Simultaneous X-ray/UV Observations of Ultraluminous X-ray Source Holmberg II X-1 with Indian Space Mission Astrosat

Abstract

We present the results of eight epochs of simultaneous UV and X-ray observations of the highly variable ultraluminous X-ray source (ULX) Holmberg II X-1 with AstroSat—Indian multiwavelength space satellite. During the entire observation period from late 2016 to early 2020, Holmberg II X-1 showed a moderate X-ray luminosity about of $8 \times {{10}^{{39}}}$ erg s$^{{ - 1}}$ and a hard power-law spectrum with $\Gamma \lesssim 1.9$. Due to low variability of the object in X-rays (by a factor 1.5) and insignificant variability in the UV range (upper limit approximately 25%) we could not find reliable correlation between flux changes in these ranges. Inside each particular observation, the X-ray variability amplitude is higher, reaching a factor of 2–3 respect to the mean level, however, it is observed in the form of relatively short stochastic bursts. We discussed our results in terms of three models of a heated donor star, a heated disk and a heated wind, and estimated the lower limit to the variability which would allow to reject at least part of them.

Appendices

APPENDIX DATA REDICTION DETAILS

Reduction the UV Data

The photometry of the UV images can be split into three steps. First of all, we determined the exact position of Ho II X-1 performing the astrometric correction of the AstroSat images with the HST data in order to center the aperture and then measured the total fluxes in it. All the flux measurements were done via the APPHOT package of IRAF. At the second step, we measured and subtracted fluxes of all the extraneous sources. At the final step, we performed the aperture corrections and converted fluxes into a single filter to be able to compare observation of different dates. For the NUV data, we decided to skip the last two steps because we have only three observations with this instrument.

Raw Aperture Photometry

We decide to perform the photometry in the same 3-pixel (1$\overset{'' }{\mathop{.}}\,$23) aperture (marked in Fig. 1) for all the observation regardless the PSF size. This aperture still collects most of the source photons even in the worst images with the PSF $FWHM$ of 1$\overset{'' }{\mathop{.}}\,$8, and, on the other hand, minimizes the contribution of neighboring stars. To be sure that our aperture is centered exactly at the ULX position, we carried out astrometric alignment of the AstroSat data to HST images where the ULX optical counterpart is clearly seen as a single point-like source. For this purpose, we have chosen the HST image⁴ obtained on August 24, 2013, with the Wide Field Camera 3 (WFC3) in the $F275W$ filter whose bandpass is close to those of the AstroSat NUV filters, and camera has a relatively large FOV about of 3′. Three single stars were used as reference sources. The resulting astrometry accuracy is better than 0$\overset{'' }{\mathop{.}}\,$13 for each AstroSat observation.

The global background that is largely associated with instrumental features of the UVIT detectors was estimated from an annular aperture with an inner and outer radii of 8′′ and 16′′, respectively. The measured count rates were corrected for this background and then multiplied by the conversion factors (Table 2) to obtain fluxes in physical units (erg s$^{{ - 1}}$ cm$^{{ - 2}}$ Å$^{{ - 1}}$). The resulting values together with their $1{\kern 1pt} \sigma$ errors are given in Table 1.

Flux Contribution from Neighboring Sources

The fluxes measured at the previous step are still contaminated by contributions from other sources: the nebula surrounding Ho II X-1 and the stars st1 and st2 (Fig. 1) directly falling into the 1$\overset{'' }{\mathop{.}}\,$23-aperture as well as from more distant stars located a few seconds away from the ULX and are likely to be members a single stellar cluster. The flux contribution from each particular sources varies between the observations depending on the PSF size, and must be carefully accounted for. To estimate these contributions in each AstroSat observation, we utilized the HST ${\text{A}}CS{\text{/}}SBC{\text{/}}F165LP$ image (Table A.1), the resolution of which was got worsen to the AstroSat level. The $F165LP$ filter was chosen because its bandpass is close to those of the FUV filters, although it does not completely coincide with them. Therefore, in order to convert the contributions measured from the HST data into the AstroSat filters with the highest accuracy, we have taken into account the spectral energy distributions of these sources modeled involving HST photometry in other filters.

Table A.1. Results of the HST photometry of Ho II X-1 and the neighboring sources

Since the extraneous sources have different nature (nebula vs stars), their contributions to the 1$\overset{'' }{\mathop{.}}\,$23-aperture must be accounted for individually, otherwise one can not be able to model their SEDs with physical models. To estimate the individual flux contribution of each extraneous source, we removed (i. e. replaced with the local background counts) the Ho II X-1 optical counterpart and all other extraneous sources except the current from the $F165LP$ image. Then we decreased the spatial resolution of the image and measured flux in the 1$\overset{'' }{\mathop{.}}\,$23-aperture centered at the Ho II X-1 position. To decrease the resolution, we passed the image by a Gaussian filter⁵, the parameters of which were determined for each AstroSat observation individually by analyzing the PSF of four bright single stars in the UVIT field of view. This procedure was repeated four times: for the nebula, for the stars st1 and st2, and for the other stars which we considered as members of a single stellar cluster (we will refer to them as the cluster).

Using this technique, we obtained that the contribution of both stars about the same; the 1$\overset{'' }{\mathop{.}}\,$23-aperture gather ${{w}_{{{\text{st}}}}}$ ranging from 0.468 to 0.566 for PSF sizes 1$\overset{'' }{\mathop{.}}\,$8 and 1$\overset{'' }{\mathop{.}}\,$4, respectively, of their total (aperture corrected) fluxes in the $F165LP$ filter. For the extended sources, namely the nebula and the cluster we measured ${{w}_{{{\text{neb}}}}}$ and ${{w}_{{{\text{cl}}}}}$ as ratios between the fluxes captured by the 1$\overset{'' }{\mathop{.}}\,$23-aperture and the fluxes used for the SED modeling (see the next paragraph), the obtained values are ${{w}_{{{\text{neb}}}}} = [0.664;0.749]$ and ${{w}_{{{\text{cl}}}}} = [0.022;0.015]$ (for 1$\overset{'' }{\mathop{.}}\,$8 and 1$\overset{'' }{\mathop{.}}\,$4).

To construct the SEDs we carried out the aperture photometry on the HST drc images (cameras, filters and other details are in Table А.1). For the two stars, we used a 4-pix aperture (0$\overset{'' }{\mathop{.}}\,$10) for the ACS/SBC images and 3-pix for ACS/WFC and WFC3/UVIS (0$\overset{'' }{\mathop{.}}\,$15 and 0$\overset{'' }{\mathop{.}}\,$12, respectively). Such small apertures were chosen to minimize the contribution from the nebula, which is especially bright in the visible band. The background was determined in annuli with an inner radius about of 0$\overset{'' }{\mathop{.}}\,$25 and an about 0$\overset{'' }{\mathop{.}}\,$15 width with small variations of about 0$\overset{'' }{\mathop{.}}\,$02 depending on a particular camera. The aperture corrections were determined by measurements of 6–17 bright isolated stars in the large (0$\overset{'' }{\mathop{.}}\,$5 for ACS and 0$\overset{'' }{\mathop{.}}\,$4 for WFC3) and the small apertures. The zero points were taken from the PySynphot v2.01 package using the effstim commands. The final magnitudes and their errors for both stars are listed in Table А.1. The provided errors correspond to the $1\sigma$ confidence intervals and include the statistical errors of the flux measurement, the aperture correction errors, the stability of zero points and the stability of the filter PSF in each particular observation.

The photometry of the nearest to Ho II X-1 region of the cluster was carried out in a 2$\overset{'' }{\mathop{.}}\,$2-aperture centered at R.A. = 08:19:28.29, Dec. = +70:42:19.9 (J2000.0). The background was measured in several areas around the cluster. The obtained magnitudes are presented in Table А.1. The relatively large photometric errors are resulted mainly from strong variations of the background level. The magnitude of the nebula ${{m}_{{{\text{neb}}}}} = 18.94 \pm 0.05$ was determined only in the $F165LP$ filter, in the 1$\overset{'' }{\mathop{.}}\,$23-aperture centered at the ULX.

The measured fluxes of st1 and st2 were fitted with the Kurucz models from ATLAS9 (Castelli and Kurucz, 2003) accounted for the interstellar extinction with ${{A}_{V}} = 0.23$ (using the curve by Cardelli et al., 1989), measured from the ratio of the Balmer lines in the nebula around Ho II X-1 (Vinokurov et al., 2013). The metallicity was $0.1 {{Z}_{ \odot }}$ (Pilyugin et al., 2014). The best agreement was obtained for the models with $\log g = 4.0$ and the effective temperatures and photosphere radii ${{T}_{{{\text{eff}}}}} = 32.2 \pm 1.4$ kK, ${{R}_{{{\text{ph}}}}} = 10.4 \pm 0.6 {{R}_{ \odot }}$ (${{\chi }^{2}}$/dof $\approx 1.2$) and ${{T}_{{{\text{eff}}}}} = 29.4 \pm 2.1$ kK, ${{R}_{{{\text{ph}}}}} = 7.2 \pm 0.7 {{R}_{ \odot }}$ (${{\chi }^{2}}$/dof $\approx 2.7$) for the brighter (st1) and the fainter (st2) stars, respectively. These parameters as well as the absolute magnitudes of ${{{\text{M}}}_{V}} = - 4.7 \pm 0.04$ and ${{{\text{M}}}_{V}} = - 3.8 \pm 0.05$ correspond to the star types B0–O9 and B0–B1 IV–V (e.g., Straizys and Kuriliene, 1981).

The cluster SED was fitted with the model spectra calculated in Starburst99 assuming the metallicity of $0.1 {{Z}_{ \odot }}$ and ages 2.5–5 Myr. The interstellar extinction was varied from the Galactic value ${{A}_{V}} = 0.09$ to the value measured by the nebula lines (A_V = 0.23). The minimal ${{\chi }^{2}}{\text{/dof}} = 2.8$ has been reached for the cluster of 2.9 Myr and ${{A}_{V}} = 0.22 \pm 0.02$ which is in a relatively good agreement with the result by Stewart et al. (2000). Besides the spectrum of stars themselves, the Starburst99 code outputs the continual spectrum of a nebula in which these stars are immersed. We adopted the desired model SED to be stars+0.5*nebula.

As a model for the nebula around Ho II X-1 was used the tabulated spectrum⁶ of a planetary nebula with the extinction of ${{A}_{V}} = 0.23$ applied. This choice is based on the fact that photoionization-dominated shells around many ULXs (and Ho II X-1 in particular) demonstrate spectra similar to those of planetary nebulae, with a large number of high-excitation lines at high intensities, and are believed to have similar gas ionization state (see e.g. Abolmasov et al., 2007). The use of the tabulated spectrum leaves only one free parameter—a normalization, which was determined from the nebula flux measured above.

The SED of each of the four considered objects was multiplied by the corresponding factor $w$ determined above to derive flux in the AstroSat 1$\overset{'' }{\mathop{.}}\,$23-aperture and then was convolved with the bandpass of the target UVIT filter. The total flux of the four sources in the 1$\overset{'' }{\mathop{.}}\,$23-aperture as well as the Ho II X-1 flux corrected for this value for each observation are presented in Table A.2. Eventually, the contaminating flux turned out to be weakly dependent on the PSF size because the contribution from the two stars and the nebula decreasing as the resolution get worse is partly compensated by growing contribution from the cluster.

Table A.2. Details of the AstroSat photometry. ${{B}_{{{\text{neib}}}}}$—total flux from the neighboring sources, captured by the 1$\overset{'' }{\mathop{.}}\,$23-aperture, ${{F}_{{{\text{net}}}}}$—Ho II X-1 flux in the 1$\overset{'' }{\mathop{.}}\,$23-aperture with background and ${{B}_{{{\text{neib}}}}}$ subtracted. ${{F}_{{F148W}}}$—net Ho II X-1 flux corrected to infinite aperture and converted to the same $F148W$ filter

Aperture Corrections and Flux Conversion between the Filters

The final step of the FUV data reduction involved the aperture correction of the obtained net Ho II X-1 fluxes and conversion to the same $F148W$ filter in order to able to study the source variability. The conversion was needed for the two observations of 2016 that were carried out in the $F154W$ filter. To do it, as in the previous section, we modelled the object SED using the HST photometry.

The aperture corrections for the AstroSat images were calculated by measuring the fluxes of four bright isolated stars in apertures of 3 (1$\overset{'' }{\mathop{.}}\,$23) and 50 (approximately 20′′) pixels. The background level was estimated in annuli with an inner radius and width of 75 and 25 pixels, respectively. The obtained values in a form of encircled energy and their $1{\kern 1pt} \sigma$ errors are listed in Table А.2.

The HST photometry of Ho II X-1 was carried out using the same images and the same methods as described above for the two neighboring stars. The resulting magnitudes are listed in Table A.1.

Ho II X-1 is a confirmed optically variable source which can potentially cause problems of two kinds. The first one is because the available HST flux measurements in different filters are not synchronous, and, therefore, they may not fit the single model. The second is that the SED, obtained from the HST data, may not be applicable at the time of our observations if the source state had changed. Fortunately, we have fount that this is not the case. Optical variability of Ho II X-1 is not high ($\Delta {{m}_{V}} \approx 0.07$ in the HST observations of 2006–2007, Tao et al., 2011); some authors have already successfully fitted its SED (Tao et al., 2012; Vinokurov et al., 2017). Fitting the fluxes from Table A.1 with a black body⁷, we obtained ${{T}_{{{\text{eff}}}}} = 35.5 \pm 2.9$ kK with ${{\chi }^{2}}{\text{/dof}} = 3.6$ which is close to the result by Tao et al. (2012). After convolving the SED model with the bandpass curves, we derived fluxes ${{M}_{{F148W}}} = (2.49 \pm 0.08) \times {{10}^{{ - 16}}}$ and ${{M}_{{F154W}}} =$ $(2.39 \pm 0.08) \times {{10}^{{ - 16}}}$ erg s$^{{ - 1}}$ cm$^{{ - 2}}$ Å$^{{ - 1}}$. These model values based on the HST photometry are close to those by AstroSat (Table A.2), so we can conclude that the source state did not change significantly, and the problem number two does not take place here. Moreover, since the $F148W$ and $F154W$ filters are very close (their bandpasses intersect by approximately 80%, Table 2), small variations in the SED shape can produce only negligible conversion error. The conversion was done by multiplying the net $F154W$ fluxes by the ${{M}_{{F148W}}}{\text{/}}{{M}_{{F154W}}}$ coefficient of $1.040 \pm 0.010$. The final aperture corrected fluxes in the $F148W$ filter are presented the last column of Table A.2. The uncertainties correspond to $\sigma$ confidence intervals and are a square root of a sum of squares of the following components: the statistical errors of the flux measurements in the aperture 1$\overset{'' }{\mathop{.}}\,$23, the uncertainties related the subtraction of the neighboring sources and the uncertainties of determining of the aperture corrections.

To control the obtained results, in particular, the issue that concerns the flux contribution from the neighboring sources varying with the PSF size, we repeated the reduction by another way. Before performing the photometry, we decreased the resolution of each AstroSat image to the worst one (approximately 1$\overset{'' }{\mathop{.}}\,$8, observation #6) which have to equalize the aperture corrections and the contributions between the observations. The images were smoothed with a 2D Gaussian filter whose width in each direction was chosen in that way to make the aperture corrections and $FWHM$s of single stars the same (within error) as observed in the image #6. Then we measured the net Ho II X-1 fluxes assuming the total contribution from the neighboring sources to be equal to that determined in Section “Flux Contribution from Neighboring Sources” for the observation #6. The fluxes obtained by both methods turned out to be in a very good agreement.

X-RAY DATA REDUCTION

For the standard analysis, the SXT team recommends⁸ extracting the source counts from a circular aperture of 16′ radius (covering about 95% PSF) in the 0.3–7.0 keV range and using the background spectrum obtained by a special calibration set of observations.⁸ This is argued by the fact that the PSF profile of SXT has a wide component extending up to 19′ (while the FOV is 40′), and therefore the “custom” background measured in areas around the source may be contaminated by the source counts. It has to lead to overestimation of the background. However, our inspection of the Ho II X-1 observation has shown that the custom background appeared to be lower than the standard one (rescaled to the same area) in all the cases. Moreover, we found that the background varies between the observations by up to 30%, so the subtraction of the same level for all the data sets may yield incorrect estimates of the net fluxes, especially for such a faint source as Ho II X-1. In this regard we decided to present our analysis in two variants. The first one (hereafter method I) is the “conservative” where the source counts are extracted from a 5′-aperture and the standard background is used. This aperture has to still cover 50% of the PSF but collect much less background counts. We found that, in this variant, the background contribution to the total flux collected by the aperture is about 20% which make the problem of choosing a particular background less important. In the second variant (method II), we used a 16′-aperture and custom background extracted from a number of regions in the same frame. The regions, rectangular and circular, were placed individually for each data set in a way as to cover maximal area and be outside both the 16′ source region and aside from calibration sources at the chip corners. In this variant, the source and background contribution are about equal. Additionally, we excluded energies below 0.7 keV that are dominated by background.

To produce the light curves (Fig. 3) we filtered the event files by energy channel with expression PI=70:700 which roughly corresponds to the energy range 0.7–7.0 keV. The count rate of the standard background in this range was obtained via xspec (0.0074 cnt s$^{{ - 1}}$). The light curves are binned to have one point per each continuous segment with duration of 200 s or more. The shorted segments were dropped.

To obtain fluxes in physical units we carried out a spectral analysis. Due to relative low number of accumulated counts, we decided to consider only the simplest models: a singe multi-color disk or a single power law modified for interstellar absorption, and use the Cash statistic (Cash, 1979). The spectra were grouped with the grppha task to have a minimum of 1 count per bin. The response matrix (RMF) was the standard one, sxt_pc_mat_g0to12.rmf; the ancillary responses (ARFs) were produced individually for each spectrum using the sxt_ARFModule_v02.py script with correction for vignetting enabled. This is strongly recommended when the SXT is not a primary instrument, so a source is shifted aside from the optical axis. In our observations, the shift was about 4′ in all the observations except #2 and #3 where the shift was 9′ and 11′, respectively. For these two the vignetting correction changed the fluxes by about 15% and 25% respect to uncorrected ones; in other cases the corrections were 6–9%. The interstellar absorption was introduced by the tbabs model with the ${{N}_{{\text{H}}}}$ restricted to be not lower than the Galactic value of $5.8 \times {{10}^{{20}}}$ cm^–2 received via the nh tool of the Heasoft package.

Both the disk and power law models have provided acceptable fits with the reduced C/d.o.f. from 0.8 to 1.2 (${{T}_{{{\text{in}}}}} \sim 1.2$ keV, $\Gamma \sim 1.6$ and ${{N}_{{\text{H}}}}$ near its lower limit). Nevertheless, the power-law model gave smaller values of the fit statistic (by 5–15%) in almost all observations, and we decided to derive fluxes from it. The unabsorbed source fluxes with $1{\kern 1pt} \sigma$ errors were measured via the cflux convolution model, the results for both method I and II are listed in Table 1 and shown in Fig. A.1. The obtained spectral indexes are also shown in that figure.

Fig. A.1.

Net X-ray flux (a) and power-law index $\Gamma$ (b). Colors, the same as in Fig. 3, denote two extraction methods (see text): blue—method I (5′), black—method II (16′).

The fluxes obtained from two apertures appeared to be different. Note that ARFs, which designed to account energy-depended effective area of a specific X-ray telescope when converting count rate to physical flux, being always produced for a certain aperture, perform essentially an “aperture corrections” making the obtained flux independent on the aperture size. However, the fluxes from the 5′-aperture are systematically lower (but not twice, which should be without the correction for the aperture size). This may indicate that the correction is not full. On the other hand, the fluxes from the larger aperture might by overestimated because in the method II we used the background taken from peripheral areas of the FOV which may suffer from vignetting. Also, the fluxes from the smaller aperture have displayed wider scatter despite it has to collects less background counts. This might be attributed to the fact that a small aperture is more sensitive to random fluctuation of the PSF. So, the fluxes from the wider aperture should be considered as more reliable. The spectral indexes, in contrast, are more stable in the 5′-aperture because they depend more on the relative background level at high energies than on the PSF shape.