Summary of Work So Far:

Write-up

May 28-June 17

My research so far has focused on calculating the velocities of single M dwarfs and M dwarfs in binary pairs.

This summer I am researching the velocities of close binary pairs. From SDSS, we have spectral data on these binaries for multiple exposures. Because the binary pairs that we’re examining are so close together and moving so quickly, in each exposure taken (which can be over a couple of hours), the binaries may have moved causing its spectrum to be redshifted.Using these SDSS exposures and previously compiled templates for each spectral type, we can actually calculate the velocity of these binary pairs. At this point in my research, I have calculated the velocities of over 4,000 M dwarfs that are in M dwarf and white dwarf binary pairs.

Getting Background Information

For some background information, I read and took notes on Silverstri et al (2005), West et al (2008), West et al (2011), and Hilton et al (2010). Also read the chapter “Stellar Activity” in the Textbook New Light on Dark Stars: Red Dwarfs, Low-Mass stars, Brown Dwarfs by Reid and Hawley. After doing this, I worked on some calculations on deriving velocity from wavelength change (Doppler shifts), and also the relationship between mass, separation, and velocity of binaries.

Calculating the velocities of M dwarfs in DR7 Catalogue

The first velocity calculation included calculating the velocities for the M dwarfs listed in AAW’s DR7 Catalogue. Using Doppler shifting techniques, we are able to calculate the velocities of M dwarfs from their spectra. Each binary is catalogued by plate, mjd, and fiber.Plate is the plug plate used, mjd is the mean julian time, which records the time that the exposure was taken, and fiber is the fiber number. In order to calculate a velocity of one of these dwarfs, we had to match spectral templates to the DR7 spectra. In order to normalize them, we zoomed into a flat area of the spectrum between 7300 and 8800 Angstrom and took the average over that region. We then divided the total flux by that average in order to normalize the spectrum. We did the same for the template spectra. Because there aren’t the same number of data points in the template and the DR7 spectra, we had to use the spline function in order to interpolate points in the DR7 spectra. Because we were going to apply this same process to the binary pairs, we zoomed in on the redder end of the spectrum, between 7300 and 8800 Angstroms. This range was determined to be the optimum range that focused on the redder range without giving up too much data accuracy in the spline process. Using the xcorl function, we were able to calculate the pixel shift between the template and the spectra.In order to convert pixel shift into velocity in units of km/s we multiplied the shift by 69.1.

Calculating the velocities of M dwarfs in dM-WD binaries

The same process was used with calculating the velocities of M dwarfs in M dwarf and white dwarf binary pairs. We first read in Dylan’s file, wddm_goods2.dat in order to get plate, mjd, fiber and template used (and therefore spectral type) for each of the M dwarfs in the binaries.We then matched the spectral types to each of the exposures. Depending on the binary, there were 3-9 exposures of each binary. Using the process described above, we calculated the velocities of the M dwarfs for each exposure. From these calculated velocities, we were able to calculate the expected spectrum Doppler shift; by plotting the image below, we can see how the expected shift (represented by dashed lines), corresponds with the movement in the corresponding exposure.

Estimating the separation between the binaries

The next step was to estimate the separation between the binaries. Using a two-body setup, we are able to calculate the separation, but we have to take into account the fact that the radial velocity of the entire system is also measured in our velocity calculation. To take this into consideration, we have to calculate what the radial velocity of the system is. See equations below:

wrapping up a bit

Things I've done:

- finished write-up

- backed up important files

- figured out velocity calculation so that it takes into account the radial velocity of the entire system.

- replied to summer stipend newletter entry/press release

- said goodbye for a couple weeks!

until then!

separation calculation

Today I worked on a separation calculation for the binaries. Now that we have their velocities, based on spectral type, and making assumptions about their masses, we can estimate the separation between the M dwarf and the WD.

I have a hard time determining what is a reasonable separation between binaries. The only limit that puts it into perspective is Saurav's binaries which are extremely far apart, which means more than 10^13 meters, as given in one of his papers. So if we're smaller than that, we're okay? We'll see.

I toyed around with my first sample before writing out a more automated code. IDL's inability to work with big numbers makes me miss mathematica a little. Ah well.

I've included the SDSS site on the binary I was looking, just to get an idea of 1) how cool the site is (just plug in plate, mjd, fiber and voila!), and 2) see what the spectrum and actual picture looks like.

Super cool!

Dylan reminded me that when looking at spectra to make sure to note if wavelength is in air wavelength -- good reminder, that actually might make the plot I posted yesterday look a little bit better.

Also worked on writing up some quick summaries about my work for KINSC stuff. It's been difficult knowing how much detail I need to put into explaining astronomy jargon and whatnot, but it's been fun. With a little down time today, I read up a little on astrobites, explored astrobetter and read quite a few articles that warned students from entering grad school in astronomy. Let's gooo.

....and it was accurate enough!

Run the entire program for the 4,274 binaries. Ran into a little holdup as I had to reindex some of my lists (had some issues with printf at index 4219), and with some help from Dylan (accidentally deleted original file paths...thought I ruined my whole code, whatevs), I've managed to put it all into a neat file that will not be written over if I decide to run my code again.

I've also outlined what I've done so far this summer, so that I can have it all written down and accounted for. Will work on writing some of that up before I head out.

spectral shifts - check!

This morning, I plotted up a couple of exposures of the same binary to make sure that we can actually see the shift we calculated.

The white spectrum is the 1st exposure of a binary, and the red spectrum is the 3rd exposure of the binary. The time between the two exposures is about 36 minutes! The space between the white and red dotted lines show the calculated shift given our calculated radial velocities. They're a little off, but a shift is definitely there! This means that in half an hour or so between exposures, the binaries were moving quickly enough to cause their spectra to be noticeably shifted.

Waiting to hear Andrew's feedback. Fingers crossed that this is accurate enough...

goals for today:

-convert TAI into something more relatable

-add signal-to-noise ratio to output table

-clean up code and add more comments

-write-up past couple of weeks (at least lay it out)

Went through and finished formatting my code -- it now additionally outputs, # of exposures and exposure time. Changed my range to 7300 to 8800 A, and this allowed me to lower my shift range to 10. Next up, calc signal-to-noise ratio in the flat part of my curve to make sure my velocities aren't too out of whack. Also hope to write up my work for the last couple of weeks in LaTeX (note to self: remember how to do that).

Still haven't run through the entire sample with my velocity calculation code, but I'll do that tomorrow (I think), once I'm sure the kinks are all out.