An Optical and Infrared Time-domain Study of the Supergiant Fast X-Ray Transient Candidate IC 10 X-2

We demonstrate mid-IR variability concurrent with the 2010 X-ray outburst by constructing a light curve using archival Spitzer-IRAC images. The flux density was calculated using a circle with 25 radius centered at X-2. Background flux density was calculated from an annulus centered at IC 10 X-2 with 35 inner radius and 6'' outer radius to avoid contamination from nearby bright sources. The raw data (counts) were photometrically calibrated using IRAC specifications from Skrutskie et al. (2006), giving fluxes in mJy. The 1σ uncertainty in the counts and fluxes were calculated by multiplying the uncertainty in the mean counts of the background annulus by the area of the 3'' circle.

To complement the Spitzer images, we obtained near-infrared images of IC 10 X-2 in the J, H, and K_s bands on 2016 July 18 using the Wide Field Infrared Camera (WIRC; Wilson et al. 2003) on the 200 inch Hale Telescope at the Palomar Observatory (P200). To allow accurate subtraction of the sky background, we took well-dithered sequences of 18 exposures of 60 s integration in J, 19 exposures of 25 s integration with 2 coadds in H, and 22 exposures of 15 s integration with 2 coadds in K_s, for total integration times of 1080 s in J, 950 s in H, and 660 s in K_s. Imaging reductions, including flat-fielding, background subtraction, astrometric alignment, and stacking of individual frames were performed using a custom pipeline. The photometric zero points of the final images were measured using aperture photometry of seven isolated 2MASS stars in the field. Flux density was calculated using a circle with 3'' radius centered at IC 10 X-2. Background flux density was calculated from an annulus centered at IC X-2 with 5'' inner radius and 10'' outer radius. Fluxes were converted to magnitudes assuming a Gaussian distribution of combined uncertainties from the 2MASS star zero points and the X-2 photometry.

Near-infrared spectroscopy was performed using the Triple Spectrograph (TripleSpec) instrument during the same observation run to complement visible-spectrum spectroscopy by Laycock et al. (2014). TripleSpec uses a 30 × 1 arcsec slit to obtain a JHK spectrum from 1 to 2.4 μm with a resolving power of 2500–2700. We obtained a sequence of 8300 s exposures, for a total integration time of 2400 s. TripleSpec data were reduced using standard procedures with bias and flat-field corrections. Wavelengths were calibrated against atmospheric lines.

We used optical photometry of IC 10 X-2 from the IPAC/iPTF Discovery Engine, which is described by Masci et al. (2017). The iPTF uses the Palomar Observatory 1.2 m Oschin Telescope with a mosaic camera consisting of 11 CCDs. The CCDs have 4 × 2 K pixels and the camera has a pixel scale of 102 pixel⁻¹, giving it a total field of view of 7.26 square degrees. The reduction pipeline for PTF applies standard debiasing, flat-fielding, and astrometric calibration to raw images (Laher et al. 2014). Relative photometry correction is applied and absolute photometric calibration to the few percent level is performed using a fit to SDSS fields observed in the same night (Ofek et al. 2012). The PTFIDE module performs image-differencing and transient extraction and returns the images to the pipeline for archiving, database-loading, and machine-learned vetting. The overall products of the iPTF pipeline and PTFIDE are difference images, mask and uncertainty images, and QA metrics, in addition to candidate transient catalogs with PSF-fit and aperture photometry, and thumbnail images of transient candidates. Optical light curves in the R and g bands, spanning 2010 November 14–2017 February 14 and 2009 August 25–2017 January 10, respectively, were generated for IC 10 X-2. All R and g band photometries are shown in Tables 2 and 3.

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Near IR and optical light curves of IC 10 X-2 are shown in Figure 2. We define the [3.6] and [4.5] quiescent levels as the average of the four most recent magnitudes between 2012 April 4 and 2016 March 23, which are 15.38 ± 0.10 and 15.24 ± 0.09 mag respectively. The initial [3.6] and [4.5] magnitudes on 2004 July 23 were 6.0σ and 8.3σ higher than the quiescent levels. Four months prior to the 2010 May X-ray outburst, ≲month-timescale variability is detected between 2010 January 29 and 2010 February 19 where the [3.6] and [4.5] fluxes decreased by factors of 0.30 and 0.35, respectively.

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Serendipitously, the three mid-IR observations preceding the outburst by ∼2–4 months were taken within ∼weeks–months of Chandra/ACIS-S nondetections on 2010 February 11 and April 4 (Laycock et al. 2014). After the X-ray outburst, there is no obvious evidence of variability in the mid-IR with observations over the following ∼6 years. Post-outburst, the [3.6] and [4.5] fluxes exhibit approximately constant values of 0.20 and 0.15 Jy, respectively.

Both the optical R- and g-band light curves of X-2 exhibit high-amplitude, short-duration flares that deviate significantly (>5σ) from the quiescent brightness levels (Figure 2). The median, "quiescent" magnitudes in the R and g bands were 18.64 ± 0.05 and 20.17 ± 0.08 Vega mag, respectively. A Lomb–Scargle periodogram analysis of the R-band light curve provided no significant periodicity in the variability.

A flare was defined to be a brightening event with an amplitude greater than 5σ above the quiescent magnitude. The brightest observed flare in the R-band occurred on 2013 October 10 (MJD 56575) and exhibited an amplitude of 1.32 mag. There were two detections of the 2013 October 10 flare taken 0.15 days apart, which provides a lower limit on the flare duration. Notably, this is the longest observed flare duration measured in the optical light curves. Upper limits were placed on the duration of each flare by defining the start and end of each flare to be magnitudes within or below 1σ of the quiescent brightness. The average upper limit determined for each flare is 8.0 days.

An average timescale between flare events of 15.1 ± 7.8 days is derived for the R-band light curve of X-2. The >60 days gaps in the light curve with no coverage of X-2 were omitted from this calculation. Interestingly, there were no flares observed at either the R- or g-band between 2015 August 5 (MJD 57239.4) and the end of the observations on 2017 February 14 (MJD 57798.1).

Short-duration and significant dips in brightness (>5σ) are also apparent in both R- and g-band light curves of X-2. Only the dip on 2014 July 24 (MJD 56862.3) was detected with multiple consecutive observations, which provides a lower limit on the dip duration of 0.10 days. The highest amplitude dip was observed on 2015 January 25 (MJD 57047.2) and decreased to 0.62 mag below the quiescent brightness.

The TripleSpec instrument detected near-IR continuum emission from X-2 and three emission lines with high signal-to-noise ratios (see Figure 3). We identified them as Helium i (He i, 1.0819 μm), Paschen-Gamma (Pa γ, 1.0926 μm), and Paschen-Beta (Pa β, 1.2805 μm). Comparing to their rest-frame wavelengths at 1.0830, 1.0933, and 1.2815 μm gives blueshifts of −314, −332, and −307 km s⁻¹, which are consistent with the −340 km s⁻¹ velocity measured for IC 10 (Laycock et al. 2014). The three emission lines appear photospheric in origin as opposed to nebular since they are not spatially extended.

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The center wavelengths and full widths at half maximum (FWHM) were determined from Gaussian fits in CurveFitMathematica,⁶ a Mathematica package. The FWHM were corrected for instrument resolution according to the following equation:

$$\begin{eqnarray}&&{\mathrm{FWHM}}_{\mathrm{corrected}}=\sqrt{{\mathrm{FWHM}}_{\mathrm{obs}}^{2}-{\mathrm{FWHM}}_{\mathrm{instr}}^{2}}\end{eqnarray} \tag{ 1 }$$

using the average spectral resolution 2600, from the 2500 to 2700 spectral resolution provided in TripleSpec instrument documentation.

The Pa γ and Pa β emission lines exhibit velocity widths near the 120 km s⁻¹ spectral resolution of TripleSpec. The velocity width of the He i 10830 Å emission line, which provides a valuable diagnostic on the physical properties of stellar winds from massive stars (e.g., Groh et al. 2007) is ∼230 km s⁻¹. This velocity is consistent with winds from quiescent LBVs (Smith 2014; Humphreys et al. 2017) and the dense equatorial outflows from sgB[e] stars (de Wit et al. 2014) but slower than the ≳1000 km s⁻¹ outflows exhibited by OB supergiants and WR stars.

The normalized continuum emission level between 1.086 μm and 1.090 μm was 0.20 ± 0.06. We do not detect any significant blueshifted absorption features characteristic of P Cygni profiles in our near-IR spectra of X-2.

In order to discern the nature of X-2's stellar counterpart, we compare its near-IR spectum with the Groh et al. (2007) spectral atlas around He i 10830 Å encompassing four categories of stars: (1) Be type, (2) LBV/LBV candidates (LBVc)/ex- or dormant LBVs, (3) OB supergiants, and (4) Wolf–Rayets. The ∼230 km s⁻¹ width of X-2's He i peak rules out the Wolf–Rayet class, which exhibits a broad (≳1000 km s⁻¹) He i emission line. Additionally, Wolf–Rayet stars are typically Hydrogen-poor, which contradicts the clear presence of hydrogen in X-2. X-2 has equally strong He i and Pa γ lines, ruling out OB supergiants, in which the former is much stronger than the latter. In the remaining two categories, X-2 most resembles the LBVc W243 (Clark & Negueruela 2004) and the classical Be star HD 120991 that exhibit He i and Pa γ lines of similar amplitude and width. It should be noted that LBVs exhibit spectroscopic variability, altering the relative strengths of the lines.

Another means of classifying the IR counterpart of IC 10 X-2 comes from plotting its [3.6] magnitude versus [3.6]–[4.5] color on a color–magnitude diagram (CMD) of known supergiant stars in the Large Magellanic Cloud (LMC) with Spitzer counterparts shown in Figure 4 of Bonanos et al. (2009). The original CMD was recreated from online data published by Bonanos et al. (2009). We used μ = 18.91 for the LMC distance modulus (Bonanos et al. 2009), and μ = 24.1 for the galaxy IC 10 (Laycock et al. 2014). We do not detect significant variations in the mid-IR Spitzer observations.

Throughout all the mid-IR observations, X-2 occupies a region in the mid-IR CMD that is consistent with A-, F-, G-type supergiants (AFG/comp in Figure 4), late and early B-type supergiants, Wolf–Rayets, and LBVs. Notably, X-2 is over two magnitudes brighter at 3.6 μm than the Be-XRB, which implies that the IR counterpart is unlikely a classical Be star. Wolf–Rayet and Early B-type supergiants are ruled out based on the properties of their near-IR emission lines discussed above. It is unlikely that X-2 is an AFG/late-B supergiant given the hardness of the radiation field required to produce the observed near-IR emission lines (Figure 3). We therefore interpret X-2 as an LBV/LBVc in quiescence, which is supported by the presence of characteristic optical emission lines revealed by Laycock et al. (2014; e.g., He ii 4686). We note that X-2 exhibited variability in the mid-IR brightness on similar amplitudes (∼0.6–0.7 mag) and timescales (≳years) as the bona fide LBV M33 Var C (Szeifert et al. 1996; Thompson et al. 2009; Clark et al. 2012).

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LBVs typically exhibit luminosities greater than a few times 10⁵ ${L}_{\odot }$ (Smith 2014). It is difficult to determine the bolometric luminosity of X-2 due to uncertainties in the line-of-sight extinction; however, Laycock et al. (2014) estimate extinction-corrected V-band magnitudes of X-2 as M_V = −6.78 for optically derived dereddening and M_V = −7.51 for X-ray derived dereddening. Assuming a bolometric correction of −1.68 mag, the approximate value for the LBV AG Carinae in 2002 March–July (Groh et al. 2009b), we estimate the luminosity of X-2 to be ∼2–4 × 10⁵ ${L}_{\odot }$. This range of luminosities is consistent with the values exhibited by lower luminosity LBVs. We note that although the bolometric corrections will depend on the effective temperature of the star, there are LBVs that have absolute visual magnitudes consistent with X-2 (M_V ∼ −7; Humphreys et al. 2014).

Massive stars with strong winds such as LBV and Wolf–Rayet stars can exhibit an IR excess due to free–free emission from their outflows (e.g., Cohen et al. 1975). However, an IR excess may also be attributed to the presence of warm circumstellar dust. We attempt to distinguish the nature of the mid-IR emission by performing a power-law fit, ${F}_{\nu }\,=C\,{\lambda }^{\alpha }$ mJy, to the 3.6, 4.5, 5.8, and 8.0 μm photometry taken 2004 July 23. The best-fit provides C = 0.9 ± 0.2 mJy and $\alpha =-0.76\pm 0.12$. This slope is consistent with the predicted α ∼ −0.6 value for free–free emission from an ionized outflow from a star with a spherical expansion and constant velocity (e.g., Wright & Barlow 1975). The source of the mid-IR emission is unlikely due to dust given that color temperature estimates for the mid-IR emission at 3.6 and 4.5 μm indicate values of ∼1700 K, which is hotter than dust sublimation temperatures (∼1200 K; Draine 2011). We therefore interpret the IR excess from X-2 as free–free emission.

Work by Humphreys et al. (2017) on distinguishing LBVs/LBVcs and supergiant B[e] stars shows that the IR spectral energy distribution from LBVs exhibit free–free emission with no evidence of warm circumstellar dust. Most supergiant B[e] stars, however, are found to have warm circumstellar dust. Humphreys et al. (2017) also indicate that dusty/non-dusty LBV/sgB[e] stars are clearly separated in mid-IR color space, where stars with [3.6]–[4.5] < 0.5 do not show warm circumstellar dust. This distinction between sgB[e] and LBV stars is also noticeable in Figure 4 and supports the interpretation of X-2 as an LBV/LBVc.

If the mid-IR flux originates from free–free emission in the winds of IC 10 X-2's optical counterpart, the fluxes can be used to estimate its mass-loss rate (e.g., Fuchs et al. 2006). Adopting the formalism of Wright & Barlow (1975) and assuming a thick geometry for the wind (i.e., the ratio of structural size scales in the outflow do not exceed ∼10), the mass-loss rate, ${\dot{M}}_{w}$, is related to the mid-IR flux at 4.5 μm, F_4.5, and other outflow properties as follows:

$$\begin{eqnarray}&&{\dot{M}}_{w}\sim 6\times {10}^{-5}\displaystyle \frac{\mu }{{\gamma }_{e}^{1/2}\,{g}^{1/2}\,Z}{\left(\displaystyle \frac{d}{660\mathrm{kpc}}\right)}^{3/2}\cdot \\ &&\quad {\left(\displaystyle \frac{{F}_{4.5}}{174\mu \mathrm{Jy}}\right)}^{3/4}\left(\displaystyle \frac{{v}_{w}}{200\,\mathrm{km}\,{{\rm{s}}}^{-1}}\right)\,{M}_{\odot }\,{\mathrm{yr}}^{-1},\end{eqnarray} \tag{ 2 }$$

where μ = 1 is the mean molecular weight per nucleon, d is the distance to IC 10 X-2, v_w is the wind velocity, γ_e = 1 is the number of free electrons per nucleon, g = 1 is the Gaunt factor, and Z = 1 is the mean charge per ion. The mass-loss rates determined by Equation (2) from the range of fluxes exhibited by IC 10 X-2 at 4.5 μm is ${\dot{M}}_{w}\approx 3\times {10}^{-5}\mbox{--}{10}^{-4}$ ${M}_{\odot }$ yr⁻¹, which is consistent with the mass-loss rates exhibited by LBVs in quiescence (e.g., Smith 2014).

Since the optical and X-ray data were not acquired contemporaneously, it is difficult to determine whether or not the X-ray and optical variability share the same origin. However, the ∼0.15 days (∼4 hr) lower limit on the optical variability timescale is consistent with observed durations of X-ray flares from known SFXTs (a few hours; Romano et al. 2014).

We can address whether the short timescale $(0.15\,\mathrm{days}\,\lesssim {\rm{\Delta }}t\lesssim 4\,\mathrm{days})$ and high-amplitude (∼1 mag) variability exhibited by X-2 (Figure 2) is due to activity from the stellar counterpart or linked to the binary nature of the system. LBVs and OB supergiants are known to exhibit optical variability on similarly short timescales of days to weeks, but the brightness only varies by up to a few tenths of a magnitude (e.g., Bresolin et al. 2004). Alternatively, LBVs are known to undergo phases of extreme photometric variability from 1 to 2 mag but on timescales of years to decades. The short timescale, high-amplitude variability from X-2 is therefore most likely due to the presence of the compact object and linked to the X-ray variability.

There are several mechanisms considered for SFXTs that could account for the short optical flares from X-2. The flares may be due to accretion of clumpy winds from the donor star, motion of the compact object through an asymmetric outflow, and/or "gated" accretion due to magnetic processes (see Sidoli 2013 and references therein). With the available data on X-2, it is difficult to address the later mechanism; however, we can study the first two in the theoretical framework of Bondi–Hoyle accretion (e.g., Davidson & Ostriker 1973).

Assuming an accreting compact object of mass M_CO is traveling at a velocity v_rel relative to the winds from the supergiant donor star of mass M_* with a mass-loss rate ${\dot{M}}_{w}$ and outflow velocity v_w, the accretion rate onto the compact object can be approximated by

$$\begin{eqnarray}&&{\dot{M}}_{\mathrm{acc}}=\zeta \displaystyle \frac{{(G{M}_{\mathrm{CO}})}^{2}}{{v}_{\mathrm{rel}}^{3}}\displaystyle \frac{{\dot{M}}_{{\rm{w}}}}{{a}^{2}\,{v}_{{\rm{w}}}},\end{eqnarray} \tag{ 3 }$$

where a is the orbital separation between the compact object and donor star, and ζ is the correction factor for radiation pressure and the finite gas cooling time (assumed to be ζ = 1, e.g., Oskinova et al. 2012). The relative velocity between the winds and the orbital motion of the compact object moving at a speed of v_CO is

$$\begin{eqnarray}&&{v}_{\mathrm{rel}}=\sqrt{{v}_{\mathrm{CO}}^{2}+{v}_{w}^{2}},\end{eqnarray} \tag{ 4 }$$

where v_CO can be approximated by ${v}_{\mathrm{CO}}\approx \sqrt{{{GM}}_{* }/a}$ assuming nearly circular orbits and ${M}_{* }\gg {M}_{\mathrm{CO}}$. The X-ray luminosity from the accreting compact object is then

$$\begin{eqnarray}&&{L}_{X}=\eta \,{\dot{M}}_{\mathrm{acc}}{c}^{2}\approx \eta \,\zeta \displaystyle \frac{{(G{M}_{\mathrm{CO}})}^{2}}{{\left(\tfrac{{{GM}}_{* }}{a},+,{v}_{w}^{2}\right)}^{3/2}}\displaystyle \frac{{\dot{M}}_{{\rm{w}}}}{{a}^{2}\,{v}_{{\rm{w}}}}{c}^{2},\end{eqnarray} \tag{ 5 }$$

where η is an efficiency factor that depends on the accretion physics and is assumed to be η ∼ 0.1 (e.g., Oskinova et al. 2012).

In order to test the viability of Equation (5), we use it to compare against the orbital period (P_orb = 8.95 days) of the well-studied wind-fed HMXB Vela X-1 (Hiltner et al. 1972; Lamers et al. 1976; Quaintrell et al. 2003). We adopt the Vela X-1 supergiant stellar wind velocity, mass, and mass-loss rate provided by Giménez-García et al. (2016) and the X-ray luminosity derived by Sako et al. (1999): v_w = 264 km s⁻¹ M_* = 21.5 ${M}_{\odot }$, $\dot{M}\,=6.3\times {10}^{-7}$ ${M}_{\odot }$ yr⁻¹, and ${L}_{X}=4.5\times {10}^{36}$ erg s⁻¹. Assuming the mass of the accreting NS is M_CO = 1.5 ${M}_{\odot }$, we estimate from Equation (5) and Kepler's 3rd Law that P_orb ∼ 16 days, which is within a factor of 2 of the observed orbital period for Vela X-1. Equation (5) should therefore provide reasonable estimates or limits for the orbital parameters of wind-fed X-ray binaries in nearly circular orbits.

First, we consider the scenario where the optical/X-ray flares were due to the compact object encountering an asymmetric outflow from the stellar counterpart. Such mass-loss asymmetries are naturally inferred for stars that are observed to be rapidly rotating like bona-fide galactic LBVs (e.g., Groh et al. 2009a). Adopting the derived mass-loss rate of ${\dot{M}}_{w}\sim 5\times {10}^{-5}$ ${M}_{\odot }$ yr⁻¹ and wind velocity v_w ∼ 200 km s⁻¹, and assuming a donor star mass of M_* ∼ 30 ${M}_{\odot }$ and compact object mass of M_CO ∼ 1.5 ${M}_{\odot }$, we find from Equation (5) and Kepler's 3rd Law that for the range of X-ray luminosities exhibited by X-2 in outburst, ${L}_{X}=3.4\times {10}^{36}\mbox{--}1.8\times {10}^{37}$ erg s⁻¹,

$$\begin{eqnarray}&&{P}_{\mathrm{orb}}\sim 500-8600\,\mathrm{days}.\end{eqnarray} \tag{ 6 }$$

The derived orbital timescales under the asymmetric outflow scenario are over an order of magnitude longer than the observed timescales between optical flares (∼15 days; Section 3.1). The timing of the flares in this scenario should also be periodic since they correspond to the orbital motion of the compact object through the stellar outflow. The lack of any significant periodicities identified in a Lomb–Scargle periodogram analysis of the X-2 optical light and the inconsistency between the theoretical and observed flare timescales suggest that the SFXT flares from X-2 did not originate from interactions between the compact object and an asymmetric outflow.

We now consider the scenario where the optical/X-ray flares from X-2 were due to accretion of clumps in an inhomogeneous outflow from the stellar counterpart. Clumping in the winds of massive stars has been observationally confirmed and is also backed by stellar wind theory (e.g., Oskinova et al. 2012). With the observational constraints on the flare duration, Δt ∼ 0.2–8 days, and the time between flares, T ∼ 15 days, the clump volume filling factor, f_V, can be estimated for the stellar outflow of X-2 and compared with the f_V of supergiant winds.

Assuming a simple model where the outflows consist entirely of clumps with radius R_cl and mass M_cl, the clump volume filling factor is given by the ratio of the homogeneous wind density, ρ_h, and the individual clump density, ρ_cl: ${f}_{V}=\tfrac{{\rho }_{h}}{{\rho }_{{cl}}}$. The homogeneous wind and clump densities can be written as

$$\begin{eqnarray}&&{\rho }_{h}=\displaystyle \frac{\dot{{M}_{{cl}}}}{4\pi \,{R}^{2}\,{v}_{{cl}}}\,\mathrm{and}\,{\rho }_{{cl}}=\displaystyle \frac{{M}_{{cl}}}{4/3\,\pi \,{R}_{{cl}}^{3}},\end{eqnarray} \tag{ 7 }$$

respectively, where $\dot{{M}_{{cl}}}$ is mass loss from the clumped outflow, R is the distance between the stellar counterpart and compact object, and v_cl is the clump outflow velocity. $\dot{{M}_{{cl}}}$ can be related to the timescale between the flares, T, as follows (see Walter & Zurita Heras 2007):

$$\begin{eqnarray}&&\dot{{M}_{{cl}}}=\displaystyle \frac{4\,{R}^{2}{M}_{{cl}}}{{R}_{{cl}}^{2}\,T}.\end{eqnarray} \tag{ 8 }$$

By combining Equations (7) and (8), f_V can then be expressed as

$$\begin{eqnarray}&&{f}_{V}=\displaystyle \frac{4\,{R}_{{cl}}}{3T\,{v}_{{cl}}}\sim \displaystyle \frac{4\,{\rm{\Delta }}t}{3T},\end{eqnarray} \tag{ 9 }$$

where we assumed ${R}_{{cl}}\sim {v}_{{cl}}\,{\rm{\Delta }}t$. Given the observed constraints for X-2 on Δ t ∼ 0.2–8 days and T ∼ 15 days, we determine from Equation (9) that

$$\begin{eqnarray}&&0.01\lt {f}_{V}\lt 0.71.\end{eqnarray} \tag{ 10 }$$

Although the upper limit of f_v is not well constrained from our observations, the range of values for f_V overlaps with observationally derived clump volume filling factors for massive star winds: f_V ∼ 0.02–0.1 (e.g., Bouret et al. 2005; Oskinova et al. 2007). The additional evidence of "eclipses" in the light curve, which may arise from optically thick clumps in the winds of the optical counterpart (Figure 2), supports the interpretation of the optical flares as clump accretion onto the compact object.