DETERMINING THE PROPERTIES OF GX GEM. L. E. Handzel1,2 and C. H. Lacy1,3, 1Arkansas Center for
Space and Planetary Sciences, University of Arkansas, Fayetteville, Arkansas 72701, 2Agnes Scott College, Decatur
GA 30030, [email protected], 3Department of Physics, University of Arkansas, [email protected].
Introduction:
From an earth observer’s
viewpoint, GX Gem appears to be a single star within
the constellation Gemini that varies in brightness
over time; however, it is actually a system of two
stars which orbit about a common center of mass.
The variation occurs when the stars eclipse each
other. Since the stars’ orbit is seen nearly edge-on
from the earth as shown in Figure 1, the “star”
appears to dim as one star passes in front of the other
thereby blocking a major fraction of its light.
Examination of these variations can give observers
insights to the various physical and orbital properties
of the two stars.
About half of all known star systems belong to
binaries, so studying these double stars is essential to
understanding how stars evolve. Many theories of
stellar evolution treat binary stars as if they develop
independently.
More recent research, though,
suggests that binaries sometimes evolve differently
than single stars, so the theories may require reassessment. Information gleaned about GX Gem will
give favor either for or against the current theories.
Primary
Secondary
Earth
Figure 1: Representation of primary eclipse as seen from Earth.
Image is not drawn to scale. The primary star is the larger, more
massive of the two, so a primary eclipse occurs when the light of
the primary is obscured by the secondary.
Observations: Images of GX Gem were taken
by Dr. Lacy using the URSA telescope on Kimpel
Hall at the University of Arkansas. The observation
period began in November 2001 and ended in April
2006 using the V filter. The radial velocity data was
determined by Dr. Torres of the Harvard-Smithsonian
Institute for Astrophysics.
Measuring Images: In order to make use of the
observational data, flat fields and sky corrections had
to be included as the images were measured with the
Multi-measure program written by Dr. Lacy. This
program plotted the results on two different light
curves. The first displayed the magnitude of the
variable star as well as those of a comparison and
check star of constant brightness for each HJD
(Heliocentric Julian Date). This light curve revealed
the times of individual eclipses. The second light
curve plotted magnitude against the phase of the
variable star. The 0 phase is set at the bottom of the
primary eclipse while 0.5 phase is in the midst of the
secondary eclipse.
This curve allowed me to
determine whether each minimum was a primary or
secondary eclipse. The final light curve can be seen
in Figure 2. From the two plots, I was able to obtain
several reliable dates of eclipses.
Figure 2: Light curve of GX Gem. As shown, the binary
seems to have a constant brightness outside eclipse since no light is
being blocked. However, when the light from the primary is
blocked by the secondary, a large dip in brightness occurs. A
similar dip occurs when the primary passes in front of the
secondary.
Data Analysis: Since only a limited number of
minima could be accurately determined, I added
dates of minima found from a variety of external
papers to my own to get a better estimate of the
period for GX Gem. The period was found using Dr.
Lacy’s program, Dates of Minima.
After learning the period, I then used the equation
HJD Min I = nP+Eo with HJD Min I being the
estimate for an eclipse date, n being the cycle number
since the first eclipse, P being the period, and Eo
being an accurate date of minimum. This ephemeris
was used to rephrase the light curve data.
Orbital Elements:
Having the period,
ephemeris, and light curve data, the orbital elements
were then found with a collection of programs
written by Dr. Lacy.
EBOPP took the variations in brightness of the
stars by date, coupled with the period and ephemeris
to find the photometric orbital elements: the
secondary surface brightness, primary radius, ratio of
radii, and orbital inclination relative to the plane of
the sky.
GLSPL used the radial velocities found by Dr.
Torres to create a radial velocity curve, shown in
Figure 3, as well as determining the spectroscopic
orbital elements which include system movement and
semi amplitudes of the stars.
Figure 3: Radial velocity curve of GX Gem. The white circles
display measured velocities of the primary star while the black
circles show measured velocities of the secondary. Since the
binary rotates nearly edge-on to Earth, the velocities are either blue
shifted from movement towards the earth or red-shifted from
movement away from the earth. As demonstrated in the figure, the
two stars will have consistently opposite shifts.
All the orbital parameters were then combined in
MRLCALC to find the absolute properties of the
binary.
Masses, radii, luminosities, absolute
magnitudes, and synchronous rotational velocities
were calculated and are displayed in Table 1.
Primary
GX Gem Properties
Mass (Solar Units)
Radius (Solar Units)
LogG (CGS Units)
LogL (Solar Units)
Absolute Magnitude
Synchronous Rotational Velocity (km/s)
Temperature (K)
Surface Brightness
Age (Billion years)
Eccentricity=0
Period=4.037934+-0.000006 days
The final step was to approximate the age and
chemical composition of the stars. Over the years,
several stellar models have been assembled to allow
astronomers to locate such values. These values were
determined by interpolation because the exact age
could not be found directly.
Conclusion: As members of a binary system, the
stars of GX Gem were ideal subjects to test the
accuracy of current theories of stellar evolution.
Though unable to disprove the theories by
themselves, GX Gem does give evidence against the
theories. Being each about one and a half times more
massive than the sun, the stars of GX Gem should
have a shorter main sequence lifetime than the sun
since more massive stars consume their hydrogen
supply sooner. However, these stars are less than
half the age of the sun, yet they have already begun
hydrogen shell burning while the sun has not. In
addition, 3% of GX Gem’s composition is heavier
elements, so the stars have a higher metallicity than
the sun which is only 1% heavier elements. Like
many binary stars studied before, GX Gem calls for a
re-evaluation of the current theories of evolution.
References: [1] Torres G. (2006) HarvardSmithsonian Center for Astrophysics, Cambridge,
MA 02138. [2] Claret A. (1997) Astron. Astrophys.
Suppl. Ser., 125, 439-443. [3] Claret A. and Gimenez
A. (1992) Astron. Astrophys. Suppl. Ser., 96, 255267. [4] Hubscher J. (2005) IAU Inform. Bull. Var.
Stars, 5643, 1. [5] Sanchez-Bajo F. et. al. (2003)
Astron. Nachr., 324, 511-515. [6] Agerer F. and
Hubscher J. (2003) IAU Inform. Bull. Var. Stars,
5484, 1. [7] Lacy C. H. (2002) IAU Inform. Bull. Var.
Stars, 5357, 1. [4] Agerer F. and Hubscher J. (1999)
IAU Inform. Bull. Var. Stars, 4711, 1-4.
1.515
2.274
3.904
0.825
2.65
28.2
6150
3.782
2.376
Uncertainty Secondary
0.014
1.499
0.05
2.24
0.019
3.913
0.023
0.803
0.06
2.71
0.6
27.8
50
6120
0.001
3.779
0.067
2.376
Inclination=85.8843º+-0.0878
Uncertainty
0.013
0.05
0.019
0.023
0.07
0.6
50
0.00275
0.067
Table 1: Table displaying the properties of GX Gem. Properties of each star in the binary are given first with their uncertainties followed by the
properties of the binary.