We choose to do these things because they are hard

In 1962 John F Kennedy made what is probably the iconic speech on space travel,

One of the key points in the speech was answering “why go to the Moon?”,

“But why, some say, the moon? Why choose this as our goal? And they may well ask why climb the highest mountain? Why, 35 years ago, fly the Atlantic? Why does Rice play Texas? We choose to go to the moon. We choose to go to the moon in this decade and do the other things, not because they are easy, but because they are hard, because that goal will serve to organize and measure the best of our energies and skills, because that challenge is one that we are willing to accept, one we are unwilling to postpone, and one which we intend to win, and the others, too”

Today I was thinking about this speech and I thought, how many times have these hard things been done since then. Well here’s the answer,

Sources, flights (I couldn’t find long-term historical traffic data), Everest (-9 ascents pre1962), Rice vs Texas. For the non-Americans the last example was because the speech was made at Rice University and every few years Rice plays the University of Texas, a school 16 times its size, at American football.

And if you think it’s bad for Rice try being a Hawaii Rainbow Warriors (7-28 last 3 seasons) fan like me.

World Cup heat, maybe not such a factor

So far in this World Cup we’ve been hearing that the heat in Brazil is responsible for a series of massive upsets and for the generally high number of goals scored in the tournament so far. In addition the old mantra of “European teams can’t play in the heat” has been trotted out. I decided to do a very rough analysis on the group games in the tournament to see if I could find any statistical evidence that any of this was true. Firstly I tabulated all the results from the group games and added the relative humidity and temperature from FIFA’s own match reports. For one match (England vs Italy) I couldn’t find a FIFA number for the humidity so I took it from a number of match reports in the press. As well as who won each game and how many goals were scored I also added a column for the number of goals scored after the 70th minute of the game.

To try to quantify the conditions in a single number I used the NOAA Heat Index* calculation to estimate how hot it felt to the players. This is a relatively crude instrument and doesn’t include direct solar irradiation but, meh, I don’t have time to do more. I also didn’t attempt to factor in the relative strengths of each side (Mexico beating Croatia was not as big a shock as Costa Rica beating Italy), that is probably worth doing so if you want to do that yourself, go ahead.

Anyway results,

1. There seems to be no correlation between goals scored and conditions. This also extends to goals scored in the last 20mins of games. I estimated the Pearson Correlation Coefficient to identify a correlation between goals scored and Heat Index. For the full match this came out at -0.051 and for the last twenty minutes -0.052. Hence there’s pretty well no correlation between high scoring games and conditions. See plot below,

Note in this plot I’ve isolated the matches between European teams and those from other continents. This leads me on to my second point,

2. The matches which were won by European teams were not that much warmer than the ones they lost or drew. Below are the histograms for the games won, lost and drawn by European teams when they face opposition from other continents.

Heat index of games played between European teams and those from other continents.

So on first inspection it appears that the European teams did better in cooler games. I did a KS test to see if the games European teams won were drawn from the same distribution of conditions as the games they lost. This resulted in a 43% chance that they are drawn from the same distribution, i.e. it’s a 43% probability that the heat had no effect. This is a fairly ambiguous region of probability space so I wouldn’t shout from the rooftops that European teams are more affected by the heat than those from other continents. There of course a flaw here, France would probably beaten Honduras if all the players had been forced to wear parkas and the game had been played in an enormous sauna run by a particularly psychotic Finn. Hence there are datapoints in this calculation which would have likely turned out as win for the European team no matter what and there are much closer games which one might expect could be effected by the heat. Hence this rather simple analysis could be affected by small number stats (it would be a truly momentous upset if European teams were to lose all games in hot conditions and win all the colder games no matter what the opposition) so it probably isn’t worth drawing too many conclusions from it. Perhaps a more in-depth analysis involving pre-match betting odds/spreads would help to get rid of that effect.

In summary I’d say

It’s often stated that hot, humid conditions lead to high-scoring matches with European teams underperforming. The results from the group stages do not significantly support these hypotheses.

One final note  to give this a vague link to astronomy. Astronomical telescopes close in conditions of high humidity to stop condensation forming on the mirrors and electronics. The specific level at which telescopes close varies between observatories. 30 out of the 48 group matches were at a sufficiently high humidity (>60%) that the ESO Very Large Telescopes would not have been able to conduct observations. 25% of games failed the 75% humidity test used by some observatories on Mauna Kea. This is one of the reasons large astronomical telescopes are not situated next to football stadia in Brazil.

*Yes, I know, it’s in Fahrenheit, I don’t like it either.

A record-breaking brown dwarf: as cold as ice and just 6 lightyears away

About a year ago I wrote about how Kevin Luhman at Penn State had discovered a pair of brown dwarfs that were the just 2 parsecs (about 6 lightyears) from the Sun. Well he’s gone and done it again, discovering another brown dwarf at about 2pc, only this time it’s colder, much, much colder.

A decade and half ago, we astronomers (being rather odd) were getting very excited about some new odd objects we were finding by looking at the sky in infrared light. These brown dwarfs bridged the gap between very low mass stars (which can go down to about 8% of the mass of the Sun) and giant planets like Jupiter (with a mass of about 0.1% of the mass of the Sun). Brown dwarfs can’t fuse hydrogen in their cores so they don’t have a stable brightness like stars do and hence cool with time. This means that a very cold brown dwarf could be very low mass or just very old. Anyway, the things we were getting excited about 15 years ago had temperatures of about 1100C. At this point the cloud physics of these objects change dramatically, their upper atmospheres clear and their colours in near-infrared light changes significantly.

A decade or so went along and we started to get more excited as we crept to lower and lower temperatures, getting down to about 400-500C. Then we got a stroke of luck, Kevin Luhman (yup, same bloke) published the discovery of a really cold brown dwarf around a dead star called a white dwarf. This has a temperature of 25-80C, so between a pleasant summers day and a hot cup of tea. This object was joined by a few other slightly hotter objects which formed a newly defined class of cold brown dwarfs, the Y dwarfs. These big balls of gas about the size of Jupiter could have water clouds in their atmospheres.

So now we have a new coldest brown dwarf. It was found by looking at images from the WISE satellite which studies the universe in mid-infrared radiation. Nearby stars and brown dwarfs move slowly across the sky compared to background stars due to proper motion. This can be pretty slow, a very nearby star might move at one arcsecond per year, about the apparent angular speed of a tortoise walking at the distance of the Sun. So Luhman looked for objects that had moved a lot between different WISE images and found one which he published last year. This was a pair of cool brown dwarfs with temperatures of about 1100C. Now he’s published another that is moving even faster, about 8 arcseconds per year. Despite this, it is about the same distance as the previously published one, 2.2pc (a bit more than 6 lightyears). This distance was determined by follow-up Spitzer Space Telescope observations using a trick called trigonometric parallax.

So what is this thing? Well, we know it is bright in the mid-infrared, light which it is difficult to observe from Earth and which is way beyond what the human eye can see. And that’s where the observations of it stop, well not really, we can tell a bit about this object from what we don’t see, near-infrared light. Luhman’s new object was observed by the VISTA telescope in Chile a few years back. Well I say observed, it didn’t see it, neither did Luhman’s follow-up observations with Gemini. But from those observations one can set a limit of how bright this object is in the near-infrared and hence constrain its properties. Luhman used these along with his measurement of how bright the object was in the mid-infrared to find that the temperature was -48 to -13C, colder than ice on Earth, you’d even struggle to play at Lambeau Field in those temperatures. Not that this is a solid, icy planet, it’s about 3 to 10 times the mass of Jupiter and about the same size. It’s also a bit warmer than Jupiter which has an effective temperature at the top of its clouds of about -160C.

What more will we find out about it? Who knows. Last year’s spectacular Luhman discovery sent astronomers into a frenzy, studying the weather on the objects, even mapping its clouds. This one will be harder as the object is so cold and faint, but I’m sure observers will be furiously writing proposals to observe this immediately. Wait, why am I blogging? I should be proposal writing. And I’m sure this object will be one of the first things the mid-infrared JWST will look at when it launches.

A really, really nearby brown dwarf binary

OK I’m going to break my blogging silence and my aversion to blogging in my subject area to post about a really cool result that came out earlier this week.

Looking up at the night sky you see a hodge-podge collection of stars, perhaps a few thousand of the hundreds of billions of stars in the Galaxy. Some are extremely bright types of star that are really far away. Others like the Sun’s nearest neighbouring system Alpha Centauri are fairly run of the mill but appear bright because they are so close. But not all stars close to the Sun can be seen with the naked eye. Take Barnard’s Star, the second closest system to the Sun, it’s situated roughly twice as far away from us as Alpha Centauri but because it’s a red, faint type of star, it’s over 6,000 times fainter and 25 times too faint to see with the naked eye. This means that even though some stars are very close to us, they are so faint that we need to use a few tricks to pick them out from bright background stars.

One of the best tricks to use is to take a picture of the sky and look back a few years later and compare the positions of stars. Stars move around the Galaxy with different orbits and hence every star has a velocity with respect to the Sun. Due to their closeness, nearby stars appear to move  more compared to background stars (their proper motion). This is simply a perspective effect, they aren’t actually moving through space faster. Hence if you look for stars moving quickly across the sky, chances are a lot of them will be near the Solar System. This isn’t simply a matter of cartography, if you want to pick out a population of faint objects, your best bet is to look close-by.

And that’s exactly what Kevin Luhman did. By taking the positions of objects observed by the WISE satellite, he found one which stuck out. It moved across the sky pretty fast and was very bright in infrared light. Looking back at images taken by other surveys he also found it detected there. This often happens in astronomy, sometimes you find an object nobody had noticed was interesting before but which may have been first detected 50 or even 100 years ago. Anyway, the object Luhman found was moving across the sky pretty fast. Well actually it wasn’t, nearby stars tend to have their motions measured in arcseconds per year. One arcsecond per year is the same angular speed as seeing the average tortoise walking at the distance of the Sun from Earth. The newly discovered high proper motion object was moving at about 2.8 Solar Tortoises, which is pretty big for stars. Well I say star, but it isn’t, it’s a brown dwarf, well actually not “a” brown dwarf.

Stars are fuelled by nuclear reactions in their core. These work because of the huge temperatures in their cores caused by all the mass above pushing down. It’s like the atomic nuclei in the core are caught at the bottom of a really big rugby ruck*. Anyway, they get so hot that they can sometimes overcome their mutual repulsion and fuse together. However some objects, with masses below about 8% of the Sun can’t reach the appropriate minimum temperature to begin stable fusion and hence are “failed” stars or brown dwarfs. When Luhman took a spectrum of his object, he found it was a brown dwarf, well actually while taking the observation he found that it was actually two brown dwarfs in orbit around one and other. Finally, using the data from the WISE satellite and other surveys he was able to work out its distance from an effect known as trigonometric parallax. This showed the two brown dwarfs are about 6.5 lightyears away, slightly more distant than Barnard’s Star.

My reaction to this was probably like others in my field, “how did we miss this?” Well the answer is simple, the system lies close to the Milky Way. The density of stars on the sky increases sharply as you go close to the plane of the Milky Way, meaning searches of nearby stars are often flooded with spurious candidates. Additionally the gas and dust in the plane make background stars appear redder and faint in the optical but still bright in the infrared. This can mimic the colour of brown dwarfs, again contaminating searches. Brown dwarf searches therefor often avoid the region around the Milky Way to make sure they can have clean samples without wading through a load of junk. Hence the extremely nearby, bright brown dwarf lay undiscovered for decades after it had first been detected.

And that brings me to my last point, this is a really cool discovery yet it hasn’t got the attention it deserves. The third closest system to the Sun was just found, that should at least be on the BBC News front page.

*There are no known instances of a rugby ruck leading to nuclear fusion