MBCAA Observatory

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".