Wezen, a Deceivingly Dim Star

The Stars in the Brazilian flag are not randomly drawn. brasil1For instance, in the lower left area of the circle are six stars from the Canis Major constellation. This morning while the rest of the family either snored or dreamed, I walked the dog at an early hour under relatively dark skies. Thanks to our dim streetlamps and a waning moon. I was able to observe the fourth brightest star of Canis Major, designated as delta (δ). Named as such because δ is the fourth letter of the Greek alphabet, it also has the common name of Wezen. Deceivingly it only seems dimmer than the very bright Sirius, the alpha-dog star, because Sirius is a lot closer to the Earth.

How do we know how far away Wezen is? 

Hold a finger close and directly in front of your nose. Close one eye. Close the other eye while opening the first one. The finger seems to move against the background. If you hold the finger further away and repeat the exercise, the finger still seems to move, but not as much. Similarly for a given star, if it can be observed from two distant viewpoints along earth’s orbit around the sun, the star, will seem to be in slightly different positions against the background of more distant stars. If the distance between viewpoints is known and the angle of apparent movement is measured, simple trigonometry can help us calculate the distance between our sun and the star. The problem is that the angle is extremely small—after all, any star is a lot further away than your finger can possibly be by a factor significantly larger than the ratio of the orbit’s diameter to that of your eye-separation. A small uncertainty in angle can be amplified into a large error in distance, limiting us to measurements of only “neighborhood stars”. For more distant stars, other techniques involving Cepheid variables and type 1a supernovae have to be used. But thanks to Hipparcos, a scientific satellite of the European Space Agency (ESA) especially devoted to astrometry, parallax measurements have improved recently and are definitely accurate enough for a Milky Way star at Wezen’s distance.

In 2007, Wezen’s parallax (p) was measured to be 2.03 milli-arcsecondsParallax schematic-729x296

Given that there are 3600 arc seconds in a degree and setting the sun-earth distance at 1 astronomical unit (AU), tan p = 1/d or d = 1 ÷ tan (2.03 × 10-3/3600) = 1.02 × 108 AU.

1 lightyear = 63240 AU, so Wezen is about 1.02 × 108 AU ÷ 63 240 AU/light year = 1607 or about 1610 light years away.

How do you get absolute luminosity from distance and apparent brightness?

Due to that distance, which is far greater than the 8.61 light years that separates us from Sirius, Wezen’s apparent brightness is only 1.83.  Compared to the number line, the stellar brightness scale runs backwards. The dimmest stars have the largest positive values and the brightest have pronounced negative values.

To get the true or intrinsic brightness ( absolute magnitude) of Wezen, we can use the following formula:

M = m – 5 log (d/10),

where m = apparent brightness and d = the star’s distance from our sun in parsecs. Since there are 3.26 light years per parsec,

M = 1.83 – 5 log(1607÷3.26÷10) =   6.63

That’s a lot more intrinsically bright than Sirius, which has an M value of +1.42. It is Sirius’ proximity to us that makes it the 2nd brightest star in the sky after our sun and puts its apparent brightness at  – 1.47. If you imagine them to be both at Sirius’ distance from Earth, by doing the math you realize that Wezen would have an apparent brightness of 9.52, which would be almost as bright as a half-moon.


By Sephirohq – Own work, CC BY-SA 3.0, https://commons.wikimedia.org/w/index.php?curid=15613651

Using Two Measurements To Learn About Wezen’s Nature

Now if you rely on one other measurement for Wezen, something even more startling will be revealed. Its color is yellow, and with spectroscopic analysis of the lines from its excited atoms, it is classified as F8Ia, which gives away its surface temperature.

If you then plot absolute magnitude versus spectral class for various stars you get astronomy’s equivalent of the “periodic table”. It’s called the Hertzsprung–Russell diagram and it reveals a star’s stage in its evolution.HR-diag-instability-strip.svg

Using F8 as its x coordinate (each class has 10 subdivisions, zero through 9, so F8 is close to G’s lower bound) and its absolute magnitude of -6.63 as its y coordinate, we end up with a coordinate point on the supergiants line on the instability strip.

Our sun’s class of G2 and absolute magnitude of 4.83 place it on the main sequence, which is why we are still alive. Notice however that the sun’s spectral class is telling us that its surface is actually a little warmer than Wezen’s. If Wezen’s luminosity is so much greater than that of the sun, Wezen has to be a lot bigger, but its energy is spread thinly over its large surface area. But with more mass, gravity is a lot stronger, driving Wezen’s core temperature exponentially higher. This accelerates its rate of fusion. To make a long story short, Wezen is only 10 million years old and has already stopped fusing hydrogen, whereas the sun has celebrated its 4.6 billionth birthday. Moreover, the sun will also stay on the main sequence long enough to double its present age.

It seems that Wezen has already started to expand. As it fuses helium, it will become a red supergiant and eventually go supernova within a mere 100 000 years. When that happens, in our night sky, Wezen will appear almost as bright as Sirius and brighter than every other star. It’s comforting to think that maybe our descendants will walk with their dogs early one morning and marvel at it.


Magueijo’s Brilliant Darkness

Ettore-Majorana-foto-1-x-sitoOn several occasions while rereading Magueijo’s Brilliant Darkness, I asked myself how I managed to forget the author’s particular insights into Ettore Majorana’s and Enrico Fermi’s characters. The answer lies in part with how we underestimate the fallibility of our memories and keep forgetting our constant tendency to oversimplify.  Equally important is the way our constant personal interactions and endeavors change who we are. Thus years or even months later, we don’t come to the same book with the same mind. If what was expressed the first time was worthwhile, a second reading will be equally rewarding.

There are more differences within a group of people than there are between groups themselves. And Magueijo’s work reveals that this certainly applies to scientists. Fermi grew up with parents who were not able to accept the death of his older teenage brother ,who was more popular and intelligent than Fermi. The guilt Fermi felt throughout his life strongly contributed to his overachieving and intolerant personality. Majorana came from a privileged family with a domineering mother. He was far more introspective and, for the most part, less ambitious than his colleagues at Via Panisperna, even though he was by far a better lateral thinker. While Fermi recognized Majorana’s genius, likening him to Newton, he was also shocked by Majorana’s indifference to publishing. The latter’s insights into neutrons and the strong force preceded their official discoveries. When ground-breaking papers were published, Majorana was relieved because it meant the work was done for him. Receiving credit was irrelevant. In contrast, even after having received the Nobel Prize for demonstrating that slow neutrons could form new elements,  Fermi was constantly tormented by the fact that he had stumbled upon fission without realizing it.

To the long list of other complex characters discussed in his book such as Heisenberg, Pontecarvo and Rasetti, we could add the author himself. Inadvertently or not, he reveals a fair deal about his own psyche. A self-proclaimed atheist, he still values the importance of morals, especially for scientists whose discoveries can become subservient to all sorts of interests. Although he doesn’t seriously entertain some of the outlandish theories about the young Majorana’s disappearance, he collects them all with the attention of a stamp collector. He carefully considers more plausible theories, but after extensive travelling and numerous interviews with Majorana’s family members and surviving contacts, he refuses to filter the conflicting data to churn out his own theory. Instead he happily resigns to uncertainty.

magueijoMagueijo, a competent physicist, intermittently devotes time to a primer on nuclear reactions and on the nature of neutrinos.  In double beta decay two protons are simultaneously transformed into a pair of neutrons, 2 electrons and a couple of antineutrinos. But if neutrinos are of a Majorana nature, the reaction will generate neutrinos that will annihilate one another and double beta decay will be observed to be neutrinoless. The Majorana neutrino is its own antiparticle, a quantum superposition of two states going forward and backward in time. For a while in the 1930s up to the 1960s, in the same way that his denial of the positron proved to be incorrect, his theory of neutrinos seemed to be baseless. For some reason although it wasn’t an original assumption about neutrinos, they were for a while perceived to be massless. But Pontecarvo, a latecomer to Via Panisperna, proposed decades later that neutrinos had oscillating states. This was confirmed experimentally, and the only way a neutrino’ s flavour could oscillate is by having mass. It’s now conceivable that in a double beta decay, when each neutron generates a neutrino capable of being an antineutrino, the two opposites would meet and leave no trace—- like Ettore Majorana himself.

Eventually that part of the neutrino-mystery will be settled. But Magueijo reminds us that other questions will surface. Not exactly in these words, he says that even though every major scientific discovery seems so grandiose, in hindsight each insight only peels away the thinnest of layers. No other brilliant scientist aside from Majorana seemed to be aware of that truth at such a young age to the point that his ego was not a driving force.