YORP and Yarkovsky effects in asteroids (1685) Toro, (2100) Ra-Shalom, (3103) Eger, and (161989) Cacus

<jats:p><jats:italic>Context. </jats:italic>The rotation states of small asteroids are affected by a net torque arising from an anisotropic sunlight reflection and thermal radiation from the asteroids’ surfaces. On long timescales, this so-called YORP effect can change asteroid spin directions and their rotation periods.</jats:p> <jats:p><jats:italic>Aims. </jats:italic>We analyzed lightcurves of four selected near-Earth asteroids with the aim of detecting secular changes in their rotation rates that are caused by YORP or at least of putting upper limits on such changes.</jats:p> <jats:p><jats:italic>Methods. </jats:italic>We use the lightcurve inversion method to model the observed lightcurves and include the change in the rotation rate d<jats:italic>ω</jats:italic>/ d<jats:italic>t</jats:italic> as a free parameter of optimization. To enlarge the time line of observations and to increase the sensitivity of the method, we collected more than 70 new lightcurves. For asteroids Toro and Cacus, we used thermal infrared data from the WISE spacecraft and estimated their size and thermal inertia by means of a thermophysical model. We also used the currently available optical and radar astrometry of Toro, Ra-Shalom, and Cacus to infer the Yarkovsky effect. </jats:p> <jats:p><jats:italic>Results. </jats:italic>We detected a YORP acceleration of d<jats:italic>ω</jats:italic>/ d<jats:italic>t</jats:italic> = (1.9 ± 0.3) × 10<jats:sup>-8</jats:sup> rad d<jats:sup>-2</jats:sup> for asteroid Cacus. The current astrometric data set is not sufficient to provide detection of the Yarkovsky effect in this case. For Toro, we have a tentative (2<jats:italic>σ</jats:italic>) detection of YORP from a significant improvement of the lightcurve fit for a nonzero value of d<jats:italic>ω</jats:italic>/ d<jats:italic>t</jats:italic> = 3.0 × 10<jats:sup>-9</jats:sup> rad d<jats:sup>-2</jats:sup>. We note an excellent agreement between the observed secular change of the semimajor axis d<jats:italic>a</jats:italic>/ d<jats:italic>t</jats:italic> and the theoretical expectation for densities in the 2–2.5 g cm<jats:sup>-3</jats:sup> range. For asteroid Eger, we confirmed the previously published YORP detection with more data and updated the YORP value to (1.1 ± 0.5) × 10<jats:sup>-8</jats:sup> rad d<jats:sup>-2</jats:sup>. We also updated the shape model of asteroid Ra-Shalom and put an upper limit for the change of the rotation rate to | d<jats:italic>ω</jats:italic>/ d<jats:italic>t</jats:italic> | ≲ 1.5 × 10<jats:sup>-8</jats:sup> rad d<jats:sup>-2</jats:sup>. Ra-Shalom has a greater than 3<jats:italic>σ</jats:italic> Yarkovsky detection with a theoretical value consistent with observations assuming its size and/or density is slightly larger than the nominally expected values. Using the convex shape models and spin parameters reconstructed from lightcurves, we computed theoretical YORP values and compared them with those measured. They agree with each other within the expected uncertainties of the model.</jats:p>