Well, here we are again waiting for the clouds to go away and now have to contend with "June Gloom", but we can still review some astrophysics of curved space and supernova explosions and enjoy the jazz festival under cloudy skies.
We look forward to the OCA Astroimagers SIG, this Wednesday, where we will hear what other travelers are planning to do to view the July total solar eclipse in Chile. In the meantime, as we prepare to attend the Hartlefest, celebration of Jim Hartle's 80th birthday, we continue on our review of general relativity from his classic textbook on gravity. Keep in mind that astronomical and cosmological observations and theories are attempts to get at the nature of our universe and whether or not the space that we inhabit is flat or curved. Mathematical theories of geometry of space tells us that space can be positively curved flat or negatively curved as illustrated in the drawing below, taken from Hartle's class textbook.
|Mathematical possibilities for the geometry of space (Source: J. Hartle, "Gravity: An Intro to Einstein's General Relativity")|
Current astrophysical measurements indicate that the geometric space of our observable universe is pretty flat within a small margin of error. This means our universe is defined by the nature illustrated in the middle portion of the diagram above. You might wonder how the evolution of the universe can be predicted and calculated? Well, keep reading in Chapter 18 and beyond in the Hartle textbook and you will be able to begin to get a handle on how general relativity can make such predictions. The Friedman equation, a differential equation, which is derived from general relativity for an isotropic, homogeneous universe, can be used, once the total amount of matter, radiation and dark energy are entered, to predict the evolution of the universe. We can also tie the concept of redshift, z, together with the scale factor, a, for the size of the universe. At the current time, a = 1, and for earlier times, say for z = 1100, when the CMB was released, the universe would have been much smaller, in fact, we can calculate a = 1/ (z+1), a = 1/ 1101, which means the universe was just one thousandth as big at the time the CMB was released.
Similarly, if we look to the future, what this means for the future of flat universes, like our universe, is that it most likely continue expanding forever. If the space were positively curved, as illustrated in the leftmost case of the diagram above, and if the universe is dominated by normal matter, then it would be possible for the universe to eventually cease expanding, slow down and reverse course and eventually return in a "big crunch."
Well, it seems that our fate is not going to be that as illustrated in the left had portion of the diagram below. In a matter dominated universe, with positive curvature, the big bang would have expanded, but then depending on how much matter was present, the bang would have re-collapse. Luckily, we don't seem to live in that kind of universe. So in our flat universe the future coarse of expansion is expected to just continue expanding forever. Other diagrams and calculations in the textbook illustrate what happens assuming different amounts of dark matter and radiation and dark energy. What you see right away by examining various combinations of matter and energy is that in order to match the measured flatness of the universe and to account for the measured acceleration of the universe, that their is this mysterious dark energy component. With the recent recognition that the expansion is accelerating, the expansion goes on at a faster and faster rate.
Ok, enough of that, so says Astronomer Assistant Ruby who wants to go out and about. On our journey outside, she spies a plastic straw in the rain gutter and stops to ponder the consequences. Now, I was normally quite skeptical of restaurants that limit the availability of plastic straws, saying that they could end up as plastic pollution in the oceans. But here was an example of a straw in the gutter some dozens of miles from the ocean, so it seems it is quite possible for straws to enter the ocean, even from miles away.
|Astronomer Assistant Ruby pauses in front of a plastic straw in gutter (Source: Palmia Observatory)|
Yep, further down the road we see the sign saying that the storm drain does indeed drain to the ocean. So, yes, it seems that straws and other plastics can indeed find their way to the ocean even when they originate from miles away from the sea shore.
|Yep, you have seen these signs about draining to the ocean (Source: Palmia Observatory)|
After our walk and discovering the straw (and yes, in case you are wondering, I picked up the straw), we received an email and question from Still into Control, Gene, who asked about the possible effects on the Earth of a nearby supernova. He had heard, as I had heard and read many times, that a nearby supernova would pretty much burn up the Earth and yet Gene referred to an article that said if some nearby star like Betelgeuse were to blow up that it was too far away to do much damage. Is this the case? Hmm, I don't know but I guessed that as a physicist wannabe or senior physics student that we could do some back of the envelope calculations and get an answer. So, let's get to it!
So, starting with the light curve data for typical supernova and if we know how far away the supernova is then we can calculate the energy flux received here on Earth. So, we have:
- Supernova 10 to the 10th power brighter than the sun
- The sun luminosity is 3.82 time 10 to the 26th power watts
- Betelgeuse is approximately 222 parsecs from Earth
- One parsec is about 3.26 light years or 31 times 10 to 12th power kilometers
- Betelgeuse is current magnitude 0.5 star with luminosity about 100,000 that of the sun
- The sun's apparent magnitude is -26.4
- The moon's apparent magnitude is -12.6
|Supernova Light Curves (Source: www.hyperphysics.phy-astr.gsu.edu)|
So, this back of the envelope calculation, which neglects any light spectrum effects or asymmetric beaming effects, indicates that we wouldn't experience a lot of hurt. For instance, it is not clear if the estimate of luminosity of supernovas includes the energy released as neutrinos. Neutrinos are expected to be the majority of energy released and if that energy if already included in the luminosity estimate, then the amount of visible radiation received here would be much less and overall less impact on us Earthlings. Anyway thanks for triggering the question, Gene!
Ok, after all of that mental gymnastics, we need to get some rest and take it easy. It is still cloudy outside, but the Hyatt Regency Jazz Festival in Newport Beach is going full swing this weekend. So, as you can see, the skies are cloudy
|Can't see stars in the sky, but jazz stars show up on Newport Beach Festival stage (Source: Palmia Observatory)|
Even during the daytime, the skies are still cloudy. In between musical sets and between walking to the bar for refreshments we found an opportunity to have fun and pose in front of one of the signs looking out over the grounds to the harbor beyond.
Our favorite performers included the likes of Morris Day and the Time; Poncho Sanchez; Jeffrey Osborne; Nick Colionne; David Benoit and Mark Antonine. The festival finished up George Benson who eventually got everyone up off their chairs and dancing in the aisles and us ready to return to the observatory to rest up.
|Jazz master George Benson closes out Hyatt Regency Newport Beach Jazz Festival (Source: Palmia Observatory)|