This paper reports new observations of pulsars B0943+10 and B1822−09 carried out with the Arecibo Observatory and the Giant Metrewave Radio Telescope, respectively. Both stars exhibit two stable emission modes. We report the discovery in B0943+10 of a highly linearly polarized ‘precursor’ (PC) component that occurs primarily in only one mode. This emission feature closely resembles B1822−09's PC which also occurs brightly in only one mode. B0943+10's other mode is well known for its highly regular drifting subpulses that are apparently produced by a rotating ‘carousel’ system of 20 ‘beamlets.’ Similarly, B1822−09 exhibits subpulse‐modulation behaviour only in the mode where its PC is absent. We survey our 18 h of B0943+10 observations and find that the ‘sideband’‐modulation features, from which the carousel‐rotation time can be directly determined, occur rarely – less than 5 per cent of the time – but always indicating 20 ‘beamlets’. We present an analysis of B1822−09's modal modulation characteristics at 325 MHz and compare them in detail with B0943+10. The pulsar never seems to null, and we find a 43‐rotation‐period P3 feature in the star's ‘Q’ mode that modulates the interpulse (IP) as well as the conal features in the main pulse (MP). We conclude that B1822−09 must have a nearly orthogonal geometry and that its carousel circulation time is long compared to the modal subsequences available in our observations, and the MP/IP separation is almost exactly 180°. We conclude the PCs for both stars are incompatible with core–cone emission. We assess the interesting suggestion by Dyks et al. that downward‐going radiation produces B1822−09's PC emission.

We report analysis of an 8-h observation of PSR B0943+10 at 325 MHz performed at the Giant Metrewave Radio Telescope (GMRT) in India. B0943+10 is well known for displaying regular subpulse drifting and two emission modes. We investigate the modal behaviour of B0943+10. By reconstructing an entire 'B' mode from two consecutive 'B' modes, we estimate that the pulsar spends roughly 7.5 h in the 'B' mode and about 2.2 h in the 'Q' mode, on average. Although the pulsar can switch modes within one pulse, the subpulse drift rate changes with a characteristic time of 1.2 h over the course of a 'B' mode. Under the subbeam carousel model we find the drift rate changes are produced by a 10 per cent increase in the average number of subbeams and a 16 per cent increase in the carousel circulation time. We speculate that under the partially screened gap model the increase in circulation time should be related to a small increase in the neutron star surface temperature.

We investigate the conditions required for planet formation via gravitational instability (GI) and protoplanetary disk (PPD) fragmentation around M-dwarfs. Using a suite of 64 SPH simulations with 10 6 particles, the parameter space of disk mass, temperature, and radius is explored, bracketing reasonable values based on theory and observation. Our model consists of an equilibrium, gaseous, and locally isothermal disk orbiting a central star of mass M * = M /3. Disks with a minimum Toomre Q of Q min 0.9 will fragment and form gravitationally bound clumps. Some previous literature has found Q min < 1.3 − 1.5 to be sufficient for fragmentation. Increasing disk height tends to stabilize disks, and when incorporated into Q as Q e f f ∝ Q(H/R) α for α = 0.18 is sufficient to predict fragmentation. Some discrepancies in the literature regarding Q crit may be due to different methods of generating initial conditions (ICs). A series of 15 simulations demonstrates that perturbing ICs slightly out of equilibrium can cause disks to fragment for higher Q. Our method for generating ICs is presented in detail. We argue that GI likely plays a role in PPDs around M-dwarfs and that disk fragmentation at large radii is a plausible outcome for these disks.

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