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The stellar mass function is one of the fundamental distributions of stellar astrophysics. Its form at masses similar to the Sun was found by Salpeter (1955) to be a power-law $m^{-alpha}$ with a slope of $alpha=1.35$. Since then the mass function in the field, in stellar clusters and in other galaxies has been studied to identify variation due to environment and mass range. Here we use results from previous papers in the SIPS series to constrain the mass function of low mass stars (0.075M$_odot$$<$m$<0.2_odot$). We use simulations of the low mass local stellar population based on those in Deacon & Hambly (2006) to model the results of the SIPS-II survey (Deacon & Hambly, 2007). We then vary the input parameters of these simulations (the exponent of the mass function $alpha$ and a stellar birthrate parameter $beta$) and compare the simulated survey results with those from the actual survey. After a correction for binarity and taking into account potential errors in our model we find that $alpha=-0.62pm0.26$ for the quoted mass range.
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The low-mass end of the stellar Initial Mass Function (IMF) is constrained by focusing on the baryon-dominated central regions of strong lensing galaxies. We study in this letter the Einstein Cross (Q2237+0305), a z=0.04 barred galaxy whose bulge acts as lens on a background quasar. The positions of the four quasar images constrain the surface mass density on the lens plane, whereas the surface brightness (H-band NICMOS/HST imaging) along with deep spectroscopy of the lens (VLT/FORS1) allow us to constrain the stellar mass content, for a range of IMFs. We find that a classical single power law (Salpeter IMF) predicts more stellar mass than the observed lensing estimates. This result is confirmed at the 99% confidence level, and is robust to systematic effects due to the choice of population synthesis models, the presence of dust, or the complex disk/bulge population mix. Our non-parametric methodology is more robust than kinematic estimates, as we do not need to make any assumptions about the dynamical state of the galaxy or its decomposition into bulge and disk. Over a range of low-mass power law slopes (with Salpeter being Gamma=+1.35) we find that at a 90% confidence level, slopes with Gamma>0 are ruled out.
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In our previous study of low mass stars using TESS, we found a handful which show a periodic modulation on a period <1 d but also displayed no flaring activity. Here we present the results of a systematic search for Ultra Fast Rotators (UFRs) in the southern ecliptic hemisphere which were observed in 2 min cadence with TESS. Using data from Gaia DR2, we obtain a sample of over 13,000 stars close to the lower main sequence. Of these, we identify 609 stars which lie on the lower main sequence and have a periodic modulation <1 d. The fraction of stars which show flares appears to drop significantly at periods <0.2 d. If the periods are a signature of the rotation rate, this would be a surprise, since faster rotators would be expected to have a stronger magnetic field and, therefore, produce more flares. We explore possible reasons for our finding: the flare inactive stars are members of binaries, in which case the stars rotation rate could have increased as the binary orbital separation reduced due to angular momentum loss over time, or that enhanced emission occurs at blue wavelengths beyond the pass band of TESS. Follow-up spectroscopy and flare monitoring at blue/ultraviolet wavelengths of these flare inactive stars are required to resolve this question.
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