TIME SEQUENCE SPECTROSCOPY OF AW UMa. THE 518 nm Mg I TRIPLET REGION ANALYZED WITH BROADENING FUNCTIONS^*

The spectral features of the primary component were fit for all BFs using the rotational profile of a rigidly rotating, limb-darkened star: $R={{S}_{1}}\times r(V{\rm sin} i,u)+{{S}_{0}}$, where $r(V{\rm sin} i,u)$ is the center-normalized profile (as given in many textbooks, e.g., Gray 2005) and S_i are the two fit constants. The profile r involves two stellar parameters, the projected equatorial velocity, $V{\rm sin} i$, which is basically the scaling constant of the X-axis, and the limb darkening coefficient, here assumed constant, u = 0.6. The profile centroid position, V₁, gives the mean velocity of the primary star and is the fourth free parameter of the fit.

The least-square fits were done using the upper 55%, 50%, and 45% of the profiles (within $-142\lt V\lt +142$ km s⁻¹ for the assumed mean $V{\rm sin} i=181.4$ km s⁻¹; see Section 4.2) to avoid complications from the "pedestal" at large rotational velocities around the primary (Section 4.4). Also, one can expect a lesser influence of the equatorial flows on the rotational profile for high latitudes of the primary component. The typical fits can be seen in Figure 1.

The rotational profile fits were well determined for all phases, as can be judged by the small scatter in the fit parameters. The baseline level S₀ has a very small scatter around zero, with a median error of $\pm 6\times {{10}^{-6}}$ in the integral BF units (as in Figure 1); when expressed relative to the maximum strength (called "intensity unit" (i.u.) below), the median error of S₀ is only 0.01%. The scaling factor S₁ shows systematic variation with phase, as shown in Figure 2, also with a very small scatter. In that figure, the factor S₁ is plotted—for convenience—as $C/{{S}_{1}}$, where C is the integral of the rotational profile. The resulting curve is very similar to the photometric light curve of AW UMa. The similarity of the shape is in fact expected (for an invariable primary), as was discussed in Section 3, thanks to (1) the built-in normalization of the BF integrals to the integral of the template spectrum and (2) the very weak variation of the apparent spectral type with orbital phase. Since the brightness and $V{\rm sin} i$ of the primary are apparently constant with phase, instead of the units resulting from the BF normalization (as in Figure 1), we will use the central intensity (S₁) as a more convenient unit in subsequent plots and figures.

The results shown in Figure 2 were obtained strictly spectroscopically, but they represent a very reasonable light curve of AW UMa, which confirms the proper system of photometric phases used in this paper. The figure also shows that most of the orbital phases were observed multiple times; the single-night coverage took place only for two narrow phase intervals, 0.98–0.01 and 0.75–0.80.

During the phase interval −0.07 to $+0.07$, the rotational-profile fits are distorted by the projection of the secondary component during its transit in front of of the primary star. This is reflected in the lower values of S₁ and by the upward spike in the very center of the primary eclipse in Figure 2. The appearance of the secondary component in the data is discussed further in Section 6.

Values of the projected equatorial velocity of the primary component, $V{\rm sin} i$, determined from the individual BF, are shown versus the orbital phase in Figure 3. The median value that will be used below, 181.4 ± 2.5 km s⁻¹, has been determined for the phase interval $0.25\lt \phi \lt +0.75$ (299 data points). The wide phase range around the primary eclipse, which was excluded, resulted from indications that gas motions around the secondary component may distort velocities of the primary star (see Section 4.3). Some traces of systematic phase trends and nightly variations in $V{\rm sin} i$ indicate that gas motions may be present at all phases and may influence the primary BF feature even within the upper 50% of its height.

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It has been long recognized that AW UMa is observed with an edge-on orbit, as implied by the long duration of the total eclipses. Thus, for solid-body rotation, the value of $V{\rm sin} i$ should be very close to the equatorial velocity of the primary. Assuming that it rotates synchronously with its orbital motion, $V{\rm sin} i=181.4$ km s⁻¹ implies a radius of $1.49\;{{R}_{\odot }}$, which is fully consistent with an F2 V star.

It is possible that the actual $V{\rm sin} i$ is smaller than the assumed median value, as indicated by a drop in its value to about 177 km s⁻¹ at the very center of the secondary eclipse (phase 0.5, the small star behind); see Figure 3. This would mean that the upper part of the BF profile is almost always broadened by gas streams. However, variations in the individual determinations of $V{\rm sin} i$ within the secondary eclipse between the individual nights force us to leave this issue open for now.

The solution of the orbital motion of the primary component of AW UMa was based on 299 data points in the phase range 0.25–0.75. Within this range, the motion of the primary appears to be sinusoidal (see Figure 4). Fits of the rotational profile to the primary component BF peaks may be affected by complications due to the presence of the "pedestal" below the level of about 0.4 of the BF maximum (see Section 4.4) and by the surface inhomogeneities when the cutoff level for the fits is set too high. It was determined that radial velocities measured with low cutoffs within the range of 0.45–0.55 of the maximum peak were least affected by both complications. Three sets of rotational profile fits were accordingly obtained for the upper 55%, 50%, and 45% of the observational BFs. The results for all phases are tabulated in Table 3.

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Table 3.  Radial Velocities of the Primary Component

T	ϕ	$V_{1}^{45}$	$V_{1}^{50}$	$V_{1}^{55}$
1.8497	0.4556	−22.40	−22.20	−21.19
1.8512	0.4590	−22.60	−23.30	−23.20
1.8527	0.4624	−22.50	−22.96	−23.06
1.8542	0.4658	−22.69	−23.33	−23.00
1.8559	0.4697	−20.46	−21.02	−21.27

Note. The mid-exposure times are given as T = HJD-2,455,630, while the phases are computed with the assumed initial epoch HJD = 2,455,631.6498 and the period 0.43872420 day. RV measurements for all observations are listed, but only those within the fractional phase interval 0.25–0.75 were used for the orbital solutions. The primary star velocities (in km s⁻¹) are given in the three columns labeled $V_{1}^{45}$, $V_{1}^{50}$, and $V_{1}^{55}$ corresponding to the low cutoff to the rotational profile fit at 0.45, 0.50, and 0.55 of the BF maximum.

Only a portion of this table is shown here to demonstrate its form and content. Machine-readable and Virtual Observatory (VO) versions of the full table are available.

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The sine fits for the phase range 0.25–0.75 for the three levels of cutoffs are given in Table 4. They are of high quality with a typical mean error of $\simeq 1.0$ km s⁻¹ per point. Such a measurement error, perhaps large by todayʼs standards, is unprecedentedly small for a component of a W UMa binary; when compared to the total width of the primary profile ($2\times V{\rm sin} i$), it amounts to only 0.3%. The individual RV determinations for the three cutoff levels are non-random and correlated (Figure 5); obviously, these intrinsic variations increase the above estimate of the fit error per point. We see a systematic dependence in the derived values of V₀ and K₁ on the cutoff level; this dependence may possibly be modeled once a correct model of the binary is developed. For the final orbital solution, we adopt the mean values of V₀ and K₁, as listed in Table 4, with the uncertainties estimated from the scatter between the three sets of the parameters: ${{K}_{1}}=28.37\pm 0.37$ km s⁻¹, ${{V}_{0}}=-15.90\pm 0.12$ km s⁻¹. The orbital amplitude K₁ is small when compared with the width of the primary profile: the star moves by only 7.8% of its full width in radial velocities. The masses of the AW UMa components resulting from the above orbital elements are discussed in Section 7.1.

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Table 4.  Orbital Solutions for the Primary Component

Cut-off	V0	K1	${{\sigma }_{1}}$
0.45	−15.78 ± 0.06	28.67 ± 0.085	0.99
0.50	−15.90 ± 0.07	28.33 ± 0.102	1.20
0.55	−16.01 ± 0.08	28.12 ± 0.115	1.34
⋯	⋯	⋯	⋯
Mean	−15.90 ± 0.12	28.37 ± 0.37	⋯

Note. The rotational profile fits were performed above the cutoff level expressed relative to the BF maximum. ${{\sigma }_{1}}$ is the fit error for one observation. All velocities are in km s⁻¹. The errors for the mean values represent the rms scatter of the determinations, not the formal Gaussian errors of the mean (i.e., divided by $\sqrt{(}3)$), because the deviations are systematic.

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The RV data deviate from the sine curve over the wide range of orbital phases close to the primary eclipse (at least within $-0.8\lt \phi \lt +0.2$), which implies that the RV curve of the primary component is perturbed by the projection of the secondary component. The perturbations show some similarity to the "Rositter–McLaughlin effect," which—in terms of the RV amplitude—was noted by Wilson (2008) on the basis of much less detailed observations to be unexpectedly small or perhaps entirely absent. Our observations confirm that the eclipse disturbance is indeed much smaller than predicted by Lucyʼs contact model. However, it extends in the orbital plane far from the center of the secondary component. In fact, judging by the extent of the perturbation, the secondary appears to be even larger than the primary component. This may be taken as one of several indications that the secondary is not a star filling its Roche lobe but rather a flattened structure. The RV disturbances within the primary eclipse ($-0.8\;\lt \phi \lt +0.2$) are asymmetric relative to the line joining the stars; a distinct isolated feature around the phase +0.05 was observed on all three nights; see Figure 4.

An additional RV component is observed at radial velocities of about 150–250 km s⁻¹ relative to the center of the primary component. It is called the "pedestal" because it presents, in Figure 1, an extended base of the central rotational profile. It is best seen when the same rotational profile (assumed to be $V{\rm sin} i=181.4$ km s⁻¹ and scaled by S₁; see Section 4.1) is subtracted from individual BFs, as in Figure 6. The pedestal was discovered by Pribulla & Rucinski (2008). No interpretation was offered there except for noting that it must be produced by an optically thick material (to produce the same absorption spectrum as the star) moving around the primary at high rotational/orbital velocities. While it is observed at both negative and positive velocities relative to the center of the primary, it is better defined for velocities opposite those of the secondary component. The phase dependence of the integrated intensity of the pedestal, after removal of portions of the orbit that can be affected by the secondary star, is shown in Figure 7. The pedestal intensities, when expressed in units of the integrated rotational profile, vary at a level of 2.5%–4% with the phase, following the double cosine curve, as expected for an elliptical distortion. The width of the pedestal does not seem to be phase dependent and stays within about 50 km s⁻¹ beyond the rotational profile, so that the variations are mostly due to the changing brightness within it.

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At this point one cannot say if the pedestal originates on the primary component as a belt of rapidly moving gas or a disk in the orbital plane, but outside the star. The moderate intensity of the pedestal suggests that this distinction is almost immaterial and that the gas must be rather strongly confined to the equatorial plane.

The 2D images of the velocity field over the disk of the primary component of AW UMa are presented in Figures 8–10. The figures show surface features that are not expected for a simple rotating star. The figures have been obtained by (1) shifting the velocities to the center of the primary component using the value of K₁ (Section 4.3), (2) subtracting the best-fitting rotational profiles from the BFs, and (3) re-sampling the individual deviations into a uniform phase grid at a step of 0.0033 in phase (125 s in time).

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In addition to the pedestal discussed in Section 4.4, which is shown in the figures as two vertical ridges along the edges of the rotational profile, one sees two main types of features on the surface. We call them "ripples" and "spots." Both appear to follow the rotational motion of the primary, but several details allow us to distinguish them in 2D figures, so we discuss them separately.

In the images of deviations from the rotational profiles in Figures 8–10, the ripples form a grid of tenuous, inclined lines crossing the whole range of velocities that are related to the primary component. They are narrow, with the width approaching the RV resolution of our data. The ripples can be distinguished from the spots by their velocity dependence: the spots tend to curve toward the stellar disk edges (somewhat similarly to the arcsin function) and do not extend beyond $\pm V{\rm sin} i$; in contrast, some of the ripples appear to continue into the pedestal, i.e., outside the stellar disk. Thus, the gas responsible for the formation of the pedestal and the ripples may have the same origin. The ripples are surprisingly straight, which may indicate that the physical structures causing them are located above the stellar surface.

Four rectangular sections of Figures 8–10, covering phases 0.60–0.87, 3.12–3.30, 5.09–5.34, and 5.36–5.51, and at the center of the disk, with velocities within ± 130 km s⁻¹ were analyzed for the frequency content in the deviations from the rotational profile. They were selected so as to avoid obvious spots or traces of the secondary transiting the primary. For each section, the FFT analysis was performed on all available observational BFs, ranging in number between 42 and 72 per segment. The median amplitudes for each segment are plotted in the upper part of Figure 11 versus the spatial (RV space) frequency expressed in the language of non-radial pulsations as l-degree modes. The amplitudes appear to rise toward low frequencies (i.e., larger RV scales), but cannot be determined for $l\lt 30$ because of the finite extent in the RV range and the presence of spots. At the lowest accessible spatial frequencies the amplitudes reach $\simeq 0.008$ i.u. Thus, the ripples are faint, and their detection at levels even below 0.001 i.u. has been only possible thanks to the high quality of the CFHT observations. The frequency content of the ripple amplitudes partly reflects the wispy structure of the thin ripples as the individual strands sometimes show larger contrast with intensities $\gt 0.01$ i.u.

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The ripples may possibly be both bright and dark, but this obviously depends on the way the rotational profile is fit and subtracted. If some are bright, as it seems for a few extending into the pedestal, this property would distinguish them from the dark spots. Taking into account the properties of the BFs (Section 3), the bright strands may in fact have a lower temperature than the surroundings as then the BF features become stronger in intensity (provided the matter remains optically thick).

The best defined ripples with amplitudes larger than about 0.005–0.007 i.u. (depending on limits set by the local difficulties with defining the shape and position) were analyzed in 2D images (Figures 8–10) for their duration (expressed in phase ϕ) and the slope $dV/d\phi$ at the center of the primary profile, i.e., at the meridian crossing point. While we do not see any regularities in the durations, the slopes (counted per one rotation synchronized with the orbital period) give some information on the typical drift velocities across the stellar disk. The lower panel of Figure 11 gives the histogram of the drift velocities for the 35 measured stronger ripples. While the accuracy is low, typically ± 25 km s⁻¹, and there may exist a genuine spread in the ripple slopes, the median $dV/d\phi /2\pi =170\pm 21$ km s⁻¹ is consistent with the projected equatorial velocity, $V{\rm sin} i=181.4$ km s⁻¹. Thus, the ripples appear to participate in the rotation of the primary component. Their straight shape and extensions into the pedestal are then hard to explain as surface features; they may very well be structures above the surface, but sharing the rotation of the star.

Spots are inhomogeneity features on the primary component that are dark in the BFs and appear within $\pm V{\rm sin} i$, but do not extend into the pedestal. Thus, they seem to be confined to the range of the surface radial velocities.

The spots are always visible at the negative-velocity side of the BFs, where they can be as deep as 0.1 i.u. As can be seen in Figures 8–10, the spots emerge slowly at negative velocities, curving upward as expected for surface features and then accelerating in radial velocities (turning more horizontal) toward the sub-observer meridian. Their apparent drift at the meridian crossing is unexpectedly slow: in 2D images they are more vertical than the synchronous rotation would imply; if they shared the surface rotation as given by $V{\rm sin} i$, then their horizontal drifts would be much faster across the profile. The mean drift velocity at the meridian is relatively uncertain, $dV/d\phi /2\pi =120\pm 30$ km s⁻¹, because most spots do not cross the central meridian to reach positive velocities; usually they disappear while still approaching the observer.

If interpreted as rotational velocities, the slow drift velocities at the meridian of $\simeq 120$ km s⁻¹ would imply a rotation period about 3/2 longer than the one resulting from $V{\rm sin} i$ and the synchronous rotation rate. Such a surprisingly slow rate finds some support in an attempt to phase the reoccurrence of the spots, as shown in Figure 12. In this figure, the spot drifts are shown for the periods that appear to give the best clustering of the individual lines, 1.00, 1.46, and 1.52 times ${{P}_{{\rm orb}}}$. While an exact alignment of the tracks is hard to achieve for any period tested, the scatter visibly diminishes for slow rotation rates of around $3/2\times {{P}_{{\rm orb}}}$. Such a slow rotation rate is unlikely given the excellent fits of the rotational profile to the upper parts of the primary star BF profiles. Thus, we may suspect that the spots are due to surface structures moving relative to the stellar surface with their own slow rotation rate. Doppler mapping of such features would be very difficult to achieve for the short rotation period of AW UMa and if the differential rotation rate is indeed as large as $\simeq 50$%.

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The lack of an obvious Stokes V signal (Section 1) suggests that spots are non-magnetic structures, but it is difficult to determine the nature of the spots and why they appear dark. They may be genuinely dark, but it is hard to imagine photospheric spots that would lower the spectral continuum locally but have not already been detected in photometry (although a comparison of the light curves by Pribulla et al. (1999) does show significant seasonal changes in AW UMa light curves). More likely, the spots are visible only spectroscopically and possibly only through the use of spectral deconvolution. This would happen if the spectral lines are locally shallower than expected, as then depressions in the BFs would appear. The lines could become more shallow due to filling in by emission or due to locally higher gas temperatures. This matter remains unresolved at this point.

Irrespective of the period assumed for the spot movement rate, synchronized with ${{P}_{{\rm orb}}}$ or equal to $3/2{{P}_{{\rm orb}}}$, as in Figure 12, the spots tend to appear mostly at the sub-secondary and the opposite "ends" on the primary component along the line joining the stars. This may be due to instabilities and/or condensations in flows predicted by Oka et al. (2002) for the mass-losing component of a semi-detached binary. According to these model computations, the flow should take place from the high-pressure polar regions to the low-pressure equatorial regions, with the latter situated along the line joining the mass centers. The high-pressure counter-rotation in the polar regions in the model of Oka et al. (2002) may be linked to the puzzling visibility of the spots at only the negative-velocity side: if the spots are extended but thin, they may be curved in such a way as to be visible at similar velocities at the negative side, but distributed in velocities (hence harder to detect) while on the positive side of the profile.

AW UMa shows a systematic period change $dP/dt=-5.3\times {{10}^{-10}}\ \;{\rm or}\ \;-1.9\times {{10}^{-7}}$ day/year (Rucinski et al. 2013b), which is typical for about a quarter of W UMa type binaries for which such changes have been detected (Kubiak et al. 2006); most of them show smaller, randomly distributed period changes. When interpreted as resulting from the conservative mass transfer from the more massive to the less massive component, the mass exchange rate (estimated using Equation (4.56) in Hilditch 2001) is

$$\begin{eqnarray*}\begin{array}{rcl} dM/dt & = & (1/3)\;({{M}_{1}}{{M}_{2}})/({{M}_{1}}-{{M}_{2}})(dP/dt)/P \\ {} & {} & \simeq -2.1\times {{10}^{-8}}{{M}_{\odot }}/{\rm year}. \\ \end{array}\end{eqnarray*}$$

Note that this is the net mass transfer rate: the actual amount of mass flowing from the primary to the secondary may be larger, as part of the flow may return to circle around the primary component and feed the pedestal. The mass-transfer process leads to accretion phenomena clearly visible spectroscopically on and around the secondary component. According to Pribulla & Rucinski (2008), the secondary may actually be an accretion disk or a star submerged in a disk-like structure.

Figure 13 shows profiles obtained by averaging nine individual BFs observed within ±0.015 in phase around each of the three fully observed orbital quadratures. The secondary shows a double-peaked shape that is characteristic of an accretion region. The shape changes from night to night in intensity and in spacing between the peaks. For the three observed quadratures, the peak separation (measurable to about±3 km s⁻¹) varied distinctly: 80, 98, and 65 km s⁻¹ with a mean half-separation of 40.5 ± 4.8 km s⁻¹. The outer wings beyond the peaks and outside of the inner $\pm (60-70)$ km s⁻¹ were the same for the two quadratures when the secondary was moving away, but they were quite different for the single quadrature when the secondary was approaching us; this was due to the influence of the pedestal, which was apparently different when seen from both sides of the binary. The mean velocities (relative to the primary mass center), determined as averages from the peak positions at the three quadratures, are surprisingly similar: −320.6, $+310.8$, $+311.2$ km s⁻¹. This gives a mean ${{K}_{1}}+{{K}_{2}}=314.2\pm 3.2$ km s⁻¹. This number, taken with ${{K}_{1}}=28.37\pm 0.37$ km s⁻¹, leads to a mass ratio ${{q}_{{\rm sp}}}={{M}_{2}}/{{M}_{1}}=0.0991\pm 0.0014$. We will use the values of K₁ and q for determining the component masses in Section 7. Here, we note that the error of ${{K}_{1}}+{{K}_{2}}$ as given above may be fortuitously small as it is based on only three determinations; we will use ± 0.003 as the error of ${{q}_{{\rm sp}}}$.

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A major difference in the interpretation results from two possible assumptions on what we actually see as the secondary component, an accretion disk or manifestations of accretion processes on the surface of a star. For a stable accretion disk, the distinct peaks in the RV profile are produced by the slow-moving material at the outer rim of the disk, while the extended wings outside of the peaks are formed by the large-velocity matter in the innermost parts of the disk (Smak 1981; Smak et al. 1993). To be visible in the BFs, such a disk would have to consist of optically thick matter to produce a stellar spectrum with the same absorption lines as the stellar surface. Obviously, the geometry of an optically thick disk would require an axis inclination of $i\ne 90$°. By contrast, for a star undergoing accretion, the observed effect would entirely depend on processes within a boundary layer between the stellar surface and the incoming material. The latter possibility, an interaction between the star and some sort of quasi-disk, seems to be more likely. In addition, the accretion-disk interpretation encounters its main difficulty in the expected size of the disk: for a stable Keplerian disk with a central object that has mass as small as the secondary of AW UMa, the observed separation between the velocity peaks implies disk dimensions of the order of $15\;{{R}_{\odot }}$ (this results from a simple scaling relative to the Earth velocity: ${{V}_{d}}\propto 30\;{{(M/{{M}_{\odot }})}^{1/2}}{{(215{{R}_{\odot }}/R)}^{1/2}}$ km s⁻¹). There is no space to accommodate such a large disk. However, we do see—through the quasi-Rossiter–McLaughlin effect (Section 4.3)—that gas extends as far from the secondary component in the orbital plane as perhaps to a distance $\simeq 1\;{{R}_{\odot }}$. Thus, most likely, the observed ring-like structure around the secondary component is neither a fully developed Keplerian disk nor a boundary layer on top of the star. It may be an interaction region where the returning matter, which had missed the secondary and already made a full revolution around the primary, encounters the one orbiting the secondary component. The losses due to the eventual accretion are replenished by the new matter coming from the relatively nearby L₁ Lagrangian point of the primary component. The amount of dispersed matter in the orbital plane may be appreciably larger than the rather moderate net mass transfer rate as indicated by the period change.

The complicated accretion flow around the secondary component is visible when velocities are shifted to the expected mass center for the assumed orbital parameters of the binary. In Figure 14, the 2D images show the secondary component with velocities shifted to its expected mass center for the assumed ${{K}_{1}}=28.37$ km s⁻¹ and for two values of the mass ratio, ${{q}_{{\rm sp}}}=0.08$ and 0.10. The motion of the secondary star is very sensitive to ${{q}_{{\rm sp}}}$, so images such as Figure 14 provide a direct check on the assumed value of ${{q}_{{\rm sp}}}$. The double-peaked structure, which is well defined during the three orbital quadratures (Figure 13), does not seem to continue as a simple, vertical band in this picture for any of the assumed values of ${{q}_{{\rm sp}}}$, but shows complex changes in brightness and position. The mass ratio ${{q}_{{\rm sp}}}\simeq 0.10$ seems to produce a more stable profile, but there still exist complex motions within the profile that are not in strict anti-phase relation to the primary component. Unfortunately, even the almost continuous monitoring on three nights did not provide sufficient coverage to establish any regularity in those strands and wobbling motions. Thus, the estimated mass ratio, ${{q}_{{\rm sp}}}=0.10$, is basically identical to that determined from the mean positions of the double peak at the orbital quadratures, ${{q}_{{\rm sp}}}={{M}_{2}}/{{M}_{1}}=0.099\pm 0.003$, where the assumed uncertainty is twice as large as the one formally determined from the mean velocity of the double-peaked structure.

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The secondary appears to look much more stable when all the data from the three nights are binned in phase and velocity, as shown in Figure 15. The individual strands within the accretion structure average out in such an image. The secondary appears to have a somewhat trapezoidal shape bordered by two ridges; the structure follows the expected sine-curve motion of the secondary component for ${{q}_{{\rm sp}}}\simeq 0.10$. In this average binned image of the whole AW UMa system, the parts that undergo the most variability are located in the region of the two peaks in the profile of the secondary component (Figure 16); most of the binary is stable and repeatable. We note that the primary component, except for its surface ripples and spots, is practically invariable anywhere in its velocity field. The pedestal feature is also surprisingly constant with respect to time.

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Eclipses have potential to shed light on the physical state of the AW UMa secondary component. However, in attempting an interpretation, one must remember that the RV data do not tell us anything about the geometry of the component stars, only about the velocities involved. Thus, the shapes in the 2D images require assumptions on how velocities relate to spatial positions. For the secondary component, any interpretation carries an important uncertainty related to the "inside-out" visibility of accretion processes where the largest velocities are expected closest to the star, rather than farthest from it, as expected for rapidly rotating stars.

During the secondary star occultations (the secondary or shallower eclipses) when it disappears behind the large star, the velocity field of the secondary component is hardly modified at all. In Figures 8–10, which show deviations from the rotational profile, we can detect slight indentations at the high-velocity edges of the secondary profiles (around phases 0.55, 3.05, 5.05, 5.45, 5.55), which suggest that the highest velocities are cut off. Otherwise, the whole system of radial velocities associated with the secondary component is eclipsed as if it was a single extended object. The phases of the eclipse contacts are given in Table 5; they were determined by eye from figures similar to Figures 8–10. While these determinations carry substantial uncertainty (±0.01 in phase) due to the presence of the pedestal, the phases of external contacts (Contacts 1 and 4 in Table 5) are definitely too large to be identified with the real geometrical contact phases, but—rather—they reflect the large range of velocities in the accretion structure.

The secondary star transits over the disk of the primary component (the primary or deeper eclipses) appear to show contacts that are more similar to what is observed in the photometric light curves. In Figures 8–10, the secondary component is visible as two or sometimes three bright ridges which continue the motion of the secondary as observed before and after the eclipses. It is dark inside, but this mainly reflects the imperfect fits of the rotational profile during the transit phases. Although the fits are indeed corrupted, the secondary does produce a very weak disturbance in the primary profiles, as can be seen in the last panel of Figure 1. Unfortunately, only one transit was observed exactly during the central eclipse phases (night 3, phase 5.0); however, the two other transits provided moderately well-defined phases of the external and internal contacts (Table 5).

The observations obtained in the center of occultation at phase 5.0 (see Figures 1 and 10) give the velocity extent of the secondary as ranging between −52 and +52 km s⁻¹, but with a faint extension on the positive side reaching +90 km s⁻¹. Thus, the full RV extent of 104 km s⁻¹ is larger than the mean peak separation during the orbital quadratures, 81 km s⁻¹ (Section 6.1), although on one occasion the separation reached 98 km s⁻¹. The amount of light loss due to the secondary within the above velocity range is hard to estimate because the depression is very shallow and comparable to the depths of the inhomogeneities on the surface of the primary component; very roughly, it absorbed 0.05 ± 0.02 of the primary light. This crude estimate, when transformed to linear dimensions, gives a linear size of about 0.22 ± 0.05 relative to the size of the primary component. Note that for Roche lobes with q = 0.1, the ratio of the "side" or orbital-plane dimensions is about 0.35–0.36 (weakly depending on the degree of fill-out).

The inner contact phases during transits when the secondary touches the edges of the primary from inside (Contacts 2 and 3) are distinctly asymmetric relative to the eclipse center, with mean values of the phases −0.061 and $+0.034$; see Table 5. While the former is the same as the well determined angle of the photometric internal contact 0.062 ± 0.005 (Mochnacki & Doughty 1972), the exit contact phases are much smaller. The same asymmetry is visible in the "light curve" of AW UMa in Figure 2. This could be explained by the shift in the direction of the mass flow close to the L₁ point, which is quite prominent in the model of Oka et al. (2002).

With the orbital velocity amplitude of the primary component, ${{K}_{1}}=28.37\pm 0.37$ km s⁻¹ (Section 4.3), and the sum of the orbital amplitudes determined from the orbital quadratures, ${{K}_{1}}+{{K}_{2}}=314.2\pm 3.2$ km s⁻¹ (Section 6.1), we find a mass ratio ${{q}_{{\rm sp}}}={{M}_{2}}/{{M}_{1}}=0.0991\pm 0.0014$, confirming the determination of Pribulla & Rucinski (2008). While this is the best value for the spectroscopic mass ratio, as described previously (Section 6.1), we adopt an error two times larger so that ${{q}_{{\rm sp}}}={{M}_{2}}/{{M}_{1}}=0.099\pm 0.003$. Even with this adjustment, our spectroscopic mass ratio is several formal errors away from the photometric determinations, which usually converge to a value within ${{q}_{{\rm ph}}}\simeq 0.07-0.08$, but with individual errors usually determined to be very small, as small as 0.0005 (e.g., Wilson 2008). Using the measured K₁ and following our assumption on ${{q}_{{\rm sp}}}$, the estimated orbital amplitude for the secondary is ${{K}_{2}}=286.6\pm 12.4$ km s⁻¹, the distance between the mass centers $A{\rm sin} i=\;2.73\pm 0.11\;{{R}_{\odot }},$ and the masses ${{M}_{1}}{{{\rm sin} }^{3}}i=1.292\;\pm 0.15\;{{M}_{\odot }}$ and ${{M}_{2}}{{{\rm sin} }^{3}}i=0.128\pm 0.016\;{{M}_{\odot }}$.

The orbital inclination of AW UMa must be close to edge-on orientation; otherwise, we would not see long-lasting total eclipses. We certainly cannot assume an orbital inclination angle of $i\simeq 78-80$°, as determined from light-curve synthesis solutions published over several decades of investigation (starting with 80°, Mochnacki & Doughty 1972, with the most recent 78°, Wilson 2008), as they all assumed the Lucy contact model. Thus, the above orbit size and mass determinations may be close to the actual values, but there will remain an additional systematic uncertainty at a level of 1.5% for the linear dimensions and 5% for the masses.

AW UMa appears to be a semi-detached binary showing mass transfer from the more massive to the less massive component. It is not a contact binary as envisaged in the contact binary model of Lucy: the complex internal velocities and obvious accretion processes on or around the low-mass secondary component invalidate the contact model for this binary.

In terms of the evolutionary status of the binary, the new data fully support the models developed by Stȩpień (2006) and Paczyński et al. (2007). The secondary is probably the helium core of a former more massive component that already evolved past the mass exchange; now it is the formerly less massive component that expands and sends matter to the small star. In terms of its kinematics and metallicity, AW UMa appears to belong to the local solar population (Rucinski et al. 2013a): the spatial velocity components $[U,V,W]=[12.5\pm 0.5,-{\mkern 1mu} 55.5\pm 4.1,-9.5\pm 0.5]$ km s⁻¹ and the metallicity $[M/H]=-0.01\pm 0.08$ are typical for an age of 3–5 Gyr. This age would be long enough to produce a system already in the stage of the former secondary expanding beyond its Roche limit.

With its systematically shortening orbital period, AW UMa appears to be evolving toward an eventual merger. Thus, on the timescale of ${{(d{\rm ln} P/dt)}^{-1}}\simeq 2\times {{10}^{6}}$ years, AW UMa will show an eruption and coalescence in the same way as was observed and analyzed recently by V1309 Sco (Stȩpień 2011; Tylenda et al. 2011; Pejcha 2014).