of town. I'm looking forward to seeing all of you at our Christmas celebration!

Saturday, December 15, 2012

Montana has very few people

I'm hanging out with Prof. Nate McCrady right now in Prof. Jason Wright's kitchen. Given that I once sat in Frank Shu's stellar astrophysics class with both of them, it's a lot of fun to append "Prof" to each of their names!

Anyway, this post is about how Nate blew my mind. He's a professor at U. Montana and he just informed me of the following facts:

  1. There is one area code in Montana. 
  2. There are only 1,000,000 people in the whole state.
  3. The biggest city is Billings, pop. 105,000 (Pasadena has 138,000)
  4. There are only fourteen high schools with 1000+ all of Montana

Discrete events, continuous flow, and why I love basketball

In high school I played football and ran track. After high school, I've tried running, biking, ultimate frisbee and a few other sports. But if you read my blog often, you know that my passion these days is basketball.

I find it challenging and exciting in much the same way that I enjoy science. There's just so many combinations of events and so much improvisation. Plus, it's something I can play alone (shooting around), with one other person, 2-on-2 or full-court 5-on-5, giving me plenty of opportunities to practice and participate. This is in contrast to, say, football, which I'll likely never be able to play again with a full team. And as a sport to watch live or on TV, it's fun and fast-paced without all the head trauma of my old sport.

A lot about why I love basketball is summarized in this outstanding sports article (h/t Bri) about the "Kobe Assist." The main point is that Basketball cannot be thought of and analyzed in the same way as baseball. While baseball has discrete, individual accomplishments (e.g. the homerun), basketball plays are much more continuous:
Most basketball statistics refer to discrete events such as shots, steals, and rebounds that occur within the continuous context of a flowing game. Basketball is very different from baseball, but in the basketball analytics world, too often we treat our sport as if it were baseball; we kid ourselves and say a rebound or a corner 3 is akin to a strikeout or a home run, a singular accomplishment achieved by a player that's fit for tallying and displaying in a cell on some spreadsheet on some website.
There is usually a singular event that ends a possession of the ball for one team and the change of possession to the other team. But everything in between is a continuous flow, with important events such as a 3-point shot preceded by maneuvering of the ball-handler, passes, one or more screens, all occurring simultaneously with the positioning of rebounders near the basket. If you stay focused solely on the ball, you'll miss the symphony occurring away from the ball. Dunks will occur apparently out of nowhere. But for every time that Blake Griffin Mozgovs someone, there was a Randy Foy who set up the pick-n-roll, Deandre Jordan diving toward the rim taking the opposing center with him, Griffin rolling to the hoop, and Foy passing.

Similarly, those put-back rebounds of a Kobe shot can be though of as an accidental assist:
Just as the theoretical butterfly flapping its wings in Rio somehow influences the formation of a faraway hurricane, basketball outcomes exhibit sensitive dependence on previous environmental conditions, yet the analytical "baseball-ification" of our fluid sport too often neglects this basic tenet of basketball ecology. We disregard too much environmental context. As an illustration of how this baseball-ification of basketball ecology can hinder our understanding, consider the Kobe Assist, those missed shots that are more like accidental passes that lead to put-backs.
I can't wait until I get back home after this long work-trip. I miss my family and my bed. I also miss playing ball at Braun Gym!

The next level after grad school

Here's a great blog post about one postdoc's first-year experience:
As of October, I have now spent one year as an astronomy postdoctoral researcher straight out of graduate school. It has been a great year, though with plenty of ups and downs. I figure I should write down my thoughts about this experience. I have both good things and bad things to say, but I try to be honest, fair, and positive throughout. This may be of interest to curious grad students, or anyone really, especially if they have wondered about pursuing a postdoc or are just interested in astronomy in Chile. One thing to keep in mind is that this is an individual, personal experience and your own story or circumstances may be quite different. It's obviously difficult to approach this critically and unbiasedly, but here goes nothing...

Wednesday, December 12, 2012

Correction: Those were real spectra!

In my last post I said that the spectra I was showing were not real, but instead models. However, it turns out those spectra I showed, the so-called Pickles library spectra, are actual stellar spectra! My bad. I was correct that there isn't a single instrument that provides that wide wavelength coverage. But that Pickles guy was pretty clever: "Each library spectrum was formed by combining data from several sources overlapping in wavelength coverage." 

Tuesday, December 11, 2012

Stars and the Exolab on PhD Comics!

Like most former and current grad students, I'm a huge fan of PhD comics. I'm also a fan of the artist behind PhD Comics, Jorge Cham, in particular his online shows on scientific topics such as dark matter, the Higgs boson and Open Access publishing. When I first watched Dark Matters, my immediate thought was "Wow, this is an amazing teaching tool. I wonder if Jorge would like to do one on exoplanets."

So, even though I had never met him, I nervously typed out an email, proof-read it, reread it, and finally hit send. Lo and behold, I managed to set up a lunch meeting with Jorge and we talked about academia, comics, teaching, and my research. He agreed that it would be fun to do a video on Exoplanets and we scheduled a date to record the audio last Summer. I also applied for and received funding from the Caltech Innovation in Education fund to contract Jorge's expertise for the whole endeavor.

Jorge and I decided to do things a bit differently than his past animated pieces. First, instead of interviewing a single scientist, he would capture the highly interactive nature of my group by gathering several scientists and having us all talk with him. So I convened a meeting in my office with my two then-first-year students Melodie Kao and Ben Montet, and one of the postdocs in my group, Jon Swift.
The second difference would be the use of full color, which as you'll see was a necessary touch given the topic of our discussion.

We recorded about 5 hours of audio (!), which included a large amount of information about stars. Our detour into stellar astronomy was no accident: in order to understand planets, one must understand the physical characteristics of stars that they orbit. Consider how the three smallest planets detected to date were uncovered by learning more about their host star. When we were done, it was clear that we not only had material for an animated piece on exoplanets, but we also had great material for stars.

The 5-hour interview was whittled down to 8 minutes and 21 seconds, and Jorge applied his magical touch to create this amazing video. After the video, I show some actual stellar spectra. Jorge and I hope that after watching this piece that you have a better appreciation for how fundamental stars are, and how astronomers can use stellar spectra to learn about our Galaxy, our Sun and ourselves as humans comprised of elements heavier than hydrogen and helium!

Bonus material:

Here are some actual stellar spectra from stars hotter and cooler than the Sun. For the aficionados among my readers, you'll note that these aren't *real* spectra, but instead model spectra (Oops! I was wrong about this. See this correction.). There are no instruments that can provide this sort of wavelength coverage in a single shot. Also, it would be exceedingly difficult to get a spectrum of an M6 dwarf of this quality even if such an instrument existed, because those tiny stars are so faint.
The spectrum shown above is that of an A0V star, which has a temperature of approximately 10,000 K (where K = Kelvin; 280 K is approximately room temperature) and a mass of about twice the Sun's. Many of the stars you see in the night sky are A-type stars, but this is because they're so bright, not because they're common. In fact, of the 100 nearest stars to the Sun, only two are A stars. Famous A-type stars include Sirius, Vega and Fomalhaut.
 This spectrum is an F0 dwarf, which has a temperature of roughly 8000 K, a bit hotter than the Sun, 30% higher mass, and very different in appearance and behavior. A star like this and the A0 star above will tend to be a very rapid rotator, lack magnetic activity and the associated spots, plage and flares common to less massive stars because they lack convective envelopes. Most naked-eye stars are F dwarfs.
 Here's a spectrum of a G2V dwarf, just like our Sun (.
 Here's a K dwarf, with a temperature of roughly 5000 K and a mass of 70% of the Sun's.
 Here's an "early" M dwarf (M1V). Note the dramatic shift in the peak of the spectrum, indicating a much cooler star (Temperature = 3700 K) and about half the mass of the Sun. These stars are the most numerous stars in the Solar Neighborhood: M dwarfs make up about 7 out of every 10 stars in the Galaxy! All of those spikes and wiggles are real features due to the more complex nature of molecular absorption lines, as opposed to the atomic lines seen in hotter stars.

Here's one of the most diminutive stars at the "bottom of the main sequence." This is an M6 dwarf with roughly 10% the mass and radius of the Sun, or about the size of Jupiter! Any less mass and it would be able to fuse hydrogen to support itself and it would instead be a brown dwarf, destined to radiate its birth heat until it fades into the thermal background of the Galaxy. Instead, a star like this one will be the last hydrogen-fusing stars in the Galaxy, with a lifetime of roughly 10,000 times longer than the Sun's 10 billion-year lifespan!

Monday, December 10, 2012

Annika Peter: First, the Facts

To continue my exploration of gender parity in astronomy, I have called on my friend and fellow astronomer Annika Peter to guest blog for me. Annika and I have had several illuminating discussions over coffee about academia in general and women in science in particular. Here's the first in a series of posts from Annika.

My name is Annika Peter.  I am a dark-matter and gravitational-dynamics junkie, currently finishing up a postdoctoral position at UC Irvine, and moving to a faculty position in the Departments of Physics and Astronomy at The Ohio State University.  My husband is also an astrophysicist, currently a professor of astrophysics at Caltech.  He is taking a professorship at OSU, too, so we have successfully found an excellent solution to our two-body problem!  My two favorite aspects of my job are thinking deeply about and trying to solve some of the major mysteries of the universe, and working with undergraduate and graduate students.  I am also a practical problem solver, which means I spend some time scheming about how to improve the scientific enterprise and university education.

John asked me to say a few words about women in (astro)physics.  I convinced him to let me actually do a series of guest posts, as I have more than a few words to say on the subject!  

Before jumping into a discussion of women in science, I thought it would be useful to provide some references and numbers.  Not only do I think that these data are good for anyone in our field to be familiar with, but it will be a good jumping off point for some of my future posts.

Participation of women in physics and astronomy in an academic setting:  We all know that there are few women in physics and astronomy, but what does “few” mean?  There are several good databases with numbers on this subject.  The first place I would recommend looking is the NSF, which maintains a set of tables on graduates and employment by field, sex, disability, race and ethnicity, citizenship, and year.  The American Astronomical Association’s Committee on the Status of Women maintains an extensive set of links to various studies and informational resources.  The American Physical Society has some useful information on its website.  

Here I will describe some of the findings from a 2005 report by the American Institute of Physics (AIP) on women academics in physics and astronomy in the United States.  Note that the AIP also maintains statistics and links to demographics in other countries, which you can find here.

Now, onto the 2005 AIP report (PDF):
  • The proportion of women in physics and astronomy has been increasing with time at all levels (undergrad through full professor).  As of 2003, 46% of bachelor’s degrees in astronomy and 22% in physics were going to women.  At the PhD level, the numbers were 26% and 18% respectively.  By contrast, in the year I was born (1982), the numbers were 20%, 10%, 15%, and 5%, respectively.  Even in my lifetime, the proportion of women getting degrees in physics and astronomy has more than doubled.  We have come a long way!
  • In astronomy, 10% of full, and 23% of associate and assistant professors were women in 2003.  In physics, 5% of full, 11% of associate, and 16% of assistant professors were women in 2002.
  • The AIP estimated how many women one would expect at each career level given the time at which the typical person at that career stage would have finished college or graduate school.  The numbers suggest that the proportion of women one would expect at a given career stage roughly matches what one would have expected given the gender split of their undergraduate and graduate cohorts, although there are some nuances to the data. 
  • This implies that one of the main reasons that physics and astronomy faculty have so few women is because those departments are OLD.  Only ~5-10% of full professors in physics and astronomy are women today because only a few women were granted PhDs in these fields thirty or forty years ago.   An interesting exercise is to count how many faculty members in your department are AARP eligible.  As older generations retire and more recently minted PhDs get hired, the proportion of women in the faculty should creep up if departments hire women at the same proportion as they are obtaining PhDs.  However, we will not achieve gender parity among the faculty until we achieve gender parity in the graduate student population, and even then there is likely to be a lag time unless future women graduates are significantly more awesome than the men. 
  • The participation of women in the faculty of physics and astronomy departments is proportionally lower at institutions that grant PhDs than institutions that grant only bachelor’s or master’s degrees.  Unfortunately, the AIP report does not parse the numbers by faculty rank (lecturer, assistant, associate, full), which I think would have been illuminating.  Without these data, it is difficult to tell if the PhD-granting institutions (the institutions that we often view as most prestigious) select against women or if their departments are simply much older.
  • In my opinion, the most depressing thing about this report is its findings about the severe underrepresentation of women from ethnic and racial minorities in physics and astronomy.  One statistic that particularly stands out in my mind is that only 35 PhDs in physics went to African-American women between 1976 and 2003.

Leaky pipeline:  If you take the AIP study at face value, the major leak in the pipeline of women into academic physics and astronomy careers occurs at the undergraduate level.  The AIP finds that almost half of the students who take high-school physics are women, yet women are only one in five of bachelor’s degree holders in physics.  They also find that a far lower proportion of girls take the AP physics tests than they take physics classes in high school. This indicates the potential importance of interventions with high-school girls and undergraduate women.

If you look at the AIP numbers as well as some other studies, some other leaks (or selection pressures) begin to appear.  First, it appears there is gap between college graduates and PhD holders in physics and astronomy among American women.  The AIP suggests that the reason there appears not to be a leak between undergraduate studies and graduate school is the influx of women from other countries into American graduate programs.  

Second, there appear to be bigger leaks in the astronomy pipeline at later stages for women than in physics, although this is largely going from undergraduates to graduate students.  

Third, at the faculty level there appears to be a strong selection pressure for childless and/or single women in the natural sciences.  Thus, even if the pipeline for women is not as so leaky going from graduate school to full professor, the women who stay in academia have very different family structures than men, with one study finding that women who have children as postdocs are far less likely to end up in tenured faculty positions than women or men with any other family structure.  
Here is the link to that particular study.  

Unfortunately, that study does not parse their findings by field, so it is unclear how much the family structures of women in physics and astronomy differ from women in the natural sciences as a whole.  There are also studies on tenure rates as a function of family structure (see, e.g., this document [PDF]), but I have not seen studies from the past couple of years, after policies have been instituted at many top-tier universities to recruit and retain more women faculty, such as to slow the tenure clock for both men and women who become parents as junior faculty.

A study by the National Academies indicates that the structure of leaks in the pipeline varies significantly by field of study.  For example, in biology, more than half of all undergraduate degrees go to women, but women only make up 35% of assistant professors.  The life sciences pipeline is leaky after the undergraduate stage, in contrast to physics where the leaks largely occur very early.

In the second part of this post I'll examine some additional leaks in the pipeline, and thereafter I'll delve into the roles of women in science and solutions to fixing the pipeline in order to achieve gender parity in (astro)physics.

Sunday, December 2, 2012

Player introductions

It's Sunday, a day of rest and football! Now for the player introductions:

Saturday, December 1, 2012