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Planet Migration and Binary Companions: the case of HD 80606b
Yanqin Wu,Norm Murray
Physics , 2003, DOI: 10.1086/374598
Abstract: The exo-solar planet HD 80606b has a highly eccentric (e=0.93) and tight (a=0.47 AU) orbit. We study how it might arrive at such an orbit and how it has avoided being tidally circularized until now. The presence of a stellar companion to the host star suggests the possibility that the Kozai mechanism and tidal dissipation combined to draw the planet inward well after it formed: Kozai oscillations produce periods of extreme eccentricity in the planet orbit, and the tidal dissipation that occurs during these periods of small pericentre distances leads to gradual orbital decay. We call this migration mechanism the 'Kozai migration'. It requires that the initial planet orbit is highly inclined relative to the binary orbit. For a companion at 1000 AU and an initial planet orbit at 5 AU, the minimum relative inclination required is ~ 85. We discuss the efficiency of tidal dissipation inferred from the observations of exo-planets. Moreover, we investigate possible explanations for the velocity residual (after the motion induced by the planet is removed) observed on the host star: a second planet in the system is excluded over a large extent of semi-major axis space if Kozai migration is to work, and the tide raised on the star by HD 80606b is likely too small in amplitude. Lastly, we discuss the relevance of Kozai migration for other planetary systems.
Testing In Situ Assembly with the Kepler Planet Candidate Sample
Brad Hansen,Norm Murray
Physics , 2013, DOI: 10.1088/0004-637X/775/1/53
Abstract: We present a Monte Carlo model for the structure of low mass (total mass < 25 earth mass) planetary systems that form by the in situ gravitational assembly of planetary embryos into final planets. Our model includes distributions of mass, eccentricity, inclination and period spacing that are based on the simulation of a disk of 20 earth masses, forming planets around a solar mass star, and assuming a power law surface density distribution $\propto a^{-1.5}$. The output of the Monte Carlo model is then subjected to the selection effects that mimic the observations of a transiting planet search such as that performed by the Kepler satellite. The resulting comparison of the output to the properties of the observed sample yields an encouraging agreement in terms of the relative frequencies of multiple planet systems and the distribution of the mutual inclinations, when moderate tidal circularisation is taken into account. The broad features of the period distribution and radius distribution can also be matched within this framework, although the model underpredicts the distribution of small period ratios. This likely indicates that some dissipation is still required in the formation process. The most striking deviation between model and observations is in the ratio of single to multiple systems, in that there are roughly 50% more single planet candidates observed than are produced in any model population. This suggests that some systems must suffer additional attrition to reduce the number of planets or increase the range of inclinations.
Migration then assembly: Formation of Neptune mass planets inside 1 AU
Brad M. S. Hansen,Norm Murray
Physics , 2011, DOI: 10.1088/0004-637X/751/2/158
Abstract: We demonstrate that the observed distribution of `Hot Neptune'/`Super-Earth' systems is well reproduced by a model in which planet assembly occurs in situ, with no significant migration post-assembly. This is achieved only if the amount of mass in rocky material is $\sim 50$--$100 M_{\oplus}$ interior to 1 AU. Such a reservoir of material implies that significant radial migration of solid material takes place, and that it occur before the stage of final planet assembly. The model not only reproduces the general distribution of mass versus period, but also the detailed statistics of multiple planet systems in the sample. We furthermore demonstrate that cores of this size are also likely to meet the criterion to gravitationally capture gas from the nebula, although accretion is rapidly limited by the opening of gaps in the gas disk. If the mass growth is limited by this tidal truncation, then the scenario sketched here naturally produces Neptune-mass objects with substantial components of both rock and gas, as is observed. The quantitative expectations of this scenario are that most planets in the `Hot Neptune/Super-Earth' class inhabit multiple-planet systems, with characteristic orbital spacings. The model also provides a natural division into gas-rich (Hot Neptune) and gas-poor (Super-Earth) classes at fixed period. The dividing mass ranges from $\sim 3 M_{\oplus}$ at 10 day orbital periods to $\sim 10 M_{\oplus}$ at 100 day orbital periods. For orbital periods $< 10$ days, the division is less clear because a gas atmosphere may be significantly eroded by stellar radiation.
Migrating Planets
Norm Murray,Brad Hansen,Matt Holman,Scott Tremaine
Physics , 1998, DOI: 10.1126/science.279.5347.69
Abstract: A planet orbiting in a disk of planetesimals can experience an instability in which it migrates to smaller orbital radii. Resonant interactions between the planet and planetesimals remove angular momentum from the planetesimals, increasing their eccentricities. Subsequently, the planetesimals either collide with or are ejected by the planet, reducing the semimajor axis of the planet. If the surface density of planetesimals exceeds a critical value, corresponding to 0.03 solar masses of gas inside the orbit of Jupiter, the planet will migrate inward a large distance. This instability may explain the presence of Jupiter-mass objects in small orbits around nearby stars.
Torsion in Groups of Integral Triangles  [PDF]
Will Murray
Advances in Pure Mathematics (APM) , 2013, DOI: 10.4236/apm.2013.31015

Let 0γ<π be a fixed pythagorean angle. We study the abelian group Hr of primitive integral triangles (a,b,c) for which the angle opposite side c is γ. Addition in Hr is defined by adding the angles β opposite side b and modding out by π-γ. The only Hr for which the structure is known is Hπ/2, which is free abelian. We prove that for generalγ, Hr has an element of order two iff 2(1-

Mapping the Outer Edge of the Young Stellar Cluster in the Galactic Center
Morten N. St?stad,Tuan Do,Norm Murray,Jessica R. Lu,Sylvana Yelda,Andrea M. Ghez
Physics , 2015, DOI: 10.1088/0004-637X/808/2/106
Abstract: We present new near-infrared spectroscopic observations of the outer edges of the young stellar cluster around the supermassive black hole at the Galactic center. The observations show a break in the surface-density profile of young stars at approximately 13 arcsec (0.52 pc). These observations spectroscopically confirm previous suggestions of a break based on photometry. Using Gemini North's Near-Infrared Integral Field Spectrometer (NIFS) we are able to detect and separate early- and late-type stars with a 75% completeness at Ks = 15.5. We sample a region with radii between 7" to 23" (0.28 pc to 0.92 pc) from Sgr A*, and present new spectral classifications of 144 stars brighter than Ks = 15.5, where 140 stars are late-type (> 1 Gyr) and only four stars are early-type (young, 4-6 Myr). A broken power-law fit of the early-type surface-density matches well with our data and previously published values. The projected surface-density of late-type stars is also measured and found to be consistent with previous results. We find that the observed early-type surface-density profile is inconsistent with the theory of the young stars originating from a tightly bound infalling cluster, as no significant trail of young stars is found at radii above 13". We also note that either a simple disk instability criterion or a cloud-cloud collision could explain the location of the outer edge, though we lack information to make conclusive remarks on either alternative. If this break in surface-density represents an edge to the young stellar cluster it would set an important scale for the most recent episode of star formation at the Galactic center.
A Roadmap for Canadian Submillimetre Astronomy
Tracy Webb,Scott Chapman,James Di Francesco,Brenda Matthews,Norm Murray,Douglas Scott,Christine Wilson
Physics , 2013,
Abstract: We survey the present landscape in submillimetre astronomy for Canada and describe a plan for continued engagement in observational facilities to ~2020. Building on Canada's decadal Long Range Plan process, we emphasize that continued involvement in a large, single-dish facility is crucial given Canada's substantial investment in ALMA and numerous PI-led submillimetre experiments. In particular, we recommend: i) an extension of Canadian participation in the JCMT until at least the unique JCMT Legacy Survey program is able to realize the full scientific potential provided by the world-leading SCUBA-2 instrument; and ii) involvement of the entire Canadian community in CCAT, with a large enough share in the partnership for Canadian astronomers to participate at all levels of the facility. We further recommend continued participation in ALMA development, involvement in many focused PI-led submillimetre experiments, and partnership in SPICA.
Galaxies on FIRE (Feedback In Realistic Environments): Stellar Feedback Explains Cosmologically Inefficient Star Formation
Philip F. Hopkins,Dusan Keres,Jose Onorbe,Claude-Andre Faucher-Giguere,Eliot Quataert,Norm Murray,James S. Bullock
Physics , 2013, DOI: 10.1093/mnras/stu1738
Abstract: We present a series of high-resolution cosmological simulations of galaxy formation to z=0, spanning halo masses ~10^8-10^13 M_sun, and stellar masses ~10^4-10^11. Our simulations include fully explicit treatment of both the multi-phase ISM (molecular through hot) and stellar feedback. The stellar feedback inputs (energy, momentum, mass, and metal fluxes) are taken directly from stellar population models. These sources of stellar feedback, with zero adjusted parameters, reproduce the observed relation between stellar and halo mass up to M_halo~10^12 M_sun (including dwarfs, satellites, MW-mass disks, and small groups). By extension, this leads to reasonable agreement with the stellar mass function for M_star<10^11 M_sun. We predict weak redshift evolution in the M_star-M_halo relation, consistent with current constraints to z>6. We find that the M_star-M_halo relation is insensitive to numerical details, but is sensitive to the feedback physics. Simulations with only supernova feedback fail to reproduce the observed stellar masses, particularly in dwarf and high-redshift galaxies: radiative feedback (photo-heating and radiation pressure) is necessary to disrupt GMCs and enable efficient coupling of later supernovae to the gas. Star formation rates agree well with the observed Kennicutt relation at all redshifts. The galaxy-averaged Kennicutt relation is very different from the numerically imposed law for converting gas into stars in the simulation, and is instead determined by self-regulation via stellar feedback. Feedback reduces star formation rates considerably and produces a reservoir of gas that leads to rising late-time star formation histories significantly different from the halo accretion history. Feedback also produces large short-timescale variability in galactic SFRs, especially in dwarfs. Many of these properties are not captured by common 'sub-grid' galactic wind models.
Approximation in C^N
Norm Levenberg
Surveys in Approximation Theory , 2006,
Abstract: This is a survey article on selected topics in approximation theory. The topics either use techniques from the theory of several complex variables or arise in the study of the subject. The survey is aimed at readers having an acquaintance with standard results in classical approximation theory and complex analysis but no apriori knowledge of several complex variables is assumed.
Media and Education: Mythologies Old and New
Norm Friesen
Medienimpulse , 2013, DOI: normen und normierungen - schwerpunkt
Abstract: Norm Friesen untersucht in seinem Beitrag die unterschiedlichen Konzeptualisierungen von Sprechen und Schreiben im rationalistischen und romantischen Paradigma der Spracherfassung und zeigt auf, welche Bedeutung diese Normsetzungen angesichts der Generation von Digital Natives haben.
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