## Online material

### Appendix A: Radial velocity measurements

Radial velocities for SW CMa (with all corrections applied) and residuals from the final spectroscopic orbit.

Radial velocities for HW CMa (with all corrections applied) and residuals from the final spectroscopic orbit.

### Appendix B: Light curve solutions for SW CMa under different limb-darkening assumptions

Tables B.1 and B.2 present our JKTEBOP solutions for fixed linear LD coefficients (*u*_{p}, *u*_{s}) from van Hamme (1993) and from Claret (2000), respectively. The uncertainties we report are formal errors from the iterative least-squares procedure, which are often found to be underestimated. In each case the agreement between the *uvby* passbands is quite good, and the results using the different LD coefficients show small but perhaps significant systematic differences, with the inclination angle being about smaller using the Claret values, the sum of the radii being ~0.5% larger, and *k* also being 1–3% larger (resulting in *r*_{p} values up to 1% smaller, and *r*_{s} values 1–3% larger). Experiments using Claret coefficients for a quadratic law instead of the linear law lead to solutions that are not significantly better and results that are not very different, and tend to be closer to those obtained with the van Hamme coefficients.

Photometric solutions for SW CMa allowing the linear limb darkening coefficients to vary freely, with the condition that they be the same for the two components.

Weighted mean photometric solutions for SW CMa for three different treatments of the linear limb darkening coefficients.

Solutions with the LD coefficients free are presented in Table B.3, subject only to the condition that the coefficients be the same for the primary and secondary since their temperatures are also very similar. These results indicate slightly better agreement than before between the four passbands. On average the fitted LD coefficients are closer to those by van Hamme than those by Claret. We summarize the elements obtained from the three different LD prescriptions in Table B.4, where the results from the separate passbands have been averaged in each case, with weights inversely proportional to the rms residual of each solution. The light elements finally adopted for the analysis of SW CMa are those with LD free, and are repeated in Table 3 of Sect. 2.3 in the main text, with more conservative errors as described there.

### Appendix C: Light curve solutions for HW CMa under different limb-darkening assumptions

Table C.1 reports the results from JKTEBOP fits using linear LD coefficients from Claret (2000). The errors listed include the uncertainty in the light ratio constraint, but are otherwise internal and unrealistically small in most cases. Similarly small errors are obtained using the van Hamme (1993) coefficients. The geometric elements show good agreement between the *v*, *b*, and *y* bands, with *u* being more discrepant (and also more uncertain). Results using the LD coefficients from van Hamme (1993) are given in Table C.2, and show similarly good agreement in *vby*. In this case we report more conservative errors from 1000 Monte Carlo simulations in which we perturbed the main adjustable quantities that were held fixed to allow their errors to propagate through: the

theoretical LD coefficients were allowed to vary by ±0.08, *e*sin*ω* and *e*cos*ω* were perturbed by amounts corresponding to the spectroscopic uncertainties in *e* and *ω*, and the flux ratios *J*_{s} were allowed to vary by ±0.002. Monte Carlo errors using LD from Claret (2000) are very similar to these.

The systematic differences between the fits with Claret and van Hamme LD coefficients are smaller than we found before for SW CMa: with the Claret coefficients the inclination angle is marginally smaller (by 001), the sum of the radii is ~0.5% larger, and *k* is also 0.1% larger, all in the same direction as found for SW CMa. The individual radii are both systematically larger by about 0.5%.

The light elements we adopt for the analysis of HW CMa are those that use the van Hamme (1993) coefficients. Final values averaged over the *vby* passbands are presented in Table 7 of Sect. 3.3.

*© ESO, 2012*