Dark Matter Halos
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Lecture 1 Overview Time Scales, Temperature-Density Scalings
I. Preliminaries The life of any star is a continual struggle between the force of gravity, seeking to reduce the star to a point, and pressure, which holds it up. Stars are gravitationally Lecture 1 confined thermonuclear reactors. So long as they remain non-degenerate and have not Overview encountered the pair instability, overheating leads to Time Scales, Temperature-density expansion and cooling. Cooling, on the other hand, leads to contraction and heating. Hence stars are generally stable. Scalings, Critical Masses The Virial Theorem works. But, since ideal gas pressure depends on temperature, stars must remain hot. By being hot, they are compelled to radiate. In order to replenish the energy lost to radiation, stars must either contract or obtain energy from nuclear reactions. Since nuclear reactions change their composition, stars must evolve. Central Conditions The Virial Theorm implies that if a star is neither too at death the degenerate nor too relativistic (radiation or pair dominated) iron cores of massive stars 2 GM are somewhat MN kT (for an ideal gas) R A degenerate GM T N AkR 1/3 ⎛ 3M ⎞ R for constant density ⎝⎜ 4πρ ⎠⎟ GM 2/3 So ρ1/3 T 3 N Ak ρ ∝ T That is as stars of ideal gas contract, they get hotter and since a given fuel (H, He, C etc) burns at about the same temperature, more massive stars will burn their fuels at lower density, i.e., higher entropy. Four important time scales for a (non-rotating) star to adjust its The free fall time scale is ~R/vesc so 1/2 structure can be noted. -
14 Timescales in Stellar Interiors
14Timescales inStellarInteriors Having dealt with the stellar photosphere and the radiation transport so rel- evant to our observations of this region, we’re now ready to journey deeper into the inner layers of our stellar onion. Fundamentally, the aim we will de- velop in the coming chapters is to develop a connection betweenM,R,L, and T in stars (see Table 14 for some relevant scales). More specifically, our goal will be to develop equilibrium models that describe stellar structure:P (r),ρ (r), andT (r). We will have to model grav- ity, pressure balance, energy transport, and energy generation to get every- thing right. We will follow a fairly simple path, assuming spherical symmetric throughout and ignoring effects due to rotation, magneticfields, etc. Before laying out the equations, let’sfirst think about some key timescales. By quantifying these timescales and assuming stars are in at least short-term equilibrium, we will be better-equipped to understand the relevant processes and to identify just what stellar equilibrium means. 14.1 Photon collisions with matter This sets the timescale for radiation and matter to reach equilibrium. It de- pends on the mean free path of photons through the gas, 1 (227) �= nσ So by dimensional analysis, � (228)τ γ ≈ c If we use numbers roughly appropriate for the average Sun (assuming full Table3: Relevant stellar quantities. Quantity Value in Sun Range in other stars M2 1033 g 0.08 �( M/M )� 100 × � R7 1010 cm 0.08 �( R/R )� 1000 × 33 1 3 � 6 L4 10 erg s− 10− �( L/L )� 10 × � Teff 5777K 3000K �( Teff/mathrmK)� 50,000K 3 3 ρc 150 g cm− 10 �( ρc/g cm− )� 1000 T 1.5 107 K 106 ( T /K) 108 c × � c � 83 14.Timescales inStellarInteriors P dA dr ρ r P+dP g Mr Figure 28: The state of hydrostatic equilibrium in an object like a star occurs when the inward force of gravity is balanced by an outward pressure gradient. -
The Underlying Physical Meaning of the Νmax − Νc Relation
A&A 530, A142 (2011) Astronomy DOI: 10.1051/0004-6361/201116490 & c ESO 2011 Astrophysics The underlying physical meaning of the νmax − νc relation K. Belkacem1,2, M. J. Goupil3,M.A.Dupret2, R. Samadi3,F.Baudin1,A.Noels2, and B. Mosser3 1 Institut d’Astrophysique Spatiale, CNRS, Université Paris XI, 91405 Orsay Cedex, France e-mail: [email protected] 2 Institut d’Astrophysique et de Géophysique, Université de Liège, Allée du 6 Août 17, 4000 Liège, Belgium 3 LESIA, UMR8109, Université Pierre et Marie Curie, Université Denis Diderot, Obs. de Paris, 92195 Meudon Cedex, France Received 10 January 2011 / Accepted 4 April 2011 ABSTRACT Asteroseismology of stars that exhibit solar-like oscillations are enjoying a growing interest with the wealth of observational results obtained with the CoRoT and Kepler missions. In this framework, scaling laws between asteroseismic quantities and stellar parameters are becoming essential tools to study a rich variety of stars. However, the physical underlying mechanisms of those scaling laws are still poorly known. Our objective is to provide a theoretical basis for the scaling between the frequency of the maximum in the power spectrum (νmax) of solar-like oscillations and the cut-off frequency (νc). Using the SoHO GOLF observations together with theoretical considerations, we first confirm that the maximum of the height in oscillation power spectrum is determined by the so-called plateau of the damping rates. The physical origin of the plateau can be traced to the destabilizing effect of the Lagrangian perturbation of entropy in the upper-most layers, which becomes important when the modal period and the local thermal relaxation time-scale are comparable. -
Leap Second - Wikipedia
Leap second - Wikipedia https://en.wikipedia.org/wiki/Leap_second A leap second is a one-second adjustment that is occasionally applied to civil time Coordinated Universal Time (UTC) to keep it close to the mean solar time at Greenwich, in spite of the Earth's rotation slowdown and irregularities. UTC was introduced on 1972 January 1st, initially with a 10 second lag behind International Atomic Time (TAI). Since that date, 27 leap seconds have been inserted, the most recent on December 31, 2016 at 23:59:60 UTC, so in 2018, UTC lags behind TAI by an offset of 37 seconds.[1] The UTC time standard, which is widely used for international timekeeping and as the reference for civil time in most countries, uses the international system (SI) definition of the second. The UTC second Screenshot of the UTC clock from time.gov has been calibrated with atomic clock on the duration of the Earth's mean day of the astronomical year (https://time.gov/) during the leap second on 1900. Because the rotation of the Earth has since further slowed down, the duration of today's mean December 31, 2016. In the USA, the leap second solar day is longer (by roughly 0.001 seconds) than 24 SI hours (86,400 SI seconds). UTC would step took place at 19:00 local time on the East Coast, ahead of solar time and need adjustment even if the Earth's rotation remained constant in the future. at 16:00 local time on the West Coast, and at Therefore, if the UTC day were defined as precisely 86,400 SI seconds, the UTC time-of-day would 14:00 local time in Hawaii. -
COORDINATE TIME in the VICINITY of the EARTH D. W. Allan' and N
COORDINATE TIME IN THE VICINITY OF THE EARTH D. W. Allan’ and N. Ashby’ 1. Time and Frequency Division, National Bureau of Standards Boulder, Colorado 80303 2. Department of Physics, Campus Box 390 University of Colorado, Boulder, Colorado 80309 ABSTRACT. Atomic clock accuracies continue to improve rapidly, requir- ing the inclusion of general relativity for unambiguous time and fre- quency clock comparisons. Atomic clocks are now placed on space vehi- cles and there are many new applications of time and frequency metrology. This paper addresses theoretical and practical limitations in the accuracy of atomic clock comparisons arising from relativity, and demonstrates that accuracies of time and frequency comparison can approach a few picoseconds and a few parts in respectively. 1. INTRODUCTION Recent experience has shown that the accuracy of atomic clocks has improved by about an order of magnitude every seven years. It has therefore been necessary to include relativistic effects in the reali- zation of state-of-the-art time and frequency comparisons for at least the last decade. There is a growing need for agreement about proce- dures for incorporating relativistic effects in all disciplines which use modern time and frequency metrology techniques. The areas of need include sophisticated communication and navigation systems and funda- mental areas of research such as geodesy and radio astrometry. Significant progress has recently been made in arriving at defini- tions €or coordinate time that are practical, and in experimental veri- fication of the self-consistency of these procedures. International Atomic Time (TAI) and Universal Coordinated Time (UTC) have been defin- ed as coordinate time scales to assist in the unambiguous comparison of time and frequency in the vicinity of the Earth. -
Hawking Temperature for Near-Equilibrium Black Holes
KUNS-2372 Hawking temperature for near-equilibrium black holes Shunichiro Kinoshita1, ∗ and Norihiro Tanahashi2, † 1 Department of Physics, Kyoto University, Kitashirakawa Oiwake-Cho, 606-8502 Kyoto, Japan 2 Department of Physics, University of California, Davis, California 95616, USA (Dated: June 18, 2018) We discuss the Hawking temperature of near-equilibrium black holes using a semiclassical analysis. We introduce a useful expansion method for slowly evolving spacetime, and evaluate the Bogoliubov coefficients using the saddle point approximation. For a spacetime whose evolution is sufficiently slow, such as a black hole with slowly changing mass, we find that the temperature is determined by the surface gravity of the past horizon. As an example of applications of these results, we study the Hawking temperature of black holes with null shell accretion in asymptotically flat space and the AdS–Vaidya spacetime. We discuss implications of our results in the context of the AdS/CFT correspondence. PACS numbers: 04.50.Gh, 04.62.+v, 04.70.Dy, 11.25.Tq I. INTRODUCTION The fact that black holes possess thermodynamic properties has been intriguing in gravitational and quantum theories, and is still attracting interest. Nowadays it is well-known that black holes will emit thermal radiation with Hawking temperature proportional to the surface gravity of the event horizon [1]. This result plays a significant role in black hole thermodynamics. Moreover, the AdS/CFT correspondence [2] opened up new insights about thermodynamic properties of black holes. In this context we expect that thermodynamic properties of conformal field theory (CFT) matter on the boundary would respect those of black holes in the bulk. -
Modeling the Temperature-Mediated Phenological Development of Alfalfa (Medicago Sativa L.)
AN ABSTRACT OF THE THESIS OF Mongi Ben-Younes for the degree of Doctor of Philosophy in Crop Science presented on January 15, 1992. Title: Modeling the Temperature Mediated Phenological Development of Alfalfa (Medicago sativa L.) Redacted for Privacy Abstract approved:__ David B. Hannaway This study was conducted to investigate the response of seedlings of nine alfalfa cultivars (belonging to three fall dormancy groups) to varying temperature regimes and relate their phenological development to accumulated growing degree days (GDD) or thermal time. Simulation algorithms were developed from controlled environment experiments and were tested in field conditions to validate the temperature- phenology relationships of alfalfa. The percent advancement to first bloom per day (% AFB day 1) method was used to relate alfalfa phenological devel- opment to temperature. The % AFB day-1 of alfalfa cultivars was best described by the equation: I AFBday-1= 2.617 loge Tm 1.746 (R2=0.94), where Tm is the mean daily temperature. The X intercept (when the I AFB day-1 is zero) indicated that 4.6 °C was an appropriate base temperature for alfalfa cultivars. Alfalfa development stage and temperature treatments had significant effects on dry matter yield, time to maturi- ty stages, accumulated GDR), GDD5, and loges GDD46. Growth and development of alfalfa cultivars was hastened by warmer temperature treatments. A transformation of the GDD method using the loges GDD46 resulted in less variability than GDD0 and GDD5 in predicting alfalfa development. The equation relating alfalfa stages of development (Y) to loges GDD4.6 was: Y = 12.734 loges (GDD46) - 33.114 (R2=0.94) . -
Modified Newtonian Dynamics, an Introductory Review
Modified Newtonian Dynamics, an Introductory Review Riccardo Scarpa European Southern Observatory, Chile E-mail [email protected] Abstract. By the time, in 1937, the Swiss astronomer Zwicky measured the velocity dispersion of the Coma cluster of galaxies, astronomers somehow got acquainted with the idea that the universe is filled by some kind of dark matter. After almost a century of investigations, we have learned two things about dark matter, (i) it has to be non-baryonic -- that is, made of something new that interact with normal matter only by gravitation-- and, (ii) that its effects are observed in -8 -2 stellar systems when and only when their internal acceleration of gravity falls below a fix value a0=1.2×10 cm s . Being completely decoupled dark and normal matter can mix in any ratio to form the objects we see in the universe, and indeed observations show the relative content of dark matter to vary dramatically from object to object. This is in open contrast with point (ii). In fact, there is no reason why normal and dark matter should conspire to mix in just the right way for the mass discrepancy to appear always below a fixed acceleration. This systematic, more than anything else, tells us we might be facing a failure of the law of gravity in the weak field limit rather then the effects of dark matter. Thus, in an attempt to avoid the need for dark matter many modifications of the law of gravity have been proposed in the past decades. The most successful – and the only one that survived observational tests -- is the Modified Newtonian Dynamics. -
Disk Galaxy Rotation Curves and Dark Matter Distribution
View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by CERN Document Server Disk galaxy rotation curves and dark matter distribution by Dilip G. Banhatti School of Physics, Madurai-Kamaraj University, Madurai 625021, India [Based on a pedagogic / didactic seminar given by DGB at the Graduate College “High Energy & Particle Astrophysics” at Karlsruhe in Germany on Friday the 20 th January 2006] Abstract . After explaining the motivation for this article, we briefly recapitulate the methods used to determine the rotation curves of our Galaxy and other spiral galaxies in their outer parts, and the results of applying these methods. We then present the essential Newtonian theory of (disk) galaxy rotation curves. The next two sections present two numerical simulation schemes and brief results. Finally, attempts to apply Einsteinian general relativity to the dynamics are described. The article ends with a summary and prospects for further work in this area. Recent observations and models of the very inner central parts of galaxian rotation curves are omitted, as also attempts to apply modified Newtonian dynamics to the outer parts. Motivation . Extensive radio observations determined the detailed rotation curve of our Milky Way Galaxy as well as other (spiral) disk galaxies to be flat much beyond their extent as seen in the optical band. Assuming a balance between the gravitational and centrifugal forces within Newtonian mechanics, the orbital speed V is expected to fall with the galactocentric distance r as V 2 = GM/r beyond the physical extent of the galaxy of mass M, G being the gravitational constant. -
California Weedy Rice (Oryza Sativa Spontanea)
California weedy rice (Oryza sativa spontanea) emergence patterns under field conditions, implications for management Liberty Galvin¹ ([email protected]), Whitney Brim-DeForest², Kassim Al-Khatib¹ ¹ University of California, Davis, Department of Plant Sciences, ²University of California Cooperative Extension, Sutter-Yuba counties Introduction Results and Discussion Weedy rice (Oryza sativa f. spontanea Rosh.), a conspecific to cultivated rice (Oryza • The majority of seeds emerged from the top 1 cm; 94% of total counted in 2019 and 80% of total counted in 2020. Emergence sativa L.), is difficult to control in California due to agronomic constraints on growers was not recorded from depths greater than 3 cm (<1%) in either year. This outcome coincides with previous experiments which including a lack of chemical control options and herbicide tolerant rice varieties, as indicated weedy rice types 1, 2, 3, & 5 would not emerge from depths at or below 2.5 cm (Galvin et al. unpublished). well as biological components of weedy rice such as early maturation and competitive • It took 14 DAF in 2019 to reach max emergence of all weedy rice types and 21 DAF in 2020. Switching to a thermal time scale, growth rate. Because of these factors, weedy rice should ideally be controlled as early these calendar time points equate to ~300 °C days (growing degree days/ thermal time) in both years (Figure 2 & 3). as possible in the season to maximize crop yields and reduce manual labor required for plant removal. Early season growth and development of California weedy rice was • Type 2 and Type 3 had significantly more total emergence in 2019 than in 2020. -
Chapter 5 Rotation Curves
Chapter 5 Rotation Curves 5.1 Circular Velocities and Rotation Curves The circular velocity vcirc is the velocity that a star in a galaxy must have to maintain a circular orbit at a specified distance from the centre, on the assumption that the gravitational potential is symmetric about the centre of the orbit. In the case of the disc of a spiral galaxy (which has an axisymmetric potential), the circular velocity is the orbital velocity of a star moving in a circular path in the plane of the disc. If 2 the absolute value of the acceleration is g, for circular velocity we have g = vcirc=R where R is the radius of the orbit (with R a constant for the circular orbit). Therefore, 2 @Φ=@R = vcirc=R, assuming symmetry. The rotation curve is the function vcirc(R) for a galaxy. If vcirc(R) can be measured over a range of R, it will provide very important information about the gravitational potential. This in turn gives fundamental information about the mass distribution in the galaxy, including dark matter. We can go further in cases of spherical symmetry. Spherical symmetry means that the gravitational acceleration at a distance R from the centre of the galaxy is simply GM(R)=R2, where M(R) is the mass interior to the radius R. In this case, 2 vcirc GM(R) GM(R) = 2 and therefore, vcirc = : (5.1) R R r R If we can assume spherical symmetry, we can estimate the mass inside a radial distance R by inverting Equation 5.1 to give v2 R M(R) = circ ; (5.2) G and can do so as a function of radius. -
A Comparison of the DC14 and Corenfw Dark Matter Halo Models on Galaxy Rotation Curves F
A&A 605, A55 (2017) Astronomy DOI: 10.1051/0004-6361/201730402 & c ESO 2017 Astrophysics Testing baryon-induced core formation in ΛCDM: A comparison of the DC14 and coreNFW dark matter halo models on galaxy rotation curves F. Allaert1, G. Gentile2, and M. Baes1 1 Sterrenkundig Observatorium, Universiteit Gent, Krijgslaan 281, 9000 Gent, Belgium e-mail: [email protected] 2 Department of Physics and Astrophysics, Vrije Universiteit Brussel, Pleinlaan 2, 1050 Brussels, Belgium Received 6 January 2017 / Accepted 15 June 2017 ABSTRACT Recent cosmological hydrodynamical simulations suggest that baryonic processes, and in particular supernova feedback following bursts of star formation, can alter the structure of dark matter haloes and transform primordial cusps into shallower cores. To assess whether this mechanism offers a solution to the long-standing cusp-core controversy, simulated haloes must be compared to real dark matter haloes inferred from galaxy rotation curves. For this purpose, two new dark matter density profiles were recently derived 10 11 from simulations of galaxies in complementary mass ranges: the DC14 halo (10 < Mhalo=M < 8 × 10 ) and the coreNFW halo 7 9 (10 < Mhalo=M < 10 ). Both models have individually been found to give good fits to observed rotation curves. For the DC14 model, however, the agreement of the predicted halo properties with cosmological scaling relations was confirmed by one study, but strongly refuted by another. A next important question is whether, despite their different approaches, the two models converge to the same solution in the mass range where both should be appropriate. To investigate this, we tested the DC14 and coreNFW halo 9 10 models on the rotation curves of a selection of galaxies with halo masses in the range 4 × 10 M – 7 × 10 M and compared their 11 predictions.