Measuring Radial Velocities of Low
Mass Eclipsing Binaries
Rebecca E. Rattray
Vanderbilt University
Senior Honors Thesis
Submitted to the Faculty of the
Department of Physics and Astronomy
of Vanderbilt University
In partial fulfillment of the requirements for
Departmental Honors in Astronomy
May 2011
Advisor:
Keivan G. Stassun
Honors Thesis Committee:
Andreas Berlind
Richard Haglund
David Weintraub
Abstract
Due to the complex nature of the spectra of low-mass M type stars, it is difficult to
determine their metallicities and temperatures directly. By studying eclipsing binary pairs
comprising one F, G, or K type star with an M type star, we are able to use what we know
about the primary star to learn more about the secondary star. Measuring the orbital reflex
motion of the primary star, together with the eclipse light curve of the M star as it transits
the primary star, allows us to determine the mass, radius, temperature, and metallicity of
the M star.
We studied 23 low mass eclipsing binaries (EBLMs) previously discovered by
SuperWASP photometry. We obtained spectra using the Cerro Tololo Inter-American
Observatory (CTIO) SMARTS 1.5-meter echelle spectrograph between June 2009 and
January 2011. Each EBLM target was typically observed ~8 times over this time period.
The spectra were processed using standard astronomical software, and a cross-correlation
method was used to measure the radial velocity of the target star at each observed epoch.
Radial velocities were successfully determined for 21 of the 23 EBLM target
objects. Orbital periods, radial velocity amplitudes, and eccentricities for these EBLMs
could be determined from these radial velocities together with the preexisting light curves.
Using these values and by assuming a mass for the primary star, we will be able to
calculate the masses of the secondary M type star in each EBLM system.
I.
Introduction
The main goals of this research were to determine radial velocities of F/G/K + M
eclipsing binary stellar systems in order to study the orbits of the systems. M type stars are
the most common class of star (with masses of 0.1 – 0.4 Msolar), but these stars are also the
most difficult for which to obtain accurate measurements. Due to this, the mass-radius
relationship currently used for M stars is not very accurate, which leads to discrepancies in
stellar evolution models. By studying F/G/K + M eclipsing binaries, also called low mass
eclipsing binaries or EBLMs, we can obtain a more accurate mass-radius relationship for M
stars in these systems, which can then be applied to M stars in general, leading to more
accurate stellar evolution models (Hebb et al 2007; Stassun et al 2006).
The cooler temperature of M type stars allows for the presence of molecules on the
stars, which make their spectra very complex. This makes the metallicity and temperature
of this class of star very difficult to measure directly. However, the simpler spectra of F, G,
and K type stars make their metallicities and temperatures possible to accurately determine
directly. Therefore, studying pairs of an M star with an F, G, or K type star is beneficial
because it allows us to determine properties like metallicity for the M star, because we can
assume that the stars have the same metallicity, so we get the metallicity for the M star
from studying the primary star.
Eclipsing binaries are classical two-body systems where two stars orbit each other
around a center of mass. In addition, the orientation of the orbit is such that the stars
2
repeatedly eclipse one another at periodic intervals through their orbit. Thus, the masses
and radii of the two stars in the binary can be derived by modeling the line-of-sight
(radial) velocity curves of the binary components combined with the photometric
brightness variations of the system (due to the eclipses) throughout an orbit. Combining
radial velocity curves with photometric light curves of eclipsing binaries can lead to
determining important properties of the stars, such as masses, radii, the period, eccentricity,
and inclination of the orbit, and the temperature ratio of the two stars. Eclipsing binaries
are extremely useful because they can lead to the calculation of these properties using
accurate direct measurements (Stassun et al 2004; Hebb et al 2010).
The study sample is 23 F/G/K + M eclipsing binaries discovered by SuperWASP, a
program that uses photometry to detect transiting extrasolar planets (Pollaceo et al 2006).
Because these EBLMs were discovered by SuperWASP, good light curves for each EBLM
already exist. Radial velocity measurements from spectra are needed to use in combination
with the photometry to determine orbital parameters and masses for these objects. The
specific goals of this research project were to reduce the raw spectra into usable spectra,
and to calculate radial velocities for EBLMs 1-23 using the reduced data.
II.
Data and Methods
II.A. Data
Research was conducted using spectra taken at the Cerro Tololo Inter-American
Observatory (CTIO) SMARTS 1.5 meter echelle spectrograph between June 2009 and
January 2010. The instrument has a fixed cross-disperser with 266 lines per millimeter.
We used a slit size of 130 m for our observations, with a spectral resolving power of
30,000. At this resolving power we expect to obtain radial velocity precision of ~0.5 km/s
(Hebb et al 2010). The range of wavelengths observable by the instrument is 4020-7300
Angstroms, with each order including 150 Angstroms.
Each night that an object was to be observed, a thorium-argon comparison spectrum
was taken before the science exposures. The ThAr calibration files are used to determine
wavelength calibration, mapping each pixel position into a wavelength. Ideally, three
science exposures were taken for each object each night it was observed in order to median
combine the exposures and remove cosmic rays. Each EBLM target was observed at five
to nine different epochs allowing the orbital parameters to be derived.
II.B. Methods
II.B.1. Data Reduction
The first step was to take the raw images from the telescope and reduce them to a
format from which I could calculate the radial velocities. Although my advisor, Dr.
Stassun, has developed a pipeline in IDL that automates this process, I first reduced some
of the data by hand using Image Reduction and Analysis Facility (IRAF) so that I could
understand the process fully.
3
The data that are obtained from the telescope are sorted into folders by observation
date. Within each folder are bias images, flat images, and target images. An example of
the raw target spectra can be seen in Figure 1.
Figure 1. Raw target spectra before data reduction process. The horizontal white lines are the separate orders
of the spectrum. The telescope uses two CCD detectors, resulting in different bias levels, which is due to the
difference in electronics between the two halves of the image.
For the first few steps of the reduction process, it is necessary to treat the two halves
of the image separately, so I first used the imcopy command to divide all images for a
given observation date into two parts and created folders called “chip1” and “chip2.” The
left side of each image was in folder chip1, and the right side of image was in folder chip2.
Within the chip1 folder, I made a list of all bias images and used the zerocombine
command to create one master bias image. Bias images are taken at the telescope with the
shutter closed. There should be no light collected during these exposures, so any signal we
know to be an inherent bias level of the device. We are then able to subtract out this bias
level from the rest of the images. I then used ccdproc’s overscan and trim functions to
eliminate the excess area on the images that do not include data. The excess area was
determined from the image headers listed as “BIASSEC” and “TRIMSEC.” I also used
ccdproc to apply the zero level correction, using the master bias image created earlier using
zerocombine. I then performed these same steps on the half-images in folder chip2.
The next step was to recombine the halves of the images to create one image and to
proceed with the rest of the data reduction working with just one combined image. To do
this, I multiplied the original whole images by zero using imarith, in order to produce a
blank image of the correct size to correspond with each image. I then used imcopy to copy
the two halves of each image into the new blank image. The rest of the data reduction steps
therefore had to be applied only once to each image, instead of once for each half.
I used apflatten to create a normalized flat from the master flat image. Flat images
are taken while pointing the telescope at a uniformly illuminated surface in order to
determine the difference in sensitivity of the pixels on the device. I then used apall to
extract the orders. For the wavelength calibration, I used a template produced by a former
student that included apertures 21-62 but not apertures 1-20. I attempted to use thoriumargon maps to identify features for the rest of the spectrum, but was unsuccessful, so I was
only able to use apertures 21-62 in the rest of the data reduction procedure.
I used scopy to renumber the aperture numbers so they began at 1 instead of 21. I
then used ecreidentify using a pre-existing reference spectrum to identify features in the
4
spectrum. I used refspec and dispcor to finish the wavelength calibration and complete the
data reduction. On every reduced set of data, I checked that the hydrogen-alpha feature
was at 6562 Angstroms, to ensure that the data reduction had been done correctly.
Once I was comfortable with the methods of data reduction, I used the data
reduction IDL pipeline to reduce all of the data. Before running the pipeline, it is important
to check that the IMAGETYP header keywords are correct for each image. The bias
images should have keyword BIAS, flats should have keyword PROJECTOR FLAT, arcs
should have keyword COMPARISON, and science targets should have keyword OBJECT.
These are usually not correctly set to begin with, so I changed them using the hedit
command.
For some of the data sets, for a given object, there was one thorium-argon exposure
and then two target exposures. In this case, it was necessary to copy the thorium-argon and
create a new object set, and then move the second target exposure to accompany the new
thorium-argon. As an example, say that for a given object, there is a thorium-argon
exposure named echelle091104.4101 and two target exposures named echelle091104.4102
and echelle091104.4103. In this case, I would copy echelle091104.4101 and make an
additional thorium-argon exposure named echelle091104.4601, then I would rename
echelle091104.4103 as echelle091104.4602. This step was not necessary for object sets
where there was one thorium-argon and one target exposure, or for object sets where there
was one thorium-argon and three target exposures. Three target exposures is ideal because
the pipeline, in order to eliminate bright pixels due to cosmic rays, takes the median value
of each pixel to produce the final image for that observation date. With only two
exposures, it is impossible to take the median, so cosmic ray clipping is not possible, which
creates issues during the fxcor process.
Next I opened IDL and ran the pipeline, which reduced all of the data for one
observation date. After the pipeline was finished running, it was necessary to renumber the
aperture numbers so that the hydrogen-alpha feature was in aperture number 65. This way
I could be sure that the same wavelengths always corresponded to the same aperture
numbers, regardless of observation date or object. I did this in IDL by using the
plot_smarts_spectra command to determine which aperture contained the hydrogen-alpha
feature originally, then using the write_smarts_spectra command to renumber the apertures.
The write_smarts_spectra command also renames the files to include the object name and
observation date (including a midexposure timestamp computed during the pipeline
process), and moves them to the library folder where all of the final reduced spectra are
located.
At this point, the data have progressed from the single image seen in Figure 1 to a
collection of spectra, one for each order. An example of what one of these orders looks
like can be seen in Figure 2.
5
Figure 2. One order of a reduced spectrum, showing the hydrogen-alpha feature at 6562 Angstroms
This particular order is number 65, so it contains the hydrogen-alpha feature at 6562
Angstroms.
Below is a table showing each EBLM target object and the timestamps for each
observation of that object.
EBLM1
EBLM2
EBLM3
2009-10-08T09:03:32.20
2009-10-14T08:34:42.60
2009-10-21T08:30:02.37
2009-12-01T06:39:11.75
2010-01-11T03:43:40.77
2010-01-17T05:13:52.71
2010-01-30T05:26:31.36
2009-08-26T06:29:56.40
2009-09-01T04:45:56.50
2009-09-10T04:42:33.40
2009-09-19T05:09:32.40
2009-09-29T03:12:13.78
2009-08-26T05:56:08.35
2009-09-01T05:18:34.40
6
EBLM4
EBLM5
EBLM6
EBLM7
EBLM8
EBLM9
EBLM10
2009-09-15T04:10:43.95
2009-09-29T02:37:47.37
2009-10-21T01:30:14.91
2009-08-26T07:02:03.45
2009-09-01T05:50:33.10
2009-09-19T05:41:24.35
2009-09-29T03:42:22.84
2009-10-14T02:43:20.25
2009-10-21T02:49:49.09
2009-12-01T01:01:01.55
2010-01-11T01:06:01.61
2009-08-26T05:15:10.45
2009-09-01T04:17:51.25
2009-09-19T03:53:56.80
2009-09-29T01:59:14.03
2009-10-21T00:52:15.99
2010-02-27T02:42:49.13
2010-03-15T02:17:39.13
2010-03-23T00:58:53.80
2010-03-23T01:34:27.84
2010-03-29T01:44:37.14
2010-04-05T01:41:28.65
2010-04-20T00:54:47.49
2010-02-04T06:14:45.48
2010-02-10T04:40:48.80
2010-02-14T02:40:56.53
2010-02-16T05:11:46.13
2010-03-15T02:51:46.13
2010-04-05T02:16:30.70
2010-04-20T01:28:53.99
2010-05-23T06:18:17.89
2010-06-01T07:23:26.94
2010-06-07T07:07:37.24
2010-06-09T06:47:17.74
2010-06-17T03:19:33.24
2010-06-30T02:42:19.29
2010-07-16T03:27:41.79
2010-02-10T05:30:31.45
2010-03-04T03:43:03.64
2010-03-23T03:06:37.16
2010-03-29T03:09:51.17
2010-04-07T01:33:49.17
2010-05-11T00:29:24.51
2010-05-19T00:12:38.01
2010-06-01T00:00:03.96
2010-08-01T07:08:51.61
7
EBLM11
EBLM13
EBLM15
EBLM16
EBLM17
EBLM18
2010-08-21T05:04:46.60
2010-08-28T05:08:59.05
2010-09-07T01:19:20.60
2010-09-15T02:54:13.90
2010-09-29T00:05:57.40
2010-08-01T08:09:20.09
2010-08-21T06:40:30.54
2010-09-06T02:22:30.59
2010-09-15T05:22:32.96
2010-09-29T02:46:01.84
2010-10-08T02:27:12.39
2010-08-06T08:16:25.69
2010-08-22T06:40:57.68
2010-09-05T05:51:41.98
2010-09-06T05:20:14.09
2010-09-15T07:08:08.78
2010-09-29T04:33:18.83
2010-10-08T04:24:40.83
2010-10-31T01:58:34.33
2010-08-28T09:48:25.04
2010-09-06T07:23:13.10
2010-09-29T08:19:47.89
2010-10-08T07:53:33.39
2010-10-21T05:23:57.89
2010-11-10T02:55:25.69
2010-11-29T02:22:35.14
2010-12-08T01:50:39.68
2010-09-07T06:51:22.04
2010-10-08T08:45:16.89
2010-10-21T06:19:01.84
2010-11-19T02:57:52.19
2010-12-08T02:54:18.68
2010-12-10T02:40:05.14
2010-12-18T02:31:33.18
2010-09-07T07:49:37.10
2010-10-21T07:16:35.35
2010-10-31T04:56:42.10
2010-11-29T03:20:38.69
2010-12-02T04:38:42.65
2010-12-08T03:55:13.20
2010-12-17T02:23:08.70
2010-09-06T08:26:57.04
2010-10-31T05:52:13.63
2010-11-10T04:35:21.63
2010-12-04T01:56:33.18
2010-12-08T04:58:52.12
8
EBLM19
EBLM20
EBLM21
EBLM22
EBLM23
2010-12-10T03:28:58.67
2010-12-22T02:07:31.97
2011-01-02T02:23:39.47
2010-11-14T06:12:27.69
2010-11-17T04:39:28.27
2010-11-19T04:44:58.69
2010-11-29T06:10:54.69
2010-12-01T06:07:56.14
2010-12-04T03:33:26.69
2010-12-10T06:14:57.15
2010-12-22T05:31:44.94
2010-11-14T07:02:06.18
2010-11-19T05:43:36.18
2010-11-25T07:27:05.18
2010-11-29T07:01:09.13
2010-12-04T04:24:27.68
2010-12-11T04:57:26.68
2010-12-17T04:46:15.68
2010-12-19T05:33:35.18
2010-12-22T06:23:37.97
2010-12-01T07:42:07.67
2010-12-04T08:54:55.82
2010-12-04T09:05:23.68
2010-12-08T08:06:52.18
2010-12-11T06:27:49.18
2010-12-17T07:01:53.17
2010-12-19T06:14:27.68
2010-12-24T06:25:05.92
2011-01-07T06:05:15.97
2010-12-02T05:54:18.12
2010-12-11T05:33:44.18
2010-12-19T07:00:10.68
2010-12-24T04:41:58.93
2010-12-27T06:06:17.97
2010-12-28T06:37:42.42
2011-01-02T06;00:07.97
2011-01-07T04:25:50.92
2010-12-11T07:18:21.69
2010-12-19T07:51:53.69
2010-12-24T05:35:03.44
2011-01-02T07:12:46.94
2011-01-07T05:15:17.44
9
II.B.2. Radial Velocity Measurements
In the library folder mentioned above, I made a list for each target object consisting
of all observations of that object. I then copied all of the target object spectra and the list
file into a directory for just that target object, outside of the library folder. I also copied the
template file for the radial velocity standard that I used into this folder.
Inside this folder, I ran a program named mk_fxcorin.pl which Dr. Leslie Hebb
wrote. This program takes the reduced spectra and puts them in files which are ready to be
run through the fxcor command in IRAF to calculate radial velocities. There is one file for
each observation date, and each file contains the separate spectra for each order. The
program also created a set of temporary files which correspond to the observation dates but
include only orders 47-53. I determined that these orders typically had strong features
which fxcor was correctly able to identify, therefore producing correct radial velocities, so I
began the fxcor process for each observation date by running fxcor on these orders to get a
feel for what range of radial velocities I should look for in the rest of the orders.
Once I knew what radial velocities to look for, I ran fxcor on all of the orders for
that observation date. Fxcor is a cross-correlation program that compares target spectra
with template spectra (the template object is an object for which the radial velocity is
already well known) and calculates the pixel shift between each pair of spectra. It then
converts the pixel shift to a wavelength shift, and uses the Doppler formula,  = 0(1+v/c),
to calculate the radial velocity of the target object. The template object that I used for all of
my calculations was HD1461. For each order, I looked at the feature that fxcor chose to
compare to the template for calculation of the radial velocity. In general, fxcor found the
correct feature and calculated the correct radial velocity. Examples of fxcor fitting the
correct peak can be found in Figure 3 and Figure 4.
10
Figure 3. Example of the fxcor process working correctly.
11
Figure 4. Example of the fxcor process working correctly.
There were also instances when fxcor fit the incorrect feature, but the correct
feature was easily apparent. In these instances, I manually fit a Gaussian to the correct
peak by lining up the red bar to the left of the peak and pressing “g,” and then lining up the
red bar to the right of the peak and pressing “g.” This allowed me to manually it the
correct peak in order to calculate the correct radial velocity. An example of fxcor fitting
the incorrect peak and then my manual fitting of the correct peak can be seen in Figure 5
and Figure 6 respectively.
12
Figure 5. Example of fxcor fitting the wrong feature
Figure 6. Example of manually fitting the correct feature in fxcor.
13
There were some orders for which fxcor fit an incorrect peak but there was too
much noise to distinguish the correct peak, probably caused by a cosmic ray or other defect
in the target spectrum, or fxcor could not find a peak at all and there was too much noise to
distinguish the correct peak. In both of these instances I did not record a radial velocity
and skipped to the next order. Examples of these instances can be seen in Figure 7 and
Figure 8.
Figure 7. Example of fxcor fitting the incorrect feature, but the correct feature is not easily visible.
14
Figure 8. Example of fxcor being unable to fit a peak to any feature.
Once the fxcor process was completed, I used a program that Dr. Leslie Hebb and I
created together called read_fxcor.pl to collect the important output data from the fxcor
process and put it in a format that can be easily read by IDL. I then used an IDL program
that Dr. Hebb wrote called get_rv_vals.pro in order to calculate the weighted radial velocity
mean for each object for each observation date. The program also outputted a graph for
each object for each observation date that shows the radial velocity measurements and
errors for each individual order. An example of these graphs can be seen in Figure 9, and
all of these individual radial velocity graphs can be found in Appendix A.
15
Figure 9. Example of radial velocity measurements for one object for one observation date. Each data
point corresponds to the radial velocity measurement for one order. The x-axis represents order number
and the y-axis represents radial velocity in units of km/s. The horizontal line through the data points
represents the mean radial velocity for this observation date. The mean radial velocity is also written at the
top of the graph.
III.
Results
I was able to calculate radial velocities for almost all of the target objects, however
there were some objects for which I encountered problems.
For EBLM2, most of the orders had too much noise to be able to distinguish any
specific features in the cross-correlation procedure. However, orders 42, 43, 55, 56, 65,
and 66 had strong enough features that I was able to get radial velocity measurements, so I
only made radial velocities for these orders.
EBLM4 had too much noise to be able to calculate radial velocities for three of the
observation dates, but there were five other observation dates for which I was able to
calculate radial velocities for most of the orders.
The processing of EBLM11 went smoothly with the exception of the fourth
observation date. For this date it was impossible to distinguish features from noise in the
spectra, so I did not calculate radial velocities for the fourth observation date.
I was unable to calculate any radial velocities at all for EBLM12. For most of the
spectra there were two equally strong features visible, so it was impossible to determine
which feature would give the correct radial velocity measurement. This may be a possible
spectroscopic binary, which could indicate that we see light from the M star.
16
The spectra for EBLM14 all had too much noise to be able to calculate radial
velocities. No measurements were made for this object.
The mean radial velocities and errors for each object on each observation date can
be found in the following table. For radial velocity plots for each observation date for each
target object showing the individual measurements for each order, see Appendix A.
Julian Date
5112.877120
5118.857690
5125.855140
5166.781620
5207.660310
5213.723590
5226.732040
Mean RV
Error
(km/s)
(km/s)
24.1
181.9
24.4
48.0
57.1
55.1
22.7
EBLM2
5069.775670
5075.703210
5084.700400
5093.718580
5103.636410
-6.2
-48.6
23.8
-46.8
-0.5
1.7
17.8
14.6
4.8
15.7
EBLM3
5069.752370
5075.726250
5089.678850
5093.695390
5103.613750
5125.565500
27.4
42.3
44.0
49.2
22.3
35.2
0.6
0.7
0.7
1.2
1.0
0.8
EBLM4
5093.741160
5103.658060
5125.620220
5166.541500
5207.542230
23.9
9.5
8.9
36.5
-8.8
1.4
1.5
2.2
3.5
9.1
EBLM5
5069.723680
5075.683720
5093.666360
5103.586120
5125.538020
-50.9
-51.4
-48.4
-29.7
-48.7
1.2
1.5
1.7
4.9
1.6
EBLM1
0.4
5.3
0.8
0.3
0.4
0.7
1.7
17
EBLM6
5254.616860
5270.599980
5278.545470
5278.570170
5284.577290
5291.575140
5306.542660
47.0
27.6
48.4
31.5
68.1
15.1
31.7
1.2
0.3
0.3
0.3
1.6
0.3
0.2
EBLM7
5231.762070
5237.697280
5241.614320
5243.718700
5270.623470
5291.599530
5306.566490
38.6
31.3
41.6
28.6
29.1
31.7
43.7
0.3
0.2
0.3
0.2
0.4
0.3
0.2
EBLM8
5339.768350
5348.813490
5354.802360
5356.788190
5364.643640
5377.617120
5393.647530
12.1
39.0
7.0
48.0
44.7
10.4
31.1
2.0
1.0
2.4
1.0
0.4
0.8
1.3
EBLM9
5237.731750
5259.658550
5278.634070
5284.636480
5293.569940
5327.524760
5335.512790
5348.503380
-6.1
9.56
-8.2
-4.5
19.6
-9.5
-1.8
18.3
0.4
0.5
0.6
0.2
0.3
0.4
0.4
1.1
EBLM10
5409.802990
5429.716170
5436.718740
5446.558680
5454.624010
5468.506060
-46.4
-62.9
-59.4
-39.1
-63.5
-39.3
0.3
0.3
0.3
0.7
0.3
0.3
18
EBLM11
5409.844940
5429.783730
5445.604490
5454.729300
5468.620020
5477.606430
-52.4
-50.1
-52.9
-8.1
-48.7
-49.0
0.6
0.4
0.3
25.5
0.3
0.5
EBLM13
5414.848730
5430.783320
5444.749590
5445.727770
5454.802850
5468.695290
5477.689100
5500.586590
-5.9
11.8
-5.4
11.9
10.0
-4.1
26.5
28.8
0.2
0.3
0.3
0.4
0.6
0.4
0.6
0.4
EBLM15
5436.909630
5445.809550
5468.850560
5477.832870
5490.729590
5510.626901
5529.603980
5538.581560
73.6
89.4
49.8
81.3
89.4
79.7
37.8
61.0
0.6
0.7
1.2
4.0
1.0
0.7
1.2
1.3
EBLM16
5446.787490
5477.868500
5490.767440
5519.628100
5538.625230
5540.615280
5548.609030
20.0
22.5
29.2
0.6
30.5
21.5
23.5
0.6
0.5
0.3
0.3
0.3
0.2
0.2
EBLM17
5446.827780
5490.808020
5500.711270
5529.644780
5532.668570
5538.668570
5547.604280
-20.5
-26.4
-33.8
-14.7
-36.1
-22.7
-42.2
1.2
0.5
0.5
0.3
0.3
0.5
0.4
19
EBLM18
5445.852080
5500.746810
5510.693660
5534.583620
5538.710220
5540.647790
5549.678380
5552.591120
5563.602120
59.5
53.3
79.8
40.3
50.3
61.9
52.9
37.2
36.5
1.0
0.6
0.9
0.5
0.8
0.6
0.5
0.6
0.7
EBLM19
5514.761020
5517.696590
5519.700510
5529.760620
5531.758620
5534.651440
5540.763780
5552.734030
59.6
57.8
60.5
59.1
60.1
52.8
60.1
58.4
0.7
2.6
1.1
0.7
2.1
1.9
0.7
0.8
EBLM20
5514.795210
5519.740940
5525.813090
5529.795250
5534.686630
5541.709770
5547.702170
5549.735080
5552.769900
103.4
32.5
79.8
67.2
93.0
60.0
97.2
82.5
120.0
1.1
1.5
1.3
0.7
0.7
0.6
0.5
0.7
0.6
EBLM21
5531.821510
5534.872350
5534.879620
5538.839340
5541.770830
5547.795020
5549.762260
5554.770060
5568.757350
1.5
-6.8
-4.3
61.3
-32.0
-6.9
58.2
62.5
-29.6
0.3
0.9
2.1
0.4
0.4
0.4
0.3
0.6
0.2
EBLM22
5532.745140
5541.731400
-0.6
-1.6
0.9
0.8
20
EBLM23
5549.791910
5554.696240
5557.754980
5558.776850
5563.751050
5568.685860
-2.6
53.5
-2.2
3.5
37.0
24.6
1.1
0.5
0.4
0.5
0.6
0.6
5541.804920
5549.828870
5554.734240
5563.802800
5568.721570
37.9
79.1
85.5
48.3
37.1
0.6
0.5
0.8
0.7
0.6
The following is a table that includes each EBLM target, the number of good radial
velocities measured for each target, and any notes regarding that object.
Name
EBLM1
EBLM2
EBLM3
EBLM4
EBLM5
EBLM6
EBLM7
EBLM8
EBLM9
EBLM10
EBLM11
EBLM13
EBLM15
EBLM16
EBLM17
EBLM18
EBLM19
EBLM20
EBLM21
EBLM22
EBLM23
# data points
notes
7
5
1 bad point
6
5
5
7
1 bad point
7
7
8
6
5
not variable?
8
8
7
7
9
8
not variable?
9
8
7
two peaks?
5
21
IV.
Discussion and Conclusions
Once I had measured the radial velocities for 21 target objects, these could be used
in combination with preexisting light curves for these objects to determine the orbital
period of the objects. Below, for each EBLM object is one figure showing both the
discovery and follow-up photometry for the object, and one figure showing the phasefolded radial velocity plots. These figures were produced by Dr. Leslie Hebb based on my
radial velocity calculations as well as some preexisting radial velocity data.
For most target objects, the radial velocity measurements phase very well with the
photometry. We expect the relative zero-velocity crossing to coincide with the eclipse,
since the radial velocity of zero must occur during the eclipse of each system, and this is
observed in almost every case. Notable exceptions include EBLM11 and EBLM19. More
research must be conducted to determine why this is, but we can speculate that these were
perhaps false eclipsing binary detections, or that maybe the M star is actually a low mass
companion, such as a brown dwarf, which would cause the radial velocity variation of the
primary star to be very slight.
The product of these radial velocity measurements is more exact knowledge of the
orbital periods, radial velocity amplitude (K1), and eccentricity for these 21 EBLM
objects. This information can be used to determine the masses of the M-type stars in
these systems once we assume a mass for the primary star. The equation for determining
the mass of the secondary star is
where P is the orbital period in days, K1 is the radial velocity amplitude in km/s, M1 and M2
are the mass of the primary and secondary stars in solar masses, and e is the eccentricity
and i is the angle of inclination of the orbit. M1 can be estimated from the temperature or
color of the star, and M2 can then be calculated based on what has previously been
5
measured. For example, for EBLM 16, we have P = 11.76119 2.08260E
1.64776E  5 days, K1 =
0.11257
16.63670 0.00578
0.00556 km/s, M1 = 1.16277 0.11267 Msolar, e = 0.00564  0.00031, i =
87.566930.29132
0.24700 degrees, from which we calculate M2 = 0.222082  0.00009 Msolar. This
makes sense because M type stars have masses of 0.1 Msolar to 0.4 Msolar. Future work will
involve deriving M2 in this manner for the rest of the sample.
22
EBLM1:
The gray points represent data from the discovery photometry, and the black points represent data from
follow-up photometry.
The triangles represent my data points, the circles and asterisks represent preexisting radial velocity
measurements. The horizontal line represents the radial velocity of the system as a whole.
23
EBLM2:
24
EBLM3:
The asterisks represent my data points, and the circles represent preexisting radial velocity measurements.
25
EBLM4:
The asterisks represent my data points, and the circles represent preexisting radial velocity measurements.
26
EBLM5:
The circles represent my data points, and the asterisks represent preexisting radial velocity measurements.
27
EBLM6:
28
EBLM7:
The asterisks represent my data points, and the circles represent preexisting radial velocity measurements.
29
EBLM8:
The asterisks represent my data points, and the circles represent preexisting radial velocity measurements.
30
EBLM9:
31
EBLM10:
The asterisks represent my data points, and the circles represent preexisting radial velocity measurements.
32
EBLM11:
33
EBLM13:
34
EBLM15:
The asterisks represent my data points, and the circles represent preexisting radial velocity measurements.
35
EBLM16:
The circles represent my data points, and the asterisks represent preexisting radial velocity measurements.
36
EBLM17:
The asterisks represent my data points, and the circles represent preexisting radial velocity measurements.
37
EBLM18:
The asterisks represent my data points, and the circles represent preexisting radial velocity measurements.
38
EBLM19:
39
EBLM20:
The asterisks represent my data points, and the circles represent preexisting radial velocity measurements.
40
EBLM21:
41
EBLM22:
42
EBLM23:
43
References:
Hebb, Leslie et al. 2010. MML 53: a new low-mass, pre-main sequence eclipsing binary in
the Upper Centaurus-Lupus region discovered by SuperWASP. Astronomy and
Astrophysics, Volume 522, id.A37.
Hebb, Leslie et al. 2006. Photometric Monitering of Open Clusters. II. A New M Dwarf
Eclipsing Binary System in the Open Cluster NGC 1647. The Astronomical Journal,
Volume 131, Issue 1: 555-561.
Pollacco, D.L. et al. 2006. The WASP Project and the SuperWASP Cameras. The
Publicatinos of the Astronomical Society of the Pacific, Volume 118, Issue 848: 14071418.
Stassun, Keivan G. et al. 2006. Discovery of two young brown dwarfs in an eclipsing
binary system. Nature, Volume 440, Issue 7082: 311-314.
Stassun, Keivan G. et al. 2004. Dynamical Mass Constraints on Low-Mass Pre-MainSequence Stellar Evolutionary Tracks: An Eclipsing Binary in Orion with a 1.0 Msolar
Primary and 0.7 Msolar Secondary. The Astrophysical Journal Supplement Series Volume
151, Issue 2: 357-385.
44
Appendix A
EBLM1:
45
46
47
EBLM2:
48
49
50
EBLM3:
51
52
53
EBLM4:
54
55
EBLM5:
56
57
58
EBLM6:
59
60
61
EBLM7:
62
63
64
65
EBLM8:
66
67
68
EBLM9:
69
70
71
72
EBLM10:
73
74
75
EBLM11:
76
77
78
EBLM13:
79
80
81
82
EBLM15:
83
84
85
86
EBLM16:
87
88
89
EBLM17:
90
91
92
93
EBLM18:
94
95
96
97
98
EBLM19:
99
100
101
102
EBLM20:
103
104
105
106
EBLM21:
107
108
109
110
111
EBLM22:
112
113
114
115
EBLM23:
116
117
118