MBCAA Observatory

VX Hya (2008-2009) phase variations

Observed: 24, 27, 28 Dec 2008, 29, 30 Jan, 17, 19, 22, 23 Mar 2009

Michel Bonnardeau
12 Feb 2009
Updated 21 Feb 2009 (phase of each pulsation)
Updated and corrected 25 Dec 2009 (more observations; the signs of the phase shifts were wrong)

Abstract

The strong phase shift that I detected in 2008 is confirmed with new observations.

Introduction

VX Hydrae is a pulsating star with multiple periodicities. It has two main pulsations with periods of 5.36h and 4.15h. I already observed it in 2005, 2006 and in 2008 when I found a strong phase shift.

Here I present new time series and a new analysis of my observations along with observations from the AAVSO.

Observations

The observations were carried out with a setup much like the one for my previous observations:

203mm f/6.3 SC telescope, Johnson B and V filter in a filter wheel, SBIG ST7E camera (KAF401E CCD);

354 usable images were obtained with the V filter, 217 with the B filter;

each exposure is 200s long, whatever the filter is;

the comparison star is Tycho 5482-01347/1 with the adopted magnitudes B=12.172 V=11.580 (the Tycho2 B magnitudes are not too good for this field);

the check star is GSC 5482-01054 with the observed magnitudes V=12.857 (average 1-sigma statistical uncertainty=0.016, standard deviation=0.024) and B=13.435 (0.031, 0.039).

An example of a light curve:

Green: with the V filter, Blue: with the B filter.
The 2 upper curves are for VX Hya; the lower 2 are the check star shifted by -1.4mag in V, -1.8 in B.
The error bars are +/- the 1-sigma statistical uncertainties.

All these data were submitted to the AAVSO International Database, observer code BZU.

Modelling

Following Fitch (1966) I fit the V magnitude measurements with the following simplified model for 2 pulsations:

where n1 and n2 are the frequencies. For the fits, I keep the frequencies fixed and I derive the Vm and a and b parameters. (A change of frequency will then show up as a phase shift).

For the frequencies, I use the values measured from the 2006-2007 AAVSO observation campaign (Templeton et al (2008)). When compared with the Fitch (1966) measurements, n1 is then slightly smaller and n2 slightly larger.

First, I fit a data set of 3098 measurements from the AAVSO (observer DKS) obtained in 2005-2006. I use this as the origin for the phases of the pulsations and, with the other fits, I will compute the phase shifts (in minutes) against this data set. I will also compute the amplitude variations against this data set. The amplitude of the second pulsation over the first one for this 2005-2006 dataset is:

For the other data sets, I call alpha and delta the a and b parameters of the fits. For the first pulsation the phase shift against the 2005-2006 observations is then:

(tau1 positive is equivalent to an increase in the frequency n1).
And the amplitude against the 2005-2006 observations is:

One has the equivalent formulae for the second pulsation.

I fit my observations (observer MB), AAVSO data sets, and data sets made of my observations and of AAVSO observations (so as to have more measurements). The results are:

Season 2004-2005 2005-
2006 2006-2007 2007-2008 2008-2009

Observer MB MB+
AAVSO
BIW DSK AAVSO
DKS MB AAVSO
PRX AAVSO
SAH MB MB+
AAVSO
PRX DKS MB AAVSO
DKS

Nb of
observat. 248 363 3098 162 1203 1379 346 775 354 712

<HJD>-
2450000 3445 3451 3794 4096 4165 4141 4508 4536 4943 4853

Vm (mag) 10.641 x x 10.638 x x 10.647 x 10.683 x

tau1 (mn) -5.4 -4.5 0 1.5 -1.3 1.1 -4.5 -5.1 -15.45 -8.6

ampli1 0.995 0.921 1 1.023 1.175 1.024 1.012 1.031 0.841 1.052

tau2 (mn) -0.5 -0.4 0 2.9 5.9 -2.4 -5.8 -5.6 -26.6 -21.4

ampli2 0.805 0.828 1 1.057 1.236 1.149 1.088 1.204 0.743 0.955

a10 0.127 0.119 0.130 0.133 0.152 0.133 0.130 0.132 0.101 0.133

b10 -0.025 -0.021 -0.012 -0.008 -0.017 -0.009 -0.023 -0.025 -0.042 -0.035

a01 -0.031 -0.032 -0.038 -0.031 -0.026 -0.051 -0.058 -0.064 -0.073 -0.085

b01 -0.088 -0.091 -0.110 -0.119 -0.142 -0.124 -0.113 -0.125 -0.047 -0.072

Link HERE x x x x x HERE x x x

Results

The two pulsations were roughtly constant in 2004-2007. In 2007-2009 the two pulsations have decreasing phase shifts, more strongly for the second pulsation; this may be interpreted as an increase of the pulsation periods:

Red: the first pulsation, Blue: the second one.
Squares: my observations, Circles: those from the AAVSO, Diamonds: my observations+AAVSO observations.

The phases of the two pulsations may be evaluated as:

One can then see that there is a phase change for the 2 pulsations starting in 2008:

Red: the phase of the 1st pulsation, Blue: of the 2nd pulsation shifted by +220°.

The phase difference phi2-phi1 shows an increase with time:

Acknowledgment

The use of the AAVSO International Database for this amateur research is acknowledged, especially for the observations of:

BIW: Butterworth Niel (Australia)
DKS: Dvorak Shawn (USA)
PRX: Poklar R. (USA, AZ)
SAH: Samolyk G. (USA, WI).

References

Fitch W.S. (1966) ApJ 143 852.

Templeton M.R., Samolyk G., Dvorak S., Poklar R., Butterworth N., Gerner H.S. (2008) AAVSO poster The 2006-2007 observing campaign on VX Hydrae available from HERE.