Building on the Macroscopic to understand the Microscopic: from Systems of Star Clusters to Individual Star-Forming Regions

Size: px
Start display at page:

Download "Building on the Macroscopic to understand the Microscopic: from Systems of Star Clusters to Individual Star-Forming Regions"

Transcription

1 ESTEC, Noodwijk, Building on the Macoscopic to undestand the Micoscopic: fom Systems of Sta Clustes to Individual Sta-Foming Regions Geneviève ve Pamentie Olympia-Moata Fellow of Heidelbeg Univesity Astonomisches-Rechen Institut Heidelbeg Zentum fü Astonomie Gemany

2 Setting the Scene: Sta Clustes (SC) as Poweful Taces of Galaxy Evolution NGC1569: iegula galaxy Cedit: ESA, NASA, Andes+ APOD Distance: 2 Mpc Radio: HI bidges M82 NGC3077 Distance: 3.6 Mpc Yun, Ho & Lo 1994 M81 Sta Clustes (SC): Goups of coeval gavity-bound stas Help us pobe the Univese in both space and time The Antennae NGC4038/9: ongoing galaxy mege Whitmoe & Schweize APOD Distance: 18 Mpc Spial NGC 6946 Lasen 2002 Distance: 5 Mpc Elliptical galaxy M49 Jodan+04 Distance: 20Mpc Geneviève Pamentie - Heidelbeg Astonomisches-Rechen Institut 2 /

3 Setting the Scene: Sta Clustes (SC) as Poweful Taces of Galaxy Evolution Sta Clustes (SC): Compact goups of stas identified on a one-by-one basis against the backgound of thei host galaxy Multi-band imaging of SC systems: Cluste magnitudes & colous combined to Stella Population Synthesis Models cluste age, mass, metallicity estimates Compehensive view of galaxy-: chemical enichment histoy, inteaction histoy, sta fomation histoy (SFH) ove the past Hubble-Time Jodan+04 (ACS Vigo Galaxy Cluste Suvey II, fig6) Elliptical galaxy M49 Backgound-subtacted image Geneviève Pamentie - Heidelbeg Astonomisches-Rechen Institut 3 /

4 Luminosity of the bightest sta cluste Setting the Scene: Sta Clustes (SC) as Poweful Taces of Sta Fomation M V max Bight cluste Faint cluste Lasen 2002, fig11a Lasen+02 (fig11a) Low level of sta High level of sta fomation activity Σ SFR fomation activity Suface density of the SFR of the host galaxy But SCs = encoded ecod of the SFH of thei host galaxy Do most stas fom in clustes? O does it exist two modes of sta fomation (diffuse and clusteed) but with some coelation between the two modes? Geneviève Pamentie - Heidelbeg Astonomisches-Rechen Institut 4 /

5 Obseved Young Sta Cluste Mass Functions Macoscopic: galaxy-wide, o multi-kpc scale mass distibution of sta clustes log ( dn / d m ) CMF (α = -2.0) CMF (α = -2.0) Fig7, Chanda+2010 log ( m [M o ] ) dn dm Note: what happens afte 100My emains disputed 2 dn logm 1 What obseves tell us No evolution of the CMF shape ove the fist few 10My Cluste mass-loss is mass-in independent Geneviève Pamentie - Heidelbeg Astonomisches-Rechen Institut 5 / d m m

6 Evolution of Young SC Mass Functions 1/2 - Tidal Field Impact: hm / t Weak t.f. impact half mass tidal = f Cluste envionment env ( ) - 1 / 3 ρ CFRg Baumgadt & Koupa (2007) paametization Fo a given envionment, highe mass-losses due to gas expulsion if highe tidal field impact e.g. smalle CFRg densities Stong t.f. impact Geneviève Pamentie - Heidelbeg Astonomisches-Rechen Institut 6 /

7 The m CFRg - CFRg Diagam as a Diagnostic Tool log ( CFRg [pc] ) half mass tidal = f env 1 3 ( ρ ) - / CFRg h / t =0.05 Σ CFRg 1/ 2 CFRg m CFRg ρ CFRg. Constant mean suface density CFRg Constant mean volume density 1/ 3 CFRg m CFRg constant log ( m CFRg [M o ] ) Geneviève Pamentie - Heidelbeg Astonomisches-Rechen Institut 7 /

8 The m CFRg - CFRg Diagam as a Diagnostic Tool log ( CFRg [pc] ) half mass tidal = f env 1 3 ( ρ ) - / CFRg h / t =0.05 Σ CFRg 1/ 2 CFRg m CFRg ρ CFRg. Constant mean suface density CFRg Constant mean volume density 1/ 3 CFRg m CFRg constant log ( m CFRg [M o ] ) Geneviève Pamentie - Heidelbeg Astonomisches-Rechen Institut 8 /

9 Young SC Mass Functions - Tidal Field Impact dn/dlogm SFE=0.40 D gal =5kpc Σ CFRg Constant Mean Suface Density CFRgs: When moe massive means moe vulneable... log ( m [M o ] ) Constant Mean Volume Density CFRgs: mass-independent infant weight-loss log ( dn / dlogm ) ρ CFRg log (m [M o ]) Geneviève Pamentie - Heidelbeg Astonomisches-Rechen Institut 9 /

10 The cluste cossing-time: you basic time-unit! A sta cluste does not cae about how long it takes fo the eath to evolve aound the sun! The basic time-unit is the cluste initial cossing-time, not the yea o My (Pamentie & Baumgadt 2012) τ ρ coss CFRg τ coss 35 1/ 2 ( ) CFRg m CFRg 3 YSC Exact coefficient depends on density pofile Sun NGC APOD Hubble Heitage Team, A. Riess 10 Geneviève Pamentie - Heidelbeg Astonomisches-Rechen Institut 10 /

11 Evolution of Young SC Mass Functions 2/2 Cluste Evolutionay Rate Simulations of sta clustes with the most massive clustes the densest ones (constant adius) highe mass objects evolve at a quicke ate. Pamentie & Baumgadt (2012) log ( dn / d m ) dn/dlogm log ( m [M o ] ) Obsevations of sta clustes in the Lage Magellanic Cloud (Chanda+ 2010) log ( m [M o ] ) 11 Geneviève Pamentie - Heidelbeg Astonomisches-Rechen Institut 11 /

12 A Volume Density Theshold fo the SF Gas? ρ CFRg = constant : povides the most obust solution to the time-invaiant shape of the cluste mass function Inteesting since: SFR and dense molecula gas mapping in: Entie galaxies. Gao & Solomon 2004 Galactic molecula clumps... Wu SFR scales as the mass of dense molecula gas: n H2 > 10 4 cm -3 CFRgs of about constant mean volume density (n H2 = few n th ) 12 Geneviève Pamentie - Heidelbeg Astonomisches-Rechen Institut 12 /

13 A Volume Density Theshold fo the SF Gas ρ CFRg = constant : povides the most obust solution to the time-invaiant shape of the cluste mass function Inteesting since: SFR and dense molecula gas mapping in: Entie galaxies. Gao & Solomon 2004 Galactic molecula clumps... Wu SFR scales as the mass of dense molecula gas: n H2 > 10 4 cm -3 CFRgs of about constant mean volume density (n H2 = few n th ) Same scaling (constant mean volume density) as fom: - the tidal field impact analysis (Pamentie & Koupa 2011) - the cossing-time analysis (Pamentie & Baumgadt 2012) 13 Geneviève Pamentie - Heidelbeg Astonomisches-Rechen Institut 13 /

14 cannot be the only explanation But what fo the sta-foming egions of the Sola Neighbouhood? Spitze-telescope obsevations: sta fomation can poceed in low-density envionments too (Allen et al. 2007, Evans et al. 2009, ) 14 Geneviève Pamentie - Heidelbeg Astonomisches-Rechen Institut 14 /

15 Sta Fomation Efficiency pe Fee-Fall Time: ε ff Sta Fomation Efficiency ε ff pe Fee-Fall Time τ ff τ ff = 3π 32 G ρ g Kumholz & McKee 2005 Fo any given time-span afte the onset of sta fomation: molecula-gas egions of highe density achieve highe SFEs On the scale of individual molecula clumps volume density gadients SFE cente >> SFE outskits Consequences? Fig 9 - Wu+2010 Dense Faste HCN3-2 Highe SFE 15 Geneviève Pamentie - Heidelbeg Astonomisches-Rechen Institut 15 /

16 Immediate consequences of the ε ff concept ρ Clump cente Conseq.1 stas gas Clump outskits Density pofiles: ρ * () steepe thanρ g () Local SFE Clump cente Radially-dependent local SFE Cluste suvival! Adams (2000) Clump outskits 16 Geneviève Pamentie - Heidelbeg Astonomisches-Rechen Institut 16 /

17 Immediate consequences of the ε ff concept Fig9, Gutemuth+ (2011) Conseq.2 Σ * ~ Σ g 2 Σ * Density pofiles: ρ * () steepe thanρ g () Σ gas Radially-dependent local SFE Local sta fomation law 17 Geneviève Pamentie - Heidelbeg Astonomisches-Rechen Institut 17 /

18 Sta and Gas Volume Density Pofiles [Conseq.1] ρ g p0 ( t = 0, ) - ε = 0. 1 ff Fig1, Gutemuth+ (2011) MonR2 cloud M tot =25,800M 0 R = 6 pc M =1E4M 0 Density pofiles: ρ * (t,) steepe thanρ g (t,) ρ g (t,) shallowe thanρ g (t=0,) 18 Geneviève Pamentie - Heidelbeg Astonomisches-Rechen Institut 18 /

19 Local Sta Fomation Law [Conseq. 2] ε ff = 0.1 Clump cente Fig9, Gutemuth+ (2011) Σ * ~ Σ g 2 Σ * Σ * Clump outskits Σ g Relation between the local suface densities of YSOs and of the esidual gas: Σ * 10-3 Σ g2 at t = 2My Σ * fo the adopted M, R, ε ff (Pamentie & Pfalzne 2013) Σ g 19 Geneviève Pamentie - Heidelbeg Astonomisches-Rechen Institut 19 /

20 Cluste Suvival Made Easie [Conseq. 1b] Clump cente ε 3D () adially-vaying: clustes suvive despite low global SFE Clump outskits Adams (2000) Local SFE = ε = 3D ( t, ) ρ* ( t, ) ρ ( t, ) + ρ ( t, ) g Pamentie & Pfalzne 2013 * Unifom ε 3D ε 3D adially constant: ε 3D = SFE (local global) Cluste suvival equies global SFE > Geneviève Pamentie - Heidelbeg Astonomisches-Rechen Institut 20 /

21 Conclusions: Fom the Cluste Mass Function to the Local Sta Fomation Law log ( dn / d m ) Macoscopic: galaxy-wide, o multi-kpc scale mass distibution of sta clustes Fig7, Chanda+2010 Σ * Clump outskits Micoscopic: sta-foming egion few-pc scale local sta fomation law ε ff = 0.1 Σ g Clump cente log ( m [M o ] ) Contact Details Talk slides at: wwwstaff.ai.uni-heidelbeg.de/mitabeite/gpam/talks.html gpam AT ai.uni-heidelbeg.de 21 Geneviève Pamentie - Heidelbeg Astonomisches-Rechen Institut 21 /

Geneviève Parmentier

Geneviève Parmentier MPIfR/AIfA Hauptkolloquium, 19 Novembe 2010 Splinte Meeting@AG2010, Bonn, 15 Septembe 2010 Fom Molecula Clump Popeties to Galaxy Evolution with Sta Clustes Geneviève Pamentie Agelande-Institut füf Astonomie

More information

4 Star Formation Relations

4 Star Formation Relations The Wonders of Star Formation - Edinburgh - 7.9.2018 4 Star Formation Relations (+ Strengthened Cluster Survival) With One Single Model Geneviève Parmentier Astronomisches-Rechen Institut Zentrum für Astronomie

More information

History of Astronomy - Part II. Tycho Brahe - An Observer. Johannes Kepler - A Theorist

History of Astronomy - Part II. Tycho Brahe - An Observer. Johannes Kepler - A Theorist Histoy of Astonomy - Pat II Afte the Copenican Revolution, astonomes stived fo moe obsevations to help bette explain the univese aound them Duing this time (600-750) many majo advances in science and astonomy

More information

Today in Astronomy 142: the Milky Way s disk

Today in Astronomy 142: the Milky Way s disk Today in Astonomy 14: the Milky Way s disk Moe on stas as a gas: stella elaxation time, equilibium Diffeential otation of the stas in the disk The local standad of est Rotation cuves and the distibution

More information

Stellar Structure and Evolution

Stellar Structure and Evolution Stella Stuctue and Evolution Theoetical Stella odels Conside each spheically symmetic shell of adius and thickness d. Basic equations of stella stuctue ae: 1 Hydostatic equilibium π dp dp d G π = G =.

More information

General momentum equation

General momentum equation PY4A4 Senio Sophiste Physics of the Intestella and Integalactic Medium Lectue 11: Collapsing Clouds D Gaham M. Hape School of Physics, TCD Geneal momentum equation Du u P Dt uu t 1 B 4 B 1 B 8 Lagangian

More information

Lecture Seven: The Milky Way: Gas

Lecture Seven: The Milky Way: Gas Lectue Seven: The Milky Way: Gas Gas in the Milky Way Between the stas in the disc of the Milky Way thee is gas, which is the stuff fom which the stas wee oiginally made, and to which stas etun heavy elements

More information

Why do globular clusters have more than one main sequence? Ref: Gratton et al. 2012, A&ARv, 20, 50

Why do globular clusters have more than one main sequence? Ref: Gratton et al. 2012, A&ARv, 20, 50 Why do globula clustes have moe than one main sequence? Ref: Gatton et al. 2012, A&ARv, 20, 50 1 st, a petty pictue Outline The lives of stas Some basic physics Impotance of clustes Globula clustes ae

More information

Section 11. Timescales Radiation transport in stars

Section 11. Timescales Radiation transport in stars Section 11 Timescales 11.1 Radiation tanspot in stas Deep inside stas the adiation eld is vey close to black body. Fo a black-body distibution the photon numbe density at tempeatue T is given by n = 2

More information

Gravitation. Chapter 12. PowerPoint Lectures for University Physics, Twelfth Edition Hugh D. Young and Roger A. Freedman. Lectures by James Pazun

Gravitation. Chapter 12. PowerPoint Lectures for University Physics, Twelfth Edition Hugh D. Young and Roger A. Freedman. Lectures by James Pazun Chapte 12 Gavitation PowePoint Lectues fo Univesity Physics, Twelfth Edition Hugh D. Young and Roge A. Feedman Lectues by James Pazun Modified by P. Lam 5_31_2012 Goals fo Chapte 12 To study Newton s Law

More information

DEVIL PHYSICS THE BADDEST CLASS ON CAMPUS IB PHYSICS

DEVIL PHYSICS THE BADDEST CLASS ON CAMPUS IB PHYSICS DEVIL PHYSICS THE BADDEST CLASS ON CAMPUS IB PHYSICS LSN 10-: MOTION IN A GRAVITATIONAL FIELD Questions Fom Reading Activity? Gavity Waves? Essential Idea: Simila appoaches can be taken in analyzing electical

More information

Universal Gravitation

Universal Gravitation Chapte 1 Univesal Gavitation Pactice Poblem Solutions Student Textbook page 580 1. Conceptualize the Poblem - The law of univesal gavitation applies to this poblem. The gavitational foce, F g, between

More information

The Spiral Structure of NGC 3198.

The Spiral Structure of NGC 3198. The Spial Stuctue of NGC 3198. Buce Rout Novembe 8, 2009 Abstact Obsevations of NGC 3198 show a discepancy between the otational velocity and its appaent geomety which defies the pedicted behaviou of Kepleian

More information

A solution of the cusp problem in virialized DM halos in standard cosmology

A solution of the cusp problem in virialized DM halos in standard cosmology DSU6, Univesidad Autonoma de Madid, June A solution of the cusp poblem in viialized DM halos in standad cosmology A.G.Dooshkevich, V.N.Lukash, E.V.Mikheeva Asto Space Cente of Lebedev Physics Institute

More information

Astronomy 111, Fall October 2011

Astronomy 111, Fall October 2011 Astonomy 111, Fall 011 4 Octobe 011 Today in Astonomy 111: moe details on enegy tanspot and the tempeatues of the planets Moe about albedo and emissivity Moe about the tempeatue of sunlit, adiation-cooled

More information

B. Spherical Wave Propagation

B. Spherical Wave Propagation 11/8/007 Spheical Wave Popagation notes 1/1 B. Spheical Wave Popagation Evey antenna launches a spheical wave, thus its powe density educes as a function of 1, whee is the distance fom the antenna. We

More information

Lecture 24 Stability of Molecular Clouds

Lecture 24 Stability of Molecular Clouds Lectue 4 Stability of Molecula Clouds 1. Stability of Cloud Coes. Collapse and Fagmentation of Clouds 3. Applying the iial Theoem Refeences Oigins of Stas & Planetay Systems eds. Lada & Kylafis http://cfa-www.havad.edu/cete

More information

Central Force Motion

Central Force Motion Cental Foce Motion Cental Foce Poblem Find the motion of two bodies inteacting via a cental foce. Examples: Gavitational foce (Keple poblem): m1m F 1, ( ) =! G ˆ Linea estoing foce: F 1, ( ) =! k ˆ Two

More information

Lecture 3. Basic Physics of Astrophysics - Force and Energy. Forces

Lecture 3. Basic Physics of Astrophysics - Force and Energy. Forces Foces Lectue 3 Basic Physics of Astophysics - Foce and Enegy http://apod.nasa.gov/apod/ Momentum is the poduct of mass and velocity - a vecto p = mv (geneally m is taken to be constant) An unbalanced foce

More information

Physics: Work & Energy Beyond Earth Guided Inquiry

Physics: Work & Energy Beyond Earth Guided Inquiry Physics: Wok & Enegy Beyond Eath Guided Inquiy Elliptical Obits Keple s Fist Law states that all planets move in an elliptical path aound the Sun. This concept can be extended to celestial bodies beyond

More information

Determining solar characteristics using planetary data

Determining solar characteristics using planetary data Detemining sola chaacteistics using planetay data Intoduction The Sun is a G-type main sequence sta at the cente of the Sola System aound which the planets, including ou Eath, obit. In this investigation

More information

Chapter 5: Uniform Circular Motion

Chapter 5: Uniform Circular Motion Chapte 5: Unifom Cicula Motion Motion at constant speed in a cicle Centipetal acceleation Banked cuves Obital motion Weightlessness, atificial gavity Vetical cicula motion Centipetal Foce Acceleation towad

More information

Between any two masses, there exists a mutual attractive force.

Between any two masses, there exists a mutual attractive force. YEAR 12 PHYSICS: GRAVITATION PAST EXAM QUESTIONS Name: QUESTION 1 (1995 EXAM) (a) State Newton s Univesal Law of Gavitation in wods Between any two masses, thee exists a mutual attactive foce. This foce

More information

A PHOTOMETRIC STUDY OF FIVE OPEN CLUSTERS IN THE SDSS

A PHOTOMETRIC STUDY OF FIVE OPEN CLUSTERS IN THE SDSS Jounal of The Koean Astonomical Society http://dx.doi.og/10.5303/jkas.11.44.5.177 44: 177 193, 11 Octobe ISSN:25-46 c 11 The Koean Astonomical Society. All Rights Reseved. http://jkas.kas.og A PHOTOMETRIC

More information

Gaia s Place in Space

Gaia s Place in Space Gaia s Place in Space The impotance of obital positions fo satellites Obits and Lagange Points Satellites can be launched into a numbe of diffeent obits depending on thei objectives and what they ae obseving.

More information

DEVIL PHYSICS THE BADDEST CLASS ON CAMPUS IB PHYSICS

DEVIL PHYSICS THE BADDEST CLASS ON CAMPUS IB PHYSICS DEVIL PHYSICS THE BADDEST CLASS ON CAMPUS IB PHYSICS TSOKOS LESSON 6- THE LAW OF GRAVITATION Essential Idea: The Newtonian idea of gavitational foce acting between two spheical bodies and the laws of mechanics

More information

Exercise sheet 8 (Modeling large- and small-scale flows) 8.1 Volcanic ash from the Eyjafjallajökull

Exercise sheet 8 (Modeling large- and small-scale flows) 8.1 Volcanic ash from the Eyjafjallajökull Execise sheet 8 (Modeling lage- and small-scale flows) last edited June 18, 2018 These lectue notes ae based on textbooks by White [13], Çengel & al.[16], and Munson & al.[18]. Except othewise indicated,

More information

Chap 5. Circular Motion: Gravitation

Chap 5. Circular Motion: Gravitation Chap 5. Cicula Motion: Gavitation Sec. 5.1 - Unifom Cicula Motion A body moves in unifom cicula motion, if the magnitude of the velocity vecto is constant and the diection changes at evey point and is

More information

ω = θ θ o = θ θ = s r v = rω

ω = θ θ o = θ θ = s r v = rω Unifom Cicula Motion Unifom cicula motion is the motion of an object taveling at a constant(unifom) speed in a cicula path. Fist we must define the angula displacement and angula velocity The angula displacement

More information

Mobility of atoms and diffusion. Einstein relation.

Mobility of atoms and diffusion. Einstein relation. Mobility of atoms and diffusion. Einstein elation. In M simulation we can descibe the mobility of atoms though the mean squae displacement that can be calculated as N 1 MS ( t ( i ( t i ( 0 N The MS contains

More information

V7: Diffusional association of proteins and Brownian dynamics simulations

V7: Diffusional association of proteins and Brownian dynamics simulations V7: Diffusional association of poteins and Bownian dynamics simulations Bownian motion The paticle movement was discoveed by Robet Bown in 1827 and was intepeted coectly fist by W. Ramsay in 1876. Exact

More information

Radial Inflow Experiment:GFD III

Radial Inflow Experiment:GFD III Radial Inflow Expeiment:GFD III John Mashall Febuay 6, 003 Abstact We otate a cylinde about its vetical axis: the cylinde has a cicula dain hole in the cente of its bottom. Wate entes at a constant ate

More information

Escape Velocity. GMm ] B

Escape Velocity. GMm ] B 1 PHY2048 Mach 31, 2006 Escape Velocity Newton s law of gavity: F G = Gm 1m 2 2, whee G = 667 10 11 N m 2 /kg 2 2 3 10 10 N m 2 /kg 2 is Newton s Gavitational Constant Useful facts: R E = 6 10 6 m M E

More information

Chapter 13 Gravitation

Chapter 13 Gravitation Chapte 13 Gavitation In this chapte we will exploe the following topics: -Newton s law of gavitation, which descibes the attactive foce between two point masses and its application to extended objects

More information

But for simplicity, we ll define significant as the time it takes a star to lose all memory of its original trajectory, i.e.,

But for simplicity, we ll define significant as the time it takes a star to lose all memory of its original trajectory, i.e., Stella elaxation Time [Chandasekha 1960, Pinciples of Stella Dynamics, Chap II] [Ostike & Davidson 1968, Ap.J., 151, 679] Do stas eve collide? Ae inteactions between stas (as opposed to the geneal system

More information

1 Dark Cloud Hanging over Twentieth Century Physics

1 Dark Cloud Hanging over Twentieth Century Physics We ae Looking fo Moden Newton by Caol He, Bo He, and Jin He http://www.galaxyanatomy.com/ Wuhan FutueSpace Scientific Copoation Limited, Wuhan, Hubei 430074, China E-mail: mathnob@yahoo.com Abstact Newton

More information

arxiv: v1 [astro-ph.ga] 27 Sep 2011

arxiv: v1 [astro-ph.ga] 27 Sep 2011 Jounal of The Koean Astonomical Society 00: 1 00, 11???????? c 11 The Koean Astonomical Society. All Rights Reseved. A Photometic Study of Five Open Clustes in the SDSS axiv:1109.5774v1 [asto-ph.ga] 27

More information

The velocity dispersion and mass profile of the Milky Way

The velocity dispersion and mass profile of the Milky Way Mon. Not. R. Aston. Soc. 369, 1688 169 (006) doi:10.1111/j.1365-966.006.10404.x The velocity dispesion and mass pofile of the Milky Way Walte Dehnen, Dean E. McLaughlin and Jalpesh Sachania Depatment of

More information

F 12. = G m m 1 2 F 21 = F 12. = G m 1m 2. Review. Physics 201, Lecture 22. Newton s Law Of Universal Gravitation

F 12. = G m m 1 2 F 21 = F 12. = G m 1m 2. Review. Physics 201, Lecture 22. Newton s Law Of Universal Gravitation Physics 201, Lectue 22 Review Today s Topics n Univesal Gavitation (Chapte 13.1-13.3) n Newton s Law of Univesal Gavitation n Popeties of Gavitational Foce n Planet Obits; Keple s Laws by Newton s Law

More information

Ch 13 Universal Gravitation

Ch 13 Universal Gravitation Ch 13 Univesal Gavitation Ch 13 Univesal Gavitation Why do celestial objects move the way they do? Keple (1561-1630) Tycho Bahe s assistant, analyzed celestial motion mathematically Galileo (1564-1642)

More information

11. Gravitational Lensing.

11. Gravitational Lensing. 11. Gavitational Lensing. 11.1. ome Histoy The fist publication on the gavitational deflection of light appeaed in 184 in Gemany: Die Ablenkung eines Lichtstahls..duch die Attaktion eines Weltköpes by

More information

1 kev Plasma. Theoretical model of a collisionally ionized plasma kt=1 kev with solar abundances The lines are 'narrow' Notice dynamic range of 10 5

1 kev Plasma. Theoretical model of a collisionally ionized plasma kt=1 kev with solar abundances The lines are 'narrow' Notice dynamic range of 10 5 1 kev Plasma Theoetical model of a collisionally ionized plasma kt=1 kev with sola abundances The lines ae 'naow' Notice dynamic ange of 10 5 Obsevational data fo a collisionally ionized plasma kt=1 kev

More information

Name Midterm Exam March 4, 2010

Name Midterm Exam March 4, 2010 Name Midtem Exam Mach 4, 00 This test consists of thee pats. Fo the fist pat, you may wite you answes diectly on the exam, if you wish. Fo the othe pats, use sepaate sheets of pape. Useful equations can

More information

Lecture 3. Basic Physics of Astrophysics - Force and Energy. Forces

Lecture 3. Basic Physics of Astrophysics - Force and Energy. Forces Lectue 3 Basic Physics of Astophysics - Foce and Enegy http://apod.nasa.gov/apod/ Foces Momentum is the poduct of mass and velocity - a vecto p = mv (geneally m is taken to be constant) An unbalanced foce

More information

Collision Frequency of Adsorbed Particles

Collision Frequency of Adsorbed Particles Bulg. J. Phys. 40 (2013) 214 218 Collision Fequency of Adsobed Paticles N.S. Peev Geogi Nadjakov Institute of Solid State Physics, Bulgaian Academy of Sciences, 72 Tzaigadsko Chaussee Blvd., 1784 Sofia,

More information

Gauss Law. Physics 231 Lecture 2-1

Gauss Law. Physics 231 Lecture 2-1 Gauss Law Physics 31 Lectue -1 lectic Field Lines The numbe of field lines, also known as lines of foce, ae elated to stength of the electic field Moe appopiately it is the numbe of field lines cossing

More information

15 B1 1. Figure 1. At what speed would the car have to travel for resonant oscillations to occur? Comment on your answer.

15 B1 1. Figure 1. At what speed would the car have to travel for resonant oscillations to occur? Comment on your answer. Kiangsu-Chekiang College (Shatin) F:EasteHolidaysAssignmentAns.doc Easte Holidays Assignment Answe Fom 6B Subject: Physics. (a) State the conditions fo a body to undego simple hamonic motion. ( mak) (a)

More information

Recap. Centripetal acceleration: v r. a = m/s 2 (towards center of curvature)

Recap. Centripetal acceleration: v r. a = m/s 2 (towards center of curvature) a = c v 2 Recap Centipetal acceleation: m/s 2 (towads cente of cuvatue) A centipetal foce F c is equied to keep a body in cicula motion: This foce poduces centipetal acceleation that continuously changes

More information

m1 m2 M 2 = M -1 L 3 T -2

m1 m2 M 2 = M -1 L 3 T -2 GAVITATION Newton s Univesal law of gavitation. Evey paticle of matte in this univese attacts evey othe paticle with a foce which vaies diectly as the poduct of thei masses and invesely as the squae of

More information

Welcome to Aerospace Engineering

Welcome to Aerospace Engineering Welcome to Aeospace Engineeing DESIGN-CENTERED INTRODUCTION TO AEROSPACE ENGINEERING Notes 9 Topics 1. Couse Oganization. Today's Deams in Vaious Speed Ranges 3. Designing a Flight Vehicle: Route Map of

More information

A simple recipe for estimating masses of elliptical galaxies and clusters of galaxies

A simple recipe for estimating masses of elliptical galaxies and clusters of galaxies A simple eipe fo estimating masses of elliptial galaxies and lustes of galaxies Quik and obust mass estimates - fo elliptial galaxies fom optial data tested on simulated galaxies by Ose et al. 010 - fo

More information

AST 121S: The origin and evolution of the Universe. Introduction to Mathematical Handout 1

AST 121S: The origin and evolution of the Universe. Introduction to Mathematical Handout 1 Please ead this fist... AST S: The oigin and evolution of the Univese Intoduction to Mathematical Handout This is an unusually long hand-out and one which uses in places mathematics that you may not be

More information

Modeling Fermi Level Effects in Atomistic Simulations

Modeling Fermi Level Effects in Atomistic Simulations Mat. Res. Soc. Symp. Poc. Vol. 717 Mateials Reseach Society Modeling Femi Level Effects in Atomistic Simulations Zudian Qin and Scott T. Dunham Depatment of Electical Engineeing, Univesity of Washington,

More information

Takuya Ohtani (Osaka University Theoretical Astrophysics Group D2) Collaborator: Toru Tsuribe(Osaka Univ.)

Takuya Ohtani (Osaka University Theoretical Astrophysics Group D2) Collaborator: Toru Tsuribe(Osaka Univ.) Simultaneous Gowth of a Potosta and a Young Cicumstella Disk in the Ealy Phase of Disk Fomation * Takuya Ohtani (Osaka Univesity Theoetical Astophysics Goup D2) Collaboato: Tou Tsuibe(Osaka Univ.) 1 Abstact

More information

SIO 229 Gravity and Geomagnetism. Lecture 6. J 2 for Earth. J 2 in the solar system. A first look at the geoid.

SIO 229 Gravity and Geomagnetism. Lecture 6. J 2 for Earth. J 2 in the solar system. A first look at the geoid. SIO 229 Gavity and Geomagnetism Lectue 6. J 2 fo Eath. J 2 in the sola system. A fist look at the geoid. The Thee Big Themes of the Gavity Lectues 1.) An ellipsoidal otating Eath Refeence body (mass +

More information

Practice. Understanding Concepts. Answers J 2. (a) J (b) 2% m/s. Gravitation and Celestial Mechanics 287

Practice. Understanding Concepts. Answers J 2. (a) J (b) 2% m/s. Gravitation and Celestial Mechanics 287 Pactice Undestanding Concepts 1. Detemine the gavitational potential enegy of the Eath Moon system, given that the aveage distance between thei centes is 3.84 10 5 km, and the mass of the Moon is 0.0123

More information

Lecture 3. Basic Physics of Astrophysics - Force and Energy. Forces.

Lecture 3. Basic Physics of Astrophysics - Force and Energy. Forces. Tue Wed Thu Thu Lectue 3 Basic Physics of Astophysics - Foce and Enegy ISB 165 Wed 5 Thu 4 http://apod.nasa.gov/apod/ Foces Momentum is the poduct of mass and velocity - a vecto p = mv (geneally m is taken

More information

Physics 111 Lecture 5 Circular Motion

Physics 111 Lecture 5 Circular Motion Physics 111 Lectue 5 Cicula Motion D. Ali ÖVGÜN EMU Physics Depatment www.aovgun.com Multiple Objects q A block of mass m1 on a ough, hoizontal suface is connected to a ball of mass m by a lightweight

More information

= 4 3 π( m) 3 (5480 kg m 3 ) = kg.

= 4 3 π( m) 3 (5480 kg m 3 ) = kg. CHAPTER 11 THE GRAVITATIONAL FIELD Newton s Law of Gavitation m 1 m A foce of attaction occus between two masses given by Newton s Law of Gavitation Inetial mass and gavitational mass Gavitational potential

More information

Quantum Mechanics and Stellar Spectroscopy

Quantum Mechanics and Stellar Spectroscopy Quantum Mechanics and Stella Spectoscopy http://apod.nasa.gov/apod/ Recall the electic foce. Like gavity it is a 1/ 2 foce/ That is: F elec = Z 1Z 2 e 2 2 whee Z 1 and Z 2 ae the (intege) numbes of electonic

More information

Today. Homework Problem Traveling Car. Announcements:

Today. Homework Problem Traveling Car. Announcements: nnouncements: Today HW#3 due by 8:00 am Wednesday Exam #1 on Thusday /11 No class on Thusday /4 Taveling a Poblem fom HW# Gavity The Newtonian Woldview Vectos (Hints fo the boat poblem) ISP09s10 Lectue

More information

Physics 111. Ch 12: Gravity. Newton s Universal Gravity. R - hat. the equation. = Gm 1 m 2. F g 2 1. ˆr 2 1. Gravity G =

Physics 111. Ch 12: Gravity. Newton s Universal Gravity. R - hat. the equation. = Gm 1 m 2. F g 2 1. ˆr 2 1. Gravity G = ics Announcements day, embe 9, 004 Ch 1: Gavity Univesal Law Potential Enegy Keple s Laws Ch 15: Fluids density hydostatic equilibium Pascal s Pinciple This week s lab will be anothe physics wokshop -

More information

Lecture 8 - Gauss s Law

Lecture 8 - Gauss s Law Lectue 8 - Gauss s Law A Puzzle... Example Calculate the potential enegy, pe ion, fo an infinite 1D ionic cystal with sepaation a; that is, a ow of equally spaced chages of magnitude e and altenating sign.

More information

Tidal forces. m r. m 1 m 2. x r 2. r 1

Tidal forces. m r. m 1 m 2. x r 2. r 1 Tidal foces Befoe we look at fee waves on the eath, let s fist exaine one class of otion that is diectly foced: astonoic tides. Hee we will biefly conside soe of the tidal geneating foces fo -body systes.

More information

GENERAL RELATIVITY: THE GEODESICS OF THE SCHWARZSCHILD METRIC

GENERAL RELATIVITY: THE GEODESICS OF THE SCHWARZSCHILD METRIC GENERAL RELATIVITY: THE GEODESICS OF THE SCHWARZSCHILD METRIC GILBERT WEINSTEIN 1. Intoduction Recall that the exteio Schwazschild metic g defined on the 4-manifold M = R R 3 \B 2m ) = {t,, θ, φ): > 2m}

More information

Flux. Area Vector. Flux of Electric Field. Gauss s Law

Flux. Area Vector. Flux of Electric Field. Gauss s Law Gauss s Law Flux Flux in Physics is used to two distinct ways. The fist meaning is the ate of flow, such as the amount of wate flowing in a ive, i.e. volume pe unit aea pe unit time. O, fo light, it is

More information

Chapter 5. Uniform Circular Motion. a c =v 2 /r

Chapter 5. Uniform Circular Motion. a c =v 2 /r Chapte 5 Unifom Cicula Motion a c =v 2 / Unifom cicula motion: Motion in a cicula path with constant speed s v 1) Speed and peiod Peiod, T: time fo one evolution Speed is elated to peiod: Path fo one evolution:

More information

OSCILLATIONS AND GRAVITATION

OSCILLATIONS AND GRAVITATION 1. SIMPLE HARMONIC MOTION Simple hamonic motion is any motion that is equivalent to a single component of unifom cicula motion. In this situation the velocity is always geatest in the middle of the motion,

More information

Uniform Circular Motion

Uniform Circular Motion Unifom Cicula Motion Intoduction Ealie we defined acceleation as being the change in velocity with time: a = v t Until now we have only talked about changes in the magnitude of the acceleation: the speeding

More information

Physics Fall Mechanics, Thermodynamics, Waves, Fluids. Lecture 6: motion in two and three dimensions III. Slide 6-1

Physics Fall Mechanics, Thermodynamics, Waves, Fluids. Lecture 6: motion in two and three dimensions III. Slide 6-1 Physics 1501 Fall 2008 Mechanics, Themodynamics, Waves, Fluids Lectue 6: motion in two and thee dimensions III Slide 6-1 Recap: elative motion An object moves with velocity v elative to one fame of efeence.

More information

arxiv: v1 [quant-ph] 15 Nov 2018

arxiv: v1 [quant-ph] 15 Nov 2018 Bayesian estimation of switching ates fo blinking emittes axiv:8.6627v [quant-ph] 5 Nov 28 Jemy Geody,, 2 Lachlan J Roges,, 2, Cameon M Roges, 3 Thomas Volz,, 2 and Alexei Gilchist, 2 Depatment of Physics

More information

Physics 181. Assignment 4

Physics 181. Assignment 4 Physics 181 Assignment 4 Solutions 1. A sphee has within it a gavitational field given by g = g, whee g is constant and is the position vecto of the field point elative to the cente of the sphee. This

More information

On the Sun s Electric-Field

On the Sun s Electric-Field On the Sun s Electic-Field D. E. Scott, Ph.D. (EE) Intoduction Most investigatos who ae sympathetic to the Electic Sun Model have come to agee that the Sun is a body that acts much like a esisto with a

More information

Lecture 1a: Satellite Orbits

Lecture 1a: Satellite Orbits Lectue 1a: Satellite Obits Outline 1. Newton s Laws of Motion 2. Newton s Law of Univesal Gavitation 3. Calculating satellite obital paametes (assuming cicula motion) Scala & Vectos Scala: a physical quantity

More information

Extrasolar Planets. Detection Methods. Direct Imaging. Introduction. = Requires two ingredients:

Extrasolar Planets. Detection Methods. Direct Imaging. Introduction. = Requires two ingredients: D D O O D D O O D D G S D X 9 1 G S D X Detection ethods 9 3 Possible ways to detect extasola planets: Diect ethod:... diect imaging of planet xtasola Planets ndiect ethods: seach fo evidence fo......

More information

Objective Notes Summary

Objective Notes Summary Objective Notes Summay An object moving in unifom cicula motion has constant speed but not constant velocity because the diection is changing. The velocity vecto in tangent to the cicle, the acceleation

More information

Revision Guide for Chapter 11

Revision Guide for Chapter 11 Revision Guide fo Chapte 11 Contents Revision Checklist Revision Notes Momentum... 4 Newton's laws of motion... 4 Wok... 5 Gavitational field... 5 Potential enegy... 7 Kinetic enegy... 8 Pojectile... 9

More information

Gravitational Dynamics: Part II. Size and Density of a BH. Adiabatic Compression due to growing BH. Boundary of Star Cluster

Gravitational Dynamics: Part II. Size and Density of a BH. Adiabatic Compression due to growing BH. Boundary of Star Cluster Lec: Gowth of a Black Hole y captuing ojects in Loss Cone Gavitational Dynamics: Pat II Non-Equiliium systems AS40, Pat II A small BH on oit with peicente p

More information

Is flat rotation curve a sign of cosmic expansion?

Is flat rotation curve a sign of cosmic expansion? MNRAS 433, 1729 1735 (2013) Advance Access publication 2013 June 11 doi:10.1093/mnas/stt847 Is flat otation cuve a sign of cosmic expansion? F. Daabi Depatment of Physics, Azabaijan Shahid Madani Univesity,

More information

Progress of HMGC Nonlinear Simulation

Progress of HMGC Nonlinear Simulation Pogess of HMGC Nonlinea Simulation Andeas Biewage [andeas@biewage.de] ENEA - Fascati Italy GSEP Wokshop 29 This wok is suppoted by SciDAC GSEP. Andeas Biewage (ENEA - Fascati) Pogess of HMGC Nonlinea Simulation

More information

Galactic Contraction and the Collinearity Principle

Galactic Contraction and the Collinearity Principle TECHNISCHE MECHANIK, Band 23, Heft 1, (2003), 21-28 Manuskipteingang: 12. August 2002 Galactic Contaction and the Collineaity Pinciple F.P.J. Rimott, FA. Salusti In a spial galaxy thee is not only a Keplefoce

More information

Physics 312 Introduction to Astrophysics Lecture 24

Physics 312 Introduction to Astrophysics Lecture 24 Physics 32 Intoduction to Astophysics Lectue 24 James Buckley buckley@wuphys.wustl.edu Lectue 24 Stella Stuctue Reading Assignment Read Chapte 5 and 8 by next Wed. Physics 25, J. Buckley The Life Stoy

More information

Optically selected clusters from DES science verification data and their SPTSZE signature

Optically selected clusters from DES science verification data and their SPTSZE signature Optically selected clustes fom DES science veification data and thei SPTSZE signatue Collaboatos: S. Boquet, E.Rozo, B.Benson, J.Moh +SPT coll. +DES coll. Alex Sao Outline SPT-SZE and DES-SV 1) Optical

More information

Chapter 4. Newton s Laws of Motion

Chapter 4. Newton s Laws of Motion Chapte 4 Newton s Laws of Motion 4.1 Foces and Inteactions A foce is a push o a pull. It is that which causes an object to acceleate. The unit of foce in the metic system is the Newton. Foce is a vecto

More information

Physics 235 Chapter 5. Chapter 5 Gravitation

Physics 235 Chapter 5. Chapter 5 Gravitation Chapte 5 Gavitation In this Chapte we will eview the popeties of the gavitational foce. The gavitational foce has been discussed in geat detail in you intoductoy physics couses, and we will pimaily focus

More information

PROBLEM SET #3A. A = Ω 2r 2 2 Ω 1r 2 1 r2 2 r2 1

PROBLEM SET #3A. A = Ω 2r 2 2 Ω 1r 2 1 r2 2 r2 1 PROBLEM SET #3A AST242 Figue 1. Two concentic co-axial cylindes each otating at a diffeent angula otation ate. A viscous fluid lies between the two cylindes. 1. Couette Flow A viscous fluid lies in the

More information

BURGERS VORTEX IN A PROTOPLANETARY DISK

BURGERS VORTEX IN A PROTOPLANETARY DISK Astophysics, Vol. 6, No. 1, ach, 17 BURGERS VORTEX IN A PROTOPLANETARY DISK. G. Abahamyan The effect of a Buges votex on the fomation of planetesimals in a potoplanetay disk is examined in a local appoximation.

More information

Search for a Critical Electron Temperature Gradient in DIII-D L-mode Discharges

Search for a Critical Electron Temperature Gradient in DIII-D L-mode Discharges Seach fo a Citical Electon Tempeatue Gadient in DIII-D L-mode Dischages.C. Deoo, S. Ciant 1, T.C. Luce, A. Manini, C.C. Petty, F. Ryte, M.E. Austin 3, D.R. ake, K.W. Gentle 3, C.M. Geenfield,.E. Kinsey

More information

Available online at ScienceDirect. Physics Procedia 74 (2015 )

Available online at   ScienceDirect. Physics Procedia 74 (2015 ) Available online at www.sciencediect.com ScienceDiect Physics Pocedia 74 (15 ) 9 96 Confeence of Fundamental Reseach and Paticle Physics, 18- Febuay 15, Moscow, Russian Fedeation Pecession of fast S stas

More information

Objectives: After finishing this unit you should be able to:

Objectives: After finishing this unit you should be able to: lectic Field 7 Objectives: Afte finishing this unit you should be able to: Define the electic field and explain what detemines its magnitude and diection. Wite and apply fomulas fo the electic field intensity

More information

DYNAMICS OF UNIFORM CIRCULAR MOTION

DYNAMICS OF UNIFORM CIRCULAR MOTION Chapte 5 Dynamics of Unifom Cicula Motion Chapte 5 DYNAMICS OF UNIFOM CICULA MOTION PEVIEW An object which is moing in a cicula path with a constant speed is said to be in unifom cicula motion. Fo an object

More information

Experiment 09: Angular momentum

Experiment 09: Angular momentum Expeiment 09: Angula momentum Goals Investigate consevation of angula momentum and kinetic enegy in otational collisions. Measue and calculate moments of inetia. Measue and calculate non-consevative wok

More information

Hopefully Helpful Hints for Gauss s Law

Hopefully Helpful Hints for Gauss s Law Hopefully Helpful Hints fo Gauss s Law As befoe, thee ae things you need to know about Gauss s Law. In no paticula ode, they ae: a.) In the context of Gauss s Law, at a diffeential level, the electic flux

More information

Diffusion and Transport. 10. Friction and the Langevin Equation. Langevin Equation. f d. f ext. f () t f () t. Then Newton s second law is ma f f f t.

Diffusion and Transport. 10. Friction and the Langevin Equation. Langevin Equation. f d. f ext. f () t f () t. Then Newton s second law is ma f f f t. Diffusion and Tanspot 10. Fiction and the Langevin Equation Now let s elate the phenomena of ownian motion and diffusion to the concept of fiction, i.e., the esistance to movement that the paticle in the

More information

11) A thin, uniform rod of mass M is supported by two vertical strings, as shown below.

11) A thin, uniform rod of mass M is supported by two vertical strings, as shown below. Fall 2007 Qualifie Pat II 12 minute questions 11) A thin, unifom od of mass M is suppoted by two vetical stings, as shown below. Find the tension in the emaining sting immediately afte one of the stings

More information

arxiv: v1 [astro-ph.ga] 4 Jan 2011

arxiv: v1 [astro-ph.ga] 4 Jan 2011 Mon. Not. R. Astron. Soc.,?? () Printed October 8 (MN LATEX style file v.) From the molecular-cloud- to the embedded-cluster-mass function with a density threshold for star formation arxiv:.8v [astro-ph.ga]

More information

TheModifiedInterfacialGravityUnifyingCDMMOGandMOND. The Modified Interfacial Gravity: Unifying CDM, MOG, and MOND

TheModifiedInterfacialGravityUnifyingCDMMOGandMOND. The Modified Interfacial Gravity: Unifying CDM, MOG, and MOND Global Jounal of Science Fontie Reseach: A Physics and Space Science Volume 15 Issue 3 Vesion 1. Yea 15 Type : Double Blind Pee Reviewed Intenational Reseach Jounal Publishe: Global Jounals Inc. (USA Online

More information

MASSACHUSETTS INSTITUTE OF TECHNOLOGY Physics Department. Problem Set 10 Solutions. r s

MASSACHUSETTS INSTITUTE OF TECHNOLOGY Physics Department. Problem Set 10 Solutions. r s MASSACHUSETTS INSTITUTE OF TECHNOLOGY Physics Depatment Physics 8.033 Decembe 5, 003 Poblem Set 10 Solutions Poblem 1 M s y x test paticle The figue above depicts the geomety of the poblem. The position

More information

- 5 - TEST 1R. This is the repeat version of TEST 1, which was held during Session.

- 5 - TEST 1R. This is the repeat version of TEST 1, which was held during Session. - 5 - TEST 1R This is the epeat vesion of TEST 1, which was held duing Session. This epeat test should be attempted by those students who missed Test 1, o who wish to impove thei mak in Test 1. IF YOU

More information

1) Consider an object of a parabolic shape with rotational symmetry z

1) Consider an object of a parabolic shape with rotational symmetry z Umeå Univesitet, Fysik 1 Vitaly Bychkov Pov i teknisk fysik, Fluid Mechanics (Stömningsläa), 01-06-01, kl 9.00-15.00 jälpmedel: Students may use any book including the tetbook Lectues on Fluid Dynamics.

More information