A Natural Formalism for Microlensing

If the standard microlensing geometry is inverted so that the Einstein ring is projected onto the observer plane rather than the source plane, then the relations between the observables (\theta_E,\tilde r_E) and the underlying physical quantities (M,\pi_rel) become immediately obvious. Here \theta_E and \tilde r_E are the angular and projected Einstein radii, M is the mass of the lens, and \pi_rel is the lens-source relative parallax. I recast the basic formalism of microlensing in light of this more natural geometry and in terms of observables. I then find that the relations between observable and physical quantities assume an exceptionally simple form. In an appendix, I propose a set of notational conventions for microlensing.Comment: 8 pages, 1 figure tells all. Interested parties are requested to vote on a proposed standard for microlensing notation given in the appendix. Submitted to Ap

The Functional Significance of Black-Pigmented Leaves: Photosynthesis, Photoprotection and Productivity in Ophiopogon planiscapus ‘Nigrescens’

Black pigmented leaves are common among horticultural cultivars, yet are extremely rare across natural plant populations. We hypothesised that black pigmentation would disadvantage a plant by reducing photosynthesis and therefore shoot productivity, but that this trait might also confer protective benefits by shielding chloroplasts against photo-oxidative stress. CO2 assimilation, chlorophyll a fluorescence, shoot biomass, and pigment concentrations were compared for near isogenic green- and black-leafed Ophiopogon planiscapus ‘Nigrescens’. The black leaves had lower maximum CO2 assimilation rates, higher light saturation points and higher quantum efficiencies of photosystem II (PSII) than green leaves. Under saturating light, PSII photochemistry was inactivated less and recovered more completely in the black leaves. In full sunlight, green plants branched more abundantly and accumulated shoot biomass quicker than the black plants; in the shade, productivities of the two morphs were comparable. The data indicate a light-screening, photoprotective role of foliar anthocyanins. However, limitations to photosynthetic carbon assimilation are relatively small, insufficient to explain the natural scarcity of black-leafed plants

Detection Rates for Close Binaries Via Microlensing

Microlensing is one of the most promising methods of reconstructing the stellar mass function down to masses even below the hydrogen-burning limit. The fundamental limit to this technique is the presence of unresolved binaries, which can in principle significantly alter the inferred mass function. Here we quantify the fraction of binaries that can be detected using microlensing, considering specifically the mass ratio and separation of the binary. We find that almost all binary systems with separations greater than $b \sim 0.4$ of their combined Einstein ring radius are detectable assuming a detection threshold of $3\%$. For two M dwarfs, this corresponds to a limiting separation of \gsim 1 \au. Since very few observed M dwarfs have companions at separations \lsim 1 \au, we conclude that close binaries will probably not corrupt the measurements of the mass function. We find that the detectability depends only weakly on the mass ratio. For those events for which individual masses can be determined, we find that binaries can be detected down to $b \sim 0.2$.Comment: 19 pages including 6 figures. Uses phyyzx format. Send requests for higher quality figures to [email protected]

Nearby Microlensing Events - Identification of the Candidates for the SIM

The Space Interferometry Mission (SIM) is the instrument of choice when it comes to observing astrometric microlensing events where nearby, usually high-proper-motion stars (``lenses''), pass in front of more distant stars (``sources''). Each such encounter produces a deflection in the source's apparent position that when observed by SIM can lead to a precise mass determination of the nearby lens star. We search for lens-source encounters during the 2005-2015 period using Hipparcos, ACT and NLTT to select lenses, and USNO-A2.0 to search for the corresponding sources, and rank these by the SIM time required for a 1% mass measurement. For Hipparcos and ACT lenses, the lens distance and lens-source impact parameter are precisely determined so the events are well characterized. We present 32 candidates beginning with a 61 Cyg A event in 2012 that requires only a few minutes of SIM time. Proxima Centauri and Barnard's star each generate several events. For NLTT lenses, the distance is known only to a factor of 3, and the impact parameter only to 1''. Together, these produce uncertainties of a factor ~10 in the amount of SIM time required. We present a list of 146 NLTT candidates and show how single-epoch CCD photometry of the candidates could reduce the uncertainty in SIM time to a factor of ~1.5.Comment: ApJ accepted, 31 pages (inc. 5 tables), 5 figures. t SIM refine

Femtolens Imaging of a Quasar Central Engine Using a Dwarf Star Telescope

We show that it is possible to image the structure of a distant quasar on scales of $\sim 1\,$AU by constructing a telescope which uses a nearby dwarf star as its ``primary lens'' together with a satellite-borne ``secondary''. The image produced by the primary is magnified by $\sim 10^5$ in one direction but is contracted by 0.5 in the other, and therefore contains highly degenerate one-dimensional information about the two-dimensional source. We discuss various methods for extracting information about the second dimension including ``femtolens interferometry'' where one measures the interference between different parts of the one-dimensional image with each other. Assuming that the satellite could be dispatched to a position along a star-quasar line of sight at a distance $r$ from the Sun, the nearest available dwarf-star primary is likely to be at \sim 15\,\pc\,(r/40\,\rm AU)^{-2}. The secondary should consist of a one-dimensional array of mirrors extending $\sim 700\,$m to achieve 1 AU resolution, or $\sim 100\,$m to achieve 4 AU resolution.Comment: 12 pages including 3 embedded figure

Improved Astrometry and Photometry for the Luyten Catalog. I. Bright Stars

We outline the construction of an updated version of the New Luyten Two-Tenths (NLTT) catalog of high proper motion stars, which will contain improved astrometry and photometry for the vast majority of the ~59,000 stars in NLTT. The bright end is constructed by matching NLTT stars to Hipparcos, Tycho-2, and Starnet; the faint end by matching to USNO-A and 2MASS. In this first paper, we detail the bright-end matching procedure. We show that for the majority of stars in his catalog, Luyten measured positions accurate to 1" even though he recorded his results much more coarsely. However, there is a long tail of position errors, with one error as large as 11 deg. Proper-motion errors for the stars with small position errors are 24 mas/yr (1 sigma) but deteriorate to 34 mas/yr for stars with inferior positions. NLTT is virtually 100% complete for V15 deg, but completeness in this magnitude range falls to about 75% at the Galactic plane. Incompleteness near the plane is not uniform, but is rather concentrated in the interval -80<l<20, where the Milky Way is brightest.Comment: Submitted to ApJ, 28 pages including 7 figure

New constraints on primordial black holes abundance from femtolensing of gamma-ray bursts

The abundance of primordial black holes is currently significantly constrained in a wide range of masses. The weakest limits are established for the small mass objects, where the small intensity of the associated physical phenomenon provides a challenge for current experiments. We used gamma- ray bursts with known redshifts detected by the Fermi Gamma-ray Burst Monitor (GBM) to search for the femtolensing effects caused by compact objects. The lack of femtolensing detection in the GBM data provides new evidence that primordial black holes in the mass range 5 \times 10^{17} - 10^{20} g do not constitute a major fraction of dark matter.Comment: 7 pages, 6 figures, submitted to Physical Review

Virus Propagation in Multiple Profile Networks

Suppose we have a virus or one competing idea/product that propagates over a multiple profile (e.g., social) network. Can we predict what proportion of the network will actually get "infected" (e.g., spread the idea or buy the competing product), when the nodes of the network appear to have different sensitivity based on their profile? For example, if there are two profiles $\mathcal{A}$ and $\mathcal{B}$ in a network and the nodes of profile $\mathcal{A}$ and profile $\mathcal{B}$ are susceptible to a highly spreading virus with probabilities $\beta_{\mathcal{A}}$ and $\beta_{\mathcal{B}}$ respectively, what percentage of both profiles will actually get infected from the virus at the end? To reverse the question, what are the necessary conditions so that a predefined percentage of the network is infected? We assume that nodes of different profiles can infect one another and we prove that under realistic conditions, apart from the weak profile (great sensitivity), the stronger profile (low sensitivity) will get infected as well. First, we focus on cliques with the goal to provide exact theoretical results as well as to get some intuition as to how a virus affects such a multiple profile network. Then, we move to the theoretical analysis of arbitrary networks. We provide bounds on certain properties of the network based on the probabilities of infection of each node in it when it reaches the steady state. Finally, we provide extensive experimental results that verify our theoretical results and at the same time provide more insight on the problem