On the Optical Variability of the eclipsing Low Mass X Ray Binary system HZ Her/HER X1

Swati Gupta

2004 June 9



Abstract

The optical source HZ Her, of the eclipsing Low Mass X Ray Binary system, Her X1-HZ Her was observed on two different nights, in the V band, with the 0.25m Great Ohio Telescope. The observations were timed to cover the light curve up to 0.2 in orbital phase. The resulting light curve was compared with three theoretical light curves, each of which propose a different explanation for the observed optical variability of HZ Her.

1. Introduction

X ray binaries are amongst the brightest X ray sources observed in the sky. An X ray binary consists of a compact object (either a neutron star or a black hole) and a normal companion star, in orbit around each other. At a certain stage of their evolution, the separation between these two stars become so close that material from the companion star begins to flow towards the compact object under the influence of the latter's gravity. This process is known as mass accretion due to "Roche-lobe overflow". The accreted matter, carrying large amount of angular momentum from the orbital motion, circulates around the compact object, and forms an accretion disk. Due to loss of angular momentum from viscous processes, matter from the companion star spirals in towards the compact object, and its gravitational energy is converted into heat. The temperature of the inner accretion disk can reach more than a million degrees, and X rays are produced.

   Hercules X1 is a X ray binary pulsar exhibiting many phenomenon of great interest. The binary is composed of 1) a neutron star (NS) surrounded by an accretion disk and 2) a main sequence star of around 2 solar masses, which fills its Roche-lobe and accretes matter on to the NS. The accretion of mass around the NS is the source of X ray radiation.

   The object of this study is HZ Her, the optical counterpart to Her X1, and optical variability of the order reaching up to an order of 2 mag in the U band with the orbital phase has been observed for this source. The primary minimum occurs at the X ray eclipse, i.e, when the X ray source, Her X1, goes behind the larger, cooler companion, HZ Her. The spectral type of HZ Her varies in a unique manner from late A to early F at minimum to B at maximum.

   Since it's discovery in 1971, a number of possible factors responsible for the variation in the optical light curve, have been proposed. The main contribution to the brightness variation comes from the reflection effect, whereby X rays from the compact object, incident on the surface of the companion star, will be absorbed in its photosphere, and be re-emitted in the optical / UV part of the spectra. This way, the hemisphere of the companion star facing the X ray source is optically brighter than the opposite hemisphere, a manifestation of which is seen in its optical light curve.

   Though the X ray flux from the compact NS is enough to cause the optical fluctuations near the maximum of the light curve, authors have argued that an additional source of photospheric heating is required to explain the entire amplitude of the light curve, especially near the primary minimum. A much sharper primary minimum is actually observed than what is predicted from the basic reflection effect model. Three such models include:
a) Direct heating ( the reflection model ) + optical light from accretion disk surrounding HZ Her (Basko et. al, 1973)
b) Direct heating + thermal emission from a corona above the photosphere of HZ Her (Joss et. al, 1973)
c) Thermal emission from the corona + cloud around Her X1 which absorbs part of the X rays and converts them into visible light (Livio et. al, 1975).

   The object of this project was to measure the light curve in the V band, in and around the time of minimum (φ = 0 to ~ 0.15) and to compare it to each of the theoretical light curves predicted by a, b, and c, each advocating a different model. A successful constraining of these models would then help to address two fundamental questions, (1) can the observed X ray flux cause sufficient photospheric heating to give the observed optical amplitude, and (2) what is the source of extra light near the optical minimum, and thus help get an insight into the structure and emission mechanism of this X-Ray Binary system,
Her X1 / HZ Her.
The orbital phases were calculated with the following elements :

Min Ihel = JD 2441329.5752 + 1d.70016773.E                                  ...(1)

from Lyutyi et.al(1989). Within the orbital phase φ = 0 - 0.15, all the theoretical models to be considered in the present study show a variation of around 0m.5 in the B band. Assuming similar variation in the V band, (Lyutyi et.al,1989), the length of exposure was set by an aim for accuracy of 5% of the 0.5 magnitude variability in the V band, translating into a SNR of ~ 65, and hence an exposure time of 60 sec, from the IRAF task ccdtime.

2. Observations

HZ Her ( RA(2000) = 16:57:49.8, Dec(2000) = +35:20:32.6 ) was observed on 2004 April 28 UT (N1) and 2004 May 6 UT (N2), using the 0.25m Great Ohio Telescope (GOT). Conditions were not photometric on either night, and exposures on N2, for the most part were taken through a fairly thick cirrus cover. The observations were made using a ST8 CCD Camera operating at -25o Celsius on N1 and at -15o Celsius on N2. The GOT has a gain of 2.9 e-/ADU, a readnoise of 11.8 e-(RMS), and a plate scale of 0.7"/ pix. A total of 61 calibration frames (28 Zeros, 9 Darks, and 24 Flats in V) were made on the two nights at evening and morning, before and after the primary science exposures. Exposures of 42x60 s in V and 10x100 s in V were taken on N1 and N2 respectively, with most of the N2 exposures having been taken through clouds of varying degree of thickness. The average airmass was about 1.22. Unmounting and remounting of the CCD camera due to ice freeze led to substantial delay in the starting of observations,and hence lack of data at the minimum of the light curve. Bad tracking toward the end of N1 led to some poorly time resolved data for this part of the night. There was some scattered light around, during the morning flats of N1. The comparison stars for finding the magnitude differences were GSC 2598-1267 ( MV = 12.8 ) and GSC 2598-1274 ( MV=13.2 ), hereafter C1 and C2 respectively, chosen on the basis of their similarity in brightness relative to HZ Her and their favorable positions in the CCD field of view. The study being based on differential photometry, instrumental magnitudes were not transformed to the standard system.

  
Table 1. V band observations of HZ Hercules near minimum, with co-added fluxes.
Column 3 gives the the magnitude difference between HZ Her and the combined comparison stars.

3. Reductions

The raw images were reduced on a Sun Ultra 1 workstation, following the prescription laid out in A User's Guide to CCD Reductions with IRAF by Massey (1997). The dark frames of the same exposure time were combined into a single frame, and the same was done to the zero frames. The combined dark frame was bias subtracted using the combined zero frame, and the resultant frame, along with the combined zero, was used to dark and zero correct the flat fields. Having dealt with standard exposure times of 60s and 100s on N1 and N2 respectively, the object frames were corrected with only the combined dark frames of the corresponding exposure times. The flats were combined into one master flat and then used to divide the object frames by. The morning flats of N1 looked significantly different from the evening flats, and were hence left out of the reduction process. The IRAF task ccdproc was used for the above steps. An inspection of the resulting images called for further elimination of noise by dividing the object frames by a more refined flat frame, Superflat, which was obtained by a pixel by pixel averaging of all the object frames, using the IRAF task imcombine. Finally, the images were examined and found to be significantly noise-free.
Figure 1. Fully reduced false color image of HZ Her, along with C1 and C2.

   Figure 1. shows a fully reduced image of HZ Her, with the two comparison stars as marked.

   Aperture photometry in the interactive mode was employed to obtain the instrumental magnitudes of HZ Her and the two comparison stars, with the help of the IRAF task phot of the noao.digiphot.daophot package. The phot task calculates an accurate sky value inside a specified annulus, around the relevant star and computes its magnitude by subtracting the local sky value from the total counts within a specified aperture around the star. The shape of the PSF for the three stars (HZ Her, C1 and C2) was a normal Gaussian for each frame. The average FWHM of the PSF was estimated to be 3.42". This was then used to estimate the aperture size of 12 pixels. The inner radius of the sky annulus was taken to be 17 pixels, with a width of 5 pixels. The execution of the phot task on each of the object frames then recorded fluxes and the instrumental magnitudes, with their respective errors for the three stars in each frame.

4. Results

Once the magnitudes of HZ Her and the two comparison stars C1 and C2 were obtained for each frame, groups of frames closely resolved in time were co-added in flux, the corresponding magnitudes for HZ Her, C1 and C2 were computed, and indexed to the average time of the co-added frames. The combined magnitude of C1 and C2 was then subtracted from that of the program star to yield the differential magnitude ΔmV recorded in Table 1. The phase φ of the 1d.70017 orbital period was calculated according to the elements given by equation 1. The errors were assumed to be independent and random. The 1σ error in magnitude for the combination of C1 and C2 was computed and added in quadrature to the corresponding 1σ error of the program star to give the final experimental error.

Figure 2. Light curve of HZ Her in the V band. The differential magnitude is in the sense of program star - comparison stars.

  

   Figure 2. shows the light curve obtained by plotting the observed instrumental V magnitudes modulo the 1d.70017 period of HZ Her. The variable nature of HZ Her is apparent, although at the time of minimum light, which corresponds to the center of the X ray eclipse (occultation of Her-X1 by HZ Her, when viewed from earth), data was not obtained due to ice crystal formation on the CCD chip. A smooth trend in variation is observed throughout the range of the observed phase, with no significant bursts in radiation, contrary to observations of Lyutyi et.al (1989) and Kilyachkov et.al (1978). The average error in one observation was
~ 0m.036 in the V band, a difference of 0m.011 from the expected σ from SNR calculations. The error is large for a bright object such as this (14m.5-14m.9), but an adequate time resolution had to be obtained, at the cost of signal integration time.

  

Figure 3. Light curve of HZ Her from present study plotted against HZ Her light curve obtained by Bahcall et.al (1972). The range in orbital phase covered in the present study was from φ = 0.014 - 0.175.

   Figure 3. shows the light curve obtained from the present study against the photographic light curve of Bahcall and Bahcall (1972), offset vertically to minimise χ2 between the present data and the best fitting polynomial to the data of Bahcall et. al., within φ = 0 - 0.2. The present observations agree well with that of Bahcall et. al within the observed range of φ.

   The three theoretical models to be constrained by this study are that by Joss et. al (1973), Livio et. al (1975), and Basko et. al (1973), hereafter, JA, LS, and BS respectively. Putting greater weightage to the observational aspect of this study, the light curves predicted by the above models were derived from the published best fitting curves to their models, given in B (JA and LS), and photovisual (BS) magnitudes respectively.

   The photovisual magnitudes of BS were transformed to the V band according to :

V ≡ mV = mpv + 0.00.                                         ...(2)

from Zombeck (1990).
The spectral type of HZ Her, according to spectroscopic observations, varies over the range B2 - A7 V, depending upon the change in effective temperature Te of the surface of HZ Her. The effective temperature Te is a sum of temperature contribution from the photospheric layer of HZ Her and a secondary contribution from an absorbing layer (a corona of constant density in the case of JA, a spherical cloud around Her X1 in the case of LS, and an accretion disk in the case of BS). But within the relevant range of orbital phase (φ = 0 - 0.2) in the present study, the flux contribution is significantly dominated by the photosphere, thus keeping the effective temperature Te, constant at a value of 7000K. The relative temperature contribution of the photosphere and the absorbing layer is shown in Figure 4 (Joss et. al, 1973). Assuming a constant Te, within the observed range of orbital phase, a (B - V)min color of 0m.3 was adopted for the present study, on the basis of results from Joss et. al (1973), Bahcall et. al (1972), Boynton et. al (1973), and Lyutyi et. al (1973).

Figure 4. Figure taken from Joss et. al (1973) showing effective Temperature Te of HZ Her (solid curve) in units of 104K as a function of orbital phase φ. The dashed curve and the dot - dashed curve show the total flux at earth from the absorbing layer and the photosphere, respectively.

   The theoretical B magnitudes of JA and LS were transformed into the V band, assuming a color index of 0m.3 as mentioned above, with each of the three theoretical model light curves represented by a best fit to the predicted V magnitudes, in this case, an eighth order polynomial, of the form A1 + A2x + A3x2 + A4x3 + A5x4 + A6x5 + A7x6 + A8x7. The model light curves were then offset in magnitude by lengths determined by a minimum χ2 fit to the model and the data, to produce the final light curves, to be compared with the data. Data over the whole range of observed phase was used in the χ2 fitting for BS and JA, while that in the range φ = 0 - 0.097 was used in the study of LS. The observational light curve is plotted against the three theoretical light curves in Figures 6, 7, and 8. All the model light curves are plotted together on Figure 5.

  

Figure 5. The V light curves predicted by the models of Basko et.al, Joss et.al and Livio et.al. The light curve of Livio et.al is sensitive to the size and relative contribution of the cloud to the total optical flux.

  

Figure 6. The V light curve obtained for HZ Her plotted against the theoretical prediction of Basko et.al. Note that the observed data are differential V magnitudes, in the sense of program star - comparison stars. The same convention holds for Figures 7, 8, 9, and 10.

  

Figure 7. The V light curve obtained for HZ Her plotted against the theoretical prediction of Joss et.al.

  

Figure 8. LS (1) : The V light curve obtained for HZ Her plotted against the theoretical prediction of Livio et.al.

5. Discussion

At first glance, the observed light curve of HZ Her, in the V band, appears to agree fairly well with the light curves predicted by the models of JA, BS, and LS, within the relevant range of orbital phase in the present study. The minimum χ2 obtained between the data and the model light curves were 135.64, 184.29, and 197.08, for the BS, JA, and the LS models respectively. The observed data didn't produce the step in the light curve as predicted by the LS model, neither is the intial flatter gradient discernible, as would be expected from the JA model, when compared to that of BS. Based on the overall but not exact agreement of the observed data from the present study with the models of BS and JA, it seems reasonable to conclude that the observed optical variability could either be a result of thermal emission from a corona ~ 0.1 stellar radii above the photosphere of HZ Her (as proposed by the JA model), or the effect of optical light from an accretion disk surrounding Her X1, (according to BS), over and above the direct X ray heating of HZ Her.

   Visual inspection of Figure 8. and the minimum χ2 value associated with it points toward the possible rejection of the LS model as a viable one. The LS model postulates a cloud of matter in the form of a spherical shell around Her - X1. This hypothesized cloud is a small feature on top of the major accretion disk structure, as deduced from mass estimates.The inclusion of this results in a cusp in the theoretical light curve. Its also postulated that the shape of the light curve and in particular, the shape of the minimum is extremely sensitive to the size of the cloud and its relative contribution to the optical light. Keeping this in view , the observational data was plotted against the model light curve of LS again, this time with a greater relative contribution of light from the cloud around Her X1, as shown in Figure 9 below.

  

Figure 9. LS (2) : The V light curve obtained for HZ Her plotted against the theoretical prediction of Livio et.al, with a greater contribution from the cloud surrounding Her X1, than in Figure 8.

   Interestingly enough, the observed data was in much better agreement with the model, with a minimum χ2 of 119.63. Correction for possible under-estimation of σmag ( due to CCD charge transfer defects, non linear response of the CCD chip, imperfect flat fielding etc. ) by a factor of 2.3 results in a minimum χ2 of 22.4, so that this model can then be excluded at a 95% confidence level. The reduced χ2 in this case is 1.72 ( the vertical offset being the only free parameter ). The resulting light curve is shown in Figure 10. below. The 5% probability of it being a good fit to the observed data, though small, cannot be ruled out. The same treatment to σmag, when applied to the BS, JA, and LS (1) models allows an exclusion of these models at confidence levels of 98%, 99.9%, and > 99.9% respectively.

  

Figure 10. LS (3) : The V light curve of HZ Her, with scaled up σmag, plotted against the LS2 model (relatively greater contribution of cloud to the optical flux, compared to LS1).

   Livio et. al have not been very explicit in stating how much of the total contribution in flux actually is taken to be from the cloud, in the above two cases (Figure 8. and Figure 9.), but, an optimum combination of parameters could be capable of a precise reproduction of the model light curve. It is evident from the present study, though, that the model of Livio et. al holds credibility only under relatively higher contribution from the absorbing cloud. Though from the available resources, absolute numbers are not available, an upper limit to the cloud contribution has been set by Livio et. al (1975), to be 0m.3.

   Though all the above three models show different trends in optical variability in the range of orbital phase considered in the present study, the difference becomes more prominent at higher orbital phases of φ ≈ 0.3 - 0.35. Hence a more extensive observation covering a greater range in phase, would be instrumental in constraining these models. A better time resolution of data than in the present study would also constrain the shape of the observed light curve to a greater extent. A check and correction on the possible charge transfer defects in the GOT CCD, if any, would ensure more accurate measurement of fluxes and their associated errors in future.

Acknowledgements

I thank Dr. T. Statler for his utmost cooperation and support at every step of the development of this project, and Mangala, for her unconditional help, with IRAF, among other things. I am also grateful to Dr. M. Boettcher for letting me take it easy with the ongoing research, allowing me to devote valuable time to this project.

  

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