MBCAA Observatory

AO Psc: modeling 4 years of observations

Observed: 13, 14, 19 July, 18 Aug 2007 and 2004-2006

Michel Bonnardeau
23 Aug 2007

Abstract

Time series from 2004 to 2007 of this intermediate polar are fitted with a single analytical function. AO Psc is then found spinning up with
dP/dt=-(4.3 +/- 2.3)*10^-11.

Introduction

AO Psc is a cataclysmic variable, that is a binary star with an accreting white dwarf. The white dwarf has a strong magnetic field that funnels the accretion from the accretion disk (an intermediate polar). The orbital period is Porb=3.59h and the white dwarf spin period is Prot=13.4mn. The light curve is modulated with these periods and is also dominated by a synodic oscillation with the beat period Psyn=14.31mn (1/Psyn=1/Prot-1/Porb). This synodic oscillation may result from the hot spot at the outer edge of the accretion disk or from the reprocessing on the secondary star of radiation from the white dwarf pole.

AO Psc is spinning up. Williams (2003) fitted the 1980-2002 O-C diagram with dP/dt=-6.01 or -6.38*10^-11.

A CBA target in 2007.

2007 observations

The observations were carried out with the same setup as in 2004, 2005 and 2006:

203mm SC telescope, a Clear filter and a SBIG ST7E camera (KAF401E CCD);

381 images are used with a 60s exposure each;

the comparison star was GSC 5238-00462, with an assumed unfiltered magnitude of 12.15;

the check star was GSC 5238-00347, with the observed magnitude 15.221, standard deviation 0.039.

Images with poor photometry were detected with the "extra losses" method (Gary (2007) chapter 13), with a threshold of 0.1 mag, and were rejected.

An example of a light curve:

Red: AO Psc, Blue: the check star shifted by -0.5 mag. The error bars are +/- 1 sigma.

All the light curves are HERE.

I observe that AO Psc is brighter than in 2004-2006, by about 0.15mag.

Modeling the oscillations

I fit all my observations, from 2004 to 2007, with the same H(t) function as in 2004:

Years Nb of
sessions Nb of
hours Nb of
measurements

2004 7 20.4 846

2005 4 13.2 600

2006 4 12.6 576

2007 4 8.8 381

Total 19 55.0 2403

with A0 a constant and the synodic oscillation:

the spin oscillation:

and the orbital modulation:

with JD0=2,453,000
and P88orb and t88orb are from the orbital ephemeris of Kaluzny & Semeniuk (1988).

The synodic period Psyn is allowed to vary with time:

and the spin period Prot may be computed as:

The model function is fitted to the observations the following way:

approximate values of the parameters and ranges of possible values are obtained from my modeling of my 2004-2006 observations;

a "Monte Carlo method" is used to derive precise values of the parameters.

The Monte Carlo method is to minimize the following quantity:

where n is the number of measurements,
magi are the measured magnitudes,
ti are the times of the measurements,
deltamagi are the uncertainties on the magnitudes and are used here as a weight so that the magnitudes with large uncertainties contribute less than the ones with small uncertainties.

The method works the following way:

a random set of parameters is generated within the ranges, and S is computed;

this is repeated 20,000 times and the set of parameters that gives the smallest S is retained.

The above is repeated 10 times. The adopted value for a parameter is then its average value and for the uncertainty one standard deviation.

For tsyn and trot, I start from the values I obtained in my modeling of my 2004-2006 observations and for the ranges I use twice the uncertainties;
For P0syn I use the value I derived from the 2004-2005 interseason that has a smaller uncertainty than the value for 2004 observations:
P0syn = 858.6426 +/- 0.0050 s;
For the derivative of the period, I start from PPsyn=0 with a range of 10^-10;
For the other parameters, I also start from my 2004-2006 modeling and I estimate the ranges by hand.
Futhermore, AO Psc being brighter in 2007, I substract 0.15mag to the 2007 magnitudes.

Parameters Initial Monte Carlo
20000x10

values ranges averages standard
deviations

Asyn (mag) -0.2 0.05 -0.162 0.009

P0syn (s) 858.6426 0.0050 858.6432 0.0019

PPsyn (10^-11) 0 10 -4.3 2.3

tsyn (HJD-2453000) 322.3750 0.0010x2 322.3747 0.0006

Arot (mag) -0.122 0.05 -0.090 0.014

trot (HJD-2453000) 322.3476 0.0016x2 322.3484 0.0011

Aorb (mag) -0.079 0.05 -0.054 0.014

A0 (mag) 14.94 0.5 14.808 0.018

S 42,867 23,227

AO Psc is found still spinning up with dP/dt=-(4.3+/2.3)*10^-11, comparable with Williams (2003).

Usually dP/dt is derived by the O-C analysis of the pulsations from observations spanning many years. I am able to detect the spinning up from a limited set of amateur observations owing to the modeling.

The resulting light curves and the model function:

Red: the observed magnitudes,
Brown: the H(t) model,
Blue: Hsyn(t)+A0 shifted by -0.2mag,
Green: Hrot(t)+A0-0.2,
Purple: Horb(t)+A0-0.2.