Measurement of atomic force microscope cantilever spring constants (k) is essential for many of the applications of this versatile instrument. Numerous techniques to measure k have been proposed. Among these, we found the thermal noise and Sader methods to be commonly applicable and relatively user-friendly, providing an in situ, non-destructive, fast measurement of k for a cantilever independent of its material or coating. Such advantages recommend these methods for widespread use. An impediment thereto is the significant complication involved in the initial implementation of the methods. Some details of the implementation are discussed in publications, while others are left unsaid. Here we present a complete, cohesive, and practically oriented discussion of the implementation of both the thermal noise and Sader methods of measuring cantilever spring constants. We review the relevant theory and discuss practical experimental means for determining the required quantities. We then present results that compare measurements of k by these two methods over nearly two orders of magnitude, and we discuss the likely origins of both statistical and systematic errors for both methods. In conclusion, we find that the two methods agree to within an average of 4% over the wide range of cantilevers measured. Given that the methods derive from distinct physics we find the agreement a compelling argument in favour of the accuracy of both, suggesting them as practical standards for the field.

We have observed a 3 • × 3 • area centered on the M81/M82 group of galaxies using the Robert C. Byrd Green Bank Telescope (GBT) in a search for analogs to the High Velocity Clouds (HVCs) of neutral hydrogen found around our galaxy. The velocity range from -605 to -85 km s −1 and 25 to 1970 km s −1 was searched for H i clouds. Over the inner 2 • × 2 • the 7σ detection threshold was 9.6 × 10 5 M . We detect 5 previously unknown H i clouds associated with the group, as well as numerous associated filamentary H i structures, all lying in the range −105 ≤ V helio ≤ +280 km s −1 . From the small angular distance of the clouds to group members, and the small velocity difference between group members and clouds, we conclude that the clouds are most likely relics of ongoing interactions between galaxies in the group.

We have observed the NGC 2403 group of galaxies using the Robert C. Byrd Green Bank Telescope in a search for faint, extended neutral hydrogen clouds similar to the clouds found around the M81/M82 group, which is located approximately 250 kpc from the NGC 2403 group along the same filament of galaxies. For an H i cloud with a size 10 kpc within 50 kpc of a group galaxy, our 7σ mass detection limit is 2.2 × 10 6 M for a cloud with a line width of 20 km s −1 , over the velocity range from −890 to 1750 km s −1 . At this sensitivity level, we detect three new H i clouds in the direction of the group, as well as the known galaxies. The mean velocity of the new clouds differs from that of the group galaxies by more than 250 km s −1 , but are in the range of Milky Way high-velocity clouds (HVCs) in that direction. It is most likely that the clouds are part of the Milky Way HVC population. If H i clouds exist in the NGC 2403 group, their masses are less than 2.2 × 10 6 M . We also compared our results to structures that are expected based on recent cosmological models, and found none of the predicted clouds. If NGC 2403 is surrounded by a population of dark matter halos similar to those proposed for the Milky Way in recent models, our observations imply that their H i content is less than 1% of their total mass.

Cosmological galaxy formation models predict the existence of dark matter minihalos surrounding galaxies and in filaments connecting groups of galaxies. The more massive of these minihalos are predicted to host H i gas that should be detectable by current radio telescopes such as the GBT. We observed the region including the M81/M82 and NGC 2403 galaxy groups, searching for observational evidence of an H i component associated with dark matter halos within the "M81 Filament", using the Robert C. Byrd Green Bank Telescope (GBT). The map covers an 8.7 • × 21.3 • (480 kpc × 1.2 Mpc) region centered between the M81/M82 and NGC 2403 galaxy groups. Our observations cover a wide velocity range, from -890 to 1320 km s −1 , which spans much of the range predicted by cosmological N-body simulations for dark matter minihalo velocities. Our search is not complete in the velocity range -210 to 85 km s −1 , containing Galactic emission and the HVC Complex A. For an H i cloud at the distance of M81, with a size ≤ 10 kpc, our average 5σ mass detection limit is 3.2 × 10 6 M , for a linewidth of 20 km s −1 . We compare our observations to two large cosmological N-body simulations and find that the simulation predicts a significantly greater number of detectable minihalos than are found in our observations, and that the simulated minihalos do not match the phase space of observed H i clouds. These results place strong constraints on the H i gas that can be associated with dark-matter halos. Our observations indicate that the majority of extragalactic H i clouds with a mass greater than 10 6 M are likely to be generated through cold accretion, or via tidal stripping caused by galaxy interactions.