Exploring A Cosmic-Ray Origin of the Multi-wavelength Emission in M31

A recent detection of spatially extended gamma-ray emission in the central region of the Andromeda galaxy (M31) has led to several possible explanations being put forth, including dark matter annihilation and millisecond pulsars. Another possibility is that the emission in M31 can be accounted for with a purely astrophysical cosmic-ray (CR) scenario. This scenario would lead to a rich multi-wavelength emission that can, in turn, be used to test it. Relativistic cosmic-ray electrons (CRe) in magnetic fields produce radio emission through synchrotron radiation, while X-rays and gamma rays are produced through inverse Compton scattering. Additionally, collisions of primary cosmic-ray protons (CRp) in the interstellar medium produce charged and neutral pions that then decay into secondary CRe (detectable through radiative processes) and gamma-rays. Here, we explore the viability of a CR origin for multi-wavelength emission in M31, taking into consideration three scenarios: a CR scenario dominated by primary CRe, one dominated by CRp and the resulting secondary CRe and gamma rays from neutral pion decay, and a final case in which both of these components exist simultaneously. We find that the multi-component model is the most promising, and is able to fit the multi-wavelength spectrum for a variety of astrophysical parameters consistent with previous studies of M31 and of cosmic-ray physics. However, the CR power injection implied by our models exceeds the estimated CR power injection from typical astrophysical cosmic-ray sources such as supernovae.Comment: Accepted to Phys Rev D, 15 Pages, 9 figures, 4 tables, updated figures/tables, added discussio

Use of Calculators in High School Mathematics

For many collegiate level mathematics courses at universities across the country, students are not allowed to use calculators. This is often a huge adjustment for students who have spent their entire high school career using calculators. Whether it is graphing or simple arithmetic, students relied on calculators in high school, but for college, the tool of a calculator may not be available for them. This leads to a multitude of questions: Should calculators be used in high school? Do calculators help students learn or are they simply a tool to get answers? Are calculators beneficial in some courses, but not others? These are the questions that will be explored in this paper. From research, interviews, and surveys, this paper will allow current and future teachers to reflect on their opinion of the use of calculators in the classroom at a high school level

Multiwavelength Analysis of Dark Matter Annihilation and RX-DMFIT

Dark matter (DM) particles are predicted by several well motivated models to yield Standard Model particles through self-annihilation that can potentially be detected by astrophysical observations. In particular, the production of charged particles from DM annihilation in astrophysical systems that contain magnetic fields yields radio emission through synchrotron radiation and X-ray emission through inverse Compton scattering of ambient photons. We introduce RX-DMFIT, a tool used for calculating the expected secondary emission from DM annihilation. RX-DMFIT includes a wide range of customizable astrophysical and particle parameters and incorporates important astrophysics including the diffusion of charged particles, relevant radiative energy losses, and magnetic field modelling. We demonstrate the use and versatility of RX-DMFIT by analyzing the potential radio and X-ray signals for a variety of DM particle models and astrophysical environments including galaxy clusters, dwarf spheroidal galaxies and normal galaxies. We then apply RX-DMFIT to a concrete example using Segue I radio data to place constraints for a range of assumed DM annihilation channels. For WIMP models with $M_{\chi} \leq 100$ GeV and assuming weak diffusion, we find that the the leptonic $\mu^+\mu^-$ and $\tau^+\tau^-$ final states provide the strongest constraints, placing limits on the DM particle cross-section well below the thermal relic cross-section, while even for the $b\bar{b}$ channel we find limits close to the thermal relic cross-section. Our analysis shows that radio emission provides a highly competitive avenue for dark matter searches.Comment: 21 pages, 9 figures, 2 tables, corrections to figures, additional text, accepted to JCA

Gamma-ray Emission from Galaxies Hosting Molecular Outflows

Many star-forming galaxies and those hosting active galactic nuclei (AGN) show evidence of massive outflows of material in a variety of phases including ionized, neutral atomic, and molecular. Molecular outflows in particular have been the focus of recent interest as they may be responsible for removing gas from the galaxy, thereby suppressing star formation. As material is ejected from the cores of galaxies, interactions of the outflowing material with the interstellar medium can accelerate cosmic rays and produce high-energy gamma rays. In this work, we search for gamma-ray emission from a sample of local galaxies known to host molecular outflows using data collected by the {\fermi} Large Area Telescope. We employ a stacking technique in order to search for and characterize the average gamma-ray emission properties of the sample. Gamma-ray emission is detected from the galaxies in our sample at the $4.4 \, \sigma$ level with a power-law photon index of $\Gamma \approx 2$ in the 1-800 GeV energy range. The emission is found to correlate with tracers of star formation activity, namely the $8-1000 \: \mu$m infrared luminosity. We also find that the observed signal can be predominantly attributed to \ion{H}{ii} galaxies hosting energy-driven outflows. While we do not find evidence suggesting that the outflows are accelerating charged particles directly, galaxies with molecular outflows may produce more gamma rays than galaxies without outflows. In particular, the set consisting of gamma-ray-detected galaxies with molecular outflows are nearly perfect calorimeters and may be future targets for searches of high-energy neutrinos.Comment: 20 pages, 9 figures, 3 tables. Accepted to The Astrophysical Journa

A Multi-Wavelength Analysis of Annihilating Dark Matter as the Origin of the Gamma-Ray Emission from M31

[Abridged] Indirect detection of dark matter (DM) by multi-wavelength astronomical observations provides a promising avenue for probing the particle nature of DM. In the case of DM consisting of Weakly-Interacting Massive Particles (WIMPs), self-annihilation ultimately produces observable products including $e^{\pm}$ pairs and gamma rays. The gamma rays can be detected directly, while the $e^{\pm}$ pairs can be detected by radio emission from synchrotron radiation or X-rays and soft gamma rays from inverse Compton scattering. An intriguing region to search for astrophysical signs of DM is the Galactic center (GC) of the Milky Way, due in part to an observed excess of gamma-rays that could be DM. A recent observation by the Fermi-LAT collaboration of a similar excess in the central region of the Andromeda galaxy (M31) leads us to explore the possibility of a DM-induced signal there as well. We use the RX-DMFIT tool to perform a multi-frequency analysis of potential DM annihilation emissions in M31. We consider WIMP models consistent with the GC excess and calculate the expected emission across the electromagnetic spectrum in comparison with available observational data from M31. We find that the particle models that best fit the M31 excess favor lower masses than the GC excess. The best fitting models are for a $b\bar{b}$ final state with $M_{\chi}=11$ GeV and \left=2.6\times 10^{-26} cm$^3$s$^{-1}$, as well as an evenly mixed $b\bar{b}/\tau^+\tau^-$ final state with $M_{\chi}=5.8$ GeV and \left=2.03\times 10^{-26} cm$^3$s$^{-1}$. For conservative estimates of the diffusion and magnetic field models the expected radio emissions appear to be in tension with currently available data in the central region of M31, although this constraint has a fairly strong dependence on the values chosen for parameters describing the magnetic field strength and geometry.Comment: 11 pages, 7 figures, 2 tables, Added Table 2 and Figure 4, added galactic center contours to Figure 3, split section VA, some changes to text, Accepted to Phys. Rev

Disentangling the Hadronic Components in NGC 1068

The recent detection of high-energy neutrinos by IceCube in the direction of the nearby Seyfert/starburst galaxy NGC 1068 implies that radio-quiet active galactic nuclei can accelerate cosmic-ray ions. Dedicated multi-messenger analyses suggest that the interaction of these high-energy ions { with ambient gas or photons} happens in a region of the galaxy that is highly opaque for GeV-TeV gamma rays. Otherwise, the GeV-TeV emission would violate existing constraints provided by {\it Fermi}-LAT and MAGIC. The conditions of high optical depth are realized near the central super-massive black hole (SMBH). At the same time, the GeV emission detected by the {\it Fermi}-Large Area Telescope (LAT) is likely related to the galaxy's sustained star-formation activity. In this work, we derive a 20\,MeV - 1\,TeV spectrum of NGC 1068 using 14\,yrs of {\it Fermi}-LAT observations. We find that the starburst hadronic component is responsible for NGC 1068's emission above $\sim$500\,MeV. However, below this energy an additional component is required. In the 20-500\,MeV range the {\it Fermi}-LAT data are consistent with hadronic emission {initiated by non-thermal ions interacting with gas or photons} in the vicinity of the central SMBH. This highlights the importance of the MeV band to discover hidden cosmic-ray accelerators.Comment: Accepted for publication in ApJ Letter

Flexi-Focus Lens: PDMS Variable Focal Length Lens

The design of a variable focal length, or flexi-focus, polydimethylsiloxane (PDMS) lens incorporating a light emitting diode (LED) source is intended for future use on board commercial aircraft. Specifically, the design is intended for the Boeing 787 Dreamliner aircraft, serving as a personal reading light for the passengers seated in the cabin. Most current reading lights on board aircraft are rigid, incandescent, and have very limited freedom in terms of adjusting the emitted light. Incandescent lamps are also inefficient with respect to energy consumption and light output as well as a high heat output. In an economy of increasing demand for cost efficiency, environmentally friendly solutions, and user friendly devices, this lighting configuration is a hindrance in its application. The Flexi-Focus LED light system will remedy this problem by allowing the passenger the freedom to refocus the light from broad flood lighting to precise spot lighting, adequate for reading. A table of user needs can be seen in Table I of Appendix F. This system involves a variable-focal length lens fabricated with PDMS, incorporated with an LED, which has the ability to flex into a range of convex surfaces when the pressure in an airtight chamber behind it is increased, thus enabling optimization for a broad range of applications. The focal length of the lens is a function of the refractive index of the lens material and the radius of curvature created by the deflection. With a known refractive index for the material, the light can be made to focus at specific distances. In the application of interest for this project, this enables the area illuminated by the LED to vary

Evaluation of Humic Fertilizers Applied at Full and Reduced Nitrogen Rates on Kentucky Bluegrass Quality and Soil Health

Soil health and sustainable management practices have garnered much interest within the turfgrass industry. Among the many practices that enhance soil health and sustainability are applying soil additives to enhance soil biological activity and reducing nitrogen (N) inputs—complimentary practices. A two-year study was conducted to investigate if reduced N fertilizer rates applied with humic substances could provide comparable turfgrass quality as full N rates, and whether humic fertilizers would increase biological aspects of soil health (i.e., microbial biomass and activity). Treatments included synthetic fertilizer with black gypsum (SFBG), poly-coated humic-coated urea (PCHCU; two rates), urea + humic dispersing granules (HDG; two rates), urea, stabilized nitrogen, HDG, and a nontreated control. Reduced rates of N with humic substances maintained turfgrass quality and cover, and reduced clipping biomass compared to full N rates. There were no differences in soil physical and chemical properties besides soil sulfur (S) concentration. SFBG resulted in the highest soil S concentration. Fertilizer treatments had minimal effect on microbial biomass and other plant-available nutrients. However, PCHCU (full rate) increased potentially mineralizable carbon (PMC) and N (PMN) by 68% and 59%, respectively, compared to the nontreated control. Meanwhile SFBG and stabilized nitrogen also increased PMC and PMN by 77% and 50%, and 65% and 59%, respectively. Overall, applications of reduced N fertilizer rates with the addition of humic substances could be incorporated into a more sustainable and environmentally friendly turfgrass fertilizer program