The most massive stars (M > 60M_⊙) play crucial roles in altering the chemical and thermodynamic properties of their host galaxies. Stellar mass is the fundamental stel-lar parameter that determines their ancillary properties and which ultimately determines the fate of these stars and their influence on their galactic environs. Unfortu-nately, stellar mass becomes observationally and theo-retically less well constrained as it increases. Theory be-comes uncertain mostly because very massive stars are prone to strong, variable mass loss which is difficult to model. Observational constraints are uncertain too. Mas-sive stars are rare, and massive binary stars (needed for dynamical determination of mass) are rarer still; and of these systems only a fraction have suitably high orbital inclinations for direct photometric and spectroscopic radial-velocity analysis. Even in the small number of cases in which a high-inclination binary near the upper mass limit can be identified, rotational broadening and contamination of spectral line features from thick cir-cumstellar material (either natal clouds or produced by strong stellar-wind driven mass loss from one or both of the stellar components) biases the analysis. In the wilds of the upper HR diagram, we’re often left with indirect and circumstantial means of determining mass, a rather unsatisfactory state of affairs.

However, in massive binaries, the strong stellar wind possessed by at least one (and, usually, both) of the stars will interact with the radiation and (in most cases) the wind outflowing from the companion star’s surface. Bob Koch and his collaborators, notably Ray Pfeiffer and Ioan-nis Pachoulakas, recognized this fact long ago (Pfeiffer et al. 1994, Pfeiffer et al. 1997), and developed surprisingly sophisticated models of the complex radiative transfer through the “moving envelope” (to use Sobolev’s termi-nology) of the binary: in these cases, in which the wind is moving in an azimuthal direction (due to orbital motion) in addition to the radial one.

A particularly interesting case occurs when the stel-lar wind from one star collides with a companion star’s wind. The shock-heated gas (typically at temperatures of millions of Kelvin) produced in this collision generates intense X-ray emission that provides a useful diagnostic of wind mass-loss rates and densities. If the cooling of the shocked gas from the star is dominated by adiabatic expansion, then simple scaling laws show that the X-ray luminosity L_x of this gas varies inversely with stellar separation D, i.e. L_x∝ D^-1M²V^-3/2 (1 + ？ ) / ？ ⁴ (see Stevens, Blondin & Pollock 1992), where

is the mass loss rate, V the wind speed, and ？ the momentum flux ratio of the two winds. This change in emission, and the variable overlying wind absorption which changes with our view-ing angle to the X-ray emitting gas, produces an orbital dependence which can be usefully analyzed to constrain the dynamical properties of the system, and, in the best case, constrain the mass of one or both components.

Eta Carinae (= HD 93308) is a long-period (P = 2022 days) colliding wind binary with an extremely bright un-stable Luminous Blue Variable primary (Eta Car A) which has a dense (

？ 10^-3 M_⊙ yr^-1) , slow (V∞ ？ 500kms^-1) wind (Hillier et al. 2001). Eta Car A is one of the most massive and luminous stars in the Galaxy, and as such has been an object of intense interest (Davidson & Humphreys 1997). Periodic variations in the nebular excitation and in the X-ray brightness of the system (Ishibashi et al. 1999) suggest that Eta Car A is orbited by a fainter, hotter, lower mass, unseen companion (Eta Car B) possessing a less dense (

？ 10^-5M_⊙ yr^-1 ) but much faster (V_∞ ？ 3000kms^-1) wind in a very eccentric orbit (e ~ 0.9 or thereabouts). Because of the large eccentricity, changes in separation (by a fac-tor of 20) and viewing geometry produce phase-depen-dent variability in nearly all bands of the electromagnetic spectrum, especially in the thermal X-ray region. This cyclical variability makes Eta Carinae a fine laboratory for studying hypersonic astrophysical shocks, the gen-eration of high-energy thermal radiation, and (possibly) the production of non-thermal high energy emission due to Fermi acceleration of charged particles and inverse-Compton scattering of seed photospheric photons (Ley-der, Walter & Rauw 2010). However, Eta Car A is also a dramatic and sporadic variable in its own right, prone to episodes of extreme brightening and mass loss (the best example of this is the “Great Eruption” of 1843, at which time the star spewed forth ~10M_⊙ of stellar material which now forms its dusty shroud). Sporadic variations in the stellar wind from Eta Car A should cause cycle-to-cycle changes in the state of the wind-wind shock. The phase-dependent and secular X-ray variations of the thermal X-ray emission have been studied in great detail by the Pro-portional Counter Array (PCA) on board the Rossi X-ray Timing Explorer (RXTE; Bradt, Rothschild & Swank 1993) for the last 3 stellar orbital cycles¹ (from 1996 to 2011; Fig. 1; Corcoran et al. 2010). We define Cycle 1 to be the orbital cycle centered on the 1997 X-ray minimum, Cycle 2 cen-tered on the 2003.5 minimum, and Cycle 3 centered on the 2009 minimum.

As discussed in Pittard & Corcoran (2002) and Parkin et al. (2009), the X-ray variations can be modelled to yield values of the stellar wind parameters of Eta Car B, the star which has otherwise not been directly observed. Since wind terminal velocity V is about 3 times the stellar es-cape velocity V_esc (Abbott 1978) we can then constrain the escape velocity and effective gravity of this hidden com-panion. In turn, the physical parameters of the compan-ion and the orbital elements so derived from these types of analyses can be used to constrain the stellar and mass-loss parameters of Eta Car A. Table 1 lists parameters de-rived from analysis of the X-ray spectra and lightcurve (Pittard & Corcoran 2002, Parkin et al. 2009).

WR 140 (= HD 193793; WC7+O4-5) is arguably the best known example of a colliding wind system, and of the range of phenomena which may be associated with

strong, time-variable astrophysical shocks. WR 140’s long period (P = 2,897d) highly eccentric (e = 0.88) orbit (Fahed et al. 2011) is congruent to Eta Car’s, but the lack of thick circumstellar material around WR 140, and the ability to detect spectral features of both stars in the system, as well as the fact that the shock has been resolved by Very Long Baseline Array interferometry (Dougherty et al. 2005) means we have a much clearer view of WR 140 and a much more direct understanding of the variations in the wind-wind interaction around the orbit.

2.2.1 Modeling WR 140’s X-ray Emission

The PCA on RXTE has measured the X-ray lightcurve of WR 140 for over two cycles². The coverage is not as ex-tensive or complete as it is for Eta Car, however two X-ray minima were measured in detail. Qualitatively, the phase-dependent X-ray variation of WR 140 is similar to that of Eta Car: there’s a gradual increase in 2？10 keV X-ray flux from apastron as the stars approach periastron passage; the X-ray flux grows as (roughly) 1/D (where D is the sep-aration between the two stars) up through orbital mean anomaly φ ？ 0.9, at which time a deviation from this re-lation begins; there’s a rapid rise to a maximum flux near the time when the X-ray emitting material near the shock

cone apex is viewed through the lower density wind of the O4 companion; the X-ray flux falls to a minimum which occurs near the time when the leading edge of the shock cone is occulted by the WR star; and after this minimum, the flux recovers but the recovery is asymmetric, i.e. the level after the minimum is lower than the level at a similar mean anomaly prior to the minimum. Fig. 2 shows the observed 2？10 keV X-ray variation for the two periastron passages observed by RXTE.

Modeling the system with smoothed particle hydrody-namics calculations similar to those used to model the X-ray flux variations in Eta Car has had some success. As shown in Russell et al. (2011), simple models in which the X-ray flux is localized very near the apex of the shock cone provide good descriptions of the observed variation, though models in which the X-ray emitting region is dis-tributed along the shock cone (as expected in a realistic wind-wind collision) don’t describe the observed varia-tions as well.

1see http://asd.gsfc.nasa.gov/Michael.Corcoran/eta_car/etacar_rxte_lightcurve/ for the latest RXTE data

2see http://asd.gsfc.nasa.gov/Michael.Corcoran/wr140/wr140_rxte_lightcurves/ for the latest RXTE data

As a canonical colliding wind binary, the X-ray flux behavior of WR 140 around the orbit is remarkably well-behaved even if not yet entirely understood in detail. Im-portant features of its X-ray lightcurve (X-ray extrema, hardness ratio maximum, etc.) are well associated with significant orbital events deduced from radial-velocity and radio interferometric studies. In the Eta Car system as well, models of the phase-locked X-ray variations have been useful in determining the system parameters. How-ever, Eta Car is a star that’s notoriously badly behaved in almost every epoch and almost every energy band, and indeed the behavior of Eta Car’s X-ray flux shows signifi-cant non-phase-locked variations. Secular changes in the observed X-ray flux from Eta Car are probably the best in-dication of a fundamental change in the wind-wind inter-action zone. Such change must indicate a real variation in the stellar winds from either or both the primary and secondary.