CYGNUS X-3's LITTLE FRIEND

For each observation, we have extracted a zeroth-order image between 1 and 8 keV binned at the nominal ACIS-S resolution (∼049). Figures 2 and 5 show images for the QS observation. In each individual image, there is a bright, unresolved core with strong radial point-spread function (PSF) wings and a strong scattering halo (Predehl et al. 2000). In each observation, the feature reported by Heindl et al. (2003) is present at the same location. An analysis of the QS observation shows that the feature (R.A.: 20^h32^m271, decl.: + 40°57'338) lies at an angular distance of 156 from Cygnus X-3 at an angle of 685 from the orientation of the observed radio jets of Cygnus X-3. The feature is extended and was fit using CIAO/SHERPA with a two-dimensional Gaussian with axes of 36 and 55 and a position angle of 787, measured counterclockwise with the top of the image being 0°. If the feature and Cygnus X-3 are at the same distance, then their separation is 2.2D₉ lt-yr (D₉: distance in units of 9 kpc). This feature is present in all observations of Cygnus X-3 made throughout the Chandra mission (1999 to present).

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The feature is located amidst a high background region. This high background is due to the telescope PSF and a dust scattering halo. The majority of the photons in the background have energies above 2 keV and as such arise from scattering off microroughness in the telescope optics; see the discussion in Predehl et al. (2000). In order to examine the temporal variability of the feature we need to subtract the background flux from the region of the feature. To do this, we used segments of annuli centered on Cygnus X-3 for the feature and background regions to extract the light curve for the feature and the background (see Figure 2). The annuli were chosen to maximize the number of counts for the feature as well as have the feature and background regions sample the same radial region of the PSF/dust halo while avoiding the readout streaks. All data extraction was done with the CIAO tool dmextract.

2.2.1. Phase-folded Analysis

The phase-folded (1–8 keV) light curves of Cygnus X-3, the background region, and background-subtracted feature region are shown in Figure 3. As might be expected the background, which is mainly due to the scattered PSF emission, demonstrates the same 4.79 hr orbital variation with the slow rise and rapid observed drop in Cygnus X-3. This is also reinforced in Figure 4 (top panel) which shows no observed lag in the cross-correlation between Cygnus X-3 and the background. However, the feature surprisingly shows the same orbital modulation but with a phase shift of ∼0.6. Phase-selected images reveal how this feature varies relative to Cygnus X-3 (see Figure 5), which can be seen more dramatically in the movie which accompanies this paper (see online version). This is also confirmed in the cross-correlation between Cygnus X-3 and the feature seen in Figure 4 (lower panel) which shows a clear lag that peaks around 9460 s which corresponds to a phase lag of ∼0.55.

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Fitting phase-folded light curves. To address questions of a possible issue with background subtraction (oversubtraction) we took the light curve from feature annulus and fitted it using the following model:

$$\begin{equation} {C}_{{\rm lf}}[{ { i}}] = C_{\rm bkgd}[{{ i}}] + {a*C}_{\rm bkgd}[{{\rm shift}({ i},{ j})}] , \end{equation} \tag{ 1 }$$

where C_lf[i] is the count rate for the feature's region in phase bin i, C_bkgd[i] is the count rate from background region (scaled to the feature's region size) in phase bin i, and the last term a*C_bkgd[shift(i, j)] is the count rate of the background region scaled by a and shifted by j in phase. The fit parameters are a and j. We used the IDL routine MPFIT (Markwardt 2009) to fit the light curve. We did multiple fits of the light curve using a number of different phase binnings and found good fits for all binnings with consistent fit values (see Table 2). Our best fit gave a = 0.29 ± 0.01 and j = 0.56 ± 0.02 (see Figure 6).

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Table 2. Phase-folded Light Curve Fitting Parameters

Model	Binning	Amplitude	Phase Shift	χ2/dof
	10	0.29 ± 0.01	0.60 ± 0.10	(9.24/8)
	20	0.29 ± 0.01	0.55 ± 0.05	(23.74/18)
Phase shift	40	0.29 ± 0.01	0.55 ± 0.03	(50.82/38)
	50	0.29 ± 0.01	0.56 ± 0.02	(51.17/48)
	100	0.29 ± 0.01	0.56 ± 0.02	(104.60/98)
	10	0.069 ± 0.002	⋅⋅⋅	(66.34/9)
	20	0.068 ± 0.002	⋅⋅⋅	(80.81/19)
Constant	40	0.068 ± 0.002	⋅⋅⋅	(108.07/39)
	50	0.068 ± 0.002	⋅⋅⋅	(110.38/49)
	100	0.067 ± 0.002	⋅⋅⋅	(166.39/99)

Notes. The phase-shifted model is the one given in Equation (1). The constant model is the same as the phase-shifted model except that the shift term has been replaced with a constant which is used as a fit parameter.

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As a further test we replaced the second term in Equation (1) with a constant term which was used as a fit parameter. We found no acceptable fits for any of the binnings (see Table 2). This result is consistent with the feature varying with the same period as Cygnus X-3 but shifted in phase.

Phase image. Finally, as another way to check whether background subtraction could be an issue for each Chandra detected event, a "Cygnus X-3" phase value was determined from its arrival time. Photons falling into certain phase ranges were broken in separate "phase" images. These images were assigned a certain color and combined to form a color-coded phase image. The bands were: (red) 0.3–0.63, (green) 0.63–0.96, and (blue) 0.96–0.3. The image is shown in Figure 7; note the blue color of the feature. This indicates that the bulk of the photons are arriving in the 0.96–0.3 phase range. If the feature was constant we would expect it to be white (equal amounts of each color). It is also important to note that no background subtraction was done in this approach and hence there is no issue with the background subtraction creating a false time/phase variation of the feature.

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2.2.2. Longer Timescale Variability

To examine the temporal behavior of the feature on longer timescales we determined the flux⁴ of Cygnus X-3 and the feature for each of the Chandra/ACIS observations (see Table 1). When Cygnus X-3's flux is plotted versus the flux from the feature there appears to be a correlation (see Figure 8) where the dashed line is a linear fit to the data. A Pearson's correlation test of the data yields a correlation coefficient of 0.98 indicating a linear correlation between the feature and Cygnus X-3.

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The annuli used to extract the light curves (see Figure 2) were also used to extract spectra for the feature and background region. The final background-subtracted spectra of the feature contained from 78 to 3216 counts in the 1–8 keV band. Table 3 shows fits to the spectrum using simple absorbed power-law and blackbody models, all of which yield acceptable fits to the spectrum.

All of the Chandra/ACIS observations were HETG grating observations. The ± first-order HEG spectra were combined and fit for each observation (see notes in Table 1). The continuum for Cygnus X-3 is complex and dependent on the state of activity (Hjalmarsdotter et al. 2008, 2009; Koljonen et al. 2010). In the X-ray (0.5–10 keV), the continuum can be modeled by a partially covered disk blackbody during flaring/quenched states (Koljonen et al. 2010) and during the quiescence/transition states we found that the continuum was best approximated by an absorbed power law. In all cases, a large number of spectral features were added (see Table 4) to improve the spectral fit.

We note that all of the spectra of the feature are more absorbed and very steep/soft, relative to the corresponding Cygnus X-3 spectra (see Tables 3 and 4). As Cygnus X-3 transitions from a quiescent (hard) to a flaring/quenched state (soft) its spectrum becomes softer. The spectrum of the feature is shown to follow suit and becomes steeper/softer as Cygnus X-3's spectrum does.

A natural explanation for the feature's time variable behavior is that it is a result of scattering from a cloud (which acts as a kind of interstellar X-ray "mirror") between Cygnus X-3 and the observer. This explanation would naturally lead to the observed phase difference between light curves as a difference in the path length of the scattered photons (Trümpler & Schönfelder 1973). This could also explain the flux correlation (see Figure 8) and overall flux difference (∼10⁻³) since only a small fraction of the total flux will be scattered toward the observer. In Figure 9, a diagram of the expected geometry for the scattering from a cloud is shown.

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The spectrum of the feature can also be modeled as a scattered version of Cygnus X-3's spectrum. At these energies scattering will modify the spectrum by A*E⁻² (Smith et al. 2002), due to the reduced scattering efficiency at higher energies (Overbeck 1965). There will be an additional reduction at low energies caused by absorption in the cloud (N_cl) and multiple scattering. We can then model the feature's spectrum due to scattering as

$$\begin{equation} {S}_{{\rm lf}} = {e}^{-\sigma {(E){N}_{\rm H}({\rm lf})}} * {A*E}^{- \alpha } * {S}_{{\rm cont}}, \end{equation} \tag{ 2 }$$

where S_lf is the scattering model for the feature, $e^{-\sigma (E)N_{\rm H}({\rm lf})}$ is the additional absorption due to the cloud (modeled using phabs in XSPEC), A*E^−α represents the high energy attenuation due to scattering (modeled using plabs from XSPEC), and S_cont is Cygnus X-3 continuum model determined from the grating data (see Table 4). The resulting fit parameters for the observations are shown in Table 5 and the fit to the QS observation's spectrum is shown in Figure 10. The resultant fluxes (1–8 keV) for the feature and Cygnus X-3 are given in Tables 4 and 5. The flux ratios of the feature to Cygnus X-3 are all in the range of (4–6) × 10⁻⁴.

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This gives rise to a natural explanation of the observed spectral differences. The loss of the flux below 2 keV is the result of additional absorption in the cloud and the reduced flux at higher energy simply reflects the drop in scattering efficiency.

Distance to and size of the feature. Assuming that this feature is due to an individual cloud, the time delay is determined by the distance to the cloud (Trümpler & Schönfelder 1973; Predehl & Klose 1996; Predehl et al. 2000). The resulting time delay can be written as

$$\begin{equation} \Delta t = \frac{\Theta ^2}{\rm 2c}\frac{Dx}{1-x} = 1.15 \Theta ^2 \frac{Dx}{1-x} , \end{equation} \tag{ 3 }$$

where Δt is the time delay (in seconds), D is the distance (in kpc) to the source, Θ is observed angular distance (in arcsec) from the source, x is the fractional distance of the scatter to the observer (see Figure 9), and c is the speed of light. From the observed phase offset, we know that the time delay is given by Δt = (0.56 + n)t_cx3 where t_cx3 = 17.25 ks is the observed orbital period of Cygnus X-3, but we have an ambiguity in the total number orbital period offsets (n). Using Δt = 0.56*t_cx3 = 9.66 ks, D = 9 kpc, and Θ = 156, the resulting fractional distance is x = 0.79. This means that the cloud is close to Cygnus X-3 (within 1.9 kpc) and if n > 0, this distance could be smaller.

This degeneracy (n) can be removed using the fact that the feature is extended. From Equation (3) we would expect that the delay that the scattered photons experience increases as a function of angle from Cygnus X-3. If we take the inner and outer edges of the feature to be 138 and 174 respectively then for x = 0.79 we would get a time delay of ∼1.2 hr across the feature. For locations closer to Cygnus X-3 we would expect the delay across the feature to increase. To test this we have taken the extraction and background annuli (see Figure 2) and divided them into an inner and outer set of annuli (112–156 and 156–200, respectively). In Figure 11, we show a cross-correlation of the inner and outer light curves (for the QS observation with 5 minute time resolution) which shows a significant lag (at the 99% confidence level) at 0.9 hr. This would correspond to the n = 0 case. Figure 12 shows the phase-folded light curves of the inner and outer regions, in which one can see that the light curve for the outer region is lagging the inner by ∼0.2 in phase. This corresponds to a lag of ∼1 hr. This puts the feature at a distance of 1.9 kpc from Cygnus X-3, making its observed dimensions 0.12 by 0.19 parsecs.

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Density of the cloud. From the spectral fit to the feature for the QS observations we have an absorbing column density of the feature of 5.0^+2.0_−1.7 × 10²² cm⁻². This value is consistent with the column density determined from spectral fits to the other observations (see Table 5). The column density of the feature can also be estimated from the flux ratio of the feature to Cygnus X-3 using the following relationship (see the Appendix for its derivation):

$$\begin{eqnarray} \frac{{F}_{{\rm lf}}}{F_{\rm cx3}} &=& N_{\rm H}({\rm lf}) \left[\frac{\pi \tan \alpha _1 \tan \alpha _2 \cos ^2 (\theta _{\rm s} -\theta)}{(1-{x})^2} \right] \nonumber \\ && \times \bigg[\sum _{{i}={\rm g,si}} {N}^{i}_{\rm d} \int ^{{E}_2}_{{E}_1}{S}({E}){e}^{-\sigma ({E}){N}_{\rm H}({\rm lf})} \!\!\!\int ^{a_{\rm max}}_{a_{\rm min}} a^{-3.5} \nonumber\\ && \times \left(\frac{{d}\sigma _{\rm s}(E,a,\theta _{\rm s})}{d\Omega }\right) dadE \bigg]. \end{eqnarray} \tag{ 4 }$$

The flux ratio is equal to the product of three quantities. The first (N_H(lf)) is the column density of the feature, the second is a solid angle term which relates to the fraction of Cygnus X-3's flux that is intercepted by the feature, and the final term is a scattering term which is a measure of the flux scattered by the dust in the cloud (this is solved for by numerical integration over the energy range and grain distribution). The last two terms depend on x, the fractional distance between the observer and Cygnus X-3. Figure 13 shows a plot of the last two terms and their product as a function of x. The solid line is for scattering due to silicates and the dotted line for scattering due to graphite. Equation (4) can be solved for the column density of the feature as a function of x as shown in Figure 14. The parameters used to create these curves are given in Table 6. Also included are lines representing the column density from the spectral fit of QS with its uncertainties and a vertical line representing its location from the observed time delay. What we find is good agreement with the column density determined from the spectral fits and the column density (N_lf = 3.6 × 10²² cm⁻²) necessary to produce the observed flux ratio.

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Table 6. Scattering Flux Calculation Parameters

Parameter	Value
Fcx3 (1–8 keV)	9.12 × 10−1 photons cm−2 s−1(6.13 × 10−9 erg cm−2 s−1)
Flf (1–8 keV)	5.6 × 10−4 photons cm−2 s−1(3.6 × 10−12 erg cm−2 s−1)
θ	156
α1	277 (5σ full width: 554)
α2	182 (5σ full width: 365)
D	9 kpc
ρ (graphite)a	2.24 g cm−3
ρ (silicate)a	3.5g cm−3
Nd (graphite)a	$\rm 7.41 \times 10^{-16} \frac{grains}{H\ atom \ \mu }$
Nd (silicate)a	$\rm 7.76 \times 10^{-16} \frac{grains}{H\ atom \ \mu }$
amina	0.005 μ
amaxa	0.25 μ
E1	1.0 keV
E2	8.0 keV

Note. ^aThe dust grain parameters were taken from Weingartner & Draine (2001).

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If we assume that path length along the line of sight through the cloud is similar to the observed dimensions of the feature ((3.7–5.9) × 10¹⁷ cm) we can make an estimate of the density of the feature. Taking the column density to be 5.0^+2.0_−1.7 × 10²² cm⁻² we arrive at a density range of (0.6–1.9) × 10⁵ cm⁻³ making the feature a dense molecular cloud.

Mass of the cloud. From the estimate of the density of the cloud and the size determined from the X-ray measurements we can make an estimate of the mass of the cloud. Using the simplifying assumption of a spherical cloud with a diameter of between 0.12 and 0.19 pc with a density of 10⁵ cm⁻³ we arrive, from X-ray observations alone, at an estimate of the mass of the cloud of 2–24 M_☉.

From the cloud's size, density, and mass the feature has all of the characteristics of a Bok Globule (Bok & Reilly 1947; Clemens et al. 1991), but instead of seeing this as a dark obscuring feature in the optical, we see it shining in scattered X-rays.

It is possible to derive some of the scattering properties by comparison of the fluxes of Cygnus X-3 and the feature. This derivation is similar to that done for the scattering halo intensity of Smith & Dwek (1998). The geometry being used can be found in Figure 9. If we take the unabsorbed luminosity of Cygnus X-3 as a function of energy to be L_cx3(E) then the X-ray luminosity at the feature is given by

$$\begin{equation} L_{\rm lf} ({E}) = \frac{{L}_{\rm cx3}({E}) {e}^{-\sigma (E)N_{\rm H} (r_s)}}{{4 \pi r_s}^2} , \end{equation} \tag{ A1 }$$

where σ(E) is the X-ray absorption cross section, N_H(r_s) is column density along the path (r_s) between Cygnus X-3 and the cloud.

The number of photons scattered into a solid angle dΩ by a single scatter for a source of luminosity L_s(E) is given by

$$\begin{equation} P (E) = L_{s} (E) \frac{d\sigma _{s}}{d\Omega } d\Omega , \end{equation} \tag{ A2 }$$

where dσ_s/dΩ is the differential scattering cross section (see Mathis & Lee 1991; Mauche & Gorenstein 1986).

For a telescope with collecting area A' we can choose dΩ such that A' = r²_odΩ, where r_o is the distance from the scatter to the observer.

The photon count rate that the observer will detect from scattering from a single dust particle is given as

$$\begin{eqnarray} C_s (E) &=& L_s (E) e^{-\sigma (E)N_{\rm H} (r_o)} \left(\frac{d\sigma _{s}}{d\Omega } \right) \frac{A^{{\prime }}}{r_o^2} \nonumber\\ &=& \frac{L_{\rm cx3}(E) e^{-\sigma (E)[N_{\rm H} (r_s) + N_{\rm H} (r_o)]}}{{4 \pi r_s}^2} \left(\frac{d\sigma _{s}}{d\Omega } \right) \frac{A^{{\prime }}}{r_o^2} , \end{eqnarray} \tag{ A3 }$$

where N_H(r_o) is the column density between the scatter and the observer.

The feature has been fitted with an elliptical Gaussian with semimajor and semiminor axes of r₁ and r₂, respectively. For a distance of xD one can use the angular measurements of the semimajor and semiminor axes, α₁ and α₂, respectively, to give the surface area of the feature as A_lf = πr₁r₂ = πx²D²tan α₁tan α₂. For a scattering region thickness of l_s the scattering volume of the feature is given by V_lf = A_lfl_s. For a dust grain number density of n_g we can determine the total count rate and flux for the feature as

$$\begin{eqnarray} F_{\rm lf}(a,E) &=& \frac{C_{{{\rm tot}}}(E)}{A^{{\prime }}} = \frac{n_g(a) L_{\rm cx3}(E) e^{-\sigma (E)[N_{\rm H} (r_s) + N_{\rm H} (r_o)]}}{4 \pi r_s^2} \nonumber\\ && \times \left(\frac{d\sigma _s}{d\Omega }\right) \frac{A_{\rm lf} l_s}{r_o^2}. \end{eqnarray} \tag{ A4 }$$

In general n_g will be a function of dust radius a. For our case we will consider n_g to be spatially uniform at the location of the feature. Integrating over the dust size distribution gives the flux for the feature as

$$\begin{eqnarray} F_{\rm lf}(E) &=& \int ^{a_{\rm max}}_{a_{\rm min}} \frac{n_g(a) L_{\rm cx3}(E) e^{-\sigma (E)[N_{\rm H} (r_s) + N_{\rm H} (r_o)]}}{4 \pi r_s^2} \nonumber\\ && \times \left(\frac{d\sigma _s}{d\Omega }\right) \frac{A_{\rm lf} l_s}{r_o^2}da. \end{eqnarray} \tag{ A5 }$$

We can simplify the above equation by noting that the observed angle θ for the feature is very small and the overall angular dimensions (α₁ and α₂) of the feature are small. In this case the path traveled by the scattered photon will be very close to the path traveled by the unscattered photon. Because of this the total hydrogen column density for both paths should be the same except for the additional column density of N_H(lf) along the scattered path due to the feature. If we take N_H(cx3) to be the column density between the observer and Cygnus X-3 then the column density along the path of the scattered photon can be written as

$$\begin{equation} N_{\rm H} (r_s) + N_{\rm H} (r_o) = N_{\rm H}({\rm cx3}) + N_{\rm H}({\rm lf}). \end{equation} \tag{ A6 }$$

F_cx3(E) the observed absorbed flux from Cygnus X-3 can be written as

$$\begin{equation} F_{\rm cx3}(E) = \frac{L_{\rm cx3}(E) e^{-\sigma (E)N_{\rm H} ({\rm cx3})}}{{4 \pi D}^2}. \end{equation} \tag{ A7 }$$

Finally, from the scattering geometry (see Figure 9), we have

$$\begin{equation} \frac{1}{r_s} = \frac{\cos (\theta _s -\theta)}{D(1-x)} , \end{equation} \tag{ A8 }$$

where x is the projected distance along the path between the observer and Cygnus X-3. The measured angle of the feature (θ) and the scattering angle (θ_s) are related to the projected distance x by θ = (1 − x)θ_s. Using the above relations we arrive at the following substitution:⁵

$$\begin{equation} \frac{L_{\rm cx3}(E) e^{-\sigma (E)[N_{\rm H} (r_s) + N_{\rm H} (r_o)]}}{4 \pi r_s^2} \! \approx \! \frac{F_{\rm cx3}(E)e^{-\sigma (E)N_{\rm H}({\rm lf})}\cos ^2 (\theta _s -\theta)}{(1-x)^2}. \end{equation} \tag{ A9 }$$

If we integrate over energy bandpass and replace F_cx3(E) by F_cx3S(E) where F_cx3 represents the measured flux from Cygnus X-3 and S(E) is its spectral form (normalized to one) we can write the flux relationship of the feature to Cygnus X-3 as

$$\begin{eqnarray} \frac{F_{\rm lf}}{F_{\rm cx3}} & = & \frac{\pi \tan \alpha _1 \tan \alpha _2 l_s \cos ^2 (\theta _s -\theta)}{(1-x)^2} \nonumber \\ && \times \int ^{E_2}_{E_1}S(E)e^{-\sigma (E)N_{\rm H}({\rm lf})}\!\!\!\int ^{a_{\rm max}}_{a_{\rm min}} n_g(a) \nonumber\\ && \times \left(\frac{d\sigma _{s}(E,a,\theta _{s})}{d\Omega }\right) dadE. \end{eqnarray} \tag{ A10 }$$

Assuming an MRN grain size distribution (Mathis et al. 1977; Weingartner & Draine 2001) then we have

$$\begin{equation} n_g (a) = n_h \sum \limits _{i=g,si} N^{i}_d a^{-3.5} , \end{equation} \tag{ A11 }$$

where n_h is the hydrogen number density of the cloud, a is the radius of the grain, and Nⁱ_d is are the normalization in (grains/H atom)/μm for graphite (g) and silicates (si). If we also note that n_hl_s is simply the column density of the cloud N_H(lf), substituting n_g(a) into Equation (A10) gives us

$$\begin{eqnarray} \frac{F_{\rm lf}}{F_{\rm cx3}} & = & N_{\rm H}({\rm lf}) \left[\frac{\pi \tan \alpha _1 \tan \alpha _2 \cos ^2 (\theta _{s} -\theta)}{(1-{x})^2} \right] \nonumber \\ && \times \bigg[ \sum \limits _{{i=g,si}} N^{i}_{d} \int ^{E_2}_{E_1}S(E)e^{-\sigma (E)N_{\rm H}({\rm lf})} \!\!\!\int ^{a_{\rm max}}_{a_{\rm min}} a^{-3.5} \nonumber\\ && \times \left(\frac{d\sigma _{s}(E,a,\theta _{s})}{d\Omega }\right) dadE \bigg]. \end{eqnarray} \tag{ A12 }$$