How distance to black hole mergers is determined;How fast does the eclipse go dark? How many camera pixels to a star? Using 21cm radiation to trace back to the first stars ever

Greetings from Palmia Observatory


Well this week we have some comments on how 21cm radiation is being used to search for the very first stars, but first we need to go over some other fruitful discussions with other astronomers, physicists and wannabes.  So, let's begin with
an email from Math Whiz, Dave, who reminded me of a physics colloquium talk at Caltech.  Well, I didn't drive up to Pasadena, but did check out some of the talk details.  Professor Vicky Kalogera, Northwestern U, talked about the astrophysics associated with mergers of compact objects like black holes and neutron stars.  Her perspective, as one of the first astronomers to join the LIGO Collaboration, back when it was made up only of physicists, provides insight into what we learn about astronomy from the merger detections.  So, from that perspective, I wanted to share one slide that shows how distance to the merger is determined by measurements of the frequency, the chirp frequency, and rate of change of frequency and amplitude of the detected signal.  See below.  Ok, ok, I don't really understand how these formulas work or were derived, but at least you can see how frequency (f) is used to calculate mass and distance.  As you know, determining distance in astronomy is one of the most difficult measurements to do, and here it can be done quite easily.  This brings a major benefit to astronomical measurements and discoveries.  Thanks for reminding me of this talk, Dave!

See, getting distance and mass from chirp frequency is easy! (Source: Vicky Kalogera, Northwestern U)

Next up, I had several discussion with folks about photographing the upcoming solar eclipse in Chile in 2019 and was wondering if I should take a tracking mount or not.  I wanted to take some longer exposures of the background stars near the edge of the blocked out sun, and again sort of pretend to collect some of the same types of solar eclipse images that Eddington had to make in order to measure the bending of light around the sun.  Of course, I know my equipment and capability don't come up to high enough standards to even come close, but it is fun to pretend and learn about some of the issues.

I talked with Physicist, Old Ben, who shared some calculations he had done for the recent 2017 eclipse.  His calculation was not of the Einstein kind, but of the kind that showed how quickly the sky brightness changes as the sun is more and more eclipsed by the moon.  One of the first things you notice during the eclipse is how it seems to take a very long time to get started and then all of a sudden the darkness comes upon you very quickly.  Well, that is exactly what you can see in the following plot where the calculated disk of the sun is eclipsed by the moving disk of the moon.  The sky darkens ever so slowly, and then, it just seems to speed up very quickly.  Pretty neat!  Thanks for that, Ben!

Calculated extinction curve for solar eclipse (Source: Dr. Ben Carter, "Old Ben")

Well, I had discussions with Gravity Guy, Ken, and Moved to the Mountains, David, about various accessories and tradeoffs.  My goal was not to pack any more weight and equipment than absolutely necessary, but the background stars might be quite dim and longer exposures might be necessary to capture them. My little Sky-Watcher polar tracking mount would add somewhere between 5-10 pounds of carry on weight.  Thanks for all the discussion, Ken and David!

The first question to ask is how fast are the background stars moving?  Well if we assume worst case, they are moving at the rotation rate of the Earth, 15 degrees per hour.  How fast will they be moving in my 300mm telephoto image?  Well 15 degrees per hour is the same as 15 arc seconds per second.  Also, the camera field of view is about 2.8 x 4.2 degrees.  The DSLR sensor has 5156 horizontal pixels, so the field of view of each pixel is (4.2 degrees) x (3600 arc seconds per degree) / (5156 pixels) = 2.93 arc seconds per pixel.

So, if the camera exposure time is 1 second, then a point source will move 15 / 2.93 = 5 pixels in that one second.  Now that is not much, but if you were trying to measure how much light showed up from that point source, you would have to sum up all the light received in 5 pixels, not just one and in addition if you were trying to measure the location of that point source, it is now spread out over 5 pixels.  Ok, so that is what could happen just based on ideal optics.  What will happen if you actually try to do this imaging?  Check out this image of the moon and the star Aldebaran, magnitude 0.9, in the upper left hand corner.

Starting image to find how many pixels for Aldebaran (upper left), 300mm, 1/15 second (Source: Palmia Observatory)

Now if we expand and magnify this image, what does Aldebaran look like in terms of actual camera pixels.  Check out the image below.  So even though the exposure time is just barely 1/15 second, the star's image covers multiple pixels using the identified camera and lens.  You can now see that the star image is spread across even more pixels, something like 20 pixels.

Aldebaran in this DSLR, 300mm, 1/15 second, 3200% image (Source: Palmia Observatory)

What happens if we take a longer exposure, say just 1/2 second?  Check out how the star's image blooms out to cover many more pixels.

Aldebaran in this DSLR, 300mm, 1/2 second, 3200% image (Source: Palmia Observatory)

What do we learn from all of this?  For the 1/15 second exposure, we see the star's image is spread over multiple pixels, even though we know for this short exposure the star should have moved less than 1/3 pixel.  So motion is not the issue here, but real performance of the camera and lens is.  But with modern astronomical software, camera images of stars can be analyzed and the centroid of the light, since we know stars are spherical, can be determined to sub pixel values.

How much resolution is needed to see the bending of light rays around the sun?  Well, for a star that just barely grazes the surface of the sun, the gravitational deflection will be just 1.75 arc seconds.  Hmm, it seems if you want to pretend to repeat something like Eddington's observation, you might want a lens with a lot longer focal length, say 2000mm, like my old Celestron 8 inch, where each pixel then corresponds to just 0.44 arc seconds per pixel.

So, in summary, no, I am not taking a tracking mount and I will just enjoy the eclipse and take a few pictures of the corona and maybe diamond ring and just enjoy the eclipse experience!

Finally, last week we mentioned that some additional comments were coming in regards to 21cm radiation and astronomy.  We know that radio astronomers have long made us of 21cm radiation to plot the location and density of atomic hydrogen throughout the universe.  What came as a surprise to me, after trying to catch up on all the magazines and journals that had arrived at the observatory, was how red-shifted 21cm radiation was being used to look all the way back in time to the cosmic dawn; the time of the first stars ever after the big bang.

Just to make sure we are all up to speed on the source of 21cm radiation, refer to the following diagram, which compares the relatively low energy 21cm radiation, here caused by spin flip between the hydrogen nucleus and the electron, and the much higher energy of the Lyman alpha spectrum.

Energy levels for Lyman alpha and spin-flip transitions (Source: Rennan Barkana, 1605.04357v2)

Now we are all familiar with how radio astronomers use various tracer frequencies, like 21cm, to determine where the hydrogen, and various other atoms and molecules, are located and from which they can determine the physical structure of the universe.  All of that is well known, but I had sort of forgotten or whatever that 21cm radiation is expected also to identify the very first stars to turn on after the big bang.  Now this is pretty neat, so you wont be able to see those stars optically, but you will be able to get some indication of them using radio.

So how does this work?  At the time when the first stars turned on, atomic hydrogen was busy emitting and absorbing radiation at 21cm.  Remember if you are more into frequency rather than wavelengths, that 21cm is the same thing as 1420 MHz.  Now as the universe expanded, this signal has been red-shifted until it shows up at our telescopes.  The figure below, taken from Rennan Barkana's referenced paper, shows at what red-shift frequency this signal is expected to show up.

Tying to detect cosmic dawn by observing red-shifted 21cm radiation (Source: Rennan Barkana, 1803.06698v1)

So you can see that the signal is expected to be seen in the 50-100 Mhz frequency range.  At the time this signal was generated at 1420 MHz, the universe was about 20 times smaller, and now we received the signal red-shifted by 20 times.

This is pretty neat stuff also!  So the radio telescopes used to detect this signal have to located in very radio quiet locations on Earth because that frequency range is quite heavily used for ordinary radio communication.  Many radio telescopes, such as the Murchison Wide Field Array in Australia, are being used to make these measurements.  Good luck and we are all waiting for the results!

My question, which I am still trying to resolve, is how this radio signal, in the 50-100 MHz range, can be tied to the red-shifted 21cm original radiation and not be confused with just ordinary astrophysical sources that generate radio waves in this frequency range today.  For instance, all stars, since their light output follows the Planckian black body radiation law, will radiate somewhat at radio frequencies, even though their maximum radiation is in the visible light range.  So what processes do the astronomers go through to filter out all of these other signal generators and be able to home in on just the red-shifted signal?

Until next time,

Resident Astronomer George

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