(no subject)
So my nth postdoc is over--I'm rewriting my statement of teaching philosophy and sending out CVs. Meanwhile, I'm excited to get some time to work on my own research. (While still tinkering with the postdoc project as well.) I've been feeling pretty good this weekend. I have both some more speculative physics ideas to work on, and also the X-ray binary research I've worked on most of my career, which is more familiar to me and easier to direct myself on than the galaxy research I've started.
I'm making some Doppler tomograms for a colleague, and this motivated me to go back to data I still haven't published on the Scorpius X-1 star system. Sco X-1 was the first X-ray binary discovered--it's the brightest persistent X-ray star in the sky. If we had X-ray vision, we'd see this as the brightest in the night sky (except perhaps for some variable stars). It's both close by and intrinsically bright--about 1038 ergs/s is the energy rate of the X-rays, whereas the Sun gives off in visible light several 1033 erg/s, so it's on the order of 100,000 times brighter in X-rays than the Sun in visible light. It's a mysterious "Z source", a neutron star system from which we've never seen the regular pulsations that mark the rotation of the neutron star.
Anyway, the problem with this data was that it was the first observation of this star system in the far ultraviolet, and it turns out that interstellar gas absorbs the spectrum that far in the UV at multiple narrow lines, corresponding to all sorts of different atoms in different stages of ionization, and also molecules in different energies of rotation and vibration.
But when you're working on your own you can afford to be a hero. So I'm trying to go through and identify all of the lines in the spectrum that were eating up the spectrum. It was quite severe: there are two bright lines from the star system itself, emission lines, that I wanted to see in this observation. However, the absorption was so severe that only one of them could be seen! And one of my scientific goals was determining the ratio between the two lines!
But I'm impressed by how much I can reconstruct of what's going on by meticulous attention to the interstellar absorption. I can probably do better, but this is a major start.
Below I'm showing only a small portion of the spectrum--it goes from 912 Angstroms (the lyman limit: this wavelength corresponds to the energy needed to take the lowest energy level of an electron in hydrogen and break it free of the atom--below this wavelength, you don't see much through normal amounts of interstellar gas until you get to wavelengths smaller than a hydrogen atom. It goes from 912 Angstroms out to 1180 Angstroms or so, where the Hubble Space Telescope picks up. I helped a couple of my ex-supervisors with Hubble observations of Sco X-1 that looked at the spectrum from 1200 to 1700 Angstroms or so.
One thing that was neat was that I was able to take the model for the continuum from the proposal I had written to get the FUSE observations of Sco X-1, based on our model of the Hubble observations--and what I wrote in the proposal matched almost perfectly with the actual data! The lines didn't match nearly as well, but the continuum did--although I am wondering whether I just got lucky. There's uncertainty in how much the interstellar gas reddened the spectrum, and I may be able to get a better handle on that.
What's going on here? The spectrum shows brightness (flux) on the y axis and the wavelength on the x axis. The jagged black curve is the actual data, averaged over 15 sub-observations. The red curve is my model--based on (1) the model for the continuum from the proposal, (2) a model for the emission lines (quintuply ionized Oxygen) as a Voigt profile (convolution of gaussian and lorenztian shapes--look up the defs in Wikipedia), with the ratio between the two lines as a free parameter, (3) absorption lines at known wavelengths from Silicon, Carbon, and Oxygen, and very deep absorption from Hydrogen ("lyman beta")--also absorption from H2, molecular hydrogen. The absorption lines are marked on the top of the graph with a little line and the name of the absorption--if it's from molecular Hydrogen I also mark the rotational level (j=0 to j=5). The smooth black curve shows my model (just continuum and Oxygen emission lines) without any of the absorption in the way.
You can see I was able to reconstruct the ratio between the two Oxygen lines!
Also, I mentioned that this is actually the sum of 15 sub-observations. I was able to measure the Doppler shift of the emission lines in each sub-observation. This tells us the velocity towards or away from us of the gas that gives off the emission lines. The observations were planned to cover the entire orbit of the star system, which lasts I think about 0.7 days. In the plot below I show my measurements with * and with a sine curve and a line I show what other researchers independently think are the expected motion of the neutron star and the velocity of the star system as a whole (it's "systemic velocity").
I think most of the observations previously had only identified emission lines from the normal star--these would be, based on the velocity, from the accretion disk surrounding the neutron star. Optical helium lines seem to move similar to these Oxygen lines, but with a phase shift.
Note that the alignment isn't perfect--it could be that I need to calibrate the zero velocity better. I will have to do that based on some of the interstellar lines. Right now I've only grouped the data to be accurate to about 15 km/s. It's also possible that the accretion disk isn't perfectly symmetric and may emit more from one side or the other. It's possible there is some emission from the normal star along with the accretion disk. Perhaps my empirical model of Voigt profile is not so good--I could make a double-peaked accretion disk model, broadened by turbulence instead.
So this might help constrain the mass of the neutron star better. Also, I want to make Doppler tomograms to see if we could map out structure in the disk. It will depend on my accurately finding the zero velocity. But also being able to correct for this multitude of interstellar lines is important.
Anyway, it's time to go to bed. I'm also excited to be reading a paper by Ted Jacobson on the Feynman checkerboard (old paper from 1984). It's much more sophisticated in regards to the physics than the other papers I've been working from. It's distinguished in several ways from what I'm doing; one is that he's not using a lattice--he's allowing one special dimension to be the spin axis/particle travel dimension, and then assumes the particle scatters randomly in the next step, defining the next special direction.
I'm making some Doppler tomograms for a colleague, and this motivated me to go back to data I still haven't published on the Scorpius X-1 star system. Sco X-1 was the first X-ray binary discovered--it's the brightest persistent X-ray star in the sky. If we had X-ray vision, we'd see this as the brightest in the night sky (except perhaps for some variable stars). It's both close by and intrinsically bright--about 1038 ergs/s is the energy rate of the X-rays, whereas the Sun gives off in visible light several 1033 erg/s, so it's on the order of 100,000 times brighter in X-rays than the Sun in visible light. It's a mysterious "Z source", a neutron star system from which we've never seen the regular pulsations that mark the rotation of the neutron star.
Anyway, the problem with this data was that it was the first observation of this star system in the far ultraviolet, and it turns out that interstellar gas absorbs the spectrum that far in the UV at multiple narrow lines, corresponding to all sorts of different atoms in different stages of ionization, and also molecules in different energies of rotation and vibration.
But when you're working on your own you can afford to be a hero. So I'm trying to go through and identify all of the lines in the spectrum that were eating up the spectrum. It was quite severe: there are two bright lines from the star system itself, emission lines, that I wanted to see in this observation. However, the absorption was so severe that only one of them could be seen! And one of my scientific goals was determining the ratio between the two lines!
But I'm impressed by how much I can reconstruct of what's going on by meticulous attention to the interstellar absorption. I can probably do better, but this is a major start.
Below I'm showing only a small portion of the spectrum--it goes from 912 Angstroms (the lyman limit: this wavelength corresponds to the energy needed to take the lowest energy level of an electron in hydrogen and break it free of the atom--below this wavelength, you don't see much through normal amounts of interstellar gas until you get to wavelengths smaller than a hydrogen atom. It goes from 912 Angstroms out to 1180 Angstroms or so, where the Hubble Space Telescope picks up. I helped a couple of my ex-supervisors with Hubble observations of Sco X-1 that looked at the spectrum from 1200 to 1700 Angstroms or so.
One thing that was neat was that I was able to take the model for the continuum from the proposal I had written to get the FUSE observations of Sco X-1, based on our model of the Hubble observations--and what I wrote in the proposal matched almost perfectly with the actual data! The lines didn't match nearly as well, but the continuum did--although I am wondering whether I just got lucky. There's uncertainty in how much the interstellar gas reddened the spectrum, and I may be able to get a better handle on that.
What's going on here? The spectrum shows brightness (flux) on the y axis and the wavelength on the x axis. The jagged black curve is the actual data, averaged over 15 sub-observations. The red curve is my model--based on (1) the model for the continuum from the proposal, (2) a model for the emission lines (quintuply ionized Oxygen) as a Voigt profile (convolution of gaussian and lorenztian shapes--look up the defs in Wikipedia), with the ratio between the two lines as a free parameter, (3) absorption lines at known wavelengths from Silicon, Carbon, and Oxygen, and very deep absorption from Hydrogen ("lyman beta")--also absorption from H2, molecular hydrogen. The absorption lines are marked on the top of the graph with a little line and the name of the absorption--if it's from molecular Hydrogen I also mark the rotational level (j=0 to j=5). The smooth black curve shows my model (just continuum and Oxygen emission lines) without any of the absorption in the way.
You can see I was able to reconstruct the ratio between the two Oxygen lines!
Also, I mentioned that this is actually the sum of 15 sub-observations. I was able to measure the Doppler shift of the emission lines in each sub-observation. This tells us the velocity towards or away from us of the gas that gives off the emission lines. The observations were planned to cover the entire orbit of the star system, which lasts I think about 0.7 days. In the plot below I show my measurements with * and with a sine curve and a line I show what other researchers independently think are the expected motion of the neutron star and the velocity of the star system as a whole (it's "systemic velocity").
I think most of the observations previously had only identified emission lines from the normal star--these would be, based on the velocity, from the accretion disk surrounding the neutron star. Optical helium lines seem to move similar to these Oxygen lines, but with a phase shift.
Note that the alignment isn't perfect--it could be that I need to calibrate the zero velocity better. I will have to do that based on some of the interstellar lines. Right now I've only grouped the data to be accurate to about 15 km/s. It's also possible that the accretion disk isn't perfectly symmetric and may emit more from one side or the other. It's possible there is some emission from the normal star along with the accretion disk. Perhaps my empirical model of Voigt profile is not so good--I could make a double-peaked accretion disk model, broadened by turbulence instead.
So this might help constrain the mass of the neutron star better. Also, I want to make Doppler tomograms to see if we could map out structure in the disk. It will depend on my accurately finding the zero velocity. But also being able to correct for this multitude of interstellar lines is important.
Anyway, it's time to go to bed. I'm also excited to be reading a paper by Ted Jacobson on the Feynman checkerboard (old paper from 1984). It's much more sophisticated in regards to the physics than the other papers I've been working from. It's distinguished in several ways from what I'm doing; one is that he's not using a lattice--he's allowing one special dimension to be the spin axis/particle travel dimension, and then assumes the particle scatters randomly in the next step, defining the next special direction.