UX Mon: time keeping and modelling of a binary
Observed: 13 Dec 2007, 11-16, 18 Feb, 8, 13, 14 March, 1, 4, 25, 29
Apr 2008
Michel Bonnardeau
2 Oct 2008
Updated 1 May 2013
Abstract
Time series of this eclipsing binary system with extra variability
are presented. The O-C analysis suggests the presence of a third star.
The observations are modelled with BinaryMaker3 and parameters of the
system are derived.
Note added 1 May 2013
UX Mon does have a high rate mass transfer (Olson et al (2009)).
According to Sudar et al (2011), UX Mon has a thick accretion disk.
Introduction
UX Mon is an eclipsing binary with an orbital period of 5.9 days.
It shows some extra variability that may come from the stars being variable
and/or bursts of mass transfer.
Observations
The observations were carried out with a 203mm SC telescope, V and B
filters in a filter wheel and a SBIG ST7E (KAF401E CCD) camera. The V
and B filters were used in alternance. 951 usable images were obtained
through the V filter, each with an exposure duration of 30s, and 941 images
with the B filter each with an exposure duration of 60s.
For the photometry, the comparison star is TYC5412-00053 with Bc=10.043
and Vc=9.087, the Tycho magnitudes being converted to the Johnson's ones
owing to Mamajek et al (2002) and (2006).
The photometry measurements are transformed with the transformation
coefficients:
TvTbv = -0.025+/-0.015
TbTbv = 0.002+/-0.027
to obtain the transformed magnitudes:
Vt = V+TvTbv*((B-V)-(Bc-Vc))
Bt = B+TbTbv*((B-V)-(Bc-Vc))
A first check star is TYC5412-00530 with the measured transformed magnitudes
V=10.606 (average 1-sigma uncertainty 0.011, standard deviation 0.017)
and B=10.966 (0.014, 0.019); the Tycho magnitudes converted to Johnson
being V=10.753, B=10.966.
A second check star is TYC5412-00283 with the measured magnitudes V=10.335
(0.010, 0.019) and B=11.365 (0.017, 0.025); the Tycho magnitudes converted
to Johnson being V=10.362, B=11.398.
For the first check star, the V measurement does not look
good. However (see below), for UX Mon my V measurements closely match
those of ASAS, and my temperature estimates made from B-V match those
of other authors.
An example of a light curve is:
Green: the V magnitudes, Blue: the B magnitudes. The error bars are
the 1-sigma uncertainties.
All the light curves are HERE.
With the orbital ephemeris (see below), the phase coverage is:
and the phase plot:
Green: the V magnitudes, Blue: the B magnitudes.
Time keeping
According to Kreiner & Ziolkowski (1978) (hereafter referred to as KZ78),
an ephemeris for the primary eclipses is T(E) = T78 + P*E with
T78 = 2,433,328.8533 HJD (16 Feb 1950)
P = 5.904,550,5 days
A phase plot of my data with this ephemeris does not match, the eclipses
being too early by deltat=-0.18day. For a good match, the T78 is to be
replaced by:
TMB = 2,454,520.105
The discrepancy between the KZ78 ephemeris and my observations suggests
that the orbital period is decreasing with the rate:
dP/dt = 2*deltat*P/(TMB-T78) = -4.7*10^-9
Actually, KZ78 also gives the ephemeris T(E) = T' + P'*E + b*E^2
with b=-1.9*10^-10
that is:
dP/dt = 2*b/P' = -4.2*10^-9
Futhermore Olson & Etzel (1995) (herefafter OE95) also suggested the period
may be decreasing with a similar rate.
I also use the ASAS data (Pojmanski (2002)), between 2001 and 2006. For
a good match, the T78 is to be replaced by:
TASAS=2,452,713.363
That is the eclipse is too early by -0.130 day from the KZ78 ephemeris.
The resulting phase plot with the ASAS data is:
To built the O-C diagram that follows, I use the measurements:
KZ78 compiled 32 measurements; however 3 of them from one observer are
excluded because "most probably in gross error" (red circles);
the measurement of OE95 (blue cross);
the ASAS observations (green square);
a measurement from Meyer (2006) (HJD=2,453,475.023) (brown diamond);
my measurement (filled red circle):
The decrease in the orbital period may be due to the transfer of mass
from the more massive star to the less massive one, at a rate of several
10^-7 solar mass/yr. Indeed there is a mass transfer in UX Mon (OE95),
but such a high rate seems unrealistic: the secondary only fills its Roche
lobe (see below the BinaryMaker3 modelling) and UX-Mon is not an X-ray
source (not detected by ROSAT).
Another explanation is that UX Mon is in a ternary system. The total
mass of the binary is 4.5 solar masses (see below). It may be orbiting
a third star with a mass of ~1 solar mass, an orbital period of ~100yr
and a half major axis of ~40au.
Temperature determination
During the eclipse (at phase 0) the secondary star hides the primary
one. Let us assume that there is then no light at all from the primary.
The transformed magnitudes of the secondary are then V2=9.330, B2=10.090
and B2-V2=0.76. The magnitudes V1,B1 of the primary may then be computed
from the observed V,B transformed magnitudes outside the eclipses as:
V1=V2-2.5*log(10^((V2-V)/2.5)-1)
B1=B2-2.5*log(10^((B2-B)/2.5)-1)
With V=8.366 B=8.773 outside the eclipses, one has:
V1=8.942 B1=9.157 B1-V1=0.215
According to Reed (1998) the effective temperature of a star may be
computed from its B-V color as:
T=10^((14.551-(B-V))/3.684) (for B-V>-0.041)
The effectives temperatures of the primary and secondary stars are then:
T1=7791°K
T2=5540°K
According to OE95, T1 is in the 7500-8000°K range (and they adopt 8000°K),
and T2=5507°K. My temperature determination is then in fairly good agreement
with their.
Position on the HR diagram
The Hipparcos parallax for UX Mon is 2.06+/-1.22m" which gives a distance
to it d=485pc (between 305 and 1180pc). UX Mon is then a nearby object
and the interstellar reddening may be neglected (it is at b=11.4°).
The absolute magnitudes vi of the primary and of the secondary may then
be evaluated as: vi=Vi+5-5*log(d) and their positions on the Hertzsprung-Russell
diagram may be plotted:
The HR diagram is made from Hipparcos data (see
M11: open cluster distance measurement).
The red error bars are for the primary and the secondary stars and are computed
from the parallax measurements. The back dots are computed from
the BinaryMaker3 modelling (see below).
The primary lies close to area where there are delta Scuti (DSCT) pulsating
stars. The secondary lies in an area where there are little stars, then
is of a rare type, and is close to the area where the irregular variable
stars lie.
Color variation
The B-V color versus the orbital phase:
Outside the eclipses, UX Mon is variable on a time scale of less than
1 hr with an amplitude of 0.25mag. The variations seem irregular. They
may come from:
DSCT activity from the primary, may be perturbated by the mass transfer
and the gravity field of the secondary;
the secondary has an unusual position in the HR diagram, close to the
instability strip, and perhaps is variable;
mass-transfer bursts.
The diagram of the B-V color versus the V magnitudes outside the eclipses
shows a cloud of points and not the loop pattern one may expect if the
variations were originating from a pulsating star:
Modelling with BinaryMaker3
I fit the ASAS observations and my B, V ones with BinaryMaker3,
using OE95's parameters. This is sensitive to the wavelength so I adjust
it to minimize the residuals; for the V measurements wavelength=6100A,
for the B ones wavelength=4100A.
The synthetic light curve is too large for the primary eclipse.
I adjust the parameters by hand, giving extra weight to the primary eclipse data,
minimizing the residuals:
Parameters |
OE95 values |
My values |
Mass ratio q |
0.80 |
0.80 |
OMEGA1 |
6.33 |
6.120 |
OMEGA2 |
3.42 |
3.485 |
r1(back) |
0.236(*) |
0.19 |
r2(back) |
0.385 |
0.37 |
Temperature T1 (°K) |
8000 |
7850 |
Temperature T2 (°K) |
5507 |
5510 |
Inclination i (°) |
89.5 |
89.5 |
(*)According to BinaryMaker3, with OMEGA1=6.33 this should
be r1(back)=0.182. r1(back)=0.236 does not fit at all the data. OMEGA2 and
r2(back) agree with BinaryMaker3.
All the BinaryMaker3 parameters are HERE.
The primary star is on the left.
The resulting synthetic light curves:
Green dots: the V magnitudes (ASAS and mine); Red line: synthetic light
curve (wavelength=6100A);
Blue dots: the B magnitudes; Black line: synthetic
light curve (wavelength=4100A).
All the light curves (measured and synthetic) are HERE.
More parameter determination
Distance between the 2 stars
OE95 measured from spectroscopy the orbital velocity of the secondary
star:
K2 = 108.3 km/s
The orbital radius of the secondary is then:
R2 = K2*P/(2*pi*sin(i))
R2 = 12.6*ro where ro=700,000km is the solar radii.
The orbital radii and the star masses are connected the following way:
M1*R1 = M2*R2
Knowing the mass ratio q=M2/M1, one can calculate the orbital radius of
the primary and the distance between the 2 stars:
R1 = q*R2 = 10.1*ro
R = R1+R2 = 22.6*ro
Radii of the stars
The radii of the stars are:
r1 = r1(back)*R = 4.30*ro
r2 = r2(back)*R = 8.37*ro
Masses of the stars
The total mass of the system M=M1+M2 is connected to the period P and
the distance R between the stars as:
M = (2*pi)^2*R^3/(G*P^2) with G the gravitational constant
M = 4.51*Mo where Mo=2*10^33g is the mass of the Sun
The masses of the stars are then:
M1 = M/(1+q) = 2.51*Mo
M2 = M*q/(1+q) = 2.00*Mo
Checking Stefan's law
Assuming that the 2 stars radiate like black bodies, their magnitudes
should be connected the following way (Stefan's law):
V1-V2 = -2.5*log(r1^2*T1^4/(r2^2*T2^4))-BC(T1)+BC(T2)
where BC(T) is the bolometric correction.
According to Reed (1998) BC(T) may be given by:
BC(T) = C6*(log(T)-4)^4+C7*(log(T)-4)^3+C8*(log(T)-4)^2+C9*(log(T)-4)+C10
with C6=-8.499 C7=13.421 C8=-8.131 C9=-3.901 C10=-0.438
That does not fit (one obtains -0.200 instead of -0.388). I suggest this
comes from the secondary being much deformed, and that r2 should be replaced
by a smaller "effective" value:
r2 = 7.67*ro
Absolute magnitudes
The absolute V magnitude of the Sun is vo=4.83 and its effective temperature
is To=5780°K. Applying Stefan's law, the absolute magnitude v1 of the
primary is then:
v1 = -2.5*log(r1^2*T1^4/(ro^2*To^4))+vo-BC(T1)+BC(To)
v1 = 0.290
And the absolute magnitude of the secondary is:
v2 = v1+V2-V1
v2 = 0.678
These absolute magnitudes are used to draw the filled black dots in the
above HR diagram.
Luminosities
The luminosity L1 of the primary is:
L1 = Lo*10^((v1-vo+BC(T1)-BC(To))/-2.5)
L1 = 63*Lo where Lo=4*10^33ergs/s is the Sun luminosity.
The same way, the luminosity of the secondary is:
L2 = 49*Lo
Distance
The distance to UX Mon is:
d = 10^((V1-v1+5)/5)
d = 537pc = 1750lyr
I suggested there is a 3rd star ~40au away to explain the O-C diagram. The
angular separation is then ~0.1".
References
Kreiner J.M., Ziolkowski J. (1978) AcA 28 497.
Mamajek E.E., Meyer M.R., Liebert J. (2002) AJ 124 1670 Appendix
C; Erratum (2006) AJ 131 2360.
Meyer R. (2006) New minimum times of eclipsing binaries
http://var.astro.cz/oejv/issues/oejv0028.pdf.
Olson E.C., Etzel P.B. (1995) AJ 110 2385.
Olson E.C., Henry G.W., Etzel P.B. (2009) AJ 138 1435.
Pojmanski G. (2002) AcA 52 397.
Reed B.C. (1998) J. Royal Astronomical Society Canada 92 36.
Sudar D., Harmanec P., Lehmann H., Yang S., Boži H., Ruždjak D. (2011) A&A 528 A146.
Technical notes
Telescope and camera configuration.
Computer and software configuration.
Data processing.
Transformation coefficients.
Modelling with BinaryMaker3.
Astronomical notes
Binary system: orbital period and mass
transfer.
Light-travel time effects in binary
systems.